Upper extremity kinematics: development of a quantitative measure of impairment severity and dissimilarity after stroke

Inclusion and exclusion criteria

All participants were recruited from the MedStar National Rehabilitation Hospital stroke patient population. Patients’ stroke diagnoses were confirmed via magnetic resonance imaging (MRI). This protocol was approved by the Medstar Rehabilitation Research Institutional Review Board under protocol number (947339-3).

Persons with stroke that were (1) at least eighteen years of age, (2) able to complete a reach-to-target task, (3) able to consent to the study and comprehend instructions, and (4) six or more months post thromboembolic non-hemorrhagic hemispheric or hemorrhagic hemispheric strokes were recruited for this study.

Potential subjects were excluded if (1) they were less than 18 years of age, (2) stroke occurred less than 6 months before participation or affected both hemispheres, (3) stroke involved the cerebellum, brainstem, or did not spare primary motor and dorsal premotor cortices, (4) there was a history of craniotomy, neurological disorders (other than stroke), cardiovascular disease, or active cancer or renal disease, (5) there was a history of orthopedic injury or disorder affecting shoulder or elbow function, or (6) they had had a seizure or taken anti-seizure medication in the past 2 years.

Subjects underwent examinations by clinicians prior to study recruitment (Folstein, Folstein & McHugh, 1975) to ensure ability to consent to all sections of the study and complete tasks as instructed. As this study features a functional reaching task for the upper extremity only, assessment of recovery was limited to the upper extremity motor function section of the Fugl-Meyer Assessment. The upper extremity Fugl-Meyer (UEFM) test was used as a criterion for classifying post-stroke impairment as either mild or severe upper limb impairment. Classifications for impairment severity have been proposed in prior literature based on a range of motor function scores (Fugl-Meyer et al., 1975; Duncan et al., 1994). The motor function domain is divided into the following: upper extremity (scored out of 36), hand (scored out of 10), wrist (scored out of 14), and coordination/speed (scored out of six) for a total of 66 indicating full performance of expected motor function for the upper limb (Fugl-Meyer et al., 1975).

Participants

Complete demographics for participants with mild and severe impairments after stroke are detailed in Tables 1 and 2. Subjects that retained partial arm function and voluntary hand function, defined by an ability to grasp and release, were classified into the mild impairment group (UEFM score: 38–66, n = 15). Subjects that (1) could not complete the hand (10) and wrist (14) sections, (2) could not display at least one finger response to upper extremity reflex tests (/4), and (3) demonstrated an inability to actively extend the paretic wrist and fingers at least 20 degrees past neutral, were classified in the severe impairment group (UEFM score: 0–37, n = 14).

A two-sample t-test with equal variance and a one-tailed distribution was performed to evaluate differences between the mild and severe impairment groups. The mean age (Mild: $61.8\pm 9.8$, Severe $62.14\pm 9.3$ years) yielded a p-value of 0.46, suggesting an absence of statistically significant differences in age between the groups. Similarly, the mean time since stroke (Mild: $39\pm 31$, Severe: $62\pm 104.2$ months) yielded a p-value of 0.21, indicating no statistically significant differences. The assessment of the more affected or paretic limb between the groups (Mild: seven right arms, eight left, Severe: six right, eight left) and whether the paretic limb is also the dominant arm (Mild: nine yes, six no, Severe: four yes, 10 no) resulted in p-values of 0.42 and 0.09, respectively, suggesting no significant distinctions between the groups in these aspects.

However, distinctions emerged in metrics assessing functional outcomes. Notably, the maximum reaching ability (Mild: $35.58\pm 8.9$, Severe: $16.86\pm 12.0$ cm) yielded a significant p-value of $2.76E-05$, and the upper extremity Fugl-Meyer (UEFM) scores demonstrated marked disparity (Mild: $52.40\pm 8.5$, Severe: $16.21\pm 7.1$), accompanied by a significant p-value of $5.88E-13$. These statistical analyses collectively suggest that the two sample groups are not significantly differentiated in the metrics of age, time since stroke, and arm dominance. Metrics describing functional outcomes, however, such as maximum reaching ability and UEFM scores, are statistically significant indicators of distinction between the two sample groups.

Experimental setup

Prior to the first data collection session, subjects were familiarized with the reaching task, and measurements of the chair height and distance of the chair from the table were recorded. These measurements were adjusted to ensure the subject sat as close to the table as was comfortable and maintained a 90-degree resting angle at the elbow. The subject was fitted with trunk restraints to reduce appreciable trunk involvement in the forward-reaching movement (Harrington et al., 2020).

A single InfraRed Emitting Diode (IRED) optical marker was placed at the dorsal surface of each hand as appropriate given each subject’s movement capability and resting hand position. A single target sensor was placed at 80% of the maximum reach of each individual subject. Placing the target within arm’s reach rather than at maximum reach capacity ensured the subject would experience typical and moderate shoulder and elbow contribution and minimize uncomfortable or compensatory movements (Ma et al., 2017). The relative positions of the subject, two IRED markers, and the reaching workspace are depicted in Fig. 1.

Hand path kinematics were recorded using the Optotrak Certus motion capture system (Northern Digital Inc., Waterloo, Ontario, Canada) at a sampling frequency of 300 Hz, and the origin was calibrated at the front edge and center of the table at the beginning of each set of ten reaches. Optical tracking of upper extremity movement allows the collection of limb trajectory in terms of 3D Cartesian coordinates. Optotrak software was used to digitize the x-y plane in front of the subject and all movements were recorded with six degrees of freedom Optotrak cameras mounted surrounding and above the work-space.

Each subject completed a passive ideal hand path test in which the hand was passively moved to the target and back to represent movement without muscle activity. This measurement was used to verify and troubleshoot the collection of all positional data between the starting position and the target. Each subject completed two sets of the simple reaching test on two separate days with both the paretic and nonparetic arms. The forward-reaching task was initiated after a “Go” signal was indicated either in text on a screen or a light box placed within sight of the subject. Subjects were prompted with “When the ‘Go’ signal appears, quickly reach out to touch the target” to encourage rapid forward movement. Each testing session consisted of ten “Go” signals delivered at random intervals to ensure subjects did not anticipate movement initiation.

Kinematic analysis

The discrete kinematic metrics of interest for this study are (1) peak velocity and time to peak velocity and (2) target accuracy. The continuous metrics of interest for this study are (1) endpoint orientation and (2) curve shape. The variables were chosen to represent movement strategy and performance, as they are often reported as related to the outcomes of therapy. The temporal location of the discrete kinematic landmarks during reach duration was used to characterize curve shapes highlighted by the Procrustes Analysis. The captured position data were transferred to MATLAB (The MathWorks Inc, Natick, MA, USA) software for analysis with custom-written scripts.

For the purposes of representing online movement refinement, we utilized the recommended method of a fixed local coordinate system with respect to the work-space (Bai et al., 2014; Valevicius et al., 2018; Wu et al., 2005). The y-axis extends directly forward and represents the primary distance covered during a reaching task. The x-axis extends laterally from the subject and the z-axis extends inferior to superior relative to the subject (Fig. 2).

The rotations of the distal coordinate system are described in terms of the proximal coordinate system. The first rotation was described as around the z-axis, the second was described around the x-axis, and the third was described around the y-axis, the longitudinal axis of the moving coordinate system. The rotation matrix in Fig. 2 describes the yaw-pitch-roll sequence of rotations; this was computed using consecutive data points for each incremental change in mean position during the forward reach. $\psi$ represents the yaw angle, $\theta$ represents the pitch angle, and $\varphi$ represents the roll angle (Sturm, Kerl & Cremers, 2015). The definitions of these angles as well as other kinematic metrics of interest are listed in Table 3.

Table 3:

Kinematic metrics of hand movement included in data analysis.

Variables	Definition used for measurements
Reach duration	Time between a non-zero positive velocity followed by displacement in the positive y-direction, and a local displacement maxima which is immediately followed by a non-zero negative velocity.
	Normalized to 0–100% reach completion
Maximum reach	Farthest forward displacement achieved independently by subject when prompted to reach as far as they can while wearing trunk restraints
Mean velocity	The mean value during forward reach; derived from the mean velocity profile of all trials for an individual subject
Peak velocity	Maximum positive velocity achieved during reach duration and corresponding to the change from acceleration to deceleration
Time of peak velocity	Percentage of total reach duration where maximum peak velocity and change from acceleration to deceleration occurs
Yaw angle	$\psi$-Extrapolated by creating a rotation matrix A from position data every two consecutive time points, signifies the first rotation around the z-axis
Pitch angle	$\theta$-Extrapolated from rotation matrix A, rotation around the x-axis,
Roll angle	$\varphi$-Extrapolated from rotation matrix A, represents the last rotation around the y-axis, i.e., the longitudinal axis of the movement arm
Target error	Accuracy of the end displacement during individual reaches compared to a target placed at 80% max reach capacity

DOI: 10.7717/peerj.16374/table-3

Velocity was extrapolated from the raw mean position data using the forward/backward/central differences in position data. Missing marker data were found for less than 10% of individual trials; missing data were corrected by extrapolating from adjacent position values. A low-pass fourth-order Butterworth filter with a cutoff frequency of 5 Hz was applied to the velocity data to reduce noise and distortion. The values of mean velocity, peak velocity, and the time-point where peak velocity was achieved were recorded for all subject data.

Finally, each trial of forward reaching was compared to the actual location of the target as recorded for each subject. The error tolerance was adjusted to account for reaches landing within the four squared inches of surface area of the target pad. Positive values of target error indicate when a subject stopped movement (identified by local maxima in displacement and subsequent movement in the negative y direction) before or at the target sensor. Negative values of target error represent when the subject has overshot or moved past the target.

Modified procrustes analysis

Four reference curves were created from reach-to-target movements performed by two able-bodied volunteers. Able-bodied persons were recruited from the MedStar Rehabilitation Hospital volunteer population. Volunteers were asked to verify they had no diagnosis of a neurological or musculoskeletal disorder that could potentially influence movement control or reaching. In order to reduce the effects of hand dominance on the reference curves, one right-hand dominant and one left-hand dominant volunteer were selected. Three-dimensional position data was collected from both right and left limbs first at a steady pace and then a rapid pace. The reference data set was used to create a mean healthy movement stereotype against which to analyze movements in the mild and severe impairment groups. The reference curves were compared against prior research to ensure curves were an appropriate representation of able-bodied movement. The values of the mean velocity, peak velocity, and time to peak velocity of our reference curves and values from other studies are compiled in Table 4. Reference curves were used only for the Procrustes trajectory analysis; each subject’s velocity, target accuracy, and orientation variability were compared between the individual’s paretic and non-paretic limbs.

Individual trials of reach-to target movements were extrapolated from raw kinematic data. The beginning of a movement was defined by displacement from the starting position and a non-zero positive velocity. The completion of a movement was defined by a local maxima in position immediately followed by a non-zero negative velocity. Reach detection was confirmed by visual inspection of each trial. Two sets of consecutive reaches were averaged to create a composite curve for each individual consisting of 20 trials. The reaching trajectory data was filtered by applying a low-pass fourth-order Butterworth filter with a cut-off frequency of 50 Hz to the trajectory data to account for minor variations in individual movement.

The reference trajectories were down-sampled to create ten fractions of the overall movement that were the same length as fractions of trajectories with motor impairments, in order to produce a dissimilarity profile of the overall reaching movement. Next, curve fragments composed of 35 time points across the reference and subject curves were compared. This required a novel modified Procrustes analysis that advanced point for point along the length of the subject and reference curves to identify segments that were congruent between both. In this particular application, the curves were not scaled, since the capacity to reach is specific to each subject. The index of dissimilarity, the sum of the squared Procrustes distance between each corresponding element in both curves, represents how incongruous the two segments may be, and was scaled to produce a value between 0 to 1, where 0 represents congruence between curves and 1 represents complete dissimilarity.

Kinematic findings

Figure 3 shows three example velocity profiles of subjects in the mild impairment group, and three example velocity profiles of subjects in the severe impairment group. Each black line indicates the averaged velocity profile across all reaching trials for a given subject, with standard deviation indicated by the blue shaded areas. The time when peak velocity is achieved is depicted in all profiles with a vertical red line.

In each mild impairment example shown, the peak velocity occurs towards the middle of the overall reach movement. For some subjects with severe impairment, the mean peak velocities were lower in magnitude (Mild: 0.97 $\pm$ 0.40 m/s, Severe: 0.76 $\pm$ 1.42 m/s) and occurred either closer to movement initiation or towards movement completion (Mild: 61.08% $\pm$ 17.08, Severe: 49.55% $\pm$ 41.51). The Anderson-Darling test for normalcy indicated for the scalar metrics of peak velocity (Mild: $p=0.25$, Severe: $p=0.73$) and velocity time location (Mild: $p=0.30$, Severe: $p=0.16$) that the hypothesis for normality was not rejected. The scalar metric of mean velocity (Mild: $p=0.20$, Severe: $p=0.95$) also showed evidence of normality.

Figures 4 and 5 show three example orientation profiles of subjects in the mild impairment group, and three example orientation profiles of subjects in the severe impairment group. Red curves indicate the averaged reach path of each subject, contrasted with blue curves illustrating reference data sets. The three sub-graphs next to each subject’s movement paths indicate the average yaw angle, average pitch angle, and average roll angle as calculated by rotation matrices during the movement. Subjects in the severe impairment group tended toward greater angular variability in the hand’s orientation in the roll angle or about the y-axis as movement is completed (Mild peak roll angle: 111.22 $\pm$ 25.44, Severe: 86.34 $\pm$ 28.82). The reference reach curve shows some variability in orientation occurring about all three axes during movement initiation.

Finally, in order to assess subject accuracy, mean target error was calculated for each subject relative to the area of the target pad. All mean target percentage error values are included in Tables A1 and A2. While both groups tended to undershoot the target rather than going beyond, the severe group had a larger mean target error (Mild: 9% $\pm$ 6, Severe: 43% $\pm$ 97) compared to the mild impairment group. The Anderson-Darling test indicated the hypothesis for normality was not rejected for the data collected on target error (Mild: $p=0.69$ Severe: $p=0.36$) was normally distributed.

Results of statistical analyses of kinematic metrics related to movement speed, range of motion and accuracy are summarized in Table 5. One-way ANOVA were performed to identify kinematic metrics that differed significantly between impairment groups.

The difference between the two groups’ time to peak velocity, as shown by the red vertical lines in Fig. 3, was not statistically significant, indicated by a p-value of 0.59. In contrast, the difference between the mean velocity of the impairment groups (Mild: 0.42 m/s, Severe: 0.30 m/s) was found to be significant with a p-value of 0.017. The peak roll angles, shown in the last sub-graph in each subject exemplar in Figs. 4 and 5, showed a statistically significant difference between the groups, with a p-value of 0.020. One-way ANOVA indicated a significant effect of group on the target error percentage by which subjects undershoot the target placed at 80% maximum reach capacity, with a p-value of 0.021.

In summary, the mild and severe groups differ significantly in the mean velocities, peak roll angle achieved during movement, and target error metrics. The kinematic findings of peak velocity and the time location during the movement when peak velocity is achieved were not found to be statistically significantly different between the two impairment groups.

Modified procrustes analysis findings

A traditional Procrustes analysis was conducted to produce an overall dissimilarity index of each subject’s mean reach path against reference data. When the complete subject reach path was compared to the complete reference reach path with a one-way ANOVA, there was no significant effect of severity on curve dissimilarity between the mild and severe groups (Mild dissimilarity index: 0.25, Severe: 0.20, $p=0.62$).

Dissimilarity indices were calculated across ten equally sized segments of each subject’s mean reach curve and compared with both the steady-paced and rapid-paced reference curves. The results are visualized as heatmaps of the median dissimilarity indices in each impairment group, shown in Fig. 6. Inspection of these heatmaps indicated higher dissimilarity indices as the movement ends in both mild and severe groups. Neither group appeared to be as dissimilar to the steady and rapid reference curves during the initiation and middle of overall movement.

When the groups were compared to the steady-paced reference, there was greater dissimilarity in the last three segments of movement (Mild median ending dissimilarity indices: (0.16, 0.6, 0.22), Severe: (0.18, 0.45, 0.2)). The rapid reference curve, which resulted from reference subjects being given the same prompt as the stroke subjects (i.e., to move as quickly as they can), also resulted in greater dissimilarities (Mild median ending dissimilarity indices: (0.19, 0.46, 0.37), Severe: (0.15, 0.44, 0.55)) in the last three segments of movement.

The Procrustes method was then modified to compare segments, defined as 35 consecutive time-points, by advancing along the mean individual and reference reach curve point for point. In all cases of mild impairment, three of which are depicted in Fig. 7, the initial subject kinematic behavior appears most congruous to the initial control kinematic behavior. This is indicated by black lines connected each matched data pair between the red subject curves and the blue reference curves. These black lines are evident during movement initiation. Three subjects from the severe impairment groups are depicted in Fig. 8. These curves were not consistent in the location of the lowest dissimilarity indices, nor the time-duration during which movement progressed similarly to the steady and rapid reference curves.

Table 6 details the one-way analysis of variance in the rotation, scaling, and translation transformation variables found through the modified Procrustes analysis of the most congruent subject and reference segments. The mean scaling factors when compared to the smooth reference curve (Mild: 3.62, Severe: 2.49), and rapid reference curve (Mild: 2.04, Severe: 1.27) all indicate that the impairment groups demonstrated stretched movement, i.e., the subjects took longer amounts of time than the reference to complete the specific segment of movement.

Table 7 shows the results of a two-way ANOVA, performed to analyze the influence of severity on the congruence of the subject curves to the steady and rapid reference curves. The only quantities found to differ significantly between impairment groups were location of the congruent subject segment ( $p=0$) and the steady reference segment to which it coordinated ( $p=0.01$).

Table 8 shows the results of a two-way ANOVA, performed to analyze the influence of severity and arm dominance on the presence of congruent segments in the subject curves. In the case of the steady curve, severity was found to influence significant differences ( $p=0.05$), as with arm dominance ( $p=0.011$), on whether segment congruence was found. In the case of the rapid reference curve, severity and arm dominance did not contribute to significant differences between the impairment groups.

Table 9 shows a two-way ANOVA, performed to analyze the influence of severity and dominance on the time-length of subject segments that appeared most congruent to reference curves. The impairment severity classification of the subject had a significant main effect on the length of congruence of the subject segment, p-value of 0.034. Where there were no significance of the other main effects, the two-way interaction of severity and arm dominance had a p-value of 0.036.

In summary, when analyzed against the rapid reference curve, the subject groups differed significantly in scaling coefficients, and the location within the overall movement of congruent sub-movements between subject and reference curves. As seen in Table 7, impairment groups differ significantly in the subject movement that most replicates a phase of movement in the steady and rapid reference curves. The effects of severity on the ability to consistently perform steady reaching movements were significantly mediated by arm dominance, seen in Table 8. As indicated in Table 9, the population marginal means of the subjects with mild impairment with a paretic non-dominant limb, and severe impairment with a paretic non-dominant limb are significantly different.

The population marginal means for both groups of impairment where the paretic limb is also the dominant limb did not have any significant differences. Other metrics derived from the traditional and modified Procrustes analysis that did not indicate significant difference between impairment groups included whole curve dissimilarity, rotation/reflection matrices, and translation coefficients.

Preliminary severity and dissimilarity scores

Metrics related to kinematics and the modified Procrustes analysis that showed significant differences between the mild and severe populations were used to compute RSDI-severity and RSDI-dissimilarity sub-scores. The severity sub-score comprised of velocity, orientation, and accuracy elements while the dissimilarity sub-score comprised of dissimilarity indices of the ending movements, and the location and length of the reference segment that was found to be most congruous. The scaling components were also included in the computation of the dissimilarity sub-score.

The preliminary RSDI sub-scores computed using these metrics were classified in terms of likely rehabilitation goals. Subjects with a higher severity indices and lower dissimilarity indices due to low mean velocities, low peak angular values, and high target error, may benefit from a classification that prioritizes speed-focused goals. Such subjects were given a Speed Emphasis classification. Alternatively, subjects with lower severity indices and higher dissimilarity indices were scored as such due to high dissimilarity to the reference movement, or elongated movement behaviors, implying a need for Strength Emphasis to produce stable movements. Subjects with comparable severity and dissimilarity indices were classified as Combined Emphasis. These classifications compared with the UEFM mild and severe classifications are cross tabulated in Table 10.

The first row in Table 10 shows that of the 15 subjects classified in the mild impairment group according to the UEFM test, 10 received a Strength Emphasis and five received a Combined Emphasis. This is consistent with the clinical observation that persons with mild impairment continue to be able to reach forward quickly while compensating for muscle weakness and loss of agility. The second row indicates that of the 14 subjects classified in the severe impairment group by the UEFM test, five can be reclassified as Speed Emphasis, seven as Strength Emphasis, and two as Combined Emphasis.