Open AccessSimple model of atherosclerosis in cylindrical arteries: impact of anisotropic growth on Glagov remodeling
Author(s) -
Navid Mohammad Mirzaei,
Pak-Wing Fok
Publication year - 2020
Publication title -
mathematical medicine and biology
Language(s) - English
Resource type - Journals
eISSN - 1477-8602
pISSN - 1477-8599
DOI - 10.1093/imammb/dqaa011
Subject(s) - isotropy , anisotropy , lumen (anatomy) , adventitia , materials science , tensor (intrinsic definition) , strain energy , phase (matter) , mechanics , condensed matter physics , chemistry , geometry , anatomy , physics , mathematics , thermodynamics , optics , biology , medicine , finite element method , organic chemistry
In 1987, Seymour Glagov observed that arteries went through a two-stage remodeling process as a result of plaque growth: first, a compensatory phase where the lumen area remains approximately constant and second, an encroachment phase where the lumen area decreases over time. In this paper, we investigate the effect of growth anisotropy on Glagov remodeling in five different cases: pure radial, pure circumferential, pure axial, isotropic and general anisotropic growth where the elements of the growth tensor are chosen to minimize the total energy. We suggest that the nature of anisotropy is inclined towards the growth direction that requires the least amount of energy. Our framework is the theory of morphoelasticity on an axisymmetric arterial domain. For each case, we explore their specific effect on the Glagov curves. For the latter two cases, we also provide the changes in collagen fiber orientation and length in the intima, media and adventitia. In addition, we compare the total energy produced by growth in radial, circumferential and axial direction and deduce that using a radially dominant anisotropic growth leads to lower strain energy than isotropic growth.