Yoram Baram

Virtual reality cues for improvement of gait in patients with multiple sclerosis.

Objective: To study the effects of visual cues, provided through a portable visual-feedback virtual reality (VR) apparatus, on the walking abilities of patients with multiple sclerosis (MS). Methods: On-line (display-on) and residual short-term therapeutic effects on walking speed and stride length were measured in 16 randomly selected patients with gait disturbances predominantly due to cerebellar ataxia. Results: Patients whose baseline walking speed (BWS) was below the median showed an average on-line improvement of 13.46% in their walking speed, while patients whose BWS was above the median improved their speed by 1.47%. The average short-term residual therapeutic improvement in walking speed was 24.49% in patients with BWS below the median, and 9.09% in patients with BWS above the median. Similar results were obtained for improvements in stride length. These results of improved functions in patients are particularly noteworthy when compared with the lack of change in healthy control subjects. Conclusions: Patients with multiple sclerosis showed improvement in walking abilities using virtual reality visual-feedback cues.

Consistent estimation on finite parameter sets with application to linear systems identification

The consistency of maximum likelihood and related Bayesian estimates for a general class of observation sequences is treated, following a result by P. E. Caines. The condition for consistency is then interpreted in terms of the statistics associated with linear systems driven by white Gaussian inputs, to establish a verifiable condition for the identifiability of such systems on finite sets of mathematical representations.

Auditory feedback control for improvement of gait in patients with Multiple Sclerosis

OBJECTIVE To study the use of auditory feedback for gait management and rehabilitation in patients with Multiple Sclerosis (MS). METHODS An auditory feedback cue, responding to the patients own steps in closed-loop, was produced by a wearable motion sensor and delivered to the patient through ear phones. On-line (device on) and residual short-term therapeutic effects on walking speed and stride length were measured in fourteen randomly selected patients with gait disturbances predominantly due to cerebellar ataxia. RESULTS Patients showed an average improvement of 12.84% on-line and 18.75% residually in walking speed. Average improvement in stride length was 8.30% on-line and 9.93% residually. The improvement results are particularly noteworthy when compared with the lack of change in healthy control subjects. CONCLUSIONS Patients with MS using auditory feedback cues showed improvement in walking abilities.

Estimability and regulability of linear systems

A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feed-back is used. These properties, which are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.

Realization and reduction of Markovian models from nonstationary data

The realization of Markovian models for nonstationary processes generated by time invariant linear systems is considered. A model is obtained by constructing an orthogonal finite-step predictor for the process. Optimal model approximation by order reduction is naturally defined in this framework. The construction and reduction of Markovian models from multiple data records and the numerical considerations involved are illustrated by examples.

Walking on Virtual Tiles

This paper examines the application of virtual reality cues, generating the biofeedback effects of a real tiled floor, reported in [8], for gait improvement in Parkinsons Disease (PD) patients. A portable apparatus, comprising head and body-mounted 3-axis accelerometers, a wearable computer and see-through head-mounted display, creates a virtual tiled floor, responding to the patients own dynamics. Performance of PD patients using the device improved (higher speed, longer stride) by about 30% on average.

Learning by Kernel Polarization

Kernels are key components of pattern recognition mechanisms. We propose a universal kernel optimality criterion, which is independent of the classifier to be used. Defining data polarization as a process by which points of different classes are driven to geometrically opposite locations in a confined domain, we propose selecting the kernel parameter values that polarize the data in the associated feature space. Conversely, the kernel is said to be polarized by the data. Kernel polarization gives rise to an unconstrained optimization problem. We show that complete kernel polarization yields consistent classification by kernel-sum classifiers. Tested on real-life data, polarized kernels demonstrate a clear advantage over the Euclidean distance in proximity classifiers. Embedded in a support vectors classifier, kernel polarization is found to yield about the same performance as exhaustive parameter search.

Gait Improvement in Patients with Cerebral Palsy by Visual and Auditory Feedback

Visual and auditory feedback cues have been shown to improve gait and balance in patients with movement disorders, such as Parkinsons disease and multiple sclerosis. Subsequently, closed-loop virtual reality was used to enhance the gait improvement effect of such cues. Objectives: To study the effects of gait training with visual and auditory feedback cues on the walking abilities of patients with gait disorders due to cerebral palsy. Methods: Visual and auditory feedback cues were generated by a wearable accelerometry-driven device. Ten randomly selected patients with gait disorders due to cerebral palsy trained with visual feedback cues while ten such patients trained with auditory feedback cues. Baseline performance (walking speed and stride length along a 10m straight track) was measured before device use. Following 20min training with the device, performance without the device was measured again and compared to the baseline performance. Results: For patients training with visual feedback, the average improvement in walking speed was 21.70%+/−36.06% and in stride length 8.72%±9.47%. For patients training with auditory feedback, average improvement in walking speed was 25.43%±28.65% and in stride length 13.58%±13.10%. Conclusion: Visual and auditory feedback cues can improve gait parameters in patients with gait disorders due to cerebral palsy.

Partial classification: the benefit of deferred decision

It is shown that partial classification which allows for indecision in certain regions of the data space, can increase a benefit function, defined as the difference between the probabilities of correct and incorrect decisions, joint with the event that a decision is made. This is particularly true for small data samples, which may cause a large deviation of the estimated separation surface from the intersection surface between the corresponding probability density functions. Employing a particular density estimation method, an indecision domain is naturally defined by a single parameter whose optimal size, maximizing the benefit function, is derived from the data. The benefit function is shown to translate into profit in stock trading. Employing medical and economic data, it is shown that partial classification produces, on average, higher benefit values than full classification, assigning each new object to a class, and that the marginal benefit of partial classification reduces as the data size increases.

Virtual sensory feedback for gait improvement in neurological patients

We review a treatment modality for movement disorders by sensory feedback. The natural closed-loop sensory-motor feedback system is imitated by a wearable virtual reality apparatus, employing body-mounted inertial sensors and responding dynamically to the patient’s own motion. Clinical trials have shown a significant gait improvement in patients with Parkinson’s disease using the apparatus. In contrast to open-loop devices, which impose constant-velocity visual cues in a “treadmill” fashion, or rhythmic auditory cues in a “metronome” fashion, requiring constant vigilance and attention strategies, and, in some cases, instigating freezing in Parkinson’s patients, the closed-loop device improved gait parameters and eliminated freezing in most patients, without side effects. Patients with multiple sclerosis, previous stroke, senile gait, and cerebral palsy using the device also improved their balance and gait substantially. Training with the device has produced a residual improvement, suggesting virtual sensory feedback for the treatment of neurological movement disorders.