## 4 Experimental Section
### Clinical Experiments of Tremor Quantification
#### 4.2.3 Results  
Figure 6 shows the IMU signals of the tremor assessment system and their power spectra for a patient with slight parkinsonian tremor (\(D=1\)). In Figure 5(a), the tremor was disappeared suddenly. However, the tremor amplitude fluctuated only on a modest scale in Figure 5(b).  
The validation results of tremor quantification and valid state detection algorithms demonstrate that the tremor amplitude calculated using PSD method is based on the premises that the tremor range is stable and its peak power is sharp.  
Figure 6: _Cont._When performing the signal processing algorithms, the rest and postural tremor tasks were assessed as either a valid state or an invalid state for PSD estimation. The amplitude of the action tremor is not included in the present results.  
Therefore, the signals in Figure 6b could be used to calculate the tremor amplitude. The assessment tasks whose signals had invalid parameters (\(V_{t}>0.7\) or \(V_{f}>0.8\)) were discarded.  
Figure 6b and d show a valid tremor task (\(D=1\)), in the time domain and frequency domain, respectively [35].  
For the action tremor assessment, it was difficult to extract the tremor from voluntary movement because there were multiple frequency components across its power spectrum [39]. A better signal filter should be employed in the future [43].  
The peak power from all IMU outputs (\(R\)) had the greatest correlation with the clinical scores (\(r=0.98\)).  
In addition to the linear regression model for tremor quantification, which involves both gyroscope and the accelerometer outputs, the tremor amplitude calculations of the gyroscope and the accelerometer were analyzed independently. Table 1 indicates the calculated parameters together with the clinical scores, which resulted from a neurologist's judgments using UPDRS ratings. These parameters were the mean values from valid postural and rest tremor assessment tasks.  
Figure 6: Tremor state for a patient with parkinsonian tremor (UPDRS score \(D=1\)): (**a**,**b**): The three-axis angular velocity and three-axis acceleration waveforms of rest tremor; (**c**,**d**): The three-axis combined power spectra of angular velocity signals (**bottom chart**) and acceleration signals (**upper chart**).  
Here _acc._ means accelerometer; gyro. represents gyroscope; _RMS_ means root-mean-square; ln denotes the natural logarithm; \(R\) represents the predicated tremor score from the tremor assessment system; and \(r\) denotes the correlation coefficient between the relative parameters calculated by the IMU signals and clinical scores judged by the neurologist. For ln(gyro.power) and \(R\), the negative values are can be regarded as zero because these values are too small.  
Table 1 shows that the gyroscope signal had a stronger correlation (_r_ = 0.93) with the clinical scores than the accelerometer signal (_r_ = 0.88 and 0.91 for _peak powers_ and _RMS_, respectively).  
Table 1 also shows that the proportion of rotational parts and translation parts of a tremor (_i.e._, ln(gyro. _power_) _versus_ ln(_acc. power_)) varies from patient to patient.  
The difference between dominant frequencies from gyroscope and accelerometer were small (\(<0.2\) Hz). For all the measured patients, the dominant tremor frequency was constant or had only small fluctuations, even if the tremor amplitude changed during ten-second task period.  
The results indicate that the tremor frequency was stable for all patients; however, the tremor amplitude fluctuated continuously. The quantitative assessment of tremor, with an IMU and employing adaptive algorithms, provided an objective rating to classify rest or postural tremor severity even on a small scale.