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The anatomy of (a) cervical and (b) lumbar facet capsular ligaments (FCLs) and their relative locations on the spine. The cervical FCL is roughly oriented in superior-inferior direction, whereas the lumbar FCL runs in the lateral-medial direction. (Online version in colour.)
Source publication
Excessive deformation of nerve fibres (axons) in the spinal facet capsular ligaments (FCLs) can be a cause of pain. The axons are embedded in the fibrous extracellular matrix (ECM) of FCLs, so understanding how local fibre organization and micromechanics modulate their mechanical behaviour is essential. We constructed a computational discrete-fibre...
Context in source publication
Citations
... The FCL is primarily made up of type I collagen [64]. Experimental works have shown that reorientation of the Engineering with Computers collagen ECM during loading is responsible for causing pain in the FCL [65]. This fiber level reorientation is not possible to capture using homogenized single-scale continuum models such as the Holzapfel-Gasser-Ogden (HGO) model. ...
... Ban et al. observed that the cervical FCL contains regions of similarly oriented collagen fibers [64]. It is suspected that these regions of oriented fibers may contribute to important mechanical processes such as the onset of collagen fiber reorientation, which has been experimentally linked to pain [65]. A complete description of our hypotheses and the modeling work required to explicate them is beyond the scope of this paper. ...
This article presents MuMFiM, an open-source application for multiscale modeling of fibrous materials on massively parallel computers. MuMFiM uses two scales to represent fibrous materials such as biological network materials (extracellular matrix, connective tissue, etc.). It is designed to make use of multiple levels of parallelism, including distributed parallelism of the macro- and micro-scales as well as GPU-accelerated data-parallelism of the microscale. Scaling results of the GPU accelerated microscale show that solving microscale problems concurrently on the GPU can lead to a 1000x speedup over the solution of a single RVE on the GPU. In addition, we show nearly optimal strong and weak scaling results of MuMFiM on up to 128 nodes of AiMOS (Rensselaer Polytechnic Institute) which is composed of IBM AC922 nodes with 6 Volta V100 GPU and 2 20 core Power 9 CPUs each. We also show how MuMFiM can be used to solve problems of interest to the broader engineering community, in particular providing an example of the facet capsule ligament (FCL) of the human spine undergoing uniaxial extension.
... Even trying to focus on the dermis alone, regional changes in collagen ultrastructure as well as other factors of structural composition of the tissue lead to different mechanical behavior from one location to another [42]. Thus, a common strategy to model soft tissue is through multiscale approaches [43]. ...
... Multiscale models of brain tissue have been developed mainly for the white matter, with particular emphasis on the brain stem and the corpus callosum (CC). Both regions are characterized by bundles of highly oriented axon fibers [23][24][25][26][27][28][29][30][31][32][33] . For the brain RVE, most studies proposed a micrometer-scale cubic geometry comprising a limited number of axons modeled as straight or wavy cylindrical inclusions uniformly distributed within a ground matrix 24,27,30,33 . ...
In this study, we propose a novel micromechanical model for the brain white matter, which is described as a heterogeneous material with a complex network of axon fibers embedded in a soft ground matrix. We developed this model in the framework of RVE-based multiscale theories in combination with the finite element method and the embedded element technique for embedding the fibers. Microstructural features such as axon diameter, orientation and tortuosity are incorporated into the model through distributions derived from histological data. The constitutive law of both the fibers and the matrix is described by isotropic one-term Ogden functions. The hyperelastic response of the tissue is derived by homogenizing the microscopic stress fields with multiscale boundary conditions to ensure kinematic compatibility. The macroscale homogenized stress is employed in an inverse parameter identification procedure to determine the hyperelastic constants of axons and ground matrix, based on experiments on human corpus callosum. Our results demonstrate the fundamental effect of axon tortuosity on the mechanical behavior of the brain’s white matter. By combining histological information with the multiscale theory, the proposed framework can substantially contribute to the understanding of mechanotransduction phenomena, shed light on the biomechanics of a healthy brain, and potentially provide insights into neurodegenerative processes.
... One objective of FE models is to estimate the stresses and strains in the spinal tissues under various loading conditions since such measurements are difficult to make in experimental examinations. [23][24][25][26][27] The excessive predicted macroscopic stress and strain within the spinal tissues of such FE models can be used to determine the microscopic tension on the afferent fibers embedded in the FCL 28,29 and potentially can be associated to pain. Such FE models can ultimately facilitate the development of subject-specific models that can be adopted as a complementary tool in clinical settings to advance prevention, diagnosis, and treatment plans in cervical injuries. ...
... suggested by others.28,43,56 Because subject-specific structural information is not obtainable in vivo, this result points to a limitation of the proposed approach: the ability to describe detailed, small-scale behavior of the tissue is limited by our ability to describe its smallscale material properties. ...
... Because subject-specific structural information is not obtainable in vivo, this result points to a limitation of the proposed approach: the ability to describe detailed, small-scale behavior of the tissue is limited by our ability to describe its smallscale material properties. For instance, to study the effect of the macroscopic loading mechanisms on the local microscopic structural deformation surrounding a neuron in the ligament, a detailed structure-based multiscale model would be needed.28,29,57 If, however, the overall average strain in the ligament in different physiological motion is one's objective, then a simple NH model could generate an acceptable estimate of strain values. ...
Background
To understand the facet capsular ligament's (FCL) role in cervical spine mechanics, the interactions between the FCL and other spinal components must be examined. One approach is to develop a subject‐specific finite element (FE) model of the lower cervical spine, simulating the motion segments and their components' behaviors under physiological loading conditions. This approach can be particularly attractive when a patient's anatomical and kinematic data are available.
Methods
We developed and demonstrated methodology to create 3D subject‐specific models of the lower cervical spine, with a focus on facet capsular ligament biomechanics. Displacement‐controlled boundary conditions were applied to the vertebrae using kinematics extracted from biplane videoradiography during planar head motions, including axial rotation, lateral bending, and flexion–extension. The FCL geometries were generated by fitting a surface over the estimated ligament–bone attachment regions. The fiber structure and material characteristics of the ligament tissue were extracted from available human cervical FCL data. The method was demonstrated by application to the cervical geometry and kinematics of a healthy 23‐year‐old female subject.
Results
FCL strain within the resulting subject‐specific model were subsequently compared to models with generic: (1) geometry, (2) kinematics, and (3) material properties to assess the effect of model specificity. Asymmetry in both the kinematics and the anatomy led to asymmetry in strain fields, highlighting the importance of patient‐specific models. We also found that the calculated strain field was largely independent of constitutive model and driven by vertebrae morphology and motion, but the stress field showed more constitutive‐equation‐dependence, as would be expected given the highly constrained motion of cervical FCLs.
Conclusions
The current study provides a methodology to create a subject‐specific model of the cervical spine that can be used to investigate various clinical questions by coupling experimental kinematics with multiscale computational models.
... The FCL is primarily made up of type I collagen [51]. Experimental works have shown that reorientation of the collagen ECM during loading is responsible for causing pain in the FCL [52]. This fiber level reorientation is not possible to capture using homogenized single-scale continuum models such as the Holzapfel-Gasser-Ogden (HGO) model. ...
... al. observed that the cervical FCL contains regions of similarly oriented collagen fibers [51]. It is suspected that these regions of oriented fibers may contribute to important mechanical processes such as the onset of collagen fiber reorientation, which has been experimentally linked to pain [52]. A complete description of our hypotheses and the modeling work required to explicate them is beyond the scope of this paper. ...
This article presents MuMFiM, an open source application for multiscale modeling of fibrous materials on massively parallel computers. MuMFiM uses two scales to represent fibrous materials such as biological network materials (extracellular matrix, connective tissue, etc.). It is designed to make use of multiple levels of parallelism, including distributed parallelism of the macro and microscales as well as GPU accelerated data-parallelism of the microscale. Scaling results of the GPU accelerated microscale show that solving microscale problems concurrently on the GPU can lead to a 1000x speedup over the solution of a single RVE on the GPU. In addition, we show nearly optimal strong and weak scaling results of MuMFiM on up to 128 nodes of AiMOS (Rensselaer Polytechnic Institute) which is composed of IBM AC922 nodes with 6 Volta V100 GPU and 2 20 core Power 9 CPUs each. We also show how MuMFiM can be used to solve problems of interest to the broader engineering community, in particular providing an example of the facet capsule ligament (FCL) of the human spine undergoing uniaxial extension.
... Multiscale models of brain tissue have been developed mainly for the white matter, with particular emphasis on the brain stem and the corpus callosum (CC). Both regions are characterized by bundles of highly oriented axon fibers [23][24][25][26][27][28][29][30][31][32][33] . For the brain RVE, most studies proposed a micrometer-scale cubic geometry comprising a limited number of axons modeled as straight or wavy cylindrical inclusions uniformly distributed within a ground matrix 24,27,30,33 . ...
... The bottom plate was constrained with a concentrated force applied to the top plate. In addition, symmetric boundary conditions for x = 0 and y = 0 planes were deployed taking into consideration of the computational efficiency and geometric symmetry [31]. In the second step, post-buckling analysis was conducted. ...
In this study, a novel artificial intervertebral disc implant with modified "Bucklicrystal" structure was designed and 3D printed using thermoplastic polyurethane. The new implant has a unique auxetic structure with building blocks joined "face-to-face". The accompanied negative Poisson's ratio enables its excellent energy absorption and stability under compression. The deformation and load distribution behavior of the implant under various loading conditions (bending, torsion, extension and flexion) has been thoroughly evaluated through finite element method. Results show that, compared to natural intervertebral disc and conventional 3D implant, our new implant exhibits more effective stress transfer and attenuation under practical loading conditions. The implant's ability to contract laterally under compression can be potentially used to alleviate the symptoms of lumbar disc herniation. Finally, the biocompatibility of the implant was assessed in vitro and its ability to restore the physiological function of the disc segment was validated in vivo using an animal model.
... Since there may be fewer of these intact tethers to the surrounding matrix to transmit force to the neuron (Sun et al. 2019), greater matrix deformation would be required to transmit the same amount of force, explaining the increase in strain thresholds that is observed in the treated NCCs (Table 1). Indeed, computational approaches modeling embedded nerve fibers in a collagen network which simulates this in vitro system find that increasing the network fiber volume concentration, which would increase the number of adhesions between the extracellular matrix and neuron, also increases the average strain across the neuron during macroscopic axial and transverse loading (Zarei et al. 2017b). NMDA receptors also contain mechanosensitive domains that provide feedback to the neuronal cytoskeleton (Wyszynski et al. 1997;Lei et al. 2001;Singh et al. 2012), with the C-terminus of the NR2B domain binding to the actin cytoskeleton indirectly through α-actinin (Wyszynski et al. 1997;Lei et al. 2001). ...
... Understanding the magnitude of load experienced by neurons embedded in the facet capsular ligament is a multiscale problem (Zarei et al. 2017b). Macroscopic loading to the ligament surrogate translates to fiber-level loading and local mechanics dictate the loading to the afferent neurons (Zarei et al. 2017b;Middendorf et al. 2021). ...
... Understanding the magnitude of load experienced by neurons embedded in the facet capsular ligament is a multiscale problem (Zarei et al. 2017b). Macroscopic loading to the ligament surrogate translates to fiber-level loading and local mechanics dictate the loading to the afferent neurons (Zarei et al. 2017b;Middendorf et al. 2021). As such, the microstructural organization and fiber-level mechanical properties of the ligament (or collagen matrix) are important in estimating the loads experienced by the neurons, and the extent to which integrin receptors translate fiber-level stresses to the neurons. ...
Stretch injury of the facet capsular ligament is a cause of neck pain, inducing axonal injury, neuronal hyperexcitability, and upregulation of pain neuromodulators. Although thresholds for pain and collagen reorganization have been defined and integrins can modulate pain signaling with joint trauma, little is known about the role of integrin signaling in neuronal dysfunction from tensile loading of the innervated capsular ligament. Using a well-characterized biomimetic collagen gel model of the capsular ligament’s microstructure and innervation, this study evaluated extrasynpatic expression of N-Methyl-d-Aspartate receptor subtype 2B (NR2B) as a measure of neuronal dysfunction following tensile loading and determined mechanical thresholds for its upregulation in primary sensory neurons, with and without integrin inhibition. Collagen gels with dissociated dorsal root ganglion neurons (n = 16) were fabricated; a subset of gels (n = 8) was treated with the β1 integrin subunit inhibitor, TC-I15. Gels were stretched to failure in tension and then immunolabeled for axonal NR2B. Inhibiting the integrin subunit does not change the failure force (p = 0.12) or displacement (p = 0.44) but does reduce expression of the β1 subunit by 41% (p < 0.001) and decrease axonal NR2B expression after stretch (p = 0.018). Logistic regressions estimating the maximum principal strain threshold for neuronal dysfunction as evaluated by Analysis of Covariance determine that integrin inhibition increases (p = 0.029) the 50th percentile strain threshold (7.1%) above the threshold for upregulation in untreated gels (6.2%). These results suggest that integrin contributes to stretch-induced neuronal dysfunction via neuron–integrin–collagen interactions.
... behaviors obtained using the nonaffine fiber kinematics. Several multiscale simulation techniques are developed to investigate the material structure-function relationship (Chandran et al. 2008;Zarei et al. 2017;Thomas et al. 2019), and the size of representative volume element is identified (Shahsavari and Picu 2013;D'Amore et al. 2014). Lake et al. (2012) developed a two-component microscale model to study the interaction between collagen and matrix material in collagen-agarose co-gels. ...
Understanding the structure-function relationship of biomaterials can provide insights into different diseases and advance numerous biomedical applications. This paper presents a finite element-based computational framework to model biomaterials containing a three-dimensional fiber network at the microscopic scale. The fiber network is synthetically generated by a random walk algorithm, which uses several random variables to control the fiber network topology such as fiber orientations and tortuosity. The geometric information of the generated fiber network is stored in an array-like data structure and incorporated into the nonlinear finite element formulation. The proposed computational framework adopts the affine fiber kinematics, based on which the fiber deformation can be expressed by the nodal displacement and the finite element interpolation functions using the isoparametric relationship. A variational approach is developed to linearize the total strain energy function and derive the nodal force residual and the stiffness matrix required by the finite element procedure. Four numerical examples are provided to demonstrate the capabilities of the proposed computational framework, including a numerical investigation about the relationship between the proposed method and a class of anisotropic material models, a set of synthetic examples to explore the influence of fiber locations on material local and global responses, a thorough mesh-sensitivity analysis about the impact of mesh size on various numerical results, and a detailed case study about the influence of material structures on the performance of eggshell-membrane-hydrogel composites. The proposed computational framework provides an efficient approach to investigate the structure-function relationship for biomaterials that follow the affine fiber kinematics.
... The significant change in collagen kinematics observed with stretch likely underlies the elevated substance P in co-cultures without an inhibitor (Figure 8). This notion is supported by a body of work demonstrating that, in collagen networks, loadinduced cellular responses are triggered by reorganization of the local fiber network surrounding its embedded cells (Sander et al., 2009;Bottini and Firestein, 2013;Zhang et al., 2016;Zarei et al., 2017). Such cellular responses include nociceptive signaling (Zhang et al., 2016;Zhang et al., 2017;Zhang et al., 2018b;Zarei et al., 2017). ...
... This notion is supported by a body of work demonstrating that, in collagen networks, loadinduced cellular responses are triggered by reorganization of the local fiber network surrounding its embedded cells (Sander et al., 2009;Bottini and Firestein, 2013;Zhang et al., 2016;Zarei et al., 2017). Such cellular responses include nociceptive signaling (Zhang et al., 2016;Zhang et al., 2017;Zhang et al., 2018b;Zarei et al., 2017). In particular, stretch-induced kinematic rearrangement of collagen fibers disrupts the α 2 ß 1 -integrin adhesion between collagen molecules and the neuronal cell surface (Jokinen et al., 2004). ...
Chronic joint pain is a major health problem that can result from abnormal loading of the innervated ligamentous capsule that surrounds synovial joints. The matrix metalloproteinases-1 (MMP-1) and MMP-9 are hypothesized pain mediators from stretch-induced injuries since they increase in pathologic joint tissues and are implicated in biomechanical and nociceptive pathways that underlay painful joint injuries. There is also emerging evidence that MMP-1 and MMP-9 have mechanistic interactions with the nociceptive neuropeptide substance P. Yet, how a ligament stretch induces painful responses during sub-failure loading and whether MMP-1 or MMP-9 modulates nociception via substance P are unknown. We used a neuron–fibroblast co-culture collagen gel model of the capsular ligament to test whether a sub-failure equibiaxial stretch above the magnitude for initiating nociceptive responses in neurons also regulates MMP-1 and MMP-9. Pre-stretch treatment with the MMP inhibitor ilomastat also tested whether inhibiting MMPs attenuates the stretch-induced nociceptive responses. Because of the role of MMPs in collagen remodeling, collagen microstructural kinematics were measured in all tests. Co-culture gels were incubated for one week in either normal conditions, with five days of ilomastat treatment, or with five days of a vehicle control solution before a planar equibiaxial stretch that imposed strains at magnitudes that induce pain in vivo and increase nociceptive modulators in vitro. Force, displacement, and strain were measured, and polarized light imaging captured collagen fiber kinematics during loading. At 24 h after stretch, immunolabeling quantified substance P, MMP-1, and MMP-9 protein expression. The same sub-failure equibiaxial stretch was imposed on all co-cultures, inducing a significant re-organization of collagen fibers (p ≤ 0.031) indicative of fiber realignment. Stretch induces a doubling of substance P expression in normal and vehicle-treated co-cultures (p = 0.038) that is prevented with ilomastat treatment (p = 0.114). Although MMP-1 and MMP-9 expression are unaffected by the stretch in all co-culture groups, ilomastat treatment abolishes the correlative relationships between MMP-1 and substance P (p = 0.002; R 2 = 0.13) and between MMP-1 and MMP-9 (p = 0.007; R 2 = 0.11) that are detected without an inhibitor. Collectively, these findings implicate MMPs in a painful ligamentous injury and contribute to a growing body of work linking MMPs to nociceptive-related signaling pathways and/or pain.
