# A Novel Criticality Analysis Method for Assessing Obesity Treatment Efficacy
## 1 Introduction  
Human gait, the intricate orchestration of biomechanical movements during ambulation, stands as a pivotal aspect of human motor function with far-reaching implications for an individual's health and overall wellbeing [1; 2; 3]. This intricate phenomenon, however, is not a static entity. It is subject to perturbations stemming from a diverse array of factors, encompassing injuries, diseases, disorders, and external conditions, thereby engendering deviations from established norms and the emergence of irregular or aberrant gait patterns [4; 5; 6].  
The traditional methodologies employed in gait analysis, predominantly reliant upon observational techniques, possess inherent limitations marked by subjectivity and inter-observer variability [7]. These methodologies, furthermore, confront difficulties in adequately encapsulating the nuanced, multifaceted, and quantitative attributes inherentin gait, particularly when confronted with intricate patterns stemming from underlying pathologies [8].  
In the contemporary landscape of medical diagnostics, artificial intelligence (AI) has emerged as a promising frontier, bearing the capacity to substantially enhance gait analysis and expedite the detection of gait-related disorders [9; 10]. Its proficiency in the processing of extensive datasets, identification of latent patterns, and facilitation of early diagnoses offers substantial promise [11]. Nonetheless, AI grapples with intricate challenges in the realm of gait analysis, stemming from the dynamic nature of gait itself and the intricate interplay of a multitude of contributory factors [11].  
In response to these exigencies, this paper introduces Criticality Analysis (CA) as an innovative and robust AI tool primed for precise identification of abnormal or irregular gait patterns, thereby indicating the presence of latent disorders or ailments. Beyond its diagnostic prowess, CA serves as a dynamic tool for the continuous monitoring of disorder progression and the systematic tracking of treatment efficacy over temporal trajectories. This innovative paradigm promises to empower medical practitioners in their clinical decision making in relation to gait-related disorders, ultimately effecting substantial enhancements in patient outcomes and the broader landscape of healthcare.  
The paper is structured as follows: Section 2 outlines a methodology employing mathematical models to assess critical aspects of human gait, emphasising the integration of mathematical modeling and criticality analysis in the context of gait study. In Section 3, the methodology applied to the Criticality Analysis of Diabetic Gait in Children (CARDIGAN) dataset is detailed, covering data collection, feature extraction, criticality analysis data representation, and spatiotemporal analysis. Section 4 explores the experimental results of the CARDIGAN dataset, including the analysis of Receiver Operating Characteristic (ROC) Curves, the calculation of Area Under the Curve (AUC), and the determination of the decision boundary of the support vector method. Section 5 provides a concise summary of the overarching results, while Section 6 concludes by highlighting the key findings of the research.