Stroke is heterogeneous, affecting sensory, motor, and cognitive functions that are required for daily activities. While there are well validated tools to assess motor and speech functions (eg. Fugl-Meyer Assessment (FMA) , the National Institute of Health Stroke Scale (NIHSS) , Chedoke-McMaster Stroke Assessment Impairment Inventory (CMSA) ) the use of high quality, validated assessment tools for measuring sensory function post-stroke (proprioception in particular) is limited , and there is still a lack of a gold standard assessment. While the FMA and NIHSS have sensory components to the assessment, they are seldom used as a sole measure of sensory impairment in research studies focused on sensation as they are based on relatively coarse scales. Yet, sensory and proprioceptive impairments have a significant negative impact on functional recovery following stroke [5, 6, 7, 8, 9]. Individuals with sensory and motor impairments, compared to those with just motor impairments, have longer lengths of hospitalization and fewer discharges home [10, 11, 12]. Furthermore, it has recently been shown that motor and proprioceptive impairments can occur independently after stroke .
Some commonly used clinical assessments of proprioception post-stroke include: 1) simple passive limb movement detection test  in which an examiner moves a subject’s limb segment with their eyes closed, and subjects are asked to say which direction the limb was moved; 2) the Revised Nottingham Sensory Assessment [15, 16] in which the subject is asked to mirror match the movement of a passively moved limb by a therapist; and 3) the Thumb Localizing Test  which involves passive movement of a subject’s arm and hand to a random position overhead, and is followed by subjects reaching to grasp their thumb with the opposite (less affected) hand. These assessments are scored crudely as normal, slightly impaired, or absent, and lack the sensitivity to detect smaller changes in proprioceptive function in part due to poor inter- and intrarater reliability [18, 19]. Therefore, establishing an objective and reproducible method to assess proprioceptive impairments post-stroke is vital to evaluating the efficacy of different treatments.
Other more advanced methods to assess proprioception have been developed [20, 21, 22, 23], with many using robotic technology to measure the kinematics of an individual’s movements. Assessment devices can now measure position sense and kinesthetic impairments after stroke using arm contralateral matching [13, 24, 25, 26], in which a subject’s affected arm is passively moved by the robot to a position, and the subject mirror-matches the movement/position with their less affected limb. Another paradigm involves passive movement of a subject’s limb to a specified position, returning the limb to the starting position, and then having subjects actively move the same arm to this remembered position [21, 26]. This method has an advantage in that it does not require interhemispheric transfer of information, but has limited value in assessing people with concurrent motor deficits, or in assessing kinematic aspects of proprioception, such movement speed and amplitude perception. Further, results can be confounded by problems with spatial working memory. Threshold for detection of passive movement paradigms have also been used to assess proprioception [27, 28]. This paradigm eliminates confounds due to motor impairment and interhemispheric transfer of information but again, little information about the kinematics of movement perception (e.g. speed or direction) are gained from this task, and it typically takes much longer to complete than position/movement matching. Lastly, Carey et al.  have developed and validated a wrist position sense test, where a subject’s wrist is moved to a position (wrist flexion or extension) and without vision of the wrist the subject has to use their other arm to move a cursor to the direction the wrist is pointing. This method minimizes confounds due to interhemispheric information transfer and motor deficits, but again does not provide information about kinesthetic impairments.
Many of these assessments are reliable, reproducible, objective, and provide quantitative measures of proprioceptive function in the upper limbs. Dukelow et al. [13, 24], used a KINARM robot (BKIN Technologies, Kingston, ON), and detailed a contralateral position-matching task for the upper extremities that can measure various aspects of an individual’s position sense including: absolute error, variability in matching positions, systematic shifts in perceived workspace, and perceived contraction or expansion of the workspace. Similarly, Semrau et al.  recently detailed a kinesthetic matching task using the KINARM robot that can measure an individual’s ability to mirror-match the speed, direction, and amplitude of a robotically moved limb [8, 25]. These tasks are reliable , and provide numerous parameters that describe an individual’s position or kinesthetic sense impairments and can be used to guide a rehabilitation program tailored to the individual. Furthermore, these studies have shown a strong relationship between proprioceptive impairments and functional independence post-stroke, yet proprioceptive impairments are often not addressed in day-to-day therapy. Reliable and quantitative assessment tools are therefore critical for testing the efficacy of rehabilitation treatments, as in clinical rehabilitation trials.
While multiple kinematic parameters can provide a level of exactness around the nature of an individual’s proprioceptive impairments and are helpful for rehabilitation planning, a summary measure is needed for clinical therapeutic trials in rehabilitation. Thus, a single continuous metric of upper limb proprioceptive function that combines all parameters from the position and kinesthetic matching robotic tasks was developed using two common measures of distance, Euclidean distance (EDist) and Mahalanobis distance (MDist) . The EDist was chosen as it is an easily interpretable calculation and considers each parameter independently. It is the square root of the sum of squared distances between data points (i.e. the straight-line distance between two points in three-dimensional space). The MDist is the next measure we used to compare with the EDist. It was chosen because the calculation accounts for correlations between parameters (by using the inverse of the variance-covariance matrix of the data set of interest), therefore preventing the overweighting of correlated parameters in the calculation. It is the distance between a point and the center of a distribution, measured along the major axes of variation (i.e. the standard deviation of an object in more than one dimension) [30, 31].. Because the kinematic parameters derived from the robotic tasks may demonstrate some degree of correlation with one another , the MDist can account for this auto-correlation. Theoretically, it should perform better at identifying stroke subjects who perform abnormally on the tasks and those who have atypical patterns of behavior relative to controls. The MDist is generally preferred over the EDist for multivariable data since it can cope with different structures of data .
MDist (or variants of it) has recently been used in other studies when examining reaching movements after stroke .. Our primary aim was to examine differences and similarities between two summary scores (EDist and MDist) in their ability to differentiate proprioceptive impairment in individuals with stroke from controls in a large patient sample. We hypothesized that using a composite proprioception score calculated from the Mahalanobis distance would more accurately identify impaired proprioception in individuals with stroke compared to a proprioception score calculated from the Euclidean distance.[…]