Next Article in Journal
Optical Non-Invasive Glucose Monitoring Using Aqueous Humor: A Review
Previous Article in Journal
QP-Adaptive Dual-Path Residual Integrated Frequency Transformer for Data-Driven In-Loop Filter in VVC
Previous Article in Special Issue
A Novel Mathematical Approach to Gait Analysis: The Reliability and Validity of the ZAY Angle for Step Length Estimation in Healthy Adults
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Entropy, Irreversibility, and Time-Series Deep Learning of Kinematic and Kinetic Data for Gait Classification in Children with Cerebral Palsy, Idiopathic Toe Walking, and Hereditary Spastic Paraplegia

by
Alfonso de Gorostegui
1,2,
Massimiliano Zanin
3,*,
Juan-Andrés Martín-Gonzalo
4,
Javier López-López
5,6,7,
David Gómez-Andrés
8,*,
Damien Kiernan
9 and
Estrella Rausell
2
1
PhD Program in Neuroscience, Universidad Autonoma de Madrid-Cajal Institute, 28029 Madrid, Spain
2
Department of Anatomy, Histology & Neuroscience, School of Medicine, Universidad Autónoma de Madrid (UAM), 28029 Madrid, Spain
3
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
4
Escuela Universitaria de Fisioterapia de la ONCE, Universidad Autónoma de Madrid, 28034 Madrid, Spain
5
Department of Rehabilitation, Hospital Universitario Infanta Sofía, 28702 Madrid, Spain
6
Fundación para la Investigación e Innovación Biomédica del Hospital Universitario Infanta Sofía y Hospital del Henares, 28702 Madrid, Spain
7
Departamento de Medicina, Salud y Deporte, Universidad Europea de Madrid, Villaviciosa de Odón, 28670 Madrid, Spain
8
Pediatric Neurology, ERN-RND, Euro-NMD, Vall d’Hebron Institut de Recerca (VHIR), Hospital Universitari Vall d’Hebron, 08035 Barcelona, Spain
9
Movement Analysis Laboratory, Central Remedial Clinic, Clontarf, D03 R973 Dublin, Ireland
*
Authors to whom correspondence should be addressed.
Sensors 2025, 25(13), 4235; https://doi.org/10.3390/s25134235
Submission received: 23 May 2025 / Revised: 30 June 2025 / Accepted: 5 July 2025 / Published: 7 July 2025
(This article belongs to the Special Issue Sensor Technologies for Gait Analysis: 2nd Edition)

Abstract

The use of gait analysis to differentiate among paediatric populations with neurological and developmental conditions such as idiopathic toe walking (ITW), cerebral palsy (CP), and hereditary spastic paraplegia (HSP) remains challenging due to the insufficient precision of current diagnostic approaches, leading in some cases to misdiagnosis. Existing methods often isolate the analysis of gait variables, overlooking the whole complexity of biomechanical patterns and variations in motor control strategies. While previous studies have explored the use of statistical physics principles for the analysis of impaired gait patterns, gaps remain in integrating both kinematic and kinetic information or benchmarking these approaches against Deep Learning models. This study evaluates the robustness of statistical physics metrics in differentiating between normal and abnormal gait patterns and quantifies how the data source affects model performance. The analysis was conducted using gait data sets from two research institutions in Madrid and Dublin, with a total of 81 children with ITW, 300 with CP, 20 with HSP, and 127 typically developing children as controls. From each kinematic and kinetic time series, Shannon’s entropy, permutation entropy, weighted permutation entropy, and time irreversibility metrics were derived and used with Random Forest models. The classification accuracy of these features was compared to a ResNet Deep Learning model. Further analyses explored the effects of inter-laboratory comparisons and the spatiotemporal resolution of time series on classification performance and evaluated the impact of age and walking speed with linear mixed models. The results revealed that statistical physics metrics were able to differentiate among impaired gait patterns, achieving classification scores comparable to ResNet. The effects of walking speed and age on gait predictability and temporal organisation were observed as disease-specific patterns. However, performance differences across laboratories limit the generalisation of the trained models. These findings highlight the value of statistical physics metrics in the classification of children with different toe walking conditions and point towards the need of multimetric integration to improve diagnostic accuracy and gain a more comprehensive understanding of gait disorders.
Keywords: cerebral palsy; idiopathic toe walking; hereditary spastic paraplegia; deep learning; entropy; time irreversibility cerebral palsy; idiopathic toe walking; hereditary spastic paraplegia; deep learning; entropy; time irreversibility

Share and Cite

MDPI and ACS Style

de Gorostegui, A.; Zanin, M.; Martín-Gonzalo, J.-A.; López-López, J.; Gómez-Andrés, D.; Kiernan, D.; Rausell, E. Entropy, Irreversibility, and Time-Series Deep Learning of Kinematic and Kinetic Data for Gait Classification in Children with Cerebral Palsy, Idiopathic Toe Walking, and Hereditary Spastic Paraplegia. Sensors 2025, 25, 4235. https://doi.org/10.3390/s25134235

AMA Style

de Gorostegui A, Zanin M, Martín-Gonzalo J-A, López-López J, Gómez-Andrés D, Kiernan D, Rausell E. Entropy, Irreversibility, and Time-Series Deep Learning of Kinematic and Kinetic Data for Gait Classification in Children with Cerebral Palsy, Idiopathic Toe Walking, and Hereditary Spastic Paraplegia. Sensors. 2025; 25(13):4235. https://doi.org/10.3390/s25134235

Chicago/Turabian Style

de Gorostegui, Alfonso, Massimiliano Zanin, Juan-Andrés Martín-Gonzalo, Javier López-López, David Gómez-Andrés, Damien Kiernan, and Estrella Rausell. 2025. "Entropy, Irreversibility, and Time-Series Deep Learning of Kinematic and Kinetic Data for Gait Classification in Children with Cerebral Palsy, Idiopathic Toe Walking, and Hereditary Spastic Paraplegia" Sensors 25, no. 13: 4235. https://doi.org/10.3390/s25134235

APA Style

de Gorostegui, A., Zanin, M., Martín-Gonzalo, J.-A., López-López, J., Gómez-Andrés, D., Kiernan, D., & Rausell, E. (2025). Entropy, Irreversibility, and Time-Series Deep Learning of Kinematic and Kinetic Data for Gait Classification in Children with Cerebral Palsy, Idiopathic Toe Walking, and Hereditary Spastic Paraplegia. Sensors, 25(13), 4235. https://doi.org/10.3390/s25134235

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop