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Portable motion transducers, suitable for measuring tremor, are now available at a reasonable cost. The use of these transducers requires knowledge of their limitations and data analysis. The purpose of this review is to provide a practical overview and example software for using portable motion transducers in the quantification of tremor.

Medline was searched via PubMed.gov in December 2015 using the Boolean expression “tremor AND (accelerometer OR accelerometry OR gyroscope OR inertial measurement unit OR digitizing tablet OR transducer).” Abstracts of 419 papers dating back to 1964 were reviewed for relevant portable transducers and methods of tremor analysis, and 105 papers written in English were reviewed in detail.

Accelerometers, gyroscopes, and digitizing tablets are used most commonly, but few are sold for the purpose of measuring tremor. Consequently, most software for tremor analysis is developed by the user. Wearable transducers are capable of recording tremor continuously, in the absence of a clinician. Tremor amplitude, frequency, and occurrence (percentage of time with tremor) can be computed. Tremor amplitude and occurrence correlate strongly with clinical ratings of tremor severity.

Transducers provide measurements of tremor amplitude that are objective, precise, and valid, but the precision and accuracy of transducers are mitigated by natural variability in tremor amplitude. This variability is so great that the minimum detectable change in amplitude, exceeding random variability, is comparable for scales and transducers. Research is needed to determine the feasibility of detecting smaller change using averaged data from continuous long-term recordings with wearable transducers.

Transducers have been used in the study of tremor for more than 100 years. Early investigators used a tambour and smoked drum to record physiologic and pathologic tremors.

The expense and size of transducers decreased dramatically with the advent of microelectromechanical systems (MEMS) technology in the 1990s. Small transducers are now integrated with microelectronic circuits for data acquisition and storage. Inertial measurement units (IMUs) contain a triaxial accelerometer, triaxial gyroscope, and frequently a triaxial magnetometer and altimeter, integrated with an electronic circuit for digital storage and wireless output.

The purpose of this review is to provide a practical overview of the use of portable motion transducers in the quantification of tremor. This is not a comprehensive review of all transducers that are currently being sold for the assessment of tremor; rather it is a practical guide to the selection and use of portable transducers in tremor analysis. MEMS technology has provided developers with an abundance of inexpensive IMUs that are being incorporated into a variety of devices that are potentially useful in the assessment of tremor. The list of such devices and applications is rapidly increasing and changing with advancing technology. Witness, for example, the Lift Pulse app for Android

Accelerometers, gyroscopes, and digitizing tablets are considered in this review because they have been used most commonly to assess tremor in ambulatory settings. Their strengths, limitations, and methods of analysis are reviewed. Example software for tremor analysis is provided in an online appendix.

Medline was searched via PubMed.gov in December 2015 using the Boolean expression “tremor AND (accelerometer OR accelerometry OR gyroscope OR inertial measurement unit OR digitizing tablet OR transducer).” This search produced 419 papers dating back to 1964. The abstracts of these papers were reviewed for relevant portable transducers and mathematical methods of tremor analysis, and 105 papers written in English were reviewed in detail. Potentially relevant publications and references cited in these publications were also reviewed.

Motion of a body part (e.g., the hand) may consist of translational motion and rotational motion in three-dimensional space (

Tremor is an oscillatory motion that is roughly sinusoidal. Fourier’s theorem states that almost any continuous, periodic signal can be represented by the weighted sum of sines and cosines.^{2} at frequency

The fast Fourier transform (FFT) is a discrete Fourier transform that is computed with a mathematical algorithm that minimizes the number of computations, thus optimizing computational speed on a computer. This algorithm is implemented in many software packages. For example, Microsoft Excel provides an FFT that will accept signal recordings consisting of N data points, where N must be some integer power of 2 (e.g., 2^{8} = 256), up to 4,096 (see online appendix). Other FFTs, such as those in MATLAB (

The frequency content of voluntary movement is generally concentrated at frequencies below 2 Hz, and most forms of tremor occur at 3 Hz or greater.

Several factors are important when selecting a transducer for tremor analysis. The kinematic characteristics of tremor and motor task must be considered, and the transducer must have sufficient sensitivity, amplitude range, and frequency range to record tremor with good fidelity. The transducer also must be small enough and light enough to mount securely on the desired body part, without impeding the motor task. These issues are now discussed.

Translational displacement tremor T can be approximated by a sine wave with amplitude A in centimeters and frequency ^{2}sin(2^{2}sin(2^{2}. Similarly, if angular velocity is measured, angular rotation is the amplitude of angular velocity divided by 2

Most tremors are primarily oscillatory rotation of a body part about a joint or multiple joints. For example, hand tremor may originate from tremulous rotation at the wrist, elbow, or shoulder. Similarly, head tremor is primarily rotation of the head about the neck. Consequently, a gyroscope mounted on the hand or head would seem ideal. However, until the advent of MEMS technology, gyroscopic transducers were too heavy and bulky for most tremor applications. These transducers are now very small and inexpensive.

Historically, accelerometers have been used more than other transducers in tremor analysis. Most accelerometers are piezoelectric, piezoresistive, or capacitive devices and have been incorporated into a variety of wearable devices.^{2}). Inertial acceleration of a body part is a function of the force F applied to the mass m of the body part, according to Newton’s law F = ma. The effect of Earth’s gravity on an accelerometer is not constant when the accelerometer is rotating in space, and some rotational movement is virtually always present when recording tremor.^{2}) at 1 Hz would require a peak-to-peak amplitude of displacement equal to 2·9.8/(2^{2} = 0.496 m, so gravitational artifact can be considerable.

Gyroscopic transducers record angular velocity. Ideally, they are free of gravitational artifact, but all commercially available gyroscopes suitable for tremor analysis have some sensitivity to gravity and linear acceleration._{x}^{2}+_{y}^{2}+_{z}^{2})^{0.5}, where _{x} is the angular velocity about the x-axis and so on.

Many commercially available motion sensors have a triaxial accelerometer and triaxial gyroscope housed in a single IMU, and a magnetometer and altimeter are also commonly included. Examples of such recording systems are presented in

Sensor
Axes
Range
Mass
Resolution
Accuracy
Sampling Rate (samples/s)
Recording Duration
Kinesia One
Accelerometer
3
±5 g
8.5 grams
12 bit
±2%
64
8 hr
Gyroscope
3
±2000 deg/s
±4%
64
8 hr
ADPM Opal
Accelerometer
3
±6 g or ±2 g
22 grams
14 bit
2%
20‐128
12‐24 hr
Gyroscope
3
±2000 deg/s
2%
ActiGraph GT9X
Accelerometer
3
±16 g
14 grams
16 bit
3%
100
>24 hr
Gyroscope
3
±2000 deg/s
4%
100
Wacom Intuos tablets
2
≥10 cm
≥700 grams
0.005 mm
±0.25 mm
≥100
As long as the pen is on the tablet

±2000 deg/s for axes X and Y, and ±1500 deg/s for axis Z

Depends on sampling rate: 12 hr when data are sampled at 128/s

Depends on the size of the tablet

The suitability of a transducer depends on the characteristics of tremor (amplitude and frequency) vis-à-vis the technical specifications of the transducer. The frequency of tremor must fall within the frequency range (bandwidth) of the transducer, and the largest anticipated tremor amplitudes should fall within the reported amplitude range of the transducer. For example, suppose the largest anticipated hand tremor amplitude is 30 cm peak to peak with a frequency of 4 Hz (a very severe tremor!). A good estimate of tremor acceleration is A(2^{2}, where A is half the peak-to-peak displacement amplitude and ^{2} or 9.67 g, so if we also account for the gravitational effect, the accelerometer should have a range of at least ±11 g. Similarly, for a 4 Hz 60-degree peak-to-peak severe rotational tremor, the maximum angular velocity is

Another important consideration is the resolution of the transducer. Until recently, most motion transducers were analog devices that produced a continuous voltage that was proportional to the physical property being measured (e.g., acceleration or angular velocity). The analog signal was sampled or digitized with a separate analog-to-digital converter, interfaced with a digital computer. The resolution of the analog-to-digital (A/D) converter was some power of 2. For example, 8-bit A/D conversion sampled the analog signal at 2^{8} = 256 increments or levels, 12-bit A/D conversion at 4,096 levels, and 16-bit A/D conversion at 65,536 levels. Many transducers are now digital and either have built-in A/D converters or use pulse-width modulation to produce voltage pulses with a width that is proportional to acceleration or angular velocity. In all cases, the available increments of measurement are some power of 2 (e.g., 12 bit, 14 bit or higher). A 12-bit resolution produces output readings in 4,096 increments. Thus, if the range of the transducer is −6 g to +6 g, the resolution is 12 g/4,096 = 0.00293 g per increment or 2.87 cm/second^{2} per increment. This resolution is quite adequate for most pathologic tremors but is marginally adequate for physiologic hand (wrist) tremor, which has a mean baseline-to-peak (one-half peak-to-peak) amplitude range of 3 to 33 cm/second^{2} when the accelerometer is mounted 14 cm from the wrist (i.e., axis of rotation).^{2} or 12.3 to 135 degrees/second^{2} (2π radians = 360 degrees). Dividing these values by (2

Tremor is measured when the body part is at rest (rest tremor), is voluntarily maintaining a constant posture (postural tremor), or is voluntarily moving (kinetic tremor). There is very little movement other than tremor during rest and constant posture, and any movement other than tremor will have frequency content below that of tremor. Therefore, the rhythmic oscillation of tremor is easily discernible in an amplitude or power spectrum. However, the frequency content of other voluntary or involuntary movements (e.g., chorea, myoclonus) may approach or overlap that of kinetic tremor if these movements are fast or jerky. The resulting spectrum will be a peak superimposed on a broad base of other spectral activity (

Gyroscopes and accelerometers accentuate tremor relative to lower-frequency voluntary movement because these devices record the first and second derivatives of rotation and displacement, respectively. Recall that the first derivative of a sinusoidal oscillation is a sinusoid multiplied by (2^{2}. Thus, higher-frequency movement (i.e., tremor) is amplified relative to lower-frequency voluntary movement, as illustrated in

There are ways of mitigating the problems produced by rapid voluntary and involuntary movements. First, one can use voluntary tasks that are relatively slow, with no abrupt accelerations or decelerations. However, this approach might have little effect on other rapid involuntary movements, if they exist, and the slow voluntary movement may not be optimal for eliciting tremor. A sensor worn on the wrist during normal daily activities will record tremor and all sorts of voluntary and involuntary activity. For these recordings of spontaneous unconstrained activity, mathematical algorithms for identifying tremor must be employed, and such algorithms usually include the detection of rhythmic oscillation with spectral analysis or with some other algorithm.

The body part being studied is another important consideration. Small body parts (e.g., the finger) require small recording devices. Many sensors for continuous monitoring of tremor are worn on the wrist like a watch, and in this location, the sensor will do a poor job of capturing tremor from rotation of the wrist and finger joints. The accelerometer in a smart phone can be programmed to record tremor, but mounting the smart phone on many body segments is difficult or impossible. The same is true for transducers housed in game controllers and other large electronic devices. Awkward or insecure mounting of a motion sensor on a body part will allow extraneous motion of the sensor and distortion of the tremor recording (i.e., motion artifact). In short, the mass, dimensions, and mounting of a motion sensor must be considered to ensure a valid recording of tremor.

Writing and drawing are favorite tasks in the assessment of upper-extremity action tremor, and digitizing tablets have sufficient resolution and accuracy to quantify tremor that is visible to the unaided eye.

The x–y displacements of the pen tip are transmitted digitally to a computer at 100 Hz or more. The x- and y-displacement data are numerically differentiated with frequency impulse response or Savistky–Golay differentiating filters

Tremor is an oscillatory movement, and all methods of analyzing recordings of tremor capitalize on this property. Here, we focus on Fourier spectral analysis because it is used most commonly. However, time-domain analyses

Analog transducers produce a continuous voltage that is typically amplified, filtered, and then digitized with an A/D converter and computer. The sampling rate of the A/D converter must be at least twice the highest frequency in the transducer signal to avoid a phenomenon called aliasing, in which frequencies that are greater than half the sampling rate (i.e., Nyquist folding frequency) appear at lower “aliased” frequencies, according to the equation f_{a} = |n·f_{s} − f|, where f_{a} is the aliased frequency, f_{s} is the sampling rate, and n is the closest integer multiple of the sampling rate to the frequency f that is being aliased. For example, if the sampling rate is 100 Hz but there is noise at 60 Hz, the 60 Hz noise will appear at 40 Hz in the frequency spectrum. Aliasing can be avoided by using a sufficiently high sampling rate and by low-pass filtering the transducer signal to remove high-frequency noise. If the transducer is a digital device, then the user must make sure that the sampling rate is adequate and that the bandwidth of the transducer encompasses the frequency range of tremor and associated movement. Most portable transducers (IMUs) are now digital, but the digitizing frequency must still be at least twice the highest frequency in the transducer signal. Some activity monitors use sampling rates that are too low for tremor analysis.

The duration of the digitized recording will vary greatly with the application. Recording may be as short as a few seconds or may last hours or days. The frequency resolution of a frequency spectrum will be approximately 1/T, where T is the duration of the recording. Thus, the frequency resolution of a 2-second recording will be 0.5 Hz. If this is not adequate, longer recordings will be necessary. Longer recordings also may be necessary to obtain a representative sample of tremor, and the optimum recording duration will depend on the type of tremor and activity of the subject. Between 30 and 60 seconds is usually ample for postural tremor and for re-emergent rest tremor.

When a Fourier amplitude spectrum of a transducer recording is computed, the result is the root mean squared amplitude (0.707 peak amplitude) plotted versus time. This is appropriate when the tremor is more or less stable (statistically stationary) over time. However, many types of tremor are intermittent and are affected by a variety of external factors such as activity, stress, and medical interventions. Long-term recordings of intermittent tremor are more appropriately characterized with a time-frequency analysis that shows how the signal power and frequency change over time. The most common type of time-frequency analysis produces images called spectrograms (

Short recordings or short segments of recordings should be multiplied by a so-called data window prior to spectral analysis to reduce a phenomenon known as spectral leakage. Spectral leakage causes spectral power from an oscillation to leak into neighboring frequencies surrounding the main spectral peak. This occurs when the frequency of the oscillation is not an integer multiple of the sampling rate divided by the number of data points in the segment being analyzed. Applying an appropriate data window (e.g., the Hanning window) reduces leakage.

Broad spectral peaks can be caused by random fluctuation in tremor frequency and inadequate spectral resolution, not just leakage. Spectral resolution of 0.2 Hz (5-second data segments) or 0.1 Hz (10-second data segments) is adequate for most types of tremor analysis. With this frequency resolution, broad tremor spectral peaks are often concluded to be due to fluctuation in tremor frequency. This conclusion can be corroborated with a time-frequency spectrogram (

It is important to recognize that all tremor recordings contain random variation in amplitude and frequency. In other words, tremor recordings are random processes or time series. Therefore, power spectra must be smoothed or averaged to obtain a spectral estimate that converges to the true spectrum of the process, without spurious spectral peaks. The most common approach is to divide a recording into L segments, compute the power spectrum of each segment, and then average the L power spectra. The variance of the power estimate at each frequency is thereby reduced by a factor of L, and the spectral estimate at each frequency is a chi-square random variable with 2L degrees of freedom.^{2} is the chi-square value for n,

The frequency resolution will be L/T Hz, where T is the duration of the recording.

Instead of spectral averaging, one may also "smooth" the spectrum of the entire recording by performing a weighted running average of sequential neighboring spectral values using a so-called spectral window, which is discussed elsewhere.

It should now be apparent that these recording and analysis procedures are not rigidly defined, and the choice of instrumentation and analysis methods requires good judgment. Anatomical placement of the transducer, selection of motor task, duration of sampling, and methods of spectral analysis may vary among users. The best or optimum protocols have not been determined, and these will vary with the type of tremor being studied, the subject population, and the context. It is necessary to acknowledge this subjectivity in the design of studies and in the reporting of clinical and experimental results.

Transducers mounted appropriately have obvious face validity. However, face validity is reduced when the complexity of motion is not adequately considered. An accelerometer or gyroscope mounted on the hand will record hand tremor that is produced by a combination of wrist, elbow, and shoulder oscillations if the entire limb is permitted to move. Tremor at different joints may have different frequencies, producing multiple spectral peaks, and hand motion may be affected primarily by oscillation in proximal joints, not the wrist. Consequently, when interpreting a frequency spectrum, one cannot assume that a particular joint is involved unless motion was somehow restricted to that joint. These caveats are not an issue if the purpose is simply to measure the displacement or rotation of the hand in space, but they are an issue if wrist tremor, for example, is the specific interest.

Another consideration is that motion of one body part can be affected by motion elsewhere. For example, trunk tremor may be transmitted to the limbs and head, thereby reducing the validity of head and limb recordings. All of these limitations and caveats also pertain to clinical rating scales, to which portable transducers are frequently compared. Neither is a true gold standard. The accurate measurement of tremor generated by multiple joints can be accomplished only with multiple motion transducers or complex three-dimensional motion analysis systems,

Accelerometers, gyroscopes, and tablets have good convergent validity. However, the correlation between a transducer measure of tremor and a relevant rating scale is logarithmic, not linear.

The great precision and accuracy of transducers are mitigated by amplitude variability of tremor over time. This was learned in the pilot trial of the At Home Testing Device for quantitative assessment of Parkinson disease.

There is far more test-retest variability when tremor is measured continuously with a wearable transducer in an ambulatory setting because tremor and activity vary throughout the day. Nevertheless, continuous long-term recordings produce far more measurements of tremor, which can be averaged to reduce variability. One can also compute the times and percentage of time (occurrence) that a patient has tremor. The percentage of time with tremor is a valid measure of essential tremor and Parkinson rest tremor severity,

The SEM and MDC of transducer data are computed with log-transformed data because transducer data are generally positively skewed and non-Gaussian. MDC is expressed as a percentage of the baseline geometric mean, and MDC% = (1−10^{−MDC}) 100, where MDC is on log_{10} scale and MDC% is the percentage decrease in the geometric mean.^{MDC}) 100. Experimentally determined MDCs have been no better than a 50% reduction or 200% increase in the baseline geometric mean.

Portable transducers for assessing tremor are now readily available at reasonable cost, and there is no question that they can provide valid measures of tremor amplitude, occurrence, and frequency. Transducers provide very precise linear measures of tremor, in contrast to the subjective, imprecise, nonlinear measures produced by clinical ratings. However, transducers have noteworthy limitations that must be considered. In the clinical assessment of tremor severity, the precision of transducers is largely mitigated by the inherent test-retest variability in tremor amplitude, resulting in minimum detectable change values that are comparable to those of clinical ratings.

The desirability of transducers versus scales depends on many factors, not just precision, and in the final analysis, the demands of an application will determine whether the cost and complexity of transducer recording and analysis are justified vis-à-vis the relative simplicity of a clinical rating scale. Transducers can be used to assess tremor without an experienced rater, can be used repeatedly with little additional cost, can be used in most locations, and can be used to corroborate the results of clinical ratings. Wearable transducers are capable of long continuous recordings, and such recordings are potentially helpful in monitoring medication response and disease progression in ambulatory settings. Transducers are necessary to measure tremor frequency accurately and to study spontaneous fluctuations in tremor amplitude, which may provide insight into underlying tremor mechanisms.

The online appendix for this article is available here: