Department of Biological Sciences

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Author: search.filters.author.Deepa, P.R.Subject: search.filters.subject.Mathematics

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    A Bio-mathematical Approach to Evaluate the Risk Burden of Hypertension and Hyperlipidemia in Diabetic Cardiovascular Disease
    (Scientific & Academic Publishing, 2012) Deepa, P.R.
    Cardiovascular disease (CVD) is a major cause of mortality in both developed and developing countries, owing to significant increase in the intake of high-energy foods, reduced physical activity, and an increase in psychosocial stress, which in turn lead to dysglycemia, hypertension, and dyslipidemia. The incidence of CVD in diabetics is very high that is further aggravated by co-morbidities such as hyperlipidemia and/or hypertension. The purpose of this study is to mathematically model the dynamics of CVD in diabetic population with hyperlipidemia and hypertension. Here, the mathematical model is a system of ordinary differential equations (ODEs). The steady states of the model are computed and their stability is studied. Numerical simulations are performed on the model, and conditions for controlling CVD in diabetics are derived. The results of this analysis suggest that the extent of control of hyperlipidemia and hypertension directly correlates with decrease in CVD development in the diabetic population. Early diagnosis of the modifiable risk factors such as hyperlipidemia and hypertension, followed by effective clinical management to regulate blood lipid levels and blood pressure in diabetics would greatly reduce the burden of cardiovascular complications in diabetic populations
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    Mathematical Modeling of Coronary Artery Disease (CAD): Analysis Reveals HbA1c and Total Cholesterol to be Significant Risk Predictors
    (Sage, 2017) Deepa, P.R.; Murali, Padma
    The increasing prevalence of CAD (Coronary Artery Disease) calls for early detection of risk factors and effective clinical management. The predictive potential of commonly estimated clinical variables on CAD incidence was assessed using mathematical modeling and analysis. A random sample of 50 patients with CAD and a control group of 50 subjects without CAD were drawn from a cardiac specialty hospital in Chennai, India during 2011-2012 (mean age = 50.2 years, SD = 11.2 years). Medical data included age, gender, height, weight, body mass index, presence/absence of hypertension, systolic blood pressure, diastolic blood pressure, presence/absence of diabetes mellitus, fasting blood sugar, post-prandial blood sugar, HbA1c, total cholesterol, family history of CAD. Mathematical modeling using discriminant analysis was performed to understand significant contributors leading to CAD. The discriminant analysis resulted in a mathematical model using parameters, HbA1c and cholesterol. The model was found to be statistically significant and this was demonstrated by computing the F value. HbA1c and total cholesterol were found to be significant in predicting the occurrence of CAD.