This is the forth time I’m posting this question, I’m running out of time. Pleas

Question

This is the forth time I’m posting this question, I’m running out of time. Please help. Only from (a) to (d). This is for a biomedical engineering class. ...

Problem 2. Given your convincing performance on your first day at the famous cardiovascular research institute (see HW #1), you decide to push it and show up for just one more day. As you begin your staff meeting, somebody asks you just how much mechanical power is actually required of the total artificial heart which your group will design. Anyone as famous as you in the field would know the answer to that off the top of your head. Unfortunately, you are not famous in the field, so you'll need to make something up. You proceed to "walk your admiring audience through the calculation (for their own edification, of course), calculating how much work the heart performs under normal (e.g. 70 bpm) and stressed (e.g. 180 bpm) conditions, to get some idea about how powerful your yet-to-be-created heart must be: a) Using the diagram of fig 9-7 for the resting condition, calculate the net external work output of the left ventricle under normal (resting) conditions for one contraction cycle. Make reasonable assumptions as needed. (Help with units: mmHg 1333 dyn/cm, and pressure in dyn/cm2 imes volume in ml yields work in ergs. Work in ergs can then be easily converted to J) b) Assuming a resting heart rate of 70 bpm, estimate the average power in watts (IW = 1 Joule/sec) of the left ventricle associated with generating external work. Be careful with your units... c Repeat these calculations for the stressed heart, assuming a rate of 180 beats/minute, a venous return such that the pre-ejection volume of the left ventricle is 175 ml, and a peak intraventricular pressure of 200 mmHg. Be sure to account for the amount of blood you might expect to be left in the ventricle after contraction (see discussion on p. 101 of the text), and justify your estimate of this volume in the context of the stressed condition. d) The human heart pumps approximately 5 liters of blood/minute at rest. If the only information available to you was this fact and any information you could gather from a standard blood pressure cuff (i.e. blood pressure measurement), could you have estimated your answer in part b) without using figure 9-7? e Using your knowledge of the timing of various parts of the cardiac cycle, estimate the peak power generated by the left ventricle under both resting and stressed conditions. Again, make reasonable assumptions as needed. ECEN 4001.5001 Homework #4 R. Mhran page 1 f)Estimate the average kinetic energy of the blood during ejection from the left ventricle. Assume a reasonable value for the stroke duration under resting conditions in calculating this average KE. (Assume the diameter of the aorta is approx. 2 cm) g) How does this compare with the pressure-volume or net extemal work performed per stroke from part a)?

Explanation / Answer

a) Net external work by the heart left ventricle is the product of stroke volume and mean aortic systolic pressure.

That is,

W(net external work by left ventricle) = stroke volume X mean aortic systolic pressure

From the given graph =>

SV= EDV-ESV= 130-50 mL = 80mL where EDV is End Diastolic Pressure and ESV is End Systolic Pressure.

Mean aortic pressure= 120 mmHg= 120X 1333 dyne/ cm2

W= 80 X 120 X 1333 erg

=12796800 erg

Erg= 10(-7)  Joules

W= 1.2796800 Joules

Thus the net external work is 1.2796800 J.

b) Power = work done per unit time

Watt = joules per second

Power of left ventricle= 1.2796800 X 70 / 60 = 1.49296 W.

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