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
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 approac...
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MDPI AG
2025-07-01
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| author | Alfonso de Gorostegui Massimiliano Zanin Juan-Andrés Martín-Gonzalo Javier López-López David Gómez-Andrés Damien Kiernan Estrella Rausell |
| author_facet | Alfonso de Gorostegui Massimiliano Zanin Juan-Andrés Martín-Gonzalo Javier López-López David Gómez-Andrés Damien Kiernan Estrella Rausell |
| author_sort | Alfonso de Gorostegui |
| collection | DOAJ |
| description | 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. |
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| institution | Kabale University |
| issn | 1424-8220 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
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| series | Sensors |
| spelling | doaj-art-dbe8997508eb4dd797d29cdedde359192025-08-20T03:28:59ZengMDPI AGSensors1424-82202025-07-012513423510.3390/s25134235Entropy, 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 ParaplegiaAlfonso de Gorostegui0Massimiliano Zanin1Juan-Andrés Martín-Gonzalo2Javier López-López3David Gómez-Andrés4Damien Kiernan5Estrella Rausell6PhD Program in Neuroscience, Universidad Autonoma de Madrid-Cajal Institute, 28029 Madrid, SpainInstituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, SpainEscuela Universitaria de Fisioterapia de la ONCE, Universidad Autónoma de Madrid, 28034 Madrid, SpainDepartment of Rehabilitation, Hospital Universitario Infanta Sofía, 28702 Madrid, SpainPediatric Neurology, ERN-RND, Euro-NMD, Vall d’Hebron Institut de Recerca (VHIR), Hospital Universitari Vall d’Hebron, 08035 Barcelona, SpainMovement Analysis Laboratory, Central Remedial Clinic, Clontarf, D03 R973 Dublin, IrelandDepartment of Anatomy, Histology & Neuroscience, School of Medicine, Universidad Autónoma de Madrid (UAM), 28029 Madrid, SpainThe 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.https://www.mdpi.com/1424-8220/25/13/4235cerebral palsyidiopathic toe walkinghereditary spastic paraplegiadeep learningentropytime irreversibility |
| spellingShingle | Alfonso de Gorostegui Massimiliano Zanin Juan-Andrés Martín-Gonzalo Javier López-López David Gómez-Andrés Damien Kiernan Estrella Rausell 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 cerebral palsy idiopathic toe walking hereditary spastic paraplegia deep learning entropy time irreversibility |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | cerebral palsy idiopathic toe walking hereditary spastic paraplegia deep learning entropy time irreversibility |
| url | https://www.mdpi.com/1424-8220/25/13/4235 |
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