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MCG4150: Final Exam 2005

Course: MCG 4150 - Bioinstrumentation
Instructor:             Andy Adler
Date: Apr. 27, 2005
Directions: You have 150 minutes (2½ hours) to complete this exam. The exam has five questions; you are required to answer any four of them. Each question is worth equal marks. This is a closed book exam; however, you are permitted to bring an 8.5" × 14" 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 as they don't change the calculations by more than 10%. You may use the following conditions and equations for your calculations:

  • Atmospheric pressure, Patm: 101.3 kPa
  • Density of air at Patm: 1.21 kg/m3
  • 1 cmH2O = 98 Pa
  • 760 mmHg = 101.3 kPa
  • Density of saline solution = 1000 kg/m3
  • A first order low-pass system response: V(t) = Vt=∞ + ( Vt=0 − Vt=∞ ) exp(−t/τ)

1. Many different instruments have been invented to measure the activity of the heart. In this question we consider three of them:

  • Body Surface Electrodes (ECG)
  • Stethoscope (heart sounds)
  • Intravenous thermodilution
While each strategy measures similar physiological properties, they are not identical. For each of the following physiological variables, discuss whether or not it can be measured by each instrument, and (briefly) why or why not
  • Timing of atrial / ventricular contraction
  • Systolic ejection volume
  • Cardiac valve insufficiency
  • Systolic arterial pressure

2. The body surface ECG is typically recorded with Ag/AgCl electrodes. While these electrodes work quite well, they are not perfect.

    2A. Using diagrams and equivalent circuit models, explain the origin of movement artefacts in the ECG

    2B. Using diagrams and equivalent circuit models, explain the origin of artefacts due to sweat in the ECG

    2C. Explain why Ag/AgCl electrodes work better than stainless steel electrodes. Note: the ECG is largely a low frequency signal.

3. An intra-arterial blood pressure transducer is to measure systolic and diastolic pressure. Assume the blood pressure has simplified rectangular waveform, as shown in the figure. The systolic pressure is 140 mmHg; the diastolic pressure is 80 mmHg. Systole lasts 150 ms, while diastole lasts 600 ms.

    3A. It is discovered that the blood pressure transducer is responding very slowly; it behaves like a first order low pass filter with time constant τ=50 ms. Sketch the blood pressure waveform and the blood pressure transducer output. Show how the true pressure readings can be underestimated by this transducer.

    3B. When viewing the transducer, the technician notices an air bubble in the line. Using the "pop response" technique, the natural frequency of the transducer is determined to be 10 Hz. Calculate the size of the bubble. The catheter is 30 cm long, with an inner diameter of 1 mm. Assume the catheter wall is completely rigid (compliance is zero), and the diaphragm has a compliance Cdiaphragm = 2.0×10−15 m3/Pa.

    r=5e-4; f=10; L=1000*.3/pi/r^2;C=1/(2*pi*f)^2/L;l=1/pi/r^2*C*101300
    l = 0.085532

4. The blood pressure transducer in the previous question is like the modern type we discussed in class. It has a saline flush line and a silicon chip covered by an insulating gel.

    4A. If the gel insulation fails, it could provide a path for microshock. Draw a circuit diagram for the microshock, showing the current pathways.

    4B. Using the value of Cdiaphragm, calculate the change in diaphragm volume, given a 1 mmHg change in blood pressure.

    DV = 101300/760*2e-15 = 2.6658e-13 m^3
    2.6658e-13 m^3 * (1e3 mm/m)^3 = 2.67e-4 mm^3

    4C. Assume that the amplifier gives a 1 Volt output for each ΔR/R = 10−3 of the sensor. Assume ΔLdiaphragm/Ldiaphragm = ΔVolumesensor/Volumesensor, and the sensor volume is 1.0 µL. What is the Gage factor of the sensor?

    G = (ΔR/R) / (ΔL/L)
      = (ΔR/R) / (ΔV/V)
    DV_V=101300/760*2e-15/(10e-9 m^3);
    G = 37.512

5. Thermodilution

    5A. Describe how thermodilution allows measurement of systolic ejection volume. Why is the injected saline cooled rather than heated?

    5B. One issue with thermodiluton is heat loss through the blood vessel walls. Describe how this effect impacts measurements

    5C. Sketch a graph of the measured blood temperature as a function of time for thermodilution measurements with and without blood vessel heat loss.

Last Updated: $Date: 2007-11-28 23:21:57 -0500 (Wed, 28 Nov 2007) $