EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
EE 518 MIDTERM EXAM
(150 minutes)
IMPORTANT NOTE: PLEASE READ BEFORE STARTING





There are five questions, attempt all.
Read the questions carefully.
Show complete work for full credit.
Include units in your answers.
ORGANIZE YOUR WORK AND WRITE LEGIBLY.
GOOD LUCK
Last
Name:
First
Name:
Student
ID:
Signature:
POINTS SCORE
20
Q1
20
Q2
20
Q3
20
Q4
20
Q5
100
TOTAL
1
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
Q1. (20 pts.)
The cardiac output curve of a heart that has been transplanted into a
patient is given in tabular form as follows:
Right
Atrial
Pressure
(mmHg)
Cardiac
output
(Lmin-1)
0 1
2
3
4
5
6
7
8
9
10
11
12
13
0 0.3 1.0 2.5 4.8 7.0 9.0 10.5 11.0 11.3 11.5 11.6 11.6 11.6
Suppose the venous return characteristics of the patient’s systemic circulation can be
expressed in the form of the following equations:
QR  14
Pr a  0
 14  2 Pr a , 0  Pr a  7
0
Pr a  7
(a) Deduce the patient’s steady-state right atrial pressure (Pra) and cardiac output,
assuming the transplant operation is successful.
(b) What would be the steady-state values for cardiac output and Pra if the total
circulatory resistance were to be doubled?
(c) To counteract the increased circulatory resistance in (b), suppose a sufficient
quantity of blood is transfused into the patient so that mean systemic pressure is
raised by 5 mmHg. What would be the new steady-state values for Pra and cardiac
output?
2
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
(Q1 continues)
3
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
Q2. (20 pts.)
Based on the verbal description of the following physiological reflex
system, construct block diagram to represent the major control mechanism involved.
Clearly identify the physiological correlates of the controller, the plant and the feedback
element, as well as the controlling, controlled and feedback variables. Describe how
negative (or positive) feedback is achieved in each case.
“The Bainbridge reflex is a cardiac reflex that aids in matching of cardiac output (the flow
rate at which blood is pumped out of the heart) to venous return (the flow rate at which blood
returns to the heart). Suppose there is a transient increase in the amount of blood returning to
the right atrium. This increases the blood pressure in the right atrium, stimulating the atrial
stretch receptors. As a result, neural traffic in the afferents to the medulla in the brain is
increased. This, in turn, leads to an increase in efferent activity in the cardiac sympathetic
nerves as a parallel decrease in efferent parasympathetic activity. Consequently, both heart
rate and cardiac contractility are increased, raising cardiac output. In this way, the reflex acts
like a servomechanism, adjusting cardiac output to track venous return.”
4
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
Q3. (20 pts.) The following model assumes that glucose uptake is dependent on
insulin concentration (I) in the plasma and that insulin production rate is dependent
on the glucose concentration (G) in the plasma. Glucose and insulin disappearance
rates are k1 and k4, respectively. P and N denote the respective constant production
rates for glucose and insulin. u(t) represent the time function of glucose injection.
a) (8 pts.) Write the differential equations governing the behavior of glucose and
insulin concentration as a function of time.
b) (8 pts.) Assume a diabetic patient with k3 = 0. If the glucose injection function
u(t) is an impulsive function, that is, u(t) = A(t), find G(t) and I(t).
c) (4 pts.) Estimate G(t) and I(t) for the same input given in (b) for a normal man.
Without making extensive calculations draw graphs and give reasoning.
Model of Glucose-Insulin interaction
5
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
(Q3 continues)
6
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
Q4 (20 pts.)
Many types of physiological receptors exhibit the property of rate
sensitivity. Carbon dioxide (CO2) receptors have been found in the lungs of birds and
reptiles. The following figure shows a highly simplified model of the way in which
ventilation may be controlled by these intrapulmonary receptors following denervation of
the carotid bodies.
The feedforward element in the closed-loop system represents the gas exchange
processes of the lungs, while the feedback element represents the dynamic characteristics
of the intrapulmonary CO2 receptors. The parameter α determines how rate-sensitive
these receptors are.
Determine the responses of this system to a large hyperventilatory sigh (which may be
approximated by an impulse function) when:
(a) α = 0 (there is no rate sensitivity),
(b) α =1/2
+
VE
+
5
1  5s
PACO2
 s 1
s 1
7
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
(Q4 continues)
8
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
Q5 (20 pts.)
(a) The cardiovascular variables (heart rate and arterial blood pressure) are
continually perturbed by respiration through the following mechanisms:
1.
2.
3.
4.
(b) Insert the necessary labels in the appropriate locations.
9
EE 518 Physiological Control Systems
Analysis, Simulation, and Estimation
April 27th, 2011
(c) Show that the frequency response of a linear system can be derived by dividing
the cross spectrum S xy ( ) of the input and output by the spectrum of the
input S xx ( ) . Assume x(t) and y(t) to represent the input and output of the linear
system with impulse response h(t). Hint: Start from the convolution equation.
10