Disturbances of Rhythm Formation in Patients with Parkinson's Disease: Part II. A Forced Oscillation Model

The origin of the characteristic disturbances of rhythm formation in patients with Parkinson's disease (the hastening phenomenon) was discussed, using a second-order system of the periodic response. The input signal was regarded as a pulse series of a Dirac function. The output process of the system had maximal errors of response at input frequencies of f = omega0/n (n = 1, 2, . . .), where omega0 was the intrinsic frequency of the system. Damping coefficient epsilon represented a function of an inhibitor against these maximal errors and the errors diverged to infinity when epsilon = 0. The solution of this forced oscillation system indicated that the intrinsic oscillation of the system has a possibility to be excited at these critical frequencies f = omega/n. Inferred from data on the tapping test, the frequency of an intrinsic oscillation was 5 Hz in the central nervous system, then the critical frequencies were predicted 5/n = 5, 2.5, . . . Hz. On the tapping test the errors of response become maximum around 2.5 and 5 Hz (taps per second), and their peak heights increased from the minimum in well trained normal subjects to the maximum in patients. An inhibitory mechanism against the maximal error would function well, i.e. epsilon greater than 0, in normal subjects but so insufficiently (epsilon leads to 0) in patients that the excited intrinsic oscillation would control their response directly. Thus some patients could no longer maintain a synchronous tapping response at 2.5 Hz or 5 Hz and showed a hastened tapping of 5 6 Hz independent of the signal frequency.