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Math models enhance current therapies for coronary heart disease
Date:12/9/2013

in the use of stents. One way to combat this has been the use of stents that release drugs to inhibit the smooth muscle cell proliferation, which causes the occlusion. However, these drug-eluting stents have been associated with incomplete healing of the artery. Studies are now being conducted to improve their performance.

"Historically, stent manufacturers have predominantly used empirical methods to design their drug-eluting stents. Those stents which show promising results in laboratory and clinical trials are retained and those that do not are discarded," explains McGinty. "However, a natural question to ask is, what is the optimal design of a drug-eluting stent?"

The design of drug-eluting stents is severely limited by lack of understanding of the factors governing their drug release and distribution. "How much drug should be coated on the stent? What type of drug should be used?" McGinty questions. "All of these issues, of course, are inter-related. By developing models of drug release and the subsequent uptake into arterial tissue for current drug-eluting stents, and comparing the model solution with experimental results, we can begin to answer these questions."

The model proposed by the authors considers a stent coated with a thin layer of polymer containing a drug, which is embedded in the arterial wall, and a porous region of smooth muscle cells embedded in an extracellular matrix.

When the polymer region and the tissue region are considered as a coupled system, it can be shown under certain conditions that the drug release concentration satisfies a special kind of integral equation called the Volterra integral equation, which can be solved numerically. The drug concentration in the system is determined from the solution of this integral equation. This gives the mass of drug within cells, which is of primary interest to clinicians.

The simple one-dimensional model proposed in the paper provides analytical
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Contact: Karthika Muthukumaraswamy
karthika@siam.org
267-350-6383
Society for Industrial and Applied Mathematics
Source:Eurekalert  

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