Reliability Test of Mobile-Embedded Accelerometers and Gyroscopes With the Goal of Measuring Postural Stability for People With Parkinson's Disease¹

Parkinson's disease (PD) is a common neurodegenerative disease that, typically, is diagnosed in older adulthood (>65 years of age) [1]. PD affects over a million people in the United States [2]. It is predicted that the number of people with PD (PwPD) will nearly double by 2030 [2].

Parkinson's disease is associated with a wide range of heterogeneous symptoms. Symptoms include nonmotor symptoms that affect a person's memory and ability to focus, plan, and follow directions (executive functioning) [3], as well as a range of motor symptoms, including difficulty initiating movements (akinesia), slowness of movement (bradykinesia), tremors, stiffness, and muscle rigidity [4]. These nonmotor and motor symptoms manifest themselves in a unique range of severity in PwPD and significantly interfere with many daily activities involving fine motor skills, such as difficulty in writing, typing, eating, drinking, and carrying out tasks of daily living. A loss of gross motor skill functioning can also lead to increased difficulty with walking (gait) and balance, which we focus on in this paper. Balance impairments are particularly challenging for PwPD. Both motor and nonmotor symptoms are present because PD disrupts a person's ability to coordinate information between the nervous system and its corresponding muscular effectors [5]. The result is that voluntary movement is inhibited in PwPD and they experience a loss of control in the precision and accuracy of their movements as well as irregular movements in response to attempting to recover their balance [6].

Problems with balance can have devastating effects on PwPD, with the most devastating effect being falls. Falls are especially dangerous for PwPD who are typically older adults [1]. Injuries, such as a broken hip, can be life-altering. Statistics show that if a person over 75 years of age breaks their hip, they have a 50% chance of dying within 6 months of their injury [7]. Quality of life (QoL) has also been shown to diminish with falls in older adults and PwPD, limiting their ability to function independently [8].

Postural stability is the ability of a person to control their bodily position in space for the purpose of balance and movement. Postural stability can be quantified with motion measures as the postural sway that occurs in a person in a medial-lateral (ML) plane and an anterior–posterior (AP) plane. This measure is important to track for PwPD because an increased measure of postural instability is correlated with an increased risk of falls [6]. Also, for PwPD who display increasing postural instability, that measure could be used to indicate worsening symptoms [9]. Meanwhile, wearable devices and smartphones have become popular and researchers started investigating using smartphone/wearable devices in measuring motions for medical-related information [10–12], including those for PwPD [13,14].

For this reason, we are developing a mobile application to empower PwPD with the ability to track their symptoms through a smartphone which, in turn, can potentially help with fall prevention for PwPD. People who present with increased postural instability would be able to track their progression and discuss it with their healthcare providers in a timely manner to proactively avoid harmful consequences. Additionally, our mobile symptom tracking application has great potential in meeting the urgent needs of the increasing number of PwPD among the aging population [1,15].

Our current research employs the use of a shaker to test the sensitivity and accuracy of sensors embedded in smartphones in measuring postural instability. We selected sample data of postural stability from a dataset that we previously collected from one healthy, male adult and used it as input signals for the shaker, simulating different conditions of a participant. These postural stability tests, such as the Romberg test, were chosen based on clinical tests for neurological diseases. The Romberg test is a proven clinical method to assess proprioception in cases of neurological diseases. It is designed to identify abnormalities in postural stability with the participant assuming certain positions with their eyes open or closed while the physician observes their ability to control their movement to balance [16]. We employed a modified version of this test in our research—the participant assumed positions with (1) eyes open while standing on both legs (“eyes open”), (2) eyes closed while standing on both legs (“eyes closed”), or (3) eyes open while standing on one leg (“one leg”). In this way, a test commonly used to assess balance will also aid in the testing of our technology for PwPD.

The input dataset was run multiple times using the shaker with two different smartphones. The time–domain signals collected were analyzed to evaluate the accuracy and precision of the measurements captured by the smartphones' embedded accelerometers and gyroscopes for predicting postural instability.

In the experiment, two smartphones were selected to conduct the measurement. We chose the smartphones based on affordability, as we thought these phones would reflect the types of phones used by a majority of PwPD. In the smartphones ranging between $150 and 200 available in the market, we chose Samsung Galaxy A31 and Motorola Mogo G Power (2021).

The reliability test of smartphone accelerometers and gyroscopes was conducted by measuring mechanical vibration that mimicked postural stability tests. The vibration stimulus was introduced by one-dimensional input signals from the shaker and two different setups (Figs. 1 and 2) introduced vibration in three-dimensional (3D), in translation and rotation dominate motions. The amplitude of vibration provided at the touch point to the smartphone was adjusted to the range of postural stability at 0.1–0.2 m/s². The equipment used included the Modal Shop SmartAmp 2100E21 and shaker amplifier.

While the shaker amplifier could be controlled by a knob, the vibration was adjusted at the input waveform and/or amplitude to the desired value. Two experimental setups that introduced vibration in 3D were designed to test the translational and rotational motions collected by the accelerometers and gyroscopes, respectively. The translational motion setup included other physical components such as a smartphone holder connected to the plate of the shaker (Fig. 1). The design was inspired by both the range of height and mobility of the shaker and the consistent efficiency required to accurately conduct the research. The phone stand was fastened to the shaker head expander with a screw and a washer, reinforced with tape. As shown in Fig. 1, while the shaker could only provide displacement in one direction, the phone stand was set at a small angle to the shaker plate; thus, the smartphone would receive vibrational motion on different axes, which can help in reliability tests and combat the common problem one may occur when collecting data from multiple axes. The mobile app was built in such a way that the smartphone is to be vertically attached to the back of the user; therefore x, y, and z-axis corresponded to the motion at Medial-Lateral (ML), Resultant Distance (RD), and AP in postural stability. During the experiment, the shaker provided excitation primarily in the AP plane, and the overall phone stand setup system also introduced movement in the ML and RD planes. Therefore, the motion patterns in 3D could be tested. Once the desired vibration amplitude was met, each smartphone was put on the stand for tests in separate trials, and the mobile app was open with a button-press to start recording measurements.

Different signal types were used during the experiment. First, a sweep signal was sent to the shaker to test the smartphone measurement ability in the targeted frequency range of 0.01–5 Hz, results shown in Fig. 3. Second, three signal samples previously recorded by a healthy male adult volunteer were used as input to the shaker, in the conditions of balancing with “eyes open,” “eyes closed,” and “one leg.” The “eyes open” and “eyes closed” signals had amplitude up to 0.12 m/s² along time. The “one leg” signal was more dynamic as shown in Fig. 4. It started with ∼ 0.2 m/s² amplitude, followed by a peak up to 0.5 m/s², then back to lower amplitude, indicating that there was a perturbation in balance that the human body corrected this perturbation. All input signals were at a 50-Hz sampling rate, each lasted 20 s and was played repeatedly by the shaker. The shaker provided primarily the AP motions by vibration in z direction, yet the setup of the smartphone holder with angles also introduced motions in RD and ML in x and y directions, respectively.

The rotational motion setup was designed to provide mainly rotational motion and allow the mobile application to measure both the acceleration by accelerometers and rotational information by gyroscopes. As shown in Fig. 2, a curved aluminum plate was attached between the smartphone and the holder. The bottom of the plate was screwed to the stand, and its top was connected to the shaker with a stinger. The shaker provided the same input linear motion to the touchpoint as in the translational motion setup. This allowed the smartphone to move with the aluminum plate and rotate around the bottom of the stand, with a major translational motion along the z-axis (AP direction) as well as rotation around the x-axis. All the input signals at the shaker were the same as the translational motion setup in Fig. 1, while the measurement was collected by both the accelerometers and gyroscopes.

The mobile app recorded 60 s in each trial with a 50 Hz sampling rate built in the app. In the results, device 1 (one smartphone) achieved a 50.05 Hz sampling rate, and device 2 (another smartphone) achieved a 52.08 Hz sampling rate. During the experiment, in order to minimize any influence caused by the finger touch on the smartphone screen to start the app and the time difference between starting the app and the shaker, we first started the app and waited for a few seconds, then started the shaker. We decided to use the first 20-s signal once the shaker started. The target signal was extracted with a rectangular window and the DC component was removed as the first step in signal processing.

The x, y, and z directions were used to describe ML, RD, and AP, respectively. Besides the direct comparison of time and frequency domain data, we also processed the data based upon the methods of Mancini et al. [17] and Prieto et al. [18]. We used their algorithm and applied to our acceleration measures and the signal processing algorithms are as followed.

where t is the time duration of the signal, in our case, 20 s.

Multitaper power spectral density estimate was used to obtain frequency information. 8 taper is used. PWR is the overall power in the frequency domain, F50 is the frequency at which 50% of power is covered below the frequency value, and F95 is where it covers 95%. CFREQ is the centroidal frequency and FREQD is frequency dispersion [18].

where $gx$ is the angular velocity (rad/s) at x-axis.

where f could be any factors mentioned above to evaluate the postural stability, subscripts 1 and 2 indicate the device number.

Here, the sweep signal was used to measure the consistency between the two smartphones. The sweep signal was administered continuously between 0.01 Hz and 5 Hz for 2 s and repeated for up to 60 s until the mobile app completed the measurement. As shown in Fig. 3, the time–domain signals overlapped with each other with small differences in the amplitude, indicating acceptable precision between the two devices. There were differences in the sensitivity of the devices depending on the frequencies, with the largest offset being observed at low frequencies ∼3 Hz.

The input signal of “one leg” was used to further evaluate the consistency of the device in the application of measuring postural stability. Figure 4 shows the input signal to the shaker and the measurement at two devices for comparison. It can be seen that a peak happened in the middle of the duration, which indicated a perturbation in balance and then balance recovery. The overall tendency of measured signals agreed with the input signal. The differences in measurement can be explained by the stand and the smartphone, both introducing more vibration to the signal measurement compared to the input signal to the shaker.

Figure 5 shows the measurements in two different devices. To test the consistency between the smartphones, results from the two different phones measuring postural stability at the same time were overlaid. As a comparison, the two smartphone measurements matched well in the time domain as shown in Fig. 5, but had slightly different frequency distribution ∼3 Hz, indicating different sensitivities along with frequencies between devices as the embedded sensor model and configuration could be different. This result also agreed with frequency distribution results in Fig. 3, when the devices were tested by sweep signal 0.01 Hz–5 Hz.

Multiple trials with each device were conducted to test the consistency of the mobile app measurement if an individual uses one particular device for multiple times. For each device and each condition, five trials were conducted. The postural stability factors introduced in the section “Signal Processing Methods” were calculated for each trial and the mean, standard deviation, and relative standard deviation in percentage are listed in Table 1, showing the consistency among different trials when using the same device. As highlighted in light gray, the difference between trials was acceptable, with relative standard deviation values varying from 0% to 61.2%, yet mostly below 10%. Some of the factors have shown better consistency than others. For example, relative standard deviation of FREDQ for trials in two devices and three conditions were 0.7%, 1.3%, 0.6%, 0.3%, 0.4%, 1.2%; JERK were 5.6%, 19.9%, 13.4%, 3.7%, 8.8%, 6.9%, respectively; and RANGE were 54.2%, 61.2%, 57.4%, 43.0%, 6.7%, 30.6%, respectively. This could be explained by the nature of factors. Factors by frequency calculation showed good consistency in general. For the factors from the time-domain information, statistical calculation, such as JERK, cumulatively evaluated the whole 20-s data. Thus, they are more reliable than those that only depend on one or several particular data point(s) along time, such as RANGE.

Differences between devices were evaluated with d_r values, highlighted in darker gray in Table 1. The d_r values are influenced by different types of postural stability factors and also vary with different devices and test conditions. JERK and PATH have shown acceptable results in time domain signal measurements, and F50 and FREQD for frequency factors. Figures 6–9 show the comparison between devices of JERK, PATH, F50, and FREQD as examples. The error bars represented the standard deviation. The measurement factors were obtained from acceleration vector a, including the motions in ML and AP planes, and calculated through algorithms introduced in the section “Signal Processing Methods.” These four measures have shown relatively lower d_r than others (Table 1), indicating better reliability, thus were recommended by our research results. It can be seen that the two devices show the same tendency on measuring multiple conditions.

The rotational motion setup shown in Fig. 2 provided both translation and rotation motions, that the translational motion captured by accelerometers and the rotational motion by gyroscopes have produced promising results.

The sweep signal was tested in the rotational motion setup shown in Fig. 2. The time and frequency domain by the accelerometer showed good consistency, as shown in Fig. 10(a). The time domain signals collected by the gyroscopes by two devices were also compared and well-matched, as shown in Fig. 10(b).

The postural stability signals were also tested in the same manner. As expected, both accelerometers and gyroscopes measurements were matched well, as shown in Fig. 11, with light offset in accelerometers at low frequency ∼ 3 Hz.

Figures 12–14 show the acceleration results during the rotational motion setup. Detailed results are shown in Table 2. Similar to the test results in translational motion setup, some measures proved to be more precise than others in replicating the input signal across the devices. Some of the factors that performed the best in the translational setup also performed strongly in the rotational motion setup. An example of this being the FREQD, which demonstrated relative differences of 0.6%, 1.1%, and 1.5% across devices for the different conditions of “eyes open,” “eyes closed,” and “one leg,” respectively.

Figure 15 shows the range of angular velocity gx, which indicates similarity between the gyroscope measurements by the two devices. The detailed results are shown in Table 3.

The measured signals from the different smartphones were able to capture the input signals with precision relative to each other. They were also able to replicate the input signals with accuracy. Differences between the two devices' signal measurements could be accounted for by the difference in embedded sensors and also the vibrations introduced by the use of the stand and smartphones themselves, which could also happen when PwPD uses the mobile app. Sensor sensitivities varied along with frequencies and have shown differences between devices at ∼ 3 Hz, but the variation did not result in major impacts on the results of postural stability factors such as JERK, PATH, F50, and FREQD.

Multiple trials with the same devices have shown good consistency. Based on our test results, some of the postural stability factors were more reliable than others when using mobile devices. Frequency factors were better than time-domain signal calculations in general, and those factors involving the whole signal information performed better than those focusing on one or several particular data points. This information helped us understand the reliability of measuring postural stability using mobile devices, and will help in selecting data processing algorithms when we improve the mobile app.

In the future, we plan to test more variety of smartphones and compare with clinical grade sensors. We also plan to conduct the test with PwPD with variation in age, gender, and different stages of PD, and develop a numerical model to match the sensor measures to the clinical scales, for a better interpretation of the participants' postural stability levels.

The research work is supported by the University of Michigan M-Cubed Fund, Undergraduate Research Opportunity Program (UROP), and Summer Undergraduate Research Experience (SURE) at the University of Michigan—Flint.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

a =

acceleration in vector

a_mag =

magnitude of acceleration, m/s²

a_x =

acceleration in x direction, m/s²

a_y =

acceleration in y direction, m/s²

a_z =

acceleration in z direction, m/s²

AREA =

total spanned by acceleration, m²/s⁴

CFREQ =

centroidal frequency, Hz

d_r =

relative difference

DIST =

distance, m/s²

FREQD =

frequency dispersion

F50 =

frequency at 50% of power covered, Hz

F95 =

frequency at 95% of power covered, Hz

$gx$ =

angular velocity at x-axis, rad/s

JERK =

jerkiness, m²/s⁵

MF =

mean frequency, Hz

MV =

mean velocity, m/s

PATH =

total path along with the acceleration, m/s²

RANGE =

range of acceleration, m/s²

RMS =

root-mean-square, m/s²

RMS_gx =

root-mean-square of angular velocity at x-axis, rad/s

t =

time of signal, seconds