3. Bimanual Kinematic and Kinetic Functions in Chronic Stroke
Motor impairments on one side of the upper body such as muscle weakness, spasticity, and loss of motor skills in the affected arm typically appear in patients with stroke 
. Further, the increased asymmetrical motor functions between paretic and non-paretic arms interfere with bimanual movement control capabilities (e.g., bimanual performances and coordination) required for successful execution of activities of daily living 
. For example, common post-stroke motor impairments include movement initiation and control on command as well as coordination problems during bimanual arm/hand reaching, moving objects, hand drawing, and finger tapping tasks 
. According to motor control theory, movement kinetics are the primary components involved in activating motor actions 
. As individuals post-stroke initiate or attempt to initiate arm movements, generating forces in the paretic arm are imperative. One way to facilitate this process or system is to require the non-paretic arm to initiate the same movement. Symmetrical motor performances are easier to execute than asymmetrical movements.
Kantak and colleagues suggested that estimating interlimb coordination is crucial for stroke motor rehabilitation because less cooperative upper limb movements post-stroke can increase motor reliance on the non-paretic arm compromising the efficiency of motor actions requiring both arms (e.g., opening the drawer with the non-paretic arm) 
. Thus, investigating potential motor rehabilitation protocols for improving bimanual coordination functions is useful for facilitating progress toward motor recovery.
A recent meta-analysis study summarized specific patterns of bimanual movement and coordination deficits post-stroke 
. Patients with stroke showed more interlimb kinematic and kinetic coordination impairments than age-matched healthy controls while executing asymmetrical movements with more difficult task goals such as asymmetric movement with independent goals and asymmetric parallel movements with a common goal for each hand 
. These impairments were additionally observed in symmetric movement tasks when two hands targeted a common task goal. Bimanual movement tasks consisting of more challenging task constraints typically require more interactive behavioral communications between two arms with increased motor-related cortical activation across the primary motor area and supplementary motor areas 
. Thus, unbalanced cortical activation and interhemispheric inhibition levels between hemispheres post-stroke may cause more impairments in bimanual movement and coordination with more difficult task goals 
. Interestingly, meta-regression results indicated that deficits in bimanual coordination were significantly associated with increased time since stroke onset 
. These findings indicate that despite relatively rapid recovery progress within six months post-stroke 
, bimanual movement control capabilities continue to be compromised in the chronic stage of motor recovery.
In addition to bimanual kinematic dysfunctions post-stroke, impairments in bimanual kinetic functions often appeared in patients with stroke. Kang and Cauraugh 
conducted a comprehensive literature review that demonstrated potential deficits in bimanual force control capabilities in post-stroke individuals. While processing visual feedback displaying isometric forces produced by both hands and a targeted submaximal force level, stroke groups revealed less force accuracy (e.g., root mean squared error) and variability (e.g., coefficient of variation), indicating more erroneous and inconsistent force generation patterns during bimanual wrist extension and gripping force tasks 
. Moreover, bimanual forces produced by participants post-stroke tended to be more regular (i.e., greater force regularity) as indicated by higher values of approximate entropy 
, and these patterns indicated decreased motor adaptability during force control tasks 
. Asymmetrical muscular functions between the paretic and non-paretic hands as well as impaired sensorimotor processing may be responsible for lower submaximal bimanual force control performances from 5% to 50% of maximum voluntary contraction (MVC) 
Importantly, interlimb force coordination patterns were additionally impaired after stroke onset. Lodha and colleagues reported lower values of cross-correlation strength with increased time-lag as compared with age-matched controls during bimanual isometric wrist and fingers extension tasks 
. These findings suggested that stroke may interfere with temporal coordination between paretic and non-paretic hands, and further non-paretic hands presumably modulated their forces to compensate for lacking forces generated by paretic hands during bimanual force control 
. These deficits in interlimb coordination in individuals with stroke were additionally observed in dynamical force control tasks (e.g., force increment and decrement phases) 
. Moreover, altered bimanual force coordination in patients with stroke were significantly associated with motor impairments as indicated by various clinical assessments (e.g., the Fugl–Meyer assessment and Pegboard assembly score) 
. Proposed neurophysiological mechanisms underlying impairments abound for bimanual movements and bimanual coordination 
, including altered sensorimotor integration capabilities post-stroke such as online motor correction using simultaneous visual information 
. Further, increased interhemispheric inhibition from the contralesional hemisphere typically suppresses cortical activation of the ipsilesional hemisphere, which may send biased efferent signals to the paretic and non-paretic arms, causing impaired interlimb coordination functions 
. Indeed, changes in somatosensory feedback influenced by stroke appear to be a crucial reason in weakening interlimb coordination because prior studies showed more deficits in force coordination without a visual feedback condition for chronic stroke patients 
Beyond the altered bimanual motor control functions within a trial, recent studies explored changes in bimanual coordination strategies across multiple trials for post-stroke individuals. Sainburg and colleagues proposed the importance of bimanual motor synergies reflecting different cooperative behaviors between hands across multiple trials in stroke motor rehabilitation 
. According to the uncontrolled manifold hypothesis 
, motor variability consists of two components: good and bad variability. During multiple trials of a bimanual force control task, the fundamental elements can include pairs of left and right mean forces within a trial. Good variability is the variance of fundamental elements projected on the uncontrolled manifold line that does not influence the stability of task performance (e.g., overall force accuracy across multiple trials). However, greater good variability indicates that the motor system produces more possible motor solutions (i.e., motor flexibility), whereas less good variability denotes that the motor system selects a more consistent motor solution (i.e., motor optimality). Bad variability is the variance of fundamental elements projected on the line orthogonal to the uncontrolled manifold line that does influence the stability of task performance. Increased bad variability impairs the stabilization of task performance across multiple trials. Taken together, given that the index of bimanual motor synergies is the proportion of good variability relative to bad variability, increased values of bimanual motor synergies across bimanual force control trials indicate better bimanual coordination strategies across trials contributing to overall task stabilization. In fact, Kang and Cauraugh 
examined bimanual motor synergies in chronic stroke patients during bimanual force control tasks.