Method for the automated anaerobic threshold determination
for by P. Kvaca [1]

Because of the above-mentioned reasons there has been need to develop a transparent method suitable for the automated computer processing of spiroergometric parameters measured in average values with the minimal influence of the physician during the Anaerobic Threshold determination.

Inspiration for the new procedure was found by the methods serving for the evaluation of invasively gained parameters. Namely; the Anaerobic Threshold determination from invasive gained parameters (Lactate level, basis surplus) is based on one principle - lactate increase is treated as exponential [2]. Therefore it is performed the interlacing of measured points by an exponential curve. This is also practised if the number of points is small. Minimal number of measured points is three; optimal number of points is seven [3].

Exercise medicine used 15 spiroergometric parameters in all - Load, Time, Oxygen Utilisation, Content of Carbon Dioxide, Minute Ventilation, Heart Rate, Minute Ventilation by BTPS factor, Minute Ventilation by STPD factor, Oxygen Uptake, Carbon Dioxide Production, Respiratory Exchange Ratio, Respiratory Equivalent (VEO2), Respiratory Equivalent of Carbon Dioxide (VECO2), Pulse Oxygen, Mass Oxygen, mutual increase of some parameters can be regarded as exponential. So hypothesis is - if a spiroergometric relation with the exponential pattern is found, then the model of exponential growth on such relation can be applied and the Anaerobic Threshold like invasive parameters can be determined. The spiroergometric relation having the best fit to the exponential model can be selected with the help of mutual analysis of spiroergometric parameters.

The algorithm of the method has four steps. Firstly, all points of the spiroergometric relation are interlaced with the exponential regression curve. Secondly, the tangents are constructed at the initial and end point of measurement. Thirdly, the intersection point of these tangents is determined. Lastly, for the nearest point on the exponential relation and the intersection of the tangents is searched. This point as an anaerobic threshold is accepted.

Contrary to used methods this procedure utilises all points of the measurement together. Moreover, the Anaerobic Threshold determination is independent of the regressive model construction against of regressive model of two linear lines. That model incorporates the Anaerobic Threshold determination and regression together and the result depends on the division of measured points. The presented procedure is uniform for all relations with the exponential trend. Mainly the evaluation is independent on physician experience, because no group division of measured point of examination is practised and the influence of physician is minimised.

Method Derivation

The method is derived from the figure.
Determination of Anaerobic Threshold
Determination of Anaerobic Threshold

The task is find the point laying on the regresive interlaced exponential closest to the intersection of tangent of the first and last point. The mathematical derivation leads to the transcendental equation; the simplest form is presented.
Determination of Anaerobic Threshold

This equation represents the mathematic model of the anaerobic threshold. A,B are coeficients from the general formula of exponential

The resultant determination of the anaerobic threshold point (xANP,yANP) by the equation is possible to achieve by various numerical ways. The final software implementation depends on a programmer and the library of the development environment.

Example of the Anaerobic Threshold determination

The procedure mentioned above is presented on the relation
Respiratory Minute Volume = f (Load).
Eleven points were measured during the examination (see table).

Minute [min.] 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Load [W] 75 150 210 240 270 300 330 360 390 420 450
MV [l/min.] 25 46 47 60 73 79 92 106 120 130 143

Figure: Example of Measured Values (Men, 19 years, Triathlon)

The suggested procedure of the anaerobic threshold determination fulfils the demanded requirements. It corresponds with the condition of:
  • Simple technical equipment – the method processes average recorded values, therefore it is no need for expensive devices measuring breath by breath, but it meets cheaper devices measuring in average values.
  • Independence of evaluator’s experience – the evaluation is executed by one algorithm independent of physician experience during evaluation. It is not executed any dividing of the measured data which could be accomplished differently by different physicians and therefore the influence of physician is minimised.
  • Reproducibility – the AT determination from the same data will be always identical. The presented procedure is uniform for all relations with the exponential trend.
  • Simple implementation – the method was implemented in various programming languages and environments (C, MATLAB Script Language, EXCEL). The EXCEL implementation [4] shows the simplicity of the method because algorithm was implemented by the exercise physiologist.
  • Transparency – the algorithm is at everyone’s disposal and it has been published. Best available in [5]


[1] Kvaca, P., Radvansky., J., Cermak, M.: "Determinaton of Anaerobic Threshold from Spiroergometric Parameters - Method for Computer Implementation." Med. Sport. Boh. Slov., Vol. 7(1), pp. 14-19: 1998 [2] Wasserman, K.W., J.E. Hansen, D.Y. Sue, B.J. Whipp: Principles of Exercise Testing and Interpretation. Philadelphia: Lea&Febigner, 1987. [3] Placheta, Z.: Exercise diagnostic and activity prescription in the internal medicine. MU Brno: Brno, 1992 [4] Vilikus, Z., Kvaca, P.: "Assessment of Anaerobic Threshold from Spiroergometric Parameters in the Spreadsheet EXCEL 97." Physician & Technology, Vol. 31 (1),pp. 7-12, 2000 [5] Kvaca, P.; Vilikus, Z.; Assessment of Anaerobic Threshold as a Software Application in MS EXCEL . Published in: Research in Sports Medicine, Volume 10, Issue 3 2001 , pages 151 - 164 ©2007