A multiscale modelling approach to understand atherosclerosis formation: A patient-specific case study in the aortic bifurcation

Abstract

Atherogenesis, the formation of plaques in the wall of blood vessels, starts as a result of lipid accumulation (low-density lipoprotein cholesterol) in the vessel wall. Such accumulation is related to the site of endothelial mechanotransduction, the endothelial response to mechanical stimuli and haemodynamics, which determines biochemical processes regulating the vessel wall permeability. This interaction between biomechanical and biochemical phenomena is complex, spanning different biological scales and is patient-specific, requiring tools able to capture such mathematical and biological complexity in a unified framework. Mathematical models offer an elegant and efficient way of doing this, by taking into account multifactorial and multiscale processes and mechanisms, in order to capture the fundamentals of plaque formation in individual patients. In this study, a mathematical model to understand plaque and calcification locations is presented: this model provides a strong interpretability and physical meaning through a multiscale, complex index or metric (the penetration site of low-density lipoprotein cholesterol, expressed as volumetric flux). Computed tomography scans of the aortic bifurcation and iliac arteries are analysed and compared with the results of the multifactorial model. The results indicate that the model shows potential to predict the majority of the plaque locations, also not predicting regions where plaques are absent. The promising results from this case study provide a proof of concept that can be applied to a larger patient population.

Keywords: Mathematical modelling; atherosclerosis; calcification; multiscale; patient-specific.

Figure 1.

Reconstructed 3D geometry of the vessels around the iliac bifurcation. Pink regions show vessel wall while green regions show plaques/calcifications. (a) Left posterior view, (b) right anterior view, (c) shows the CT scan at the location indicated by the blue line in panels (a) and (b) and (d) shows the same slice with the plaque/calcification identified.

Figure 2.

Reconstructed 3D geometry of the vessels around the iliac bifurcation. Pink regions show vessel wall while green regions show plaques/calcifications. (a) Left posterior view, (b) right anterior view, (c) shows the CT scan at the location indicated by the blue line in panels (a) and (b) and (d) shows the same slice with the plaque/calcification identified.

Figure 3.

3D geometry used in CFD simulation, with boundary geometries and flow rates. Cross-sectional areas: distal abdominal aorta – 3.82 cm², left internal iliac – 0.38 cm², left external iliac – 0.34 cm², right internal iliac – 0.41 cm² and right external iliac – 0.39 cm².

Figure 4.

TAWSS: (a) left posterior view and (b) right anterior view.

Figure 5.

OSI: (a) left posterior view and (b) right anterior view.

Figure 6.

HOLMES: (a) left posterior view and (b) right anterior view.

Figure 7.

J_v: (a) left posterior view and (b) right anterior view.

Figure 8.

Comparison between predicted (top row) and observed (bottom row) plaque locations around the iliac bifurcation. Arrows indicate plaques, with colour coding to rate the quality of the match between the simulated J_v and the clinical data: green – good match, grey – reasonable match and black – failed to match. (a) and (d) Right anterior view, (b) and (e) left posterior view and (c) and (f) view from right side.