An Inverse Modeling Approach to Estimate Three-Dimensional Aortic Valve Interstitial Cell Stress Fiber Force Levels

Abstract

Within the aortic valve (AV) leaflet exists a population of interstitial cells (AVICs) that maintain the constituent tissues by extracellular matrix (ECM) secretion, degradation, and remodeling. AVICs can transition from a quiescent, fibroblast-like phenotype to an activated, myofibroblast phenotype in response to growth or disease. AVIC dysfunction has been implicated in AV disease processes, yet our understanding of AVIC function remains quite limited. A major characteristic of the AVIC phenotype is its contractile state, driven by contractile forces generated by the underlying stress fibers (SF). However, direct assessment of the AVIC SF contractile state and structure within physiologically mimicking three-dimensional environments remains technically challenging, as the size of single SFs are below the resolution of light microscopy. Therefore, in the present study, we developed a three-dimensional (3D) computational approach of AVICs embedded in 3D hydrogels to estimate their SF local orientations and contractile forces. One challenge with this approach is that AVICs will remodel the hydrogel, so that the gel moduli will vary spatially. We thus utilized our previous approach (Khang et al. 2023, "Estimation of Aortic Valve Interstitial Cell-Induced 3D Remodeling of Poly (Ethylene Glycol) Hydrogel Environments Using an Inverse Finite Element Approach," Acta Biomater., 160, pp. 123-133) to define local hydrogel mechanical properties. The AVIC SF model incorporated known cytosol and nucleus mechanical behaviors, with the cell membrane assumed to be perfectly bonded to the surrounding hydrogel. The AVIC SFs were first modeled as locally unidirectional hyperelastic fibers with a contractile force component. An adjoint-based inverse modeling approach was developed to estimate local SF orientation and contractile force. Substantial heterogeneity in SF force and orientations were observed, with the greatest levels of SF alignment and contractile forces occurring in AVIC protrusions. The addition of a dispersed SF orientation to the modeling approach did not substantially alter these findings. To the best of our knowledge, we report the first fully 3D computational contractile cell models which can predict locally varying stress fiber orientation and contractile force levels.

Keywords: 3D traction force microscopy; adjoint method; aortic valve interstitial cell; cell mechanics modeling; computational modeling.