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

Fibrous finite element modeling of the optic nerve head region

The optic nerve head (ONH) region at the posterior pole of the eye is supported by a fibrous structure of collagen fiber bundles. Discerning how the fibrous structure determines the region biomechanics is crucial to understand normal physiology, and the roles of biomechanics on vision loss. The fiber bundles within the ONH structure exhibit complex three-dimensional (3D) organization and continuity across the various tissue components. Computational models of the ONH, however, usually represent collagen fibers in a homogenized fashion without accounting for their continuity across tissues, fibers interacting with each other and other fiber-specific effects in a fibrous structure. We present a fibrous finite element (FFE) model of the ONH that incorporates discrete collagen fiber bundles and their histology-based 3D organization to study ONH biomechanics as a fibrous structure. The FFE model was constructed using polarized light microscopy data of porcine ONH cryosections, representing individual fiber bundles in the sclera, dura and pia maters with beam elements and canal tissues as continuum structures. The FFE model mimics the histological in-plane orientation and width distributions of collagen bundles as well as their continuity across different tissues. Modeling the fiber bundles as linear materials, the FFE model predicts the nonlinear ONH response observed in an inflation experiment from the literature. The model also captures important microstructural mechanisms including fiber interactions and long-range strain transmission among bundles that have not been considered before. The FFE model presented here advances our understanding of the role of fibrous collagen structure in the ONH biomechanics. STATEMENT OF SIGNIFICANCE: The microstructure and mechanics of the optic nerve head (ONH) are central to ocular physiology. Histologically, the ONH region exhibits a complex continuous fibrous structure of collagen bundles. Understanding the role of the fibrous collagen structure on ONH biomechanics requires high-fidelity computational models previously unavailable. We present a computational model of the ONH that incorporates histology-based fibrous collagen structure derived from polarized light microscopy images. The model predictions agree with experiments in the literature, and provide insight into important microstructural mechanisms of fibrous tissue biomechanics, such as long-range strain transmission along fiber bundles. Our model can be used to study the microstructural basis of biomechanical damage and the effects of collagen remodeling in glaucoma.

Histology-informed multiscale modeling of human brain white matter

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.

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.

Characterization of the L4/L5 rat facet capsular ligament macromechanical and microstructural responses to tensile failure loading

Low back pain is a prevalent condition that affects the global population. The lumbar facet capsular ligament is a source of pain since the collagenous tissue of the ligament is innervated with sensory neurons that deform with the capsule's stretch. Regional differences in the microstructural and macrostructural anatomy of the spinal facets affect its capsule's mechanical behavior. Although there are many studies of the cervical facet in human and rodent models, the lumbar capsular ligament's multiscale behavior is less well-defined. This study characterizes the macroscale and fiber-scale changes of the rat lumbar facet capsule during tensile failure loading. An integrated polarized light imaging setup captured local fiber alignment during 0.08 mm/s distraction of 7 lumbar facets. Force, displacement, strain, and circular variance were measured at several points along the failure curve: the first instance when the local collagen fiber network realigns differentially (anomalous realignment), yield, the first peak in force corresponding to the capsule's first failure, and peak force, defined as ultimate rupture. Those outcomes were compared across events. While each of force, displacement, and average maximum principal strain increased with applied tension, so did the circular variance of the collagen, suggesting that the fibers were becoming more disorganized. From the fiber alignment maps collected at each mechanical event, the number of anomalous realignment events were counted and found to increase dramatically with loading. The increased collagen disorganization and increasing regions of such disorganization in the facet capsule during loading can provide insights about how loading to the ligament afferent nerves may be activated and thereby produce pain.

3D-printed auxetic-structured intervertebral disc implant for potential treatment of lumbar herniated disc

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.

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Auxetic-structured IVD implant features negative Poisson's ratio (NPR) behavior.

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Modified “Bucklicrystal”structure exhibits better energy absorption and stability.

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The stress effectively and evenly transfers/attenuates in the auxetic implant.

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Auxetic implant potentially alleviates the symptoms of lumbar disc herniation.

On the microstructurally driven heterogeneous response of brain white matter to drug infusion pressure

Delivering therapeutic agents into the brain via convection-enhanced delivery (CED), a mechanically controlled infusion method, provides an efficient approach to bypass the blood–brain barrier and deliver drugs directly to the targeted focus in the brain. Mathematical methods based on Darcy’s law have been widely adopted to predict drug distribution in the brain to improve the accuracy and reduce the side effects of this technique. However, most of the current studies assume that the hydraulic permeability and porosity of brain tissue are homogeneous and constant during the infusion process, which is less accurate due to the deformability of the axonal structures and the extracellular matrix in brain white matter. To solve this problem, a multiscale model was established in this study, which takes into account the pressure-driven deformation of brain microstructure to quantify the change of local permeability and porosity. The simulation results were corroborated using experiments measuring hydraulic permeability in ovine brain samples. Results show that both hydraulic pressure and drug concentration in the brain would be significantly underestimated by classical Darcy’s law, thus highlighting the great importance of the present multiscale model in providing a better understanding of how drugs transport inside the brain and how brain tissue responds to the infusion pressure. This new method can assist the development of both new drugs for brain diseases and preoperative evaluation techniques for CED surgery, thus helping to improve the efficiency and precision of treatments for brain diseases.

A computational framework for biomaterials containing three-dimensional random fiber networks based on the affine kinematics

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.

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.

Intra-articular collagenase in the spinal facet joint induces pain, DRG neuron dysregulation and increased MMP-1 absent evidence of joint destruction

Degeneration is a hallmark of painful joint disease and is mediated by many proteases that degrade joint tissues, including collagenases. We hypothesized that purified bacterial collagenase would initiate nociceptive cascades in the joint by degrading the capsular ligament's matrix and activating innervating pain fibers. Intra-articular collagenase in the rat facet joint was investigated for its effects on behavioral sensitivity, joint degeneration, and nociceptive pathways in the peripheral and central nervous systems. In parallel, a co-culture collagen gel model of the ligament was used to evaluate effects of collagenase on microscale changes to the collagen fibers and embedded neurons. Collagenase induced sensitivity within one day, lasting for 3 weeks (p < 0.001) but did not alter ligament structure, cartilage health, or chondrocyte homeostasis. Yet, nociceptive mediators were increased in the periphery (substance P, pERK, and MMP-1; p ≤ 0.039) and spinal cord (substance P and MMP-1; p ≤ 0.041). The collagen loss (p = 0.008) induced by exposing co-cultures to collagenase was accompanied by altered neuronal activity (p = 0.002) and elevated neuronal MMP-1 (p < 0.001), suggesting microscale collagen degradation mediates sensitivity in vivo. The induction of sustained sensitivity and nociception without joint damage may explain the clinical disconnect in which symptomatic joint pain patients present without radiographic evidence of joint destruction.

Iris stromal cell nuclei deform to more elongated shapes during pharmacologically-induced miosis and mydriasis

Nuclear shape alteration in ocular tissues, which can be used as a metric for overall cell deformation, may also lead to changes in gene expression and protein synthesis that could affect the biomechanics of the tissue extracellular matrix. The biomechanics of iris tissue is of particular interest in the study of primary angle-closure glaucoma. As the first step towards understanding the mutual role of the biomechanics and deformation of the iris on the activity of its constituent stromal cells, we conducted an ex-vivo study in freshly excised porcine eyes. Iris deformation was achieved by activating the constituent smooth muscles of the iris. Pupillary responses were initiated by inducing miosis and mydriasis, and the irides were placed in a fixative, bisected, and sliced into thin sections in a nasal and temporal horizontal orientation. The tissue sections were stained with DAPI for nucleus, and z-stacks were acquired using confocal microscopy. Images were analyzed to determine the nuclear aspect ratio (NAR) using both three-dimensional (3D) reconstructions of the nuclear surfaces as well as projections of the same 3D reconstruction into flat two-dimensional (2D) shapes. We observed that regardless of the calculation method (i.e., one that employed 3D surface reconstructions versus one that employed 2D projected images) the NAR increased in both the miosis group and the mydriasis group. Three-dimensional quantifications showed that NAR increased from 2.52 ± 0.96 in control group to 2.80 ± 0.81 and 2.74 ± 0.94 in the mydriasis and miosis groups, respectively. Notwithstanding the relative convenience in calculating the NAR using the 2D projected images, the 3D reconstructions were found to generate more physiologically realistic values and, thus, can be used in the development of future computational models to study primary angle-closure glaucoma. Since the iris undergoes large deformations in response to ambient light, this study suggests that the iris stromal cells are subjected to a biomechanically active micro-environment during their in-vivo physiological function.

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.

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.

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.

Using Hands-On Physical Computing Projects to Teach Computer Programming to Biomedical Engineering Students

Rapid advancements in the multidisciplinary field of biomedical engineering (BME) require competitive engineers with skill sets in a broad range of subjects including biology, physiology, mechanics, circuits, and programming. Accordingly, such a need should be reflected in the training of BME students. Among those skills, computer programming is an essential tool that is used in a wide variety of applications. In this paper, we have provided our experience in incorporating project-based learning, a promising approach in active learning, for teaching computer programming to BME students. We describe a low-cost method for using physical, hands-on computing that directly relates to BME. Additionally, we detail our efforts to teach multiple programming languages in one semester and provide a detailed analysis of the outcomes. We also provide basic materials for other instructors to adapt to fit their own needs.

Repeated High Rate Facet Capsular Stretch at Strains That are Below the Pain Threshold Induces Pain and Spinal Inflammation With Decreased Ligament Strength in the Rat

Repeated loading of ligamentous tissues during repetitive occupational and physical tasks even within physiological ranges of motion has been implicated in the development of pain and joint instability. The pathophysiological mechanisms of pain after repetitive joint loading are not understood. Within the cervical spine, excessive stretch of the facet joint and its capsular ligament has been implicated in the development of pain. Although a single facet joint distraction (FJD) at magnitudes simulating physiologic strains is insufficient to induce pain, it is unknown whether repeated stretching of the facet joint and ligament may produce pain. This study evaluated if repeated loading of the facet at physiologic nonpainful strains alters the capsular ligament's mechanical response and induces pain. Male rats underwent either two subthreshold facet joint distractions (STFJDs) or sham surgeries each separated by 2 days. Pain was measured before the procedure and for 7 days; capsular mechanics were measured during each distraction and under tension at tissue failure. Spinal glial activation was also assessed to probe potential pathophysiologic mechanisms responsible for pain. Capsular displacement significantly increased (p = 0.019) and capsular stiffness decreased (p = 0.008) during the second distraction compared to the first. Pain was also induced after the second distraction and was sustained at day 7 (p < 0.048). Repeated loading weakened the capsular ligament with lower vertebral displacement (p = 0.041) and peak force (p = 0.014) at tissue rupture. Spinal glial activation was also induced after repeated loading. Together, these mechanical, physiological, and neurological findings demonstrate that repeated loading of the facet joint even within physiologic ranges of motion can be sufficient to induce pain, spinal inflammation, and alter capsular mechanics similar to a more injurious loading exposure.