A Mathematical Model of Statin Anti-Hyperlipidemic Drug Reactivity and Diverse Concentrations of Risk Toxicity

Background/Objectives: Statins decrease the risk of cardiovascular events by lowering low-density lipoproteins (LDLs). Despite this, statins induce toxic effects by a mechanism of action that has not yet been elucidated. The aim of the present work was to create a mathematical simulation model to evaluate the effect of statins on LDL concentration reduction and the threshold value of toxic reversible concentrations. Methods: Fifteen calcified coronary artery biopsies from non-diabetic hyperlipidemic patients treated with statins were used. For this study, an advanced modified model including the Caputo Fractional Operator and molecular dynamics was employed. Results: The new characteristic absorption bands in the FTIR spectral region frequencies near 1744 and 976 cm^-1, assigned to the chemical functional groups of aldehydes (vCHO) and phosphates V(PO₄^3-) of the atheromatic plaques, respectively, were used for mathematical model development. The energy of the functional chemical bonds caused by redox modifications during atheromatic plaque progression was used to show the effects of statin concentrations numerically. The model provides the anti-atheromatic effects of statins by the inhibition of LDL formation. Furthermore, the mathematical model highlights the dose medication-statin dependence on the reverse point of the statins' protective role. Conclusions: The new mathematical model shows both the beneficial and harmful actions of statins, which are associated with critical dose-dependent treatments with statins. The model also indicates that, upon increasing the statin dose, excessive secondary oxidation products were obtained. These products control the upregulation of the biological response by triggering other new pathways of redox homeostasis reactions.