Beyond Static Assessment: A Proof-of-Concept Evaluation of Functional Data Analysis for Assessing Physiological Responses to High-Intensity Effort

Abstract

Background: Conventional analyses of physiological recovery often rely on discrete metrics that assume independence across time points, thereby ignoring intrinsic temporal continuity and masking substantial interindividual heterogeneity. This proof-of-concept study assesses the efficacy of Functional Data Analysis (FDA) as a promising framework for characterizing individual response dynamics following a functional threshold power (FTP) test. Methods: Physiological time-series data (including blood lactate, heart rate, blood pressure, and glucose levels) collected from 21 trained cyclists (10 professionals, 11 amateurs) were represented as functional objects using FDataGrid on the original sampling grid (0, 3, 5, 10, 20 min), without basis expansion or smoothing. We conducted unsupervised functional clustering (K-means; Fuzzy K-means) and supervised classification (Maximum Depth with Modified Band Depth, K-Nearest Neighbors, Nearest Centroid, functional QDA with parametric Gaussian covariance). Model performance was estimated via Repeated Stratified 5-Fold Cross-Validation with 10 repetitions (50 folds), reporting accuracy, balanced accuracy (mean ± SD), 95% CIs, permutation p-values, and sensitivity/specificity from aggregated confusion matrices. Results: Lactate (CL) and diastolic blood pressure (DBP) provided useful and statistically significant discrimination across several classifiers (e.g., KNN, Nearest Centroid, functional QDA), whereas heart rate showed modest discriminative value and glucose intermediate performance. Unsupervised analyses revealed distinct lactate recovery profiles and graded membership for hemodynamic/metabolic variables, supporting the value of FDA for resolving heterogeneity beyond group-average trends. Conclusions: FDA offers a feasible and informative approach for classifying recovery phenotypes while preserving temporal structure. Findings are promising but should be interpreted with caution due to the small sample size, sparse time points, and the need for external validation in larger, independent cohorts before translation into routine decision-making.