Anesthesia induces muscle relaxation (paralysis) and unconsciousness in the patient. Muscle relaxation can be monitored using electromyogram signals from nerves in the hand; unconsciousness can be monitored using the cardiovascular system's mean arterial pressure. The anesthetic drug is a mixture of isoflurane and atracurium. An approximate model relating muscle relaxation to the percent isoflurane in the mixture is
where P(s) is muscle relaxation measured as a fraction of total paralysis (normalized to unity) and U(s) is the percent mixture of isoflurane (Link- ens, 1992).
a. Find the damping ratio and the natural frequency of the paralysis transient response.
b. Find the maximum possible percent paralysis if a 2% mixture of isoflurane is used.
c. Plot the step response of paralysis if a 1% mixture of isoflurane is used.
d. What percent isoflurane would have to be used for 100% paralysis?