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

Q: What are the key findings of this study?

Functional Data Analysis of blood lactate and diastolic blood pressure curves discriminated professional from amateur cyclists, outperforming heart rate.

Q: What is the clinical evidence from this study?

Study design: Observational. Population: Physiological recovery following high-intensity cycling effort (20-min functional threshold power test) (n=21). Intervention: Functional Data Analysis (FDA) of continuous physiological recovery curves vs. Conventional discrete polynomial regression (linear, quadratic, and cubic models). Primary outcome: Supervised classification accuracy and balanced accuracy for discriminating cyclist competitive status (Professional vs. Amateur) via Repeated Stratified 5-Fold Cross-Validation (p=<0.01).

Q: What does this research mean for the field?

Functional Data Analysis of blood lactate and diastolic blood pressure recovery curves significantly discriminates professional from amateur cyclists, outperforming heart rate dynamics. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Q: What question did this study set out to answer?

To evaluate the efficacy of Functional Data Analysis (FDA) for characterizing individual dynamic physiological recovery trajectories following a functional threshold power test in trained cyclists.

Adrian Odriozola; Cristina Tîrnȃucȃ; A. Hernández González; Francesc Corbi; Jesús Álvarez-Herms

doi:10.3390/jfmk11020151

April 10, 2026Journal of Functional Morphology and KinesiologyOpen Access

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

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Key result

Functional Data Analysis of lactate and diastolic pressure recovery curves differentiates professional from amateur cyclists.

P<0.01
n=21

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Why the study?

Conventional analyses of physiological recovery rely on discrete metrics that assume independence across time points, ignoring temporal continuity and masking interindividual heterogeneity.

Does Functional Data Analysis (FDA) improve the characterization of individual physiological recovery phenotypes and discrimination of athlete status (professional vs. amateur) compared to conventional discrete polynomial regression in trained cyclists following a maximal 20-minute FTP test?

Key Points

To evaluate the efficacy of Functional Data Analysis (FDA) for characterizing individual dynamic physiological recovery trajectories following a functional threshold power test in trained cyclists.
Physiological time series (blood lactate, heart rate, blood pressure, glucose) from 21 trained cyclists (10 professionals, 11 amateurs) were modeled as functional objects using FDataGrid at 0, 3, 5, 10, and 20 min without smoothing or basis expansion.
Unsupervised clustering (K-means and Fuzzy K-means) and supervised classification (Maximum Depth with Modified Band Depth, K-Nearest Neighbors, Nearest Centroid, and functional QDA) were evaluated using Repeated Stratified 5-Fold Cross-Validation across 50 folds.
Blood lactate and diastolic blood pressure trajectories achieved the strongest discrimination between professional and amateur cyclists across classifiers (e.g., KNN, Nearest Centroid, functional QDA) with permutation p-values generally below 0.01.
Unsupervised functional clustering of lactate curves identified two distinct phenotypes: a fast-recovery cluster containing exclusively professionals and a delayed-recovery cluster with amateurs and three professionals, showing membership degrees >0.80.
Heart rate trajectories showed modest classification accuracy and mostly non-significant permutation tests, while conventional cubic polynomial models masked individual variation despite group fits of R² = 0.60 to 0.89.

Study Design

Type

Observational (n=21)

Structured PICO

Does Functional Data Analysis (FDA) improve the characterization of individual physiological recovery phenotypes and discrimination of athlete status (professional vs. amateur) compared to conventional discrete polynomial regression in trained cyclists following a maximal 20-minute FTP test?

P

Population

21 trained cyclists (10 professionals and 11 amateurs) undergoing a maximal 20-minute functional threshold power test and monitored for 20 minutes of acute post-exercise recovery.

E

Exposure

Functional Data Analysis (FDA) using FDataGrid on the original sampling grid (0, 3, 5, 10, 20 min) without smoothing or basis expansion, employing unsupervised clustering (K-means, Fuzzy K-means) and supervised classification (Maximum Depth with Modified Band Depth, K-Nearest Neighbors, Nearest Centroid, functional QDA)

C

Comparator

Conventional polynomial regression (linear, quadratic, and cubic models) fitted to group-averaged discrete time points

O

Outcome

Discrimination of athlete competitive status (Professional vs. Amateur) and identification of physiological recovery phenotypes using accuracy, balanced accuracy, 95% CIs, and permutation p-values across 50 cross-validation folds (Repeated Stratified 5-Fold Cross-Validation, 10 repetitions) over a 20-minute recovery periodsurrogate

Main Result

p-value: p=<0.01

Limitations

Small sample size (n=21)
Sparse and limited number of sampling time points (0, 3, 5, 10, and 20 min)
Lack of external validation in larger, independent cohorts
Secondary methodological analysis of an existing dataset
Sparse time points (limited to 0, 3, 5, 10, and 20 min)
Need for external validation in larger, independent cohorts before translation into routine decision-making
Secondary methodological analysis reusing a previously collected dataset

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Implication

Functional Data Analysis preserves the temporal continuity of post-exercise recovery trajectories, enabling superior identification of metabolic and hemodynamic responder phenotypes compared to static group-average regression.

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.

Discussion

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Cite This Study

Odriozola et al. (2026) conducted an observational in Physiological recovery following high-intensity cycling effort (20-min functional threshold power test) (n=21). Functional Data Analysis (FDA) of continuous physiological recovery curves vs. Conventional discrete polynomial regression (linear, quadratic, and cubic models) was evaluated on Supervised classification accuracy and balanced accuracy for discriminating cyclist competitive status (Professional vs. Amateur) via Repeated Stratified 5-Fold Cross-Validation (p=<0.01). Functional Data Analysis of blood lactate and diastolic blood pressure curves discriminated professional from amateur cyclists, outperforming heart rate.

synapsesocial.com/papers/69db36c24fe01fead37c4ba0 https://doi.org/10.3390/jfmk11020151

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

Figures

Key Points

Study Design

Structured PICO

Main Result

Limitations

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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

Figures

Key Points

Study Design

Structured PICO

Main Result

Limitations

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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