# Essential tremor frequency decreases with time

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## Abstract

** Objective:** To quantify the extent to which tremor frequency changes with time in patients with essential tremor.

** Background:** Tremor frequency tends to be lower in older patients. The author’s previous study of 18 patients with essential tremor produced evidence that tremor frequency decreases slowly over a period of 4 to 8 years. A decrement in frequency will increase tremor amplitude because there is less attenuation of lower-frequency tremor by the low-pass filtering properties of muscle and limb mechanics.

** Methods:** Nineteen women and 25 men with essential tremor and no other neurologic conditions were followed for 4 years. Accelerometry and surface electromyography (EMG) were used to measure hand tremor and motor unit entrainment in the extensor carpi radialis brevis every 2 years. Tremor frequency was computed from the spectral peak in the rectified filtered EMG spectrum under the condition of 300-gram loading.

** Results:** The patients’ mean ± SD age was 68.0 ± 9.95 years. The mean tremor frequency at baseline was 5.79 ± 1.32 Hz. The mean decrement in tremor frequency over 4 years was 0.332 Hz (95% CI = 0.141 to 0.523) and was 0.270 Hz (95% CI = 0.122 to 0.418) when a 61-year-old outlier patient was excluded. Tremor frequency and patient age were linearly related: frequency = −0.061(age) + 9.94 (

*r*= 0.459;

*p*< 0.002).

** Conclusions:** The frequency of essential tremor decreases by ∼0.06 to 0.08 Hz/year. This decrement in frequency is consistent with the linear relationship between age and tremor frequency.–1551

Skeletal muscles have low-pass filtering properties such that the amplitude fluctuations in force decrease with increasing frequency of rhythmic motor unit drive.1 The mechanical properties of a limb (mass, stiffness, and viscosity) have a similar low-pass filtering effect on displacement fluctuations.2 Consequently, for a given intensity of motor unit entrainment, tremor amplitude will increase as its frequency decreases. This effect of muscle and limb dynamics is consistent with the logarithmic relationship between tremor amplitude, frequency, and intensity of motor unit entrainment that we previously reported.3

Age and the frequency of motor unit entrainment in the forearms of patients with essential tremor have a linear relationship: frequency = −0.077(age) + 11.4.3,4⇓ Furthermore, we previously measured wrist tremor and forearm electromyography (EMG) in 18 essential tremor patients on two occasions, 4 to 8 years apart, and found a tendency for the frequency of tremor to decrease over time.5 These observations led us to hypothesize that the frequency of abnormal motor unit entrainment in essential tremor decreases slowly over a period of years, due to progression of the underlying pathology or to concomitant age-related changes in the nervous system.5,6⇓ A gradual decline in tremor frequency was confirmed in a larger study, reported herein.

## Methods.

Nineteen women and 25 men with essential tremor participated in this study after giving informed consent, approved by the Springfield Committee for Research Involving Human Subjects. Forty-three patients were referred for the diagnosis and treatment of their tremor. One patient was recruited through an advertisement for normal control subjects and was unaware that his tremor was abnormal. Each patient agreed to be examined every other year for at least 4 years. The diagnostic criteria did not differ from the consensus diagnostic criteria for definite (classic) essential tremor formulated by an ad hoc scientific committee of the Movement Disorders Society.7 All patients had roughly symmetric postural and kinetic tremor in the upper limbs and had no signs or symptoms of another neurologic disease. Twenty-seven patients in this study participated in our previous cross-sectional study,3 but the two studies did not overlap.

The study was designed to measure tremor every 2 years (±1 month). Postural tremor of the dominant wrist and forearm EMG were recorded. A 15-gram triaxial piezoresistive accelerometer was secured to a plastic splint that was taped to the dorsum of the hand. The accelerometer was thereby located over the middle finger, 14 centimeters from the distal wrist fold, and the fingers were splinted in extension. The accelerometer had a sensitivity of 5.9 mV/*g*. The forearm was pronated and supported such that only motion about the wrist was recorded during steady horizontal extension of the hand.

Forearm EMG was recorded with 7-mm-diameter Ag–AgCl skin electrodes that were positioned in a bipolar arrangement over the extensor carpi radialis brevis and flexor carpi radialis. All EMG were full-wave rectified and low-pass filtered (−3 dB at 30 Hz) before subsequent analyses.

Tremor and rectified filtered EMG (hereafter EMG) were recorded simultaneously for 62 seconds, with and without a 300-gram load attached to the hand. We performed each measurement twice and averaged the results. Tremor and EMG were digitized at 200 samples/second using a personal computer and a 16-bit analog-to-digital converter. Spectral analysis of the tremor and EMG were computed using a fast Fourier transform, as previously described.3 Autospectra of six sequential 10.24-second data epochs tremor and EMG were averaged to produce smoothed autospectra with a frequency resolution of 0.098 Hz. We computed peak-to-peak tremor amplitude in the vertical direction (centimeters per square second) by taking the square root of the total power within the spectral peak of wrist tremor. The intensity of motor unit entrainment (EMG peak amplitude ratio) was estimated by computing square root of the spectral power within the EMG peak and dividing this peak amplitude by the square root of the total spectral power from 0 to 15 Hz. An EMG peak amplitude ratio of 0 indicates the complete absence of a tremor peak in the EMG spectrum, whereas an EMG peak amplitude ratio of 1 indicates that all of the EMG spectral power resided in the tremor spectral peak.

Tremor frequency was computed from the autospectrum of rectified filtered extensor carpi radialis brevis EMG. A weighted average measure of tremor frequency was computed for the EMG spectral peak by summing the product of EMG spectral amplitude and frequency for each spectral band within the spectral peak and dividing this sum by the sum of the spectral amplitudes. This measure of tremor frequency, rather than peak frequency, is less dependent on trial-to-trial variations in the shape of the spectral peak and produces the measure of tremor frequency with least trial-to-trial variability.3 We previously reported the intertrial variability of our methods; assuming a statistical power of 0.9, we found that a change in frequency of 0.17 Hz could be detected in a population of 30 patients at a significance level of 0.05.3

The principal experimental hypothesis was that tremor frequency decreases with time. This hypothesis was tested with a repeated-measures analysis of variance (ANOVA), using SYSTAT software (SPSS, Chicago, IL). Multiple post hoc comparisons of means were performed with Student’s *t*-tests, using Bonferroni-adjusted probabilities. Bonferroni-adjusted probabilities were also used when performing multiple correlations.

## Results.

The mean ± SD age of the patients was 68.0 ± 9.95 years (range 27 to 85 years). One patient, a 67-year-old man, answered an advertisement for normal control subjects and was unaware of his abnormal tremor. Therefore, his unknown age at onset was treated as missing data. Estimated age at onset for the remaining 43 patients ranged from 2 to 72 years (mean ± SD = 36.0 ± 22.1 years), and the estimated duration of illness ranged from 3 to 66 years (mean ± SD = 32.0 ± 18.9 years). One 68-year-old man was told by his mother that he was tremulous since age 2. Thirty-six patients had at least one parent, sibling, or child with monosymptomatic (essential) tremor.

Six patients took no medications. Thirty patients took one or more medications for chronic medical conditions (antihypertensive, thyroid supplement, diuretic, insulin, oral diabetic medication, estrogen supplement); none of the patients noticed an effect of these medications on tremor. Twelve of these patients and eight others also took a β-blocker, benzodiazepine, primidone, phenobarbital, or some combination of these drugs for tremor. Four of the 30 patients on medications took an antidepressant (desipramine [1], amitriptyline [1], fluoxetine [1], trazodone [1]). Medications for tremor were not taken on the day of experimentation. Analysis of variance (ANOVA) revealed that age, duration of disease, tremor amplitude, tremor frequency, and change in tremor frequency did not differ between those patients who took medications for tremor (n = 20) and those who did not (n = 24) (*p* > 0.2 for all comparisons). Therefore, all patients were pooled into one group for the statistical analyses in this report.

The mean ± SD tremor frequencies for the three consecutive measurements were 5.79 ± 1.32, 5.58 ± 1.20, and 5.46 ± 1.06 Hz (figure 1 ). Repeated-measures ANOVA revealed an effect of time on frequency (F = 9.28; *df* = 2, 86; *p* = 0.0002), and post hoc Bonferroni-adjusted contrasts revealed that the mean decrements in tremor frequency between years 0 and 2 (0.207 Hz) and between years 2 and 4 (0.125 Hz) were significant. We failed to find a group effect of gender (F = 0.035; *df* = 1, 42; *p* = 0.852) or a time-by-gender interaction (F = 0.519; *df* = 2, 84; *p* = 0.597), and the men and women did not differ in age (*p* = 1.00), age at onset (*p* = 1.00), or duration of illness (*p* = 1.00). Therefore, the effect of gender was not considered further.

Distribution plots of the tremor frequencies revealed a 27-year-old man with an initial tremor frequency of 10.64 Hz that could have biased our results (see figure 1). However, the decrement in tremor frequency with time remained significant when this patient was excluded (F = 8.53; *df* = 2, 84; *p* = 0.0004) and when the repeated-measures ANOVA was restricted to an initial tremor frequency range of 3 to 8 Hz (F = 7.64; *df* = 2, 80; *p* = 0.0009), 3 to 7 Hz (F = 5.57; *df* = 2, 76; *p* = 0.006), 4 to 7 Hz (F = 6.25; *df* = 2, 72; *p* = 0.003), and 4 to 8 Hz (F = 8.47; *df* = 2, 76; *p* = 0.0005). Distribution plots of the changes in frequency revealed a definite outlier, who was a 61-year-old woman with tremor frequencies of 8.86, 6.19, and 5.85 Hz at years 0, 2, and 4 (figure 2 ). Excluding this patient, the repeated-measures ANOVA still revealed a highly significant decrement in frequency with time (F = 9.51; *df* = 2, 84; *p* = 0.0002).

The mean decrement in frequency between the first and third measurements was 0.332 Hz (95% CI = 0.141 to 0.523) for all 44 patients and 0.270 Hz (95% CI = 0.122 to 0.418) when the 61-year-old outlier was excluded. In other words, the yearly decrement in frequency was ∼0.06 to 0.08 Hz. This decrement is consistent with the 0.061-Hz decrement in frequency predicted by the linear regression equations for age and tremor frequency at year 0 (frequency = −0.061[age] + 9.94; *r* = 0.459, *p* = 0.0017), year 2 (frequency = −0.066[age] + 10.1; *r* = 0.544, *p* = 0.0001), and year 4 (frequency = −0.055[age] + 9.20; *r* = 0.518, *p* = 0.0003).

There was no correlation between the change in frequency over 4 years and the patient’s baseline age (*r* = 0.094; *p* = 1.0), duration of illness (*r* = −0.091; *p* = 1.0), or age at onset (*r* = 0.121; *p* = 1.0). There was also no correlation between frequency and baseline duration of illness or age at onset for years 0, 2, and 4 (*r* no better than −0.171 and *p* = 1.0). The insignificant correlations between these variables did not improve when the patients were stratified into two groups, consisting of those patients who exhibited a decrement in frequency over 4 years (n = 32) and those who did not (n = 11).

The wrist oscillations produced by motor unit entrainment (i.e., essential tremor) and those due to physiologic mechanical resonance overlapped in frequency, producing a single spectral peak in the acceleration and EMG autospectra (figure 3 ). Mass loading moved the mechanical resonance oscillations to a lower frequency, whereas the frequency of motor unit entrainment (essential tremor) changed <1 Hz. As previously demonstrated in our laboratory, this separation of mechanical resonant oscillation from essential tremor permits the most consistent and unambiguous measure of essential tremor frequency from the rectified filtered EMG spectrum.3 Therefore, the remaining report is limited to the data obtained during mass loading, although a 0.3-Hz decrement in tremor frequency over 4 years was also observed in the condition of no mass loading (F = 7.49; *df* = 2, 74; *p* = 0.0011).

The mean ± SD tremor amplitudes during mass loading were 180 ± 194, 246 ± 334, and 233 ± 282 cm/sec^{2}, but this rise in amplitude failed to reach significance (F = 2.53; *df* = 2, 82; *p* = 0.086). Similarly, the mean ± SD EMG peak amplitude ratios were 0.708 ± 0.158, 0.729 ± 0.163, and 0.725 ± 0.165 and did not change with time (F = 0.458; *df* = 2, 86; *p* = 0.634).

Tremor amplitude, frequency, and EMG peak amplitude ratio exhibited a logarithmic relationship, as shown in the table . Essentially the same relationship and significance were obtained for years 0, 2, and 4 (see table), and this relationship did not differ significantly from that obtained in our previous cross-sectional study.3 Log frequency and log EMG peak amplitude ratio made roughly equal contributions to log tremor amplitude and explained ∼50% of the total amplitude variance. Frequency and EMG peak amplitude ratio were not correlated, with or without log transformation (*r* no better than −0.281 and *p* > 0.2 for years 0, 2, and 4). The change in log tremor amplitude over 4 years correlated with the change in log frequency (*r* = −0.435; *p* = 0.011), and the correlation between the changes in log tremor amplitude and log EMG peak amplitude ratio was nearly significant (*r* = 0.355; *p* = 0.059).

## Discussion.

We conclude that the frequency of essential tremor decreases each year by ∼0.06 to 0.08 Hz. This result confirms the result of our previous study of 18 patients evaluated on two occasions, 4 to 8 years apart,5 and is consistent with the linear relationship between age and tremor frequency.3,4⇓

Motor unit firing frequencies and frequency modulation of motor unit firing produce decreasing ripple or fluctuations in force with increasing frequency above 3 Hz because muscles in the upper limbs behave like a second-order low-pass filter with a cutoff frequency of ∼3 Hz.1 This second-order model of skeletal muscle predicts that a fall in tremor frequency from 10 to 5 Hz will increase tremor amplitude by a factor of 3.065. Similarly, a reduction in tremor frequency from 5.79 to 5.46 Hz, as occurred over 4 years in this study, would result in a 1.091-fold increase in tremor amplitude, assuming no other factors contributed to tremor amplitude. The 1.29-fold increase (233 cm/sec^{2} ÷ 180 cm/sec^{2}) observed in this study was probably due to decreased tremor frequency, increased motor unit entrainment, and possibly other factors not measurable with our techniques. This increase in amplitude narrowly missed statistical significance, probably due to the lack of statistical power of our study. We previously found that the intertrial variability in tremor amplitude is such that the minimum detectable difference in tremor amplitude is 30%, assuming a statistical power of 0.9 and a significance level of 0.05.3 Nevertheless, in this and our previous study,3 we found a logarithmic relationship between tremor amplitude, frequency, and motor unit entrainment, and frequency and motor unit entrainment made comparable and independent contributions to tremor amplitude.

The pathophysiology of decreasing tremor frequency over time was not addressed by our study. The cerebellum is known to be metabolically hyperactive in patients with essential tremor,8 and the indole alkaloids harmaline and ibogaine produce enhanced olivocerebellar oscillation and a tremor in laboratory animals that resembles essential tremor.9-11⇓⇓ Lesions in the cerebellum reduce the frequency of harmaline tremor from 8–12 to 6–7 Hz,9 and the enhanced rhythmic olivary drive to the cerebellum, produced by harmaline and ibogaine, causes excitotoxic damage to Purkinje neurons.11,12⇓ Similar mechanisms could be involved in essential tremor. If so, early diagnosis and effective treatment would be important. However, we found that tremor frequency is a function of age but not duration of illness. Therefore, the linear relationship between age and tremor frequency may be independent of the pathology of essential tremor and might instead reflect age-related change in the cerebellum or other parts of the motor system.6 Of course, this speculation hinges on the important caveat that the retrospective estimation of age at onset is notoriously inaccurate for essential tremor because many patients do not recognize their condition when it is mild.13 Inaccuracies in our estimates of age at onset may have obscured a relationship between disease duration and tremor frequency.

## Acknowledgments

Supported by NS20973 from the National Institute of Neurological Disorders and Stroke, and by the Spastic Research Foundation of Kiwanis International, IL, Eastern Iowa District.

**Acknowledgment**

The author thanks Connie Higgins and Suzanne Elble for their help in collecting and analyzing the data in this report.

- Received May 12, 2000.
- Accepted July 20, 2000.

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