Exercise-specific mechanical stimuli are associated with regional lumbar bone adaptation: A combined in vivo and in silico multi-scale study

Exercise-specific mechanical stimuli are associated with regional lumbar bone adaptation: A combined in vivo and in silico multi-scale study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Exercise-specific mechanical stimuli are associated with regional lumbar bone adaptation: A combined in vivo and in silico multi-scale study Xiaoyu Xia, Shizhong Liu, Pu Duan, Jiayu Di, Rui Xu, Simin Li, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9197056/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Background Exercise is widely recommended to maintain lumbar bone mineral density (BMD), the tissue-level mechanical environment generated within the lumbar spine during different exercises remains difficult to assess in vivo. This study integrated individualized musculoskeletal modelling, finite element analysis, and longitudinal quantitative computed tomography (QCT) to characterise exercise-specific lumbar loading patterns and interpret them alongside regional BMD adaptation. Methods Ten postmenopausal women with low BMD who completed a 6-month combined exercise intervention were included (ChiCTR2400081574). QCT scans were acquired at baseline and follow-up to quantify BMD changes in the vertebral body (VB) and posterior region (PR). Individualized musculoskeletal models of walking, heel drops, jumping, and resistance exercise were developed to estimate joint reaction forces and muscle forces. These loads were transferred to individualized lumbar finite element models using a MATLAB–Python workflow to calculate segmental and regional von Mises stresses. Statistical analysis was performed using one-way ANOVA, with p < 0.05 considered statistically significant. Results Longitudinal QCT revealed that BMD was preserved or increased in the VB, whereas BMD declined in the PR, particularly at L1–L3. Jumping produced the highest peak joint reaction forces and von Mises stresses in the superior lumbar segments, whereas resistance exercise generated the greatest loading at L4–L5. Across all tasks and vertebral levels, von Mises stresses were consistently higher in the VB than in the PR. Conclusions Distinct exercise modalities generated different segmental and regional loading environments within the lumbar spine. These mechanical patterns were broadly consistent with the observed regional BMD changes, providing a mechanically informed interpretation of lumbar bone adaptation during exercise. Trial registration: Chinese Clinical Trial Registry, ChiCTR2400081574 (retrospectively registered 5 March 2024). Lumbar spine Exercise Musculoskeletal model Finite element model Bone adaptation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Background Osteoporosis is a systemic metabolic bone disease characterized by reduced bone mineral density (BMD) and deterioration of bone microarchitecture, resulting in increased skeletal fragility and a greater risk of fracture[ 1 ]. Approximately one in three women over the age of 50 will experience an osteoporotic fracture. Among common sites of insufficiency fractures, the lumbar spine is particularly vulnerable compared to the wrist and hip[ 2 ]. Exercise has emerged as a critical non-pharmacological intervention for preserving or improving BMD, as it promotes bone adaptation through mechanical loading without the adverse effects associated with pharmacological therapies[ 3 ]. Despite these benefits, the mechanobiological mechanisms through which exercise influences lumbar spine BMD remain incompletely understood. This knowledge gap is primarily attributed to the paucity of robust methodologies capable of linking whole-body exercise tasks to tissue-level mechanical stimuli. Clinical practice guidelines consistently advocate for exercise training as a viable non-pharmacological strategy for the maintenance or enhancement of BMD in populations with osteopenia or osteoporosis[ 4 ]. Nevertheless, the efficacy of various exercise modalities on lumbar BMD demonstrates considerable heterogeneity across the literature. For instance, an investigation into prescribed brisk walking programs yielded no significant effect on lumbar BMD[ 5 ]. Similarly, a longitudinal study incorporating heel drops, muscular endurance, and balance exercises reported no significant skeletal adaptations compared to a sedentary control group[ 6 ]. In contrast, a six-month randomized controlled trial involving tri-weekly resistance training-comprising exercises such as bench press and leg extensions-demonstrated that while lumbar BMD significantly declined in the placebo group, it was successfully preserved in the intervention cohorts[ 7 ]. A systematic review of 75 studies involving postmenopausal women further concluded that multi-component interventions, particularly those combining jumping and resistance exercises, conferred superior benefits to the lumbar spine compared to single-modality protocols[ 8 ]. These findings suggest that BMD adaptations are highly sensitive to specific exercise prescriptions[ 9 ]. Such variability may be attributed to the divergent mechanical loading profiles imposed upon the lumbar spine by different physical activities. However, there remains a paucity of research on the tissue-level loading associated with various exercise programs, despite these mechanical stimuli being the fundamental drivers of bone adaptation and BMD fluctuations. Musculoskeletal (MS) models have been extensively utilized to analyse human activities and predict mechanical loading, including intervertebral compression, shear forces, and paravertebral muscle forces during exercise[ 10 ]. These analytical frameworks account for complex muscle–muscle and muscle–bone interactions[ 11 , 12 ]. Researchers have established and validated MS models across various anatomical regions, such as the lumbar spine[ 13 ], and wrist[ 14 ], to simulate diverse motor tasks and predict joint kinetics and muscle activation patterns. Specifically, whole-body MS models have been employed to estimate lumbar spinal loads and muscular recruitment during asymmetric lifting tasks[ 15 ]. However, MS simulations are inherently limited to providing mechanical data at the joint and muscle levels, failing to capture loading characteristics at the bone tissue level[ 16 ]. Biomechanical stimuli, specifically stress [ 17 ], are more directly associated with the biological mechanisms of bone adaptation and have been demonstrated to influence BMD adaptation[ 18 ]. Finite element (FE) analysis is frequently employed to investigate the stress-strain distributions and other mechanical behaviours of bone at the tissue level. Consequently, simulations of bone adaptation have been performed wherein modifications to BMD and microarchitecture are driven by localized mechanical criteria[ 19 – 22 ]. While such simulations can predict BMD and structural distributions consistent with experimental observations[ 23 , 24 ], the outcomes remain highly sensitive to the complexity of the prescribed loading conditions. The absence of accurate local boundary conditions may result in significant discrepancies between simulation results and actual clinical presentations. Existing FE–MS coupling studies have demonstrated the feasibility of applying physiologically realistic loads[ 25 , 26 ], yet their integration with longitudinal in vivo bone density measurements remains limited. In particular, the lack of studies that directly connect exercise-specific tissue-level mechanical stimuli with the observed region-specific bone adaptation has hindered translation of biomechanical modelling into clinically meaningful exercise prescription. Therefore, the objective of this study was to establish an individualized multi-scale MS–FE framework and to interpret its mechanical outputs alongside six-month longitudinal QCT-derived BMD changes in the lumbar spine. This study aimed to provide a mechanically informed interpretation of how different exercise modalities may generate distinct segmental and regional loading environments that are broadly consistent with the observed region-specific BMD changes. Methods Multiscale simulation workflow The MS model was scaled uniformly to each participant based on torso length (Fig. 1 (a)) and simulated using collected kinematics and dynamics data (Fig. 1 (b)). The individualized lumbar FE model was established based on CT data (Fig. 1 (c)). Lumbar spine muscle attachment locations were obtained from the MS model[ 25 , 27 ] and transferred to the FE model for application of muscle forces (Fig. 1 (d)). The degrees of freedom in all directions of the lower surface of the FE model was restricted, and the joint reaction force (JRF) of the MS model was applied as input to the FE model. Translational DOFs at each intervertebral level remained free in the FE model to enable realistic spinal motion and load transfer. Study design and imaging This study used a subset of participants from a previously reported 6-month combined exercise intervention, for which the detailed recruitment process, eligibility criteria, and training protocol have been described elsewhere [ 28 ]. The present analysis focused on 10 postmenopausal women with low BMD who completed both baseline and follow-up imaging assessments. To quantify regional changes in BMD, CT scans were collected at baseline and after the intervention, and the lumbar vertebrae were divided into the vertebral body (VB) and posterior region (PR). Conventional CT scans of the T12–S1 segments were acquired using a CT scanner (Somatom Sensation 64, Siemens, Germany) under a standard in vivo protocol (110 kVp, 20 mAs). Participants were scanned in the supine position, with a manufacturer-provided support pad placed beneath the lumbar region. Additional scan parameters were as follows: slice thickness 0.5 mm, matrix size 512 × 512, and pixel spacing 0.488 × 0.488 mm. QCT measurements were performed by experienced radiologists, and all images were stored in DICOM format. The L1–L5 segments were segmented at both time points and subdivided into the VB and PR. To ensure spatial consistency between scans, all follow-up CT images were rigidly registered to the baseline scans using a three-dimensional rigid transformation algorithm[ 29 ]. The resulting transformation matrix was then applied to the baseline region-of-interest masks to propagate them to the follow-up images. This procedure reduced positional mismatch between scans and minimized manual segmentation bias. The Musculoskeletal Model Experimental data collection Participant characteristics and the combined exercise intervention have been reported previously [ 28 ]. In brief, the present study included 10 women with low bone mass (age 59.56 ± 7.18 years, weight 59.83 ± 7.59 kg, height 160.78 ± 5.45 cm). All participants provided written informed consent before inclusion, and the study was approved by the Ethics Committee of Tianjin University (Approval No. TJUE-2023-113, Registration No. ChiCTR2400081574). After completion of the 6-month intervention, participants performed four representative tasks for biomechanical analysis, each repeated three times: walking, heel drops, jumping, and resistance exercise with elastic bands. For the walking task, participants were required to walk at a comfortable pace, alternating between left and right feet over the central position of 4 force plates. During heel drops, participants rose onto the forefoot and then allowed the heels to descend freely while maintaining an upright posture. During jumping, participants performed a maximal vertical jump with free arm swing. During the resistance exercise, participants stepped on an elastic band, grasped both ends, and raised the band overhead before lowering it. Kinematic and dynamic data were sampled at 100 Hz using a motion capture system comprising 15 cameras from VICON (VICON motion system, Ltd., Oxford, UK) and 3 force plates (BP400600, AMTI, Watertown, USA). Reflective markers were placed on segments of the body, including the head, torso, arms, pelvis, and lower limbs, for a total of 77 markers to track full-body activities. The placement of reflective markers are shown in Fig. 2 (a). Surface electromyography was recorded bilaterally from the longest thoracic muscle (LTpT), latissimus dorsi (LD), and external oblique (EO) muscles using six electrodes (Noraxon USA Inc.) at 2000 Hz. The placement of electromyography sensors are shown in Fig. 2 (b). Musculoskeletal model construction The MS models used in this study were adapted from our previously reported framework [ 28 ], which was based on the full-body spine (FBLS) model in OpenSim 4.1 (SimTK, Stanford, CA) [ 30 ]. The base model comprised 21 body segments, 30 degrees of freedom, and 324 muscle–tendon actuators. Two task-specific MS configurations were used. For impact tasks (walking, heel drops, and jumping), the original FBLS model was used without modifying the joint degrees of freedom (Fig. 2 (c)-(e)). For the resistance task, the upper-limb flexion–extension range was adjusted from − 90°–90° to − 90°–180° to better represent overhead elastic-band exercise (Fig. 2 (f)). In addition, bilateral springs were introduced between the palm and ipsilateral calcaneus to simulate elastic-band loading. The spring rest length was set to 0.35 m and the stiffness to 28.29 N/m, based on tensile testing. All models were scaled to participant anthropometry before simulation. Inverse kinematics (IK), residual reduction algorithm (RRA), and static optimization (SO) were then performed to estimate muscle activations and paraspinal muscle forces during each task[ 31 , 32 ]. The model calculated muscle forces using the algorithm that minimized the sum of squared muscle activations (Eq. (1) and Eq. (2))[ 10 ]. \(\:J=\:\sum\:_{m=1}^{n}{\left({a}_{m}\right)}^{p}\) Eq. (1) subject to the following constraints, for j = 1:k \(\:\sum\:_{m=1}^{n}\left[{a}_{m}f\left({F}_{m}^{0},{l}_{m},{v}_{m}\right)\right]{r}_{m,j}={\tau\:}_{j}\) Eq. (2) where n is the number of muscles in the model; \(\:{a}_{m}\) is the activation level of muscle m at a discrete time step, \(\:f\left({F}_{m}^{0},{l}_{m},{v}_{m}\right)\) is its force-length-velocity surface; \(\:{r}_{m,j}\) is its moment arm about \(\:{j}^{th}\) joint axis; \(\:{\tau\:}_{j}\) is the generalized force acting about the \(\:{j}^{th}\) joint axis; and p is a user-defined constant. Joint reaction analysis [ 33 ] was subsequently used to calculate lumbar JRFs under the combined effects of kinematics, external loads, and internal muscle forces. The paraspinal muscles included in the model were the multifidus (MF), LTpT, iliocostalis lumborum (IL), latissimus dorsi (LD), quadratus lumborum (QL), and psoas major (Ps). These muscles are shown in Fig. 2 (g). Lumbar spine FE Model Model construction Personalized FE models were constructed based on lumbar CT images of 10 subjects. The complete lumbar FE model construction process is shown in Fig. 1 (c). The components of the FE model are shown in Fig. 3 . The model construction primarily involved the following steps: First, segmentation and reconstruction. The CT images were segmented to reconstruct the three-dimensional geometry of the T12-S1 segments. DICOM format CT images were imported into Mimics Research 21.0 software to delineate the T12-S1 vertebral segments. The segmentation of the T12 and S1 segments was prepared for the subsequent creation of T12-L1 and L5-S1 IVD. Second, smoothing operations. Due to CT resolution and the inherent shape of the lumbar vertebrae, local smoothing operations were performed on the vertebral segments to facilitate subsequent mesh generation. The vertebral features were used to reconstruct the IVD, including the annulus fibrosus, endplates, annular matrix, and nucleus pulposus. The nucleus pulposus occupies approximately 44% of the IVD volume [ 34 , 35 ]. Additionally, the vertebral bodies were divided into an outer layer of hard cortical bone and an inner layer of less dense cancellous bone, with the cortical bone thickness set to 1mm. Finally, the ligaments were constructed and the model was meshed. The vertebral bones were meshed with tetrahedral elements (C3D4) with a size of 1mm, and the IVDs were meshed with hexahedral elements (C3D8R) with a size of 0.5mm. Based on previous studies, the endplate thickness of the IVD was set to 0.5mm, and the articular cartilage thickness was set to approximately 0.2mm[ 36 , 37 ]. The annular fibers of the IVD were simulated using T3D2 elements, arranged in five layers at an angle of approximately 45° and added to the annulus fibrosus matrix. The ligaments consisted of the anterior longitudinal ligament, posterior longitudinal ligament, ligamentum flavum, supraspinous ligament, interspinous ligament, transverse ligament, and capsular ligament. These seven ligaments were defined as T3D2 elements with different cross-sectional areas (CSA). The articular cartilage between the two adjacent vertebrae was defined as surface-to-surface contact with a friction coefficient set to 0.1[ 38 , 39 ]. The coordinate systems of the vertebrae were adjusted to match the joint definitions used in the MS model. The material properties and mesh element settings for all components of the model are listed in Table 1 [ 40 – 44 ]. Table 1 The FE model material property related parameters setting Part Young's modulus (MPa) Poisson's ratio Cross-section area (mm 2 ) Element Type Total number of elements Bone : Cortical bone 12000 0.3 - C3D4 210877 Cancellous bone 100 0.2 - 314946 Posterior region 3500 0.25 - 384065 Facet cartilage 24 0.4 - 543885 Endplate 1000 0.4 - S4R 5422 IVD : AF1 550 0.3 0.76 T3D2 1962 AF2 502.5 0.5928 1962 AF3 455 0.4712 1962 AF4 407.5 0.3572 1962 AF5 357.5 0.16 1962 Nucleus pulposus 1 0.48 - C3D8R 9300 Annulus pulposus 4 0.4 - 11739 Ligament : ALL 12.8 0.3 63.7 T3D2 80 PLL 10 20 80 LF 10 40 80 SSL 2.8 25 80 ISL 2.8 30 80 ITL 10 25 80 CL 8 30 154 IVD: Intervertebral disc; AF: Annulus fibrosus; ALL: Anterior longitudinal ligament; PLL: Posterior longitudinal ligament; LF: ligamentum flavum; SSL: supraspinal ligament; ISL: interspinous ligament; ITL: intertransverse ligament; CL: Capsular ligament. Loading and boundary conditions The muscle forces and joint reaction forces obtained from the MS model during four exercises were applied to the FE model. Since the magnitude and direction of the paraspinal muscle forces change during exercise, manually creating all paraspinal muscle forces in the FE model is challenging. This study used a plugin [ 27 ] to extract the coordinates of each muscle attachment point on the lumbar spine, the direction of muscle fibers, and the magnitude of muscle forces from the MS model. A MATLAB script was then written to locate the surface node in the FE model closest to the attachment point, which was matched as the muscle insertion point. Muscle forces were created in batches using a Python script, applied as point loads with magnitudes and directions corresponding to those obtained from the MS model, as shown in Fig. 1 (d). In all models, the joint reaction force at T12-L1 was applied to the RP nodes on the upper surface of the IVD, with the JRFs also being applied as point loads, as shown in Fig. 1 (d). By applying JRFs to the upper surface of the IVD, the point loads obtained from the MS model were transferred to the endplate region and then dispersed to the bone surface via mechanical coupling. This loading strategy was used to assess exercise-induced mechanical differences in the lumbar spine and to explore how combined exercise may influence lumbar BMD. To ensure the stability of the FE model, the lower surface of the L5-S1 IVD was fixed, with all six degrees of freedom constrained, as shown in Fig. 1 (d). Validation Validation of MS model To validate the MS model, we used the same method as Beaucage-Gauvreau et al.[ 11 ]. Strong correlations were observed between muscle activations predicted by the model and EMG measurements, with cross-correlation values above 0.8 for most muscles across all three trials and up to 0.96 (Fig. 4 ). Details of the validation procedure have been reported previously by our group [ 28 ]. Validation of FE model In the FE model, the inferior endplate of L5 was fixed and a pure moment of 7.5 Nm was applied on the superior endplate of L1 to mimic the physiological motions of extension, flexion, lateral bending, and torsion. Under flexion, extension, lateral bending, and torsional loading conditions, the ROMs of each segment were compared with the previous studies[ 45 – 50 ] and showed satisfactory agreement (Fig. 5 ). Therefore, the lumbar spine FE model was considered suitable for assessing the biomechanical effects of different exercises. Statistical Analysis All data were tested for normal distribution. The one-way analysis of variance (ANOVA) was employed to describe the statistical significance of von Mises stress changes among walking, heel drops, and jumping, as well as resistance exercises. Statistical significance was defined as a p-value less than 0.05 for all analyses. Results Changes of BMD at two regions After six months of exercise training, region-specific changes in lumbar vertebral BMD were observed (Table 2 ). In the lumbar vertebrae (VB), the BMD changes ranged from − 0.14 ± 6.22 mg/cm³ at L5 to 2.40 ± 6.25 mg/cm³ at L2. In contrast, the PR consistently exhibited a decrease in BMD across all lumbar levels, with the greatest reduction observed at L3 (–6.57 ± 6.73 mg/cm³). Statistical analysis revealed significant differences between VB and PR in BMD changes at L1 (p = 0.023), L2 (p = 0.012), and L3 (p = 0.038). No significant differences were found at L4 (p = 0.078) and L5 (p = 0.170). These findings suggest that the anterior and posterior regions of the lumbar spine exhibit distinct adaptive responses to exercise loading, with the VB showing relatively better maintenance of, or increased, BMD compared to the PR, particularly at the upper lumbar levels (L1–L3). Table 2 Changes in lumbar VB and PR BMD (mean ± SD) after six months of exercise training Segment ΔBMD mg/cm 3 P Value VB PR L1 1.54 ± 5.06* -5.48 ± 5.87* 0.023 L2 2.40 ± 6.25* -6.36 ± 6.34* 0.012 L3 0.65 ± 6.36* -6.57 ± 6.73* 0.038 L4 0.68 ± 5.19 -4.68 ± 6.49 0.078 L5 -0.14 ± 6.22 -4.45 ± 6.07 0.17 VB: vertebral bodies; PR: posterior region; *p < 0.05. Paravertebral Muscle Forces & Joint Reaction Forces The joint reaction forces and muscle forces of the lumbar spine exhibited distinct patterns across walking, heel drops, jumping, and resistance exercise (Fig. 6 ). During walking, the joint reaction forces remained relatively stable with moderate fluctuations throughout the gait cycle, accompanied by low forces. Heel drops produced a sharp peak in joint reaction forces at the moment of impact, with a concurrent transient rise in muscle activation, particularly in the LTpT. Jumping elicited the largest transient peak in joint reaction forces, which exceeded 2000 N, and was accompanied by a pronounced but short-lived spike in muscle forces, especially in the QL, IL and LTpT. Resistance exercise, in contrast, demonstrated sustained high joint reaction forces across the cycle, with values comparable to or exceeding those observed in walking and heel drops. Compared with the other three exercises, muscle forces remained at relatively high levels during resistance training. Moreover, during all four exercises, the joint reaction forces were consistently greater than the paravertebral muscle forces. Peak JRF for each segment during four exercises is shown in Fig. 6 (b). The results indicated that during jumping, the JRF for all vertebral segments was significantly greater than walking, heel drops and resistance exercise (p < 0.05), approximately 1.50 to 1.91 times higher. Under heel drop, all segmental JRF values were significantly greater than walking (p < 0.05), approximately 1.23 to 1.27 times higher. Meanwhile, under resistance exercise, the JRF for the L3-L5 segments was significantly greater than walking (p < 0.05), approximately 1.26 to 1.29 times higher. The JRFs exhibited a decreasing trend from L5 to L1 for all the exercises, but there were no statistically significant differences observed among the vertebral segments. Peak MFs of the six paraspinal muscles during the exercises were calculated using a semi-automatic in-house MATLAB algorithm (Fig. 6 (c)). There were significant differences in the paraspinal MFs during various exercises. Except for Ps, the forces of the other 5 paraspinal muscles exhibited a pattern in which jumping yielded the highest force with up to 303.00N. During jumping, the forces of the 5 paraspinal muscles were significantly greater than those during both heel drop and walking (p < 0.01), ranging from 2.12 to 13.97 times higher than heel drop and 1.73 to 3.66 times higher than walking. Additionally, during resistance exercise, the forces of the LTpT and IL were significantly greater than the forces during walking and heel drop (LTpT: 231.79N vs 97.96N vs 23.67N, IL: 150.49N vs 54.70N vs 14.31N, p < 0.05). However, the force of the Ps during walking and jumping was 30.79N and 30.02N, which were significantly higher than those during heel drops (approximately 4.08 and 3.99 times) and resistance exercise (approximately 5.45 and 5.31 times) (p < 0.05). Different effects of exercise on lumbar segmental biomechanical responses The finite element results showed significant differences in von Mises stress among the four exercises (Fig. 7 ). Jumping induced the highest stress in the upper and mid-lumbar vertebrae, with significantly greater values than walking at L1–L4 (p < 0.05 or p < 0.001). Heel drops also generated elevated stress compared with walking, particularly at L1 (p < 0.05). In contrast, resistance exercise exerted more pronounced effects on the lower lumbar region, with greater stress observed at L4–L5 than during walking and jumping, although the differences were not statistically significant. Overall, the four exercises exhibited a similar pattern of average stress across the lumbar segments, characterized by a progressive increase from L1 to L5. Different effects of exercise on lumbar regional biomechanical responses The L1-L5 stress cloud maps of a representative subject in four exercises are shown in Fig. 8 . It can be observed that all four exercises generated relatively large stress at the posterior part of the VB. Stress in the L5 segment during jumping reached up to 150MPa. In addition, the average stress of the L1-L5 segments in the four exercises all showed that stress in the VB was significantly greater than that in the PR (p < 0.05), which was 1.92–4.78 times of the PR. Overall, PR responses were significantly smaller than VB, indicating that the VB bore the majority of the load during the four exercises. Finite element analysis revealed distinct regional differences in the VB and PR during walking, heel drops, jumping and resistance exercise (Table 3 ). For the VB, jumping produced stress values that were significantly higher than those during walking at L1–L3 (p < 0.05 or p < 0.001). Resistance exercise induced the greatest stress at L4 (8.04 ± 3.65 MPa) and L5 (12.94 ± 5.42 MPa), significantly exceeding walking (p < 0.05). For the PR, stress was consistently lower in magnitude than in VB. Jumping and resistance exercise increased PR stress relative to walking and heel drops at L1–L5, but no statistical differences were found. Table 3 Average von Mises stress (MPa, mean ± SD) of different regions in four exercises L1 VB W HD J R Significance 3.25 ± 0.65 4.62 ± 0.92 6.64 ± 0.97 4.44 ± 2.20 J > W**, HD*, R* L1 PR 0.85 ± 0.34 1.04 ± 0.46 1.27 ± 0.49 1.03 ± 0.53 L2 VB 3.45 ± 0.93 4.56 ± 1.16 6.57 ± 1.09 4.87 ± 1.82 J > W**, HD* L2 PR 1.48 ± 0.91 1.55 ± 1.17 2.10 ± 1.26 2.24 ± 2.15 L3 VB 3.61 ± 0.86 4.63 ± 1.43 6.49 ± 1.64 6.67 ± 2.64 J, R > W* L3 PR 1.83 ± 0.86 1.81 ± 1.15 2.69 ± 0.97 2.63 ± 1.45 L4 VB 3.98 ± 1.02 4.73 ± 1.56 7.12 ± 2.15 8.04 ± 3.65 R > W* L4 PR 1.96 ± 0.86 1.94 ± 0.85 2.86 ± 1.00 3.02 ± 1.37 L5 VB 5.85 ± 1.55 5.59 ± 1.49 9.79 ± 4.54 12.94 ± 5.42 R > W*, HD* L5 PR 1.89 ± 0.57 1.92 ± 1.01 2.64 ± 1.60 3.32 ± 2.10 W: Walking; HD: Heel drops; J: Jumping; R: Resistance exercise; *p < 0.05; **p < 0.001. Discussion This study integrated individualized MS modelling and FE analysis with longitudinal QCT-derived regional BMD changes, thereby establishing a mechanically interpretable framework that links exercise-specific internal loading and tissue-level mechanical stimuli to observed lumbar spine adaptation. Rather than relying on exercise efficacy alone, the combined modelling–imaging strategy helps explain why mechanically distinct exercise modalities may preferentially benefit particular lumbar segments and regions. This is a key added value beyond MS or FE modelling in isolation and addresses a translational gap that has limited the clinically meaningful interpretation of exercise-related spinal adaptation. Region-specific adaptations were observed after six months of training, with the VB showing preservation or modest gains, particularly at L1–L3, whereas the PR exhibited consistent decreases. The integrated analysis offers a mechanistic rationale: compressive load transfer and higher mechanical stimuli were predominantly concentrated within the VB across tasks, consistent with trabecular-rich regions being more responsive to osteogenic loading[ 51 , 52 ]. In contrast, the PR experienced lower stress magnitudes across exercises, which may contribute to its comparatively unfavourable BMD trend[ 53 , 54 ]. Importantly, these longitudinal in vivo outcomes provide important empirical support for the mechanical interpretation—supporting that regions exposed to greater mechanical stimuli tend to show more favourable BMD changes over time. Exercise-specific loading patterns further indicate that uniform exercise recommendations may be suboptimal. Jumping produced the largest transient joint reaction force peaks and preferentially elevated stresses in upper and mid-lumbar segments, reflecting high-impact, high strain-rate stimuli that are commonly associated with osteogenic potential. By contrast, resistance exercise generated sustained loading with relatively greater stress in the lower lumbar region (L4–L5), suggesting a different mechanical signature that may be advantageous for segment-dependent bone status[ 51 ]. Heel drops provided intermediate impact-driven stimuli, whereas walking produced comparatively low and stable loading[ 55 ]. Collectively, these results demonstrate that mechanically distinct exercise modalities impose heterogeneous stimuli across lumbar regions that cannot be captured by clinical imaging or motion analysis alone[ 56 , 57 ]. From a clinical perspective, the proposed framework suggests that exercise selection may influence the distribution of mechanical stimuli across lumbar segments and regions. Instead of prescribing exercise solely on the basis of type or intensity, the results suggest that exercise selection may be guided by the mechanical demands imposed on specific lumbar regions. For example, jumping increased mechanical stimuli more prominently in upper lumbar vertebral bodies, whereas resistance exercise produced sustained loading and relatively higher stresses in the lower lumbar segments compared with jumping. Such regional specificity provides a mechanistic basis for understanding exercise programs in relation to individual bone status, particularly in patients with segment-dependent bone loss. Although the current framework is not yet designed for prospective prediction, it should be regarded as providing a mechanistically informed interpretation of lumbar adaptation. This study has several limitations. Firstly, in terms of model construction, current studies usually require the separate establishment of MS and FE models for each participant. This results in substantial work and time consumption during the initial modelling phase, with potential human error due to the variability in modelling by different individuals. There is a lack of rapid modelling methods applicable to larger sample sizes. Machine learning models or the development of algorithms that automatically link MS model inputs and outputs may address these issues. Secondly, this study did not thoroughly investigate the relationship between the distribution of mechanical parameters and lumbar spine BMD. Third, although longitudinal QCT outcomes support the mechanical interpretation, prospective validation in larger and more diverse populations will be necessary before clinical translation to predictive prescription. Conclusions This study demonstrates the value of integrating MS modelling, FE analysis, and longitudinal QCT imaging to interpret exercise-induced bone adaptation in the lumbar spine. While MS models quantify exercise-specific internal loading and FE models resolve tissue-level mechanical responses, their integration with observed regional BMD changes over six months enables a mechanically interpretable link from exercise to stimulus and to adaptation. The results indicate that different exercise modalities generate distinct regional mechanical environments: jumping preferentially increased mechanical stimuli in upper lumbar vertebral bodies, whereas resistance exercise imposed more sustained loading in lower lumbar segments. These mechanical signatures are consistent with the region-specific BMD changes observed on follow-up QCT. Overall, the proposed framework provides a mechanically informed interpretation of exercise-related lumbar adaptation and may help guide future research on spinal bone health. Abbreviations BMD Bone mineral density QCT Quantitative computed tomography VB Vertebral body PR Posterior region MS Musculoskeletal FE Finite element DOF Degree of freedom JRF Joint reaction force EMG Electromyography IK Inverse kinematics RRA Residual reduction algorithm SO Static optimization MF Multifidus LTpT Longest thoracic muscle IL Iliocostalis lumborum EO external oblique LD Latissimus dorsi QL Quadratus lumborum Ps Psoas major IVD Intervertebral disc AF Annulus fibrosus ALL Anterior longitudinal ligament PLL Posterior longitudinal ligament LF Ligamentum flavum SSL Supraspinal ligament ISL Interspinous ligament ITL Intertransverse ligament CL Capsular ligament CSA Cross-sectional area ROM Range of motion ANOVA Analysis of variance Declarations Ethics approval and consent to participate This study was approved by the Ethics Committee of the Medical School, Tianjin University (Approval No. TJUE-2023-113). All procedures performed in this study involving human participants were in accordance with the ethical standards of the institutional research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. Written informed consent was obtained from all participants prior to participation. Consent for publication Written informed consent for publication was obtained from all participants prior to their inclusion in the study. Competing interests The authors declare no competing interests. Funding This study was supported by the Natural Science Fund Program of China [12302420] and Key Program of Tianjin Natural Science Foundation [23JCZDJC00830, 24JCYBJC01370]. Author Contribution Conceptualisation: XYX, SZL, JD; Data curation: XYX, SZL, PD, JYD; Formal analysis: XYX, SZL, PD, JYD; Funding acquisition: JD; Investigation: XYX, SZL, PD, JYD; Methodology: XYX, JD; Project administration: JD; Resources: JD; Software: XYX; Supervision: RX, SL, VS, LM, JD, DM; Validation: XYX, JD; Writing–original draft: XYX; Writing–review & editing: RX, SL, VS, LM, JD, DM. All authors read and approved the final manuscript. Acknowledgement The authors would like to acknowledge all participants involved in this study, as well as Mengen Huang from Tianjin University and the exercise trainers involved in the intervention. We would also like to thank the Rehabilitation Department of Tianjin Medical University General Hospital for providing the QCT scanner. Data Availability The datasets generated and/or analysed during the current study are not publicly available due to concerns regarding patient privacy and confidentiality but are available from the corresponding author on reasonable request. References Sozen T, Ozisik L, Basaran NC. An overview and management of osteoporosis. Eur J Rheumatol. 2017;4(1):46–56. Rachner TD, Khosla S, Hofbauer LC. Osteoporosis: now and the future. Lancet. 2011;377(9773):1276–87. Zhao R, Zhao M, Xu Z. The effects of differing resistance training modes on the preservation of bone mineral density in postmenopausal women: a meta-analysis. Osteoporos Int. 2015;26(5):1605–18. Zhang S, Huang X, Zhao X, Li B, Cai Y, Liang X, et al. Effect of exercise on bone mineral density among patients with osteoporosis and osteopenia: a systematic review and network meta-analysis. J Clin Nurs. 2022;31(15–16):2100–11. Brooke-Wavell K, Jones PR, Hardman AE. Brisk walking reduces calcaneal bone loss in post-menopausal women. Clin Sci. 1997;92(1):75–80. Marques EA, Mota J, Machado L, Sousa F, Coelho M, Moreira P, et al. Multicomponent training program with weight-bearing exercises elicits favorable bone density, muscle strength, and balance adaptations in older women. Calcif Tissue Int. 2011;88(2):117–29. Chuin A, Labonte M, Tessier D, Khalil A, Bobeuf F, Doyon CY, et al. Effect of antioxidants combined to resistance training on BMD in elderly women: a pilot study. Osteoporos Int. 2009;20(7):1253–8. Shojaa M, von Stengel S, Schoene D, Kohl M, Kemmler W. Effect of different types of exercise on bone mineral density in postmenopausal women: A systematic review and meta-analysis. Osteologie. 2020;29(03):179–93. Fountoulis G, Kerenidi T, Kokkinis C, Georgoulias P, Thriskos P, Gourgoulianis K, et al. Assessment of bone mineral density in male patients with chronic obstructive pulmonary disease by DXA and quantitative computed tomography. Int J Endocrinol. 2016;2016(1):6169721. Delp SL, Anderson FC, Arnold AS, Loan P, Habib A, John CT, et al. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans Biomed Eng. 2007;54(11):1940–50. Honegger JD, Actis JA, Gates DH, Silverman AK, Munson AH, Petrella AJ. Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand. Biomech Model Mechanobiol. 2021;20(1):339–58. Abe T, Kumagai K, Brechue WF. Fascicle length of leg muscles is greater in sprinters than distance runners. Med Sci Sports Exerc. 2000;32(6):1125–9. Christophy M, Faruk Senan NA, Lotz JC, O'Reilly OM. A musculoskeletal model for the lumbar spine. Biomech Model Mechanobiol. 2012;11(1–2):19–34. McFarland DC, Binder-Markey BI, Nichols JA, Wohlman SJ, de Bruin M, Murray WM. A Musculoskeletal Model of the Hand and Wrist Capable of Simulating Functional Tasks. IEEE Trans Biomed Eng. 2023;70(5):1424–35. Kim HK, Zhang Y. Estimation of lumbar spinal loading and trunk muscle forces during asymmetric lifting tasks: application of whole-body musculoskeletal modelling in OpenSim. Ergonomics. 2017;60(4):563–76. Favier CD, Finnegan ME, Quest RA, Honeyfield L, McGregor AH, Phillips ATM. An open-source musculoskeletal model of the lumbar spine and lower limbs: a validation for movements of the lumbar spine. Comput Methods Biomech BioMed Eng. 2021;24(12):1310–25. Kerner J, Huiskes R, van Lenthe GH, Weinans H, van Rietbergen B, Engh CA, et al. Correlation between pre-operative periprosthetic bone density and post-operative bone loss in THA can be explained by strain-adaptive remodelling. J Biomech. 1999;32(7):695–703. Pizzolato C, Lloyd DG, Barrett RS, Cook JL, Zheng MH, Besier TF, et al. Bioinspired Technologies to Connect Musculoskeletal Mechanobiology to the Person for Training and Rehabilitation. Front Comput Neurosci. 2017;11:96. Fyhrie DP, Carter DR. A unifying principle relating stress to trabecular bone morphology. J Orthop Res. 1986;4(3):304–17. Adachi T, Tomita Y, Sakaue H, Tanaka M. Simulation of trabecular surface remodeling based on local stress nonuniformity. JSME Int J C. 1997;40(4):782–92. Du J, Li S, Silberschmidt VV. Remodelling of trabecular bone in human distal tibia: a model based on an in-vivo HR-pQCT study. J Mech Behav Biomed Mater. 2021;119:104506. Tsubota K, Adachi T, Tomita Y. Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state. J Biomech. 2002;35(12):1541–51. Du J, Hartley C, Brooke-Wavell K, Paggiosi MA, Walsh JS, Li S, et al. High-impact exercise stimulated localised adaptation of microarchitecture across distal tibia in postmenopausal women. Osteoporos Int. 2021;32(5):907–19. Du J, Brooke-Wavell K, Paggiosi MA, Hartley C, Walsh JS, Silberschmidt VV, et al. Characterising variability and regional correlations of microstructure and mechanical competence of human tibial trabecular bone: An in-vivo HR-pQCT study. Bone. 2019;121:139–48. Phillips AT, Villette CC, Modenese L. Femoral bone mesoscale structural architecture prediction using musculoskeletal and finite element modelling. Int Biomech. 2015;2(1):43–61. Geraldes DM, Modenese L, Phillips ATM. Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur. Biomech Model Mechanobiol. 2016;15(5):1029–42. van Arkel RJ, Modenese L, Phillips AT, Jeffers JR. Hip abduction can prevent posterior edge loading of hip replacements. J Orthop Res. 2013;31(8):1172–9. Liu S, Xia X, Nie Y, Huang M, Meng L, Du J. Musculoskeletal model predicted paraspinal loading may quick estimate the effect of exercise on spine BMD. Front Bioeng Biotechnol. 2024;12:1464067. Christen P, Ito K, Ellouz R, Boutroy S, Sornay-Rendu E, Chapurlat RD, et al. Bone remodelling in humans is load-driven but not lazy. Nat Commun. 2014;5(1):4855. Raabe ME, Chaudhari AM. An investigation of jogging biomechanics using the full-body lumbar spine model: Model development and validation. J Biomech. 2016;49(7):1238–43. Ueno R, Ishida T, Yamanaka M, Taniguchi S, Ikuta R, Samukawa M, et al. Quadriceps force and anterior tibial force occur obviously later than vertical ground reaction force: a simulation study. BMC Musculoskelet Disord. 2017;18:1–8. Mokhtarzadeh H, Yeow CH, Goh JCH, Oetomo D, Malekipour F, Lee PV-S. Contributions of the soleus and gastrocnemius muscles to the anterior cruciate ligament loading during single-leg landing. J Biomech. 2013;46(11):1913–20. Aghdam HA, Haghighat F, Rezaie M, Kavyani M, Karimi MT. Comparison of the knee joint reaction force between individuals with and without acute anterior cruciate ligament rupture during walking. J Orthop Surg Res. 2022;17(1):1–11. Kurutz M. Finite element modelling of human lumbar spine. Finite element analysis. 2010:209 – 36. Kurutz M, Oroszváry L. Finite element modeling and simulation of healthy and degenerated human lumbar spine. Finite Elem Analysis—From Biomedical Appl Industrial Developments. 2012:193–216. Zou D, Yue L, Fan Z, Zhao Y, Leng H, Sun Z, et al. Biomechanical analysis of lumbar interbody fusion cages with various elastic moduli in osteoporotic and non-osteoporotic lumbar spine: a finite element analysis. Global Spine J. 2024;14(7):2053–61. Spina NT, Moreno GS, Brodke DS, Finley SM, Ellis BJ. Biomechanical effects of laminectomies in the human lumbar spine: a finite element study. Spine J. 2021;21(1):150–9. Khuyagbaatar B, Kim K, Kim YH. Recent developments in finite element analysis of the lumbar spine. Int J Precis Eng Manuf. 2024;25(2):487–96. Leszczynski A, Meyer F, Charles YP, Deck C, Willinger R. Development of a flexible instrumented lumbar spine finite element model and comparison with in-vitro experiments. Comput Methods Biomech BioMed Eng. 2022;25(2):221–37. Pitzen T, Geisler F, Matthis D, Müller-Storz H, Barbier D, Steudel WI, et al. A finite element model for predicting the biomechanical behaviour of the human lumbar spine. Control Eng Pract. 2002;10(1):83–90. Schmidt H, Shirazi-Adl A, Galbusera F, Wilke HJ. Response analysis of the lumbar spine during regular daily activities–a finite element analysis. J Biomech. 2010;43(10):1849–56. Shin DS, Lee K, Kim D. Biomechanical study of lumbar spine with dynamic stabilization device using finite element method. Comput Aided Des. 2007;39(7):559–67. Wagnac E, Arnoux PJ, Garo A, Aubin CE. Finite element analysis of the influence of loading rate on a model of the full lumbar spine under dynamic loading conditions. Med Biol Eng Comput. 2012;50(9):903–15. Zhao G, Wang L, Wang H, Li C, Yuan S, Sun J, et al. Biomechanical Effects of Multi-segment Fixation on Lumbar Spine and Sacroiliac Joints: A Finite Element Analysis. Orthop Surg. 2024;16(10):2499–508. Shim CS, Park SW, Lee SH, Lim TJ, Chun K, Kim DH. Biomechanical evaluation of an interspinous stabilizing device. Locker Spine. 2008;33(22):E820–7. Panjabi MM. Cervical spine models for biomechanical research. Spine. 1998;23(24):2684–700. Rana M, Roy S, Biswas P, Biswas SK, Biswas JK. Design and development of a novel expanding flexible rod device (FRD) for stability in the lumbar spine: A finite-element study. Int J Artif Organs. 2020;43(12):803–10. Yamamoto I, Panjabi MM, Crisco T, Oxland T. Three-dimensional movements of the whole lumbar spine and lumbosacral joint. Spine. 1989;14(11):1256–60. Gong Z, Chen Z, Feng Z, Cao Y, Jiang C, Jiang X. Finite element analysis of 3 posterior fixation techniques in the lumbar spine. Orthopedics. 2014;37(5):e441–8. Renner SM, Natarajan RN, Patwardhan AG, Havey RM, Voronov LI, Guo BY, et al. Novel model to analyze the effect of a large compressive follower pre-load on range of motions in a lumbar spine. J Biomech. 2007;40(6):1326–32. Rubin CT, Lanyon LE. Regulation of bone formation by applied dynamic loads. JBJS. 1984;66(3):397–402. Frost HM. Bone's mechanostat: a 2003 update. The Anatomical record part a: discoveries in molecular, cellular, and evolutionary biology: an official publication of the american association of anatomists. 2003;275(2):1081–101. Brinckmann P, Grootenboer H. Change of disc height, radial disc bulge, and intradiscal pressure from discectomy an in vitro investigation on human lumbar discs. Spine. 1991;16(6):641–6. Adams MA, Dolan P. Biomechanics of vertebral compression fractures and clinical application. Arch Orthop Trauma Surg. 2011;131(12):1703–10. Winter DA. Biomechanics and motor control of human movement. Wiley; 2009. McGill S. Low back disorders: evidence-based prevention and rehabilitation. Human Kinetics; 2015. Schoenau E. From mechanostat theory to development of the Functional Muscle-Bone-Unit. J Musculoskel Neuronal Interact. 2005;5(3):232–8. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 16 Apr, 2026 Reviewers invited by journal 02 Apr, 2026 Editor invited by journal 31 Mar, 2026 Editor assigned by journal 31 Mar, 2026 Submission checks completed at journal 30 Mar, 2026 First submitted to journal 30 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9197056","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":618201928,"identity":"d128dd9a-11c9-4f8b-86b4-a593eb3f34ff","order_by":0,"name":"Xiaoyu Xia","email":"","orcid":"","institution":"Tianjin University","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyu","middleName":"","lastName":"Xia","suffix":""},{"id":618201929,"identity":"7a82fff6-becb-4403-8c9f-987cb2b4339a","order_by":1,"name":"Shizhong Liu","email":"","orcid":"","institution":"Tianjin University","correspondingAuthor":false,"prefix":"","firstName":"Shizhong","middleName":"","lastName":"Liu","suffix":""},{"id":618201930,"identity":"e48ab1c5-d358-4e97-88e7-f269c1be8592","order_by":2,"name":"Pu Duan","email":"","orcid":"","institution":"Tianjin University","correspondingAuthor":false,"prefix":"","firstName":"Pu","middleName":"","lastName":"Duan","suffix":""},{"id":618201931,"identity":"612fd0d1-30b6-49c1-a907-93b2eae7f320","order_by":3,"name":"Jiayu Di","email":"","orcid":"","institution":"Tianjin University","correspondingAuthor":false,"prefix":"","firstName":"Jiayu","middleName":"","lastName":"Di","suffix":""},{"id":618201932,"identity":"faf61e53-c915-41bb-8ec7-c67794e1afb6","order_by":4,"name":"Rui Xu","email":"","orcid":"","institution":"Tianjin University","correspondingAuthor":false,"prefix":"","firstName":"Rui","middleName":"","lastName":"Xu","suffix":""},{"id":618201934,"identity":"9c65966d-2cae-44bf-9c94-83046d5f09c6","order_by":5,"name":"Simin Li","email":"","orcid":"","institution":"Loughborough University","correspondingAuthor":false,"prefix":"","firstName":"Simin","middleName":"","lastName":"Li","suffix":""},{"id":618201935,"identity":"ef2e0288-44c2-49c0-bac1-9db9ebf50d60","order_by":6,"name":"Vadim V Silberschmidt","email":"","orcid":"","institution":"Loughborough University","correspondingAuthor":false,"prefix":"","firstName":"Vadim","middleName":"V","lastName":"Silberschmidt","suffix":""},{"id":618201936,"identity":"5f669091-1310-4723-9c2d-bea8fe133854","order_by":7,"name":"Lin Meng","email":"","orcid":"","institution":"Tianjin University","correspondingAuthor":false,"prefix":"","firstName":"Lin","middleName":"","lastName":"Meng","suffix":""},{"id":618201937,"identity":"178c6f76-711c-4a54-a4f4-20080ca61604","order_by":8,"name":"Juan Du","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAq0lEQVRIiWNgGAWjYBACxgYGA4YPDGwgtgHxWhhnJJCiBaSSmSeBgQQtzA3M26Rtf/AlNrA3b5NgqLlDjMPYyqRzEtgSG3iOlUkwHHtGjBYeM4gWiRwzCcaGw0RqsQBpkX9DihYGsC08RGthK7bsSWMzbuNJK7ZIOEaEFsMG5o03ftgck+1nP7zxxocaYrTMfwCijkHiP4GwBgYGeQhVQ4zaUTAKRsEoGKkAAHAjMMu7iZwFAAAAAElFTkSuQmCC","orcid":"","institution":"Tianjin University","correspondingAuthor":true,"prefix":"","firstName":"Juan","middleName":"","lastName":"Du","suffix":""},{"id":618201938,"identity":"cec31b94-97b6-407c-b5a3-45043edf040a","order_by":9,"name":"Dong Ming","email":"","orcid":"","institution":"Tianjin University","correspondingAuthor":false,"prefix":"","firstName":"Dong","middleName":"","lastName":"Ming","suffix":""}],"badges":[],"createdAt":"2026-03-23 07:40:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9197056/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9197056/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106534720,"identity":"002c3e76-b2c9-46ee-8144-8c76caba8578","added_by":"auto","created_at":"2026-04-09 15:05:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1997625,"visible":true,"origin":"","legend":"\u003cp\u003eMulti-scale model workflow\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/6ae8631b42b4ba9f73f8452f.png"},{"id":106725678,"identity":"c4530385-1ef8-47d8-bc04-43ae4cfc2bac","added_by":"auto","created_at":"2026-04-12 18:33:27","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":2656658,"visible":true,"origin":"","legend":"\u003cp\u003e(a) The placement of reflective markers and (b) the placement of electromyography sensors (c)Walking MS model; (d) Heel drops MS model; (e) Jumping MS model; (f) Resistance exercise MS model; and (g)Diagram of the muscle groups of the paraspinal muscles in the MS model. MF: multifidus; LTpT: longest thoracic muscle; IL: iliocostalis lumborum; LD: latissimus dorsi; QL: quadratus lumborum; Ps: psoas major\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/8c902cc70376c28eae8c0bc6.png"},{"id":106725816,"identity":"fc1728f7-d542-48c3-9e2d-d768d0d6a58a","added_by":"auto","created_at":"2026-04-12 18:33:58","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1559830,"visible":true,"origin":"","legend":"\u003cp\u003eThe components of the FE model. ALL: Anterior longitudinal ligament; PLL: Posterior longitudinal ligament; LF: ligamentum flavum; SSL: supraspinal ligament; ISL: interspinous ligaments; ITL: intertransverse ligament; CL: Capsular ligament.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/c0ac02873a8f404b4c28173e.png"},{"id":106534721,"identity":"2ab404ae-6fd6-409e-a981-bd2839293710","added_by":"auto","created_at":"2026-04-09 15:05:59","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":205129,"visible":true,"origin":"","legend":"\u003cp\u003eFor the 4 types of exercises, the cross-correlation (r values) between the muscle activation obtained from the MS model and the average peak values of muscle activation processed from EMG. W: Walking; HD: Heel drops; J: Jumping; R: Resistance exercise\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/291e01bbc1bffcff2b7b868f.png"},{"id":106726179,"identity":"42ae17b9-f59d-4237-989b-7092d8bf1aa6","added_by":"auto","created_at":"2026-04-12 18:35:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":419996,"visible":true,"origin":"","legend":"\u003cp\u003eThe FE model established in this study and the FE model obtained in previous studies were Flexion-Extension (FL-EX), Bending and Torsion (a)L1-L2 segment ROM; (b)L2-L3 segment ROM; (c)L3-L4 segment ROM; (d)L4-L5 segment ROM comparison verification\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/793df271c42cf9621f3d136b.png"},{"id":106534722,"identity":"9e56e740-01bf-40b0-8d24-325bf223fc39","added_by":"auto","created_at":"2026-04-09 15:05:59","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":771370,"visible":true,"origin":"","legend":"\u003cp\u003e(a)The curves of joint reaction force and muscle force during four exercises. (b) Joint reaction force during different exercises. (c) Paravertebral muscle forces. MF: multifidus; LTpT: longest thoracic muscle; IL: iliocostalis lumborum; LD: latissimus dorsi; QL: quadratus lumborum; Ps: psoas major.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/275702c9bb09d6a3db12788a.png"},{"id":106534727,"identity":"77ee9b2a-f379-486e-ad85-4281ac6437ee","added_by":"auto","created_at":"2026-04-09 15:05:59","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":38020,"visible":true,"origin":"","legend":"\u003cp\u003eAverage von Mises stress (MPa, mean ± SD) of L1-L5 segments in four exercise tasks. W: Walking; HD: Heel drops; J: Jumping; R: Resistance exercise; *p\u0026lt;0.05; **p\u0026lt;0.001\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/4c94f5febd3d2379e26c5bd8.png"},{"id":106534726,"identity":"30b5b169-eb40-43c5-83b3-b1e7337fec74","added_by":"auto","created_at":"2026-04-09 15:05:59","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":2453988,"visible":true,"origin":"","legend":"\u003cp\u003evon Mises stress distribution results of vertebrae in four exercises (*p\u0026lt;0.05; **p\u0026lt;0.001)\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/fc8f24f647b5a3d8c1e5599a.png"},{"id":106727577,"identity":"b91767a3-d715-4048-a6ee-05fe89767c74","added_by":"auto","created_at":"2026-04-12 18:39:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":11232571,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9197056/v1/98456abf-0476-4668-827c-556cf583f9f4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Exercise-specific mechanical stimuli are associated with regional lumbar bone adaptation: A combined in vivo and in silico multi-scale study","fulltext":[{"header":"Background","content":"\u003cp\u003eOsteoporosis is a systemic metabolic bone disease characterized by reduced bone mineral density (BMD) and deterioration of bone microarchitecture, resulting in increased skeletal fragility and a greater risk of fracture[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Approximately one in three women over the age of 50 will experience an osteoporotic fracture. Among common sites of insufficiency fractures, the lumbar spine is particularly vulnerable compared to the wrist and hip[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Exercise has emerged as a critical non-pharmacological intervention for preserving or improving BMD, as it promotes bone adaptation through mechanical loading without the adverse effects associated with pharmacological therapies[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Despite these benefits, the mechanobiological mechanisms through which exercise influences lumbar spine BMD remain incompletely understood. This knowledge gap is primarily attributed to the paucity of robust methodologies capable of linking whole-body exercise tasks to tissue-level mechanical stimuli.\u003c/p\u003e \u003cp\u003eClinical practice guidelines consistently advocate for exercise training as a viable non-pharmacological strategy for the maintenance or enhancement of BMD in populations with osteopenia or osteoporosis[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Nevertheless, the efficacy of various exercise modalities on lumbar BMD demonstrates considerable heterogeneity across the literature. For instance, an investigation into prescribed brisk walking programs yielded no significant effect on lumbar BMD[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Similarly, a longitudinal study incorporating heel drops, muscular endurance, and balance exercises reported no significant skeletal adaptations compared to a sedentary control group[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. In contrast, a six-month randomized controlled trial involving tri-weekly resistance training-comprising exercises such as bench press and leg extensions-demonstrated that while lumbar BMD significantly declined in the placebo group, it was successfully preserved in the intervention cohorts[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. A systematic review of 75 studies involving postmenopausal women further concluded that multi-component interventions, particularly those combining jumping and resistance exercises, conferred superior benefits to the lumbar spine compared to single-modality protocols[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. These findings suggest that BMD adaptations are highly sensitive to specific exercise prescriptions[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Such variability may be attributed to the divergent mechanical loading profiles imposed upon the lumbar spine by different physical activities. However, there remains a paucity of research on the tissue-level loading associated with various exercise programs, despite these mechanical stimuli being the fundamental drivers of bone adaptation and BMD fluctuations.\u003c/p\u003e \u003cp\u003eMusculoskeletal (MS) models have been extensively utilized to analyse human activities and predict mechanical loading, including intervertebral compression, shear forces, and paravertebral muscle forces during exercise[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. These analytical frameworks account for complex muscle\u0026ndash;muscle and muscle\u0026ndash;bone interactions[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Researchers have established and validated MS models across various anatomical regions, such as the lumbar spine[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], and wrist[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], to simulate diverse motor tasks and predict joint kinetics and muscle activation patterns. Specifically, whole-body MS models have been employed to estimate lumbar spinal loads and muscular recruitment during asymmetric lifting tasks[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. However, MS simulations are inherently limited to providing mechanical data at the joint and muscle levels, failing to capture loading characteristics at the bone tissue level[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBiomechanical stimuli, specifically stress [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], are more directly associated with the biological mechanisms of bone adaptation and have been demonstrated to influence BMD adaptation[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Finite element (FE) analysis is frequently employed to investigate the stress-strain distributions and other mechanical behaviours of bone at the tissue level. Consequently, simulations of bone adaptation have been performed wherein modifications to BMD and microarchitecture are driven by localized mechanical criteria[\u003cspan additionalcitationids=\"CR20 CR21\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. While such simulations can predict BMD and structural distributions consistent with experimental observations[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], the outcomes remain highly sensitive to the complexity of the prescribed loading conditions. The absence of accurate local boundary conditions may result in significant discrepancies between simulation results and actual clinical presentations.\u003c/p\u003e \u003cp\u003eExisting FE\u0026ndash;MS coupling studies have demonstrated the feasibility of applying physiologically realistic loads[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], yet their integration with longitudinal in vivo bone density measurements remains limited. In particular, the lack of studies that directly connect exercise-specific tissue-level mechanical stimuli with the observed region-specific bone adaptation has hindered translation of biomechanical modelling into clinically meaningful exercise prescription. Therefore, the objective of this study was to establish an individualized multi-scale MS\u0026ndash;FE framework and to interpret its mechanical outputs alongside six-month longitudinal QCT-derived BMD changes in the lumbar spine. This study aimed to provide a mechanically informed interpretation of how different exercise modalities may generate distinct segmental and regional loading environments that are broadly consistent with the observed region-specific BMD changes.\u003c/p\u003e "},{"header":"Methods","content":"\u003cp\u003eMultiscale simulation workflow\u003c/p\u003e \u003cp\u003eThe MS model was scaled uniformly to each participant based on torso length (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a)) and simulated using collected kinematics and dynamics data (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b)). The individualized lumbar FE model was established based on CT data (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c)). Lumbar spine muscle attachment locations were obtained from the MS model[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] and transferred to the FE model for application of muscle forces (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d)). The degrees of freedom in all directions of the lower surface of the FE model was restricted, and the joint reaction force (JRF) of the MS model was applied as input to the FE model. Translational DOFs at each intervertebral level remained free in the FE model to enable realistic spinal motion and load transfer.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eStudy design and imaging\u003c/p\u003e \u003cp\u003eThis study used a subset of participants from a previously reported 6-month combined exercise intervention, for which the detailed recruitment process, eligibility criteria, and training protocol have been described elsewhere [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The present analysis focused on 10 postmenopausal women with low BMD who completed both baseline and follow-up imaging assessments. To quantify regional changes in BMD, CT scans were collected at baseline and after the intervention, and the lumbar vertebrae were divided into the vertebral body (VB) and posterior region (PR).\u003c/p\u003e \u003cp\u003eConventional CT scans of the T12\u0026ndash;S1 segments were acquired using a CT scanner (Somatom Sensation 64, Siemens, Germany) under a standard in vivo protocol (110 kVp, 20 mAs). Participants were scanned in the supine position, with a manufacturer-provided support pad placed beneath the lumbar region. Additional scan parameters were as follows: slice thickness 0.5 mm, matrix size 512 \u0026times; 512, and pixel spacing 0.488 \u0026times; 0.488 mm. QCT measurements were performed by experienced radiologists, and all images were stored in DICOM format.\u003c/p\u003e \u003cp\u003eThe L1\u0026ndash;L5 segments were segmented at both time points and subdivided into the VB and PR. To ensure spatial consistency between scans, all follow-up CT images were rigidly registered to the baseline scans using a three-dimensional rigid transformation algorithm[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The resulting transformation matrix was then applied to the baseline region-of-interest masks to propagate them to the follow-up images. This procedure reduced positional mismatch between scans and minimized manual segmentation bias.\u003c/p\u003e \u003cp\u003eThe Musculoskeletal Model\u003c/p\u003e \u003cp\u003eExperimental data collection\u003c/p\u003e \u003cp\u003eParticipant characteristics and the combined exercise intervention have been reported previously [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. In brief, the present study included 10 women with low bone mass (age 59.56\u0026thinsp;\u0026plusmn;\u0026thinsp;7.18 years, weight 59.83\u0026thinsp;\u0026plusmn;\u0026thinsp;7.59 kg, height 160.78\u0026thinsp;\u0026plusmn;\u0026thinsp;5.45 cm). All participants provided written informed consent before inclusion, and the study was approved by the Ethics Committee of Tianjin University (Approval No. TJUE-2023-113, Registration No. ChiCTR2400081574).\u003c/p\u003e \u003cp\u003eAfter completion of the 6-month intervention, participants performed four representative tasks for biomechanical analysis, each repeated three times: walking, heel drops, jumping, and resistance exercise with elastic bands. For the walking task, participants were required to walk at a comfortable pace, alternating between left and right feet over the central position of 4 force plates. During heel drops, participants rose onto the forefoot and then allowed the heels to descend freely while maintaining an upright posture. During jumping, participants performed a maximal vertical jump with free arm swing. During the resistance exercise, participants stepped on an elastic band, grasped both ends, and raised the band overhead before lowering it.\u003c/p\u003e \u003cp\u003eKinematic and dynamic data were sampled at 100 Hz using a motion capture system comprising 15 cameras from VICON (VICON motion system, Ltd., Oxford, UK) and 3 force plates (BP400600, AMTI, Watertown, USA). Reflective markers were placed on segments of the body, including the head, torso, arms, pelvis, and lower limbs, for a total of 77 markers to track full-body activities. The placement of reflective markers are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a). Surface electromyography was recorded bilaterally from the longest thoracic muscle (LTpT), latissimus dorsi (LD), and external oblique (EO) muscles using six electrodes (Noraxon USA Inc.) at 2000 Hz. The placement of electromyography sensors are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b).\u003c/p\u003e \u003cp\u003eMusculoskeletal model construction\u003c/p\u003e \u003cp\u003eThe MS models used in this study were adapted from our previously reported framework [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], which was based on the full-body spine (FBLS) model in OpenSim 4.1 (SimTK, Stanford, CA) [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. The base model comprised 21 body segments, 30 degrees of freedom, and 324 muscle\u0026ndash;tendon actuators.\u003c/p\u003e \u003cp\u003eTwo task-specific MS configurations were used. For impact tasks (walking, heel drops, and jumping), the original FBLS model was used without modifying the joint degrees of freedom (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c)-(e)). For the resistance task, the upper-limb flexion\u0026ndash;extension range was adjusted from \u0026minus;\u0026thinsp;90\u0026deg;\u0026ndash;90\u0026deg; to \u0026minus;\u0026thinsp;90\u0026deg;\u0026ndash;180\u0026deg; to better represent overhead elastic-band exercise (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(f)). In addition, bilateral springs were introduced between the palm and ipsilateral calcaneus to simulate elastic-band loading. The spring rest length was set to 0.35 m and the stiffness to 28.29 N/m, based on tensile testing.\u003c/p\u003e \u003cp\u003eAll models were scaled to participant anthropometry before simulation. Inverse kinematics (IK), residual reduction algorithm (RRA), and static optimization (SO) were then performed to estimate muscle activations and paraspinal muscle forces during each task[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. The model calculated muscle forces using the algorithm that minimized the sum of squared muscle activations (Eq.\u0026nbsp;(1) and Eq.\u0026nbsp;(2))[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:J=\\:\\sum\\:_{m=1}^{n}{\\left({a}_{m}\\right)}^{p}\\)\u003c/span\u003e \u003c/span\u003e Eq.\u0026nbsp;(1)\u003c/p\u003e \u003cp\u003esubject to the following constraints, for j\u0026thinsp;=\u0026thinsp;1:k\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{m=1}^{n}\\left[{a}_{m}f\\left({F}_{m}^{0},{l}_{m},{v}_{m}\\right)\\right]{r}_{m,j}={\\tau\\:}_{j}\\)\u003c/span\u003e \u003c/span\u003e Eq.\u0026nbsp;(2)\u003c/p\u003e \u003cp\u003ewhere n is the number of muscles in the model; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{m}\\)\u003c/span\u003e\u003c/span\u003e is the activation level of muscle m at a discrete time step, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\left({F}_{m}^{0},{l}_{m},{v}_{m}\\right)\\)\u003c/span\u003e\u003c/span\u003e is its force-length-velocity surface; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{r}_{m,j}\\)\u003c/span\u003e\u003c/span\u003e is its moment arm about \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{j}^{th}\\)\u003c/span\u003e\u003c/span\u003e joint axis; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}_{j}\\)\u003c/span\u003e\u003c/span\u003e is the generalized force acting about the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{j}^{th}\\)\u003c/span\u003e\u003c/span\u003e joint axis; and p is a user-defined constant. Joint reaction analysis [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] was subsequently used to calculate lumbar JRFs under the combined effects of kinematics, external loads, and internal muscle forces. The paraspinal muscles included in the model were the multifidus (MF), LTpT, iliocostalis lumborum (IL), latissimus dorsi (LD), quadratus lumborum (QL), and psoas major (Ps). These muscles are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(g).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eLumbar spine FE Model\u003c/p\u003e \u003cp\u003eModel construction\u003c/p\u003e \u003cp\u003ePersonalized FE models were constructed based on lumbar CT images of 10 subjects. The complete lumbar FE model construction process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c). The components of the FE model are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The model construction primarily involved the following steps: First, segmentation and reconstruction. The CT images were segmented to reconstruct the three-dimensional geometry of the T12-S1 segments. DICOM format CT images were imported into Mimics Research 21.0 software to delineate the T12-S1 vertebral segments. The segmentation of the T12 and S1 segments was prepared for the subsequent creation of T12-L1 and L5-S1 IVD. Second, smoothing operations. Due to CT resolution and the inherent shape of the lumbar vertebrae, local smoothing operations were performed on the vertebral segments to facilitate subsequent mesh generation. The vertebral features were used to reconstruct the IVD, including the annulus fibrosus, endplates, annular matrix, and nucleus pulposus. The nucleus pulposus occupies approximately 44% of the IVD volume [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Additionally, the vertebral bodies were divided into an outer layer of hard cortical bone and an inner layer of less dense cancellous bone, with the cortical bone thickness set to 1mm. Finally, the ligaments were constructed and the model was meshed. The vertebral bones were meshed with tetrahedral elements (C3D4) with a size of 1mm, and the IVDs were meshed with hexahedral elements (C3D8R) with a size of 0.5mm.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBased on previous studies, the endplate thickness of the IVD was set to 0.5mm, and the articular cartilage thickness was set to approximately 0.2mm[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The annular fibers of the IVD were simulated using T3D2 elements, arranged in five layers at an angle of approximately 45\u0026deg; and added to the annulus fibrosus matrix. The ligaments consisted of the anterior longitudinal ligament, posterior longitudinal ligament, ligamentum flavum, supraspinous ligament, interspinous ligament, transverse ligament, and capsular ligament. These seven ligaments were defined as T3D2 elements with different cross-sectional areas (CSA). The articular cartilage between the two adjacent vertebrae was defined as surface-to-surface contact with a friction coefficient set to 0.1[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. The coordinate systems of the vertebrae were adjusted to match the joint definitions used in the MS model. The material properties and mesh element settings for all components of the model are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e[\u003cspan additionalcitationids=\"CR41 CR42 CR43\" citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe FE model material property related parameters setting\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePart\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYoung's modulus (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoisson's ratio\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCross-section area (mm\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eElement Type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eTotal number of elements\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBone\u003c/b\u003e:\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCortical bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eC3D4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e210877\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCancellous bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e314946\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePosterior region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e384065\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFacet cartilage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e543885\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEndplate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eS4R\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e5422\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIVD\u003c/b\u003e:\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e550\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eT3D2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e1962\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e502.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5928\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e1962\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e455\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4712\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e1962\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e407.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.3572\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e1962\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e357.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e1962\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNucleus pulposus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eC3D8R\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e9300\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnnulus pulposus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e11739\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLigament\u003c/b\u003e:\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eALL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e63.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003eT3D2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePLL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSSL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eISL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eITL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e154\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eIVD: Intervertebral disc; AF: Annulus fibrosus; ALL: Anterior longitudinal ligament; PLL: Posterior longitudinal ligament; LF: ligamentum flavum; SSL: supraspinal ligament; ISL: interspinous ligament; ITL: intertransverse ligament; CL: Capsular ligament.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eLoading and boundary conditions\u003c/p\u003e \u003cp\u003eThe muscle forces and joint reaction forces obtained from the MS model during four exercises were applied to the FE model. Since the magnitude and direction of the paraspinal muscle forces change during exercise, manually creating all paraspinal muscle forces in the FE model is challenging. This study used a plugin [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] to extract the coordinates of each muscle attachment point on the lumbar spine, the direction of muscle fibers, and the magnitude of muscle forces from the MS model. A MATLAB script was then written to locate the surface node in the FE model closest to the attachment point, which was matched as the muscle insertion point. Muscle forces were created in batches using a Python script, applied as point loads with magnitudes and directions corresponding to those obtained from the MS model, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (d). In all models, the joint reaction force at T12-L1 was applied to the RP nodes on the upper surface of the IVD, with the JRFs also being applied as point loads, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (d). By applying JRFs to the upper surface of the IVD, the point loads obtained from the MS model were transferred to the endplate region and then dispersed to the bone surface via mechanical coupling. This loading strategy was used to assess exercise-induced mechanical differences in the lumbar spine and to explore how combined exercise may influence lumbar BMD. To ensure the stability of the FE model, the lower surface of the L5-S1 IVD was fixed, with all six degrees of freedom constrained, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (d).\u003c/p\u003e \u003cp\u003eValidation\u003c/p\u003e \u003cp\u003eValidation of MS model\u003c/p\u003e \u003cp\u003eTo validate the MS model, we used the same method as Beaucage-Gauvreau et al.[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Strong correlations were observed between muscle activations predicted by the model and EMG measurements, with cross-correlation values above 0.8 for most muscles across all three trials and up to 0.96 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Details of the validation procedure have been reported previously by our group [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eValidation of FE model\u003c/p\u003e \u003cp\u003eIn the FE model, the inferior endplate of L5 was fixed and a pure moment of 7.5 Nm was applied on the superior endplate of L1 to mimic the physiological motions of extension, flexion, lateral bending, and torsion. Under flexion, extension, lateral bending, and torsional loading conditions, the ROMs of each segment were compared with the previous studies[\u003cspan additionalcitationids=\"CR46 CR47 CR48 CR49\" citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e] and showed satisfactory agreement (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Therefore, the lumbar spine FE model was considered suitable for assessing the biomechanical effects of different exercises.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003eStatistical Analysis\u003c/h2\u003e \u003cp\u003eAll data were tested for normal distribution. The one-way analysis of variance (ANOVA) was employed to describe the statistical significance of von Mises stress changes among walking, heel drops, and jumping, as well as resistance exercises. Statistical significance was defined as a p-value less than 0.05 for all analyses.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eChanges of BMD at two regions\u003c/p\u003e \u003cp\u003eAfter six months of exercise training, region-specific changes in lumbar vertebral BMD were observed (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In the lumbar vertebrae (VB), the BMD changes ranged from \u0026minus;\u0026thinsp;0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;6.22 mg/cm\u0026sup3; at L5 to 2.40\u0026thinsp;\u0026plusmn;\u0026thinsp;6.25 mg/cm\u0026sup3; at L2. In contrast, the PR consistently exhibited a decrease in BMD across all lumbar levels, with the greatest reduction observed at L3 (\u0026ndash;6.57\u0026thinsp;\u0026plusmn;\u0026thinsp;6.73 mg/cm\u0026sup3;). Statistical analysis revealed significant differences between VB and PR in BMD changes at L1 (p\u0026thinsp;=\u0026thinsp;0.023), L2 (p\u0026thinsp;=\u0026thinsp;0.012), and L3 (p\u0026thinsp;=\u0026thinsp;0.038). No significant differences were found at L4 (p\u0026thinsp;=\u0026thinsp;0.078) and L5 (p\u0026thinsp;=\u0026thinsp;0.170). These findings suggest that the anterior and posterior regions of the lumbar spine exhibit distinct adaptive responses to exercise loading, with the VB showing relatively better maintenance of, or increased, BMD compared to the PR, particularly at the upper lumbar levels (L1\u0026ndash;L3).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChanges in lumbar VB and PR BMD (mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD) after six months of exercise training\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSegment\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eΔBMD mg/cm\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c5\" namest=\"c4\" rowspan=\"2\"\u003e \u003cp\u003eP Value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVB\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePR\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.54\u0026thinsp;\u0026plusmn;\u0026thinsp;5.06*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-5.48\u0026thinsp;\u0026plusmn;\u0026thinsp;5.87*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.40\u0026thinsp;\u0026plusmn;\u0026thinsp;6.25*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-6.36\u0026thinsp;\u0026plusmn;\u0026thinsp;6.34*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.65\u0026thinsp;\u0026plusmn;\u0026thinsp;6.36*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-6.57\u0026thinsp;\u0026plusmn;\u0026thinsp;6.73*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.038\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.68\u0026thinsp;\u0026plusmn;\u0026thinsp;5.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-4.68\u0026thinsp;\u0026plusmn;\u0026thinsp;6.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.078\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;6.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-4.45\u0026thinsp;\u0026plusmn;\u0026thinsp;6.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003eVB: vertebral bodies; PR: posterior region; *p\u0026thinsp;\u0026lt;\u0026thinsp;0.05.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eParavertebral Muscle Forces \u0026amp; Joint Reaction Forces\u003c/p\u003e \u003cp\u003eThe joint reaction forces and muscle forces of the lumbar spine exhibited distinct patterns across walking, heel drops, jumping, and resistance exercise (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). During walking, the joint reaction forces remained relatively stable with moderate fluctuations throughout the gait cycle, accompanied by low forces. Heel drops produced a sharp peak in joint reaction forces at the moment of impact, with a concurrent transient rise in muscle activation, particularly in the LTpT. Jumping elicited the largest transient peak in joint reaction forces, which exceeded 2000 N, and was accompanied by a pronounced but short-lived spike in muscle forces, especially in the QL, IL and LTpT. Resistance exercise, in contrast, demonstrated sustained high joint reaction forces across the cycle, with values comparable to or exceeding those observed in walking and heel drops. Compared with the other three exercises, muscle forces remained at relatively high levels during resistance training. Moreover, during all four exercises, the joint reaction forces were consistently greater than the paravertebral muscle forces.\u003c/p\u003e \u003cp\u003ePeak JRF for each segment during four exercises is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b). The results indicated that during jumping, the JRF for all vertebral segments was significantly greater than walking, heel drops and resistance exercise (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), approximately 1.50 to 1.91 times higher. Under heel drop, all segmental JRF values were significantly greater than walking (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), approximately 1.23 to 1.27 times higher. Meanwhile, under resistance exercise, the JRF for the L3-L5 segments was significantly greater than walking (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), approximately 1.26 to 1.29 times higher. The JRFs exhibited a decreasing trend from L5 to L1 for all the exercises, but there were no statistically significant differences observed among the vertebral segments.\u003c/p\u003e \u003cp\u003ePeak MFs of the six paraspinal muscles during the exercises were calculated using a semi-automatic in-house MATLAB algorithm (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c)). There were significant differences in the paraspinal MFs during various exercises. Except for Ps, the forces of the other 5 paraspinal muscles exhibited a pattern in which jumping yielded the highest force with up to 303.00N. During jumping, the forces of the 5 paraspinal muscles were significantly greater than those during both heel drop and walking (p\u0026thinsp;\u0026lt;\u0026thinsp;0.01), ranging from 2.12 to 13.97 times higher than heel drop and 1.73 to 3.66 times higher than walking. Additionally, during resistance exercise, the forces of the LTpT and IL were significantly greater than the forces during walking and heel drop (LTpT: 231.79N vs 97.96N vs 23.67N, IL: 150.49N vs 54.70N vs 14.31N, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). However, the force of the Ps during walking and jumping was 30.79N and 30.02N, which were significantly higher than those during heel drops (approximately 4.08 and 3.99 times) and resistance exercise (approximately 5.45 and 5.31 times) (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDifferent effects of exercise on lumbar segmental biomechanical responses\u003c/p\u003e \u003cp\u003eThe finite element results showed significant differences in von Mises stress among the four exercises (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). Jumping induced the highest stress in the upper and mid-lumbar vertebrae, with significantly greater values than walking at L1\u0026ndash;L4 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 or p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Heel drops also generated elevated stress compared with walking, particularly at L1 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). In contrast, resistance exercise exerted more pronounced effects on the lower lumbar region, with greater stress observed at L4\u0026ndash;L5 than during walking and jumping, although the differences were not statistically significant. Overall, the four exercises exhibited a similar pattern of average stress across the lumbar segments, characterized by a progressive increase from L1 to L5.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDifferent effects of exercise on lumbar regional biomechanical responses\u003c/p\u003e \u003cp\u003eThe L1-L5 stress cloud maps of a representative subject in four exercises are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. It can be observed that all four exercises generated relatively large stress at the posterior part of the VB. Stress in the L5 segment during jumping reached up to 150MPa. In addition, the average stress of the L1-L5 segments in the four exercises all showed that stress in the VB was significantly greater than that in the PR (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), which was 1.92\u0026ndash;4.78 times of the PR. Overall, PR responses were significantly smaller than VB, indicating that the VB bore the majority of the load during the four exercises.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFinite element analysis revealed distinct regional differences in the VB and PR during walking, heel drops, jumping and resistance exercise (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). For the VB, jumping produced stress values that were significantly higher than those during walking at L1\u0026ndash;L3 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 or p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Resistance exercise induced the greatest stress at L4 (8.04\u0026thinsp;\u0026plusmn;\u0026thinsp;3.65 MPa) and L5 (12.94\u0026thinsp;\u0026plusmn;\u0026thinsp;5.42 MPa), significantly exceeding walking (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). For the PR, stress was consistently lower in magnitude than in VB. Jumping and resistance exercise increased PR stress relative to walking and heel drops at L1\u0026ndash;L5, but no statistical differences were found.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage von Mises stress (MPa, mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD) of different regions in four exercises\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eL1\u003csub\u003eVB\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eW\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eJ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.25\u0026thinsp;\u0026plusmn;\u0026thinsp;0.65\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.62\u0026thinsp;\u0026plusmn;\u0026thinsp;0.92\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.64\u0026thinsp;\u0026plusmn;\u0026thinsp;0.97\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.44\u0026thinsp;\u0026plusmn;\u0026thinsp;2.20\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eJ\u0026thinsp;\u0026gt;\u0026thinsp;W**, HD*, R*\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL1\u003csub\u003ePR\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.85\u0026thinsp;\u0026plusmn;\u0026thinsp;0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.27\u0026thinsp;\u0026plusmn;\u0026thinsp;0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL2\u003csub\u003eVB\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.45\u0026thinsp;\u0026plusmn;\u0026thinsp;0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.56\u0026thinsp;\u0026plusmn;\u0026thinsp;1.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.57\u0026thinsp;\u0026plusmn;\u0026thinsp;1.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.87\u0026thinsp;\u0026plusmn;\u0026thinsp;1.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eJ\u0026thinsp;\u0026gt;\u0026thinsp;W**, HD*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL2\u003csub\u003ePR\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.48\u0026thinsp;\u0026plusmn;\u0026thinsp;0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.55\u0026thinsp;\u0026plusmn;\u0026thinsp;1.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.10\u0026thinsp;\u0026plusmn;\u0026thinsp;1.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.24\u0026thinsp;\u0026plusmn;\u0026thinsp;2.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL3\u003csub\u003eVB\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.63\u0026thinsp;\u0026plusmn;\u0026thinsp;1.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.49\u0026thinsp;\u0026plusmn;\u0026thinsp;1.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.67\u0026thinsp;\u0026plusmn;\u0026thinsp;2.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eJ, R\u0026thinsp;\u0026gt;\u0026thinsp;W*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL3\u003csub\u003ePR\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.83\u0026thinsp;\u0026plusmn;\u0026thinsp;0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.81\u0026thinsp;\u0026plusmn;\u0026thinsp;1.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.69\u0026thinsp;\u0026plusmn;\u0026thinsp;0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.63\u0026thinsp;\u0026plusmn;\u0026thinsp;1.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL4\u003csub\u003eVB\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.98\u0026thinsp;\u0026plusmn;\u0026thinsp;1.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.73\u0026thinsp;\u0026plusmn;\u0026thinsp;1.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.12\u0026thinsp;\u0026plusmn;\u0026thinsp;2.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.04\u0026thinsp;\u0026plusmn;\u0026thinsp;3.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;W*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL4\u003csub\u003ePR\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.96\u0026thinsp;\u0026plusmn;\u0026thinsp;0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.94\u0026thinsp;\u0026plusmn;\u0026thinsp;0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.86\u0026thinsp;\u0026plusmn;\u0026thinsp;1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.02\u0026thinsp;\u0026plusmn;\u0026thinsp;1.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL5\u003csub\u003eVB\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.85\u0026thinsp;\u0026plusmn;\u0026thinsp;1.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.59\u0026thinsp;\u0026plusmn;\u0026thinsp;1.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9.79\u0026thinsp;\u0026plusmn;\u0026thinsp;4.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e12.94\u0026thinsp;\u0026plusmn;\u0026thinsp;5.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;W*, HD*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL5\u003csub\u003ePR\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.89\u0026thinsp;\u0026plusmn;\u0026thinsp;0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.92\u0026thinsp;\u0026plusmn;\u0026thinsp;1.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.64\u0026thinsp;\u0026plusmn;\u0026thinsp;1.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.32\u0026thinsp;\u0026plusmn;\u0026thinsp;2.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eW: Walking; HD: Heel drops; J: Jumping; R: Resistance exercise; *p\u0026thinsp;\u0026lt;\u0026thinsp;0.05; **p\u0026thinsp;\u0026lt;\u0026thinsp;0.001.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study integrated individualized MS modelling and FE analysis with longitudinal QCT-derived regional BMD changes, thereby establishing a mechanically interpretable framework that links exercise-specific internal loading and tissue-level mechanical stimuli to observed lumbar spine adaptation. Rather than relying on exercise efficacy alone, the combined modelling\u0026ndash;imaging strategy helps explain why mechanically distinct exercise modalities may preferentially benefit particular lumbar segments and regions. This is a key added value beyond MS or FE modelling in isolation and addresses a translational gap that has limited the clinically meaningful interpretation of exercise-related spinal adaptation.\u003c/p\u003e \u003cp\u003eRegion-specific adaptations were observed after six months of training, with the VB showing preservation or modest gains, particularly at L1\u0026ndash;L3, whereas the PR exhibited consistent decreases. The integrated analysis offers a mechanistic rationale: compressive load transfer and higher mechanical stimuli were predominantly concentrated within the VB across tasks, consistent with trabecular-rich regions being more responsive to osteogenic loading[\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. In contrast, the PR experienced lower stress magnitudes across exercises, which may contribute to its comparatively unfavourable BMD trend[\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. Importantly, these longitudinal in vivo outcomes provide important empirical support for the mechanical interpretation\u0026mdash;supporting that regions exposed to greater mechanical stimuli tend to show more favourable BMD changes over time.\u003c/p\u003e \u003cp\u003eExercise-specific loading patterns further indicate that uniform exercise recommendations may be suboptimal. Jumping produced the largest transient joint reaction force peaks and preferentially elevated stresses in upper and mid-lumbar segments, reflecting high-impact, high strain-rate stimuli that are commonly associated with osteogenic potential. By contrast, resistance exercise generated sustained loading with relatively greater stress in the lower lumbar region (L4\u0026ndash;L5), suggesting a different mechanical signature that may be advantageous for segment-dependent bone status[\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. Heel drops provided intermediate impact-driven stimuli, whereas walking produced comparatively low and stable loading[\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e]. Collectively, these results demonstrate that mechanically distinct exercise modalities impose heterogeneous stimuli across lumbar regions that cannot be captured by clinical imaging or motion analysis alone[\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFrom a clinical perspective, the proposed framework suggests that exercise selection may influence the distribution of mechanical stimuli across lumbar segments and regions. Instead of prescribing exercise solely on the basis of type or intensity, the results suggest that exercise selection may be guided by the mechanical demands imposed on specific lumbar regions. For example, jumping increased mechanical stimuli more prominently in upper lumbar vertebral bodies, whereas resistance exercise produced sustained loading and relatively higher stresses in the lower lumbar segments compared with jumping. Such regional specificity provides a mechanistic basis for understanding exercise programs in relation to individual bone status, particularly in patients with segment-dependent bone loss. Although the current framework is not yet designed for prospective prediction, it should be regarded as providing a mechanistically informed interpretation of lumbar adaptation.\u003c/p\u003e \u003cp\u003eThis study has several limitations. Firstly, in terms of model construction, current studies usually require the separate establishment of MS and FE models for each participant. This results in substantial work and time consumption during the initial modelling phase, with potential human error due to the variability in modelling by different individuals. There is a lack of rapid modelling methods applicable to larger sample sizes. Machine learning models or the development of algorithms that automatically link MS model inputs and outputs may address these issues. Secondly, this study did not thoroughly investigate the relationship between the distribution of mechanical parameters and lumbar spine BMD. Third, although longitudinal QCT outcomes support the mechanical interpretation, prospective validation in larger and more diverse populations will be necessary before clinical translation to predictive prescription.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study demonstrates the value of integrating MS modelling, FE analysis, and longitudinal QCT imaging to interpret exercise-induced bone adaptation in the lumbar spine. While MS models quantify exercise-specific internal loading and FE models resolve tissue-level mechanical responses, their integration with observed regional BMD changes over six months enables a mechanically interpretable link from exercise to stimulus and to adaptation. The results indicate that different exercise modalities generate distinct regional mechanical environments: jumping preferentially increased mechanical stimuli in upper lumbar vertebral bodies, whereas resistance exercise imposed more sustained loading in lower lumbar segments. These mechanical signatures are consistent with the region-specific BMD changes observed on follow-up QCT. Overall, the proposed framework provides a mechanically informed interpretation of exercise-related lumbar adaptation and may help guide future research on spinal bone health.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eBMD\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eBone mineral density\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eQCT\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eQuantitative computed tomography\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eVB\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eVertebral body\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003ePR\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ePosterior region\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMS\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMusculoskeletal\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eFE\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eFinite element\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eDOF\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eDegree of freedom\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eJRF\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eJoint reaction force\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eEMG\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eElectromyography\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eIK\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eInverse kinematics\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eRRA\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eResidual reduction algorithm\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSO\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eStatic optimization\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMF\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMultifidus\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eLTpT\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eLongest thoracic muscle\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eIL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eIliocostalis lumborum\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eEO\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eexternal oblique\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eLD\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eLatissimus dorsi\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eQL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eQuadratus lumborum\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003ePs\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ePsoas major\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eIVD\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eIntervertebral disc\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eAF\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAnnulus fibrosus\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eALL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAnterior longitudinal ligament\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003ePLL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ePosterior longitudinal ligament\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eLF\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eLigamentum flavum\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSSL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSupraspinal ligament\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eISL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eInterspinous ligament\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eITL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eIntertransverse ligament\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eCapsular ligament\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCSA\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eCross-sectional area\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eROM\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eRange of motion\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eANOVA\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAnalysis of variance\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e \u003cp\u003e This study was approved by the Ethics Committee of the Medical School, Tianjin University (Approval No. TJUE-2023-113). All procedures performed in this study involving human participants were in accordance with the ethical standards of the institutional research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. Written informed consent was obtained from all participants prior to participation.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for publication\u003c/strong\u003e \u003cp\u003e Written informed consent for publication was obtained from all participants prior to their inclusion in the study.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis study was supported by the Natural Science Fund Program of China [12302420] and Key Program of Tianjin Natural Science Foundation [23JCZDJC00830, 24JCYBJC01370].\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualisation: XYX, SZL, JD; Data curation: XYX, SZL, PD, JYD; Formal analysis: XYX, SZL, PD, JYD; Funding acquisition: JD; Investigation: XYX, SZL, PD, JYD; Methodology: XYX, JD; Project administration: JD; Resources: JD; Software: XYX; Supervision: RX, SL, VS, LM, JD, DM; Validation: XYX, JD; Writing\u0026ndash;original draft: XYX; Writing\u0026ndash;review \u0026amp; editing: RX, SL, VS, LM, JD, DM. All authors read and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors would like to acknowledge all participants involved in this study, as well as Mengen Huang from Tianjin University and the exercise trainers involved in the intervention. We would also like to thank the Rehabilitation Department of Tianjin Medical University General Hospital for providing the QCT scanner.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and/or analysed during the current study are not publicly available due to concerns regarding patient privacy and confidentiality but are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSozen T, Ozisik L, Basaran NC. An overview and management of osteoporosis. Eur J Rheumatol. 2017;4(1):46\u0026ndash;56.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRachner TD, Khosla S, Hofbauer LC. Osteoporosis: now and the future. Lancet. 2011;377(9773):1276\u0026ndash;87.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao R, Zhao M, Xu Z. The effects of differing resistance training modes on the preservation of bone mineral density in postmenopausal women: a meta-analysis. Osteoporos Int. 2015;26(5):1605\u0026ndash;18.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang S, Huang X, Zhao X, Li B, Cai Y, Liang X, et al. Effect of exercise on bone mineral density among patients with osteoporosis and osteopenia: a systematic review and network meta-analysis. J Clin Nurs. 2022;31(15\u0026ndash;16):2100\u0026ndash;11.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrooke-Wavell K, Jones PR, Hardman AE. Brisk walking reduces calcaneal bone loss in post-menopausal women. Clin Sci. 1997;92(1):75\u0026ndash;80.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMarques EA, Mota J, Machado L, Sousa F, Coelho M, Moreira P, et al. Multicomponent training program with weight-bearing exercises elicits favorable bone density, muscle strength, and balance adaptations in older women. Calcif Tissue Int. 2011;88(2):117\u0026ndash;29.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChuin A, Labonte M, Tessier D, Khalil A, Bobeuf F, Doyon CY, et al. Effect of antioxidants combined to resistance training on BMD in elderly women: a pilot study. Osteoporos Int. 2009;20(7):1253\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShojaa M, von Stengel S, Schoene D, Kohl M, Kemmler W. Effect of different types of exercise on bone mineral density in postmenopausal women: A systematic review and meta-analysis. Osteologie. 2020;29(03):179\u0026ndash;93.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFountoulis G, Kerenidi T, Kokkinis C, Georgoulias P, Thriskos P, Gourgoulianis K, et al. Assessment of bone mineral density in male patients with chronic obstructive pulmonary disease by DXA and quantitative computed tomography. Int J Endocrinol. 2016;2016(1):6169721.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDelp SL, Anderson FC, Arnold AS, Loan P, Habib A, John CT, et al. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans Biomed Eng. 2007;54(11):1940\u0026ndash;50.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHonegger JD, Actis JA, Gates DH, Silverman AK, Munson AH, Petrella AJ. Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand. Biomech Model Mechanobiol. 2021;20(1):339\u0026ndash;58.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbe T, Kumagai K, Brechue WF. Fascicle length of leg muscles is greater in sprinters than distance runners. Med Sci Sports Exerc. 2000;32(6):1125\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChristophy M, Faruk Senan NA, Lotz JC, O'Reilly OM. A musculoskeletal model for the lumbar spine. Biomech Model Mechanobiol. 2012;11(1\u0026ndash;2):19\u0026ndash;34.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcFarland DC, Binder-Markey BI, Nichols JA, Wohlman SJ, de Bruin M, Murray WM. A Musculoskeletal Model of the Hand and Wrist Capable of Simulating Functional Tasks. IEEE Trans Biomed Eng. 2023;70(5):1424\u0026ndash;35.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKim HK, Zhang Y. Estimation of lumbar spinal loading and trunk muscle forces during asymmetric lifting tasks: application of whole-body musculoskeletal modelling in OpenSim. Ergonomics. 2017;60(4):563\u0026ndash;76.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFavier CD, Finnegan ME, Quest RA, Honeyfield L, McGregor AH, Phillips ATM. An open-source musculoskeletal model of the lumbar spine and lower limbs: a validation for movements of the lumbar spine. Comput Methods Biomech BioMed Eng. 2021;24(12):1310\u0026ndash;25.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKerner J, Huiskes R, van Lenthe GH, Weinans H, van Rietbergen B, Engh CA, et al. Correlation between pre-operative periprosthetic bone density and post-operative bone loss in THA can be explained by strain-adaptive remodelling. J Biomech. 1999;32(7):695\u0026ndash;703.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePizzolato C, Lloyd DG, Barrett RS, Cook JL, Zheng MH, Besier TF, et al. Bioinspired Technologies to Connect Musculoskeletal Mechanobiology to the Person for Training and Rehabilitation. Front Comput Neurosci. 2017;11:96.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFyhrie DP, Carter DR. A unifying principle relating stress to trabecular bone morphology. J Orthop Res. 1986;4(3):304\u0026ndash;17.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdachi T, Tomita Y, Sakaue H, Tanaka M. Simulation of trabecular surface remodeling based on local stress nonuniformity. JSME Int J C. 1997;40(4):782\u0026ndash;92.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDu J, Li S, Silberschmidt VV. Remodelling of trabecular bone in human distal tibia: a model based on an in-vivo HR-pQCT study. J Mech Behav Biomed Mater. 2021;119:104506.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTsubota K, Adachi T, Tomita Y. Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state. J Biomech. 2002;35(12):1541\u0026ndash;51.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDu J, Hartley C, Brooke-Wavell K, Paggiosi MA, Walsh JS, Li S, et al. High-impact exercise stimulated localised adaptation of microarchitecture across distal tibia in postmenopausal women. Osteoporos Int. 2021;32(5):907\u0026ndash;19.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDu J, Brooke-Wavell K, Paggiosi MA, Hartley C, Walsh JS, Silberschmidt VV, et al. Characterising variability and regional correlations of microstructure and mechanical competence of human tibial trabecular bone: An in-vivo HR-pQCT study. Bone. 2019;121:139\u0026ndash;48.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePhillips AT, Villette CC, Modenese L. Femoral bone mesoscale structural architecture prediction using musculoskeletal and finite element modelling. Int Biomech. 2015;2(1):43\u0026ndash;61.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGeraldes DM, Modenese L, Phillips ATM. Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur. Biomech Model Mechanobiol. 2016;15(5):1029\u0026ndash;42.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003evan Arkel RJ, Modenese L, Phillips AT, Jeffers JR. Hip abduction can prevent posterior edge loading of hip replacements. J Orthop Res. 2013;31(8):1172\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu S, Xia X, Nie Y, Huang M, Meng L, Du J. Musculoskeletal model predicted paraspinal loading may quick estimate the effect of exercise on spine BMD. Front Bioeng Biotechnol. 2024;12:1464067.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChristen P, Ito K, Ellouz R, Boutroy S, Sornay-Rendu E, Chapurlat RD, et al. Bone remodelling in humans is load-driven but not lazy. Nat Commun. 2014;5(1):4855.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRaabe ME, Chaudhari AM. An investigation of jogging biomechanics using the full-body lumbar spine model: Model development and validation. J Biomech. 2016;49(7):1238\u0026ndash;43.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUeno R, Ishida T, Yamanaka M, Taniguchi S, Ikuta R, Samukawa M, et al. Quadriceps force and anterior tibial force occur obviously later than vertical ground reaction force: a simulation study. BMC Musculoskelet Disord. 2017;18:1\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMokhtarzadeh H, Yeow CH, Goh JCH, Oetomo D, Malekipour F, Lee PV-S. Contributions of the soleus and gastrocnemius muscles to the anterior cruciate ligament loading during single-leg landing. J Biomech. 2013;46(11):1913\u0026ndash;20.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAghdam HA, Haghighat F, Rezaie M, Kavyani M, Karimi MT. Comparison of the knee joint reaction force between individuals with and without acute anterior cruciate ligament rupture during walking. J Orthop Surg Res. 2022;17(1):1\u0026ndash;11.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKurutz M. Finite element modelling of human lumbar spine. Finite element analysis. 2010:209\u0026thinsp;\u0026ndash;\u0026thinsp;36.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKurutz M, Oroszv\u0026aacute;ry L. Finite element modeling and simulation of healthy and degenerated human lumbar spine. Finite Elem Analysis\u0026mdash;From Biomedical Appl Industrial Developments. 2012:193\u0026ndash;216.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZou D, Yue L, Fan Z, Zhao Y, Leng H, Sun Z, et al. Biomechanical analysis of lumbar interbody fusion cages with various elastic moduli in osteoporotic and non-osteoporotic lumbar spine: a finite element analysis. Global Spine J. 2024;14(7):2053\u0026ndash;61.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSpina NT, Moreno GS, Brodke DS, Finley SM, Ellis BJ. Biomechanical effects of laminectomies in the human lumbar spine: a finite element study. Spine J. 2021;21(1):150\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhuyagbaatar B, Kim K, Kim YH. Recent developments in finite element analysis of the lumbar spine. Int J Precis Eng Manuf. 2024;25(2):487\u0026ndash;96.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLeszczynski A, Meyer F, Charles YP, Deck C, Willinger R. Development of a flexible instrumented lumbar spine finite element model and comparison with in-vitro experiments. Comput Methods Biomech BioMed Eng. 2022;25(2):221\u0026ndash;37.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePitzen T, Geisler F, Matthis D, M\u0026uuml;ller-Storz H, Barbier D, Steudel WI, et al. A finite element model for predicting the biomechanical behaviour of the human lumbar spine. Control Eng Pract. 2002;10(1):83\u0026ndash;90.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchmidt H, Shirazi-Adl A, Galbusera F, Wilke HJ. Response analysis of the lumbar spine during regular daily activities\u0026ndash;a finite element analysis. J Biomech. 2010;43(10):1849\u0026ndash;56.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShin DS, Lee K, Kim D. Biomechanical study of lumbar spine with dynamic stabilization device using finite element method. Comput Aided Des. 2007;39(7):559\u0026ndash;67.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWagnac E, Arnoux PJ, Garo A, Aubin CE. Finite element analysis of the influence of loading rate on a model of the full lumbar spine under dynamic loading conditions. Med Biol Eng Comput. 2012;50(9):903\u0026ndash;15.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao G, Wang L, Wang H, Li C, Yuan S, Sun J, et al. Biomechanical Effects of Multi-segment Fixation on Lumbar Spine and Sacroiliac Joints: A Finite Element Analysis. Orthop Surg. 2024;16(10):2499\u0026ndash;508.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShim CS, Park SW, Lee SH, Lim TJ, Chun K, Kim DH. Biomechanical evaluation of an interspinous stabilizing device. Locker Spine. 2008;33(22):E820\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePanjabi MM. Cervical spine models for biomechanical research. Spine. 1998;23(24):2684\u0026ndash;700.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRana M, Roy S, Biswas P, Biswas SK, Biswas JK. Design and development of a novel expanding flexible rod device (FRD) for stability in the lumbar spine: A finite-element study. Int J Artif Organs. 2020;43(12):803\u0026ndash;10.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYamamoto I, Panjabi MM, Crisco T, Oxland T. Three-dimensional movements of the whole lumbar spine and lumbosacral joint. Spine. 1989;14(11):1256\u0026ndash;60.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGong Z, Chen Z, Feng Z, Cao Y, Jiang C, Jiang X. Finite element analysis of 3 posterior fixation techniques in the lumbar spine. Orthopedics. 2014;37(5):e441\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRenner SM, Natarajan RN, Patwardhan AG, Havey RM, Voronov LI, Guo BY, et al. Novel model to analyze the effect of a large compressive follower pre-load on range of motions in a lumbar spine. J Biomech. 2007;40(6):1326\u0026ndash;32.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRubin CT, Lanyon LE. Regulation of bone formation by applied dynamic loads. JBJS. 1984;66(3):397\u0026ndash;402.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFrost HM. Bone's mechanostat: a 2003 update. The Anatomical record part a: discoveries in molecular, cellular, and evolutionary biology: an official publication of the american association of anatomists. 2003;275(2):1081\u0026ndash;101.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrinckmann P, Grootenboer H. Change of disc height, radial disc bulge, and intradiscal pressure from discectomy an in vitro investigation on human lumbar discs. Spine. 1991;16(6):641\u0026ndash;6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdams MA, Dolan P. Biomechanics of vertebral compression fractures and clinical application. Arch Orthop Trauma Surg. 2011;131(12):1703\u0026ndash;10.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWinter DA. Biomechanics and motor control of human movement. Wiley; 2009.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcGill S. Low back disorders: evidence-based prevention and rehabilitation. Human Kinetics; 2015.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchoenau E. From mechanostat theory to development of the Functional Muscle-Bone-Unit. J Musculoskel Neuronal Interact. 2005;5(3):232\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-musculoskeletal-disorders","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmsd","sideBox":"Learn more about [BMC Musculoskeletal Disorders](http://bmcmusculoskeletdisord.biomedcentral.com/)","snPcode":"","submissionUrl":"https://author-welcome.nature.com/12891","title":"BMC Musculoskeletal Disorders","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Lumbar spine, Exercise, Musculoskeletal model, Finite element model, Bone adaptation","lastPublishedDoi":"10.21203/rs.3.rs-9197056/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9197056/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eExercise is widely recommended to maintain lumbar bone mineral density (BMD), the tissue-level mechanical environment generated within the lumbar spine during different exercises remains difficult to assess in vivo. This study integrated individualized musculoskeletal modelling, finite element analysis, and longitudinal quantitative computed tomography (QCT) to characterise exercise-specific lumbar loading patterns and interpret them alongside regional BMD adaptation.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eTen postmenopausal women with low BMD who completed a 6-month combined exercise intervention were included (ChiCTR2400081574). QCT scans were acquired at baseline and follow-up to quantify BMD changes in the vertebral body (VB) and posterior region (PR). Individualized musculoskeletal models of walking, heel drops, jumping, and resistance exercise were developed to estimate joint reaction forces and muscle forces. These loads were transferred to individualized lumbar finite element models using a MATLAB\u0026ndash;Python workflow to calculate segmental and regional von Mises stresses. Statistical analysis was performed using one-way ANOVA, with p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 considered statistically significant.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eLongitudinal QCT revealed that BMD was preserved or increased in the VB, whereas BMD declined in the PR, particularly at L1\u0026ndash;L3. Jumping produced the highest peak joint reaction forces and von Mises stresses in the superior lumbar segments, whereas resistance exercise generated the greatest loading at L4\u0026ndash;L5. Across all tasks and vertebral levels, von Mises stresses were consistently higher in the VB than in the PR.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eDistinct exercise modalities generated different segmental and regional loading environments within the lumbar spine. These mechanical patterns were broadly consistent with the observed regional BMD changes, providing a mechanically informed interpretation of lumbar bone adaptation during exercise.\u003c/p\u003e\u003ch2\u003eTrial registration:\u003c/h2\u003e \u003cp\u003eChinese Clinical Trial Registry, ChiCTR2400081574 (retrospectively registered 5 March 2024).\u003c/p\u003e","manuscriptTitle":"Exercise-specific mechanical stimuli are associated with regional lumbar bone adaptation: A combined in vivo and in silico multi-scale study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-09 15:05:54","doi":"10.21203/rs.3.rs-9197056/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"179494986128394068428944708796595622933","date":"2026-04-16T15:55:05+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-02T14:53:43+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-03-31T14:43:20+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-31T14:42:00+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-30T07:48:32+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Musculoskeletal Disorders","date":"2026-03-30T07:40:42+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-musculoskeletal-disorders","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmsd","sideBox":"Learn more about [BMC Musculoskeletal Disorders](http://bmcmusculoskeletdisord.biomedcentral.com/)","snPcode":"","submissionUrl":"https://author-welcome.nature.com/12891","title":"BMC Musculoskeletal Disorders","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d5d35129-d756-4c74-a432-ddfe2f485566","owner":[],"postedDate":"April 9th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-09T15:05:54+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-09 15:05:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9197056","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9197056","identity":"rs-9197056","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}