A tri-phasic continuum model for the numerical analysis of biological tissue proliferation using the Theory of Porous Media: Application to cardiac remodelling in rheumatic heart disease

¹ Computational Continuum Mechanics Group, Department of Civil Engineering, University of Cape Town, South Africa
² Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa
³ Division of Cardiology, Department of Medicine, University of Cape Town, South Africa

^* e-mail: msmada002@myuct.ac.za

Abstract

This research is part of an on-going project aimed at describing the mechanotransduction of rheumatic heart disease (RHD), in order to study long-term effects of new therapeutic concepts to treat inflammatory heart diseases and ultimately, estimate their effectiveness to prevent heart failure. RHD is a condition which is mostly common amongst low-income countries and accounts for approximately 250 000 deaths per annum. The Theory of Porous Media (TPM) can represent the proliferative growth and remodelling processes related to RHD within a thermodynamically consistent framework and is additionally advantageous with application to biological tissue due to the ability to couple multiple constituents.

The research presented will extend an existing biphasic TPM model for the solid cardiac tissue (solid phase) saturated in a blood and interstitial fluid (liquid phase) [1], to a triphasic model with the inclusion of a third nutrient phase towards growth. This inclusion is motivated by the reason to constrain the volume of the liquid phase within the system in response to the description of growth, which is modelled through a mass exchange between the solid phase and liquid phase within the biphasic model. Although the nutrient phase acts as a source for growth, the proposed mass supply function used to correlate the deposition of sarcomeres in relation to growth is predominantly mechanically driven and bears no connection to any biochemical constituent, which therefore renders the nutrient phase as a physiologically arbitrary quantity. However, the provision of the nutrient phase is a platform for the inclusion of known constituents which actively contribute towards growth, which may be explored in future research.

The triphasic model is applied to a full cardiac cycle of a left ventricle model, extracted from cardiovascular magnetic resonance (CMR) scans of patients diagnosed with RHD.