ps1_solutions

ps1_solutions - Harvard-MIT Division of Health Sciences and...

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Unformatted text preview: 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 1 SOLUTIONS February 10, 2004 Problem 1 Certain traumatic injuries such as gunshots or knife wounds to the groin may lead to the develop- ment of a “short circuit” or fistula between the large femoral artery and the adjacent femoral vein. (See Figure 1.) The fistula may have a very low resistance to fluid flow, and may carry large blood flow rates. Figure 1: Two medical students were arguing about the expected effect of a large femoral AV fistula on the blood supply to the leg. One student was certain that the leg would be deprived of its blood supply and would become gangrenous. The other student violently disagreed, and insisted that the leg would be in no danger. Who was correct? A. Propose a simple resistive model to represent the blood supply to the leg with and without the presence of the fistula. The model should include the aorta, the femoral artery, the leg circulation, and the corresponding veins. Assume that the resistance of the fistula (when open) is much lower than the resistance of the leg vascular bed, but higher than the (negli- gible) resistance of the aorta. Assume negligible resistance for the large veins as well as the aorta. Assume the aortic pressure, P , is constant. The following variables may be used to model the system: R A : Large Artery Resistance R L : Leg Resistance R F : Fistula Resistance (venous resistance is negligible) P : Constant Pressure Source (due to baroreceptor reflexes) P L : Pressure above Leg Resistance and Fistula Resistance Q T : Cardiac Output (Total Flow) Q F : Fistula Flow Q L : Leg Flow 6.022j—2004: Solutions to Problem Set 1 2 B. Calculate the blood flow to the leg with and without the fistula, and referee the argument. Express your answers in terms of resistances and aortic pressure. Determine the ratio: ( Blood flow to the leg with the fistula ) ( Blood flow to the leg without the fistula ) and plot this ratio as a function of relevant resistances, R A . R F C. What will be the change in cardiac output when the fistula opens? Express this change as a ratio: ( cardiac output with the fistula ) ( cardiac output without the fistula ) in terms of relevant resistances, R A ....
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This note was uploaded on 11/11/2011 for the course BIO 2.797j taught by Professor Matthewlang during the Fall '06 term at MIT.

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ps1_solutions - Harvard-MIT Division of Health Sciences and...

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