Image-based multiscale mechanical modeling shows the importance of structural heterogeneity in the human lumbar facet capsular ligament

Residual Strain and Joint Pressurization Maintain Collagen Tension for On-Joint Lumbar Facet Capsular Ligaments

Modeling the lumbar facet capsular ligament's (FCL) mechanical behavior under various physiological motions has often been a challenge due to limited knowledge about the on-joint in situ ligament state arising from attachment to the bone or other internal loads. Building on prior work, this study presents an enhanced computational model of the lumbar facet capsular ligament by incorporating residual strain and joint pressurization strain, factors neglected in prior models. Further, the model can predict strain and stress distribution across the ligament under various spinal motions, highlighting the influence of the ligament's attachment to the bone, internal synovial fluid pressurization, and distribution of collagen fiber alignment on the overall mechanical response of the ligament. Joint space inflation was found to influence the total observed stress and strain fields, both at rest and during motion. A significant portion of the ligament was found to be in tension, even in the absence of external load. Additionally, the model's ability to account for residual strain offers a more realistic portrayal of the collagen fibers and elastin matrix's role in ligament mechanics. We conclude that (1) computational models of the lumbar facet capsular ligament should not assume that the ligament is unloaded when the joint is in its neutral position, and (2) the ligament is nearly always in tension, which may be important in terms of its long-term growth and remodeling.

Three-dimensional fiber orientation mapping of the human brain at micrometer resolution

The accurate measurement of three-dimensional (3D) fiber orientation in the brain is crucial for reconstructing fiber pathways and studying their involvement in neurological diseases. Comprehensive reconstruction of axonal tracts and small fascicles requires high-resolution technology beyond the ability of current in vivo imaging (e.g. diffusion magnetic resonance imaging). Optical imaging methods such as polarization-sensitive optical coherence tomography (PS-OCT) and polarization microscopy can quantify fiber orientation at micrometer resolution but have been limited to two-dimensional in-plane orientation or thin slices, preventing the comprehensive study of connectivity in 3D. In this work we present a novel method to quantify volumetric 3D orientation in full angular space with PS-OCT. We measure the polarization contrasts of the brain sample from two illumination angles of 0 and 15 degrees and apply a computational method that yields the 3D optic axis orientation and true birefringence. We further present 3D fiber orientation maps of entire coronal cerebrum sections and brainstem with 10 μm in-plane resolution, revealing unprecedented details of fiber configurations. We envision that our method will open a promising avenue towards large-scale 3D fiber axis mapping in the human brain as well as other complex fibrous tissues at microscopic level.

Quantitative imaging of three-dimensional fiber orientation in the human brain via two illumination angles using polarization-sensitive optical coherence tomography

The accurate measurement of three-dimensional (3D) fiber orientation in the brain is crucial for reconstructing fiber pathways and studying their involvement in neurological diseases. Optical imaging methods such as polarization-sensitive optical coherence tomography (PS-OCT) provide important tools to directly quantify fiber orientation at micrometer resolution. However, brain imaging based on the optic axis by PS-OCT so far has been limited to two-dimensional in-plane orientation, preventing the comprehensive study of connectivity in 3D. In this work, we present a novel method to obtain the 3D fiber orientation in full angular space with only two illumination angles. We measure the optic axis orientation and the apparent birefringence by PS-OCT from a normal and a 15 deg tilted illumination, and then apply a computational method yielding the 3D optic axis orientation and true birefringence. We verify that our method accurately recovers a large range of through-plane orientations from -85 deg to 85 deg with a high angular precision. We further present 3D fiber orientation maps of entire coronal sections of human cerebrum and brainstem with 10 μm in-plane resolution, revealing unprecedented details of fiber configurations. We envision that further development of our method will open a promising avenue towards large-scale 3D fiber axis mapping in the human brain and other complex fibrous tissues at microscopic level.

Cervical facet capsular ligament mechanics: Estimations based on subject-specific anatomy and kinematics

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 non-affine fiber network solver: A multiscale fiber network material model for finite-element analysis

Multiscale mechanical models in biomaterials research have largely relied on simplifying the microstructure in order to make large-scale simulations tractable. The microscale simplifications often rely on approximations of the constituent distributions and assumptions on the deformation of the constituents. Of particular interest in biomechanics are fiber embedded materials, where simplified fiber distributions and assumed affinity in the fiber deformation greatly influence the mechanical behavior. The consequences of these assumptions are problematic when dealing with microscale mechanical phenomena such as cellular mechanotransduction in growth and remodeling, and fiber-level failure events during tissue failure. In this work, we propose a technique for coupling non-affine network models to finite element solvers, allowing for simulation of discrete microstructural phenomena within macroscopically complex geometries. The developed plugin is readily available as an open-source library for use with the bio-focused finite element software FEBio, and the description of the implementation allows for the adaptation to other finite element solvers.

The Lumbar Facet Capsular Ligament Becomes More Anisotropic and the Fibers Become Stiffer With Intervertebral Disc and Facet Joint Degeneration

Degeneration of the lumbar spine, and especially how that degeneration may lead to pain, remains poorly understood. In particular, the mechanics of the facet capsular ligament may contribute to low back pain, but the mechanical changes that occur in this ligament with spinal degeneration are unknown. Additionally, the highly nonlinear, heterogeneous, and anisotropic nature of the facet capsular ligament makes understanding mechanical changes more difficult. Clinically, magnetic resonance imaging (MRI)-based signs of degeneration in the facet joint and the intervertebral disc (IVD) correlate. Therefore, this study examined how the nonlinear, heterogeneous mechanics of the facet capsular ligament change with degeneration of the lumbar spine as characterized using MRI. Cadaveric human spines were imaged via MRI, and the L2-L5 facet joints and IVDs were scored using the Fujiwara and Pfirrmann grading systems. Then, the facet capsular ligament was isolated and biaxially loaded. The nonlinear mechanical properties of the ligament were obtained using a nonlinear generalized anisotropic inverse mechanics analysis (nGAIM). Then a Holzapfel-Gasser-Ogden (HGO) model was fit to the stress-strain data obtained from nGAIM. The facet capsular ligament is stiffer and more anisotropic at larger Pfirrmann grades and higher Fujiwara scores than at lower grades and scores. Analysis of ligament heterogeneity showed all tissues are highly heterogeneous, but no distinct spatial patterns of heterogeneity were found. These results show that degeneration of the lumbar spine including the facet capsular ligament appears to be occurring as a whole joint phenomenon and advance our understanding of lumbar spine degeneration.

In vivo assessment of mitral valve leaflet remodelling following myocardial infarction

Each year, more than 40,000 people undergo mitral valve (MV) repair surgery domestically to treat regurgitation caused by myocardial infarction (MI). Although continual MV tissue remodelling following repair is believed to be a major contributor to regurgitation recurrence, the effects of the post-MI state on MV remodelling remain poorly understood. This lack of understanding limits our ability to predict the remodelling of the MV both post-MI and post-surgery to facilitate surgical planning. As a necessary first step, the present study was undertaken to noninvasively quantify the effects of MI on MV remodelling in terms of leaflet geometry and deformation. MI was induced in eight adult Dorset sheep, and real-time three-dimensional echocardiographic (rt-3DE) scans were collected pre-MI as well as at 0, 4, and 8 weeks post-MI. A previously validated image-based morphing pipeline was used to register corresponding open- and closed-state scans and extract local in-plane strains throughout the leaflet surface at systole. We determined that MI induced permanent changes in leaflet dimensions in the diastolic configuration, which increased with time to 4 weeks, then stabilised. MI substantially affected the systolic shape of the MV, and the range of stretch experienced by the MV leaflet at peak systole was substantially reduced when referred to the current time-point. Interestingly, when we referred the leaflet strains to the pre-MI configuration, the systolic strains remained very similar throughout the post-MI period. Overall, we observed that post-MI ventricular remodeling induced permanent changes in the MV leaflet shape. This predominantly affected the MV's diastolic configuration, leading in turn to a significant decrease in the range of stretch experienced by the leaflet when referenced to the current diastolic configuration. These findings are consistent with our previous work that demonstrated increased plastic (i.e. non-recoverable) leaflet deformations post-MI, that was completely accounted for by the associated changes in collagen fiber structure. Moreover, we demonstrated through noninvasive methods that the state of the MV leaflet can elucidate the progression and extent of MV adaptation following MI and is thus highly relevant to the design of current and novel patient specific minimally invasive surgical repair strategies.

A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density

Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.

Data-driven modeling of heterogeneous viscoelastic biofilms

Biofilms are typically heterogeneous in morphology, structure, and composition, resulting in non-uniform mechanical properties. The distribution of mechanical properties, in turn, determines the biofilm behavior, such as deformation and detachment. Most biofilm models neglect biofilm heterogeneity, especially at the microscale. In this study, an image-based modeling approach was developed to transform two-dimensional optical coherence tomography (OCT) biofilm images to a pixel-scale non-Newtonian viscosity map of the biofilm. The map was calibrated using the bulk viscosity data from rheometer tests, based on assumed maximum and minimum viscosities and a relationship between OCT image intensity signals and non-Newtonian viscosity. While not quantitatively measuring biofilm viscosity for each pixel, it allows a rational spatial allocation of viscosities within the biofilm: areas with lower cell density, e.g., voids, are assigned lower viscosities, and areas with high cell densities are assigned higher viscosities. The spatial distribution of non-Newtonian viscosity was applied in an established Oldroyd-B constitutive model and implemented using the phase-field continuum approach for the deformation and stress analysis. The heterogeneous model was able to predict deformations more accurately than a homogenous one. Stress distribution in the heterogeneous biofilm displayed better characteristics than that in the homogeneous one, because it is highly dependent on the viscosity distribution. This work, using a pixel-scale, image-based approach to map the mechanical heterogeneity of biofilms for computational deformation and stress analysis, provides a novel modeling approach that allows the consideration of biofilm structural and mechanical heterogeneity. Future research should better characterize the relationship between OCT signal and viscosity, and consider other constitutive models for biofilm mechanical behavior. This article is protected by copyright. All rights reserved.

Through-thickness regional variation in the mechanical characteristics of the lumbar facet capsular ligament

The human lumbar facet capsule, with the facet capsular ligament (FCL) that forms its primary constituent, is a common source of lower back pain. Prior studies on the FCL were limited to in-plane tissue behavior, but due to the presence of two distinct yet mechanically different regions, a novel out-of-plane study was conducted to further characterize the roles of the collagen and elastin regions. An experimental technique, called stretch-and-bend, was developed to study the tension-compression asymmetry of the FCL due to varying collagen fiber density throughout the thickness of the tissue. Each healthy excised cadaveric FCL sample was tested in four conditions depending on primary collagen fiber alignment and regional loading. Our results indicate that the FCL is stiffest when the collagen fibers (1) are aligned in the direction of loading, (2) are in tension, and (3) are stretched - 16% from its off-the-bone, undeformed state. An optimization routine was used to fit a four-parameter anisotropic, hyperplastic model to the experimental data. The average elastin modulus, E, and the average collagen fiber modulus, ξ, were 13.15 ± 3.59 kPa and 18.68 ± 13.71 MPa (95% CI), respectively.

A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model [1, 2] to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the "identifiability" or "uniqueness" of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.

Glomerular filtration and podocyte tensional homeostasis: importance of the minor type IV collagen network

The minor type IV collagen chain, which is a significant component of the glomerular basement membrane in healthy individuals, is known to assemble into large structures (supercoils) that may contribute to the mechanical stability of the collagen network and the glomerular basement membrane as a whole. The absence of the minor chain, as in Alport syndrome, leads to glomerular capillary demise and eventually to kidney failure. An important consideration in this problem is that the glomerular capillary wall must be strong enough to withstand the filtration pressure and porous enough to permit filtration at reasonable pressures. In this work, we propose a coupled feedback loop driven by filtration demand and tensional homeostasis of the podocytes forming the outer portion of the glomerular capillary wall. Briefly, the deposition of new collagen increases the stiffness of basement membrane, helping to stress shield the podocytes, but the new collagen also decreases the permeability of the basement membrane, requiring an increase in capillary transmural pressure drop to maintain filtration; the resulting increased pressure outweighs the increased glomerular basement membrane stiffness and puts a net greater stress demand on the podocytes. This idea is explored by developing a multiscale simulation of the capillary wall, in which a macroscopic (µm scale) continuum model is connected to a set of microscopic (nm scale) fiber network models representing the collagen network and the podocyte cytoskeleton. The model considers two cases: healthy remodeling, in which the presence of the minor chain allows the collagen volume fraction to be increased by thickening fibers, and Alport syndrome remodeling, in which the absence of the minor chain allows collagen volume fraction to be increased only by adding new fibers to the network. The permeability of the network is calculated based on previous models of flow through a fiber network, and it is updated for different fiber radii and volume fractions. The analysis shows that the minor chain allows a homeostatic balance to be achieved in terms of both filtration and cell tension. Absent the minor chain, there is a fundamental change in the relation between the two effects, and the system becomes unstable. This result suggests that mechanobiological or mechanoregulatory therapies may be possible for Alport syndrome and other minor chain collagen diseases of the kidney.

Asymmetric in-plane shear behavior of isolated cadaveric lumbar facet capsular ligaments: Implications for subject specific biomechanical models

The facet capsular ligaments (FCLs) flank the spinous process on the posterior aspect of the spine. The lumbar FCL is collagenous, with collagen fibers aligned primarily bone-to-bone (medial-lateral) and experiences significant shear, especially during spinal flexion and extension. We characterized the mechanical response of the lumbar FCL to in-plane shear, and we evaluated that response in the context of the fiber architecture. In-plane shear tests with both positive and negative shear (i.e., corresponding to flexion and to extension) were performed on eight cadaveric human L4-L5 FCLs. Our most striking observation was subject-dependent asymmetry in the response. All samples showed a toe region of low stiffness, transitioning to greater stiffness at higher strains, for both shear directions. Different samples showed profoundly different transition strains, with some samples stiffening more rapidly in positive shear and some in negative shear. This unpredictable asymmetry, which did not correlate with age, side, or degeneration state, suggesting that collagen fibers in the FCL are sometimes aligned at a slight positive angle from the bone-to-bone axis and sometimes at a negative angle. Fitting the experimental data to a fiber-composite-based finite element model supported this idea, yielding optimal fits with positive or negative off-axis fiber directions (-40° to +40°). Subsequent examination of selected FCLs by small-angle x-ray scattering (SAXS) showed a similar variability in fiber direction. We conclude that small individual differences in lumbar FCL architecture may have a significant effect on lumbar FCL mechanics, especially at moderate strains.

Effects of Collagen Heterogeneity on Myocardial Infarct Mechanics in a Multiscale Fiber Network Model

The scar that forms after a myocardial infarction is often characterized by a highly disordered architecture but generally exhibits some degree of collagen fiber orientation, with a resulting mechanical anisotropy. When viewed in finer detail, however, the heterogeneity of the sample is clear, with different subregions exhibiting different fiber orientations. In this work, we used a multiscale finite element model to explore the consequences of the heterogeneity in terms of mechanical behavior. To do so, we used previously obtained fiber alignment maps of rat myocardial scar slices (n = 15) to generate scar-specific finite element meshes that were populated with fiber models based on the local alignment state. These models were then compared to isotropic models with the same sample shape and fiber density, and to homogeneous models with the same sample shape, fiber density, and average fiber alignment as the scar-specific models. All simulations involved equibiaxial extension of the sample with free motion in the third dimension. We found that heterogeneity led to a lower degree of mechanical anisotropy and a higher level of local stress concentration than the corresponding homogeneous model, and also that fibers failed in the heterogeneous model at much lower macroscopic strains than in the isotropic and homogeneous models. Taken together, these results suggest that scar heterogeneity may impair myocardial mechanical function both in terms of anisotropy and strength, and that individual variations in scar heterogeneity could be an important consideration for understanding scar remodeling and designing therapeutic interventions for patients after myocardial infarction.

The role of the facet capsular ligament in providing spinal stability

Low back pain (LBP) is the most common type of pain in America, and spinal instability is a primary cause. The facet capsular ligament (FCL) encloses the articulating joints of the spine and is of particular interest due to its high innervation - as instability ensues, high stretch values likely are a cause of this pain. Therefore, this work investigated the FCL's role in providing stability to the lumbar spine. A previously validated finite element model of the L4-L5 spinal motion segment was used to simulate pure moment bending in multiple planes. FCL failure was simulated and the following outcome measures were calculated: helical axes of motion, range of motion (ROM), bending stiffness, facet joint space, and FCL stretch. ROM increased, bending stiffness decreased, and altered helical axis patterns were observed with the removal of the FCL. Additionally, a large increase in FCL stretch was measured with diminished FCL mechanical competency, providing support that the FCL plays an important role in spinal stability.

A noninvasive method for the determination of in vivo mitral valve leaflet strains

Assessment of mitral valve (MV) function is important in many diagnostic, prognostic, and surgical planning applications for treatment of MV disease. Yet, to date, there are no accepted noninvasive methods for determination of MV leaflet deformation, which is a critical metric of MV function. In this study, we present a novel, completely noninvasive computational method to estimate MV leaflet in-plane strains from clinical-quality real-time three-dimensional echocardiography (rt-3DE) images. The images were first segmented to produce meshed medial-surface leaflet geometries of the open and closed states. To establish material point correspondence between the two states, an image-based morphing pipeline was implemented within a finite element (FE) modeling framework in which MV closure was simulated by pressurizing the open-state geometry, and local corrective loads were applied to enforce the actual MV closed shape. This resulted in a complete map of local systolic leaflet membrane strains, obtained from the final FE mesh configuration. To validate the method, we utilized an extant in vitro database of fiducially labeled MVs, imaged in conditions mimicking both the healthy and diseased states. Our method estimated local anisotropic in vivo strains with less than 10% error and proved to be robust to changes in boundary conditions similar to those observed in ischemic MV disease. Next, we applied our methodology to ovine MVs imaged in vivo with rt-3DE and compared our results to previously published findings of in vivo MV strains in the same type of animal as measured using surgically sutured fiducial marker arrays. In regions encompassed by fiducial markers, we found no significant differences in circumferential(P = 0.240) or radial (P = 0.808) strain estimates between the marker-based measurements and our novel noninvasive method. This method can thus be used for model validation as well as for studies of MV disease and repair.

Multiscale modelling of the human lumbar facet capsular ligament: analysing spinal motion from the joint to the neurons

Due to its high level of innervation, the lumbar facet capsular ligament (FCL) is suspected to play a role in low back pain (LBP). The nociceptors in the lumbar FCL may experience excessive deformation and generate pain signals. As such, understanding the mechanical behaviour of the FCL, as well as that of its underlying nerves, is critical if one hopes to understand its role in LBP. In this work, we constructed a multiscale structure-based finite-element (FE) model of a lumbar FCL on a spinal motion segment undergoing physiological motions of flexion, extension, ipsilateral and contralateral bending, and ipsilateral axial rotation. Our FE model was created for a generic FCL geometry by morphing a previously imaged FCL anatomy onto an existing generic motion segment model. The fibre organization of the FCL in our models was subject-specific based on previous analysis of six dissected specimens. The fibre structures from those specimens were mapped onto the FCL geometry on the motion segment. A motion segment model was used to determine vertebral kinematics under specified spinal loading conditions, providing boundary conditions for the FCL-only multiscale FE model. The solution of the FE model then provided detailed stress and strain fields within the tissue. Lastly, we used this computed strain field and our previous studies of deformation of nerves embedded in fibrous networks during simple deformations (e.g. uniaxial stretch, shear) to estimate the nerve deformation based on the local tissue strain and fibre alignment. Our results show that extension and ipsilateral bending result in largest strains of the lumbar FCL, while contralateral bending and flexion experience lowest strain values. Similar to strain trends, we calculated that the stretch of the microtubules of the nerves, as well as the forces exerted on the nerves' membrane are maximal for extension and ipsilateral bending, but the location within the FCL of peak microtubule stretch differed from that of peak membrane force.

Tissue loading and microstructure regulate the deformation of embedded nerve fibres: predictions from single-scale and multiscale simulations

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 model of an axon embedded in a collagen fibre network attached to the axon by distinct fibre-axon connections. This model was used to relate the axonal deformation to the fibre alignment and collagen volume concentration of the surrounding network during transverse, axial and shear deformations. Our results showed that fibre alignment affects axonal deformation only during transverse and axial loading, but higher collagen volume concentration results in larger overall axonal strains for all loading cases. Furthermore, axial loading leads to the largest stretch of axonal microtubules and induces the largest forces on axon's surface in most cases. Comparison between this model and a multiscale continuum model for a representative case showed that although both models predicted similar averaged axonal strains, strain was more heterogeneous in the discrete-fibre model.

Multiscale mechanics of the cervical facet capsular ligament, with particular emphasis on anomalous fiber realignment prior to tissue failure

The facet capsular ligaments encapsulate the bilateral spinal facet joints and are common sources of painful injury due to afferent innervation. These ligaments exhibit architectural complexity, which is suspected to contribute to the experimentally observed lack of co-localization between macroscopic strain and microstructural tissue damage. The heterogeneous and multiscale nature of this ligament, combined with challenges in experimentally measuring its microscale mechanics, hinders the ability to understand sensory mechanisms under normal or injurious loading. Therefore, image-based, subject-specific, multiscale finite-element models were constructed to predict the mechanical responses of the human cervical facet capsular ligament under uniaxial tensile stretch. The models precisely simulated the force-displacement responses for all samples ([Formula: see text]) and showed promise in predicting the magnitude and location of peak regional strains at two different displacements. Yet, there was a loss of agreement between the model and experiment in terms of fiber organization at large tissue stretch, possibly due to a lack of accounting for tissue failure. The mean fiber stretch ratio predicted by the models was found to be significantly higher in regions that exhibited anomalous fiber realignment experimentally than in regions with normal realignment ([Formula: see text]). The development of microstructural abnormalities was associated with the predicted fiber-level stretch ([Formula: see text]), but not with the elemental maximum principal stress or maximum principal strain by logistic regression. The multiscale models elucidate a potential mechanical basis for predicting injury-prone tissue domains and for defining the relationships between macroscopic ligament stretch and microscale pathophysiology in the subfailure regime.

Collagen Organization in Facet Capsular Ligaments Varies With Spinal Region and With Ligament Deformation

The spinal facet capsular ligament (FCL) is primarily comprised of heterogeneous arrangements of collagen fibers. This complex fibrous structure and its evolution under loading play a critical role in determining the mechanical behavior of the FCL. A lack of analytical tools to characterize the spatial anisotropy and heterogeneity of the FCL's microstructure has limited the current understanding of its structure-function relationships. Here, the collagen organization was characterized using spatial correlation analysis of the FCL's optically obtained fiber orientation field. FCLs from the cervical and lumbar spinal regions were characterized in terms of their structure, as was the reorganization of collagen in stretched cervical FCLs. Higher degrees of intra- and intersample heterogeneity were found in cervical FCLs than in lumbar specimens. In the cervical FCLs, heterogeneity was manifested in the form of curvy patterns formed by collections of collagen fibers or fiber bundles. Tensile stretch, a common injury mechanism for the cervical FCL, significantly increased the spatial correlation length in the stretch direction, indicating an elongation of the observed structural features. Finally, an affine estimation for the change of correlation length under loading was performed which gave predictions very similar to the actual values. These findings provide structural insights for multiscale mechanical analyses of the FCLs from various spinal regions and also suggest methods for quantitative characterization of complex tissue patterns.

Multi-resolution geometric modeling of the mitral heart valve leaflets

An essential element of cardiac function, the mitral valve (MV) ensures proper directional blood flow between the left heart chambers. Over the past two decades, computational simulations have made marked advancements toward providing powerful predictive tools to better understand valvular function and improve treatments for MV disease. However, challenges remain in the development of robust means for the quantification and representation of MV leaflet geometry. In this study, we present a novel modeling pipeline to quantitatively characterize and represent MV leaflet surface geometry. Our methodology utilized a two-part additive decomposition of the MV geometric features to decouple the macro-level general leaflet shape descriptors from the leaflet fine-scale features. First, the general shapes of five ovine MV leaflets were modeled using superquadric surfaces. Second, the finer-scale geometric details were captured, quantified, and reconstructed via a 2D Fourier analysis with an additional sparsity constraint. This spectral approach allowed us to easily control the level of geometric details in the reconstructed geometry. The results revealed that our methodology provided a robust and accurate approach to develop MV-specific models with an adjustable level of spatial resolution and geometric detail. Such fully customizable models provide the necessary means to perform computational simulations of the MV at a range of geometric accuracies in order to identify the level of complexity required to achieve predictive MV simulations.

Planar biaxial extension of the lumbar facet capsular ligament reveals significant in-plane shear forces

The lumbar facet capsular ligament (FCL) articulates with six degrees of freedom during spinal motions of flexion/extension, lateral bending, and axial rotation. The lumbar FCL is composed of highly aligned collagen fiber bundles on the posterior surface (oriented primarily laterally between the rigid articular facets) and irregularly oriented elastin on the anterior surface. Because the FCL is a capsule, it has multiple insertion sites across the lumbar facet joint, which, along with its material structure, give rise to complicated deformations in vivo. We performed planar equibiaxial mechanical tests on excised healthy cadaveric lumbar FCLs (n=6) to extract normal and shear reaction forces, and fit sample-specific two-fiber-family finite element models to the experimental force data. An eight-parameter anisotropic, hyperelastic model was used. Shear forces at maximum extension (mean values of 1.68N and 3.01N in the two directions) were of comparable magnitude to the normal forces perpendicular to the aligned collagen fiber bundles (4.67N) but smaller than normal forces in the fiber direction (16.11N). Inclusion of the experimental shear forces in the model optimization yielded fits with highly aligned fibers oriented at a specific angle across all samples, typically with one fiber population aligned nearly horizontally and the other at an oblique angle. Conversely, models fit to only the normal force data resulted in a broad range of fiber angles with low specificity. We found that shear forces generated through planar equibiaxial extension aided the model fit in describing the anisotropic nature of the FCL surface.