Tissue Growth Model for Maintaining Tensional Homeostasis With Applications to Hypertension and Stented Artery

Abstract

In this work, a theoretical growth model for maintaining a homeostatic mechanical environment was developed to capture the growth behavior of the artery and its association with its mechanical environment. The multiplicative decomposition approach was adopted to decompose the deformation matrix into an elastic term and a growth term. A growth factor relating to homeostatic stress was used to regulate the progressive changes in the arterial morphology. In addition, a growth coefficient was adopted to avoid unlimited growth. The arterial growth model was implemented in a commercial finite element software and tested in the cases of hypertension and stenting. Results have demonstrated that the arterial growth induced by hypertension can mitigate abnormal arterial stresses and restore the stress level in the artery back to its homeostasis. Following stenting, the arterial growth pattern was consistent with the distribution of the von Mises stresses in the artery. The arterial growth homogenized the stress distribution in the artery, except for the regions under the stent struts. The heterogeneous growth of the artery disrupted the alignment of the maximum principal stresses in the artery, elongated the stent, reduced the lumen area, and aggregated the tissue prolapse. It is expected that the growth model developed in this work could help to understand and regulate the chronic response of the tissue. Appropriate modeling of arterial growth in connection with tensional homeostasis provided insights for predicting alterations to the arterial mechanical environment, identifying biomechanical factors leading to restenosis, and designing therapeutic strategies to regulate the tissue adaptations.