💻 computer science

Non-invasive lactate threshold estimation using deep learning: practical applications across endurance sports

This study demonstrates that a deep learning model can accurately estimate heart rate at the 2 mmol·L⁻¹ lactate threshold across running, cycling, rowing, and kayaking, outperforming traditional methods within specific sports but requiring sport-specific validation due to reduced generalization accuracy across different disciplines.

Original authors: Mehrnaz Eskandarisani¹, Farhad Daryanoosh

Published 2026-09-01

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CC BY 4.0

Original authors: Mehrnaz Eskandarisani¹, Farhad Daryanoosh

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, coaches and sports scientists have relied on a single, critical number to design training for endurance athletes: the point at which the body's fuel switches from efficient burning to a state of accumulating fatigue. This moment, known as the lactate threshold, marks the intensity where lactic acid begins to build up in the blood faster than the muscles can clear it. To find this precise point, athletes traditionally undergo a grueling laboratory test. They run or cycle at increasing speeds while a technician pricks their finger repeatedly to draw blood, measuring the acid levels after each stage. While this method is the gold standard for accuracy, it is invasive, expensive, and requires specialized equipment and staff. For many recreational runners, young athletes, or patients in clinical settings, this barrier means they simply cannot access the data needed to train effectively. The question has long been whether it is possible to predict this threshold using only the heart rate and speed data already collected during a standard test, without ever drawing a drop of blood.

A team of researchers set out to answer this by building a sophisticated computer model capable of learning the hidden patterns between an athlete's performance and their physiological limits. Instead of relying on simple formulas that have been used for years, they employed a deep learning system, a type of artificial intelligence that can analyze complex sequences of data to find relationships humans might miss. The team fed the model data from 823 separate exercise tests involving over 800 athletes of both sexes. These tests covered four distinct endurance disciplines: running, cycling, rowing, and kayaking. For every test, the model was shown the athlete's heart rate and speed or power output at each stage, along with their age and gender, and asked to predict the exact heart rate where their blood lactate would reach a specific, fixed level of two millimoles per liter. The researchers then compared the model's predictions against the actual blood test results to see how close it came.

The results showed that within the sports the model had studied, it could estimate the threshold with remarkable precision. On average, the model's guess was off by only about 5.5 beats per minute. To put this in perspective, this level of error is comparable to the natural variation seen when the same athlete takes the exact same blood test twice in a row under laboratory conditions. The computer model significantly outperformed the best existing non-invasive methods, which are based on mathematical curves drawn through the data points. Those older methods were often off by nearly nine beats per minute, a difference that could easily push an athlete into the wrong training zone. The new model proved particularly effective for runners, rowers, and cyclists, where it successfully identified the threshold for the vast majority of participants, often landing within a range that would be useful for general training guidance.

However, the study also revealed a clear limitation: the model does not automatically work for every sport. When the researchers tested the system on athletes from a sport it had not seen during its training, the accuracy dropped sharply. This was most evident in kayaking, a sport that relies heavily on upper-body strength, where the error rate more than doubled compared to the leg-dominant sports. The researchers investigated whether this failure was simply because they had fewer kayaking tests in their data or because the physiology of paddling is fundamentally different from running or cycling. Their analysis suggested that both factors likely play a role, though they could not definitively separate the two with the current data. The model struggled most with the smallest group, indicating that it needs a substantial amount of specific examples to learn the unique patterns of each discipline.

The authors conclude that this technology is a powerful tool for screening and monitoring, but it is not yet a perfect replacement for the traditional blood test. For coaches working with runners, cyclists, or rowers, the model offers a way to track an athlete's progress over time without the need for repeated finger pricks, making frequent testing practical and affordable. It can help identify when an athlete is getting fitter or when their training intensity needs adjustment. Yet, for setting the precise boundaries of a training zone for an individual, especially in less common sports or for high-stakes decisions, direct blood sampling remains the necessary standard. The model serves best as a bridge, allowing for more frequent observation and reducing the burden of invasive testing, while acknowledging that the final, most accurate measurement still requires a drop of blood.

Technical Summary: Non-invasive Lactate Threshold Estimation Using Deep Learning

Problem Statement
The lactate threshold (LT), specifically the heart rate corresponding to a fixed blood lactate concentration of 2 mmol·L⁻¹ ( $HR_{2mmol}$ ), is a cornerstone for prescribing endurance training intensity. However, determining $HR_{2mmol}$ traditionally requires graded exercise tests with repeated capillary blood sampling. This process imposes significant barriers in clinical, youth, and recreational settings due to the need for trained personnel, calibrated equipment, and the invasiveness of skin puncture. While non-invasive curve-fitting heuristics (e.g., D-max) exist, their agreement with directly measured LT is often inconsistent. There is a need for a non-invasive method that leverages standard heart rate and power/pace data to estimate $HR_{2mmol}$ accurately and generalizes across different endurance disciplines.

Methodology
The study utilized a secondary analysis of a publicly available, anonymized database of 835 incremental exercise tests from the Human Performance Laboratory at Trinity College Dublin. After excluding 12 tests due to missing lactate sequences or physiological quality failures (e.g., unrealistic heart rates or lactate values), the final analytic sample consisted of 823 tests involving 537 male and 286 female athletes across four disciplines: running, cycling, rowing, and kayak.

Target Variable: $HR_{2mmol}$ , defined as the heart rate at the 2 mmol·L⁻¹ blood lactate reference point, determined via linear interpolation between stages.
Input Features: The deep learning model was trained on stage-wise physiological features, including heart rate reserve, normalized power/pace (relative to the individual's maximum within that specific test), heart rate dynamics, participant characteristics, and a categorical sport indicator.
Model Architecture: A deep learning model incorporating Long Short-Term Memory (LSTM) layers with attention mechanisms and sport-specific embeddings was developed.
Validation Strategy:
- Within-Sport: Subject-wise 5-fold cross-validation ensured no athlete's data appeared in both training and test sets.
- Cross-Sport Generalization: Leave-one-sport-out (LOSO) validation was employed to test if a model trained on three sports could predict $HR_{2mmol}$ for the fourth.
- Causal Analysis: To distinguish between physiological dissimilarity and sample size limitations (particularly for the smaller kayak dataset, n=54), a bootstrap-resampled matched-downsampling experiment was conducted. This compared LOSO performance when kayak was excluded versus when an equally sized random subset of rowing was excluded.
Comparators: The model was benchmarked against established physiological heuristics (D-max, modified D-max, OBLA-4) and machine learning baselines (Linear Regression, Random Forest, XGBoost, vanilla LSTM).

Key Results

Accuracy Within Trained Sports: The deep learning model achieved a Mean Absolute Error (MAE) of 5.56 ± 0.64 bpm and an Intraclass Correlation Coefficient (ICC) of 0.662. This performance outperformed the best existing heuristic, modified D-max (MAE = 8.66 bpm), by 35.8% (3.10 bpm).
Comparison to Baselines: The deep learning model surpassed all machine learning baselines and physiological heuristics. Notably, curve-fitting heuristics like D-max and OBLA-4 showed negative $R^2$ values, indicating poor transfer to the 2 mmol·L⁻¹ definition used in this study.
Sport-Specific Performance:
- Running and Rowing: Showed the highest accuracy (MAE ≈ 4.9 bpm).
- Cycling: Intermediate accuracy (MAE = 5.86 bpm).
- Kayak: Showed the highest error (MAE = 10.01 bpm) and variability, with 3.7% of tests exceeding a 30 bpm error.
Cross-Sport Generalization: When applied to a sport entirely absent from training, error increased by 37–103%.
- Kayak: As the held-out sport, it showed the most severe degradation (MAE = 11.27 bpm, $R^2$ = -0.802).
- Bootstrap Analysis: The study found that excluding kayak specifically improved transfer accuracy for running more than excluding an equal-sized subset of rowing, suggesting a potential physiological barrier. However, for cycling, both exclusions improved accuracy similarly, suggesting sample size might be the limiting factor. A Mann-Whitney U test comparing these distributions yielded p = 0.65, meaning the distinction between physiological dissimilarity and sample size effects is not statistically significant and should be viewed as hypothesis-generating.

Significance and Claims
The paper positions this work as a proof-of-concept demonstrating the feasibility of non-invasive $HR_{2mmol}$ estimation using deep learning within a single-laboratory protocol.

Practical Utility: The model's average accuracy (MAE ~5.5 bpm) is comparable to published test-retest variability for laboratory LT determination (4–8 bpm). This suggests the model can serve as a valuable screening and monitoring tool for running, cycling, and rowing, allowing for frequent, non-invasive tracking of training adaptations without repeated blood sampling.
Limitations and Scope: The authors explicitly state the model cannot replace direct blood sampling for precise individual training prescription. The Bland-Altman limits of agreement (±18 bpm) are too wide for individual zone-setting, and the model lacks a mechanism to indicate when its own estimates are likely inaccurate.
Generalization: The study concludes that while the model works well within trained sports, sport-specific validation is essential before deployment, particularly for upper-body dominant sports like kayaking where performance degrades significantly.
Future Requirements: The authors emphasize that for this technology to be integrated into individual clinical or coaching prescriptions, future work requires sport-balanced training data, validated uncertainty estimates, and multi-centre validation.

In summary, the study provides a non-invasive, deep learning-based alternative to traditional heuristics for estimating lactate threshold heart rates, offering a practical tool for reducing testing burdens in well-represented endurance sports while acknowledging the necessity of direct blood sampling for high-precision individual prescription.

Technical Summary: Non-invasive Lactate Threshold Estimation Using Deep Learning

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