Mathematical modeling of uniaxial mechanical properties of collagen gel scaffolds for vascular tissue engineering

A viscoelastic model for human myocardium

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena. STATEMENT OF SIGNIFICANCE: The viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.

Viscoelastic properties of multi-layered cellularized vascular tissues fabricated from collagen gel

Since collagen is one of the major extracellular matrix components in vascular tissues, its use for vascular tissue engineering has several advantages. However, collagen extraction and processing for tissue engineering application alters its structure. As a result, collagen-based vascular constructs show poor mechanical properties compared to native tissues. In this work, multi-layer (single, double, and triple) vascular tissue constructs were engineered from porcine smooth muscle cells (PSMCs) entrapped in collagen gel by concentrically and sequentially layering after compaction of the previous layer(s). The engineered tissues were matured for either 14 or 21 days to allow the collagen gel to remodel before viscoelasticity, compliance, histological, and protein expression studies were conducted. While there was no significant difference upon addition of the different layers on the elastic modulus (p > .05), the viscous modulus of the single layer construct was significantly lower than the double and triple layer constructs (p < .05). Increasing the number of layers of the cellularized collagen construct increased the wall thickness and the viscous modulus of the construct. Furthermore, the cellularized single-layer construct had a relatively high compliance, but the double and triple layer constructs had compliance values comparable to both engineered vessels and native vessels. PSMCs were uniformly distributed throughout the cross-section and expressed the anticipated marker proteins smooth muscle-α actin, calponin, and smooth muscle myosin heavy chain. Taken together, this study demonstrated the viscoelastic responsiveness of multi-layer collagen-gel based vascular tissues.

Cadherin- and Rigidity-Dependent Growth of Lung Cancer Cells in a Partially Confined Microenvironment

During tumor development, cancer cells constantly confront different types of extracellular barriers. However, fundamental questions like whether tumor cells will continue to grow against confinement or away from it and what key factors govern this process remain poorly understood. To address these issues, here we examined the growth dynamics of human lung epithelial carcinoma A549 cells partially confined in micrometer-sized cylindrical pores with precisely controlled wall stiffness. It was found that, after reaching confluency, the cell monolayer enclosed by a compliant wall was able to keep growing and pushing the boundary, eventually leading to a markedly enlarged pore. In contrast, a much reduced in-plane growth and elevated strain level among cells were observed when the confining wall becomes stiff. Furthermore, under such circumstance, cells switched their growth from within the monolayer to along the out-of-plane direction, resulting in cell stacking. We showed that these observations can be well explained by a simple model taking into account the deformability of the wall and the threshold stress for inhibiting cell growth. Interestingly, cadherins were found to play an important role in the proliferation and stress buildup within the cell monolayer by aggregating at cell-cell junctions. The stiff confinement led to an elevated expression level of cadherins. Furthermore, inhibition of N-cadherin resulted in a significantly suppressed cell growth under the same confining conditions.