Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis
In this work, we analyse the influence of the parameters of a mathematical model, previously proposed by the authors, for reproducing atheroma plaque in arteries. The model uses Navier–Stokes equations to calculate the blood flow along the lumen in a transient mode. It also uses Darcy’s law, Kedem–K...
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MDPI AG
2023-02-01
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/829 |
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| author | Patricia Hernández-López Miguel A. Martínez Estefanía Peña Myriam Cilla |
| author_facet | Patricia Hernández-López Miguel A. Martínez Estefanía Peña Myriam Cilla |
| author_sort | Patricia Hernández-López |
| collection | DOAJ |
| description | In this work, we analyse the influence of the parameters of a mathematical model, previously proposed by the authors, for reproducing atheroma plaque in arteries. The model uses Navier–Stokes equations to calculate the blood flow along the lumen in a transient mode. It also uses Darcy’s law, Kedem–Katchalsky equations, and the three-pore model to simulate plasma and substance flows across the endothelium. The behaviours of all substances in the arterial wall are modelled with convection–diffusion–reaction equations, and finally, plaque growth is calculated. We consider a 2D geometry of a carotid artery, but the model can be extrapolated to other geometries or arteries, such as the coronaries or the aorta. A mono-variant sensitivity analysis of the model parameters was performed, with values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>25</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>10</mn><mo>%</mo></mrow></semantics></math></inline-formula>, with respect to the values of the previous model. The results were analysed with respect to the volume in the plaque of foam cells (FC), synthetic smooth muscle cells (SSMC), and collagen fibre. It was observed that the volume in the plaque of the different substances (FC, SSMC, and collagen) has a strong influence on the results, so it could be used to analyse the vulnerability of plaque. The stenosis ratio of the plaque was also analysed, showing a strong influence on the results as well. Parameters that influence all the results considered when ranged <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>10</mn><mo>%</mo></mrow></semantics></math></inline-formula> are the rate of LDL degradation and the diffusion coefficients of LDL and monocytes in the arterial wall. Furthermore, it was observed that the change in the volume of foam cells in the plaque has a greater influence on the stenosis ratio than the change of synthetic smooth muscle cells or collagen fibre. |
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| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-11T08:28:32Z |
| publishDate | 2023-02-01 |
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| spelling | doaj.art-945b37ac0efd4815a515b61c8e80375a2023-11-16T21:54:37ZengMDPI AGMathematics2227-73902023-02-0111482910.3390/math11040829Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of AtherosclerosisPatricia Hernández-López0Miguel A. Martínez1Estefanía Peña2Myriam Cilla3Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, SpainApplied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, SpainApplied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, SpainApplied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, SpainIn this work, we analyse the influence of the parameters of a mathematical model, previously proposed by the authors, for reproducing atheroma plaque in arteries. The model uses Navier–Stokes equations to calculate the blood flow along the lumen in a transient mode. It also uses Darcy’s law, Kedem–Katchalsky equations, and the three-pore model to simulate plasma and substance flows across the endothelium. The behaviours of all substances in the arterial wall are modelled with convection–diffusion–reaction equations, and finally, plaque growth is calculated. We consider a 2D geometry of a carotid artery, but the model can be extrapolated to other geometries or arteries, such as the coronaries or the aorta. A mono-variant sensitivity analysis of the model parameters was performed, with values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>25</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>10</mn><mo>%</mo></mrow></semantics></math></inline-formula>, with respect to the values of the previous model. The results were analysed with respect to the volume in the plaque of foam cells (FC), synthetic smooth muscle cells (SSMC), and collagen fibre. It was observed that the volume in the plaque of the different substances (FC, SSMC, and collagen) has a strong influence on the results, so it could be used to analyse the vulnerability of plaque. The stenosis ratio of the plaque was also analysed, showing a strong influence on the results as well. Parameters that influence all the results considered when ranged <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>10</mn><mo>%</mo></mrow></semantics></math></inline-formula> are the rate of LDL degradation and the diffusion coefficients of LDL and monocytes in the arterial wall. Furthermore, it was observed that the change in the volume of foam cells in the plaque has a greater influence on the stenosis ratio than the change of synthetic smooth muscle cells or collagen fibre.https://www.mdpi.com/2227-7390/11/4/829atherosclerosismechanobiological modelparameter analysiscarotid artery |
| spellingShingle | Patricia Hernández-López Miguel A. Martínez Estefanía Peña Myriam Cilla Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis Mathematics atherosclerosis mechanobiological model parameter analysis carotid artery |
| title | Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis |
| title_full | Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis |
| title_fullStr | Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis |
| title_full_unstemmed | Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis |
| title_short | Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis |
| title_sort | understanding the parameter influence on lesion growth for a mechanobiology model of atherosclerosis |
| topic | atherosclerosis mechanobiological model parameter analysis carotid artery |
| url | https://www.mdpi.com/2227-7390/11/4/829 |
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