| Background/Aim: Statins are a class of drugs which by lowering the cholesterol minimise the progression of atherosclerosis and plaque formation and the thickening of the inner layer of arterial walls. The purpose of the present work is to create a mathematical simulation model to predict the health benefits of statins. Methods: The Caputo Fractional Operator (C), the more appropriate for biological systems, in combination with fractional differential equations systems (FDE’s) were used for our non-local biological system. The parameter of fractional order γ was used to describe the effect of statin dose administration and their reverse point of the pharmacodynamic and pharmacokinetic properties. The numerical results were based on the energies of the most important functional chemical groups of the products produced by hyperlipidaemia. Results: For the mathematical model the characteristic energies of the functional chemical groups -CH2 of lipids (8.35 kcal/mol) and -NH2 groups of protein amide I in β-sheet conformation (4.837 kcal/mol) were used. These compounds are strongly related to foam cells and fibrosis of atheromatic plaque formation with the disease progression. From the model it was suggested that by increasing the statin dose administration decrease the products caused by lipid peroxidation and cholesterol development. Moreover, it has been shown that upon statin administration a shift on time delay exists for irreversible products formation. Conclusions: The mathematical simulation model based on the energy of the functional chemical groups of characteristic components of atheromatic plaques caused by hypercholesteremia, showed that the beneficial effects of statins on foam cell and amyloidosis reduction were caused by lipid peroxidation and excess of serum cholesterol. Our model could be used for early diagnosis of statin medication dose to prevent cardiovascular events. |
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