Problem set 14

Problem set 14 - What are the pertinent system parameters?...

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Problem Set 14 Compartmental Analysis
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14-1 . Compartmental Analysis - Two unequal serial compartments. Consider the following system: Blood flow,F, is in steady-state is considered to be flowing into the circulation represented by 2 compartments. Consider that V 1 V 2 , compartments are well-mixed. Material with mass M is introduced to compartment 1 at time 0 (pulse injection). There is no trace material in the system before time 0. a. Derive differential equation(s) for the variation of the system output concentration with time. Assume the mass is present in compartment 1 only at time =0 and that C i (t) = 0. b. Find the LaPlace transform of the output concentration f8e5 C 2 (s). c. Find the time-domain solution to the equations.
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Unformatted text preview: What are the pertinent system parameters? Plot the solution on semi-log axes for various values of the parameters 14-2. Two Parallel Compartments with Unequal Volumes Consider the following system designed to simulate the flow of contrast medium through the brain circulation: Where flow F 1 = F 2 , V 1 V 2 , C 1 (0) = M/V 1 , C 2 (0) = M/ V 2 , and C i =0. a. Find the output concentration as a function of time (use Laplace transforms). b. Compare to the solution to that for problem No. 1. Could you distinguish a serial compartment system from a parallel compartment from observing concentration time data? Would it matter? F 1 2 C i (t) V 1 V 2 F C i F 1 F 2 V 1 V 2...
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Problem set 14 - What are the pertinent system parameters?...

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