Spiroergomteric relation for automated method
anaerobicthresold.org by P.Kvaca [1]

The automated method can be used only if the mutual increase of spiroergometric parameters is exponential. Exponential trend of the spiroergometric relation can be roughly judged by three ways. The first two are based on an experience - either own experience of exercise physiologist from the 1st and 2nd Faculty of Medicine, Charles University Prague collaborating on this research or their knowledge from the world literature - experience of other exercise physiologists. The third way is the data analysis of measured data set.

The following procedure of solving has been chosen. Firstly, the data analysis of the measured data files was executed - an algorithm applying two criterions mentioned further in the text detected the exponential trend of spiroergometric relation. The algorithm selected some relations with the possible exponential trend and this selection for the further analysis was employed. Subsequently the selected relations with the relations mentioned in world literature were confronted. Lastly the suitable relations, which would be advisable for the AT determination from spiroergometric parameters, were chosen with the help of experienced exercise physiologists of the Charles University.

Data analysis of two months examination set of the Department of Exercise Medicine has been executed. The examinations were executed on healthy persons by reason of the prescription of physical activity. The same exercise protocol for all tested persons was applied. The load 1 W/kg for the first two minute were set, afterwards the load every minute by 0,5 W/kg to the maximum was escalated. The minimum of measured points in exercise were 3, maximum were 11 points.

The mutual combinations of 15 used spiroergometric parameters in exercise medicine represent 210 relations. The total number of the relations for the set of 28 people reaches 5880 relations, which had to be judged for the exponential pattern. It has been necessary to execute the evaluation automatically (by means of program) because the manual evaluation would be unreasonable in first impression.

The algorithm of the program has to implement the definition - what is an exponential trend of a relation and it has to operate according to unambiguous rules for the selection. The following deliberation has been used for the description of exponential trend. The rules ensue from the figure.

Figure: Criteria for Selection

Deliberation and criteria

The first point of a proper exponential curve is always located bellow the last point. The other points of an exponential curve are located below the constructed join line if the first and the last point of the proper exponential curve are connected.

Two criteria result from mentioned deliberation.
  • Criterion one: The relation is probably unsuitable for the interlacing of exponential curve if the last point is reclined higher than the first point.
  • Criterion two: The rate of points laying below the constructed join line and the total points between the extreme points of the exponential curve gives certain information about the possible exponential trend of the relation; Exponential Trend Ratio - ETR. (We are interested in the number of points placed above the join line contrary to the total number of measured points). ETR equals 100% means the nearly definite exponential trend and 0% vice versa.
The program for data analysis according to the mentioned criteria was compiled and it incorporated following procedure with the data set of spiroergometric examinations. Firstly, the ETR of all the spiroergometric parameters of each examined person are calculated and then the resultant ETR as an average of all persons was achieved. The suitable relation for the next appraisal has been the relation having the ETR higher than 50 %. 30 relations with possible exponential trend from the total number of 210 relations were qualified. They are presented in table.

no. Parameter X Parameter Y ETR (%)
1 Minute Ventilation Oxygen Uptake 90
2 Minute Ventilation Heart Rate 83
3 VCO2 Oxygen Uptake 80
4 Minute Ventilation Pulse Oxygen 80
5 Load Heart Rate 78
6 VEO2 RER 77
7 VEO2 Heart Rate 76
8 VCO2 Pulse Oxygen 76
9 VEO2 Pulse Oxygen 76
10 VCO2 Heart Rate 75
11 VEO2 Load 74
12 VEO2 Oxygen Uptake 74
13 VEO2 VCO2 72
14 RER Heart Rate 71
15 Minute Ventilation VCO2 71
16 Minute Ventilation Load 70
17 VEO2 O2 Utilisation 69
18 VEO2 Minute Ventilation 69
19 RER Pulse Oxygen 63
20 Oxygen Uptake Heart Rate 61
21 RER Oxygen Uptake 61
22 Load Oxygen Uptake 60
23 VCO2 Load 59
24 Load Pulse Oxygen 58
25 RER VCO2 56
26 Oxygen Uptake Pulse Oxygen 56
27 RER Load 54
28 VEO2 VECO2 52
29 Minute Ventilation RER 51
30 RER VECO2 51

Table: Exponential Trend Ratio of 30 Selected Spiroergometric Reactions

The next step has been the confrontation of data analysis results with the world literature according to knowledge of medical co-workers. They selected from the exercise medicine literature six relations with the possible exponential trend [26]. They are mentioned in the table with the ETR.

Parameter Y Parameter X ETR (%)
1 Minute Ventilation VO2 90
2 VCO2 VO2 80
3 VEO2 Load 74
4 Minute Ventilation Load 70
5 RER VO2 61
6 VCO2 Load 59

Table: Spiroergometric relation from the world literature (with Exponential Trend Ratio)

It is evident that spiroergometric relations mentioned in the world literature have very high Exponential Trend Ratio obtained from the data analysis.

The final solution about spiroergometric relation suitability for the AT determination should be considered as a recommendation arisen in accordance with exercise physiologists. They insisted on six spiroergometric parameters (Heart Rate, Minute Ventilation, Load, Oxygen Uptake, Respiration Equivalent, Carbon Dioxide Production). The heart rate is the most important parameter for the prescription of exercise activity. This parameter is easy achieved without complicate devices and therefore is suitable for assignment of the topical level of the organism workload with respect to its anaerobic threshold.

The review of the recommended relations in the following table 2.4 is mentioned. It includes selected spiroergometric parameter together with relation and the value of the exponential trend ratio. Two relations are stated with the heart rate because the approximately same results were achieved - Minute Ventilation 83% and Load 78%.

Parameter Y=f (X) X ETR (%)
1 Heart Rate Minute Ventilation Heart Rate 83
Load 78
2 Oxygen Uptake Minute Ventilation Oxygen Uptake 90
3 Load Load Heart Rate 78
4 Minute Ventilation Minute Ventilation Oxygen Uptake 90
5 VEO2 VEO2 Load 74
6 VCO2 VCO2 Oxygen Uptake 80

Table: Final Recommendation of Spiroergometric Relation


[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
anerobicthreshold.org 2007