Using models to advance medicine: mathematical modeling of post-myocardial infarction left ventricular remodeling.

The heart is an organ with limited capacity for regeneration and repair. The irreversible cell death and corresponding diminished ability of the heart to repair after myocardial infarction (MI), is a leading cause of morbidity and mortality worldwide. In this paper, a new mathematical model is presented to study the left ventricular (LV) remodeling and associated events after MI. The model accurately describes and predicts the interactions among heart cells and the immune system post-MI in the absence of medical interventions. The resulting system of nonlinear ordinary differential equations is studied both analytically and numerically in order to demonstrate the functionality and performance of the new model. To the best of our knowledge, this model is the only one of its kind to consider and correctly apply all of the known factors in diseased heart LV modeling. This model has the potential to provide researchers with a predictive computational tool to better understand the MI pathology and develop various cell-based treatment options, with benefits of lowering the cost and reducing the development time.

A simple model of immune and muscle cell crosstalk during muscle regeneration.

Muscle injury during aging predisposes skeletal muscles to increased damage due to reduced regenerative capacity. Some of the common causes of muscle injury are strains, while other causes are more complex muscle myopathies and other illnesses, and even excessive exercise can lead to muscle damage. We develop a new mathematical model based on ordinary differential equations of muscle regeneration. It includes the interactions between the immune system, healthy and damaged myonuclei as well as satellite cells. Our new mathematical model expands beyond previous ones by accounting for 21 specific parameters, including those parameters that deal with the interactions between the damaged and dead myonuclei, the immune system, and the satellite cells. An important assumption of our model is the replacement of only damaged parts of the muscle fibers and the dead myonuclei. We conduce systematic sensitivity analysis to determine which parameters have larger effects on the model and therefore are more influential for the muscle regeneration process. We propose additional validation for these parameters. We further demonstrate that these simulations are species-, muscle-, and age-dependent. In addition, the knowledge of these parameters and their interactions, may suggest targeting or selecting these interactions for treatments that accelerate the muscle regeneration process.

Transit times and mean ages for nonautonomous and autonomous compartmental systems.

We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von Förster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory generalises the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford approach model, and we demonstrate that the nonautonomous versions of transit time and mean age differ significantly from the autonomous quantities when calculated for that model.

Modeling Chagas Disease at Population Level to Explain Venezuela's Real Data.

OBJECTIVES: In this paper we present an age-structured epidemiological model for Chagas disease. This model includes the interactions between human and vector populations that transmit Chagas disease. METHODS: The human population is divided into age groups since the proportion of infected individuals in this population changes with age as shown by real prevalence data. Moreover, the age-structured model allows more accurate information regarding the prevalence, which can help to design more specific control programs. We apply this proposed model to data from the country of Venezuela for two periods, 1961-1971, and 1961-1991 taking into account real demographic data for these periods. RESULTS: Numerical computer simulations are presented to show the suitability of the age-structured model to explain the real data regarding prevalence of Chagas disease in each of the age groups. In addition, a numerical simulation varying the death rate of the vector is done to illustrate prevention and control strategies against Chagas disease. CONCLUSION: The proposed model can be used to determine the effect of control strategies in different age groups.