A topological data analysis-based method for gait signals with an application to the study of multiple sclerosis.

In the past few years, light, affordable wearable inertial measurement units have been providing to clinicians and researchers the possibility to quantitatively study motor degeneracy by comparing gait trials from patients and/or healthy subjects. To do so, standard gait features can be used but they fail to detect subtle changes in several pathologies including multiple sclerosis. Multiple sclerosis is a demyelinating disease of the central nervous system whose symptoms include lower limb impairment, which is why gait trials are commonly used by clinicians for their patients' follow-up. This article describes a method to compare pairs of gait signals, visualize the results and interpret them, based on topological data analysis techniques. Our method is non-parametric and requires no data other than gait signals acquired with inertial measurement units. We introduce tools from topological data analysis (sublevel sets, persistence barcodes) in a practical way to make it as accessible as possible in order to encourage its use by clinicians. We apply our method to study a cohort of patients suffering from progressive multiple sclerosis and healthy subjects. We show that it can help estimate the severity of the disease and also be used for longitudinal follow-up to detect an evolution of the disease or other phenomena such as asymmetry or outliers.

Effects of the duper mutation on circadian responses to light.

The circadian mutation duper in Syrian hamsters shortens the free-running circadian period (τ(DD)) by 2 hours when expressed on a tau mutant (τ(ss)) background and by 1 hour on a wild-type background. We have examined the effects of this mutation on phase response curves and entrainment. In contrast to wild types, duper hamsters entrained to 14L:10D with a positive phase angle. Super duper hamsters (expressing duper on a τ(ss) background) showed weak entrainment, while τ(ss) animals either completely failed to entrain or showed sporadic entrainment with episodes of relative coordination. As previously reported, wild-type and τ(ss) hamsters show low amplitude resetting in response to 15-minute light pulses after short-term (10 days) exposure to DD. In contrast, super duper hamsters show high amplitude resetting. This effect is attributable to the duper allele, as hamsters carrying duper on a wild-type background also show large phase shifts. Duper mutants that were born and raised in DD also showed high amplitude resetting in response to 15-minute light pulses, indicating that the effect of the mutation on PRC amplitude is not an aftereffect of entrainment to 14L:10D. Hamsters that are heterozygous for duper do not show amplified resetting curves, indicating that for this property, as for determination of free-running period, the mutant allele is recessive. In a modified Aschoff type II protocol, super duper and duper hamsters show large phase shifts as soon as the second day of DD. Despite the amplification of the PRC in super duper hamsters, the induction of Period1 gene expression in the SCN by light is no greater in these mutants than in wild-type animals. Period2 expression in the SCN did not differ between super duper and wild-type hamsters exposed to light at CT15, but albumin site D-binding protein (Dbp) mRNA showed higher basal levels and greater light induction in the SCN of super duper compared to wild-type animals. These results indicate that the duper mutation alters the amplitude of the circadian oscillator and further distinguish it from the tau mutation.