Lactate threshold models compared: Mader, Dickhuth, D-Max and log-log
There is no single lactate threshold. Widely used models set different points on the same measured curve, for example the fixed 4 mmol/l threshold according to Mader, the lactate equivalent minimum according to Dickhuth, the geometric methods D-Max and modified D-Max, and the log-log regression according to Beaver. These points are sometimes 20 per cent or more apart4,12. So what matters is not which model is theoretically the best. What matters is that you keep a model chosen on sound grounds over the years and document it in the report.
Why the same curve has several thresholds
At first, a lactate step test only provides pairs of values: load and blood lactate for each stage, usually together with heart rate and perceived exertion. The resulting curve rises gently at first and then bends upwards somewhere. It is exactly this transition that is of interest. But it is not a point, it is a range. Every threshold model is a rule that turns this range into a point.
The models differ in what they use to fix this point. Some set a fixed lactate value. Some measure a distance from the individual resting value. Some determine a geometric distance from a reference line. Some calculate a regression over the transformed course of the curve. From the same measurements, these rules can produce different results. The default in Plenea that is based on the resting value is explicitly a practice heuristic without a publication of its own.
This is not a measurement error. Nor is it a dispute between schools of thought that could be resolved. Reviews of threshold concepts have stated for years that no method has the status of a gold standard and that the concepts produce systematically different values1. Anyone comparing reports from different sources therefore compares the method first and only then the performance.
Try it · example bike step test
Overview of the widely used models
The overview shows the models that regularly appear in performance diagnostics in German-speaking countries. For each one, it states how it calculates and what data it needs.
| Model | Principle | Needs | Typical use |
|---|---|---|---|
| Mader 4 mmol/l | Fixed lactate value of 4 mmol/l; the threshold is where the curve crosses this line | Only the stage values | Comparisons across large groups and with older data sets |
| Models based on the resting value | Fixed distance from the individually measured resting lactate, for example +0.5 and +1.5 mmol/l | Reliable resting value before exercise | Practice heuristic when the curve is flat |
| Dickhuth | Minimum of the lactate equivalent (lactate per unit of power) plus 1.5 mmol/l | Enough stages to determine the minimum | Individual aerobic–anaerobic transition |
| D-Max (Cheng 1992) | Point with the greatest perpendicular distance from the line between the first and last measurement point | Rising, convex curve with enough stages for curve fitting | Geometric estimate that depends on the protocol |
| Modified D-Max (Bishop) | Like D-Max, but the secant only starts at the stage before the first rise of more than 0.4 mmol/l | Recognisable first rise in the curve | Makes D-Max less dependent on the starting point |
| Log-log (Beaver 1985) | Two-segment regression over log-transformed lactate and power values (Beaver et al. originally used log(VO₂); the power-based version is a common adaptation) | Enough stages in the lower range | First threshold (aerobic threshold) |
| Stegmann IAT (1981) | Tangent from a recovery point to the lactate curve | Additional lactate measurements after the end of exercise | Individual anaerobic threshold taking elimination into account |
Methodologically, Beaver’s log-log approach has only one threshold13. If you calculate with this model, you do not get a second, higher threshold. This is not because data is missing, but because the method does not define one. If software shows one anyway, it has derived it in a different way.
Fixed, individual and geometric models
A fixed reference value makes the curve easier to describe. But it does not make results from different protocols, different devices or different people comparable. The power at 4 mmol/l is not automatically the individual limit of sustainable performance.
Individual models solve this by taking the reference point from the test itself: the resting value, the minimum of the lactate equivalent or the course of recovery. The price: they depend on exactly the value from which they take their reference. If the resting value was measured poorly, for example after too intensive a warm-up, the entire threshold shifts in models based on the resting value. The method is then formally correct and still wrong.
In the original publication, D-Max depends on curve fitting and on the chosen end points11. Plenea does not fit a polynomial here but evaluates the measured stage points directly. The result still depends on the protocol and the end points. Whether a calculated value can be interpreted professionally is something you have to judge from the complete test.
Modified D-Max changes how the starting point of the secant is chosen12. This method also depends on the measurements and the protocol. And here too, Plenea does without curve fitting.
What the choice of model changes in practice
Different threshold values can lead to different training zones. How much depends on the zone model used. A difference of ten watts does not generally correspond to a whole training zone.
In everyday work this matters mainly in three situations: when the responsible practice changes, when the software changes and when you compare with reference values from the literature. In all three cases the first question is not “How high was the threshold?” but “Which method was used to determine it?”
If the model is changed and this is not documented, histories become harder to compare. A difference may then reflect a real change or the analysis.
- Choose the model once on sound grounds and name it visibly in the report
- Only compare histories within the same model3
- When you deliberately change the model, recalculate old reports instead of reinterpreting them
- Keep the raw data: without stage values, the model cannot be changed later
- For reference values, check which method was used to obtain them
How to choose a model on sound grounds
In practice, what decides is less which method is physiologically the most elegant. Four sober questions decide: Which method was used for this person’s previous reports? What data does your protocol actually provide? Which sport and which performance level are involved? And which external values must the report remain comparable with, for example for a federation or a referring practice?
Justify the choice with the relevant evidence, the test protocol and the question being asked. Neither an individual approach nor a fixed lactate value is superior for all people and purposes.
Heart rate, perceived exertion and, if measured, ventilatory thresholds complement the interpretation. If they differ, this can have methodological and individual causes. It is not automatically an error in the test.
Sources of error that affect every model
Stage duration, load increment and sampling affect the curve5. If the protocol changes, you have to interpret differences with caution.
Contamination, sampling time and a change of device can also affect measurements. Whether this influence is larger or smaller than the difference between two models cannot be said in general.
Rule of thumb: keep the protocol stable first, then talk about the model. A test carried out the same way every time with the theoretically second-best model says more about the history than an inconsistent test with the theoretically best one.
How Plenea handles this
Plenea does not calculate one model instead of another, but all of them together on the same raw data. In the analysis step, they appear side by side: the fixed 4 mmol/l threshold according to Mader6,7, the lactate equivalent minimum according to Dickhuth8,9,10, D-Max, modified D-Max according to Bishop, log-log according to Beaver and a default based on the resting value. Which model applies is decided by the person professionally responsible for the report. This decision is visible and documented, not an invisible default value.
Every model states its source. This explicitly also applies where there is none: the default based on the resting value is a practice heuristic without a publication, and that is exactly how the software labels it. A method that looks scientific in the report without being so is the bigger problem than one that discloses its origin.
Because the stage values are kept, an old report can be recalculated with a different model instead of being reinterpreted. This keeps the history comparable even after a deliberate change of model.
Frequently asked questions
Which lactate threshold model is the most accurate?
There is no universally valid ranking. It depends on which target variable you are examining, what the protocol looks like and how good the data is. A calculated lactate threshold is not automatically a directly measured maximal lactate steady state2.
Why does my report show two thresholds?
Not every method determines two thresholds. An additional threshold may come from a different rule. That is why the report has to show how both values are defined.
Can I compare values from different models?
No, not directly. A 4 mmol value and a value determined according to Dickhuth describe differently defined points on the same curve. Only reports calculated with the same method can be compared meaningfully. If the raw data is still available, the older test can be re-analysed afterwards for this purpose.
What is the difference between D-Max and modified D-Max?
Both look for the point with the greatest perpendicular distance from a secant through the lactate curve. With D-Max, this secant starts at the first measurement point. That is why the chosen starting load affects the result. Modified D-Max according to Bishop12 only starts the secant at the stage before the first clear rise in lactate and therefore depends less on the first measurement point.
Why does the Stegmann method need measurements after the test?
Stegmann, Kindermann and Schnabel construct the individual anaerobic threshold using a tangent that starts from a point on the recovery curve. This requires lactate measurements after the end of exercise. Without post-exercise values, the method cannot be calculated14.
Does stage duration shift the threshold?
Stage duration can change the lactate curve and the calculated result. Direction and extent depend on the protocol, the person and the model. Tests with different stage durations are therefore only comparable to a limited extent.
Sources
- 1
Faude O, Kindermann W, Meyer T. Lactate threshold concepts: how valid are they? Sports Medicine. 2009;39(6):469–490.
- 2
Jamnick NA, Pettitt RW, Granata C, Pyne DB, Bishop DJ. An Examination and Critique of Current Methods to Determine Exercise Intensity. Sports Medicine. 2020;50(10):1729–1756.
- 3
Heuberger JAAC, Gal P, Stuurman FE, de Muinck Keizer WAS, Mejia Miranda Y, Cohen AF. Repeatability and predictive value of lactate threshold concepts in endurance sports. PLoS One. 2018;13(11):e0206846.
Original researchDOI 10.1371/journal.pone.0206846PubMed 30427900
- 4
Jamnick NA, Botella J, Pyne DB, Bishop DJ. Manipulating graded exercise test variables affects the validity of the lactate threshold and V̇O2peak. PLoS One. 2018;13(7):e0199794.
Original researchDOI 10.1371/journal.pone.0199794PubMed 30059543
- 5
Bentley DJ, Newell J, Bishop D. Incremental exercise test design and analysis: implications for performance diagnostics in endurance athletes. Sports Medicine. 2007;37(7):575–586.
- 6
Heck H, Mader A, Hess G, Mücke S, Müller R, Hollmann W. Justification of the 4-mmol/l lactate threshold. International Journal of Sports Medicine. 1985;6(3):117–130.
Original researchDOI 10.1055/s-2008-1025824PubMed 4030186
- 7
Kindermann W, Simon G, Keul J. The significance of the aerobic-anaerobic transition for the determination of work load intensities during endurance training. European Journal of Applied Physiology and Occupational Physiology. 1979;42(1):25–34.
Original researchDOI 10.1007/BF00421101PubMed 499194
- 8
Dickhuth HH, Huonker M, Münzel T, Drexler H, Berg A, Keul J. Individual Anaerobic Threshold for Evaluation of Competitive Athletes and Patients with Left Ventricular Dysfunction. In: Bachl N, Graham TE, Löllgen H (Hrsg.). Advances in Ergometry. Berlin, Heidelberg: Springer. 1991:173–179.
Book chapterDOI 10.1007/978-3-642-76442-4_26
- 9
Dickhuth HH, Yin L, Niess A, Röcker K, Mayer F, Heitkamp HC, et al. Ventilatory, lactate-derived and catecholamine thresholds during incremental treadmill running: relationship and reproducibility. International Journal of Sports Medicine. 1999;20(2):122–127.
Original researchDOI 10.1055/s-2007-971105PubMed 10190774
- 10
Roecker K, Schotte O, Niess AM, Horstmann T, Dickhuth HH. Predicting competition performance in long-distance running by means of a treadmill test. Medicine and Science in Sports and Exercise. 1998;30(10):1552–1557.
Original researchDOI 10.1097/00005768-199810000-00014PubMed 9789858
- 11
Cheng B, Kuipers H, Snyder AC, Keizer HA, Jeukendrup A, Hesselink M. A new approach for the determination of ventilatory and lactate thresholds. International Journal of Sports Medicine. 1992;13(7):518–522.
Original researchDOI 10.1055/s-2007-1021309PubMed 1459746
- 12
Bishop D, Jenkins DG, Mackinnon LT. The relationship between plasma lactate parameters, Wpeak and 1-h cycling performance in women. Medicine and Science in Sports and Exercise. 1998;30(8):1270–1275.
Original researchDOI 10.1097/00005768-199808000-00014PubMed 9710868
- 13
Beaver WL, Wasserman K, Whipp BJ. Improved detection of lactate threshold during exercise using a log-log transformation. Journal of Applied Physiology. 1985;59(6):1936–1940.
Original researchDOI 10.1152/jappl.1985.59.6.1936PubMed 4077801
- 14
Stegmann H, Kindermann W, Schnabel A. Lactate kinetics and individual anaerobic threshold. International Journal of Sports Medicine. 1981;2(3):160–165.
Original researchDOI 10.1055/s-2008-1034604PubMed 7333753
Specialist information on the methods of performance diagnostics. No medical advice, no diagnosis and no substitute for assessment by qualified professionals.
Further reading
Six models on the same raw data.
In Plenea you choose the model in the analysis step, and the decision is documented. Every method states its source, and older reports can be recalculated.