Mathematical modelling of atherosclerosis

Khatib, Nader El; Kafi, Oualid; Sequeira, Adélia; Simakov, Sergey; Vassilevski, Yuri; Volpert, Vitaly

doi:10.1051/mmnp/2019050

Cited by 23 publications

(10 citation statements)

References 173 publications

(193 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While some mathematical models consider biochemical reactions that initiate and maintain the overall progress of inflammation, some other works examine the contribution of fluid mechanics by investigating the fluid structure interaction and the effects of haemodynamic factors. For instance, in [31], plaqueflow interaction in atherosclerosis is investigated in an FSI model that considers the blood as a viscous fluid and the carotid artery with the atheromatous plaque as hyperelastic materials. In the same manner, in [55], the authors take into account the blood flow to investigate the wall shear stress in cap degradation, as well as the wound healing applied to plaque rupture.…”

Section: Mathematical Modeling Of Atherosclerosis In the Literaturementioning

confidence: 99%

See 1 more Smart Citation

Mathematical modeling of inflammatory processes of atherosclerosis

Younes

Khatib

2022

Math. Model. Nat. Phenom.

Self Cite

View full text Add to dashboard Cite

In this paper we study the early stages of atherosclerosis via a mathematical model of partial differential equations of reaction-diffusion type. The model includes several key species and identifies endothelial hyperpermeability, believed to be a precursor on the onset of atherosclerosis. We reduce the system to a monotone system and provide a biological interpretation for the stability analysis according to endothelial functionality. We investigate as well the existence of solutions of traveling waves type along with numerical simulations. The obtained results are in good agreement with current biological knowledge. Likewise, they confirm and generalize results of mathematical models previously performed in literature. Then, we study the non monotone reduced model and prove the existence of perturbed solutions and perturbed waves, particularly in the bistable case. Finally, we consider the complete model proposed initially, perform numerical simulations and provide more specific results. We study the consistency between the reduced and complete models for a certain range of parameters. We elaborate bifurcation diagrams showing the evolution of inflammation upon endothelial permeability and LDL accumulation. We show that the regulation of atherosclerosis progression is mediated by anti-inflammatory responses that, up to certain extent, lead to plaque regression.

show abstract

Section: Mathematical Modeling Of Atherosclerosis In the Literaturementioning

confidence: 99%

“…Several models provide numerical simulations and rely on existing data to convey to reliable predictive conclusions. One can list the following works : [3,8,31,33,42,43].…”

Section: Mathematical Modeling Of Atherosclerosis In the Literaturementioning

confidence: 99%

Mathematical modeling of inflammatory processes of atherosclerosis

Younes

Khatib

2022

Math. Model. Nat. Phenom.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many authors have done theoretical modeling on atherosclerosis, especially to model the mechanisms of chronic inflammation of artery walls [7], [8], [9]. Khatib et al [7] use a reaction-diffusion model to understand the chronic inflammation of blood vessel walls. Calvez et al [8] made a numerical approach to understanding atherosclerotic plaque formation.…”

Section: Introductionmentioning

confidence: 99%

Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model

Aldila

Islamilova

Khosnaw

et al. 2021

CBMS

View full text Add to dashboard Cite

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.

show abstract

“…In Table 1, some advantages and disadvantages of these different assumptions, in vivo, in vitro, ex vivo, and in silico are summarized. More detailed information about the evolution and importance of numerical methods in atherosclerosis investigation can be found elsewhere [66,67].…”

Section: Introductionmentioning

confidence: 99%

In vitro Biomodels in Stenotic Arteries to Perform Blood Analogues Flow Visualizations and Measurements: A Review

Carvalho¹,

Maia²,

Souza³

et al. 2020

TOBEJ

View full text Add to dashboard Cite

Cardiovascular diseases are one of the leading causes of death globally and the most common pathological process is atherosclerosis. Over the years, these cardiovascular complications have been extensively studied by applying in vivo, in vitro and numerical methods (in silico). In vivo studies represent more accurately the physiological conditions and provide the most realistic data. Nevertheless, these approaches are expensive, and it is complex to control several physiological variables. Hence, the continuous effort to find reliable alternative methods has been growing. In the last decades, numerical simulations have been widely used to assess the blood flow behavior in stenotic arteries and, consequently, providing insights into the cardiovascular disease condition, its progression and therapeutic optimization. However, it is necessary to ensure its accuracy and reliability by comparing the numerical simulations with clinical and experimental data. For this reason, with the progress of the in vitro flow measurement techniques and rapid prototyping, experimental investigation of hemodynamics has gained widespread attention. The present work reviews state-of-the-art in vitro macro-scale arterial stenotic biomodels for flow measurements, summarizing the different fabrication methods, blood analogues and highlighting advantages and limitations of the most used techniques.

show abstract

Mathematical modelling of atherosclerosis

Cited by 23 publications

References 173 publications

Mathematical modeling of inflammatory processes of atherosclerosis

Mathematical modeling of inflammatory processes of atherosclerosis

Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model

In vitro Biomodels in Stenotic Arteries to Perform Blood Analogues Flow Visualizations and Measurements: A Review

Contact Info

Product

Resources

About