BIEN 435 Laboratory

Simulation of Cardiac Output Measurement

Null Hypothesis

This laboratory will be designed to simulate the measurement of cardiac output by the thermal dilution method.  See the accompanying description of the thermal dilution method (download doc).  The null hypotheses you would like to test are:

1. The measured value of cardiac output does not depend on the time of injection of the test fluid.
2. The measured value of cardiac output does not depend on the total amount of fluid injected.

In addition, you will compare the signal that you obtain in the “aorta” to the derived relationship of concentration (temperature) as a function of time.

Theory

There are two parts to the theoretical development.  The first is the determination of concentration at the detector as a function of time.  This has been provided in the thermal dilution method handout.  The second part is the determination of flow rate from the measured concentration, which is developed here.

Consider the situation in Figure 1.  Blood is injected into a mixing chamber along with a dye.  The concentration is measured at the outlet (Blood + Dye Out).  Conservation of mass says that the total mass of dye in must be the total mass of dye out.  Total mass of dye in is the concentration in the syringe multiplied by the total volume injected (cin V).  Total mass out is the integral with respect to time of concentration at the outlet times flow rate.  Therefore:

Assume that the flow rate out is constant with time.  This assumption is reasonable as long as the amount of fluid injected is small (otherwise the additional fluid injected with the dye will transiently change the flow rate).  Then  can be taken out of the integral and the equation can be solved for  to yield.

Here,  is known because it is the number of drops per unit volume in the injection syringe.   is the amount of fluid you inject.  The integral in the bottom must be obtained from the trace that you will get on the oscilloscope (the output of your concentration detection device).  You must find a reasonable way of integrating this trace.  One way is to pick values off of the oscilloscope, fit these to the theoretical curve of concentration as a function of time, and then integrate the theoretical curve.  Another simple method is to trace the curve on a piece of semitransparent paper, cut out the area under the curve, and weigh the paper.  You can also simply do a Simpson’s rule type of integration, again, from the numbers you pick off the oscilloscope.  Whatever method you pick, you must use your calibration curve for concentration to determine concentration from the voltage values and then use this to determine .

Experimental Setup

The flow system is shown in Figure 2.  Some of the pieces are simple, given what you have done already.  Certainly, the two reservoirs and the tubing are already available.  You will need to add something to make sure that the injected dye (or hot/cold water) is mixed thoroughly with the flowing water.  The concentration detection system can be easily made from a laser, a photoresistor, a voltage supply and a second resistor.  You cannot use the digital mutimeter to take readings as a function of time because the concentration will change too quickly to capture.  Thus, you will need to use an oscilloscope.

Figure 3 shows a simple concentration detector circuit.  The photoresistor changes its resistance according to the amount of light incident on its sensor.   As the dye passes in front of the laser, it attenuates the light, causing less light to impinge on the photoresistor.  The resistor and the photoresistor form a simple voltage divider so that the output is:

where  is the resistance of the photoresistor,  is the resistance of the resistor, and  is the dc voltage supplied to the circuit.  Increased light casues decreased photoresistor voltage, causing reduced output voltage.  Since an increased concentration will decrease the amount of light, output voltage increases with concentration.

You will find it difficult to obtain a good trace on the oscilloscope if there is a significant DC offset on your signal.  Notice that with the circuit above there will be a DC offset of:

There are two ways to eliminate this problem.  One is to feed the output of your sensor into the instrumentation amplifier and use the DC offset control to eliminate the offset.  Another is to use the ±6 Volt supplies on the instrumentation amplifier.  I.e., use +6 volts in place of V and use -6 Volts in place of ground.  This second strategy will work only if the resistor value for your circuit is close to the nominal resistance value of your photoresistor (i.e. the resistance in the photoresistor when the laser shines directly on it with no dye in the fluid.

Transducer Calibration

You will need to calibrate your detector.  This should be done in a manner similar to the way you calibrated the pressure transducer in the previous experiment.  Should the output be linear, based on the circuit design?  It is clear from Eq. 3 that the circuit itself is inherently nonlinear with respect to , but if  this nonlinearity can be minimized.  Nonetheless, the resistance may still be nonlinear with respect to the amount of light impinging on the photoresistor.

To obtain the calibration, perform a linear least squares fit of concentration as a function of voltage out.  This will enable you to translate all of the voltage readings directly to concentration.

1. Fill a short piece of the tubing you will be using (the ¼ inch ID tubing) with water.
2. Shine the laser through the tubing so that the light hits the photodetector, and record the output voltage.
3. In a beaker, mix 10 mL of water with 1 drop of dye.
4. Empty the short piece of tubing and refill it with the water-dye mixture.
5. Again, shine the laser through the tubing so that the light hits the photodetector, and record the output voltage.
6. Repeat steps 3 and 4 up to 10 times, increasing the number of drops of dye each time by one.

Remember to measure the true diameter of the tubing used in this experiment.

Flow Rate

As in the pressure drop experiment, determine the true flow rate.  Use a graduated cylinder to set the flow rate to approximately this value.  Measure the flow rate as precisely as possible.

Experimental Procedure

To test the two null hypotheses, you will need to measure concentration as a function of time for three cases:  1) Standard amount of injectate over a standard amount of time.  2) Twice the amount of injectate in the same amount of time.  3) Standard amount of injectate over twice the time.  You will need at least 5 repetitions for each case to perform your t-test.  You will need to use the storage and single sweep trigger features of your oscilloscope.  You must record the data as indicated in Table 1.

 Collected Volume (mL) Collection Time (sec) Injected Volume (mL) Injection Time (sec) Concentration of Injectate (drops/mL)

Table 1: Data to be collected for each experimental condition.

In addition, for each experimental condition you must record several data points of voltage vs. time on the oscilloscope screen.  You will need to generate a trace on the oscilloscope that resembles that shown in Figure 4.  The rising part of this curve is the “charging” part of the RC circuit analogue and represents the time during which dye is being injected into the system (hence the concentration is rising).  The rest of the curve is the “discharging” part of the RC circuit analogue and represents the time during which dye is being cleared from the system.  You will need to determine the time constants for both the rising and falling parts of the curve so that you can properly model the signal.

To obtain this signal, you will need to use the “single sweep” mode of the oscilloscope.

Ask your instructor for a demonstration of single sweep mode.  Briefly, the “mode” is set to “single sweep,” and the “trigger” is set to channel 1.  A trace begins when the signal reaches a set voltage level (indicating that the concentration has changed) and then stops at the end of the screen.  If single sweep is not set, then you will not have time to record the data from the screen because it will be erased by subsequent sweeps.

Data analysis

1.     Use a least squares fit to determine the calibration factor of your sensor (concentration as a function of voltage).

2.     For each data set value of (Volume Collected, Time of Collection), translate to flow rate (Q)

1.     Determine a reasonable way to get flow rate from the concentration measurements.  This will most likely involve integrating the signal on the oscilloscope in some way.  Refer to the following document (download doc).

2.     For each data set of voltage as a function of time, plot concentration as a function of time.

3.     For each experimental condition (i.e. quick injection, slow injection, double injected volume) plot the theoretical curve, based on the experimental values used.

4.     Discuss reasons for any differences (theory vs experiment).

5.     Perform Student’s T-tests to test the two hypotheses.  Provide a p-value in both cases.  Are the results significant?