submit your solutions on gradescope 1 total 16 pts the figure below sh

Question

Submit your solutions on Gradescope.
1. [Total: 16 pts] The figure below shows a schematic control block diagram of the control of
respiration, with the respiratory controller representing the respiratory chemoreflexes, brain
respiratory neural centers and the respiratory muscles, and the lungs representing the CO₂
exchange in the lungs. In amyotrophic lateral sclerosis (ALS, also known as Lou Gehrig's
disease), motor neuron degeneration results in weakness and eventual paralysis of the
respiratory muscles. Note that the regulation of ventilation model here is slightly different
(more simplified) from the one we discussed in class.
V/₁
Respiratory
controller
Lungs
Pacoz
a) [2 pts] Suppose that, in a particular ALS patient, the (steady-state) respiratory controller
equation (which characterizes the chemoreflex response) is given by the following
equation:
V₁ = Paco2 - 37
Where V represents the alveolar ventilation (in L/min), and Pacoz is the partial pressure
for CO₂ in the arterial blood (in units of mmHg). Draw (as accurately as possible on the
provided graph) the line representing the steady-state controller response to Paco2- Note
that we are neglecting the effects of O₂ here. Label this line as "(a)".
b) [2 pts] Assume that gas exchange in this patient is normal and can be characterized by
the following plant equation:
Paco2 = 200/V
Draw (as accurately as possible on the provided graph) the relationship between Pacoz
and V. Label the curve as "(b)"./nVdotA (L/min)
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
40
41
(mm Hg)
c) [2 pts] Estimate the steady-state operating values of Pacoz and V₁ in this patient.
d) [4 pts] In a normal healthy person, the controller response is given by
V₁ = 2(Paco2-37).
Draw this controller response on the graph below. Estimate the steady-state operating
values of Paco2 and V in the normal subjects. Label the curve as "(d)".
35
36 37
38
39
P
aCO2
42
43
44
45
e) [4 pts] A pressure support ventilator can be used to provide assistance to the ALS patient
- such a ventilator would produce an increase of x L/min on top of the subject's own
natural ventilatory output, independent of the Pacoz level. However, the ventilator has
to be triggered by a minimal inspiratory effort by the patient himself. If the patient does
not generate any effort, the ventilator does not provide any ventilatory assistance. Draw
on the graph below the total controller response (patient+ ventilator) required to restore
the steady-state V and Pacoz values to the levels seen in the normal subject. Label the
total controller response as "(e)".
f) [2 pts] What is the value of x (L/min)?