3/6/2000
EE 518 Physiological Control System Analysis
Final Exam
1.
(25 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
.”
2.
(20 pts.) In the generation of an action potential by the neuron of a sensory receptor -
neuron pair, starting at the extinguishing level (V
E
), the voltage exponentially rises toward the receptor potential (V r
) with a time constant

0
. However, the neuron fires when the firing level V
F
is reached. a) (10 pts.) Derive an expression for the firing frequency in terms of V r
, V
E
, V
F
and

0
. b) (5 pts.) Given V
E
= -90mV,

0
= 0.062s and V
F
= -82mV evaluate firing frequency for
V r
= -80mV and V r
= -61 mV. c) (5 pts.) Comment on the change in firing frequency with respect to change in receptor potential (Draw figures if necessary).
3.
(15 pts.) The spindle compares the actual position with the desired position;
the difference is an error signal that the spindle feeds back to motor neuron.
Explain the mechanism in the spindle that produces this error signal.
4.
(25 pts.) The following model (Fig.1) 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 k
1 and k
4
, respectively. P and N denotes the respective constant production rates for glucose and insulin. u(t) represent the time function of glucose injection. a) (10 pts.) Write the differential equations governing the behavior of glucose and insulin concentration as a function of time. b) (10 pts.) Assume a diabetic patient with k
3
= 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) (5 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.

Fig.1 Model of Glucose-Insulin interaction
5) (15 pts.) Let us assume that the heart is a continuous flow pump with outflow = Q = Q
R
=
Q
L
. We can investigate the variations of average pressures and volumes in the circulatory system when Q and/or parameters of the system change (Fig.2).
Fig.2 Model of circulatory system
The parameters in Fig.2 denote the following:
Q
L
: out-flow of left ventricle,
Q
R
: out-flow of right ventricle,
Rs: resistance of systemic arteriolar and capillary bed,
Rp: resistance of pulmonary arteriolar and capillary bed,
C
AS
: compliance of major systemic arteries,
C
VS
: compliance of major systemic veins,
C
AP
: compliance of major pulmonary arteries,
C
VP
: compliance of major pulmonary veins,
P
AS
: average systemic arterial pressure,
P
VS
: average systemic venous pressure,
P
AP
: average pulmonary arterial pressure,
P
VP
: average pulmonary venous pressure,
Write differential equations governing the behavior P
AS
, P
VS
, P
AP
, and P
VP.
Find their steady-state values. Assume that pulmonary blood volume is B
P
and systemic blood volume is B
S
.