2. [15 pts] Assume the metabolic hyperbola for CO₂ given by the following equation:

863 - Vcoz

V₁

PACO2 Pico2+

where the normal steady-state CO₂ production is 235 mL/min and the inspired CO₂

concentration (or volumetric fraction) is 0. Also, assume a dead-space ventilation rate of 1

L/min. Also, suppose the steady-state ventilatory response to CO₂ is given by the following

equation:

32

Vc = Drive external +(1.46 +

(Paco2-37) and Vc 20

Pa02-38.6)

Note that the above equation is slightly modified from what we derived in class in that a

constant term, Drive external is added to the equation. This drive represents an additional source

of control that affects ventilatory response e.g., sleep-wake state, alertness, etc. At normal

state (resting and awake), let Drive external = 0.

a) [5 pts] Use MATLAB to plot the metabolic hyperbola for CO₂ and the ventilatory response

to CO₂ under normal condition. Show both graphs on the same figure (see hold function).

Label both axes with appropriate units. Also indicate which graph represents the me the

metabolic hyperbola for CO₂ and which graph represents the ventilatory response to CO₂

(see legend function). The plot should show the range of ventilation from 0-20 L/min

and the range of PACO₂ from 30-60 mmHg (see xlim and ylim functions). Determine the

normal steady-state values of ventilation and Pacoz from the plot (e.g., click on the plot

where you want to obtain the x-y coordinates).

Note: For the metabolic hyperbola for CO₂, please plot V against PACO₂ i.e., you would

take the dead-space ventilation into consideration.

b) [4 pts] The onset of sleep causes the external drive to breathe to drop by -5 L/min. State

which parameter changes and to what value. Show the graphs representing this situation

and report the steady-state values of ventilation and Pacoz.

c) [4 pts] Follows from b), how would inhalation of a gas mixture containing 3% CO₂ in air

(i.e., volumetric fraction of 0.03) during sleep affect the steady-state values of ventilation

and Pacoz? State which parameter changes and to what value. Show the graphs

representing this situation and report the steady-state values of ventilation and Pacoz. You

may assume that the subject is at sea level.

d) [2pt] Copy and paste the MATLAB code you used in this question (all parts). You may

take a picture of your MATLAB script, but please make sure that the code is clearly

readable from the image.