Harvard-MIT Division of Health Sciences and Technology HST.542J: Quantitative Physiology: Organ Transport Systems Instructors: Roger Mark and Jose Venegas MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departments of Electrical Engineering, Mechanical Engineering, and the Harvard-MIT Division of Health Sciences and Technology 6.022J/2.792J/BEH.371J/HST542J: Quantitative Physiology: Organ Transport Systems PROBLEM SET 2 Assigned: February 10, 2004 Due: February 19, 2004Problem 1 A twenty-year-old student was involved in an automobile accident and sustained a chest injury. Upon admission to the hospital he had a rapid, weak pulse, feeble heart sounds, and a low blood pressure. Because of the suspicion of heart damage, he was evalated in the cardiac catheterization laboratory. A left-sided cath study was performed, complete with bi-plane cine ventriculograms (X-ray movies of the ventricle obtained in orthogonal projections following injection of radio-opaque dye into the ventricle). It was discovered that the patient had a significant amount of blood in the pericardial cavity (between the heart and the pericardial sac). Three hundred milliliters of blood were removed and the patient improved considerably. As part of the evaluation procedure, diastolic pressure-volume curves for the left ventricle were measured both before and after the pericardial tap (removal of the pericardial blood). (This was done by simultaneous measurement of LV volume from the cine data, and of the LV pressure from and intracardiac pressure transducer.) These curves are presented in Figure 1. Figure 2A shows the LV and aortic pressures recorded prior to removal of the pericardial blood. Figure 2B shows these pressures after removal when the cardiovascular system had reached steady state. At the time indicated by the arrow, a balloon was suddenly inflated in the ascending aorta (see Figure 3), which presented an increased afterload to the left ventricle. Note that the aortic pressure was measured proximal to (on the heart side of) the balloon. The added pressure load was sudden, and compensatory mechanisms did not have time to act for several beats. Thus, the heart’s contractile state may be considered constant for 10-15 seconds, and this period certainly includes beats numbered 3, 4, and 5 in the figure. Additional data gathered during the work-up included: A. Fick data during steady state before the pericardium was drained: O2 uptake 300 cc/min. Arterial O2 content 180 cc/liter Mixed venous O2 content 80 cc/liter B. Individual stroke volumes during the balloon test are indicated in Figure 2B. The steady state stroke volume was 75 cc. before balloon inflation. Questions: A. From the raw data supplied, complete the table below. //Before tap Beat 2 Beat 3 Beat 4 Beat 5 Heart Rate (b m) Stroke Vol. (cc.) 75 64 70 75 Aortic Pressure (max) (min) Aortic valve opens (mmHg) LV end systolic pressure (mmHg) LVEDP (mmHg) LVEDV (cc.) 6.022j—2004: Problem Set 2 2Figure 1: Pressure (mmHg) 180 160 140 120 100 80 60 40 20 Diastolic LV Pressure/Volume Curves1. Before Tap 2. After aT p 1 2 0 20 40 60 80 100 120 140 160 180 200 Vo l ume (cc.) B. Sketch the pressure-volume loop for the heart prior to the pericardial tap (on Figure 1). C. Plot the pressure-volume loops for beats numbered 2, 3, 4, and 5 (on Figure 1). D. Construct the end-systolic pressure-volume curve for the normal left ventricle (on Figure 1). 3 6.022j—2004: Problem Set 2Figure 2:AorticL.V.11122334452255075100255075100125150175Time (sec.)Time (sec.)Pressure (mmHg)Pressure (mmHg)Stroke Vol. = 75 cc. 75 cc. 64 cc. 70 cc. 75 cc.Balloon InflatedB: After TapA: Before Tap6.022j—2004: Problem Set 2 4Figure 3: Relative Positions of Balloon and Aortic Pressure Measurement Site Aortic Pressure port Balloon Valve L.V. 2004/11 5 6.022j—2004: Problem Set 2Problem 2 In the case study introduced at the beginning of the course, the patient’s heart required the tempo-rary assistance of a ballon pump placed in his aorta (“intra-aortic balloon pump” or IABP). This device may be life-saving in situations where the heart muscle has been weakened by disease (such as loss of blood supply). One possible design for the IABP is shown in Figure 4. It consists of a long, thin, inflatable balloon which is inserted via the femoral artery to the aortic arch. It may be in one of two states: deflated with an internal pressure of zero, or inflated at an internal pressure PB. By appropri-ate timing of the two states, considerable improvement may result in circulatory function. The pressure-volume characteristics of the aorta with the balloon both deflated and inflated are shown in Figure 5. The heart and peripheral circulation may be modeled as shown in Figure 6. The left ventricle is represented by a time-varying capacitor C(t) driven by a constant filling pressure, Pf . The peripheral circulation is represented by the Windkessel approximation where the pressure/volume relationships of Ca are shown in Figure 5. (Ca is a 2-state device.) Assume that the systolic ejection time is very short, dt. A. What must be the timing of the balloon inflation/deflation sequence in order to assist the heart? Plot the required switching function f (t) on the same time axis as C(t). Note: f (t) is defined in Figure 4, and C(t) in Figure 6. B. Indicate on Figure 5 the pressure-volume cycle followed in the aorta (i) with the balloon assist device inoperative, and (ii) with the assist device operating as defined by you in the previous question. C. Using graphical techniques, indicate on Figure 5 the area representing the net energy sup-plied to the circulation by the balloon device per cycle. D. Sketch the expected blood flow through the peripheral resistance, R, as a function of time with the assist device on. E. A representative LV pressure-volume loop for a damaged heart is shown in Figure 7. Show qualitatively how the ballon pump will enhance cardiac output by sketching the expected new PV loop with the balloon operating. 2004/10 6.022j—2004: Problem Set 2 6Figure 4: 6.022j—2004: Problem Set 2 7Figure 5: Figure 6: 6.022j—2004: Problem Set 2 8Figure 7: 6.022j—2004: Problem Set 2 9Problem 3 You are a physiologist studying the effects of hypertension (high blood pressure) on the heart. Your studies involve the use of the pig, whose heart size is similar to that of humans. To evaluate the short and long-term effects, you