The three disease states included in the model and discussed in this paper are mitral stenosis (MS), aortic stenosis (AS), and aortic regurgitation (AR). The representation of these disorders was determined by the physiologic effect of the disorder on the relationships between the cardiovascular parameters. To test and refine the predictive capability of these representations we have compared the results to published data on patients with these disorders.
MS causes a pressure gradient in diastole between the left atrium and left ventricle. For most situations, it is reasonable to assume that the area of the mitral valve orifice is constant. With that assumption, the flow across the valve obeys the properties of turbulent flow, expressed for valve oriface area as Gorlin's formulas. Thus, the pressure gradient is the square of the flow across the valve during diastole:
To preserve the intuition of causality in direction of flow, this formula is used to determine the LVEDP from the LAP in the model, which in turn is used as the filling pressure for computing LVO. Thus, LVEDP is determined by the LAP and the pressure drop across the valve.
AS is analogous to MS, except that the pressure gradient occurs between the left ventricle and the aorta and the flow happens in systole. Thus, the relationship drawn from the Gorlin formula is:
The left ventricular systolic pressure is the pressure the ventricle is
pumping against, determining the emptying. There is an assumption here
that is an appropriate approximation for the pressure
gradient. From the data we have so far, there is evidence that the
relationships are more complex, but not enough evidence to suggest a
better set of formulas.
Aortic regurgitation is somewhat more complicated because it depends on the reverse gradient between the aorta and ventricle in diastole. From the Gorlin formula the relationship is:
The pressure gradient in turn has been approximated as proportional to
mean arterial pressure by determined from data in a paper in
which the heart rate was varied[7]. Given this regurgitant
volume, the effective cardiac output (CO) is the difference.
In the papers used for refining the model, the patients were tested for their response to exercise and three therapies: propranolol, nitroglycerin, and hydralazine. Exercise is included in the model as a factor increasing sympathetic stimulation, decreasing vagal stimulation, decreasing vascular resistance, and increasing venous return.
Propranolol decreases the sympathetic stimulation to systolic function and heart rate and to a lessor extent increases the stimulation to systemic vascular resistance and pulmonary vascular resistance by leaving the alpha stimulation unopposed. Hydralazine decreases both the systemic and pulmonary vascular resistances. The effect of hydralazine in increasing cardiac output cannot always be accounted for by these factors alone. Therefore, we tried assuming a small direct positive effect on the inotropic state as well. Nitroglycerin causes venodilitation and a small decrease in the SVR.
With these relations for diseases and therapies included in the model, the model appears as shown in figure 1. The figure also includes some of the parameters for renal function and myocardial ischemia to show how these fit into the overall model, but they will not affect the following discussion. The model has been initialized to the rest state in the first paper and is shown predicting the result of exercise on that state. The highlighting shows the primary determinants of the increase in cardiac output. The mechanism for prediction makes it possible to identify the relative contributions of different pathways from the stimulus to any parameter. Thus, the pathways from exercise through sympathetic stimulation both directly and as a result of decreasing the SVR are the strongest influences on cardiac output in this situation.
