A 3D Finite Element Constrained Mixture Approach to Ventricular Growth

Charles Mann, Samuel Wall, Joakim Sundnes
Simula Research Laboratory


Abstract

Cardiac growth and remodeling is a dynamic process that leads to physiological and pathological adaptations. Traditional computational models of ventricular growth follow the volumetric growth framework and require the specification of phenomenological growth laws in local tissue directions, focusing on the consequences of growth rather than the underlying physiological mechanisms. Understanding and modeling the underlying growth processes and how they respond to perturbations would aid in predicting patient outcomes and identifying potential therapeutic pathways.

Constrained mixture modeling is an alternative framework for growth modeling, which is prevalent in arterial modeling but sparsely used in ventricular mechanics. In this study a thin slab of mid-ventricular tissue is modeled as a constrained mixture, with myocytes and collagen as the major structural constituents. Both constituents are assigned mechanically dependent mass production and removal functions. Biaxial simulations mimicking baseline, pressure overload, and volume overload conditions were performed in accordance with a previous study by Witzenburg & Holmes (2017) comparing ventricular growth laws.

This modeling approach maintained homeostasis during baseline conditions and predicted fiber-to-radial growth ratios that are within the range from compiled literature for each overload condition. Furthermore, the model predicted an increase in collagen concentration in the pressure overload condition, and a decrease in collagen concentration in the volume overload condition, a prediction that is unable to be made in the widely used volumetric growth framework.

The constrained mixture modeling approach is able to capture hallmarks of both concentric and eccentric hypertrophy, while avoiding the explicit specification of a growth tensor, and allowing the separation of contributions from individual constituents. The model framework connects tissue level structural changes to perturbations in mass production, which are known to be altered in pressure and volume overload conditions.