HW_1_Solution - BME 365R Quantitative Physiology Homework 1...

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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 folder. 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). Physiologic Systems: 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 enteral feeding 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 noted. 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 20 25 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. Units: mL/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 140 Algebraic Numerical estimation 120 100 80 60 40 20 0 0 5 10 15 20 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 = 0 and Flow=Vol/t 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 F 1 p m1 ! P. dt ! A . dt A " ! F. dt # #A"v ! #! 0 0 0 A =A A I= = = = = Vol / t A"l /t A"l /t A"v A"v A So to convert the units 1 1 ! 133.33N • s ! 133.33kg • m / s mmHg • s 133.33Pa • s 133.33N / m 2 • s m 2 kg m2 Iunits = = = = = = 4 ! 133 2 2 2 "3 ml / s ml / s cm ! cm / s cm ! cm / s m ! m ! 10 / s m = 1 ! 133.33kg " m / s m2 = 133.33 " 10 6 kg / m 4 3 #6 m ! 10 so the inertance in cardiovascular units will be I=1.06g/cm3*10cm/(π*(2.5mm)2)=1.06*103kg/m3*0.1m/( π*6.25*10-6m2) =5.3985*106kg/m4=5.3985*106/(133.33*106) mmHg.s2/ml =0.04mmHg.s2/ml 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 Momentum=I* Flow =0.04mmHg.s2/ml*15ml/s=0.6mmHg.s ...
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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.

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