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MCG4150: Midterm 2005
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Course:
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MCG 4150 - Bioinstrumentation and Biocontrols
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Instructor:
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Andy Adler
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Date:
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Feb. 18, 2005
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Directions:
You have 80 minutes to complete this exam.
Each question has equal marks.
This is a closed book exam; however,
you are permitted to bring a 8.5" × 11"
sheet of notes into the exam.
You are permitted to use a calculator.
You may not communicate with anyone during the exam except the instructor.
You may make assumptions to simplify the problems as long a they
don't change the calculations by more than 10%.
You may use the following conditions for your calculations:
- Atmospheric pressure, Patm: 101.3 kPa
- Density of air at Patm: 1.21 kg/m3
- 1 cmH2O = 98 Pa
1.
Esophageal balloon Catheter
In order to estimate pleural pressure, an esophageal balloon
catheter is used. The catheter is 1.5m long with an inner
diameter of 1mm. In order to inflate the balloon, a pressure of
20 cm H2O
is applied, and giving the balloon a volume of 2 ml.
Assume that the compliance
of the catheter is zero and the compliance of the balloon is infinite.
- 1A.
Estimate the compliance and inertance of the gas
in the catheter.
answer:
Volume Bubble = 2e-6 m3
Volume Catheter = 1.5*pi*(1e-3/2)^2 = 1.18e-6 m3
Absolute Pressure at 20cmH2O = 101.3 + 20/9.8 = 103.34 kPa
Density at 20cmH2O = (1.21)*(103.34)/(101.3) = 1.23 (can ignore)
Inertance in catheter = rho*L/pi/rē
= (1.23)*1.5/pi/(1e-3/2)^2 = 2.35e6 kg/m4
Compliance in catheter = V/P = pi*rē*L/P =
pi*(1e-3/2)^2*1.5/103340 = 1.14e-11 m5/N
Compliance of bubble = V/P = 2e-6/103340 = 1.94e-11 m5/N
- 1B.
Based on the compliance and inertance, the catheter may be
modelled using lumped parameter model.
Estimate the resonance frequency (fn) of
the catheter based on these parameters
answer:
Effective Inertance
Model bubble as cylinder of 2cm x 1cm2
Radius = sqrt(1/pi) = .562cm
Inertance of bubble = rho*L/pi/rē
= (1.23)*0.02/pi/(5.62e-3)^2 = 248 kg/m4 ==> Ignore
Effective Inertance = 2.35e6 kg/m4
Effective Compliance = 3.08e-11 m5/N
Freq = (1/2/pi)*1/sqrt(Inertance*Compliance) =
1/2/pi/sqrt(2.35e6*3.08e-11)= 18.7 Hz
Absolute Pressure at 20cmH2O = 101.3 + 20/9.8 = 103.34 kPa
Density at 20cmH2O = (1.21)*(103.34)/(101.3) = 1.23 (can ignore)
Inertance in catheter = rho*L/pi/rē
= (1.23)*1.5/pi/(1e-3/2)^2 = 2.35e6 kg/m4
Compliance in catheter = V/P = pi*rē*L/P =
pi*(1e-3/2)^2*1.5/103340 = 1.14e-11 m5/N
Compliance of bubble = V/P = 2e-6/103340 = 1.94e-11 m5/N
2.
Measurement of obstructive lung disease
- 2A.
Measurement of esophageal pressure allow calculation
or airways resistance (Raw)
Briefly discuss a simple mechanical model of the lungs
and indicate the role of Raw and its relation
to obstructive lung disease.
- 2B.
The pressure sensor is based on a semiconductor
strain guage placed on a diaphragm which bends
under pressure. Sketch a diagram of a such
pressure transducer. The compliance
of the diaphragm is its ratio of deformation
to pressure change. If the strain guage
were made of metal instead of semiconductor,
would the diaphragm be required to be more or less
compliant?
Last Updated:
$Date: 2006-03-06 10:30:58 -0500 (Mon, 06 Mar 2006) $
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Engineering