To determine the ability of the model to predict the changes in patient parameters, we selected papers reporting on patients with one of these lesions undergoing a therapy and/or exercise and reporting extensive hemodynamic data. The five papers include two describing mitral stenosis in adults exercised and given propranolol or nitroglycerin, one describing aortic regurgitation in adults exercised and given hydralazine, one describing aortic stenosis in children with exercise and one describing aortic stenosis and heart failure in adults given hydralazine.
The model was adjusted to the patients in each control state by setting constants in the relations between the parameters in the paper to be consistent with the reported values. These adjustments include shifting the Frank-Starling curve up or down to reflect the output at the reported end diastolic pressure and setting the base blood pressure, heart rate, and resistances. To determine the model's prediction for an action, the value of the changed parameter(s) is selected that produces the reported cardiac output, since all of the interventions we considered have a significant effect on cardiac output. The remaining parameters then reflect the ability of the model to predict appropriately.
The two papers on MS used patients with pure MS, no heart failure, and only somewhat elevated pulmonary vascular resistance. The paper by Giuffrida, et al[8], measured the patients at rest, after 10 minutes of exercise, after resting for 20 minutes, 10 minutes after administration of propranolol, and after further exercise. We modeled the experiment by fitting the model to the initial rest state and then applying an amount of exercise that increased the CO to the reported level. In addition, the influence of flow on PVR was changed to reflect the trend of increased resistance with increased flow present in both MS papers. That is, it appears that at the levels of LAP present and the chronic pulmonary changes that take place at high pressures, the resistance no longer decreases with increasing flow, but actually increases slightly. With this adjustment to the model, all of the predicted changes (figure 2) closely match the reported changes.
Since the second rest state varies from the first in that the heart rate is still high, the model was readjusted to the second rest state before adding the propranolol. The propranolol change was adjusted to bring the cardiac output down to the reported level. With this change, the parameters changed appropriately. In our experimentation, we initially modeled propranolol as only decreasing sympathetic stimulation to inotropic state and heart rate, but it was clear that to account for the reported changes it was necessary to include small effects increasing SVR and PVR. Expert judgment and the literature indicate that these effects are reasonable.
The final state was simulated by adding exercise to the state with propranolol. The model required less exercise to predict the reported cardiac output, which is consistent with the reported decrease in exercise tolerance among the patients. The combination of effects on SVR from the propranolol and exercise resulted in a lower SVR even though simply adding the effects would have resulted in an increase in SVR. This total effect is consistent with parallel resistances only part of which is affected by the exercise.
In the second MS paper by Bornheimer, et al[9], the patients went through a similar protocol, except they were given nitroglycerin. These patients also had some heart failure with the majority on digitalis and diuretics. As a result, the SVR was elevated in these patients and decreased more with exercise than in normal patients. When the model was adjusted to account for this behavior, the predictions were as indicated in figure 3. The measured parameters changed as reported except for the LAP which is predicted to be somewhat higher than it actually was. This may be a problem with the assumptions about MS since the difference in mitral valve areas computed from the two rest states is more than enough to account for the LAP difference.
The changes with nitroglycerin were made from the second rest state. The appropriate level of nitroglycerin to produce the reported cardiac output produced the reported change in all of the parameters. When exercise was added to this state, again at a lower level reflecting the decreased exercise tolerance, the parameters changed as indicated. The predicted HR was higher than actual and the LAP lower. There is a pattern of differences among the parameters indicating that the patients probably had additional impediments to increasing their cardiac output.
The second disease studied was AS. The first paper[10] considered the effects of exercise in children with AS. From the data it was clear that the PVR decreased with increased flow as in normal individuals. Also, exercise seems to produce more decrease in SVR than in the adult chronic cases considered before. Finally, the relationship between heart rate and systolic time is altered in AS. A suitable systolic time relationship was derived from the two papers. With these changes to the model, the predictions were all within the limits in the paper.
The second AS paper[11] considered patients with AS and congestive heart failure who were given hydralazine. This paper illustrates a problem with the modeling of hydralazine. If hydralazine is assumed to have no inotropic effect, it is impossible to duplicate the changes that occurred. Giving enough hydralazine to produce the reported change in SVR yields the first line of predictions in figure 5. The CO is too low and LAP is increasing instead of decreasing. If it is assumed that there is some inotropic effect, the prediction labeled I is produced. This second prediction accounts for all of the changes except that the HR is still too high. This inotropic effect for hydralazine may have some other explanation with a more detailed model of the effects of afterload on CO, but inotropy is the simplest hypothesis at this level of modeling.
The final paper[12] reports on patients with chronic aortic regurgitation exercised and given hydralazine. These patients were all chronic cases with mild to severe heart failure. Digitalis and diuretics were continued without change. Again, the SVR was higher than normal and responded more to exercise than in patients without heart failure. There was also a reported increase in the LAP that was not consistent with the model predictions. It was hypothesized that since these patients had a large blood volume, the exercise effects on the venous volume may be accentuated. With these modifications the predicted values after exercise are all within the stated limits. It may be that the explanation is a flatter Frank-Starling curve, but there is not enough data to distinguish between these possibilities. It is also true that without some quantitative measure of exercise, increasing venous volume response and SVR response is equivalent to decreasing the sympathetic response, which is also likely in these patients.
The patients were then given hydralazine and brought to maximum beneficial level over 24 hours. This time delay complicates the analysis again, since it is possible that the blood volume has changed. Hydralazine was modeled as in the previous case, but at the appropriate SVR, the pressures and output are all too low. If blood volume were to increase 400ml the results in figure 6 are obtained. This is consistent with the tendency of hydralazine to cause water retention, but there may be other explanations. With exercise and hydralazine at the increased blood volume, the predicted changes were consistent with the reported changes except that LAP was lower than reported.