Therapy effect prediction uses the physiologic state determined by the diagnosis and the values of parameters to estimate the effect of adding or removing one or more therapies. The mechanism for prediction of the effects of therapy is based on signal flow analysis[17] and computes the changes in the parameters from steady state to steady state. The choice of a constraint representation for therapy prediction rather than a probabilistic representation is appropriate because there is usually enough information available to solve the constraints and because the complex interactions among the parameters make the generation of a probabilistic model extremely difficult.
The advantage of the signal flow mechanism over other means of solving the equations is that it produces a record of the paths of influence on the parameters and their relative contribution. This record provides the basis for an explanation of the change and may in the future allow a way to deal with some of the uncertainty in the relationships and measurements. Initially, we applied this mechanism to a model with qualitative relations on the links between parameters. This worked well in our early tests in which the actions of drugs in the normal patient were compared to the model predictions[14], but we had considerable difficulty extending the model to account for the behavior of mitral stenosis, the first valvular disease considered. Since most of the parameters have known quantitative relationships to other parameters and the computational mechanism supports quantitative reasoning, we converted the model to use quantitative relations. To do so required adding the handling of integrated parameters and compensating for non-linearities as well as developing a new model.
The prediction constraint model conforms to the usual notion of causality in the cardiovascular system. Since one normally thinks of the hemodynamic relations on the right and left sides of the heart separately, there is a problem in representing the equality of left and right outputs in steady state. Physiologically blood volume shifts between circulations equalizing the outputs. To capture this we have levels (integrated variables) representing the volume in each circulation.
Integrated relationships can be handled because the derivative of an integrated parameter in steady state is zero. This provides the additional constraint needed to determine the level of the parameter. The steady state assumption is justified because the time constants of concern differ by an order of magnitude or more. Typically, we are either interested in the changes that take place in minutes (immediate hemodynamic changes) or in the fluid balance involving renal function which takes place in days. Other changes require weeks or longer to take place. Thus, physiologic mechanisms with longer time constants than the time of interest can be ignored. With this extension the procedure for determining the change in all parameters requires two steps: determine the levels of the integrated parameters necessary for their derivatives to be zero, then use these values plus the original change to determine the final values of all of the parameters.
The second extension to the reasoning was to handle non-linearities in the relationships between parameters. A non-linearity implies that the gain between two parameters varies over the amount of the change. For example, in the relation determining the blood pressure (section 3.2) the effect of cardiac output depends on the systemic vascular resistance, which will also change. The algorithm uses the initial gain to determine the changes, but that is not always adequate. Our solution is to adjust all of the gains to be the average gain over the range of the change and iterate until the final values conform to the constraint equations. This approach has theoretical limitations, but it usually converges rapidly to a consistent solution. Once a solution is proposed, its adequacy can easily be tested by verifying that all of the equations are satisfied.
The model has been validated by comparing published data to the model predictions. The data came from papers in the literature in which patients with one of the diseases were given a therapy or exercised and the hemodynamic variables are reported before and after the intervention. When the hemodynamic data are fairly complete, the initial values of the model parameters can be computed or estimated and the model can simulate the patient. Our efforts in validating the model were very fruitful[13]. The model proved sufficient to account for the average behavior reported in each of the five papers studied. With only two or three minor exceptions, the predictions were within the errors of the mean reported for all of the modeled parameters, once appropriate distributions of direct effect were determined for the therapies and the exercise the patients experienced.
Therapy prediction starts with the PSM as determined so far. Since this is a quantitative model, the primary source of data is the parameter values that are entered in the input. For example, if the user enters a heart rate of 110 in the input, the diagnostic reasoning treats that as a high heart rate, but the therapy prediction reasoning uses the actual value. Many of the other parameter values needed in the model are computable from those that the user enters, and the program automatically computes these. Estimates of other parameter values are determined from the diagnosis. Most of these are simple to determine. For example, all of the diseases that are not in the diagnosis are given the parameter value zero. However, when important parameters such as the cardiac output have to be estimated, the program picks a number in the appropriate range that is consistent with the other parameters that influence it. Once a complete and consistent initial state is determined, the program can be used to predict the effect of one or more therapies. This is done by indicating a change in the value of the desired therapy (an increase, a decrease, or multiple therapies). The primary effects of examples of most of the important classes of therapies have been determined by our study of the literature and are included in the model. However, other therapies can be considered if the user knows the primary effects by specifying changes in the values of the primary effect parameters. The program then shows the predicted changes in all of the parameters. One problem is determining the appropriate dose for comparing effects. There is a mechanism in the program that will adjust the dose until a desired change is achieved in a particular parameter. That allows the user to answer such questions as, ``if enough of the therapy is given to increase the cardiac output to 5.0 L/min, what will happen to the other parameters?''
Figure 3 goes here.
Figure 3 shows the prediction of the exercise response of a patient with mitral stenosis (actually the average data for 10 patients). The display excludes unneeded diseases and associated parameters and links with no or very small gain. The parameters are organized by type and region of circulation with arrows showing the circulatory flow. The data in the paper included the heart rate, cardiac output, left ventricular systolic pressure, left ventricular end diastolic pressure, pulmonary artery pressure, and pulmonary wedge pressure[5]. The rest of the initial parameter values (shown at the bottoms of the parameters) were computed from these to run the model, making assumptions consistent with the state of the patient. For this example, the amount of exercise applied was chosen to produce the cardiac output of 8.0 L/min reported in the paper. The changed values are printed at the tops of the parameters. The predictions for the other reported parameters were all within the errors of the mean.