With disease-modifying approaches under evaluation in ataxia-telangiectasia and other ataxias, there is a need for objective and reliable biomarkers of free-living motor function. In this study, we test the hypothesis that metrics derived from a single wrist sensor worn at home provide accurate, reliable, and interpretable information about neurological disease severity in children with A-T. A total of 15 children with A-T and 15 age- and sex-matched controls wore a sensor with a triaxial accelerometer on their dominant wrist for 1 week at home. Activity intensity measures, derived from the sensor data, were compared with in-person neurological evaluation on the Brief Ataxia Rating Scale (BARS) and performance on a validated computer mouse task. Children with A-T were inactive the same proportion of each day as controls but produced more low intensity movements ( p < 0.01; Cohen’s d = 1.48) and fewer high intensity movements ( p < 0.001; Cohen’s d = 1.71). The range of activity intensities was markedly reduced in A-T compared to controls ( p < 0.0001; Cohen’s d = 2.72). The activity metrics correlated strongly with arm, gait, and total clinical severity ( r : 0.71–0.87; p < 0.0001), correlated with specific computer task motor features ( r : 0.67–0.92; p < 0.01), demonstrated high reliability ( r : 0.86–0.93; p < 0.00001), and were not significantly influenced by age in the healthy control group. Motor activity metrics from a single, inexpensive wrist sensor during free-living behavior provide accurate and reliable information about diagnosis, neurological disease severity, and motor performance. These low-burden measurements are applicable independent of ambulatory status and are potential digital behavioral biomarkers in A-T.
Novel disease modifying therapies are being evaluated in spinocerebellar ataxias and multiple system atrophy. Clinician-performed disease rating scales are relatively insensitive for measuring disease change over time, resulting in large and long clinical trials. We tested the hypothesis that sensors worn continuously at home during natural behavior and a web-based computer mouse task performed at home could produce interpretable, meaningful, and reliable motor measures for potential use in clinical trials. Thirty-four individuals with degenerative ataxias (spinocerebellar ataxia types 1, 2, 3, and 6 and multiple system atrophy of the cerebellar type) and eight age-matched controls completed the cross-sectional study. Participants wore an ankle and wrist sensor continuously at-home for one week and completed the Hevelius computer mouse task eight times over four weeks. We examined properties of motor primitives called “submovements” derived from the continuous wearable sensors and properties of computer mouse clicks and trajectories in relationship to patient-reported measures of function (PROM-Ataxia) and ataxia rating scales (Scale for the Assessment and Rating of Ataxia and the Brief Ataxia Rating Scale). The test-retest reliability of digital measures and differences between ataxia and control participants were evaluated. Individuals with ataxia had smaller, slower, and less powerful ankle submovements during natural behavior at home. A composite measure based on ankle submovements strongly correlated with ataxia rating scale scores (Pearson’s r = 0.82-0.88), strongly correlated with self-reported function (r = 0.81), had high test-retest reliability (intraclass correlation coefficient = 0.95), and distinguished ataxia and control participants, including preataxic individuals (N=4) from controls. A composite measure based on computer mouse movements and clicks strongly correlated with ataxia rating scale total (r = 0.86-0.88) and arm scores (r = 0.65-0.75), correlated well with self-reported function (r = 0.72-0.73), and had high test-retest reliability (intraclass correlation coefficient = 0.99). These data indicate that interpretable, meaningful, and highly reliable motor measures can be obtained from continuous measurement of natural movement, particularly at the ankle location, and from computer mouse movements during a simple point-and-click task performed at home. This study supports the use of these two inexpensive and easy-to-use technologies in longitudinal natural history studies in spinocerebellar ataxias and multiple system atrophy of the cerebellar type and shows promise as potential motor outcome measures in interventional trials.
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Abstract. We consider the problem of representing numbers in close to optimal space and supporting increment, decrement, addition and subtraction operations efficiently. We study the problem in the bit probe model and analyse the number of bits read and written to perform the operations, both in the worst-case and in the average-case. A counter is space-optimal if it represents any number in the range [0, . . . , 2 n − 1] using exactly n bits. We provide a space-optimal counter which supports increment and decrement operations by reading at most n − 1 bits and writing at most 3 bits in the worst-case. To the best of our knowledge, this is the first such representation which supports these operations by always reading strictly less than n bits. For redundant counters where we only need to represent numbers in the range [0, . . . , L] for some integer L < 2 n − 1 using n bits, we define the efficiency of the counter as the ratio between L + 1 and 2 n . We present various representations that achieve different trade-offs between the read and write complexities and the efficiency. We also give another representation of integers that uses n + O(log n) bits to represent integers in the range [0, . . . , 2 n − 1] that supports efficient addition and subtraction operations, improving the space complexity of an earlier representation by Munro and Rahman [Algorithmica, 2010].
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