HW2_Solution-1

# HW2_Solution-1 - BME 365R Quantitative Physiology Homework...

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BME 365R Quantitative Physiology Homework 2 Solution Due September 20, 2011; 6:00PM 1. (20) Airway resistance is important in respiratory medicine. The following questions are related to the paper entitled “Extrathoracic airway resistance in man.” Download the paper from Blackboard to answer the following questions: A. (6) Consider Figure 2 showing plots of air flow vs. pressure difference in the upper airway. Identify which plotted quantities correspond to an effort and which correspond to a flow. From Figure 2A estimate the upper airway resistance during resting ventilation when the pressure difference ( Δ p ) is 1 cmH 2 O. During hyperventilation does the upper airway resistance (at a pressure difference p = 1 cmH 2 O) increase or decrease relative to resting ventilation? Estimate the upper airway resistance at a pressure difference p = 1 cmH 2 O during hyperventilation. x axis p is effort, y axis exp flow and insp flow is flow since the plot is not linear, we need to draw a line on the partial linear part on p = 1 cmH 2 O point(flow is approximately 0.75), the intercept of this line on y axis approximately 0.4 is the flow when p = 0 cmH 2 O Rr= p/flow=1/(0.75-0.4)=2.86 cmH 2 O/(l/secs) Similar for hyperventilation Rh= p/flow=1/(1.25-0.5)=1.33 cmH 2 O/(l/secs) During hyperventilation the upper airway resistance (at a pressure difference Δ p = 1 cmH2O) decrease relative to resting ventilation. B. (6) Considering the upper airway as a discrete element with a flow and pressure difference, use the values determined in Part A to compute the power in Watts input into the upper airway for both resting ventilation and hyperventilation (take a pressure difference of p = 1 cmH 2 O). Using the computed powers into the upper airway and considering a 1 Ω linear resistor, determine the current into and voltage across the resistor so that the thermal power generated by the resistor is equivalent to the power input into the upper airway during resting ventilation and hyperventilation. For resting ventilation The power is Pr= = p*flow=1*0.75=0.75 cm H 2 O *L/secs =750cm H 2 O *ml/secs*133Pa/1.36 cm H 2 O*m 3 /10 6 ml=0.073Watts I=(P/R) 1/2 =(0.073/1) ½ =0.27A V=IR=0.27V For hyperventilation The power is Pr= = p*flow=1*1.25=1.25 cm H 2 O *L/secs =1250cm H 2 O *ml/secs*133Pa/1.36 cm H 2 O*m 3 /10 6 ml=0.12Watts I=(P/R) 1/2 =(0.12/1) ½ =0.35A

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V=IR=0.35V
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HW2_Solution-1 - BME 365R Quantitative Physiology Homework...

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