ECE 4455/MEDBIO 4455 Final Project
Due December 16, 2022 at 11:55 pm

Instructions
You are to complete this project, which is the summative assessment for the course in lieu of a
final exam, independently and alone. Collaborating, discussing, or sharing of information during
the project is not permitted. The mark you earn on this project applies to you alone, so the responses
you submit must be uniquely produced by you.

This is a fully open-book assessment. You may refer to any written or online sources you think are
appropriate, including the lecture slides posted on the ECE 4455 OWL site. Cite your references
if you use any information from them in your responses.

If you have questions about the project, you should e-mail Dr. Lacefield at jlacefie@uwo.ca.
Dr. Lacefield will also be available during his regularly scheduled office hours on December 1 and
December 8. Office hours during the exam period will be Wednesday, December 14 at 3:00-4:00
pm.

The questions in this assignment are related to the Case Study 4 journal article, D.P. Francis,
K. Willson, et al.³Quantitative general theory for periodic breathing in chronic heart failure and
its clinical implications´Circulation, vol. 102, pp. 2214-2221, 2000, which can be downloaded
from the Unit 5 course content module on the ECE 4455 OWL site.

The questions also require the MATLAB scripts test_Khoo_margins.m,
test_Francis_margins.m, and validate_Francis_Fig3.m, as well as the MATLAB
functions they call (Khoo_model.m, Francis_model.m, evaluate_gain_margin.m, and
evaluate_delay_margin.m), each of which can be downloaded from WKH ³&DVH 6WXG\
0$7/$%ILOHV´IROGHU within the Unit 5 module on the OWL site.

Responses to Questions 2(a)-(b) and 3(a)-(c) should include the Nyquist and Bode plots produced
by those computations. Responses to Questions 4 and 5 should include the scatter plots produced
by those computations.

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ECE 4455 OWL site. Submit your responses as an attachment in Word or PDF format. Include
your last name as part of the file name for your submission. Late submissions will not be accepted.


ECE 4455/MEDBIO 4455 Final Project Fall Term 2022 Page 2 of 4
1(a). Draw a block diagram of the closed-loop respiratory regulation model employed in
Francis_model.m and label each signal in the diagram. State the Laplace-domain transfer
functions for each block. In addition, for the respiration subsystem, provide equations for the gain
and time constant of that process. To obtain full marks, your diagram must include a disturbance
signal and be formulated to permit application of Nyquist stability analysis to the system.
[8 marks]
(b) Where should the closed loop be cut to obtain the open-loop transfer function of the system?
[1 mark]


2. [This question, asks you to LQYHVWLJDWHZKHWKHUWKH³FRQYHQWLRQDOZLVGRP´H[SODQDWLRQreviewed during
the November 30 lecture that prolonged chemoreceptor delay are the cause of respiratory instability is a
thorough interpretation of the predictions of the Khoo model. Specifically, in the Khoo textbook and the
November 30 lecture, the cardiac output and chemoreceptor delays were varied simultaneously. Here we
consider the effects of varying each factor individually.]
Use test_Khoo_margins to produce Nyquist and Bode plots for two hypothetical subjects:
(a) An individual who has the cardiac output Khoo assumes for a congestive heart failure (CHF)
patient (Qb = 0.05 L/s) but the chemoreceptor delays of a healthy subject (Tp = 6.1 s and Tc = 7.1 s),
and«
(b) An individual who has the cardiac output of a healthy subject (Qb = 0.10 L/s) but the
chemoreceptor delays Khoo assumes for a CHF patient (Tp = 12.2 s and Tc = 14.2 s).
In your response for both (a) and (b), report the gain and time-delay margins for each subject.
Indicate the point on each Nyquist plot where the gain margin should be measured and the point
on each Bode plot where the time-delay margin should be measured and confirm that the margins
output by the MATLAB script are correct.
[3 marks each for (a) and (b)]
(c) Based on the results from parts (a) and (b), does instability appear to be caused primarily by
changes in cardiac output, primarily by changes in the chemoreceptor delays, or do both factors
contribute? Explain your reasoning.
[2 marks]
(d) Why does the reduced cardiac output modeled in part (a) alter the stability of respiratory
regulation? In other words, what other parameter of the Khoo model changes when cardiac output
decreases and why does that change reduce the stability margins of the system?
[2 marks]
(e) You should observe that the time-delay margin for part (a), where the chemoreceptor delays
are fixed at their healthy-subject values, is less than the time-delay margin for part (b), where the
chemoreceptor delays are abnormally long. Explain this result.
[2 marks]


ECE 4455/MEDBIO 4455 Final Project Fall Term 2022 Page 3 of 4
3. [This question asks you to evaluate how well the Francis et al. model and their experimental data support
WKHDUWLFOH¶VFRQFOXVLRQWKDWUHVSLUDWRU\LQVWDELOLW\is more likely to be caused by elevated chemoreceptor
sensitivity than prolonged feedback delay. Parts (d) and (e) draw on your knowledge of statistics. You may
find the function normcdf in the MATLAB Statistics and Machine Learning Toolbox to be useful.]
(a) Use test_Francis_margins to compute the gain and time-delay margins for the average
VXEMHFW IURP WKH SDSHU¶V JURXS RI &+) SDWLHQWV ZLWK VWDEOH UHVSLUDWRU\ FRQWURO
(GF = 620 (L/min)/atm and G = 0.40 min). Based on these results, what is the smallest value of GF
that would make this patient unstable if G was held constant? What is the smallest value of G that
would make this patient unstable if GF was held constant?
[3 marks]
(b) Use test_Francis_margins to confirm that the increased value of GF you computed in
part (a) makes the patient unstable if G is fixed at 0.40 min.
[1 mark]
(c) Use test_Francis_margins to confirm that the increased value of G you computed in
part (a) makes the patient unstable if GF is fixed at 620 (L/min)/atm.
[1 mark]
(d) What is the probability that a patient selected from Francis et al.¶Vgroup of CHF patients with
unstable respiration would have a chemoreflex sensitivity greater than or equal to the value you
tested in part (b)? Explain how you obtained your result. (Note that patient parameters are reported
in the Francis et al. paper as mean r standard error of the mean, not mean r standard deviation.)
[3 marks]
(e) What is the probability that a patient selected from Francis et al.¶Vgroup of CHF patients with
unstable respiration would have a chemoreceptor delay greater than or equal to the value you tested
in part (c)? Explain how you obtained your result.
[3 marks]
(f) What do your results from Questions 3(d) and 3(e) suggest about the relative likelihood of
unstable respiratory control arising from elevated chemoreflex sensitivity as compared to
prolonged chemoreceptor delay?
[1 mark]

4. Use validate_Francis_Fig3 WRYHULI\WKDWWKHDUWLFOH¶VOLQHDUFODVVLILHULVFRQVLVWHQWZLWK
Nyquist stability analysis of the underlying closed-loop model when, as in the article, cardiac
output is assumed to not be altered by the presence of congestive heart failure
(i.e., min_fract_HF = 1). Take time to refine the slope and intercept of the classifier to obtain
the best classification accuracy you can as evaluated by the TPF and TNF. Report your slope,
intercept, TPF, and TNF values and include the final version of your scatter plot in your response.
[3 marks]

ECE 4455/MEDBIO 4455 Final Project Fall Term 2022 Page 4 of 4
5. [In this question, part (a) models the assumption that even a patient with severe CHF will compensate
cardiac output to at least 80% of its normal value (see the December 5 lecture slides), whereas part (b) is
PRGHOHGRQ WKH.KRR WH[WERRN¶VCHF demonstration, which assumes a CHF patient may have cardiac
output in the neighbourhood of 50% of its normal value.]
Use validate_Francis_Fig3 to investigate the effect of assuming CHF can reduce cardiac
output on the performance of the linear classifier. Use the same slope and intercept that you
selected in Question 4. Report the TPF and TNF and present the scatter plots produced when:
(a) min_fract_HF = 0.80 and
(b) min_fract_HF = 0.40.
[2 marks each for parts (a) and (b)]
(c) What do your results from Questions 5(a) and 5(b) suggest about the effect of cardiac output
on the accuracy of the Francis et al. linear classifier?