A Nonliner Poroelastic Model for the Trabecular Embryonic Heart

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Abstract
A theoretical model is presented for the primitive right ventricle of the stage 21 chick embryo. At this stage of development, the wall of the heart is trabecular with direct intramyocardial blood flow. The model is a pressurized fluid-filled cylinder composed of a porous inner layer of isotropic myocardium and a relatively thin compact outer layer of transversely isotropic myocardium. The analysis is based on nonlinear poroelasticity theory, modified to include residual strain and muscle activation. Correlating theoretical and experimental pressure-volume loops and epicardial strains gives first-approximation constitutive relations for stage 21 embryonic myocardium. The results from the model suggest three primary conclusions: (1) Some muscle fibers likely are aligned in the compact layer, with a fiber angle approximately +10 deg from the circumferential direction. (2) Blood is drawn into the wall of the ventricle during diastolic filling and isovolumic contraction and is squeezed out of the wall during systolic ejection, giving a primitive intramyocardial circulation before the coronary arteries form. As the heart rate increases, the transmural bloodflow velocity increases, but the volume of blood exchanged with the lumen per beat decreases. (3) Residual strain affects transmural stress distributions, producing nearly uniform stresses in the porous layer, where the peak end-systolic stress occurs. These results improve our understanding of the relation between form and function in the developing heart and provide directions for biological experiments to study cardiac morphogenesis.

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