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.