Intention tremor and deficits of sensory feedback control in multiple sclerosis: a pilot study
© Heenan et al.; licensee BioMed Central. 2014
Received: 3 June 2014
Accepted: 12 December 2014
Published: 19 December 2014
Intention tremor and dysmetria are leading causes of upper extremity disability in Multiple Sclerosis (MS). The development of effective therapies to reduce tremor and dysmetria is hampered by insufficient understanding of how the distributed, multi-focal lesions associated with MS impact sensorimotor control in the brain. Here we describe a systems-level approach to characterizing sensorimotor control and use this approach to examine how sensory and motor processes are differentially impacted by MS.
Eight subjects with MS and eight age- and gender-matched healthy control subjects performed visually-guided flexion/extension tasks about the elbow to characterize a sensory feedback control model that includes three sensory feedback pathways (one for vision, another for proprioception and a third providing an internal prediction of the sensory consequences of action). The model allows us to characterize impairments in sensory feedback control that contributed to each MS subject’s tremor.
Models derived from MS subject performance differed from those obtained for control subjects in two ways. First, subjects with MS exhibited markedly increased visual feedback delays, which were uncompensated by internal adaptive mechanisms; stabilization performance in individuals with the longest delays differed most from control subject performance. Second, subjects with MS exhibited misestimates of arm dynamics in a way that was correlated with tremor power. Subject-specific models accurately predicted kinematic performance in a reach and hold task for neurologically-intact control subjects while simulated performance of MS patients had shorter movement intervals and larger endpoint errors than actual subject responses. This difference between simulated and actual performance is consistent with a strategic compensatory trade-off of movement speed for endpoint accuracy.
Our results suggest that tremor and dysmetria may be caused by limitations in the brain’s ability to adapt sensory feedback mechanisms to compensate for increases in visual information processing time, as well as by errors in compensatory adaptations of internal estimates of arm dynamics.
Accurate arm and hand movements are the key to performing many daily tasks, but in individuals with Multiple Sclerosis (MS), the processes that control these movements are disrupted due to demyelination of the axonal projections that transmit information within and between brain areas. Upper extremity motor dysfunction in MS most often manifests as kinetic tremor (uncontrolled rhythmic motion of the joints during goal-directed movements) or dysmetria (a lack of coordination of movements typified by the under- or overshoot of the intended position of the hand or arm). Up to seventy-five percent of individuals with MS experience tremor in the arms and hands, with as many as 27% of those reporting tremor-related disability [1–4]. Drug therapies [5–9] and surgical treatments [2, 10–12] can mitigate some effects of tremor, although their effectiveness decreases over time  (for review see ). Recently, rTMS has been used to reduce tremor , however, the effects are short-lived.
Because neural lesions that develop in MS are distributed throughout the central nervous system, similar movement deficits (i.e. tremor) may result from differing impairments in the sensory feedback control pathways. Consequently, the specific neuroanatomical etiology of tremor and dysmetria remain unclear. Tremor and dysmetria are most often associated with lesions in the cerebellum and/or the thalamic nuclei, suggesting impairment of the cortico-cerebellar sensorimotor control loops used for the planning and adaptive control of movement [16, 17]; for review see Koch, et al. . Recent studies also implicate impairments of the predictive mechanisms used to guide movement and/or degradation of the sensory information upon which such predictions are based, including impairment in sensory transmission of information, which is lengthened in those with MS [1, 2, 18–21]. The many-to-one mapping of the source of impairment onto clinical symptoms poses significant challenges for developing effective therapies. For example, a therapy designed to compensate for one patient’s dysmetria caused by increased sensory processing delays may not be effective for another patient whose dysmetria is due to impaired prediction of limb dynamics.
Exercise-based rehabilitation strategies can improve posture and movement control over the short-term, but they have had less success in achieving significant long-term reductions in motor incoordination generally, and tremor or ataxia specifically (for review see Brown and Kraft 2005) [22–28]. Recent studies by Feys and colleagues have demonstrated that motor performance in MS can be enhanced by exploiting the inherent adaptability of sensorimotor control mechanisms. For example, Feys, et al. (2001, 2006) have found that altering visual feedback information can reduce intention tremor and improve performance on functional tasks [22, 23]. Other studies that use robotic devices to introduce mechanical perturbations and practice correcting erroneous movements, can improve movement control, reduce tremor, and improve coordination [27–29]. However, the mechanisms by which these approaches are able to improve functional performance remains unclear.
In this study, we describe a systems-level computational model and an experimental technique that parameterizes subject-specific deficits in sensory feedback control of the elbow joint [30–33] in individuals diagnosed with MS. We used this approach to test the hypothesis that tremor in MS results from subject-specific impairments in the adaptive feedback processes that guide movement. Specifically, we fit the parameters of a dual-feedback, sensorimotor control model to the kinematic data obtained from each subject’s responses to perturbations during a series of continuous elbow flexion/extension tasks [31, 33]. We compared the parameters obtained from subjects with MS to those of age- and gender-matched, healthy control subjects to identify the sensory and/or motor processes affected by MS, and the extent to which they correlate with intention tremor. Future studies could use this approach to characterize changes in sensory feedback control induced by therapeutic intervention to advance understanding of how to best mitigate individuals’ deficits of motor function as they evolve with progression of the disease.
Sixteen subjects participated in the study. Eight subjects had clinical diagnoses of MS and exhibited mild to severe tremor (ages 25–68 years old, 6 female, 7 right-handed). Eight healthy participants served as age- (±7 yrs) and gender-matched control subjects (ages 26–61 years old, 6 female, 8 right-handed). All participants provided written, informed consent in accordance with the Declaration of Helsinki and as approved by institutional review boards at Marquette University and the Medical College of Wisconsin.
Clinical characteristics of MS subjects including disease type (RR: relapsing remitting, PP: primary progressive, SP: secondary progressive, PR: progressive relapsing), expanded disability status scale (EDSS), tremor and ataxia scores obtained during a separate clinical evaluation
Sensory feedback control model
This generic controller, which has previously been used to model movement control , contains separate derivative (Kd) proportional (Kpr) and integral (Ki) gains to allow the controller to minimize transient response errors as well as steady state errors. The output of the controller is a scalar quantity representing the intended net muscle activations, which in turn act through the musculoskeletal geometry (muscle attachment points and moment arms) to give rise to a net torque applied to the physical plant (the forearm/hand pivoting about the elbow). Note that we have simplified our model of the physical plant by discounting muscle activation/contraction dynamics, which are assumed to be dominated by the second-order passive dynamics of the arm. We do, however, account for variations in muscle fiber recruitment  by reducing the precision of the intended torque by a multiplicative motor noise (α).
This model simulates the passive mechanical properties of the forearm and hand about the elbow via separate inertia (J), viscosity (B), and stiffness (K) terms.
The sensory feedback control model also includes an internal feedback path (referred to here as a forward model), which provides predictions of movement kinematics and the sensory consequences of those actions based on efference copy of the intended motor actions and internal estimates of the sensory gains (Kv*, Kp*), system delays (Tv*, Tp*), and limb dynamics (Plant* - Eq. 4). One important effect of the forward model is to compensate for the long-latency feedback loops (>100 ms) associated with sensory processing.
Experimental tasks and analysis
f t , M t
Tremor frequency and magnitude
Power spectrum analysis
Low frequency visual perturbation
Visual response delay
Cross correlation of subject response with input
Predictive response delay
Low-frequency torque perturbation
Proprioceptive response delay
Cross correlation of subject response with input
Predictive proprioceptive response delay
Fixed levels of isometric torque
Multiplicative motor noise
Linear fit of variance vs. average torque
High-frequency visual perturbation
J, B, K
Inertia, viscosity, stiffness of arm
Bootstrapped model fit to the subject’s measured frequency response function (FRF)
J*, B*, K*
Predictive inertia, viscosity, stiffness of arm
Kv, Kp, Kv*, Kp*, Kd, Kpr, Ki
Sensory and Controller gains
Continuous, visual or torque perturbations were applied to the cursor or arm, respectively, during the 1-D target tracking tasks described below. Subjects were asked to compensate for low- or high-frequency perturbations (low-frequency: 0-1Hz, band-limited white noise; high-frequency: 0-10Hz, band-limited white noise, low-pass filtered at 1 Hz) by returning the cursor or arm back to the desired target location as quickly and accurately as possible. Subjects performed between 10 and 25 trials per task. Trial lengths varied by task and ranged from 8–32 seconds, with 15–30 seconds of rest between trials. During the rest period, the screen displayed the instruction “relax”. Two seconds before the start of the next trial, subjects were cued to “get ready”. The trial then began when the cursor and target appeared on the screen.
Target tracking tasks
2D spiral tracing task
A digitized spiral tracing task (adapted from Feys and colleagues) , was used to characterize the temporal frequency and signal power of each subject’s tremor. During the task, subjects used a digital pen to trace the line of an Archimedes spiral (center-out) overlaid on a Wacom digital tablet (12×18.2 inch drawing surface; Wacom Technology Corporation, Vancouver, WA). Throughout the task, subjects self-supported their arm against gravity and were instructed not to rest their arm or hand on the table while they traced the spiral in the transverse plane. Pen location data was collected at 200 samples/second in Matlab ver. 8.2 using the Cogent 2000 toolbox (Laboratory of Neurobiology, University College London, London, UK). The spiral was labeled with tick marks every 3 cm. To prevent the adoption of strategies that would compensate for tremor during the task, subjects were instructed to adjust their tracing speed according to a metronome such that they crossed one tick mark per beat, while keeping the movement as smooth as possible. Metronome speeds were adjusted based on the subject’s ability to maintain the target speed, and ranged from 60 bpm (3 cm/sec) to 240 bpm (12 cm/sec). Prior to the task, subjects performed five practice trials to familiarize themselves with the task and timing requirements. The first two practice trials were completed at the subjects’ self-selected speeds without the metronome. In the remaining practice trials, subjects performed the task with the metronome, starting at 60 bpm and increasing the metronome speed by an additional 40 bpm in each subsequent trial to identify a comfortable base speed. Following the practice trials, subjects completed ten “test” trials limited to 20 seconds each. During the first eight test trials, task difficulty was increased from the base speed on every second trial by incrementing the metronome speed an additional 40 bpm (2 cm/sec) until the subjects’ tracing speed fell below 90% of the metronome speed. During the last two trials, subjects were told to move as quickly as possible while accurately tracing the entire spiral.
1-D target tracking
Tasks 1 and 2
compensatory tracking with low-frequency perturbations Visual (T v , T v *) and proprioceptive (T p , T p *) delays were characterized in separate compensatory tracking tasks. Subjects performed 10 trials per task and trial duration was 20 seconds in each case. In the first task (Task 1), visual response delays (T v , T v *) were characterized by applying continuous pseudorandom visual displacements (0.05 – 1 Hz; RMS = 10° visual angle) to the cursor position while subjects applied counter movements to the manipulandum so as to maintain the cursor on a stationary target presented at the center of the display.
In the second task (Task 2), proprioceptive response delays (T p , T p *) were characterized by applying continuous pseudorandom torque perturbations (0.05 – 1 Hz; RMS = 0.3 Nm) to the manipulandum while subjects applied counter torques to keep the manipulandum aligned parallel to their sagittal plane. No visual feedback of arm position was provided during the torque perturbations so as to constrain sensory feedback to the proprioceptive path.
Subjects’ internal prediction of their visual and proprioceptive response delays (T v * , T p * ) were estimated based on the timing and duration of corrective submovements in Tasks 1 & 2 respectively. Computationally, submovements have been associated with a discretization of corrective movements that minimize movement error and energy expenditure during closed-loop sensorimotor control [42–45]. Analysis of corrective submovements can also provide an estimate of the visual response delay  along with other neurocomputational processes associated with movement planning and execution during a corrective movement.
To account for passive dynamics of the arm in the measured torque response during the second task, an additional five “control” trials (30 sec. each) were collected during which subjects were instructed not to apply corrective torques (i.e. subjects were instructed to maintain the same posture and level of stiffness as in the other tasks, but to not otherwise interfere with the task). During these trials, a high frequency torque perturbation was applied to the arm (0-30Hz, first-order zero-phase Butterworth filter with 1Hz cutoff). The contribution of the passive mechanical impedance of the arm to the measured torque was estimated from the least-squares linear regression between the measured and applied torques during the passive trials (R2 > 0.75). The contribution of the passive mechanical impedance of the arm was then subtracted from the measured torque to estimate subjects’ voluntary corrective torque during proprioceptive task trials.
Pursuit tracking of step torque Signal-dependent motor variability (“motor noise”), was assessed using an isometric task adapted from Jones et al. , which measured joint torque variability as a function of average joint torque. During the task, the manipulandum position was fixed parallel to the subject’s sagittal plane while subjects produced several isometric torque contractions. Displacement of the cursor from the center of the screen scaled in proportion to the torque applied to the manipulandum. The subject was required to place the cursor on one of five targets (desired elbow joint torques of 4, 6, 8, 10, and 12 Nm flexion) by applying the appropriate isometric contraction. Five trials were collected at each of the five torque levels (25 trials total). During each eight-second trial, visual feedback of the target and cursor was shown for the first three seconds. Visual feedback was then removed, while subjects attempted to maintain the specified torque level for remaining five seconds.
Compensatory tracking with high-frequency perturbations
A high-frequency compensatory tracking task was used to characterize the remaining elements of the sensory feedback control model including the controller gains (K d , K pr , K i ), visual and proprioceptive feedback gains (K v , K p ), and arm dynamics (J, B, K) together with their internal estimates (K v * , K p * , J * , B * , K * ), vis-à-vis the forward model. During the task, high frequency, continuous, pseudorandom displacements (0–10 Hz, RMS = 20° visual angle, first-order zero-phase Butterworth filter with 1 Hz cutoff) were applied to the cursor. Subjects were instructed to make corrective movements as quickly and accurately as possible so as to maintain the cursor on a central stationary target. Ten 32-second trials were obtained for each subject.
Pursuit tracking of step displacements A step displacement task was used to characterize the functional impact of subjects’ deficits during a reach and hold task and compare target capture movements invoked by the subjects to those predicted by the sensory feedback control model of Figure 1. Subjects performed ten trials of the task. Each 10-second trial started with the target and cursor located at the same screen position. After a one second delay, the target was randomly displaced to the left or right by a randomly selected distance ranging ±24.4 cm along the horizontal midline of the display (corresponding to ±11.5 degrees of visual angle). Subjects were instructed to center the cursor on the target as quickly and accurately as possible and to maintain the cursor position until the end of the trial.
Intention tremor frequency and power
Tremor frequency and power were quantified using each subject’s performance during the spiral drawing task. For each spiral trace, we performed a least-squared-error linear regression of the pen-tip trace angle vs. radial distance from the spiral’s center (Matlab command: polyfit) to remove the linear increase in angular position associated with the spiral. The best-fit regression was subtracted from the pen-tip data to obtain the variation in the subject’s movement about the spiral trajectory. The power spectrum of the residual pen-tip data was calculated for each trace and the best-fit (1/f) frequency spectrum was subtracted to account for low-frequency (<1 Hz) drift and to isolate the spectral power due to tremor. Tremor frequency was defined as the frequency that contained the maximum power in each trial; frequencies were averaged across trials to estimate the average tremor frequency. Tremor amplitude was defined as the maximum power in the tremor frequency range (2–6 Hz) for the trial performed at each subject’s fastest speed; this frequency range was chosen from the distribution of upper limb tremor frequencies associated with kinetic tremor .
Model parameter estimation
Sensory delays (Tasks 1 & 2
We used cross correlation analysis to estimate delays in the visual and proprioceptive feedback-driven responses to band-limited low-frequency perturbations applied in the two low-frequency compensatory tracking tasks (Tasks 1 & 2). The visual response delay, T v , was estimated as the trial-wise average of the temporal offset (lag) between the perturbations in cursor position applied in Task 1 and the subject’s corrective responses measured by the robot’s handle position. The proprioceptive response delay was obtained by correlating the subject’s voluntary corrective torque response in Task 2 with the applied torque perturbations. The proprioceptive response delay, T p , was estimated as the trial-wise average of the temporal lag between the continuous torque perturbations applied to the arm in Task 2 and the subject’s voluntary corrective responses.
We estimated each subject’s internal prediction of their visual and proprioceptive response delays (T v * , T p * ) using the average interval between successive corrective submovements measured in Tasks 1 & 2, respectively. Submovement intervals were defined as the times between zero-crossings of the elbow angular velocity. We accounted for event detection failures in each task (i.e. overestimation of submovement intervals) using a Gaussian mixture model fit to the distribution of submovement intervals across trials. In each task, the means (and variances) of the component Gaussians in the mixture model were constrained to be integer multiples of the primary (i.e. shortest) interval, thus reflecting a doubling and tripling of interval durations (and variability in their estimates). The internal estimate of the visual and proprioceptive response delays were taken as the means of the primary distributions of submovements in Tasks 1 & 2, respectively.
Signal-dependent motor noise (Task 3)
The gain of the multiplicative (signal-dependent) motor noise, α, was estimated using the torques measured during Task 3, which involved pursuit tracking of step torque targets. For each target torque level, the mean and variance in the applied torque was measured during the last five seconds of each trial (i.e. after visual feedback was removed). The gain of the multiplicative noise α was estimated as the slope of the linear regression between the mean and the variance of the trial-averaged torque as a function of target torque level.
Frequency response analysis (Task 4)
For each subject, we estimated the remaining model parameters (K d , K pr , K i , K v , K p , J, B, K), together with the internal estimates (K v * , K p * , J * , B * , K * ) using a two-stage frequency response analysis, which related the experimentally-imposed cursor and torque perturbations to compensatory changes in arm position. During the analysis, each subject’s sensory delays and motor noise parameters were held constant at values derived during the analysis of data from the first three tasks. The remaining model parameters were fit to each subject’s responses in the frequency domain using the simplex method (Matlab: fminsearch).
where N is the number of trials and M is the total number of trial-wise pairs.
characterizes the forward model prediction of arm kinematics. The closed-loop model (Eq. 3) was fit to a separate FRF formed from the ratio of trial-wise differences between the applied perturbation (D ext ) and measured arm position (θ a ) computed for all pair-wise combinations of trials (See Appendix). Visual and proprioceptive feedback gains (Kv*, Kp*) were assigned using the subject’s fitted sensory gains (Kv, Kp). Motor noise (α), visual and proprioceptive response delays were fixed at the mean values estimated from tasks 1–3.
Phase data was excluded from the model fit due to the noise in FRF phase estimates, particularly at higher (>2 Hz) frequencies where the power of both the input signal and the subject response were attenuated. For frequencies below two hertz, the model and FRF phase profiles were driven primarily by the visual delay in the system, which was more accurately estimated using the cross-correlation between the applied perturbations and the subject’s corrective response.
We performed bootstrap analysis for each stage of analysis to quantify uncertainty in our estimates of the FRF and to quantify sensitivity of parameter estimates to measurement noise and model initial conditions. For each bootstrap, 10,000 model fits were performed (with random sampling of the initial conditions for each parameter and of the FRF data points included in each fit): Initial conditions for each parameter were selected from a uniform distribution spanning one order of magnitude centered on nominal values estimated across subjects in a previous analysis ; Three hundred data points were selected randomly with replacement across the three-decade range of the FRF. Model fits that did not converge to a solution within 400 iterations due to poor initial parameter estimates (~10% of cases) were discarded from subsequent analysis. For the remaining fits, the mean and standard deviation of the fitted parameters were used to estimate the nominal best-fit value and magnitude of uncertainty in the model parameters. For the second-stage bootstrap, plant parameter triplets (J, B and K) were randomly sampled from the first-stage FRF analysis to propagate the accumulated error across sequential model fits. During the second stage fits, these triplets were held constant.
For completeness, model and FRF phases for each subject were compared post-hoc using the best-fit model parameters to the FRF magnitude. Due to the noise in FRF phase estimates at higher frequencies, phase profiles could not be reliably “unwrapped” using a one sample unwrapping procedure. Instead, a multi-sample unwrapping procedure was implemented using a linear regression of phase estimates across the preceding 20 frequency samples to generate a 95% confidence interval around the location of the next “unwrapped” phase value. The FRF phase was then unwrapped by adding or subtracting multiples of 2π until the estimate fell within the confidence interval. In cases were the phase estimate could be unwrapped to two or more locations within the confidence interval, the median was chosen. Uncertainty in the phase profile resulting from the interaction between the unwrapping procedure and the occurrence of multiple phase estimates for confidence intervals exceeding 2π were quantified using a bootstrap analysis. During the bootstrap analysis, the unwrapping procedure was applied to the FRF phase estimates 1000 times, randomly sampling the phase at each frequency containing two or more unwrapped phase estimates within the confidence interval. The 95% confidence interval associated with the unwrapped phase profile was defined at each frequency from the distribution of samples obtained from the bootstrap analysis.
Pursuit tracking of step target displacements (Task 5)
We evaluated the ability of each subject’s best-fit model to characterize sensory feedback control in a separate task that required pursuit tracking in response to step displacements (task 5). For each subject, the trial-wise measures of target acquisition time and mean squared endpoint error were calculated. Target acquisition time was calculated as the time required for the subject to move within two degrees of the target. Endpoint error was calculated as the mean-square error (MSE) from the moment of target acquisition to the end of the trial. Target acquisition time and endpoint error were then compared with those of the best fit model to determine the extent to which subject performance was constrained by limitations of sensory feedback control as identified by the model of Figure 1.
where C is a scaling factor, r is a constant, and x is tremor power.
Tremor frequency and power
Visual and proprioceptive response delays (Tasks 1 & 2)
Motor noise (Task 3)
One subject with MS (Subject 5) was unable to complete the task due to time constraints. For the remaining subjects, the scaling of elbow torque variability with mean elbow torque showed no significant differences between groups (control subjects: 0.021 ± 0.010; subjects with MS: 0.025 ± 0.011; paired samples: t(6) = 0.72, p = 0.48).
Frequency response analysis (Task 4)
Of the thirteen parameters estimated using the frequency responses analysis, significant differences between groups were observed only for the integral and derivative gains of the generic feedback controller. Subjects with MS exhibited higher integral gains than control subjects (6.86 ± 4.71 vs. 4.71 ± 2.39 Nm/deg-s; t(7) = -3.62, p < 0.01) and higher derivative gains than control subjects (8.3×10-3 ± 3.8 ×10-3 vs. 3.3 ×10-3 ± 1.8 ×10-3 Nm-s/deg; t(7) = -3.38, p < 0.05). In control subjects, the derivative gain was significantly correlated with integral gain, musculoskeletal viscosity, and musculoskeletal stiffness (r = 0.81, 0.71, and 0.75 respectively; p < 0.05). In subjects with MS, these correlations were absent; derivative gain was not correlated with actual (or predicted) musculoskeletal viscosity or stiffness and it was not correlated with tremor assessment score and tremor amplitude measured by the spiral tracing task (r < 0.50; p > 0.25). Instead, the best-fit derivative gain was significantly correlated with visual response delay in subjects with MS (r = 0.77; p = 0.024). This shift in coupling from the plant (in controls) to the visual delay (in subjects with MS) is interesting in light of the derivative gain’s traditional role in modulating the transient response of the system. This finding suggests the increased visual processing delay seen in MS may play a central role in causing subjects to alter the effective closed-loop dynamic response of the arm during goal-directed movement.
Mismatches in inertia and stiffness also varied systematically with tremor power characterized using the spiral tracing task (Figure 8B); In both cases, the relationship was well approximated by a saturating exponential function (R2 > 0.73). By contrast, no systematic relationship was observed between mismatches in viscosity and tremor power (Figure 8B).
Pursuit tracking of step target displacements
Functional impact of mismatch between actual and predictive limb dynamics
We used a multisensory model of sensory feedback control to individually characterize sources of sensorimotor dysfunction in subjects with MS performing a series of goal-directed stabilization and movement tasks about the elbow. In contrast to the initial supposition that MS might impact sensory feedback control uniquely in each subject, the results suggest that upper extremity tremor and dysmetria may result from systematic changes in sensory feedback control. Specifically, subjects with moderate to severe tremor (TAS ≥ 2) exhibited increased visual response delays relative to normal control subjects. They also exhibited systematic mismatches between predictions of arm dynamics (vis-à-vis the forward model) and actual arm dynamics which were not present in normal control subjects; the degree of mismatch in subjects with MS correlated with tremor signal power measured in our spiral tracing task. We also observed group-wise differences in the integral and derivative gains of a generic model of the neural feedback controller. Whereas the controller gain parameters covaried with the dynamic properties (i.e., apparent viscosity and stiffness) of the musculoskeletal system in normal control subjects, the derivative gain parameter in subjects with MS correlated instead with the visual delay. A comparison of actual and simulated responses to step changes in desired performance suggests that the apparent mismatch between subject predictions of arm dynamics and actual arm dynamics may actually serve to improve response times in subjects with MS, despite their long visual delays. Taken together, our results suggest that tremor and dysmetria in MS may be caused by a combination of two factors: an inability of the brain to adequately adapt to increases in the time required to process visual information related to movement and by compensatory – but maladaptative – errors in predictions of arm dynamics.
An increased visual delay such as the one observed here is consistent with reductions in the conduction speed of action potentials due to disease-induced demyelination in MS  and it agrees well with the increased time required by MS subjects to perceive visual information and perform visually-guided tasks [47–49]. Proprioceptive conduction time in the lower extremities has also been shown to increase in MS , although we did not find a corresponding increase in proprioceptive response delay for the upper extremity. This may be due to the longer path length in the spinal cord for the transmission of motor control signals to the lower extremities.
Interestingly, the increased visual response delay in subjects with MS was not accompanied by an increase in the latency of submovements (i.e. their submovement interval). Submovements have been used previously to study impairments in movement control [51, 52]. Current theories of intermittent control during goal-directed movement associate individual submovements with discretization of sensorimotor control, such that each submovement represents a complete “primitive” movement profile comprised of movement planning, movement execution and sensory feedback phases [42–45]. For the purpose of characterizing feedback control in MS, we have assumed that the combined time delays associated with these three submovement phases form the basis of the expected response delays characterized by the model (Figure 1). Correspondingly, the submovement intervals measured experimentally in response to corrective movements mediated by visual or proprioceptive motion cues (Exp. 1a and 1b respectively) reflect internal estimates of the open-loop sensory processing delays. This interpretation is supported by the consistent match in control subjects between visual and proprioceptive response delays and the measured submovement intervals (Figure 6B).
In subjects with MS, submovement interval and visual response delay differed significantly in four of the eight subjects, suggesting that they failed to adjust (or were unable to adjust) their expectations of visual processing delays to compensate for the full increase in visual processing time resulting from the disease. A previous study by Miall and Jackson has demonstrated that it is possible to adapt to increases in extrinsic feedback delays . However, the visual delays seen here in subjects with MS were markedly larger than those that Miall and Jackson used to adapt their neurologically intact subjects (<300 ms). Moreover, the delays experienced by MS subjects reflect intrinsic, rather than extrinsic sources. It is possible that intrinsic sources of delay may not engage adaptive mechanisms that respond to task-specific changes in the environment (cf. ).
Although continuous control models, such as the one used here, make simplifying assumptions that neglect the impact of intermittent feedforward control actions, continuous control models have been shown to accurately predict human performance in a variety of single joint motor tasks that minimize the predictability of environmental or target perturbations [30–33]. Additional simplifications of our model include the use of a 1-D task to characterize movement control and the use of a second-order musculoskeletal plant model. These simplifications were made because the plant model of the arm becomes much more complicated with the inclusion of additional joints or by including higher-order models of muscle activation contraction dynamics . We believe these simplifications are justified because the bandwidth limitations of the plant are dominated by the effects of the arm’s inertia and mechanical viscoelasticity rather than by low-pass filter properties of the activation/contraction dynamics - at least in quasi-isometric conditions such as the stabilization tasks studied here.
For subjects with MS, the pattern of mismatch in the limb dynamics (stiffness and inertia) co-varied with tremor assessment score and tremor power calculated from the spiral-tracing task (Figure 8). This was despite marked differences in task design; the model was characterized using single-joint compensatory tracking movements with the arm supported against gravity whereas the clinical assessments and spiral tracing required the subject to generate motion at multiple joints without arm support. Correspondence in the results of these disparate tasks is to be expected; a disease-related increase in visual processing time is expected to impact motor performance in any visuomotor task. The simulation results of Figure 10 suggest that the observed mismatch between internal estimates of plant dynamics and actual plant dynamics may actually help subjects with moderate tremor reduce steady-state movement error despite an inability to compensate for long visual delays. This form of compensation would not be unreasonable, particularly for adaptive mechanisms in the brain that seek to minimize discrepancy between the predicted and realized sensory consequences of actions (cf. ). Uncompensated increases in visual delay would yield lagged perceptions of arm position, compromising limb state estimation . Considering that a delay in the limb’s response to descending motor commands also occurs when the hand grasps an object that is heavier than expected, an uncompensated lag in the visual perception of limb motion could be misconstrued as an unexpected increase in limb inertia. Therefore, increasing the internal estimate of limb inertia (Figure 10) could, within narrow limits, partially compensate the functional impact of inaccurate predictions of sensory delay. Beyond those limits, changes in the estimated limb dynamics could lead to increased joint torque production (intended to overcome an environmental load that is not in fact present) and inappropriate compensatory responses to the perceived error. This notion is consistent with the suggestion that intention tremor in MS is due, in part, to inaccurate voluntary corrections to errors in position . From a neurological standpoint, cerebellar damage, which has been linked with tremor in previous studies ([16, 17, 56, 57]), could degrade pathways necessary for effective sensorimotor adaptations, causing inappropriate compensatory responses to become more likely, and exacerbate tremor severity.During the reach-and-hold task, subjects with MS tended to move more slowly than the control subjects. They also moved more slowly than the performance predicted by best-fit models of Figure 1. These results are consistent with a favoring of accuracy over speed in the pursuit tracking of step changes in target location and may reflect a strategic choice by subjects to minimize endpoint errors associated with delay and kinematic mismatches. This bias toward accurate (rather than fast) movements is not surprising since in many daily activities (e.g. eating, dressing) it is more important to bring the hand accurately to a desired spatial location than to do so with speed.
Our results suggest a possible reinterpretation of results of prior studies seeking to reduce tremor in MS. Tasks which force subjects to adapt to novel force fields or to perturbations [27–29] could allow subjects to “reset” maladaptive models and form a new model that is better able to compensate for long visual delays. Our results also suggest novel rehabilitative strategies for reducing intention tremor in subjects with MS. We envision at least two possibilities: one approach would require subjects to hold the handle of a rehabilitation robot while making goal directed movements within a simple virtual-reality environment. As training progresses, subjects would be required to adapt to slowly-increasing visuomotor delays while the robot would simulate mechanical loads that vary unpredictably from trial to trial, thus discouraging compensatory mal-adaptation of musculoskeletal property estimates. We speculate that providing practice in compensating for visuomotor delays while discouraging adaptation of limb dynamics will favor appropriate adaptive compensations for physiological visual processing delays, thereby mitigating tremor.
A second approach centers on the idea that the brain’s effort to minimize performance error hinders the ability to adapt to changes in the physiological visual delay. That is, we speculate the presence of a non-monotonic relationship between performance error and increases in predictive delay such that small increases in predictive delay would lead to increased errors, while large changes in expected delay could lead to optimal performance. This non-linear relationship may preclude the inherent adaptive mechanisms from matching the predictive delay to the true physiological delay. Rehabilitation under this approach would involve using the feedback control model (Figure 1) to identify and tailor the visual feedback to gradually shift the minimum performance error to the actual visual delay .
The preliminary findings presented here demonstrate that systems identification techniques provide an informative framework for investigating how neuromotor disease affects motor control and the neuromotor causes of motor disability. Specifically, we have done so by examining deficits in the neural processes underlying upper extremity motor dysfunction in a small cohort of individuals with clinical diagnoses of Multiple Sclerosis. We found evidence that tremor and dysmetria may be caused by an inability of the brain to adequately adapt to increases in the time required to process visual information related to movement as well as by compensatory mal-adaptations of internal estimates of arm dynamics. Future studies should seek to confirm the findings reported here with a larger cohort of individuals with MS. Subsequent studies could then seek effective ways to reduce intention tremor by identifying strategies that mitigate motor instability due to slowed visual processing caused by MS.
Appendix 1. Subtraction Analysis
where the first term characterizes the difference FRF of the system and second reflects the contribution due to noise. The frequency response due to noise has zero mean and variance .
where M is the number of pairwise trial combinations and the contribution of the (zero-mean) noise spectrum decreases as the inverse square root of M.
This work was supported by the National Center for Advancing Translational Sciences, National Institutes of Health, through Grant Number 8UL1TR000055, and the Clinical and Translational Science Institute through CTSA Grant UL1 RR 031973. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH. Additional funding was provided by the National Institute of Health under Grant R01 HD53727, the Alvin and Marion Birnschein Foundation, and the Department of Biomedical Engineering at Marquette University. Additional support was provided by a Johnson’s Wax Research Fellowship, and an Arthur J. Schmitt Fellowship to M.H.
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