Model of Cardiovascular Physiology

We are developing a cardiovascular model to cover the physiology and pathophysiology as well as the therapies and actions that might be important in managing a patient in heart failure. Several cardiovascular models have been reported in the literature, but none meet the needs of this project. Since the program will ultimately be used in the service of patients, the parameters in the model should be ones that are either measurable in the patient or of demonstrated usefulness for physicians in understanding patient states. Furthermore, only those parameters that are needed to discriminate among the conditions that might respond differently to therapy should be included. Conditions such as valvular lesions, myocardial disease, and renal failure must be included among the parameters because they are important causes of heart failure.

The model is based on constraint relations among the parameters. These relations come from both the physiology literature and clinical judgment guided by the medical literature, including some relations derived from those in Coleman's HUMAN model[6]. Since the model is also the primary vehicle for explaining the predictions, it is important that the model be arranged in such a way that the relations are intuitive. The most natural way to think of relations seems to be causally in terms of blood flow. Therefore, that was the primary determinant in selecting the form of each constraint.

The model includes both left and right sides as well as sympathetic response and heart rate. Such factors as renal function, the determinants of ischemia and oxygen supply are also included in the model but are not of concern for this paper. The following is a qualitative view of the model:

1. Left atrial pressure (LAP) is a function of the volume in the pulmonary circuit approximated from the physiological limits and normal values of the parameters. Variations in compliance are not included.

2. Left ventricular output (LVO) is a function of ventricular filling, determined by the Frank-Starling curve, ventricular compliance, and ventricular emptying.

3. Blood pressure (BP) is the product of systemic vascular resistance (SVR) and cardiac output (CO).

4. SVR is modified by sympathetic stimulation as well as exercise and a number of therapies.

5. Left ventricular emptying is a function of left heart strength, sympathetic stimulation, and the load of left ventricular systolic pressure (LVSP).

6. Right atrial pressure (RAP) is the difference between a function of the venous volume and venous return gradient computed from CO and resistance to venous return.

7. Right ventricular output (RVO) is analogous to LVO, as is right ventricular emptying.

8. Pulmonary artery pressure (PAP) is RVO times pulmonary vascular resistance (PVR) plus left atrial pressure (LAP).

9. PVR is modified by the RVO (the flow through the pulmonary vessels).

10. Blood volume, a constant for short time periods, is divided into pulmonary volume, venous volume, and a factor representing unstressed volume that is a function of venous constriction, sympathetic stimulation, and exercise.

11. Pulmonary volume is determined by the integration of the difference between the output of the two ventricles. Therefore in stable states the two ventricles must have equal outputs.

12. Sympathetic stimulation and vagal stimulation are both functions of the change in BP from its normal state and exercise.

13. Heart rate (HR) is a function of normal heart rate, sympathetic stimulation, and vagal stimulation.

14. Time in systole per minute (and therefore diastole) is determined by heart rate.