Agent Based and Finite Element Method for Plaque Development in the Carotid Artery

Objectives: Atherosclerosis is an inflammatory disease that is characterized by the accumulation of lipids and formation of plaque within the arterial wall.¹ It is characterized by dysfunction of endothelium, vasculitis and accumulation of lipid, cholesterol and cell elements inside blood vessel wall. This process develops in arterial walls with discrete nature between cells, molecular biomarkers, which indicate that discrete modelling approach like Agent Based Model (ABM) can be used for simulation of complex process for plaque development. We here concentrate for carotid artery plaque development.

Materials and Methods: The US images obtained during clinical examination for a set of patients are annotated by the clinical experts and used to train a convolutional neural network. Afterwards, for a particular patient, the collection of longitudinal and transversal US images is imported into the deep learning module and the 3D reconstruction module to create the patient-specific geometry. The procedure is related to the reconstruction of the lumen of the carotid bifurcation, and the same procedure is also applied for the wall reconstruction, with the only difference being in the fact that an additional set of contours for the wall is segmented from the US images. Blood flow through a curve blood vessel with stenosis was modeled using 3D finite element method (FEM). Fluid dynamics computation is performed by PAK solver, giving velocity and pressure field, as well as wall shear stress distribution.² ABM method was applied on the arterial wall taken into account cell mitosis and ECM production in the intima including lipid cells.

Results: The reconstructed geometry with overall five chosen cross-sections has been presented in the Figure 1. The model on the left is colored according to the distribution of total displacement of the nodes on the surface between lumen and intima. On the right, the change of the shape of the cross-sections of the arterial wall is shown in three specific moments in time (baseline, after 3 months and after 6 months). [Fig. 1]. The results of the plaque progression simulation. The distribution of displacement of nodes of the arterial wall (left); the change of shape of chosen cross-sections over time (right)

Conclusion: Specific carotid artery patient from US was modeled with coupled FEM and ABM method. First results show good agreement between proposed method and clinical measurements in the follow up 3D US image reconstruction. The integrated model ABM and FEM can help to predict the evolution of atherosclerotic plaque which is very significant for appropriate diagnostics and vascular treatment planning.

Acknowledgements

The research presented in this study was part of the project that has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 755320-2 - TAXINOMISIS.

Fig. 1 The results of the plaque progression simulation. The distribution of displacement of nodes of the arterial wall (left); the change of shape of chosen cross-sections over time (right) Figure 1

References

1. Libby P Inflammation in atherosclerosis. Nature 420:868–874. (2002)

2. Filipovic ND, Zivic M, Obradovic M, Djukic T, Markovic ZS, Rosic M. Numerical and experimental LDL transport through arterial wall. Microfluidics and Nanofluidics 2014;16(3):455–464

3. Rakocevic G, Djukic T, Filipovic N, Milutinovic V. Computational Medicine in Data Mining and Modeling. Springer, New York, USA, (2013).

No conflict of interest has been declared by the author(s).

Publication History

Article published online:
10 June 2022