42-101 Intro to BME  (Przybycien)

Spring 2005

PROBLEM SET No. 8

Posted:

4/2/05

Due:

4/8/05 in class

Note: turn in final team evaluation sheet for Team B in class on Monday, 11 April.  Be thinking about who you’d like to work with for Team C; we’ll form teams in class on Monday, 18 April.  Ground rules for forming new teams same as before….

1.

Enzyme Kinetics.  MMD text chapter 6, problem 11.

2.

Metabolic Pathway Control.  MMD text chapter 6, problem 13.

3.

Enzyme Inhibition.  A competitively-inhibited enzyme is well-described by the parameters KI = 1.2 mM, KM = 4.9 mM and nmax = 0.67 mM substrate/min.

 

a.   Which species binds to the enzyme more strongly, substrate or inhibitor?  Why?

 

b.   What would the volumetric rate of substrate consumption be if [S] = [I] = 3.7 mM?

 

c.   Suppose [I] was held constant at 0.88 mM and [S] at t = 0 min was 0.22 mM.  How long, in minutes, would it take for 90% of the substrate present initially to be consumed?

4.

Mass Balance on a Hollow Fiber Hemodialyzer.  Arterial blood flows through the lumen of a hollow fiber dialyzer and dialyzing fluid, consisting of water and dissolved salts, flows on the shell side of the dialyzer.  Water and small waste metabolites, mainly urea, creatinine, uric acid and phosphate ions, pass through the hollow fiber membrane walls from the blood to the dialyzing fluid; the purified blood is returned to a vein.  At a given time during a dialysis procedure, a patient's arterial blood flow into the device is 185 mL/min and the venous blood flow out of the device is 183 mL/min.  At the same point in time, the arterial urea concentration is 1.92 mg/mL and that in the spent dialysate is 0.25 mg/mL.  A schematic diagram of the system is shown below.  The dialyzing fluid enters the device at a rate of 975 mL/min.

For this system:

a.  Calculate the concentration of urea in the venous blood and the rates at which urea and water are removed from the blood at this particular point in time.  Use our mass balance problem format please.

b.  If we want to reduce the patient's urea level from an initial value of 2.95 mg/mL to a final level of 0.60 mg/mL, the total blood volume is 4.9 L and the rate of urea removal is equivalent to that calculated in part (a), how long must the patient be dialyzed? 

5.

Biomechanics – Stride Analysis.  MMD text chapter 10, problem 7.

6.

Biofluid Mechanics – Inviscid Flow.  Assume that the blood enters an aorta with a diameter of 1.0 cm, an average velocity of 55 cm/s (at rest) and an average pressure of 100 mmHg.  Downstream of the aorta inlet is an aneurysm (bulge in the blood vessel) with a diameter of 2.1 cm. What is the pressure in the aneurysm?  Suppose blood velocity at the inlet to the aorta becomes 200 cm/s during vigorous exercise.  What will the pressure in the aneurysm become?  What happens if the aneurysm increases in size?

7.

Biofluid Mechanics – Viscous Flow.  Circulation of a dog. Aorta: 1.0 cm in diameter, 40 cm in length.  Large arteries:  ~40 in number, 0.3 cm in average diameter, 20 cm in average length, 23 cm/s average velocity in large arteries.  Blood: viscosity at high shear rates is ~3.0 cP; density is 1.057 g/cm3.

a.    What is the total volumetric flow rate, in cm3/s, of blood in a dog?

b.    What is the pressure drop, in mmHg, across the length of a large artery in a dog?

c.    What is the average shear rate at the blood vessel wall, in 1/s, of a large artery in a dog?

d.   Determine the average velocity, in cm/s, of the blood in the aorta.

a.    What is a typical value for the Reynolds number in the aorta of a dog?  Is the flow laminar or turbulent?

Updated on 4/2/05 by TMP