The circuit shown below has an inflow pressure of 120 mmHg and an outflow pressure of 40 mmHg. Resistance in each of the four vessels shown is 2 mmHg/mL/min (R1 = R2 = R3 = R4 = 2 mmHg/mL/min). What is the total peripheral resistance of the circuit shown on the slide?

Question

The circuit shown below has an inflow pressure of 120 mmHg and an outflow pressure of 40 mmHg.  Resistance in each of the four vessels shown is 2 mmHg/mL/min (R1 = R2 = R3 = R4 = 2 mmHg/mL/min).  What is the total peripheral resistance of the circuit shown on the slide?

Quizplus · Accepted Answer

The diagram given in the question stem illustrates a set of vessels arranged in parallel. Systemic circulation is often simplified in this way for the purposes of calculating total peripheral resistance (TPR). Each branch of the aorta can be visualized as one of the vessel branches on the above graph. For example, the four vessels above could represent coronary, splanchnic, renal, and cerebral circulation. The formula for calculating the total restistance for parallel circuits is as follows. RT represents total peripheral resistance, and the circuits represent blood vessels. 1/R_T = 1/R1 + 1/R2 + 1/R3 + … 1/Rn In this calculation, the inverse of the TPR (or RT) is equal to the sum of the inverse of each vessel or system that lies in parallel. The resistance of the vessels are R1 = R2 = R3 = R4 = 2 mmHg/ml/min. Therefore 1/TPR = ½ + ½ + ½ +½ = 4(½) = 2 so TPR= ½ = 0.5 Therefore, the TPR = ½ or 0.5 mmHg/ml/min. (Choice A) Eight (8) mmHg/ml/min would be the resistance if each of the above vessels were arranged in series, rather than in parallel. A series arrangement does not estimate total body circulation well, but is a good way to describe blood flow in an individual organ. To calculate the resistance of a circuit in series, the individual values for resistance are summed as follows: Total resistance in organ = R_artery + R_arteriole + R_capillary + R_venule + R_vein Educational Objective: The total resistance for a group of vessels arranged in parallel is equal to one divided by the sum of the inverse values for resistance of each of the contributing vessels as follows: 1/TPR = 1/R1 + 1/R2 + 1/R3 + … 1/Rn. Total body circulation can be best described as a parallel circuit, whereas circulation in an individual organ is often best described by a series arrangement.

The Circuit Shown Below Has an Inflow Pressure of 120