c06c84dae7acaafc806bae426506b3eb 320773.pdf 0042372451cad39bea356df14d407fb2990813f5 320773.pdf 6a7edc4d1b8747f707fc218d02af1be57097ae7696d77eedfa85a8988bdbd325 320773.pdf 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 Subject: 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 Author: Alfonso de Gorostegui, Massimiliano Zanin, Juan-Andrés Martín-Gonzalo, Javier López-López, David Gómez-Andrés Damien Kiernan and Estrella Rausell Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Wed Jul 9 08:43:08 2025 CEST ModDate: Wed Jul 9 08:48:04 2025 CEST Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 41 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 7371916 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- BUZBIP+URWPalladioL-Roma Type 1 Custom yes yes yes 10 0 OVFNFO+URWPalladioL-Bold Type 1 Custom yes yes yes 16 0 KDRSWV+URWPalladioL-Ital Type 1 Custom yes yes yes 21 0 WBVKDJ+URWPalladioL-BoldItal Type 1 Custom 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PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-10-21 12:24:54 CEST Size: 7371916 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 13398 FreeObjects: 3909 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: section.1 Item: Title: Methods Destination: section.2 Children: Item: Title: Participants Destination: subsection.2.1 Children: Item: Title: Movement Analysis Laboratory, CRC, Dublin Destination: subsubsection.2.1.1 Item: Title: Laboratory of Human Movement, ONCE-UAM, Madrid Destination: subsubsection.2.1.2 Item: Title: Gait Data Collection and Data Preprocessing Destination: subsection.2.2 Item: Title: Statistical Physics Metrics Destination: subsection.2.3 Item: Title: Linear Mixed Effect Models Destination: subsection.2.4 Item: Title: Classification and Validation Destination: subsection.2.5 Item: Title: Deep Learning Classification Destination: subsection.2.6 Item: Title: Results Destination: section.3 Children: Item: Title: Description of Distribution of Statistical Physics Metrics Within and Between Groups of Gait Disorders Destination: subsection.3.1 Item: Title: Comparison of Statistical Physics Metrics Between Groups of Gait Disorders Destination: subsection.3.2 Item: Title: Classification Scores per Group and Time-Series Type Destination: subsection.3.3 Item: Title: Inter-Laboratory Comparison Destination: subsection.3.4 Item: Title: Analysis of Feature Importance in Statistical Physics Models Destination: subsection.3.5 Item: Title: Classifications Based on Individual Time Series Destination: subsection.3.6 Item: Title: Optimal Resolution of Time Series Destination: subsection.3.7 Item: Title: Analysis of Gait Sub-Windows Destination: subsection.3.8 Item: Title: Discussion Destination: section.4 Children: Item: Title: Discussion from the Data Analysis Perspective Destination: subsection.4.1 Item: Title: Insights into Motor Control Through Statistical Physic Metrics and Deep Learning Destination: subsection.4.2 Item: Title: Considerations from a Medical Point of View Destination: subsection.4.3 Item: Title: Conclusions Destination: section.5 Item: Title: Appendix A Destination: appendix.A. Item: Title: References Destination: appendix.B. Info: 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 Author: Alfonso de Gorostegui, Massimiliano Zanin, Juan-Andrés Martín-Gonzalo, Javier López-López, David Gómez-Andrés Damien Kiernan and Estrella Rausell Subject: 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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