^{1}

^{2}

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: