Strain-induced tissue growth laws: applications to embryonic cardiovascular development

Hemodynamic conditions play an essential role in the cardiovascular system, with abnormal blood flow conditions leading to growth and remodeling of cardiovascular walls. During embryonic development, altered hemodynamic conditions lead to congenital heart disease, which affects about 1% of newborn babies in developed countries. However, the mechanisms by which hemodynamic conditions affect cardiovascular development have not been fully elucidated. In this paper, we propose a model of cardiac growth in response to hemodynamic conditions, in which growth is modulated by a combination of wall strains and wall shear stresses. This is in contrast to previous models that proposed stress-induced growth laws. Because during embryonic development blood pressure increases over time, and this increase in blood pressure produces an increase in wall stresses, stress-induced growth laws would require time-dependent parameters. While blood pressure increases during development, cardiovascular walls become stiffer and thicker, and thus we postulate that instead strains experienced by cells remain approximately the same during development. This assumption motivated our cardioavascular model of strain-induced growth in response to hemodynamic conditions, which we implemented using finite element methods. Model simulations show that the proposed model results in tissue growth that is physiologically reasonable. Further, our analyses demonstrate that mechanical coupling - that results from residual stresses originating from differential tissue growth - may play a more important role in the modulation of cardiovascular tissue growth and remodeling than currently acknowledged.