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

A computational bridge between traction force microscopy and tissue contraction

Arterial wall active mechanics are driven by resident smooth muscle cells, which respond to biological, chemical, and mechanical stimuli and activate their cytoskeletal machinery to generate contractile stresses. The cellular mechanoresponse is sensitive to environmental perturbations, often leading to maladaptation and disease progression. When investigated at the single cell scale, however, these perturbations do not consistently result in phenotypes observed at the tissue scale. Here, a multiscale model is introduced that translates microscale contractility signaling into a macroscale, tissue-level response. The microscale framework incorporates a biochemical signaling network along with characterization of fiber networks that govern the anisotropic mechanics of vascular tissue. By incorporating both biochemical and mechanical components, the model is more flexible and more broadly applicable to physiological and pathological conditions. The model can be applied to both cell and tissue scale systems, allowing for the analysis of in vitro, traction force microscopy and ex vivo, isometric contraction experiments in parallel. When applied to aortic explant rings and isolated smooth muscle cells, the model predicts that active contractility is not a function of stretch at intermediate strain. The model also successfully predicts cell-scale and tissue-scale contractility and matches experimentally observed behaviors, including the hypercontractile phenotype caused by chronic hyperglycemia. The connection of the microscale framework to the macroscale through the multiscale model presents a framework that can translate the wealth of information already collected at the cell scale to tissue scale phenotypes, potentially easing the development of smooth muscle cell-targeting therapeutics.

Computationally Efficient Concept of Representative Directions for Anisotropic Fibrous Materials

The concept of representative directions allows for automatic generation of multi-axial constitutive equations, starting from simplified uni-axial material models. In this paper, a modification of the concept is considered suitable for the analysis of fibrous polymeric materials, which are anisotropic in the as-received state. The modification of the concept incorporates an orientation probability density function (OPDF), which explicitly accounts for the material anisotropy. Two versions of the concept are available. The first version utilizes the homogeneous distribution of the representative directions, with the entire anisotropy being contained in the weighting factors. The second encapsulates the anisotropy in the distribution of the representative directions. Due to its nature, the second version allows for a more efficient use of computational power. To promote this efficient version of the concept, we present new algorithms generating required sets of representative directions that match a given OPDF. These methods are based (i) on the minimization of a potential energy, (ii) on the equilibration method, and (iii) on the use of Voronoi cells. These three methods are tested and compared in terms of various OPDFs. The applicability of the computationally efficient modeling method to mechanical behavior of an anisotropic polymeric material is demonstrated. In particular, a calibration procedure is suggested for the practically important case when the OPDF is not known a-priori.