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1. A Robust Multiscale and Multiphasic Structure-Based Modeling Framework for the Intervertebral Disc

   https://doi.org/10.3389/fbioe.2021.685799  

   Zhou, Minhao; Lim, Shiyin; O’Connell, Grace D. (June 2021, Frontiers in Bioengineering and Biotechnology)

   A comprehensive understanding of multiscale and multiphasic intervertebral disc mechanics is crucial for designing advanced tissue engineered structures aiming to recapitulate native tissue behavior. The bovine caudal disc is a commonly used human disc analog due to its availability, large disc height and area, and similarities in biochemical and mechanical properties to the human disc. Because of challenges in directly measuring subtissue-level mechanics, such as in situ fiber mechanics, finite element models have been widely employed in spinal biomechanics research. However, many previous models use homogenization theory and describe each model element as a homogenized combination of fibers and the extrafibrillar matrix while ignoring the role of water content or osmotic behavior. Thus, these models are limited in their ability in investigating subtissue-level mechanics and stress-bearing mechanisms through fluid pressure. The objective of this study was to develop and validate a structure-based bovine caudal disc model, and to evaluate multiscale and multiphasic intervertebral disc mechanics under different loading conditions and with degeneration. The structure-based model was developed based on native disc structure, where fibers and matrix in the annulus fibrosus were described as distinct materials occupying separate volumes. Model parameters were directly obtained from experimental studies without calibration. Under the multiscale validation framework, the model was validated across the joint-, tissue-, and subtissue-levels. Our model accurately predicted multiscale disc responses for 15 of 16 cases, emphasizing the accuracy of the model, as well as the effectiveness and robustness of the multiscale structure-based modeling-validation framework. The model also demonstrated the rim as a weak link for disc failure, highlighting the importance of keeping the cartilage endplate intact when evaluating disc failure mechanisms in vitro . Importantly, results from this study elucidated important fluid-based load-bearing mechanisms and fiber-matrix interactions that are important for understanding disease progression and regeneration in intervertebral discs. In conclusion, the methods presented in this study can be used in conjunction with experimental work to simultaneously investigate disc joint-, tissue-, and subtissue-level mechanics with degeneration, disease, and injury. 

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2. Multiscale mechanical characterization and computational modeling of fibrin gels

   https://doi.org/10.1016/j.actbio.2023.03.026  

   Jimenez, Julian M.; Tuttle, Tyler; Guo, Yifan; Miles, Dalton; Buganza-Tepole, Adrian; Calve, Sarah (May 2023, Acta Biomaterialia)

   Fibrin is a naturally occurring protein network that forms a temporary structure to enable remodeling during wound healing. It is also a common tissue engineering scaffold because the structural properties can be controlled. However, to fully characterize the wound healing process and improve the design of regenerative scaffolds, understanding fibrin mechanics at multiple scales is necessary. Here, we present a strategy to quantify both the macroscale (1–10 mm) stress-strain response and the deformation of the mesoscale (10–1000 µm) network structure during unidirectional tensile tests. The experimental data were then used to inform a computational model to accurately capture the mechanical response of fibrin gels. Simultaneous mechanical testing and confocal microscopy imaging of fluorophore-conjugated fibrin gels revealed up to an 88% decrease in volume coupled with increase in volume fraction in deformed gels, and non-affine fiber alignment in the direction of deformation. Combination of the computational model with finite element analysis enabled us to predict the strain fields that were observed experimentally within heterogenous fibrin gels with spatial variations in material properties. These strategies can be expanded to characterize and predict the macroscale mechanics and mesoscale network organization of other heterogeneous biological tissues and matrices. 

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3. Torque- and Muscle-Driven Flexion Induce Disparate Risks of In Vitro Herniation: A Multiscale and Multiphasic Structure-Based Finite Element Study

   https://doi.org/10.1115/1.4053402  

   Zhou, Minhao; Huff, Reece D.; Abubakr, Yousuf; O'Connell, Grace D. (June 2022, Journal of Biomechanical Engineering)

   Abstract The intervertebral disc is a complex structure that experiences multiaxial stresses regularly. Disc failure through herniation is a common cause of lower back pain, which causes reduced mobility and debilitating pain, resulting in heavy socioeconomic burdens. Unfortunately, herniation etiology is not well understood, partially due to challenges in replicating herniation in vitro. Previous studies suggest that flexion elevated risks of herniation. Thus, the objective of this study was to use a multiscale and multiphasic finite element model to evaluate the risk of failure under torque- or muscle-driven flexion. Models were developed to represent torque-driven flexion with the instantaneous center of rotation (ICR) located on the disc, and the more physiologically representative muscle-driven flexion with the ICR located anterior of the disc. Model predictions highlighted disparate disc mechanics regarding bulk deformation, stress-bearing mechanisms, and intradiscal stress–strain distributions. Specifically, failure was predicted to initiate at the bone-disc boundary under torque-driven flexion, which may explain why endplate junction failure, instead of herniation, has been the more common failure mode observed in vitro. By contrast, failure was predicted to initiate in the posterolateral annulus fibrosus under muscle-driven flexion, resulting in consistent herniation. Our findings also suggested that muscle-driven flexion combined with axial compression could be sufficient for provoking herniation in vitro and in silico. In conclusion, this study provided a computational framework for designing in vitro testing protocols that can advance the assessment of disc failure behavior and the performance of engineered disc implants. 

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4. On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

   https://doi.org/10.1063/5.0085025  

   Guo, Yifan; Mofrad, Mohammad R.; Tepole, Adrian Buganza (September 2022, Biophysics Reviews)

   Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology. 

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5. Quantifying Localized Stresses in the Matrix of a Fiber‐Reinforced Composite via Mechanophores

   https://doi.org/10.1002/macp.202300298  

   Haque, Nazmul; Gohl, Jared; Chang, Chia‐Chih; Chang, Hao Chun; Davis, Chelsea S. (December 2023, Macromolecular Chemistry and Physics)

   Abstract Understanding the stress distribution within fiber‐reinforced polymers (FRPs) is critical to extending their operational lifespan. The integration of mechanoresponsive molecular force probes, referred to as mechanophores, presents a potential solution by enabling direct monitoring of stress concentrations. In this study, spiropyran (SP) mechanophores (MPs) are embedded within a polydimethylsiloxane (PDMS) matrix to visualize stress localization during loading within a single fiber‐reinforced framework. The SP mechanophore undergoes a transition from a non‐fluorescent state to an active state (merocyanine) through isomerization in response to mechanical forces. Using a single fiber mounted axially within the matrix, the fundamental failure modes observed in conventional fiber‐reinforced composites are replicated. Samples are strained under uniaxial tensile loading along the fiber direction and the localization of stresses is observed via MP activation. Stresses are concentrated in the matrix near the fiber region that gradually decreases away from the fiber surface. Confocal microscopy is used to visualize mechanophore activation and quantitatively assess fluorescence intensity. Finite element modeling is used to develop a calibration to quantify the stresses based on the observed fluorescence intensity. These outcomes underscore the viability of employing these mechanoresponsive molecules as a potential means to visualize real‐time stress distribution, thereby facilitating the design of high‐performance composites. 

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