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)?

Fig: 1

Fig: 2