Computational modeling of hypertensive growth in the human carotid artery

Abstract

Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.

Computational modeling of acute myocardial infarction

“…We can think of the growth tensor F g as a second-order internal variable to characterize arbitrary forms of isotropic or anisotropic growth [33]. Here we consider two types of growth and parameterize the two growth tensors exclusively in terms of two single scalar-valued internal variables, the growth multipliers ϑ ⊥ and ϑ ‖ , which characterize growth in the muscle sheet direction n ⊥ and in the muscle fiber direction n ‖ [17,39]. The Jacobian of the deformation gradient J = det( F ) characterizes changes in volume, which we can decompose into reversible elastic volume changes J e = det( F e ) and volume changes attributed to growth, J g = det( F g ), $$\mathrm{normalJ}=\text{det}false(\mathrm{boldF}false)={\mathrm{J}}^{\mathrm{e}}{\mathrm{J}}^{\mathrm{g}}.$$ We further introduce the right Cauchy Green tensor, $$\mathrm{boldC}={\mathbf{F}}^{\mathrm{t}}·\mathrm{boldF}={false({\mathbf{F}}^{\mathrm{g}}false)}^{\mathrm{t}}·{\mathbf{C}}^{\mathrm{e}}·{\mathbf{F}}^{\mathrm{g}}\hspace{1em}\text{with}\hspace{1em}{\mathbf{C}}^{\mathrm{e}}={false({\mathbf{F}}^{\mathrm{e}}false)}^{\mathrm{t}}·{\mathbf{F}}^{\mathrm{e}},$$ as the covariant pull back of the elastic right Cauchy Green tensor C e .…”

Patient-Specific Airway Wall Remodeling in Chronic Lung Disease

“…The fluid mechanics of the lung have been extensively studied using both idealized and patient-specific models [32,59]. However, existing solid mechanics studies which focus on three-dimensional biological geometries are few [54,63], mainly analytical [7,17], fail to predict emerging surface morphologies beyond the onset of folding [60,73], and typically neglect the characteristic branching of the lung [8, 27, 38]. Here we address these limitations by extending airway remodeling mechanics to realistic patient-specific airway branch models created from magnetic resonance images.…”

A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues

“…In this sense, much effort is directed towards representing remodelling in vascular tissue [40][41][42][43], with a particular focus on the pathological remodelling observed in aortic aneurysm tissue [44][45][46]. The mathematical modelling of the inflammation, proliferation and remodelling phases in ligament tissue has also been addressed [47,48].…”