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Stability analysis of a model of atherosclerotic plaque growth.

Reddy S, Seshaiyer P - Comput Math Methods Med (2015)

Bottom Line: Atherosclerosis, the formation of life-threatening plaques in blood vessels, is a form of cardiovascular disease.In this paper, we analyze a simplified model of plaque growth to derive physically meaningful results about the growth of plaques.In particular, the main results of this paper are two conditions, which express that the immune response increases as LDL cholesterol levels increase and that diffusion prevails over inflammation in a healthy artery.

View Article: PubMed Central - PubMed

Affiliation: Thomas Jefferson High School for Science and Technology, Alexandria, VA 22312, USA.

ABSTRACT
Atherosclerosis, the formation of life-threatening plaques in blood vessels, is a form of cardiovascular disease. In this paper, we analyze a simplified model of plaque growth to derive physically meaningful results about the growth of plaques. In particular, the main results of this paper are two conditions, which express that the immune response increases as LDL cholesterol levels increase and that diffusion prevails over inflammation in a healthy artery.

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Related in: MedlinePlus

Spatial integrals of squared perturbations over time for f′(Le) < 0.
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Related In: Results  -  Collection


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fig5: Spatial integrals of squared perturbations over time for f′(Le) < 0.

Mentions: Mathematically, f′(Le) < 0 implies the existence of an eigenvalue with positive real part of the coefficient matrix A in the proof of Theorem 2. It is well known that this causes the space-integral of at least one of the reactants to diverge over time in the context of the linear system. f′(Le) > 0 is thus a necessary condition for stability of the linearized system and seems to also be necessary for the stability of the initial system, as illustrated by Figures 2–5.


Stability analysis of a model of atherosclerotic plaque growth.

Reddy S, Seshaiyer P - Comput Math Methods Med (2015)

Spatial integrals of squared perturbations over time for f′(Le) < 0.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4389920&req=5

fig5: Spatial integrals of squared perturbations over time for f′(Le) < 0.
Mentions: Mathematically, f′(Le) < 0 implies the existence of an eigenvalue with positive real part of the coefficient matrix A in the proof of Theorem 2. It is well known that this causes the space-integral of at least one of the reactants to diverge over time in the context of the linear system. f′(Le) > 0 is thus a necessary condition for stability of the linearized system and seems to also be necessary for the stability of the initial system, as illustrated by Figures 2–5.

Bottom Line: Atherosclerosis, the formation of life-threatening plaques in blood vessels, is a form of cardiovascular disease.In this paper, we analyze a simplified model of plaque growth to derive physically meaningful results about the growth of plaques.In particular, the main results of this paper are two conditions, which express that the immune response increases as LDL cholesterol levels increase and that diffusion prevails over inflammation in a healthy artery.

View Article: PubMed Central - PubMed

Affiliation: Thomas Jefferson High School for Science and Technology, Alexandria, VA 22312, USA.

ABSTRACT
Atherosclerosis, the formation of life-threatening plaques in blood vessels, is a form of cardiovascular disease. In this paper, we analyze a simplified model of plaque growth to derive physically meaningful results about the growth of plaques. In particular, the main results of this paper are two conditions, which express that the immune response increases as LDL cholesterol levels increase and that diffusion prevails over inflammation in a healthy artery.

Show MeSH
Related in: MedlinePlus