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Unformatted text preview: BME 365R Quantitative Physiology
Homework 1 - Solution
Due September 6, 2011; 6:00PM
1. (10) Review the article on Induced Hypothermia posted on Blackboard in the HW1
A. Select three physiological systems mentioned in the section “physiologic effects of
IH” and identify at least two effects of induced hypothermia for that system (you
should have 6 effects).
1. Central Nervous System
A. For each 1°C decrease in temperature, the cerebral metabolic rate
decreases by 6–7%
B. In addition, hypothermia decreases intracranial pressure.
2. Cardiovascular System
A. With shivering abolished, mild hypothermia (32–34°C) decreases heart
rate and increases systemic vascular resistance, whereas stroke volume
and mean arterial blood pressure are maintained
B. At 33°C, the electrocardiogram may show a notch on the downstroke of
the QRS complex (the Osbourne wave)
3. Respiratory System
A. Since metabolic rate is decreased by 25–30% at 33°C, the ventilator minute
volume is decreased to maintain the PCO2 in the normal range
B. Pneumonia is a risk of IH; however, this is relatively uncommon during in
brief (12–24 hrs) IH
4. Renal System, Electrolytes
A. The induction of hypothermia shifts potassium into the cells (26), and the
administration of potassium to correct hypokalemia during induction of IH
may lead to significant hyperkalemia during rewarming.
B. Hypothermia also decreases phosphate concentrations
5. Gastrointestinal System
A. During hypothermia, there is decreased gut motility and this may delay
B. Hypothermia increases blood glucose concentrations, probably due to
decreased insulin released from the pancreas
6. Hematologic System
A. During prolonged IH, the numbers and function of white blood cells
decrease, and this may increase the incidence of sepsis, particularly
pneumonia during prolonged IH (24 hrs).
B. Hypothermia prolongs clotting times, and this might contribute to an
increase in the risk of bleeding in the setting of major trauma
B. Review the section entitled “Clinical Applications of IH” and select three clinical
applications of IH and indicate whether IH is generally accepted, somewhat accepted, controversial or not generally accepted and provide a brief explanation supporting your
answer in each case.
1. Anoxic Brain Injury: Somewhat accepted, improvements in cooling methodologies
being investigate to improve outcomes.
2. Traumatic Head Injury: Somewhat accepted or not generally accepted. Special cases
may exist where IH is beneficial to patients suffering from traumatic head injury.
3. Traumatic Cardiac Arrest. Somewhat accepted to controversial. Ongoing clinical
trials are investigating the use of IH during traumatic cardiac arrest.
4. Stroke: Controversial. Increased number of deaths and complications have been
5. Newborn Hypoxic-Ischemic Encephalopathy. Somewhat accepted. Awaiting results
of a large multi-center clinical trial.
6. Hepatic Encephalopathy: Somewhat accepted. Initial studies have positive results.
Larger studies are planned.
7. Encephalitis: Controversial. Limited data available.
8. Bacterial Meningitis: Not generally accepted. Animal studies only
9. Cardiac Failure: Somewhat accepted. Limited studies show positive results.
10. Adult Respiratory Distress Syndrome: Controversial. Some limited studies show
improvement, risk in patients with sepsis is noted.
2. (35) A model constitutive relationship for a human lung is Where V is volume in ml and P is pressure in cmH2O. For the following assume that
a=15ml, b=1000ml, c=25cmH2O and d=2cmH2O.
A. (5) Plot the Volume(V) vs. Pressure(P) relationship for pressures from 0 to 35 cmH2O
Volume versus pressure from model of human lung
1200 1000 volume (mL) 800 600 400 200 0 0 5 10 15
pressure (cm H2O) 30 35 B. (10) Find an algebraic expression for the compliance of the lung at any pressure,
simplify the expression to the best of your ability. C. (5) Using the algebraic expression found in part B, evaluate the compliance of the
lung at pressures of 15, 20 and 25 cmH2O.
P = 15 cmH20: C = 3.324 mL/cmH2O
P = 20 cmH20: C = 35.052 mL/cmH2O
P = 25 cmH20: C = 125 mL/cmH2O
D. (5) For pressures of 15, 20 and 25 cmH2O draw a tangent line to the curve generated
in part A, find the slope of the tangent line and compare with the computed
compliances in part C.
The slopes of the tangent line of the volume/pressure curve should be close to the
computed compliances from part C at each point. The tangents can be calculated
numerically or drawn and measured by hand on a plot of the volume versus pressure. compliance (mL/cmH20) Algebraic and numerical estimation of compliance from model of human lung
0 0 5 10 15
pressure (cm H2O) 25 30 35 E. (5) If during breathing the lung expands at a pressure of 15 cmH2O to 25 cmH2O,
estimate how much energy is required to expand the lung. Describe how you
computed the energy.
First, use the original equation to calculate the volume at P = 15 and 25 cmH2O, and then
solve for pressure in terms volume: mL, mL Then, numerically estimate the following integral:
Energy = = 1.1e4 mL*cmH2O = 1.08 J Unit conversions:
1 cmH20 = 98.1 Pa = 98.1 N/m2
1 mL = 1 cm3 = 1e-6 m3
1 mL*cmH20 = 98.1e-6 J
F. (5) Assume that no energy is gained or lost during exhalation, if a person is breathing
between pressures of 15 and 25 cmH2O at 1 breath per second, find the power
expended to breathe. Show your work.
Power = energy/time = 1.08 Joules/second = 1.08 W
3. (15) Consider an aorta that has a circular cross section with a diameter of 5mm and a
length of 10cm. Assume that the density of blood is 1.06 gm/cm3. Cardiovascular
effort/flow units are effort (mmHg) and flow (ml/s).
A. (5) What are the cardiovascular units for inertance? Show your work. The inertance
I = Momentum / Flow
t Momentum= ! Effort. dt =
So the inertance t ! P. dt
0 t I= ! P. dt
0 Vol / t has the units mmHg.s/(ml/s)=mmHg.s2/ml
B. (5) What is the inertance of blood in the given aorta in cardiovascular units?
t t t
! P. dt ! A . dt A " ! F. dt
A =A A
Vol / t
A So to convert the units 1
! 133.33N • s
! 133.33kg • m / s
mmHg • s 133.33Pa • s 133.33N / m 2 • s m 2
= 4 ! 133
ml / s
ml / s
cm ! cm / s
cm ! cm / s
m ! m ! 10 / s
m = 1
! 133.33kg " m / s
= 133.33 " 10 6 kg / m 4
m ! 10 so the inertance in cardiovascular units will be
C. (5) If the flow through the aorta is 15 ml/s, what is the hydraulic momentum of the
blood flow (give in cardiovascular units). I = Momentum / Flow
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This note was uploaded on 12/13/2011 for the course BME 365R taught by Professor Rylander during the Spring '09 term at University of Texas at Austin.
- Spring '09