Despite extensive study over the past six decades the coupling of chemical reaction and mechanical processes in muscle dynamics is not well understood. We lack a theoretical description of how chemical processes (metabolite binding, ATP hydrolysis) influence and are influenced by mechanical processes (deformation and force generation). To address this need, a mathematical model of the muscle cross-bridge (XB) cycle based on Huxley's sliding filament theory is developed that explicitly accounts for the chemical transformation events and the influence of strain on state transitions.
The asserted dominant role of the kidneys in the chronic regulation of blood pressure and in the etiology of hypertension has been debated since the 1970s. At the center of the theory is the observation that the acute relationships between arterial pressure and urine production—the acute pressure-diuresis and pressure-natriuresis curves—physiologically adapt to perturbations in pressure and/or changes in the rate of salt and volume intake.
The integrated cardiovascular model combines a simple model of the cardiovascular system (Smith, 2004) and a model describing baroreflex control of the heart (Bugenhagen, 2010). The resulting closed loop model simulates pressures flows and volumes in the rat cardiovascular system as well as the dynamics of the baroreflex system. Both the Smith and Bugenhagen models are available for download in the links below. A Matlab version of the integrated model is included for comparison.
We present a phenomenological ODE model of baroreflex open-loop control of heart rate. The signal flow of the model is diagrammed in Figure 1. An aortic blood pressure signal (the driving signal for the model) is transduced by afferent baroreceptor nerve fibers in the wall of the aortic arch into a neural (firing rate) signal. This transduction process is governed by mechanical strain in the wall of the aorta. This neural signal is then relayed and further processed by the central and peripheral nervous systems into parallel sympathetic and parasympathetic tone signals.