A Galerkin-type finite element solution for simulation of mass diffusion in the application of tissue engineering: Heterogeneous and non-porous media

Abstract

This study is an effort to produce a generic and comprehensive solution to the simulation of mass diffusion through a multiphasic and heterogeneous material model. A Galerkin-type finite element formulation is developed to solve Fick's equation for steady-state and time-dependent analysis. The effect of the interface in modelling of a liquid-solid medium is presented in this work. To show the robustness of the proposed approach, the gas exchange (oxygen and carbon dioxide) process through the capillary network between the alveolar membrane and red blood cells has been analysed and then validated with experimental data. The current work is a significant asset to modelling the diffusion of oxygen between cells and scaffolds in tissue engineering or tissue regeneration/repair studies. It is one step towards the development of high-order elements for application of the simulation of mass transfer through a multiphasic and porous model with varying degrees of interconnectivity and pore size for tissue engineering applications.

Prosthetic Aortic Heart Valves

“…The subdivisions of the main left coronary are two smaller arteries, called the anterior descending and the circumflex arteries. The areas covered by the left coronary artery are mainly the left ventricle and the interventricular septum [15][16][17][18][19][20][21]. The left circumflex artery is positioned along the atrioventricular groove, which is then divided into an arterialand the obtuse marginal branch.…”

“…First, blood is pumped through the tricuspid and mitral valves as the atria contract. Following the ventricle contraction, blood is pushed backward, flowing between the flaps and walls of the ventricles [20][21][22][23]. The flaps are consequently pushed upward sothat the valvesare closed completely.…”

“…The closing phase of the heart valves is associated with an audible sound, known as the heartbeat. The first sound is because of the closure of the mitral and tricuspid valves, and the second one is when the pulmonary and aortic valves close [18][19][20][21][22].…”

“…The mechanism by which valves open and close during the cardiac cycle is known to be almost passive as the pressure gradient before and after the valves is the driving force. This pressure gradient is generated within the heart and highly depends on the compliance of the heart and arteries [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. However,in the mitral valve, the opening and closing phases are not completely passive as the papillary muscles and the chordae tendineaelocated within the left ventricle partly contribute, as mentioned before.…”

“…44.3C is a constant thatis assumed to be 0.1 for the aortic valve. In this formula,the unit of time is min, the unit of length is cm, delta P is the pressure drop across the valve with the unit of mmHg [21][22][23][24][25][26][27][28][29][30][31][32].…”