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:
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 (c_{in} 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.
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 ttest. 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 Ttests to test
the two hypotheses. Provide a pvalue in
both cases. Are the results significant?
Please
provide your raw data as an appendix to your report.