PROBLEM4. (14 points) You have been asked to evaluate the efficacy of a new drug to prevent the onset of clonus in ankle joints of spinal cord injured (SCI) patients. (Clonus is the clinical term referring to the sustained oscillations occurring in spasticity, which is related to hyperreflexia. A video of clonus can be found at: www.youtube.com/watch?v=liE9IVMYZPU). In laboratory animals, the drug has been shown to reduce the gain of the stretch reflex by a factor of 1.6 (i.e., the original gain is divided by 1.6), but it also has the effect of slowing the conduction velocity of neural action potentials from 40 m/s to 30 m/s. You generate a model of clonus which incorporates muscle, spindle, and neuror properties. Your model without the drug produces the Nyquist plot on following page (arrows indicate increasing frequency). See for example, Hidler JM, Rymer WZ. A simulation study of reflex instability in spasticity: origins of clonus. IEEE Trans Rehabil Eng. 1999 Sep:7(3):327-40. Some other additional information youll need: . The distance from the ankle muscle spindles to the innervating motoneurons is 1 m So the time delay due to the neural transmission is the time it takes for action potentials to travel from the spindles to the motoneurons and back. Assume that when the drug is used, the phase of the loop transfer function is equal to -180° at the frequency of 3 Hz. The Nyquist plot is scaled such that both the x and y axes correspond to a scale of 5 cm per 1 unit on both of the axes. . . a) Do you predict that the drug prevents clonus? Show your work on the Nyquist plot. b) Is clonus in SCI patients more of a potential problem in the wrist or the elbow? Justify your answer.
PROBLEM4. (14 points) You have been asked to evaluate the efficacy of a new drug to prevent the onset of clonus in ankle joints of spinal cord injured (SCI) patients. (Clonus is the clinical term referring to the sustained oscillations occurring in spasticity, which is related to hyperreflexia. A video of clonus can be found at: www.youtube.com/watch?v=liE9IVMYZPU). In laboratory animals, the drug has been shown to reduce the gain of the stretch reflex by a factor of 1.6 (i.e., the original gain is divided by 1.6), but it also has the effect of slowing the conduction velocity of neural action potentials from 40 m/s to 30 m/s. You generate a model of clonus which incorporates muscle, spindle, and neuror properties. Your model without the drug produces the Nyquist plot on following page (arrows indicate increasing frequency). See for example, Hidler JM, Rymer WZ. A simulation study of reflex instability in spasticity: origins of clonus. IEEE Trans Rehabil Eng. 1999 Sep:7(3):327-40. Some other additional information youll need: . The distance from the ankle muscle spindles to the innervating motoneurons is 1 m So the time delay due to the neural transmission is the time it takes for action potentials to travel from the spindles to the motoneurons and back. Assume that when the drug is used, the phase of the loop transfer function is equal to -180° at the frequency of 3 Hz. The Nyquist plot is scaled such that both the x and y axes correspond to a scale of 5 cm per 1 unit on both of the axes. . . a) Do you predict that the drug prevents clonus? Show your work on the Nyquist plot. b) Is clonus in SCI patients more of a potential problem in the wrist or the elbow? Justify your answer.
