Common scales for clinical evaluation of post-stroke upper-limb motor recovery are often complemented with kinematic parameters extracted from movement trajectories. However, there is no a general consensus on which parameters to use. Moreover, the selected variables may be redundant and highly correlated or, conversely, may incompletely sample the kinematic information from the trajectories. Here we sought to identify a set of clinically useful variables for an exhaustive but yet economical kinematic characterization of upper limb movements performed by post-stroke hemiparetic subjects.
For this purpose, we pursued a top-down model-driven approach, seeking which kinematic parameters were pivotal for a computational model to generate trajectories of point-to-point planar movements similar to those made by post-stroke subjects at different levels of impairment.
The set of kinematic variables used in the model allowed for the generation of trajectories significantly similar to those of either sub-acute or chronic post-stroke patients at different time points during the therapy. Simulated trajectories also correctly reproduced many kinematic features of real movements, as assessed by an extensive set of kinematic metrics computed on both real and simulated curves. When inspected for redundancy, we found that variations in the variables used in the model were explained by three different underlying and unobserved factors related to movement efficiency, speed, and accuracy, possibly revealing different working mechanisms of recovery.
This study identified a set of measures capable of extensively characterizing the kinematics of upper limb movements performed by post-stroke subjects and of tracking changes of different motor improvement aspects throughout the rehabilitation process.
Upper limb functions are altered in about 80 % of acute stroke survivors and in about 50 % of chronic post-stroke patients . With the increasing of life expectancy, it has been estimated that stroke related impairments will be ranked to the fourth most important causes of adult disability in 2030 , prompting the need to design more effective diagnostic and rehabilitative tools [3, 4].
Together with more traditional and widely accepted clinical scales in the last two decades investigators have characterized post-stroke motor recovery also in terms of kinematic parameters extracted from hand and arm task-oriented movements [3, 5], which offer more objective measures of motor performance . Indeed, clinical scales, whose reliability has often been questioned [7, 8, 9], may not be sensitive to small and more specific changes  and could be of limited use to distinguish different aspects of motor improvement [11, 12].
Previous robot-assisted clinical and pilot studies have proposed a large set of kinematic parameters to characterize motor improvements [5, 6, 11]. A few of them focused on finding a significant relationship between robotic measures collected longitudinally in post-stroke patients and clinical outcome measures, to increase acceptance of kinematic evaluation scales in practice [5, 6]. Too little effort, however, has been made to identify the different aspects of movement improvement, how they can be described by kinematic robot-based measures , and whether they may dissociate with respect to recovery time course and to training response .
Indeed the range of potential changes in limb trajectory during recovery is not known a priori  and might not be fully represented by a set of arbitrarily selected parameters extracted from limb trajectories, even if the parameters were chosen according to a certain number of study hypotheses or to significant relationships with clinical scales. Moreover, these variables can be highly correlated and, thus, redundant. Although redundancy can be tackled by data reduction algorithms, such as Principal Component Analysis (PCA) or Independent Component Analysis (ICA) [5, 6], incomplete representation of information might still remain an overlooked issue.
In the present study we aimed at devising a novel method for identifying a set of kinematic measures potentially capable of fully highlighting and tracking changes of different aspects of movement performance throughout the rehabilitation training. Instead of starting from a certain number of a priori hypotheses, we sought to find which variables were essential for modeling trajectories of post-stroke patients and were, thus, informative of kinematic features of upper limb movements. We then tested whether the identified kinematic parameters i) were capable of highlighting changes in movement performance, ii) were to some extent redundant, and iii) were informative of different factors of post-stroke motor impairment, such as paresis, loss of fractionated movement and somatosensation, and abnormal muscle tone .