Equilibrium mechanical properties of the human uterus in tension and compression

A workflow for mechanical testing and data analysis was previously developed to investigate the equilibrium mechanical properties of the nonhuman primate (NHP) cervix [ 20 ]. In this section, the methods adopted from previous work are summarized, and those that differ are described in greater detail. Briefly, forty four human uterine specimens were mechanically tested under spherical indentation and uniaxial tension, coupled with digital image correlation (DIC). A fibrous anisotropic material model informed by imaging results was then applied to capture uterine material behavior. Lastly, an inverse finite element analysis was performed and the material model was validated to determine the mechanical properties of uterine tissue. Human uterine specimens were collected from 16 patients (< 50 years old) away from visible sites of pathology. Nonpregnant individuals underwent a total hysterectomy for non-cancerous indications, while pregnant patients underwent a cesarean hysterectomy in the early third trimester due to suspected abnormal placentation. Patient information, including age, race, ethnicity, diagnosis, and obstetric history, is listed in Table 1 . This study was approved by the Institutional Review Board at Columbia University Irving Medical Center (CUIMC), and each subject provided written informed consent. Our previous work on characterizing human uterine tissue anisotropic properties using spherical indentation described the tissue collection and processing procedure performed for this study [ 11 ]. In summary, each specimen slice measured 15–25mm in both length and width and approximately 4mm in thickness (see Fig. 1 ) and was stored at −80°C. Prior to testing, frozen tissue was equilibrated at 4°C overnight using phosphate-buffered saline (PBS) solution supplemented with 2mM ethylenediaminetetraacetic acid (EDTA) to minimize tissue degradation. In our previous work, 14 specimens of a single NP patient and 13 specimens of a single PG patient were imaged using OCT and mechanically tested via spherical indentation. These 27 specimens were collected from three anatomical locations (anterior, fundus, and posterior) throughout the full uterine wall thickness, including all three uterine layers (endometrium, myometrium, and perimetrium). Because the mechanical properties of uterine tissue at the fundus were between the properties of the anterior and posterior tissue samples, all tissue tested in this study was taken from the fundus region. Additionally, because the middle myometrial layer provides the primary mechanical role of the uterus during gestation, this study focuses on the myometrium. Hence, two fundus myometrium specimens per patient from 14 patients (7 NP and 7 PG) were added to the existing 22 myometrial specimens from Fang et al. [ 11 ]. Therefore, 44 specimens were studied in this work, including 21 NP samples from 8 patients and 23 PG samples from 8 patients. Each tissue specimen was mechanically tested in PBS+EDTA solution under indentation (6-mm diameter) followed by uniaxial tension ( Fig. 2(a - d) ). All specimens were speckled with water-insoluble ink (Chartpak, Inc., Leeds, MA) using an airbrush (Harder & Steenbeck GmbH & Co., Germany) and a Sprint Jet air compressor (Iwata Medea Inc., Portland, OR) to enable tracking of full-field displacements. One front camera and two orthogonal cameras (Point Gray Grasshopper, GRAS-50S5M-C75 mm, f/4 lens) were used for the indentation and tension tests, respectively, to track deformations ( Fig.2(a - d) ). The mechanical tests were performed using a universal testing machine (Instron, Inc., Norwood, MA) with a 5N load cell (Instron, Inc., Norwood, MA, accuracy of 0.005N). For indentation, a three-level load-hold protocol was performed with indentation depths prescribed as displacement — 15%, 30%, 45% of the specimen thickness ( Fig.2(e) ). After each ramp, the indenter was held in place for 480, 600, and 720 seconds, respectively, for the specimen to approach equilibrium. Similar compression testing protocols involving multi-step strains have been used to study the equilibrium stress-stretch response of other collagenous and soft biological tissues [ 21 , 22 ]. After indentation, each sample was allowed to recover and was processed for testing in tension. Specifically, the specimen was cut into rectangular strips with an approximate length-to-width ratio of 2. The length direction was determined by aligning the fiber direction (as observed by OCT) with the tension loading direction. For each tension test, to prevent slippage of the sample during testing, the specimen was placed between metal tensile grips fastened with a section of water-resistant sandpaper (McMaster-Carr, Aurora, OH) using Krazy glue (KrazyGlue, High Point, NC). Before each test, the tissue was pre-tensioned to 1mN to remove any slack. A pre-test load-unload-recover protocol was conducted on the tissue consisting of five load-unload cycles at 10% engineering strain. The ramp rate of the first three cycles was equivalent to 1% strain·second −1 ; the fourth cycle had a ramp rate of 0.5% strain·second −1 ; the last ramp cycle had a ramp rate of 5.0% strain·second −1 . Tissues were allowed to recover for 10 minutes between each pre-test load-unload cycle. A three-level load–hold–unload protocol was then performed with extensions prescribed as engineering strains—15%, 30%, 45% calculated as the grip-to-grip (G2G) distance divided by the specimen gage length ( Fig. 2(e) ). The engineering strain rate was set as 0.1%·second −1 . At each hold, the specimen was kept in place for 30, 45, and 60 minutes, respectively, to approach equilibrium. After each load-hold-unload cycle, the specimen was left unstressed for 20 min to allow recovery. Calibration images were taken for each test using a ruler with 1/16-inch gradations in the field of view (FOV). For both mechanical tests, force-displacement-time (N-mm-s) data were collected using the material tester software (Instron, Inc., Blue Hill version 3.11.1209). Following testing, hysteresis curves for tension tests were reviewed, and ones that exhibited discontinuities in the loading curve, suggestive of tissue damage or slippage, were excluded from subsequent FEA analysis. Representative hysteresis curves are shown in Fig. S1 in Supplementary Materials . Digital image correlation (DIC) (Correlated Solutions, v6) and image segmentation (MATLAB) were performed following the previous workflow to measure and calculate the Green-Lagrange strain, stretch, and Cauchy stress.[ 11 ] For indentation, DIC was performed in a 2-mm diameter circle centered under the indenter (defined as the region of interest [ROI]). FEA shows an approximately uniform stress distribution within this circle (data not shown). Because tensile grips are known to induce non-homogeneous strains adjacent to the grips, DIC was performed to characterize the 2D strain field [ 23 ]. A middle gauge region with an approximate uniform strain distribution was chosen as the region of interest (ROI) to ensure a rather homogeneous uniaxial tensile condition. The finite element modeling used for subsequent analysis utilized the strain from the DIC analysis instead of the G2G strain. Image segmentation was performed for the tension test recordings to extract three dimensions measuring the tensile specimen: length [ l ] , width [ w ] , and thickness [ d ] . Stretch ( λ z = l l 0 , λ x = w w 0 , λ y = d d 0 ) and Cauchy stress σ = F A were subsequently calculated. To determine the equilibrium mechanical properties of the human uterus, inverse finite element analysis (IFEA) was performed based on the previously developed workflow described in [ 20 ]. For this purpose, finite element (FE) models of the indentation and tension tests were built in the FEBio 2.9.1 (Salt Lake City, Utah) with the setup illustrated in Fig. 3(a - b) . The fiber-based constitutive law described in [ 19 , 20 ] was adopted to model the uterus material behavior. More details of the model are given in [ 19 ], where the load-bearing collagenous extra-cellular matrix that sheaths the smooth muscle fascicles is considered. This constitutive model combines an isotropic compressible ground substance and an anisotropic extensible fiber network, similar to the approach in [ 24 , 25 , 26 ]. The fiber network or bundles are formed of collagen fibrils, which consist of a crosslinked tropocollagen network. A statistical mechanics approach is used to model the tropocollagen molecule chain as a freely jointed chain, similar to the Arruda-Boyce 8-chain [ 27 ] and Bischoff et al.[ 28 ] material models. The mechanical behavior of the ground substance is captured by shear and bulk terms with moduli μ and κ , respectively. The behavior of the collagen fiber distribution and the passive smooth muscle cells (SMC) is determined by material parameters such as the initial stiffness ( ξ ) , locking stretch ( ζ ) , and a fiber distribution parameter ( b ). The force response for some specimens did not reach equilibrium at the highest prescribed strain level (45%) within 12 minutes for indentation and 60 minutes for uniaxial tension. Hence for the purpose of mechanical property optimization, we extrapolated the equilibrium load by curve-fitting the experimental relaxation data using the following exponential function: (1) F ( t ) = C 1 ⋅ exp − t / τ + C 0 where t [ s ] is the time during the loading step, C 0 [ N ] is the extrapolated equilibrium load, and C 1 [ N ] and τ [ s ] are relaxation constants. Equation 1 was found to fit well our experimental transient force relaxation data. The new extrapolated equilibrium force C 0 was calculated for specimens whose difference between the extrapolated equilibrium load and the actual achieved load in the experiment was greater than 10%. Only the force data at times greater than 200 s and 100 s from the application of 45% strain were used for curve fitting in the indentation and tension experiments, respectively. Equation 1 produced good fits for both indentation and tension force relaxation responses (R 2 > 0.985 and 0.988 for indentation and tension, respectively). In our previous human uterine study, optical coherence tomography (OCT) and curve fitting were used to characterize the fiber distribution of 27 uterine specimens (13 from one NP patient and 14 from one PG) [ 11 ]. A von Mises distribution with a preferential direction θ and a concentration factor b was fitted to the directions of fiber bundles. Here, concentration is the reciprocal of the commonly used concept of dispersion. In this study, the fiber distributions of these 27 specimens were directly adopted. For the rest of the specimens, the first principal strain angle γ derived from the indentation DIC analysis was used to calculate the preferential fiber group direction θ with the assumption that γ is perpendicular to θ . This assumption is based on the anisotropy of a fibrous structure that the tensile modulus along the fiber is higher than one perpendicular to the fiber. Hence, fiber-embedded tissue is more likely to deform orthogonal to the preferential fiber direction under indentation. The concentration factor of the von Mises distribution was left as a fitting parameter in the IFEA. The constitutive model parameters were obtained by minimizing the following objective function: (2) Ξ ( κ , ξ , ζ , b ) = 1 8 ∑ i = 1 N = 3 | e 1 FEA , i − e 1 E X P , i e norm EXP , N | + 1 8 ∑ i = 1 N = 3 | e 2 FEA , i − e 2 EXP , i e norm EXP , N | + 1 4 ∑ i = 1 N = 3 | F I FEA , i − F I EXP , i F I EXP , N | + 1 2 ∑ i = 1 N = 3 | F T FEA , i − F T EXP , i F T EXP , N | where the superscript i represents the index of the prescribed strain levels N , F I is the equilibrium force response from indentation, F T is the equilibrium force response from uniaxial tension, and e 1 and e 2 correspond to the principal Lagrangian strains obtained from indentation experiments. The superscripts FEA and EXP denote the finite element and experimental results, respectively. The term e norm is the Euclidean norm of the vector e = { e 1 , e 2 } . A natural selection-based genetic algorithm (GA) implemented in MATLAB was used to minimize the objective function, with details described in [ 29 ]. For this study, the population size was assigned as n = 4 , the mutation rate μ m = 0.15 , and a minimum of 40 generations were iterated to find a stable solution for all cases, that is, the values of material model parameters and objective function converged. Best-fit material models were validated against experimental data that were not directly used for IFEA. The same workflow as the NHP cervical study was adopted [ 20 ]. Briefly, the principal strain fields outside the ROI were validated for indentation, and the stretch ratios and Cauchy stress were validated for tension. Specifically, the first and second principal strains within a 4-mm diameter circle centered under the indenter were compared between the experiment and FEA. Experimental values were determined by DIC analysis and FEA values were simulation outputs. A normalized error map was generated using equation error = | e FEA − e EXP | e EXP to quantify the comparison. Stretch ratios and Cauchy stress of the tension specimen were compared between the experiment and FEA. Experimental stretch ratios were calculated using dimensions derived from the image segmentation detailed in Sec. 2.3. Width and thickness ( λ x and λ y ) were measured from the front and the side of the specimen. FEA values were direct simulation outputs. Experimental sensitivity studies were performed to assess the impact of experimental procedures on uterine tissue behaviors. Specifically, impacts caused by freeze-thaw cycles and the specimen topology were determined. Due to the nature of tissue collection and the restrictions we faced in the operating room, the specimens went through two freeze-thaw cycles in total, from tissue collection to OCT scanning and mechanical testing. Many previous studies on soft tissues with similar components have found mixed results on whether and how freeze-thaw cycles affect the tissue’s mechanical properties [ 30 , 31 ]. Therefore, comparison mechanical tests were performed on a different set of PG uterine tissue (16 C/S uteri) when they were fresh and frozen-thawed. These specimens were collected from a separate cohort of third-trimester pregnant women who underwent C/S at term for a nonpathological delivery, where a portion of the anterior lower uterine segment was resected (approved by IRB). A small strip of the uterine sample was collected at the incision. Due to the nature of the collection, no orientation was recorded and the specimens varied in dimensions. Immediately after collection, the specimen was placed on wet ice and transferred to the laboratory and “freshly” tested within 2 hrs of collection. The indentation test was performed at the center of the specimen held in a PBS-filled petri dish. The protocol included three displacement-controlled steps with sufficient time in between for the specimen to relax and reach equilibrium. After the fresh test, the specimen was padded dry with paper towels and stored at −80°C. At least 24 hours elapsed before the same sample was tested for freeze-thaw effects. During the freeze-thaw testing, the frozen specimen was thawed in PBS solution at room temperature for three hours. Then the same protocol was performed on the tissue at the same location. For both fresh and freeze-thaw testing, the force-time-displacement data were recorded and the equilibrium force responses at three levels were compared. The human uterine tissue was dissected using a customized slicer designed to divide large samples into thinner even-surface specimens. In an effort to quantitatively determine whether the tissue surface is sufficiently smooth, a topology study was performed using spherical nanoindentation (Piuma, Optics11Life, Amsterdam, NE) on one NP and one PG slice. Using a 100μm probe radius, two square regions, each sized 6mm x 6mm, were tested for each slice 5mm apart from each other. The size of this testing area was equivalent to the maximum contact area during the indentation test. Within each area, 49 individual indentation points in a 7×7 equally-spaced mesh grid were tested ( Fig. 4(a) ). Three FEA models were then constructed, where the specimen had undulations (as tall as the largest detected height difference) on its top surface to simulate the unevenness, and the indenter tip was placed on top of, in the valley of, and on the ridge of the undulations ( Fig. 4(b) ). Due to the undulations on the surface, the geometry was meshed using linear tetrahedral elements with an edge length ranging from 0.5–0.7mm. The same boundary conditions as the indentation test were implemented and all material parameters were set to be the average of all specimens. The indenter force and the first and second principal strains centered at the specimen bottom were compared between scenarios. A linear mixed-effect model was used to assess differences in material parameters and experimental results between pregnant (PG) and nonpregnant (NP) specimens using the software RStudio (Version 2023.12.0). Patient ID was set as the random variable to capture the effect of parameters obtained from multiple specimens dissected from the same patient. A logarithmic transformation was applied to material properties such as bulk modulus, initial fiber stiffness, experimental equilibrium force, and principal lagrangian strains because the data exhibited non-normal distributions.

Under indentation, the human uterus exhibits a force–relaxation response to a ramp–hold displacement protocol. Similar to our previous findings, both force and Lagrange strain responses at equilibrium are nonlinear with respect to prescribed strains ( Fig. 5(a - b) ).[ 11 ] Among all specimens, differences are observed between the first ( e 1 ) and second ( e 2 ) principal strains ( Fig. 5(b) ). The ratio distribution between these two strains of all specimens at the third strain level is 2.02 ± 0.66. Under tension, the human uterine tissue displays a J-shaped stress response to linear strains and a force–relaxation response to a load–hold displacement protocol ( Fig.6(a) ). The Lagrange strain, force, and Cauchy stress response at equilibrium states are nonlinear to G2G strains ( Fig.6(b) and Fig.5(a) (c) ). The stress responses at the tensile equilibrium of the NP uterus are larger than the PG ones. For example, the equilibrium stress response distributions at the third strain level are 7.69 ± 5.89 kPa and 3.04 ± 0.80 kPa for NP and PG specimens, respectively ( Fig. 5(c) ). The strain fields of the human uterus during a uniaxial tension test are complex ( Fig. 6(b) ). Compared to the G2G strain levels of 15%, 30%, and 45%, the actual Lagrange strains across the specimen are non-homogeneous, larger than the G2G strain value in certain areas and smaller in others. The average values of the full field are similar to the prescribed strains. The edge of the specimen is excluded from the analysis to avoid geometric distortions from gripping. Within the analyzed area of this specific specimen, the top left corner and the middle gauge region show larger values whereas the lower quarter and the top right corner show smaller values. All specimen geometries and equilibrium force and strain data are available at the Columbia University Libraries’ Academic Commons ( https://doi.org/10.7916/ag0r-9356 ). The equilibrium mechanical properties of the human uterus for nonpregnancy and early third trimester are reported in this section ( Fig. 7 ). The ground substance bulk modulus κ , fiber network locking stretch ζ , and initial stiffness ξ of all specimens are computed by the GA-based IFEA. Among four properties, (1) the bulk modulus κ , describing the ground substance compressibility, is not significantly different between NP and PG tissues; (2) the locking stretch ζ , describing the fiber network extensibility under loading, is significantly smaller for the NP tissue; (3) the initial stiffness ξ shows no significant difference between NP and PG specimens; and (4) the fiber concentration factor b , describing the fiber bundle group alignment, is not significantly different between NP and PG tissues. The value distributions of the locking stretch and the fiber concentration are larger for the NP tissue, while the value distributions of the bulk modulus are similar between NP and PG tissue. The bulk modulus dictates the material’s resistance to volumetric change under hydrostatic pressure and is the major contributor to the force response in indentation. The fiber concentration factor directly dictates the anisotropic behavior of the tissue. In general, the material model captures tissue behaviors well under both indentation and tension as shown by a single NP uterine sample ( Fig. 8 ). In indentation, the model closely matches the experiment in terms of the magnitude, pattern, and direction of principal Lagrange strains of the bottom surface ( Fig. 8(a - c) ). In this representative specimen at the third equilibrium (45% prescribed strain) level, the first principal strain has a maximum of about 0.25 around the center and an elliptical distribution pattern with a nearly horizontal major axis. The directions of the strain close to the center point toward the positive y-direction. The second principal strain has a maximum of 0.15 around the center and an elliptical distribution pattern with a nearly vertical major axis. The directions of the strain close to the center point toward the negative x-direction. These features are captured well by the FEA model ( Fig. 8(b) ). When comparing the principal strain outside the ROI for IFEA, the strains of the experiment and the material model match well in terms of magnitude, shown by the small errors ( Fig. 8(c) ). However, areas further away from the center exhibit larger errors. In tension, the model matches the experiment well with regard to the Cauchy stress and the orthogonal stretch ratios ( Fig. 8(d - f) ). In this representative specimen, the material model captures the magnitude and the nonlinearity of the Cauchy stress. The sample deformations of the material model also closely match the experiment from both the front and the side. After one freeze-thaw cycle, there is no significant change in the raw force responses at equilibrium for the PG tissue tested under indentation ( Fig. 9 ). No systematic alterations of tissue properties were observed as the median changes in percentage center around zero ( Fig. 9(b) ). Although the dimensions are not consistent across all specimens due to tissue collection restrictions and the raw force response is not a normalized variable, the comparison is performed within each sample that underwent the same testing protocol before and after freezing. Therefore, one freeze-thaw cycle has a minimal effect on the material properties on macroscale uterine material properties. For assessment of specimen topology, scenarios 1 to 3 are when the indenter is placed on top of, in the valley of (between), and on the ridge of undulations. As shown in Fig. 10 , in terms of the principal strains, scenario 2 shows higher values than scenario 3, followed by scenario 1, at the first and second strain levels. At the last strain level, all three scenarios exhibit similar principal strain values. For the indenter force response, scenario 2 shows a higher value than scenario 3, followed by scenario 1, and this difference exists for all three strain levels (see Fig. 10 ). However, all differences at the third strain level are less than 5% between scenarios.

Characterizing the baseline mechanical properties of the uterus is critical for advancing in vitro and in silico models of pregnancy and gynecologic disorders. Additionally, biomechanical factors that distinguish normal and pathological conditions may serve as biomarkers for which novel therapeutic approaches may be developed and applied on a patient-specific basis. Clinically, uterine over-distention has been associated with spontaneous preterm birth because twin pregnancies [ 32 , 33 , 34 ] and patients with excess amniotic fluid tend to deliver early [ 35 ]. Studies on uterine smooth muscle cells have established a well-known electro-mechanical coupling [ 36 ], where stretch-activated calcium channels have been linked to the molecular pathways that insight contractility and labor. Additionally, a study on monkeys found that uterine over-distention is associated with inflammatory pathways that lead to preterm contractions [ 34 ]. Multi-physics material models of the uterus have addressed this stretch-excitation-contraction coupling to simulate contraction strength and conduction [ 37 , 38 ]. Yet, the evolution of passive uterine stretch in pregnancy, the structural precursor that controls the mechanobiology of uterine contractility, has not been discerned. While we work towards integrating electro-mechanical coupling and active uterine material properties into computational biomechanical models of pregnancy, the first step is to discern and spatially map passive uterine tissue stress and stretch throughout pregnancy. To do this, uterine biomechanical properties in tension and compression are presented in this study. The mechanical behaviors of the human uterine tissue under both compressive and tensile loads are time-dependent, non-homogeneous, and nonlinear ( Fig. 6(a) , [ 11 ]). Further, similar to human and NHP cervical tissue, the human uterus is anisotropic under indentation ( Fig. 5(b) ) and exhibits tension-compression asymmetry [ 29 , 20 , 19 ]. The human uterus displays a force–relaxation response to a load–hold displacement ( Fig. 6(a) , [ 11 ]). The time dependency of the human uterus is likely a product of viscoelastic and poroelastic mechanisms which can be attributed to the uncrimping and rearrangement of the fiber network and the escape of fluid through the pores of the tissue, respectively. Parallel work by our group has characterized the time-dependent behavior of NP and PG uterine tissue from an overlapping patient cohort using nanoindentation [ 13 ]. Analysis of the data with a combined poroelastic-viscoelastic model reveals that the innermost uterine layer, known as the endometrium-decidua, exhibits the greatest alterations in time-dependent mechanical properties in pregnancy as evidenced by changes in viscoelastic ratio and diffusivity parameters [ 13 ]. No change in the time-dependent properties of the myometrium is observed at this micrometer length scale [ 13 ]. Future work is still needed to determine the degree to which poroelastic and viscoelastic mechanisms contribute to the overall time-dependent behavior of the uterus. The tensile Lagrangian strain fields are non-homogeneous across the uterine specimen. Several concurrent mechanisms could contribute to this phenomenon, including collagen fiber alignment, fiber group interactions, and the existence of different tissue structural components within one area. Previous work from our lab which characterized the human uterine fiber orientation within a small area found that multiple fiber families with different preferential directions exist.[ 11 ] The actual mechanism behind this observation remains an open question due to the lack of comprehensive histological and microscopic inferences. The human uterus displays a nonlinear force, strain, and stress response to linear prescribed strains. This nonlinearity manifests at two scales, the instantaneous/temporal behavior at every displacement cycle ( Fig. 6(a) ) and the equilibrium behavior across multiple strain levels (( Fig. 5 ). At the instantaneous state, the tensile stress response resembles a J-shaped curve consisting of two different segments, a low-slope linear region followed by a transition to a higher-sloped linear one. This indicates at least two different mechanisms behind the tissue stress responses. Fibrous biological tissues are known to have similar behavior [ 39 ]. The contribution of the ground substance and elastic fibers are associated with the small-strain regime, whereas the engagement of the collagen fibers is found at larger strains [ 39 ]. Across multiple equilibrium states, both indentation and tension responses exhibit a curve with an increasing slope. The rate of increase in the force response is larger for tension than indentation. Wavy fibers mainly hold tension and have a more pronounced effect on mechanical properties in the tension tests [ 40 ]. Indentation applies a complex stress condition, and the tensile properties of the fibers engage due to Poisson’s effect at large compressive stresses [ 41 ]. Under indentation for a given ROI, the first and second principal strain fields differ significantly, indicating anisotropic tissue behavior. This anisotropy is dictated by the fiber alignment described by the fiber group’s preferential orientation and the fiber bundles’ dispersion. Our results show a higher fiber concentration factor is associated with a larger anisotropy. When fiber bundles are less dispersed, this group of fibers exhibits greater direction-dependent behaviors. Under tension, the Lagrange strain fields are non-homogeneous across the specimen and the strain patterns are inconsistent across different samples. The non-homogeneity of the strain pattern is most likely the result of, although not limited to, the directional fiber orientations, another manifestation of anisotropy. Collagen fibers are known to have higher stiffness along their length versus orthogonally, and hence, deform less when loading aligns with the length dimension. The strain field is complex when multiple fiber groups interact within a single tissue by interweaving or crossing. The pattern of the strain field is also dynamic over time as observed between different equilibrium G2G strain levels ( Fig. 6(b) ). The fiber network movement likely causes this changing pattern. We hypothesize that the fibers rearrange themselves under loading by uncrimping and untangling to resist deformation and avoid damage, thus causing the changing strain patterns. A significant asymmetry was observed when comparing uterine material behaviors between indentation and tension. The tensile Cauchy stress is an order of magnitude higher than the indentation stress at the maximum. A combination of the fibers’ robe-like structure and the ground substance’s low stiffness dictates the primary contribution to this phenomenon. Fibers cannot engage under compressive loading due to their rope-like structure and hence, do not contribute significantly to the force response under indentation. Instead, the ground substance engages in compressive resistance, and its low stiffness contributes to the lower force response. Lastly, although uterine tissue exhibits time-dependent properties under both indentation and tension, the primary deformation mechanisms are thought to differ between these conditions. Under tension, as the fiber network rearranges its alignment, stress relaxation is thought to be dominated by the viscoelastic nature of the fiber network. In compression, the ground substance’s volumetric stiffness resists hydrostatic pressures. Therefore, under indentation, the measured force relaxation is thought to be dominated by poroelastic mechanisms draining the pressure from interstitial pores. Additional experiments and modeling efforts are warranted to characterize these time-dependent features of the material. Overall, bulk modulus κ of the ground substance is 4.28 ± 4.33kPa for the NP uterus and 3.11 ± 2.02kPa for the PG uterus. These values are larger than that of the human cervix (1.40 ± 1.40kPa for NP and 0.26 ± 0.20kPa for PG) but are within the same order of magnitude [ 19 ]. This difference indicates that the human uterus has a lower compressibility level than the cervix. Though not statistically significant, the ground substance of the NP uterus is, on average, less compressible than the PG tissue. This trend is the same as the human uterus characterized using a neo-Hookeanbased model under only indentation[ 11 ]. The locking stretch ζ of the PG tissue (2.82 ± 0.32) is significantly larger than the NP uterus (2.44 ± 0.50), indicating a more extensible tissue property for the PG uterus. This difference in extensibility is observed in the tension test, where PG tissue 405 can extend more than the NP tissue when subjected to the same amount of force. The initial stiffness ξ describes the small-strain stiffness and is almost identical between the NP and PG tissue, indicating the behavior of the uterine tissue under small strain does not change over pregnancy. Previous work done in our lab characterized the human uterus stiffness under small strains using an isotropic material model and found a similar trend[ 11 ]. The fiber concentration b is the reciprocal of fiber dispersion and the PG fiber network is more dispersed than the NP one. A higher dispersion facilitates the fiber network’s extensibility under tensile loading; this change is also observed in the nonhuman primate cervix [ 20 ]. Finally, although both direct stiffness measurements, bulk modulus and the initial fiber stiffness, do not change significantly over pregnancy, the overall stiffness of the uterus is a combined contribution from κ , ζ , and ξ . Therefore, the increase in locking stretch, which is dominant under tension, indicates that the human uterus is less stiff during late pregnancy than in nonpregnancy. In other words, there is no stiffness change in the initial loading, but there is an overall difference when accounting for larger strains (> 0.3). To adequately perform essential reproductive functions, the uterus exhibits a unique hierarchy of structural components, spanning from micro- to milli-meter length scales. The relative contribution of different tissue components varies depending on the loading condition. Macro-scale mechanical testing used in this study measures the combined contribution of smooth muscle fascicles and collagen fibers under tension and compression at high strains. In contrast, micro-mechanical testing probes on the scale of individual smooth muscle cells and collagen fibers. Yet, despite these differences in length scales, there is a striking similarity in the data trends observed for the myometrium, as shown by a parallel study conducted in our lab[ 13 ]. Interestingly, no change in stiffness is observed for the myometrium in pregnancy at low strains for both micro- and macro-scale testing [ 13 ]. Further, both testing modalities yield stiffness values for the myometrium within the same order of magnitude (10 0 kPa). Differences in the mechanical behavior of pregnant uterine tissue only emerge under large deformations for strains above 0.30, as demonstrated by increased tissue extensibility. A constitutive model previously developed for the human cervix is adopted in this work to capture the material behaviors of the NP and PG human uterus [ 19 ]. In this model, material parameters are inspired by the properties of the collagen network, providing an advantage over other phenomenological models of soft fibrous biological tissues. Compared to the cervix, the uterus has a larger proportion of smooth muscle cells (SMCs) to collagen content[ 42 ]. Despite these basic compositional differences, the approach of adopting the same material model is supported by the following considerations. First, mechanically, SMCs play an important role in active material behaviors instead of passive equilibrium behaviors, as they contribute to the force response by contracting. The passive material response to loading of the uterus shares similar patterns with that of the cervix, a material mostly composed of collagens. Second, also mechanically, the stiffness modulus of the muscle-collagen fiber composite of the skeletal muscle tissue was found to be five times the muscle fiber modulus alone, indicating collagens are the primary passive load-bearing component in the tissue [ 43 ]. Third, biologically, SMCs are surrounded by a collagenous membrane called endomysium, which separates and groups smooth muscle fibers, resulting in larger fiber bundles of the same alignment [ 44 ]. Consequently, the combination of smooth muscle fibers and collagen fibers in the uterus was treated together as one fiber network, a condition similar to the cervix and suitable for the previously developed material model. Inherent experimental errors include the load cell tolerance (0.005 N), the displacement resolution of the Instron (8 μ m), and the buoyancy force on the indenter ( F b < ρ gV < 0.001 N ) and the tensile grips (< 0.009 N). Further, the effect of uneven sample topology is negligible for the indentation methods used in this study given that the maximum difference in all three variables under three scenarios of sample topology is less than 5% ( Fig. 10 ) and the samples do not have larger variations in the height of the top surface, the effect of sample topology is negligible. Inherent computational errors introduced by the DIC process and fixing the far-end specimen side surface in FEA are both found to be less than 2% [ 20 , 11 ]. GA-based IFEA was examined the same way as our previous study to ensure the global optimum is found [ 45 ]. The validation study shows that the fitted material model captures principal strains effectively within the 4-mm diameter circle around the indenter, but less accurately near the edge of this circle ( Fig. 8(c) ). This is expected for the following reasons: first, the fiber distribution outside the original ROI (2-mm diameter circle) is different and not characterized in the IFEA; second, the stress closer to the edge of the circle differs more from the center under spherical indentation. Although smooth muscle fibers and collagen fibers share many similarities in biological structures and mechanical functions, the assumption of treating these two as one fiber network may be an oversimplification. However, our current approach is taken as there is no further knowledge of the interactions between these two fibers. For obvious reasons, specimens collected from a hysterectomy are often pathological ( Table 1 ), which may contribute to alterations in normal mechanical properties [ 11 ]. Ethnicity is demonstrated to affect tissue behaviors elsewhere,[ 46 ] but the effect is not explored here. Biological tissues behave differently under differing loading conditions, and hence, the reported mechanical properties should only be applied to similar strain regimes. Only for patients NP1 and PG1, the anterior and posterior myometrium tissue were studied for reasons explained in sec. 2.1. Fundal myometrium tissue was measured for the rest of the study participants. As the mechanical properties of the human uterus were found to be inherently heterogeneous across anatomic regions and tissue layers, the reported results should be applied with consideration. Furthermore, we acknowledge that specimens subjected to uniaxial tension exhibited signs of softening between load-hold-unload cycles at grip-to-grip strains of 30% and 45%. This softening is characterized by reduced stress levels at specific stretch values during the loading part of the load cycle (see Fig. S1(a) and (d) in the supplementary material ). Notably, this softening effect was less pronounced for cycles at strains between 15% and 30%. Consequently, this softening effect inherently affects the equilibrium forces used for IFEA and estimates of material properties. Future work will address the impact of structural softening on force relaxation and its dependence on the strain and strain rate.

In this study, the equilibrium mechanical properties of the human uterus under indentation and tension are characterized using a single set of mechanical parameters. The fiber architecture (directionality and dispersion) was characterized using OCT and incorporated into the material model to describe tissue anisotropy. The oriented fiber network dictates tissue strains under both indentation and tension. Although spherical indentation results in a complex stress distribution, it reveals the directional material behavior and preserves specimen integrity to enable follow-up tension tests. While indentation testing primarily assesses the response of the ground substance, tension testing fully engages the fiber network for mechanical characterization. A 3-dimensional anisotropic constitutive model is adapted from a human cervical study to assess the mechanical properties of the NP and PG uterus, given the similarities of the two tissue types. The model is optimized using inverse finite element analysis to best fit the mechanical tests and validated against the experiments. The material parameters correlate with the tissue microstructure and can capture the structure–function relationship. The PG human uterus in the third trimester is found to be more extensible compared to nonpregnancy. This study is the first to characterize both compressive and tensile equilibrium behaviors of the NP and PG human uterus using one set of parameters. The mechanical characterization of the human uterus is fundamental to guiding other research in biomechanics, mechanobiology, biomaterials, and tissue engineering, as well as informing the development of novel therapeutic approaches for obstetric and gynecologic conditions.

The uterus is a critical organ in human pregnancy. In nonpregnancy, the uterus is a pear-shaped thick-walled muscular organ. In an uncomplicated pregnancy, the uterus undergoes significant growth and remodeling, expanding and stretching to more than 500 times its original volume-carrying capacity to accommodate the growing fetus and amniotic sac [ 1 , 2 ]. At term, initiated by a combination of biochemical and biomechanical signals, the uterus must contract rapidly and intensely to enable safe delivery of the baby. Premature activation of uterine contraction is one known cause of preterm labor and birth (PTB) [ 3 ]. PTB remains the leading cause of neonatal death, with one in every ten babies born preterm yearly around the globe [ 4 , 5 ]. Conversely, late activation of uterine contraction contributes to long gestational lengths greater than 40 weeks and prolonged labor, which often require pharmocologic (e.g., pitocin) or surgical (e.g. Cesarean section) interventions [ 6 ]. Increased uterine stretch, resulting in uterine overdistension, is thought to be associated with the premature onset of contractions and higher rates of PTB among women carrying twins or excessive amniotic fluid [ 7 , 8 ]. Therefore, timely uterine remodeling and appropriate biomechanical properties are critical for ensuring a healthy pregnancy and labor. Characterizing the normal and abnormal remodeling of the uterus from nonpregnant (NP) to pregnant (PG) states can contribute to an increased fundamental understanding of pregnancy biomechanics. Previously, the mechanical properties of the human uterus have been evaluated in vivo with diffusion MRI and shear wave elastography and ex vivo with traditional mechanical tests under compression, indentation, and tension [ 9 , 10 , 11 , 12 , 13 , 14 ]. The mechanical properties of the human uterus are nonlinear, anisotropic, and tension-compression asymmetric [ 15 , 11 ]. This complexity reflects the uterus’s unique structure, composed of architected smooth muscle cell fascicles sheathed in the collagen-rich extracellular matrix [ 16 , 17 , 18 ]. Previous ex vivo mechanical testing studies of the uterus reported tensile engineering stress–strain relationships between PG and NP uteri, and found a less steep slope for PG tissue [ 9 ]. A previous study by our lab on a smaller patient cohort used a fibrous material model to describe the equilibrium compressive properties of the uterus under indentation and found the uterine tissue anisotropic [ 11 ]. Building on previous studies, this work seeks to characterize the tensile and compressive properties of the human uterus under large strains, as seen in gestation. In particular, this study focuses on the middle, muscular myometrium layer of the uterus, as it bears the greatest mechanical loads [ 17 ]. A single set of material parameters from a previously described microstructurally-inspired, hyperelastic material constitutive model describes the tensile and compressive uterine properties [ 19 ]. Forty four uterine specimens from 16 patients (8 nonpregnant and 8 pregnant) were studied. To obtain mechanical properties, fiber structural data from previous optical coherence tomography (OCT) imaging studies were integrated into the model a priori, and spherical indentation and uniaxial tension tests were performed to measure tissue material response under different loading conditions [ 11 , 16 ]. Then, inverse finite element analysis was performed to determine the material parameters for each specimen [ 11 , 16 ]. While the time-dependent properties of biological tissues play an important role in their material functions, this study first focuses on the equilibrium properties. Future modeling studies will use this equilibrium modeling foundation to fully characterize uterine material behavior.