Simulating the dynamics of atherosclerosis to the incidence of myocardial infarction, applied to the KORA population

Analyzing epidemiological data with simplified mathematical models of disease development provides a link between the time-course of incidence and the underlying biological processes. Here we point out that considerable modeling flexibility is gained if the model is solved by simulation only. To this aim, a model of atherosclerosis is proposed: a Markov Chain with continuous state space which represents the coronary artery intimal surface area involved with atherosclerotic lesions of increasing severity. Myocardial infarction rates are assumed to be proportional to the area of most severe lesions. The model can be fitted simultaneously to infarction incidence rates observed in the KORA registry, and to the age-dependent prevalence and extent of atherosclerotic lesions in the PDAY study. Moreover, the simulation approach allows for non-linear transition rates, and to consider at the same time randomness and inter-individual heterogeneity. Interestingly, the fit revealed significant age dependence of parameters in females around the age of menopause, qualitatively reproducing the known vascular effects of female sex hormones. For males, the incidence curve flattens for higher ages. According to the model, frailty explains this flattening only partially, and saturation of the disease process plays also an important role. This study shows the feasibility of simulating subclinical and epidemiological data with the same mathematical model. The approach is very general and may be extended to investigate the effects of risk factors or interventions. Moreover, it offers an interface to integrate quantitative individual health data as assessed, for example, by imaging.

Automated summary

Analyzing epidemiological data with simplified mathematical models of disease development provides a link between incidence over time and biological processes. A proposed model based on a Markov Chain simulates atherosclerosis progression in coronary arteries, showing significant age dependence in females around menopause. Simulation allows for non-linear transition rates and consideration of randomness and inter-individual heterogeneity.