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ps8_solutions

# ps8_solutions - Harvard-MIT Division of Health Sciences and...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departments of Electrical Engineering, Mechanical Engineering, and the Harvard-MIT Division of Health Sciences and Technology 6.022J/2.792J/BEH.371J/HST542J: Quantitative Physiology: Organ Transport Systems PROBLEM SET 8 SOLUTIONS April 15, 2004 Harvard-MIT Division of Health Sciences and Technology HST.542 J : Quantitative Physiology: Organ Transport Systems Instructors: Roger Mark and Jose Venegas

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Problem 1 A student with a mild case of asthma was feeling perfectly well when she left for class. On the way to class she breathes cold, dry air and develops a moderate asthma attack. She takes an inhaled medication (isoproterenol) that relieves the symptoms. A. Modeling the lung as a single resistor and a single capacitor attached in series, what are the peak-to-peak pleural pressure swings in each case below? Assume lung compliance C L stays fixed at 0.1 L · cm H 2 O –1 , that the student breathes using a square-wave flow pattern with equal inspiratory and expiratory times, and that R insp and R exp are equal. R aw (cmH 2 O · L –1 · s) f (breaths/min) V T (ml) Normal 1 20 500 Asthma 20 40 250 Treated 5 25 400 The difference between pleural pressure (P pl ) and atmospheric or airway opening pressure (P ao ) can be thought of as the sum of ( P pl - P alv ) and ( P alv - P ao ) , where the former rep- resents the effect of lung compliance and the latter, airway resistnace. These pressure differ- ences for a square wave flow pattern are sketched below. RV inspiration expiration P alv – P ao C L –1 V T P pl – P alv 2 RV + C L –1 V T P pl – P ao It can be seen that the maximum swing in P pl - P ao is equal to 2 R aw ˙ V + V T C L 6.022j—2004: Solutions to Problem Set 8 2
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