What question did this study set out to answer?

This study evaluates the effectiveness of Functional Data Analysis to capture individual physiological response dynamics after high-intensity exercise.

April 12, 2026Open Access

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

Key Result

Functional Data Analysis of post-exercise recovery in cyclists revealed that blood lactate and diastolic blood pressure provided statistically significant discrimination of recovery phenotypes.

Key Points

This study evaluates the effectiveness of Functional Data Analysis to capture individual physiological response dynamics after high-intensity exercise.
Collected physiological time-series data from 21 trained cyclists after a functional threshold power (FTP) test.
Utilized FDataGrid for representing data without smoothing or basis expansion.
Employed unsupervised clustering (K-means, Fuzzy K-means) and supervised classification methods (K-nearest Neighbors, functional QDA).
Estimated model performance with 5-Fold Cross-Validation, analyzing accuracy and sensitivity.
Examined recovery profiles for lactate and other metabolic variables.
Lactate and diastolic blood pressure showed significant distinction across classification models.
Heart rate provided modest discrimination and glucose had intermediate performance.
Unsupervised analyses indicated diverse lactate recovery profiles that address interindividual differences.
Functional Data Analysis proved beneficial in capturing temporal dynamics of recovery.

Structured PICO

Does Functional Data Analysis (FDA) effectively characterize individual physiological response dynamics following high-intensity effort in trained cyclists?

Population

21 trained cyclists (10 professionals, 11 amateurs)

Intervention

Functional Data Analysis (FDA) of physiological time-series data (blood lactate, heart rate, blood pressure, and glucose levels) following a functional threshold power (FTP) test

Outcome

Efficacy of Functional Data Analysis (FDA) for characterizing individual response dynamics and classifying recovery phenotypes

Functional Data Analysis is a feasible and informative approach for classifying physiological recovery phenotypes after high-intensity effort while preserving temporal structure.

Main Result

Absolute Event Rate: 0% vs 0%

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.