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

Mechanical Models of Collagen Networks for Understanding Changes in the Failure Properties of Aging Skin

Skin undergoes mechanical alterations due to changes in the composition and structure of the collagenous dermis with aging. Previous studies have conflicting findings, with both increased and decreased stiffness reported for aging skin. The underlying structure-function relationships that drive age-related changes are complex and difficult to study individually. One potential contributor to these variations is the accumulation of nonenzymatic crosslinks within collagen fibers, which affect dermal collagen remodeling and mechanical properties. Specifically, these crosslinks make individual fibers stiffer in their plastic loading region and lead to increased fragmentation of the collagenous network. To better understand the influence of these changes, we investigated the impact of nonenzymatic crosslink changes on the dermal microstructure using discrete fiber networks representative of the dermal microstructure. Our findings suggest that stiffening the plastic region of collagen's mechanical response has minimal effects on network-level stiffness and failure stresses. Conversely, simulating fragmentation through a loss of connectivity substantially reduces network stiffness and failure stress, while increasing stretch ratios at failure.

An Approach to Quantify Anisotropic Multiaxial Failure of the Annulus Fibrosus

Tears in the annulus fibrosus (AF) of the intervertebral disk (IVD) occur due to multiaxial loading on the spine. However, most existing AF failure studies measure uniaxial stress, not the multiaxial stress at failure. Delamination theory, which requires advanced structural knowledge and knowledge about the interactions between the AF fibers and matrix, has historically been used to understand and predict AF failure. Alternatively, a simple method, the Tsai-Hill yield criteria, could describe multiaxial failure of the AF. This yield criteria uses the known tissue fiber orientation and an equation to establish the multiaxial failure stresses that cause failure. This paper presents a method to test the multiaxial failure stress of the AF experimentally and evaluate the potential for the Tsai-Hill model to predict these failure stresses. Porcine AF was cut into a dogbone shape at three distinct angles relative to the primary lamella direction (parallel, transverse, and oblique). Then, each dogbone was pulled to complete rupture. The Cauchy stress in the material's fiber coordinates was calculated. These multiaxial stress parameters were used to optimize the coefficients of the Tsai-Hill yield. The coefficients obtained for the Tsai-Hill model vary by an order of magnitude between the fiber and transverse directions, and these coefficients provide a good description of the AF multiaxial failure stress. These results establish both an experimental approach and the use of the Tsai-Hill model to explain the anisotropic failure behavior of the tissue.

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.

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.

Porous interbody fusion cage design via topology optimization and biomechanical performance analysis

The porous interbody fusion cage could provide space and stable mechanical conditions for postoperative intervertebral bone ingrowth. It is considered to be an important implant in anterior cervical discectomy and internal fixation. In this study, two types of unit cells were designed using topology optimization method and introduced to the interbody fusion cage to improve the biomechanical performances of the cage. Topology optimization under two typically loading conditions was first conducted to obtain two unit cells (O-unit cell and D-unit cell) with the same volume fraction. Porous structures were developed by stacking the obtained unit cells in space, respectively. Then, porous interbody fusion cages were obtained by the Boolean intersection between the global structural layout and the porous structures. Finite element models of cervical spine were created that C5-C6 segment was fused by the designed porous cages. The range of motion (ROM) of the cervical spine, the maximum stress on the cage and the bone graft, and the stress and displacement distributions of the cage were analyzed. The results showed the ROMs of C5-C6 segment in D-unit cell and O-unit cell models were range from 0.14° to 0.25° under different loading conditions; the cage composed of the D-unit cells had a more uniform stress distribution, smaller displacement on cage, a more reasonable internal stress transfer mode (transmission along struts of the unit cell), and higher stress on the internal bone graft (0.617 MPa). In conclusion, the optimized porous cage is a promising candidate for fusion surgery, which would avoid the cage subsidence, and promote the fusion of adjacent endplates.

Multiscale Computational Model Predicts Mouse Skin Kinematics Under Tensile Loading

Skin is a complex tissue whose biomechanical properties are generally understood in terms of an incompressible material whose microstructure undergoes affine deformations. A growing number of experiments, however, have demonstrated that skin has a high Poisson's ratio, substantially decreases in volume during uniaxial tensile loading, and demonstrates collagen fiber kinematics that are not affine with local deformation. In order to better understand the mechanical basis for these properties, we constructed multiscale mechanical models (MSM) of mouse skin based on microstructural multiphoton microscopy imaging of the dermal microstructure acquired during mechanical testing. Three models that spanned the cases of highly aligned, moderately aligned, and nearly random fiber networks were examined and compared to the data acquired from uniaxially stretched skin. Our results demonstrate that MSMs consisting of networks of matched fiber organization can predict the biomechanical behavior of mouse skin, including the large decrease in tissue volume and nonaffine fiber kinematics observed under uniaxial tension.

Local tissue heterogeneity may modulate neuronal responses via altered axon strain fields: insights about innervated joint capsules from a computational model

In innervated collagenous tissues, tissue scale loading may contribute to joint pain by transmitting force through collagen fibers to the embedded mechanosensitive axons. However, the highly heterogeneous collagen structures of native tissues make understanding this relationship challenging. Recently, collagen gels with embedded axons were stretched and the resulting axon signals were measured, but these experiments were unable to measure the local axon strain fields. Computational discrete fiber network models can directly determine axon strain fields due to tissue scale loading. Therefore, this study used a discrete fiber network model to identify how heterogeneous collagen networks (networks with multiple collagen fiber densities) change axon strain due to tissue scale loading. In this model, a composite cylinder (axon) was embedded in a Delaunay network (collagen). Homogeneous networks with a single collagen volume fraction and two types of heterogeneous networks with either a sparse center or dense center were created. Measurements of fiber forces show higher magnitude forces in sparse regions of heterogeneous networks and uniform force distributions in homogeneous networks. The average axon strain in the sparse center networks decreases when compared to homogeneous networks with similar collagen volume fractions. In dense center networks, the average axon strain increases compared to homogeneous networks. The top 1% of axon strains are unaffected by network heterogeneity. Based on these results, the interaction of tissue scale loading, collagen network heterogeneity, and axon strains in native musculoskeletal tissues should be considered when investigating the source of joint pain.

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.

Concentration-Dependent Effects of Fibroblast-Like Synoviocytes on Collagen Gel Multiscale Biomechanics and Neuronal Signaling: Implications for Modeling Human Ligamentous Tissues

Abnormal loading of a joint's ligamentous capsule causes pain by activating the capsule's nociceptive afferent fibers, which reside in the capsule's collagenous matrix alongside fibroblast-like synoviocytes (FLS) and transmit pain to the dorsal root ganglia (DRG). This study integrated FLS into a DRG-collagen gel model to better mimic the anatomy and physiology of human joint capsules; using this new model, the effect of FLS on multiscale biomechanics and cell physiology under load was investigated. Primary FLS cells were co-cultured with DRGs at low or high concentrations, to simulate variable anatomical FLS densities, and failed in tension. Given their roles in collagen degradation and nociception, matrix-metalloproteinase (MMP-1) and neuronal expression of the neurotransmitter substance P were probed after gel failure. The amount of FLS did not alter (p > 0.3) the gel failure force, displacement, or stiffness. FLS doubled regional strains at both low (p < 0.01) and high (p = 0.01) concentrations. For high FLS, the collagen network showed more reorganization at failure (p < 0.01). Although total MMP-1 and neuronal substance P were the same regardless of FLS concentration before loading, protein expression of both increased after failure, but only in low FLS gels (p ≤ 0.02). The concentration-dependent effect of FLS on microstructure and cellular responses implies that capsule regions with different FLS densities experience variable microenvironments. This study presents a novel DRG-FLS co-culture collagen gel system that provides a platform for investigating the complex biomechanics and physiology of human joint capsules, and is the first relating DRG and FLS interactions between each other and their surrounding collagen network.

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.

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.