Nonlinear mathematical model for predicting long term cardiac remodeling in Chagas' heart disease: Introducing the concepts of ‘limiting cardiac function’ and ‘cardiac function deterioration period’ - Benchimol-Barbosa, Paulo Roberto (International journal of cardiology, 2010)
Cardiac remodeling has been recently investigated in long term follow-up introducing a simple exponential model to describe the time course of cardiac function and dimension changes in Chagas' disease. In the present study, an improved mathematical model to equate time course and cardiac functional changes has been proposed. Present model has been derived from previously validated intuitive assumptions and tested on data set of outpatients with chronic Chagas' disease (51.3 ± 9.4 years old), followed for up to 10 years in Rio de Janeiro, Brazil. The variables representing cardiac status at admission were plotted against respective time derivative, which appropriately fit a second order polynomial (adjusted r 2 = 0.956; p < 0.001), indicating that long term cardiac remodeling followed a Verhulst–Pearl (Logistic) model. The derived Logistic model provided two output constants: a time-function (2.0 · 10 − 3 ± 5.4 · 10 − 4 months − 1 ·% − 1 ; p < 0.001) and an inferior limit for left ventricular ejection fraction (19.0 ± 0.9%; p < 0.001), standing for a limit beyond life expectation is unsustainable, in Chagas' disease. Cardiac function deterioration period was promptly derived from the model, representing the period of time following indeterminate stages of the disease when cardiac function start deteriorating, and ranged from 3 to 15.8 years. An example of data of left ventricular ejection fraction of a subject followed during 10 years illustrated the model, further validating its robustness. Present data confirms that, in chronic Chagas' disease, initial insult is connected to the progression of myocardial remodeling and introduces the concepts of limiting cardiac function and cardiac deterioration period.