$$\rightleftharpoonup{xx}$$
$$\longleftharp{xx}$$,
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Parameters of interest
There are many motion parameters that we can extract from the trajectories of biophysical digital signals generated by the person’s nervous systems. Here we focus on the electroencephalogram EEG waveforms (representative of the central nervous systems, CNS output), bodily movements (representative of the peripheral nervous systems, the PNS output), and the heart signals (representative of the autonomic nervous systems, ANS output).
For the CNS- and ANS- related signals, we use the fluctuations in peak amplitude of the EEG and ECG waveforms (µV) converted to the unitless (standardized) micro-movement spikes (MMS) (see below). For the PNS-related signals, we use the trajectories of the center of mass (COM) and their speed profiles’ time series (m/s), to derive the corresponding unitless MMS. Once we gather the MMS, we can integrate them into a weighted-undirected graph, based on a set of pairwise signal analytics across sensors and levels of nervous systems function. This step enables us to use network connectivity analyses on the combined signals. We then produce interpretable graphs14,15 depicting changes in self-emerging network topology. In particular, when we compare these graphs across the three pointing and/or walking tasks, we can observe how the biophysical signals respond to an external rhythm in a passive manner (i.e., when the metronome beats spontaneously entrain the biorhythm) and in an active manner (i.e., when the participant deliberately attempts to pace the hand pointing or the walking motions to the metronome beat). We can also study patterns of information transmission across the network nodes representing the CNS, the PNS and the ANS levels of function.
Stochastic Analyses on the MMS from multi-functional layers of biophysical signals
The biophysical signals harnessed from the wearable grid of sensors across the body, give rise to time series of peaks and valleys, which vary in amplitude and timing. The MMS of these biophysical signals16 are the fluctuations in amplitude and timing of the peaks, whereby the amplitudes are normalized to a unitless value ranging in the real [0,1] interval, thus allowing integration and comparison across signals from different functional layers of the nervous systems: CNS, PNS and ANS. These disparate layers of functionality require different levels of neuromotor control and possess different amplitude ranges across individuals. They also have different inter-peak-interval timings. While the MMS normalization conserves the timing of the original peaks, it also captures the variations in the amplitude. Such a normalization is obtained by dividing each local peak amplitude by the sum of the peak amplitude and the average of the signals sampled within the two neighboring local minima surrounding the peak:

These continuous spikes in the [0,1] real numbers interval preserve the information on the timing and amplitude fluctuations, while enabling us to treat the time series as a random process. We then adopt a Gamma process under the general rubric of Poisson random processes, commonly used in the field of computational neuroscience to analyze binary spikes.
These analytical methods have been explained elsewhere in detail3,14,17,18 and see Figure 6 for explanation of the analytical pipeline and proposed visualization to aid clinical interpretation. Here, we use the Gamma parameter plane spanned by the shape and scale parameters of the Gamma PDFs that we empirically estimate from the MMS waveforms. We also plot the points of the corresponding Gamma moments on a four-dimensional graph, whereby the mean, variance and skewness span three of the dimensions and the kurtosis is represented in the size of the marker that we use to denote the person’s stochastic signatures.
For each task, the MMS peak data derived from the biophysical time series are gathered and fitted to a Gamma PDF using maximum likelihood estimation (MLE) with 95% confidence intervals for each Gamma-parameter: the shape denoting the distribution’s shape, and the scale denoting the dispersion (noise to signal ratio). As such, we estimate with high confidence, the best continuous family of PDFs that captures the biorhythms fluctuations of the person’s nervous systems across different levels of functionality that these tasks demand. These functional layers span from high-level abstract cognitive skills and memory abilities, to voluntary neuromotor control and spontaneous consequential motions derived from the goal-directed tasks. We also examine automatic motions and the system’s capacity for physical entrainment with the metronome’s beats per minute.

Figure 6: Statistical analytical pipeline for development of dynamic digital biomarkers and applications to future application (APP) development. (A) Center of mass (COM) 3D positional trajectory while the person walks around. (B) Speed fluctuations of the COM with peaks in amplitude highlighted with a red dot. (C) Standardized MMS from the fluctuations in COM-speed peaks (red dots) in the [0,1] real-value interval. (D) Frequency histograms of the MMS peaks (red dots in MMS). (E) Probability density functions (PDF) fitting the frequency histogram evolving in time from the memory less, most random, exponential distribution (red) to some transitional skewed distribution (blue), to the Gaussian (predictive) with low dispersion (GOAL, green circle). This ideal distribution (green) appears in young athletes and sets the target for predictive, high signal-to-noise ratio cases. (F) Maximum likelihood estimation (MLE) used to fit the best PDF (with 95% confidence) to the empirical data. Resulting parameter values localize on the Gamma parameter plane the evolving stochastic signatures (Gamma process) from the COM speed fluctuations: “log shape” represents the shape of the distribution ranging from exponential to skewed to symmetric (ideal Gaussian); “log scale” is the noise-to-signal ratio (dispersion) implying the type of kinesthetic feedback the brain (most likely) gets22,23. Colors represent stochastic states as they dynamically evolve over time. (G) Probability distance (Wasserstein metric distance7) from the ideal GOAL of low noise-to-signal ratio (low dispersion) and high predictability (symmetric distribution) found in neurotypicals; away from poor feedback (random noise) found in more advanced PD, deafferented patients24,25,26,27, schizophrenia28 and autistic individuals3,18,22,29. (H) Simplified visualization to represent these stochastic states evolving in time is based on the power law relationship between the shape and scale parameters. Such visuals for future app development can provide real-time, easy to understand, clinical feedback to PWP and the healthcare team in order to improve precision in assessment and treatment planning. Please click here to view a larger version of this figure.
Results from Different Modes of Data
For the purpose of this paper, we examined three PWP and three healthy participants’ data with the demographics shown in Table 1. The three PWP were chosen from 10 PWP we recorded, to represent a case with mild PD (unified Parkinson's disease rating scale [UPDRS] score 16), a moderate case (UPDRS score 25), and a severe case (UPDRS score 44). Two healthy participants were chosen from 15 healthy individuals we recorded, as they most closely matched the PWP in age and gender; one healthy participant was chosen from the younger age group to represent an ideal healthy reference for comparison.
| Participant | Disorder | Sex | Age | UPDRSa |
| 1 | PWP | F | 64 | 44 |
| 2 | PWP | M | 65 | 25 |
| 3 | PWP | M | 64 | 16 |
| 4 | none | M | 26 | n/a |
| 5 | none | F | 65 | n/a |
| 6 | none | M | 67 | n/a |
| aMaximum score 108. | | | |
Table 1: Demographics of the participants.
In the cognitive and memory test (pen movement), the positional trajectories of the pen motions were recorded, and the linear velocity was extracted to derive the time series of the speed amplitude. Then the MMS from the fluctuations in speed amplitude were derived for each drawing task. The patients were grouped according to the Movement Disorder Society−UPDRS (MDS-UPDRS) median ranked scores, with highest PD severity indicated by the highest ranked score above the median value of the cohort. Three representative participants from each cluster that the median ranking of the scores determined are used to display the results in relation to three representative controls. One control is young (26-year-old male) representing an ideal state of neuromotor control during youth. The other two are healthy aging controls; one 65-year-old female and one 67-year-old male. Figure 7 depicts the trajectories of COM and Figure 8 depicts the corresponding Gamma processes from the MMS derived from its trajectory speed profiles.

Figure 7: Sample trajectories of the COM summarizing the trajectories of 17 body locations during the performance of select cognitive drawing tests with actual digitized traces. Sample performance during the Benson complex figure (tasks 1 and 7) and Trail making tests (tasks 2−5). (A) Benson complex figure used in this protocol. (B) Trail test with numbers and letters whereby the aim is to connect them in a prescribed order by drawing a line along an orderly path (task 4 — Trail B). (C) Sample pen traces of the Benson complex figure and COM 3D trajectory from 65-year-old female control (blue) and PWP with MDS-UPDRS score of 44 (red). Left side shows the results when the participant immediately copied the figure (task 1), and right side is when the participant recalled the figure after 10 minutes of delay (task 7). In both cases the continuous drawing along with pen lifts are captured to show variations from hesitation, etc. (D) Performance of the control vs. PWP in the Trail A (task 3) and Trail B (task 5) tasks. Notice the changes in the COM trajectories and actual drawings. Please click here to view a larger version of this figure.
Figure 8 shows the results from the best MLE fitted Gamma-PDF with 95% confidence for the healthy participants and patient participants. In each drawing task, the patients stratified apart from the controls. Further, they stratified within their group and differentiated according to the MDS-UPDRS median-ranked scores. Each patient is represented as the moments of the empirically estimated PDF on the top panels, while the bottom panels depict the PDF curves for each participant. Across panels, the reader can appreciate the family of PDFs spanned by each person across the tasks. Contrast this approach with the one-size-fits all (assumed) parametric models. Figure 8D shows the continuous drawing of the clock figure (task 6) as captured by the tip of the pen (including pen lifts).

Figure 8: Micro-movement spikes (MMS) stratify the cohorts and build interpretable personalized dynamic digital biomarkers for cognitive tasks. The moment-by-moment fluctuations (the unitless MMS) derived from the 3D trajectories of the COM during cognitive testing uniquely localize each participant along a stochastic map. The COM summarizes 17 position-trajectories across the body co-registering motions while the person performs cognitive tasks and draws on a digital tablet. (A) The Gamma moments were empirically estimated during the Trail B test (task 5) connecting letters and numbers (mean x-axis; standard deviation y-axis; skewness z-axis and kurtosis marker size) from max-likelihood estimation with 95% confidence on the top panel. Each marker represents the person’s unique location in probability space. Each point denotes a unique separable PDF shown on the bottom panel, thus stratifying the UPDRS median ranked scores of the PWP (legend). (B) The task of copying the complex Benson figure (task 1). (C) Clock drawing task (task 6). (D) the actual clock drawings captured by the digitized pen showing the continuous trace (inclusive of pen lifting). All kinematics from the pen and full body in motion are synchronously registered with EEG-EKG (not shown) to empirically derive the multi-layered (cognitive, voluntary, spontaneous, automatic, autonomic) stochastic signatures. This personalized approach (Gamma process) contrasts with the ‘one-size-fits-all-model’ that assumes a theoretical PDF, and through grand averages, smooths out as ‘noise’ important fluctuations in amplitude and timing of the waveforms. The micro-movement spikes (MMS) and Gamma process approach stratify the cohorts and build interpretable personalized digital biomarkers for cognitive tasks. Please click here to view a larger version of this figure.
Next we present results from bodily movements (voluntary pointing vs. automatic walking). The drawing motions do not require the same level of goal-directness as the task of pointing to a target (i.e., tasks 10−12). To be able to assess the levels of volitional control, we next use the task of pointing to a spatial target. As before, we use the trajectories from the COM summarizing the kinematic motions of 17 sensor positions (Figure 9). We first take the speed amplitude time series and then derived the MMS from the moment-by-moment fluctuations in amplitude. Left panel in Figure 10 shows results from the stochastic analyses during the pointing task at baseline (task 10). Middle panel in Figure 10 shows the results from the pointing task when a metronome is set at 35 bpm, without instructing the participant of its presence (task 11). Right panel in Figure 10 shows the results from the case when the participants are instructed to pace their pointing movements to the metronome’s rhythm (task 12).

Figure 9: Three-dimensional trajectories of the COM during the pointing tasks in three different contexts, regular pointing to take a baseline measurement (task 10), pointing while a metronome beats in the background at 35 bpm without alerting the participant of the presence of the metronome (task 11), and pointing in the presence of the same metronome beat but after instructing the participant to pace the motions to the metronome’s rhythm (task 12). (A) Performance of the control participant. (B) Performance of the PWP in the group with the lowest severity rating according to the median ranking of the MDS-UPDRS scores of the entire cohort. (C) PWP in the mid severity-range group. (D) PWP in the highest severity group. Note the degradation of the COM trajectory with the increase in the MDS-UPDRS scores. Please click here to view a larger version of this figure.
The results from the Gamma process are shown in Figure 10 whereby it is possible to distinguish each PWP sub-type and track the change in stochastic signatures from context to context.
The pointing task revealed the sensitivity of these analyses to contextual situations. For the same pointing task, changes in the metronome condition elicited different stochastic signatures between conditions. Particularly, we can observe the change in COM biorhythms when they spontaneously (without instructions) entrained with the metronome beat against the condition whereby the participant was instructed to deliberately pace the pointing motions to the metronome’s beat. This task demonstrated that at baseline of upper body motions, the levels of voluntary control differ across PWP according to different MSD-UPDRS scores. Specifically, the lower the score, the lower the noise to signal ratio (the scale parameter value) on the Gamma parameter plane is (Figure 10A), and the more symmetric the PDF shape value is. This orderly relation between median-ranked UPDRS scores and digital data was altered with the presence of the metronome and further differentiated between the spontaneous (uninstructed) and the deliberate (instructed) pointing conditions.

Figure 10: Dynamic digital assessment of three specific pointing tasks. Gamma process output from the MMS derived from the fluctuations in the COM speed time series differentiates within and between PWP and controls groups during the three pointing tasks (tasks 10−12). (A) The Gamma parameter plane shows the differences between PWP and controls. (B) For each pointing condition, the Gamma moments empirically estimated from the Gamma process, distinguish between PWP and controls; and within each group, the stochastic signatures stratify the participants into different points. Each task context changes the location of the point on the map. (C) The family of PDFs also distinguish each participant, each group and reveals the statistical differentiation across task contexts for goal-directed pointing. Please click here to view a larger version of this figure.
We then asked if these influences of the different conditions on the voluntary pointing behavior would extend to automatic walking motions. To that end, we performed the same protocol as above, i.e., using the metronome, while the participant walked in the room. The metronome’s beat was set in this case to 12 bpm. Figure 11 shows the COM trajectories for the controls and the PWP median-ranked by the MDS-UPDRS scores. The results from the stochastic analysis of the walking task are depicted in Figure 12.

Figure 11: Dynamic digital assessment of three specific walking tasks. Walking task to ascertain noise-to-signal ratio of the fluctuations in speed amplitude, derived from the 3D trajectories of the COM from 17 locations across the body. (A) 3D trajectories of the COM in the control participant, while the person paces back and forth during natural walking (task 13); walking in the presence of a metronome without instruction, to measure spontaneous entrainment to the metronome beats (task 14); and walking while deliberately pacing the breathing rate to the metronome’s beats, as instructed (task 15). (B) PWP with lower ranked UPDRS score. (C) PWP with higher UPDRS score degrades the 3D COM trajectory. (D) PWP with the highest ranked UPDRS score shows very perturbed COM trajectories. Please click here to view a larger version of this figure.

Figure 12: Capacity for spontaneous and instructed physical entrainment while walking. MDS-UPDRS-informed digital biomarker of walking task. (A) Stratification of PWP during natural walking in line with median-ranked scores. (B) Metronome spontaneously shifts stochastic signatures. (C) Instructed paced walking to the metronome’s beat again changes signatures. (D-F) Gamma log-log parameter plane localizes groups along different PDFs shapes and scale (noise-to-signal ratio) with noisier and more random fluctuations in PWP. (G-I) Empirically estimated PDFs represented in panels D-F above span a family that shifts with context in a manner that is unique to each person. Please click here to view a larger version of this figure.
Since all cognitive and memory tasks can be performed while the computer’s webcam records the face, it is possible to use OpenPose, an open source machine learning software that is openly available to researchers35, and extract the facial information, which can be used to infer information related to sentiment or emotional content. Often in PD the facial expressions decrease as the dopamine depletion may eventually result in low muscle tone. Here the Gamma Process can also be used to ascertain areas of the face that are most active during a given task, or to probe emotional content by ascertaining area-transitions across emotions. Figure 13 shows an example of such analyses using video from the face of a participant during tasks 16 and 17. The 70 points used to capture micro-motions of the face are placed in correspondence with the known trigeminal nerves areas V1 (29), V2 (14), V3 (27)8 (Figure 13A) to assess, for example, in this case, which area changes maximally when transitioning from a neutral face to a smile. This type of analysis can be systematically used to probe other non-motor aspects of PD, including depression and social communication in general.
To compensate for uncertain camera zoom, natural human motion, and actual face size, we normalize the face in the following way: Assuming the camera is stationary, we map each face to a “unit face” with x̄’, ȳ’ = 0 and unit variance. For each frame in the video, we normalize each point x’ = x- x̄, y’ = y- ȳ, and scale each coordinate by the variance of the overall mask for the given frame, to achieve unit variance for each mask. We then treat each point in the time series of faces as deviations from the previous mask, as we assume that the face does not plastically deform during the recording. The result is a 70-channel timeseries of position coordinates (Figure 13B). The fluctuations in speed amplitude extracted from the positional and velocity flows giving raise to these time series are converted to MMS and input to the Gamma process, thus revealing PDFs and their shifts with emotional transitions (Figure 13C). For example, transitioning from a neutral expression to a smile seems imperceptible in Figure 13B, yet the stochastic shifts reveal the zone V2 as the most sensitive, maximally changing the PDF.

Figure 13: Sentiment analyses from video data captured using OpenPose. (A) Facial areas according to the trigeminal nerve, which carries general somatic afferent fibers (GSA). These fibers innervate the skin of the face via ophthalmic (V1), maxillary (V2) and mandibular (V3) divisions used here to study the transitions across facial expressions (neutral vs. smile). (B) Using a few minutes of video captured with commercially available video cameras, it is possible to extract face information with OpenPose and render the 70 points across the face according to the V1, V2, V3 areas (color codes as in panel A). The MMS from these time series are then input to a Gamma process and the scale and shape Gamma parameters empirically estimated for each condition. (C) The analyses reveal the area V2 is in this case maximally affected by transitioning from neutral to smile, for this particular person, as the change in PDF is the largest. Please click here to view a larger version of this figure.

Figure 14: Integrating digital biophysical signals from multiple layers of the nervous systems using weighted un-directed graphs and information theoretical methods. Network connectivity of pair-wise mutual information between all EEG, motion (magnetometer), and EKG signals. (A) Representative healthy participant’s connectivity measure during the three walking tasks - task 13 control (left), task 14 spontaneous metronome placement (middle), and task 15 instructed paced breathing (right). Each node represents a single sensor’s signal; the color of the line represents the level of MI, where brighter color indicates higher connectivity; the node color represents the average MI of that sensor’s signal with all other sensors. The color scale is set to be the same across all tasks and all participants and is arbitrarily set to have the brightest color for the maximum MI value across all tasks and participants, and to have the darkest color for the minimum MI value across all tasks and participants. The healthy participant’s connectivity shows the strongest connection across the brain and body nodes. (B) PWP with UPDRS 16 connectivity measure, with the same schematic layout as in panel A, shows less density in its connectivity than the healthy participant’s network. (C) PWP with UPDRS 44 connectivity measure, with the same schematic layout as in panel A, shows the sparsest connectivity pattern across the brain and body. Please click here to view a larger version of this figure.
We next ascertain the amount of information transmitted by these biorhythms. To that end, we use the information theoretical approach developed by Shannon19, using mutual information (MI) between each pair of sensors’ signals (i.e., EEG sensor, motion sensor, ECG sensor). To that end, we obtained the MMS amplitudes from each waveform type.
MI between two sensors assesses the level of uncertainty reduced in one sensor’s signal by introducing the information of the other sensor’s signal; when MI is high, this implies that the two signals are highly connected, and when it is low, this implies that the two signals are mostly independent. Specifically, MI is computed as:

where
is the normalized histogram value of the distribution of values for signal X, and
is the normalized histogram value of the joint distribution of values for signal X and Y. The sampling bins were set to increment in 0.05, ranging from 0.5 to the maximum amplitude value. Details on the derivation of this formula can be found in many literature on information theory with application on clinical analyses20,21.
Overall, the healthy participant exhibited a more connected network during the three walking tasks, while the patient participants had a sparser connection, as shown in Figure 13. Not only information transmission across the network, whereby mutual information was derived from self-sensed biorhythms, is much lower in PWP; more importantly, there are fundamental differences in patterns of MI transmission between conditions, that vary from patient to patient. Here we can further utilize connectivity metrics from network analyses to summarize topological features of these evolving networks and as such, provide additional indexes of physical entrainment capacity, reflecting as well the communication levels between brain, body and heart when physical entrainment related to the metronome occurs vs. when it does not.