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

Abstract

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.

Breast Cancer Radiation Therapy and the Risk of Acute Coronary Events: Insights From a Process-Oriented Model

“…For analysis of these data, we applied a derivative of the process-oriented model published in (10). In the model, coronary atherosclerosis is characterized by the coronary artery surface covered with fatty streaks, fibrous plaques, and complicated lesions.…”

“…The extent of fatty streaks, fibrous plaques and complicated lesions is not known for the breast cancer cohort. Therefore, following previous studies [10,11], model parameters were simultaneously adjusted to the breast cancer cohort and to some autopsy data [18]. The autopsy data provide age dependent extent and distribution of the above mentioned lesion types.…”

“…Consequently, in the model ACEs were assumed to follow complicated lesions, with some rate that connects the underlying biological processes to the hazard rate. In earlier applications of the process oriented model (10,11) the endpoint was restricted to myocardial infarction.…”

“…Midpoint values of the strata were applied for age and dose. Simulation and evaluation were performed with software adapted from (10). More explanations on the model and the fitting procedure can be found in the Supplemental Material.…”

“…Age-time patterns in risk are shaped by the way risk factors affect disease development. Recently, this relationship has been illustrated using a process oriented, mathematical model of atherosclerosis and subsequent myocardial infarction (10,11). The model describes the incidence in the general population as a consequence of risk factors perturbing disease development (11).…”