Midterm1Solution

Midterm1Solution - BME 210 Spring 2008 Name: _ MIDTERM...

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BME 210 Spring 2008 Name: _______________________________ MIDTERM EXAMINATION #1 (1 hr 15 min) (15 points) 1. A dye-dilution procedure was performed in a patient in which 0.5 mg of dye was injected into the right femoral artery (provides the blood supply to the right leg) and the dye concentrations (C(t)) given in the table below were measured in the right femoral vein (collects all blood supplied to the left leg) at several times. These data have been corrected for any recirculation. The patient’s right femoral artery blood flow was assumed to be constant during the course of the experiment. t - time (sec) C ( t ) – dye concentration (mg/L) 0.0 0.0 2.0 20.0 4.0 15.0 6.0 10.0 8.0 2.0 Using these data, estimate the area under the dye concentration-time curve using the following numerical integration methods: trapezoidal rule and Simpson’s method . Also use these two approximations to calculate the corresponding values of blood flow, F. Express your answer for F in L/min . () 4 15 2 1234 5 2 ( ; ) ( ) ( ) ( ) 2(45) (0 2) 92mg sec/ 22 and F 0.326 / min (;) 2 () 4( ) 2( )4( ) ( ) 3 101.3mg sec/ and F 0.296 / min i i h TCP h ct L D L SCP L D L = =+ + = + + = == + + + =− 1
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(15 points) 2. Consider the system shown below in which the heart and lungs are represented by a single well-stirred tank (concentration in the tank is homogeneous) whose volume is V. The flow through the system (cardiac output) is Q. A mass D of dye is introduced at time 0 into the tank (and mixes instantly), and the concentration of the dye C(t) is measured at the outflow of the tank. Assume no dye enters the tank via the input tube. a) Write the mass balance differential equation for the dye the concentration C(t). Be sure to give the initial value C(0).
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This note was uploaded on 06/23/2008 for the course BME 210 taught by Professor D'argenio during the Spring '07 term at USC.

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Midterm1Solution - BME 210 Spring 2008 Name: _ MIDTERM...

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