Temperature and Frequency Dependent Viscoelasticity of Brain Tissue under Dynamic Shear Loading

Temperature and Frequency Dependent Viscoelasticity of Brain Tissue under Dynamic Shear Loading | 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 Temperature and Frequency Dependent Viscoelasticity of Brain Tissue under Dynamic Shear Loading Hadi Nosrati, Mehdi Shafieian, Nabiollah Abolfathi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6196580/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In traffic crashes, mechanical loads are applied within milliseconds, resembling frequency sweeps in dynamic mechanical testing. While brain mechanics have been widely studied, the effect of temperature on brain tissue’s mechanical response remains unclear, with limited and inconsistent findings. Additionally, few studies have examined how temperature affects brain tissue model parameters, which could provide a more detailed mechanical analysis of such effects. To address this, we conducted dynamic shear experiments on bovine brain tissue within the linear viscoelastic region and developed a generalized Maxwell model. Our primary objective was to investigate the influence of temperature on the dynamic properties of brain tissue, focusing on temperature-dependent changes in viscoelastic parameters, while also assessing frequency effects. Results showed that storage and loss moduli increased with frequency at all tested temperatures (5°C, 25°C, and 35°C), indicating stronger elastic responses and greater energy dissipation at higher frequencies. Both moduli decreased with rising temperature, demonstrating a softening effect, with more pronounced differences at 5°C. Dynamic viscosity was higher at lower temperatures, especially at low frequencies, but differences diminished at higher frequencies. The generalized Maxwell model revealed that absolute parameters decreased with temperature, while normalized parameters showed increased elasticity at higher temperatures and stronger viscosity at lower temperatures. These findings provide detailed insights into the temperature-dependent mechanical properties of brain tissue, enhancing computational simulations of brain behavior under varying thermal conditions and advancing research on brain injuries and biomechanical studies. Brain dynamic shear response Temperature-effect Viscoelastic behavior Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction Road traffic crashes represent a significant global health challenge, contributing to high mortality rates and substantial resource allocation (Chang et al., 2020 ). Among the most severe injuries sustained in traffic accidents, those involving the head are particularly life-threatening (Leszczyński et al., 2022 ). Physiological brain damage is frequently attributed to tissue deformation resulting from the brain's inertial movement following rapid head rotation (Zhan et al., 2022 ). The well-established concept that brain injury arises from shear strains due to direct skull deformation or brain rotations is central to understanding such injuries (Holbourn, 1943 ). Experiments with primates and rabbits have confirmed that brain injuries can result from rotational movements independent of direct impact (Pudenz and Shelden, 1946 , Ommaya, 1966). Other prevailing theories include the idea of hydrostatic tension during impact and the reflection of compressive waves as tensile waves, potentially causing cavitation (Goldsmith, 1966 ). The typical duration of mechanical loads experienced during traffic accidents ranges from 1 to 50 milliseconds, corresponding to frequency sweeps in dynamic mechanical testing (Peters et al., 1997 ). As such, the dynamic properties of brain tissue are described as important for advancing our understanding of brain injuries (Bilston et al., 1997 ). Computational models have become essential tools for investigating the mechanical properties of brain tissue. Precise characterization of these properties is crucial for developing material constitutive laws, which can subsequently be integrated into finite element models of the head (Chatelin et al., 2010 ). To improve the predictive accuracy of these models, a more precise characterization of the mechanical properties of brain tissue is necessary (Jin et al., 2013 , Gefen and Margulies, 2004 ). Hence, investigating the factors influencing brain tissue material's constitutive parameters is paramount. Ex-vivo mechanical experiments have consistently demonstrated that brain tissue exhibits both viscoelastic and nonlinear behavior (Takhounts et al., 2003, Hiscox et al., 2020 ). At small strains, regardless of strain rate, brain tissue displays linear viscoelastic properties (Brands et al., 1999 ). Constitutive models often describe brain tissue using a nonlinear viscoelastic framework, which aligns with the generalized Maxwell model at small strains (Peters et al., 1997 ). However, significant variability has been reported in the mechanical properties of brain tissue, including storage and loss moduli, which describe linear viscoelastic behavior (Arbogast and Margulies, 1998 , Bilston et al., 2001 , Brands, 2000 , Hrapko et al., 2006 , Nicolle et al., 2004 , Peters et al., 1997 , Shen et al., 2006 , Shuck and Advani, 1972 ). This variability in the linear viscoelastic region at small strains (Zhang et al., 2018 ) is also observed under large strains in tension, compression, and shear experiments (Budday et al., 2020 , Chatelin et al., 2010 ). It's crucial to recognize that many factors could potentially affect the mechanical properties of brain tissue, such as different testing modalities (Cheng and Bilston, 2007 ), anatomical location (Prange and Meaney, 2000 , Jin et al., 2013 , Christ et al., 2010 , Velardi et al., 2006 ), maturity (Prange and Margulies, 2002 , Dickerson and Dobbing, 1967 ), gender (Finan et al., 2017 ), interspecies variation (Galford and McElhaney, 1970 , Takhounts et al., 2003), storage conditions (Zhang et al., 2018 ), post-mortem interval (Garo et al., 2007 , Zhang et al., 2018 ), preconditioning (Hrapko et al., 2008a , Nicolle et al., 2005 ), and sample shape (Budday et al., 2017 ). One of the critical issues in the study of brain tissue mechanics is the effect of temperature on tissue stiffness. Despite its importance, only a few studies have addressed this topic (Hrapko et al., 2008b , Guan et al., 2021 , Zhang et al., 2011 , Zhang et al., 2018 ), and no consensus has been reached. Some studies report increased stiffness at higher temperatures (Zhang et al., 2011 ), while others observed decreased stiffness (Hrapko et al., 2008b , Rashid et al., 2013 ) or no significant effect (Arbogast et al., 1997). Another study found that the mechanical properties of brain tissue were significantly influenced by sample temperature only under high strain rates (Guan et al., 2021 ). Moreover, investigating the effect of temperature on the constitutive parameters of materials is stated to be highly important (Guan et al., 2021 ), among the studies referenced, only Rashid et al. ( 2013 ) examined the influence of temperature on the nonlinear parameters of the Ogden model. In the context of dynamic loading, Shen et al. ( 2006 ) and Hrapko et al. ( 2008b ) conducted experimental studies to explore the influence of temperature on the mechanical properties of brain tissue. However, neither of these studies examined the effect of temperature on the constitutive model parameters of the tissue, which could provide more profound mechanical insights into the temperature-dependent behavior of brain tissue. Research on the temperature-dependent mechanical properties of brain tissue remains limited and inconclusive, raising important questions about whether higher temperatures cause brain tissue to stiffen or soften, how viscoelastic parameters vary with temperature, and the role of frequency in these temperature effects. To study the influence of temperature and loading frequency on the viscoelastic properties of brain tissue under dynamic loading, experiments were conducted at three temperatures (35°C, 25°C, and 5°C). A dynamic mechanical thermal analyzer (DMTA) was used to characterize the mechanical behavior of bovine brain tissue across thermal and frequency ranges. The experimental data were then employed to develop a viscoelastic constitutive model for brain tissue using a generalized Maxwell framework. This model is designed to enhance the fidelity of computational predictions of brain tissue mechanics under varying thermal and dynamic loading scenarios. Materials and methods 4.1. Experimental setup Fresh bovine brains (n = 3) were obtained from a local slaughterhouse and immediately immersed in phosphate-buffered saline (PBS) to prevent osmotic swelling. The brains were transported to the laboratory on ice to maintain tissue integrity. Upon arrival, each brain was dissected along the corpus callosum using a scalpel to yield two symmetrical hemispheres. Cylindrical tissue samples, approximately 25 mm in diameter and 2 mm in height were excised from the midbrain region. Each sample contained a mixture of white and gray matter. Two samples were extracted from each hemisphere. The dimensions were selected to match the plate and gap geometry of the testing device. Frequency sweep tests were performed utilizing a parallel-plate measuring system of the rheometer (Paar Physica MCR300). The tests spanned a frequency range of 0.1 to 100 rad/s, incorporating 16 logarithmically spaced frequency points. It has been reported that the frequency order does not influence the outcomes of the tests (Barnes et al., 2015 ). To enhance grip during testing, sandpaper disks were affixed to the parallel plates. The samples were irrigated with PBS and positioned between the plates, with the upper plate oscillating rotationally while the bottom plate remained stationary. Tests were conducted using the rheometer's Peltier temperature control system at constant temperatures of 5°C, 25°C, and 35°C. The temperature was gradually adjusted between tests to avoid thermal gradients (Shen et al., 2006 ), allowing sufficient time for thermal equilibration before data acquisition. A strain amplitude of 1%, confirmed to be within the linear viscoelastic region (Peters et al., 1997 , Brands et al., 1999 , Garo et al., 2007 , Shen et al., 2006 , Hrapko et al., 2008b ), was applied. The results from four individual samples for each specific temperature were averaged to produce representative values. All experiments were conducted within 5 hours of sample collection to minimize microbiological degradation and preserve tissue integrity. 4.2. Dynamic Viscoelastic Description The Stress (τ) and strain (γ) were calculated as follows (Laun et al., 2014 ): $$\:{\tau\:}=\frac{2M}{\pi\:{R}^{3}}$$ 1 $$\:{\gamma\:}=\frac{\theta\:R}{h}$$ 2 where M is torque, R is plate radius, θ is angular displacement, and h is plate gap height. For dynamic measurements, a sinusoidal shear strain \(\:\:\:{\gamma\:}\left(\text{t}\right)\) was applied to the sample, defined as (Peters et al., 1997 ): $$\:{\gamma\:}\left(\text{t}\right)={{\gamma\:}}_{0}\text{sin}\left(\omega\:t\right)$$ 3 For a sufficiently small shear strain amplitude \(\:{{\gamma\:}}_{0}\) , the shear stress will oscillate sinusoidally in the steady state. It will exhibit a phase shift δ and maintain a linear relationship with the strain. $$\:{\tau\:}\left(\text{t}\right)={{\text{G}}^{\text{*}}{\gamma\:}}_{0}\text{sin}\left(\omega\:t+\delta\:\right)$$ 4 The dynamic modulus G*(ω,T) and the phase shift δ(ω,T) depend on both the frequency and the temperature. Subsequently, the dynamic viscoelastic parameters including, storage modulus (G'), loss modulus (G''), and loss factor (tanδ) of each sample can be determined as (Ferry, 1948 ): $$\:{\text{G}}^{\text{*}}=\:{\text{G}}^{{\prime\:}}+i{\text{G}}^{{\prime\:}{\prime\:}},\:\:\left|{\text{G}}^{\text{*}}\right|=\:\sqrt{{{\text{G}}^{{\prime\:}}}^{2}+{{\text{G}}^{{\prime\:}{\prime\:}}}^{2}}$$ 5 $$\:{\text{G}}^{{\prime\:}}={\text{G}}^{\text{*}}\text{cos}\left(\delta\:\right)$$ 6 $$\:{\text{G}}^{{\prime\:}{\prime\:}}={\text{G}}^{\text{*}}\text{sin}\left(\delta\:\right)$$ 7 $$\:\text{tan}\left(\delta\:\right)=\frac{{\text{G}}^{{\prime\:}{\prime\:}}}{{\text{G}}^{{\prime\:}}}$$ 8 The dynamic viscosity (η') could be derived using the following relationship (Fallenstein et al., 1969 ): $$\:{\eta\:}{\prime\:}=\frac{{\text{G}}^{{\prime\:}{\prime\:}}}{\omega\:}$$ 9 The energy dissipated per cycle of deformation can be calculated using the loss modulus and the strain amplitude as (Ferry, 1980 ): $$\:Energy\:Dissipation=\:{\pi\:{\text{G}}^{{\prime\:}{\prime\:}}{{\gamma\:}}_{0}}^{2}$$ 10 4.3. Model definition To illustrate the viscoelastic behavior of brain tissue and its dependence on temperature and frequency, the generalized Maxwell model was applied. The model captures the experimental dynamic response of brain tissue at various frequencies and temperatures. The storage modulus of the model and loss modulus, are defined as functions of angular frequency at a constant temperature (Zhang and Gan, 2014 ). $$\:{{G}^{{\prime\:}}}_{model\left({\omega\:},\text{T}\right)}={G}_{0}+\:\sum\:_{i=1}^{n}\frac{{G}_{i}\left(T\right){{\omega\:}}^{2}{{\tau\:}_{i}}^{2}}{1+{{\omega\:}}^{2}{{\tau\:}_{i}}^{2}}$$ 11 $$\:{{G}^{{\prime\:}{\prime\:}}}_{model\left({\omega\:},\text{T}\right)}=\:\sum\:_{i=1}^{n}\frac{{G}_{i}\left(T\right){\omega\:}{\tau\:}_{i}}{1+{{\omega\:}}^{2}{{\tau\:}_{i}}^{2}}$$ 12 The model parameters include the temperature (T), steady-state elastic modulus (G 0 ​), and the elastic modulus of the i-th Maxwell branch (G i ). The time constant (τ i ) for each branch is defined as the ratio of the viscosity coefficient (η i ​) to G i . The number of Maxwell branches is denoted by n. The number of branches was selected to achieve the best fit with the fewest unknown parameters. Based on pilot analysis, the model used in this study consists of one elastic branch and three viscous branches. For each temperature, the parameters (G 0 ​ and G i ​​) were determined by fitting the experimental results (loss and storage modulus). For three Maxwell branches, the time constants were fixed at τ 1 = 0.01, τ 2 = 0.1, and τ 3 = 1 s. The least-squares method was used to optimize the fit to the experimental data by minimizing the sum of squared errors (SSE) (Montgomery et al., 2021). $$\:SSE=\:\sum\:_{i=1}^{n}\left[{{\left({G}_{exp}^{{\prime\:}}-{G}_{model}^{{\prime\:}}\:\right)}_{i}}^{2}+{{\left({G}_{exp}^{{\prime\:}{\prime\:}}-{G}_{model}^{{\prime\:}{\prime\:}}\:\right)}_{i}}^{2}\right]$$ 13 Where n represents the total number of sets of pairs, which corresponds to the total number of measurements in the respective angular frequency series. To gain a clearer insight into the influence of temperature on the model parameters, the values of G 0 and G i were normalized using Eq. 14 . $$\:{G}_{i}^{norm}=\:\frac{{G}_{i}}{\sum\:_{i=0}^{3}{G}_{i}}\:,\:i=0,\:1,\:2,\:3$$ 14 Using the generalized Maxwell model's normalized constants, the reduced relaxation modulus ( \(\:{G}_{R}^{norm}\:)\:\) can be plotted for each temperature over time, as defined by Eq. 15 , to predict the temperature's effect on the stress relaxation behavior of the tissue. $$\:{G}_{R}^{norm}\:(t,T)={G}_{0}^{norm}\left(T\right)+\sum\:_{i=1}^{3}{G}_{i}^{norm}\left(T\right){e}^{(-\frac{t}{{\tau\:}_{i}})}$$ 15 Results Figure 1 illustrates the storage and loss moduli of brain tissue in dynamic shear as a function of frequency, measured at three different temperatures (5°C, 25°C, and 35°C). The storage modulus exhibited a consistent rise with increasing frequency at all tested temperatures, reflecting a more dominant elastic response in the brain tissue at higher frequencies. Similarly, the loss modulus demonstrated an upward trend with frequency, indicating greater energy dissipation as the deformation rate increased. The pattern emerged, showing that both storage and loss moduli were elevated at lower temperatures. This suggests that the brain tissue becomes stiffer and exhibits enhanced energy dissipation capabilities as temperatures decrease. Figure 2 presents the average dissipated energy at four frequencies (0.1, 1, 10, and 100 rad/s) for three temperatures (5°C, 25°C, and 35°C). The energy dissipation per unit volume exhibited a consistent increase with rising frequency across all tested temperatures, reflecting the frequency-dependent viscoelastic response of brain tissue. Notably, lower temperatures (5°C) demonstrated significantly higher energy dissipation compared to elevated temperatures (35°C and 25°C), indicating enhanced stiffness and energy loss at reduced thermal conditions. This temperature-dependent disparity became increasingly pronounced at higher frequencies. Dynamic viscosity of brain tissue was measured across a frequency range of 0.1–100 rad/s at three temperatures (5°C, 25°C, and 35°C), revealing distinct temperature- and frequency-dependent behavior (Fig. 3 ). Findings demonstrated that the dynamic viscosity of brain tissue decreased with increasing frequency, with pronounced temperature effects at low frequencies. To achieve a more thorough understanding of the influence of temperature at constant frequency and the effect of frequency at constant temperature on energy dissipation in the shear response of brain tissue, Fig. 4 presents the elliptic Lissajous plots for various temperatures across different frequencies. The Generalized Maxwell model was applied to perform curve fitting on the averaged experimental values of the loss modulus and storage modulus. The optimized model parameters, presented in Table 1 , exhibit a monotonic decrease with increasing temperature. Figure 5 compares the experimentally averaged complex modulus with the corresponding model values, demonstrating curve-fitting quality. To further illustrate the effect of temperature on the elastic and viscous components of the model, Fig. 6 presents the absolute and normalized model parameters as a function of temperature. Results demonstrated that all absolute parameters of the model decreased with increasing temperature. The normalized parameters indicated that temperature changes significantly impacted the viscoelastic properties of brain tissue. G 0 norm demonstrated an increasing trend with higher temperatures, reflecting higher elastic behavior and a decrease in the tissue's elastic nature as temperatures dropped. In contrast, viscous effects became more prominent at lower temperatures. G 1 norm showed an increase, and similarly, G 2 norm and G 3 norm also exhibited rising values as temperatures decreased, emphasizing the dominance of viscous behavior in colder conditions. Figure 7 illustrates the predicted outcomes of the generalized Maxwell model for the reduced relaxation modulus of brain tissue at varying temperatures (5°C, 25°C, and 35°C). The results indicate that relaxation behavior was more pronounced at 5°C. Table 1 Viscoelastic parameters of brain tissue at varying temperatures (5°C, 25°C, 35°C). G₀ G₁ G₂ G₃ T = 35°C 297.43 211.28 25.72 77 T = 25°C 351.53 278.1 79.93 113.06 T = 5°C 441.25 542.94 146.54 211.1 τ - 0.01 0.1 1 Discussion A comprehensive understanding of the dynamic properties of brain tissue is essential for advancing research on brain injuries (Bilston et al., 1997 ). Studies, particularly those incorporating accurate material definitions that integrate structural configurations and experimental data, could be reliable tools in the field of brain biomechanics. To investigate the effect of temperature on the viscoelastic properties of the brain we conducted oscillatory shear tests. The tests are commonly employed to assess the rate-dependent mechanical properties of soft tissues. In these tests, sinusoidal shear displacements are applied to the sample, creating a time-dependent strain profile. The resulting force is measured and converted to reflect the stress response of the sample. The storage and loss moduli are calculated based on the amplitude and phase angle differences between the steady-state strain and stress responses. These oscillatory tests effectively determine the viscoelastic properties of materials at low and non-destructive strain levels, remaining within the linear viscoelastic strain limit. In dynamic frequency sweep tests, all samples showed consistent behavior, with both the storage modulus and loss modulus increasing with frequency. Our experimental results are in good agreement with published data in the literature (Shen et al., 2006 , Hrapko et al., 2008b , Peters et al., 1997 , Garo et al., 2007 ), although some variations were observed. In this study, the material properties were derived from a combination of white and gray matter, treating the brain as an isotropic material. This approach is consistent with studies confirming the isotropy of brain tissue (Budday et al., 2017 ). The influence of temperature on the mechanical properties of brain tissue was investigated. Both the loss modulus and storage modulus were found to be temperature-dependent, with both moduli increasing as temperature decreased. This suggests that brain tissue becomes stiffer and exhibits enhanced energy dissipation capabilities at lower temperatures, a trend that has been reported in previous studies (Shen et al., 2006 , Hrapko et al., 2008b ). This behavior reflects a transition in the material's viscoelastic properties, with brain tissue displaying more solid-like behavior at 5°C compared to the more fluid-like behavior observed at 35°C and 25°C. The difference in energy dissipation between temperatures became more pronounced at higher frequencies. It has been proposed that examining the impact of temperature on the constitutive parameters of the brain is of great importance (Guan et al., 2021 ). Consequently, we explored how temperature influences the parameters of the generalized Maxwell model. Temperature significantly influenced the viscoelastic model parameters of brain tissue. This study found that all absolute model parameters decreased as temperature increased. Considering normalized model parameters, higher temperatures enhanced elastic behavior, while lower temperatures increased viscous effects. The model in this study was developed using experimental data acquired under shear dynamic loading conditions at a 1% strain amplitude. To validate its predictive capability for brain tissue stress relaxation, Fig. 8 compares the Generalized Maxwell model’s predictions of the reduced relaxation modulus at 35°C with experimental data from Nicolle et al. ( 2004 ) at 37°C. The analysis focuses on shear relaxation behavior over a 2-second duration at 1% strain, due to closely aligned testing parameters (temperature, loading mode, strain amplitude) between studies. Results demonstrated general agreement between model predictions and experimental data across the evaluated timescale. The stiffer response observed in Nicolle et al.'s dataset likely stems from their use of tissue samples with a 24–48-hour post-mortem interval, in contrast to the shorter 5-hour post-mortem interval maintained in the present study. Garo et al. ( 2007 ) conducted oscillatory shear tests with 1% strain amplitude and frequencies ranging from 1 to 10 Hz. They found that the stress response was dependent on post-mortem time, with the tissue becoming stiffer as time increased. Post-mortem time selection in dynamic testing varied significantly across studies. Differences in post-mortem intervals among studies, such as Shen et al. ( 2006 ) (48–120 hours), Peters et al. ( 1997 ) (27–51 hours), and Hrapko et al. ( 2006 ) (5 hours), may account for discrepancies in reported mechanical properties. Shen et al. ( 2006 ) reported an increasing trend in both the loss modulus and storage modulus of the brain as the temperature decreased. Hrapko et al. ( 2008b ) observed that the dynamic shear modulus of brain tissue significantly depends on temperature, with increased hardening as the temperature decreases. Zhang et al. ( 2011 ) found that, at a strain of 10%, the engineering stress and tangent modulus of the brain at 37°C were 3.5 and 3.2 times higher than at 0°C, respectively. When the strain increased to 70%, these values were 2.4 and 2.2 times higher at 37°C compared to 0°C. Rashid et al. ( 2013 ) found that the temperature at which porcine brain tissue is stored or preserved before testing significantly influences the mechanical properties of the brain tissue, even when the tests are carried out at the same temperatures. Guan et al. ( 2021 ) noted that temperature significantly affects the engineering stress of the brain at high strain rates, particularly at 13°C. No significant differences were observed between 20°C and 37°C at both low and high strain rates. Our results on decreasing stiffness with increasing temperature align with the works of Hrapko et al. ( 2008b ), Shen et al. ( 2006 ), Rashid et al. ( 2013 ), and Guan et al. ( 2021 ), but contradict the study by Zhang et al. ( 2011 ). It is significant to note that Zhang et al. (2010) investigated the effects of temperatures on the high strain-rate material properties of porcine brain tissues using a split-Hopkinson pressure bar (SHPB) at an approximate strain rate of 2487 s⁻¹, relevant to blast scenarios. Furthermore, among the studies mentioned, only Rashid et al. ( 2013 ) investigated the impact of temperature on the model parameters of brain tissue, utilizing a one-term Ogden model. Their findings indicated that raising the tissue's storage temperature resulted in a decline in the initial shear modulus. Although their research concentrated on the nonlinear domain, the observed temperature effects align with our findings in the linear domain. Our findings show that temperature-dependent differences in mechanical response are more pronounced at higher frequencies, consistent with Guan et al. ( 2021 ), who noted significant temperature effects on engineering stress at high strain rates. The findings of Birkl et al. ( 2013 ) reveal that the temperature coefficient in brain tissue is strongly influenced by cellular structures that restrict molecular mobility. Reduced molecular mobility at lower temperatures and stiffness changes underscore the interconnected thermal, structural, and mechanical behavior of brain tissue. In our investigation, the dynamic viscosity measured at an angular frequency of 63.1 rad/s (approximately 10 Hz) yielded values of 66.6 P, 95.5 P, and 144.9 P for temperatures of 35°C, 25°C, and 5°C, respectively. Notably, while the original results were acquired in pascal-seconds (Pa·s), they were converted to poise (1 Pa·s = 10 P) to standardize comparisons with prior literature. These findings align closely with the work of Fallenstein et al. ( 1969 ), who reported dynamic shear viscosities of 56–96 P for in-vitro human brain tissue at comparable frequencies (9–10 Hz). Earlier studies reported lower viscosity values. For instance, Koeneman (1966, unpublished M.S. thesis, Case Institute of Technology, USA) documented a dynamic viscosity of 43.5 P, while Franke ( 1956 ) obtained a shear viscosity of 14.9 P through impedance measurements on in vitro pig brain tissue. This discrepancy likely arises from the higher testing frequencies (100–500 Hz) employed in these studies, as viscoelastic materials exhibit frequency-dependent mechanical behavior characterized by reduced viscosity at elevated frequencies. Additionally, interspecies variations between human and non-primate brain tissue properties may further contribute to observed differences (Fallenstein et al., 1969 ). Our experiments revealed that the storage and loss moduli of brain tissue increased with frequency, while higher temperatures led to a decrease in tissue stiffness. Building on the methodology of Najafidoust et al. ( 2023 ), who observed a temperature-driven stiffening in periodontal ligaments and a frequency-dependent rise in storage modulus (with loss modulus attenuation at higher frequencies), we applied their framework to brain tissue. Despite methodological alignment, our results diverged markedly. Considering other soft tissues, studies have shown that skin's compressive stiffness increased with rising temperature (Bianchi et al., 2022 ), whereas the tensile stiffness of skin and lumbar spine ligaments decreased (Xu et al., 2008 , Bass et al., 2007 ). Under dynamic loading, some tissues exhibited reduced storage modulus at higher temperatures, including the stapedial annular ligament (dynamic shear loading) (Zhang and Gan, 2014 ), tympanic membrane (dynamic tensile loading) (Zhang and Gan, 2013 ), and vocal folds (dynamic shear loading) (Chan, 2001 ). The complex moduli of subcutaneous adipose tissue also decreased under dynamic shear loading as temperature increased (Geerligs et al., 2008 ), which is similar to what we observed for brain tissue. These findings underscore the diverse, tissue-specific effects of temperature on the mechanical properties of soft tissues. Conclusion Our study investigated the influence of temperature and frequency on the dynamic properties of brain tissue under shear loading, focusing on temperature-driven changes in viscoelastic model parameters. Findings showed that storage and loss moduli decreased with rising temperature, indicating softening, while moduli increased with frequency, with greater temperature-related disparities at higher frequencies. Dynamic viscosity was higher at low temperatures and frequencies but decreased as frequency increased. The generalized Maxwell model revealed that absolute parameters declined with temperature, while normalized parameters showed increased elasticity at higher temperatures and stronger viscosity at lower temperatures. These findings provide insights into the temperature-sensitive mechanics of brain tissue, supporting advancements in computational modeling and brain injury research. Declarations Acknowledgements . The authors have no acknowledgments to declare The authors have not received any funding for this research. References ARBOGAST, K. B. & MARGULIES, S. S. 1998. Material characterization of the brainstem from oscillatory shear tests. 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Mechanical difference between white and gray matter in the rat cerebellum measured by scanning force microscopy. Journal of biomechanics, 43 , 2986-2992. https://doi.org/10.1016/j.jbiomech.2010.07.002 DICKERSON, J. & DOBBING, J. 1967. Prenatal and postnatal growth and development of the central nervous system of the pig. Proceedings of the Royal Society of London. Series B. Biological Sciences, 166 , 384-395. https://doi.org/10.1098/rspb.1967.0002 FALLENSTEIN, G., HULCE, V. D. & MELVIN, J. W. 1969. Dynamic mechanical properties of human brain tissue. Journal of biomechanics, 2 , 217-226.https://doi.org/10.1016/0021-9290(69)90079-7 FERRY, J. 1980. Viscoelastic Properties of Polymers , Wiley. https://doi.org/10.1126/science.133.3460.1251-a FERRY, J. D. 1948. Viscoelastic properties of polymer solutions. J. Res. Natl. Bur. Stand, 41 , 53-61. https://doi.org/10.6028/jres.041.008 FINAN, J. D., SUNDARESH, S. N., ELKIN, B. S., MCKHANN II, G. M. & MORRISON III, B. 2017. Regional mechanical properties of human brain tissue for computational models of traumatic brain injury. Acta biomaterialia, 55 , 333-339. https://doi.org/10.1016/j.actbio.2017.03.037 FRANKE, E. K. 1956. Response of the human skull to mechanical vibrations. The Journal of the Acoustical Society of America, 28 , 1277-1284. https://doi.org/10.1121/1.1908622 GALFORD, J. E. & MCELHANEY, J. H. 1970. A viscoelastic study of scalp, brain, and dura. Journal of biomechanics, 3 , 211-221. https://doi.org/10.1016/0021-9290(70)90007-2 GARO, A., HRAPKO, M., VAN DOMMELEN, J. & PETERS, G. 2007. Towards a reliable characterisation of the mechanical behaviour of brain tissue: the effects of post-mortem time and sample preparation. Biorheology, 44 , 51-58. https://doi.org/10.1177/0006355x2007044001003 GEERLIGS, M., PETERS, G. W., ACKERMANS, P. A., OOMENS, C. W. & BAAIJENS, F. P. 2008. Linear viscoelastic behavior of subcutaneous adipose tissue. Biorheology, 45 , 677-688. https://doi.org/10.3233/bir-2008-0517 GEFEN, A. & MARGULIES, S. S. 2004. Are in vivo and in situ brain tissues mechanically similar? Journal of biomechanics, 37 , 1339-1352. https://doi.org/10.1016/j.jbiomech.2003.12.032 GOLDSMITH, W. Pulse propagation in rocks. ARMA US Rock Mechanics/Geomechanics Symposium, 1966. ARMA, ARMA-66-0528. https://doi.org/10.1016/0148-9062(84)90088-3 GUAN, F., ZHANG, G., JIA, X. & DENG, X. 2021. Study on the Effect of Sample Temperature on the Uniaxial Compressive Mechanical Properties of the Brain Tissue. Applied Bionics and Biomechanics, 2021 , 9986395. https://doi.org/10.1155/2021/9986395 HISCOX, L. V., MCGARRY, M. D., SCHWARB, H., VAN HOUTEN, E. E., POHLIG, R. T., ROBERTS, N., HUESMANN, G. R., BURZYNSKA, A. Z., SUTTON, B. P. & HILLMAN, C. H. 2020. Standard‐space atlas of the viscoelastic properties of the human brain. Human brain mapping, 41 , 5282-5300. https://doi.org/10.1002/hbm.25192 HOLBOURN, A. 1943. Mechanics of head injuries. The Lancet, 242 , 438-441. https://doi.org/10.1016/s0140-6736(00)87453-x HRAPKO, M., VAN DOMMELEN, J., PETERS, G. & WISMANS, J. 2006. The mechanical behaviour of brain tissue: large strain response and constitutive modelling. Biorheology, 43 , 623-636. https://doi.org/10.1177/0006355x2006043005004 HRAPKO, M., VAN DOMMELEN, J., PETERS, G. & WISMANS, J. 2008a. Characterisation of the mechanical behaviour of brain tissue in compression and shear. Biorheology, 45 , 663-676. https://doi.org/10.3233/bir-2008-0512 HRAPKO, M., VAN DOMMELEN, J., PETERS, G. & WISMANS, J. 2008b. The influence of test conditions on characterization of the mechanical properties of brain tissue. https://doi.org/10.1115/1.2907746 JIN, X., ZHU, F., MAO, H., SHEN, M. & YANG, K. H. 2013. A comprehensive experimental study on material properties of human brain tissue. Journal of biomechanics, 46 , 2795-2801. https://doi.org/10.1016/j.jbiomech.2013.09.001 LAUN, M., AUHL, D., BRUMMER, R., DIJKSTRA, D. J., GABRIEL, C., MANGNUS, M. A., RÜLLMANN, M., ZOETELIEF, W. & HANDGE, U. A. 2014. Guidelines for checking performance and verifying accuracy of rotational rheometers: viscosity measurements in steady and oscillatory shear (IUPAC Technical Report). Pure and Applied Chemistry, 86 , 1945-1968. https://doi.org/10.1515/pac-2013-0601 LESZCZYŃSKI, P. K., KALINOWSKA, J., MITURA, K. & SHOLOKHOVA, D. 2022. Injuries to users of single-track vehicles. International journal of environmental research and public health, 19 , 12112. https://doi.org/10.3390/ijerph191912112 MONTGOMERY, D. C., PECK, E. A. & VINING, G. G. 2021. Introduction to linear regression analysis , John Wiley & Sons. NAJAFIDOUST, M., HASHEMI, A. & OSKUI, I. Z. 2023. Effect of temperature on dynamic compressive behavior of periodontal ligament. Medical Engineering & Physics, 116 , 103986. https://doi.org/10.1016/j.medengphy.2023.103986 NICOLLE, S., LOUNIS, M. & WILLINGER, R. 2004. Shear properties of brain tissue over a frequency range relevant for automotive impact situations: new experimental results. SAE Technical Paper. https://doi.org/10.4271/2004-22-0011 NICOLLE, S., LOUNIS, M., WILLINGER, R. & PALIERNE, J. F. 2005. Shear linear behavior of brain tissue over a large frequency range. Biorheology, 42 , 209-223. https://doi.org/10.1177/0006355x2005042003003 OMMAYA, A. K., HIRSCH, A. E., FLAMM, E. S. & MAHONE, R. H. 1966. Cerebral concussion in the monkey: an experimental model. Science , 153(3732), 211-212. https://doi.org/10.1126/science.153.3732.211 PETERS, G., MEULMAN, J. & SAUREN, A. 1997. The applicability of the time/temperature superposition principle to brain tissue. Biorheology, 34 , 127-138. https://doi.org/10.1016/s0006-355x(97)00009-7 PRANGE, M. & MEANEY, D. F. 2000. Defining brain mechanical properties: effects of region, direction, and species. SAE Technical Paper. https://doi.org/10.4271/2000-01-sc15 PRANGE, M. T. & MARGULIES, S. S. 2002. Regional, directional, and age-dependent properties of the brain undergoing large deformation. J. Biomech. Eng., 124 , 244-252. https://doi.org/10.1115/1.1449907 PUDENZ, R. H. & SHELDEN, C. H. 1946. The lucite calvarium—a method for direct observation of the brain: II. Cranial trauma and brain movement. Journal of neurosurgery, 3 , 487-505. https://doi.org/10.3171/jns.1946.3.6.0487 RASHID, B., DESTRADE, M. & GILCHRIST, M. D. 2013. Influence of preservation temperature on the measured mechanical properties of brain tissue. Journal of biomechanics, 46 , 1276-1281. https://doi.org/10.1016/j.jbiomech.2013.02.014 SHEN, F., TAY, T., LI, J., NIGEN, S., LEE, P. & CHAN, H. 2006. Modified Bilston nonlinear viscoelastic model for finite element head injury studies. https://doi.org/10.1115/1.2264393 SHUCK, L. & ADVANI, S. 1972. Rheological response of human brain tissue in shear. https://doi.org/10.1115/1.3425588 TAKHOUNTS, E. G., CRANDALL, J. R. & DARVISH, K. 2003. On the importance of nonlinearity of brain tissue under large deformations. SAE Technical Paper. https://doi.org/10.4271/2003-22-0005 VELARDI, F., FRATERNALI, F. & ANGELILLO, M. 2006. Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomechanics and modeling in mechanobiology, 5 , 53-61. https://doi.org/10.1007/s10237-005-0007-9 XU, F., SEFFEN, K. & LU, T. 2008. Temperature-Dependent Mechanical Behaviors of Skin Tissue. IAENG International Journal of Computer Science, 35. https://doi.org/10.1007/s10409-007-0128-8 ZHAN, X., OEUR, A., LIU, Y., ZEINEH, M. M., GRANT, G. A., MARGULIES, S. S. & CAMARILLO, D. B. 2022. Translational models of mild traumatic brain injury tissue biomechanics. Current Opinion in Biomedical Engineering, 24 , 100422. https://doi.org/10.1016/j.cobme.2022.100422 ZHANG, J., YOGANANDAN, N., PINTAR, F. A., GUAN, Y., SHENDER, B., PASKOFF, G. & LAUD, P. 2011. Effects of tissue preservation temperature on high strain-rate material properties of brain. Journal of Biomechanics, 44 , 391-396. https://doi.org/10.1016/j.jbiomech.2010.10.024 ZHANG, W., LIU, L.-F., XIONG, Y.-J., LIU, Y.-F., YU, S.-B., WU, C.-W. & GUO, W. 2018. Effect of in vitro storage duration on measured mechanical properties of brain tissue. Scientific reports, 8 , 1247. https://doi.org/10.1038/s41598-018-19687-2 ZHANG, X. & GAN, R. Z. 2013. Dynamic properties of human tympanic membrane based on frequency-temperature superposition. Annals of biomedical engineering, 41 , 205-214. https://doi.org/10.1007/s10439-012-0624-2 ZHANG, X. & GAN, R. Z. 2014. Dynamic properties of human stapedial annular ligament measured with frequency–temperature superposition. Journal of Biomechanical Engineering, 136 , 081004. https://doi.org/10.1115/1.4027668 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-6196580","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":427348401,"identity":"2f098518-264e-40b5-9ee7-76a676da295c","order_by":0,"name":"Hadi Nosrati","email":"","orcid":"","institution":"Amirkabir University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Hadi","middleName":"","lastName":"Nosrati","suffix":""},{"id":427348402,"identity":"d3077332-58e2-4fbc-b973-72df118a05c9","order_by":1,"name":"Mehdi Shafieian","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYDACCQaGDwkgkr0BKsJMWAvjDLAWngMMDAeI1gJhJEC1EALys5sfNjyosJA3l3z8TPoDg508AzvvA7xaDO4cM2xIOCNhuHN2mpnEAYZkwwZmdgP8WiQSzB8ktkkwbridANLCnMDAzEbAYTPSPzYk/pOw33Dz+DeglnrCWhhu5Bg2JDZIJG64wQOy5TBhLQY3cgobEo5JJG84k1NsccbguGEbEQ7b2Pijps52w/HjG29UVFTL8/MfI+AwNEsZGAj5ZBSMglEwCkYBEQAA/QFCDm25eOoAAAAASUVORK5CYII=","orcid":"","institution":"Amirkabir University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Mehdi","middleName":"","lastName":"Shafieian","suffix":""},{"id":427348403,"identity":"c9dbd2fd-7479-4647-ba26-5b91838e4a34","order_by":2,"name":"Nabiollah Abolfathi","email":"","orcid":"","institution":"Amirkabir University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Nabiollah","middleName":"","lastName":"Abolfathi","suffix":""}],"badges":[],"createdAt":"2025-03-10 14:38:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6196580/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6196580/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":78462307,"identity":"57d8f280-c443-48c0-800d-65f1bc121a08","added_by":"auto","created_at":"2025-03-13 13:50:50","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":139825,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental findings (storage modulus and loss modulus) plotted against frequency from oscillation tests conducted at different temperatures (with four samples tested per temperature). Error bars represent standard deviations. The results demonstrate the influence of temperature on the dynamic viscoelastic properties of brain tissue\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/075d2dd633b1bc320ed0396c.png"},{"id":78462308,"identity":"0cda5525-71a9-4a89-aca8-c858fdfe9518","added_by":"auto","created_at":"2025-03-13 13:50:50","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":101961,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe mean energy dissipated per unit volume measured at three temperatures (5°C, 25°C, and 35°C) and across four frequencies (0.1, 1, 10, and 100 rad/s). Each curve in the plot represents the average values derived from four samples tested at a specific temperature\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/7a865b2418bd501ef4348e8b.png"},{"id":78462309,"identity":"b45eb6b7-ecaf-4f98-83d9-4dfce6f1398f","added_by":"auto","created_at":"2025-03-13 13:50:50","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":78311,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDynamic viscosity of brain tissue measured from 0.1 to 100 rad/s at 5°C, 25°C, and 35°C, showing clear dependencies on both temperature and frequency. Each curve represents the average values of four samples at a specific temperature\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/f77b58a47a1c77739b809a27.png"},{"id":78463432,"identity":"d944b0c6-9f76-41b9-bc65-b4ca293be98c","added_by":"auto","created_at":"2025-03-13 14:06:50","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":331883,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe low amplitude elliptical stress-strain curves for three temperatures at various frequencies. The area within the elliptical curves indicates energy dissipation, while the slope of the main axis represents the brain's complex modulus. Each shape represents the average values of four samples at a specific temperature and frequency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/123863d1761a24fed384b55d.png"},{"id":78463255,"identity":"2dcb61ed-5718-49ad-bb29-ecf30c55709c","added_by":"auto","created_at":"2025-03-13 13:58:50","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":240497,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA comparison between the Generalized Maxwell model and the averaged experimental data for complex moduli at three different temperatures: (a) 35°C, (b) 25°C, and (c) 5°C. This comparison demonstrates the quality of the curve-fitting\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/2f7d3847566789bb21d5c05b.png"},{"id":78463251,"identity":"6355ac43-e9ad-4622-a6e7-78de28f89239","added_by":"auto","created_at":"2025-03-13 13:58:50","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":156656,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGraphs depicting the normalized and absolute parameters of the Generalized Maxwell model as a function of temperature. Nearly all parameters, except for G\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/sub\u003e\u003csup\u003e\u003cstrong\u003enorm\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e, decreased as the temperature increased\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/0c0e042f6227b1cc8a174f83.png"},{"id":78463250,"identity":"a2e74e94-9206-4ab1-8a83-ceba5bb09577","added_by":"auto","created_at":"2025-03-13 13:58:50","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":191021,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe predicted results of the generalized Maxwell model on the reduced relaxation modulus of the brain at different temperatures. Relaxation was more pronounced at 5°C compared to 25°C and 35°C\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/dc5abac7c5983fc57db3ecd7.png"},{"id":78463258,"identity":"4b80560b-58a3-45c9-891f-fe6b9b6eec8a","added_by":"auto","created_at":"2025-03-13 13:58:50","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":107519,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA comparison of the Generalized Maxwell model's predictions at 35°C with the data from Nicolle et al. (2004) at 37°C\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/b062229b08da966cdd6e4527.png"},{"id":79674757,"identity":"b43be355-b825-49df-90d2-8c9ca16480e7","added_by":"auto","created_at":"2025-04-01 11:54:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2676095,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6196580/v1/40e9c812-7e60-42bb-af44-16d6b32cfff0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Temperature and Frequency Dependent Viscoelasticity of Brain Tissue under Dynamic Shear Loading","fulltext":[{"header":"Introduction","content":"\u003cp\u003eRoad traffic crashes represent a significant global health challenge, contributing to high mortality rates and substantial resource allocation (Chang et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Among the most severe injuries sustained in traffic accidents, those involving the head are particularly life-threatening (Leszczyński et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Physiological brain damage is frequently attributed to tissue deformation resulting from the brain's inertial movement following rapid head rotation (Zhan et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The well-established concept that brain injury arises from shear strains due to direct skull deformation or brain rotations is central to understanding such injuries (Holbourn, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1943\u003c/span\u003e). Experiments with primates and rabbits have confirmed that brain injuries can result from rotational movements independent of direct impact (Pudenz and Shelden, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1946\u003c/span\u003e, Ommaya, 1966). Other prevailing theories include the idea of hydrostatic tension during impact and the reflection of compressive waves as tensile waves, potentially causing cavitation (Goldsmith, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1966\u003c/span\u003e). The typical duration of mechanical loads experienced during traffic accidents ranges from 1 to 50 milliseconds, corresponding to frequency sweeps in dynamic mechanical testing (Peters et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). As such, the dynamic properties of brain tissue are described as important for advancing our understanding of brain injuries (Bilston et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1997\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eComputational models have become essential tools for investigating the mechanical properties of brain tissue. Precise characterization of these properties is crucial for developing material constitutive laws, which can subsequently be integrated into finite element models of the head (Chatelin et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). To improve the predictive accuracy of these models, a more precise characterization of the mechanical properties of brain tissue is necessary (Jin et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2013\u003c/span\u003e, Gefen and Margulies, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). Hence, investigating the factors influencing brain tissue material's constitutive parameters is paramount.\u003c/p\u003e \u003cp\u003e \u003cem\u003eEx-vivo\u003c/em\u003e mechanical experiments have consistently demonstrated that brain tissue exhibits both viscoelastic and nonlinear behavior (Takhounts et al., 2003, Hiscox et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). At small strains, regardless of strain rate, brain tissue displays linear viscoelastic properties (Brands et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Constitutive models often describe brain tissue using a nonlinear viscoelastic framework, which aligns with the generalized Maxwell model at small strains (Peters et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). However, significant variability has been reported in the mechanical properties of brain tissue, including storage and loss moduli, which describe linear viscoelastic behavior (Arbogast and Margulies, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1998\u003c/span\u003e, Bilston et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, Brands, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2000\u003c/span\u003e, Hrapko et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, Nicolle et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2004\u003c/span\u003e, Peters et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1997\u003c/span\u003e, Shen et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, Shuck and Advani, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e1972\u003c/span\u003e). This variability in the linear viscoelastic region at small strains (Zhang et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) is also observed under large strains in tension, compression, and shear experiments (Budday et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, Chatelin et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). It's crucial to recognize that many factors could potentially affect the mechanical properties of brain tissue, such as different testing modalities (Cheng and Bilston, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), anatomical location (Prange and Meaney, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2000\u003c/span\u003e, Jin et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2013\u003c/span\u003e, Christ et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, Velardi et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), maturity (Prange and Margulies, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2002\u003c/span\u003e, Dickerson and Dobbing, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1967\u003c/span\u003e), gender (Finan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), interspecies variation (Galford and McElhaney, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1970\u003c/span\u003e, Takhounts et al., 2003), storage conditions (Zhang et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), post-mortem interval (Garo et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2007\u003c/span\u003e, Zhang et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), preconditioning (Hrapko et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2008a\u003c/span\u003e, Nicolle et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), and sample shape (Budday et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOne of the critical issues in the study of brain tissue mechanics is the effect of temperature on tissue stiffness. Despite its importance, only a few studies have addressed this topic (Hrapko et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e, Guan et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, Zhang et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2011\u003c/span\u003e, Zhang et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), and no consensus has been reached. Some studies report increased stiffness at higher temperatures (Zhang et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), while others observed decreased stiffness (Hrapko et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e, Rashid et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) or no significant effect (Arbogast et al., 1997). Another study found that the mechanical properties of brain tissue were significantly influenced by sample temperature only under high strain rates (Guan et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Moreover, investigating the effect of temperature on the constitutive parameters of materials is stated to be highly important (Guan et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), among the studies referenced, only Rashid et al. (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) examined the influence of temperature on the nonlinear parameters of the Ogden model. In the context of dynamic loading, Shen et al. (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) and Hrapko et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e) conducted experimental studies to explore the influence of temperature on the mechanical properties of brain tissue. However, neither of these studies examined the effect of temperature on the constitutive model parameters of the tissue, which could provide more profound mechanical insights into the temperature-dependent behavior of brain tissue. Research on the temperature-dependent mechanical properties of brain tissue remains limited and inconclusive, raising important questions about whether higher temperatures cause brain tissue to stiffen or soften, how viscoelastic parameters vary with temperature, and the role of frequency in these temperature effects.\u003c/p\u003e \u003cp\u003eTo study the influence of temperature and loading frequency on the viscoelastic properties of brain tissue under dynamic loading, experiments were conducted at three temperatures (35\u0026deg;C, 25\u0026deg;C, and 5\u0026deg;C). A dynamic mechanical thermal analyzer (DMTA) was used to characterize the mechanical behavior of bovine brain tissue across thermal and frequency ranges. The experimental data were then employed to develop a viscoelastic constitutive model for brain tissue using a generalized Maxwell framework. This model is designed to enhance the fidelity of computational predictions of brain tissue mechanics under varying thermal and dynamic loading scenarios.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Experimental setup\u003c/h2\u003e \u003cp\u003eFresh bovine brains (n\u0026thinsp;=\u0026thinsp;3) were obtained from a local slaughterhouse and immediately immersed in phosphate-buffered saline (PBS) to prevent osmotic swelling. The brains were transported to the laboratory on ice to maintain tissue integrity. Upon arrival, each brain was dissected along the corpus callosum using a scalpel to yield two symmetrical hemispheres. Cylindrical tissue samples, approximately 25 mm in diameter and 2 mm in height were excised from the midbrain region. Each sample contained a mixture of white and gray matter. Two samples were extracted from each hemisphere. The dimensions were selected to match the plate and gap geometry of the testing device. Frequency sweep tests were performed utilizing a parallel-plate measuring system of the rheometer (Paar Physica MCR300). The tests spanned a frequency range of 0.1 to 100 rad/s, incorporating 16 logarithmically spaced frequency points. It has been reported that the frequency order does not influence the outcomes of the tests (Barnes et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). To enhance grip during testing, sandpaper disks were affixed to the parallel plates. The samples were irrigated with PBS and positioned between the plates, with the upper plate oscillating rotationally while the bottom plate remained stationary. Tests were conducted using the rheometer's Peltier temperature control system at constant temperatures of 5\u0026deg;C, 25\u0026deg;C, and 35\u0026deg;C. The temperature was gradually adjusted between tests to avoid thermal gradients (Shen et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), allowing sufficient time for thermal equilibration before data acquisition. A strain amplitude of 1%, confirmed to be within the linear viscoelastic region (Peters et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1997\u003c/span\u003e, Brands et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1999\u003c/span\u003e, Garo et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2007\u003c/span\u003e, Shen et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, Hrapko et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e), was applied. The results from four individual samples for each specific temperature were averaged to produce representative values. All experiments were conducted within 5 hours of sample collection to minimize microbiological degradation and preserve tissue integrity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Dynamic Viscoelastic Description\u003c/h2\u003e \u003cp\u003eThe Stress (τ) and strain (γ) were calculated as follows (Laun et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2014\u003c/span\u003e):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\tau\\:}=\\frac{2M}{\\pi\\:{R}^{3}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\gamma\\:}=\\frac{\\theta\\:R}{h}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere M is torque, R is plate radius, θ is angular displacement, and h is plate gap height. For dynamic measurements, a sinusoidal shear strain\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\:{\\gamma\\:}\\left(\\text{t}\\right)\\)\u003c/span\u003e\u003c/span\u003e was applied to the sample, defined as (Peters et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1997\u003c/span\u003e):\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\gamma\\:}\\left(\\text{t}\\right)={{\\gamma\\:}}_{0}\\text{sin}\\left(\\omega\\:t\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFor a sufficiently small shear strain amplitude \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\gamma\\:}}_{0}\\)\u003c/span\u003e\u003c/span\u003e, the shear stress will oscillate sinusoidally in the steady state. It will exhibit a phase shift δ and maintain a linear relationship with the strain.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\tau\\:}\\left(\\text{t}\\right)={{\\text{G}}^{\\text{*}}{\\gamma\\:}}_{0}\\text{sin}\\left(\\omega\\:t+\\delta\\:\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe dynamic modulus G*(ω,T) and the phase shift δ(ω,T) depend on both the frequency and the temperature. Subsequently, the dynamic viscoelastic parameters including, storage modulus (G'), loss modulus (G''), and loss factor (tanδ) of each sample can be determined as (Ferry, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1948\u003c/span\u003e):\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\text{G}}^{\\text{*}}=\\:{\\text{G}}^{{\\prime\\:}}+i{\\text{G}}^{{\\prime\\:}{\\prime\\:}},\\:\\:\\left|{\\text{G}}^{\\text{*}}\\right|=\\:\\sqrt{{{\\text{G}}^{{\\prime\\:}}}^{2}+{{\\text{G}}^{{\\prime\\:}{\\prime\\:}}}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\text{G}}^{{\\prime\\:}}={\\text{G}}^{\\text{*}}\\text{cos}\\left(\\delta\\:\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{\\text{G}}^{{\\prime\\:}{\\prime\\:}}={\\text{G}}^{\\text{*}}\\text{sin}\\left(\\delta\\:\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:\\text{tan}\\left(\\delta\\:\\right)=\\frac{{\\text{G}}^{{\\prime\\:}{\\prime\\:}}}{{\\text{G}}^{{\\prime\\:}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe dynamic viscosity (η') could be derived using the following relationship (Fallenstein et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1969\u003c/span\u003e):\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:{\\eta\\:}{\\prime\\:}=\\frac{{\\text{G}}^{{\\prime\\:}{\\prime\\:}}}{\\omega\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe energy dissipated per cycle of deformation can be calculated using the loss modulus and the strain amplitude as (Ferry, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1980\u003c/span\u003e):\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:Energy\\:Dissipation=\\:{\\pi\\:{\\text{G}}^{{\\prime\\:}{\\prime\\:}}{{\\gamma\\:}}_{0}}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Model definition\u003c/h2\u003e \u003cp\u003eTo illustrate the viscoelastic behavior of brain tissue and its dependence on temperature and frequency, the generalized Maxwell model was applied. The model captures the experimental dynamic response of brain tissue at various frequencies and temperatures. The storage modulus of the model and loss modulus, are defined as functions of angular frequency at a constant temperature (Zhang and Gan, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:{{G}^{{\\prime\\:}}}_{model\\left({\\omega\\:},\\text{T}\\right)}={G}_{0}+\\:\\sum\\:_{i=1}^{n}\\frac{{G}_{i}\\left(T\\right){{\\omega\\:}}^{2}{{\\tau\\:}_{i}}^{2}}{1+{{\\omega\\:}}^{2}{{\\tau\\:}_{i}}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\:{{G}^{{\\prime\\:}{\\prime\\:}}}_{model\\left({\\omega\\:},\\text{T}\\right)}=\\:\\sum\\:_{i=1}^{n}\\frac{{G}_{i}\\left(T\\right){\\omega\\:}{\\tau\\:}_{i}}{1+{{\\omega\\:}}^{2}{{\\tau\\:}_{i}}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe model parameters include the temperature (T), steady-state elastic modulus (G\u003csub\u003e0\u003c/sub\u003e​), and the elastic modulus of the i-th Maxwell branch (G\u003csub\u003ei\u003c/sub\u003e). The time constant (τ\u003csub\u003ei\u003c/sub\u003e) for each branch is defined as the ratio of the viscosity coefficient (η\u003csub\u003ei\u003c/sub\u003e​) to G\u003csub\u003ei\u003c/sub\u003e. The number of Maxwell branches is denoted by n. The number of branches was selected to achieve the best fit with the fewest unknown parameters. Based on pilot analysis, the model used in this study consists of one elastic branch and three viscous branches. For each temperature, the parameters (G\u003csub\u003e0\u003c/sub\u003e​ and G\u003csub\u003ei\u003c/sub\u003e​​) were determined by fitting the experimental results (loss and storage modulus). For three Maxwell branches, the time constants were fixed at τ\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.01, τ\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1, and τ\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1 s. The least-squares method was used to optimize the fit to the experimental data by minimizing the sum of squared errors (SSE) (Montgomery et al., 2021).\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\:SSE=\\:\\sum\\:_{i=1}^{n}\\left[{{\\left({G}_{exp}^{{\\prime\\:}}-{G}_{model}^{{\\prime\\:}}\\:\\right)}_{i}}^{2}+{{\\left({G}_{exp}^{{\\prime\\:}{\\prime\\:}}-{G}_{model}^{{\\prime\\:}{\\prime\\:}}\\:\\right)}_{i}}^{2}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere n represents the total number of sets of pairs, which corresponds to the total number of measurements in the respective angular frequency series. To gain a clearer insight into the influence of temperature on the model parameters, the values of G\u003csub\u003e0\u003c/sub\u003e and G\u003csub\u003ei\u003c/sub\u003e were normalized using Eq.\u0026nbsp;\u003cspan refid=\"Equ14\" class=\"InternalRef\"\u003e14\u003c/span\u003e.\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$\\:{G}_{i}^{norm}=\\:\\frac{{G}_{i}}{\\sum\\:_{i=0}^{3}{G}_{i}}\\:,\\:i=0,\\:1,\\:2,\\:3$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eUsing the generalized Maxwell model's normalized constants, the reduced relaxation modulus (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{R}^{norm}\\:)\\:\\)\u003c/span\u003e\u003c/span\u003ecan be plotted for each temperature over time, as defined by Eq.\u0026nbsp;\u003cspan refid=\"Equ15\" class=\"InternalRef\"\u003e15\u003c/span\u003e, to predict the temperature's effect on the stress relaxation behavior of the tissue.\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$$\\:{G}_{R}^{norm}\\:(t,T)={G}_{0}^{norm}\\left(T\\right)+\\sum\\:_{i=1}^{3}{G}_{i}^{norm}\\left(T\\right){e}^{(-\\frac{t}{{\\tau\\:}_{i}})}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates the storage and loss moduli of brain tissue in dynamic shear as a function of frequency, measured at three different temperatures (5\u0026deg;C, 25\u0026deg;C, and 35\u0026deg;C). The storage modulus exhibited a consistent rise with increasing frequency at all tested temperatures, reflecting a more dominant elastic response in the brain tissue at higher frequencies. Similarly, the loss modulus demonstrated an upward trend with frequency, indicating greater energy dissipation as the deformation rate increased. The pattern emerged, showing that both storage and loss moduli were elevated at lower temperatures. This suggests that the brain tissue becomes stiffer and exhibits enhanced energy dissipation capabilities as temperatures decrease.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the average dissipated energy at four frequencies (0.1, 1, 10, and 100 rad/s) for three temperatures (5\u0026deg;C, 25\u0026deg;C, and 35\u0026deg;C). The energy dissipation per unit volume exhibited a consistent increase with rising frequency across all tested temperatures, reflecting the frequency-dependent viscoelastic response of brain tissue. Notably, lower temperatures (5\u0026deg;C) demonstrated significantly higher energy dissipation compared to elevated temperatures (35\u0026deg;C and 25\u0026deg;C), indicating enhanced stiffness and energy loss at reduced thermal conditions. This temperature-dependent disparity became increasingly pronounced at higher frequencies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDynamic viscosity of brain tissue was measured across a frequency range of 0.1\u0026ndash;100 rad/s at three temperatures (5\u0026deg;C, 25\u0026deg;C, and 35\u0026deg;C), revealing distinct temperature- and frequency-dependent behavior (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Findings demonstrated that the dynamic viscosity of brain tissue decreased with increasing frequency, with pronounced temperature effects at low frequencies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo achieve a more thorough understanding of the influence of temperature at constant frequency and the effect of frequency at constant temperature on energy dissipation in the shear response of brain tissue, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the elliptic Lissajous plots for various temperatures across different frequencies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe Generalized Maxwell model was applied to perform curve fitting on the averaged experimental values of the loss modulus and storage modulus. The optimized model parameters, presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, exhibit a monotonic decrease with increasing temperature. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e compares the experimentally averaged complex modulus with the corresponding model values, demonstrating curve-fitting quality. To further illustrate the effect of temperature on the elastic and viscous components of the model, Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents the absolute and normalized model parameters as a function of temperature. Results demonstrated that all absolute parameters of the model decreased with increasing temperature. The normalized parameters indicated that temperature changes significantly impacted the viscoelastic properties of brain tissue. G\u003csub\u003e0\u003c/sub\u003e\u003csup\u003enorm\u003c/sup\u003e demonstrated an increasing trend with higher temperatures, reflecting higher elastic behavior and a decrease in the tissue's elastic nature as temperatures dropped. In contrast, viscous effects became more prominent at lower temperatures. G\u003csub\u003e1\u003c/sub\u003e\u003csup\u003enorm\u003c/sup\u003e showed an increase, and similarly, G\u003csub\u003e2\u003c/sub\u003e\u003csup\u003enorm\u003c/sup\u003e and G\u003csub\u003e3\u003c/sub\u003e\u003csup\u003enorm\u003c/sup\u003e also exhibited rising values as temperatures decreased, emphasizing the dominance of viscous behavior in colder conditions. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrates the predicted outcomes of the generalized Maxwell model for the reduced relaxation modulus of brain tissue at varying temperatures (5\u0026deg;C, 25\u0026deg;C, and 35\u0026deg;C). The results indicate that relaxation behavior was more pronounced at 5\u0026deg;C.\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\u003eViscoelastic parameters of brain tissue at varying temperatures (5\u0026deg;C, 25\u0026deg;C, 35\u0026deg;C).\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=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" 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\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG₀\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eG₁\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eG₂\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eG₃\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT\u0026thinsp;=\u0026thinsp;35\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e297.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e211.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT\u0026thinsp;=\u0026thinsp;25\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e351.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e278.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e79.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e113.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT\u0026thinsp;=\u0026thinsp;5\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e441.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e542.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e146.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e211.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eτ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eA comprehensive understanding of the dynamic properties of brain tissue is essential for advancing research on brain injuries (Bilston et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). Studies, particularly those incorporating accurate material definitions that integrate structural configurations and experimental data, could be reliable tools in the field of brain biomechanics.\u003c/p\u003e \u003cp\u003eTo investigate the effect of temperature on the viscoelastic properties of the brain we conducted oscillatory shear tests. The tests are commonly employed to assess the rate-dependent mechanical properties of soft tissues. In these tests, sinusoidal shear displacements are applied to the sample, creating a time-dependent strain profile. The resulting force is measured and converted to reflect the stress response of the sample. The storage and loss moduli are calculated based on the amplitude and phase angle differences between the steady-state strain and stress responses. These oscillatory tests effectively determine the viscoelastic properties of materials at low and non-destructive strain levels, remaining within the linear viscoelastic strain limit.\u003c/p\u003e \u003cp\u003eIn dynamic frequency sweep tests, all samples showed consistent behavior, with both the storage modulus and loss modulus increasing with frequency. Our experimental results are in good agreement with published data in the literature (Shen et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, Hrapko et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e, Peters et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1997\u003c/span\u003e, Garo et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), although some variations were observed. In this study, the material properties were derived from a combination of white and gray matter, treating the brain as an isotropic material. This approach is consistent with studies confirming the isotropy of brain tissue (Budday et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe influence of temperature on the mechanical properties of brain tissue was investigated. Both the loss modulus and storage modulus were found to be temperature-dependent, with both moduli increasing as temperature decreased. This suggests that brain tissue becomes stiffer and exhibits enhanced energy dissipation capabilities at lower temperatures, a trend that has been reported in previous studies (Shen et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, Hrapko et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e). This behavior reflects a transition in the material's viscoelastic properties, with brain tissue displaying more solid-like behavior at 5\u0026deg;C compared to the more fluid-like behavior observed at 35\u0026deg;C and 25\u0026deg;C. The difference in energy dissipation between temperatures became more pronounced at higher frequencies.\u003c/p\u003e \u003cp\u003eIt has been proposed that examining the impact of temperature on the constitutive parameters of the brain is of great importance (Guan et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Consequently, we explored how temperature influences the parameters of the generalized Maxwell model. Temperature significantly influenced the viscoelastic model parameters of brain tissue. This study found that all absolute model parameters decreased as temperature increased. Considering normalized model parameters, higher temperatures enhanced elastic behavior, while lower temperatures increased viscous effects. The model in this study was developed using experimental data acquired under shear dynamic loading conditions at a 1% strain amplitude. To validate its predictive capability for brain tissue stress relaxation, Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e compares the Generalized Maxwell model\u0026rsquo;s predictions of the reduced relaxation modulus at 35\u0026deg;C with experimental data from Nicolle et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) at 37\u0026deg;C. The analysis focuses on shear relaxation behavior over a 2-second duration at 1% strain, due to closely aligned testing parameters (temperature, loading mode, strain amplitude) between studies. Results demonstrated general agreement between model predictions and experimental data across the evaluated timescale. The stiffer response observed in Nicolle et al.'s dataset likely stems from their use of tissue samples with a 24\u0026ndash;48-hour post-mortem interval, in contrast to the shorter 5-hour post-mortem interval maintained in the present study. Garo et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) conducted oscillatory shear tests with 1% strain amplitude and frequencies ranging from 1 to 10 Hz. They found that the stress response was dependent on post-mortem time, with the tissue becoming stiffer as time increased. Post-mortem time selection in dynamic testing varied significantly across studies. Differences in post-mortem intervals among studies, such as Shen et al. (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) (48\u0026ndash;120 hours), Peters et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1997\u003c/span\u003e) (27\u0026ndash;51 hours), and Hrapko et al. (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) (5 hours), may account for discrepancies in reported mechanical properties.\u003c/p\u003e \u003cp\u003eShen et al. (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) reported an increasing trend in both the loss modulus and storage modulus of the brain as the temperature decreased. Hrapko et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e) observed that the dynamic shear modulus of brain tissue significantly depends on temperature, with increased hardening as the temperature decreases. Zhang et al. (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) found that, at a strain of 10%, the engineering stress and tangent modulus of the brain at 37\u0026deg;C were 3.5 and 3.2 times higher than at 0\u0026deg;C, respectively. When the strain increased to 70%, these values were 2.4 and 2.2 times higher at 37\u0026deg;C compared to 0\u0026deg;C. Rashid et al. (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) found that the temperature at which porcine brain tissue is stored or preserved before testing significantly influences the mechanical properties of the brain tissue, even when the tests are carried out at the same temperatures. Guan et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) noted that temperature significantly affects the engineering stress of the brain at high strain rates, particularly at 13\u0026deg;C. No significant differences were observed between 20\u0026deg;C and 37\u0026deg;C at both low and high strain rates. Our results on decreasing stiffness with increasing temperature align with the works of Hrapko et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008b\u003c/span\u003e), Shen et al. (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), Rashid et al. (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), and Guan et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), but contradict the study by Zhang et al. (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). It is significant to note that Zhang et al. (2010) investigated the effects of temperatures on the high strain-rate material properties of porcine brain tissues using a split-Hopkinson pressure bar (SHPB) at an approximate strain rate of 2487 s⁻\u0026sup1;, relevant to blast scenarios. Furthermore, among the studies mentioned, only Rashid et al. (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) investigated the impact of temperature on the model parameters of brain tissue, utilizing a one-term Ogden model. Their findings indicated that raising the tissue's storage temperature resulted in a decline in the initial shear modulus. Although their research concentrated on the nonlinear domain, the observed temperature effects align with our findings in the linear domain. Our findings show that temperature-dependent differences in mechanical response are more pronounced at higher frequencies, consistent with Guan et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), who noted significant temperature effects on engineering stress at high strain rates. The findings of Birkl et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) reveal that the temperature coefficient in brain tissue is strongly influenced by cellular structures that restrict molecular mobility. Reduced molecular mobility at lower temperatures and stiffness changes underscore the interconnected thermal, structural, and mechanical behavior of brain tissue.\u003c/p\u003e \u003cp\u003eIn our investigation, the dynamic viscosity measured at an angular frequency of 63.1 rad/s (approximately 10 Hz) yielded values of 66.6 P, 95.5 P, and 144.9 P for temperatures of 35\u0026deg;C, 25\u0026deg;C, and 5\u0026deg;C, respectively. Notably, while the original results were acquired in pascal-seconds (Pa\u0026middot;s), they were converted to poise (1 Pa\u0026middot;s\u0026thinsp;=\u0026thinsp;10 P) to standardize comparisons with prior literature. These findings align closely with the work of Fallenstein et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1969\u003c/span\u003e), who reported dynamic shear viscosities of 56\u0026ndash;96 P for in-vitro human brain tissue at comparable frequencies (9\u0026ndash;10 Hz). Earlier studies reported lower viscosity values. For instance, Koeneman (1966, unpublished M.S. thesis, Case Institute of Technology, USA) documented a dynamic viscosity of 43.5 P, while Franke (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1956\u003c/span\u003e) obtained a shear viscosity of 14.9 P through impedance measurements on in vitro pig brain tissue. This discrepancy likely arises from the higher testing frequencies (100\u0026ndash;500 Hz) employed in these studies, as viscoelastic materials exhibit frequency-dependent mechanical behavior characterized by reduced viscosity at elevated frequencies. Additionally, interspecies variations between human and non-primate brain tissue properties may further contribute to observed differences (Fallenstein et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1969\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOur experiments revealed that the storage and loss moduli of brain tissue increased with frequency, while higher temperatures led to a decrease in tissue stiffness. Building on the methodology of Najafidoust et al. (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), who observed a temperature-driven stiffening in periodontal ligaments and a frequency-dependent rise in storage modulus (with loss modulus attenuation at higher frequencies), we applied their framework to brain tissue. Despite methodological alignment, our results diverged markedly. Considering other soft tissues, studies have shown that skin's compressive stiffness increased with rising temperature (Bianchi et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), whereas the tensile stiffness of skin and lumbar spine ligaments decreased (Xu et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2008\u003c/span\u003e, Bass et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Under dynamic loading, some tissues exhibited reduced storage modulus at higher temperatures, including the stapedial annular ligament (dynamic shear loading) (Zhang and Gan, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), tympanic membrane (dynamic tensile loading) (Zhang and Gan, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), and vocal folds (dynamic shear loading) (Chan, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). The complex moduli of subcutaneous adipose tissue also decreased under dynamic shear loading as temperature increased (Geerligs et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), which is similar to what we observed for brain tissue. These findings underscore the diverse, tissue-specific effects of temperature on the mechanical properties of soft tissues.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eOur study investigated the influence of temperature and frequency on the dynamic properties of brain tissue under shear loading, focusing on temperature-driven changes in viscoelastic model parameters. Findings showed that storage and loss moduli decreased with rising temperature, indicating softening, while moduli increased with frequency, with greater temperature-related disparities at higher frequencies. Dynamic viscosity was higher at low temperatures and frequencies but decreased as frequency increased. The generalized Maxwell model revealed that absolute parameters declined with temperature, while normalized parameters showed increased elasticity at higher temperatures and stronger viscosity at lower temperatures. These findings provide insights into the temperature-sensitive mechanics of brain tissue, supporting advancements in computational modeling and brain injury research.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e. The authors have no acknowledgments to declare\u003c/p\u003e\n\u003cp\u003eThe authors have not received any funding for this research. \u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eARBOGAST, K. B. \u0026amp; MARGULIES, S. S. 1998. Material characterization of the brainstem from oscillatory shear tests. \u003cem\u003eJournal of biomechanics,\u003c/em\u003e 31\u003cstrong\u003e,\u003c/strong\u003e 801-807. https://doi.org/10.1016/S0021-9290(98)00068-2\u003c/li\u003e\n\u003cli\u003eARBOGAST, K. B., THIBAULT, K. L., PINHEIRO, B. S., WINEY, K. I. \u0026amp; MARGULIES, S. S. 1997. 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Dynamic properties of human stapedial annular ligament measured with frequency\u0026ndash;temperature superposition. \u003cem\u003eJournal of Biomechanical Engineering,\u003c/em\u003e 136\u003cstrong\u003e,\u003c/strong\u003e 081004. https://doi.org/10.1115/1.4027668\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Brain, dynamic shear response, Temperature-effect, Viscoelastic behavior","lastPublishedDoi":"10.21203/rs.3.rs-6196580/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6196580/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn traffic crashes, mechanical loads are applied within milliseconds, resembling frequency sweeps in dynamic mechanical testing. While brain mechanics have been widely studied, the effect of temperature on brain tissue’s mechanical response remains unclear, with limited and inconsistent findings. Additionally, few studies have examined how temperature affects brain tissue model parameters, which could provide a more detailed mechanical analysis of such effects. To address this, we conducted dynamic shear experiments on bovine brain tissue within the linear viscoelastic region and developed a generalized Maxwell model. Our primary objective was to investigate the influence of temperature on the dynamic properties of brain tissue, focusing on temperature-dependent changes in viscoelastic parameters, while also assessing frequency effects. Results showed that storage and loss moduli increased with frequency at all tested temperatures (5°C, 25°C, and 35°C), indicating stronger elastic responses and greater energy dissipation at higher frequencies. Both moduli decreased with rising temperature, demonstrating a softening effect, with more pronounced differences at 5°C. Dynamic viscosity was higher at lower temperatures, especially at low frequencies, but differences diminished at higher frequencies. The generalized Maxwell model revealed that absolute parameters decreased with temperature, while normalized parameters showed increased elasticity at higher temperatures and stronger viscosity at lower temperatures. These findings provide detailed insights into the temperature-dependent mechanical properties of brain tissue, enhancing computational simulations of brain behavior under varying thermal conditions and advancing research on brain injuries and biomechanical studies.\u003c/p\u003e","manuscriptTitle":"Temperature and Frequency Dependent Viscoelasticity of Brain Tissue under Dynamic Shear Loading","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-13 13:50:45","doi":"10.21203/rs.3.rs-6196580/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"586a300c-da6a-4936-ab38-c74d5c5703e3","owner":[],"postedDate":"March 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-04-01T11:38:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-13 13:50:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6196580","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6196580","identity":"rs-6196580","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}