Citation: Römer, C.; Wolfarth, B.
Prediction of Relevant Training
Control Parameters at Individual
Anaerobic Threshold without Blood
Lactate Measurement. Int. J. Environ.
Res. Public Health 2023, 20, 4641.
https://doi.org/10.3390/
ijerph20054641
Academic Editor: Lana Ruži´c
Received: 30 January 2023
Revised: 24 February 2023
Accepted: 28 February 2023
Published: 6 March 2023
Copyright:
© 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
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4.0/).
International  Journal  of
Environmental Research
and Public Health
Article
Prediction of Relevant Training Control Parameters at Individual
Anaerobic Threshold without Blood Lactate Measurement
Claudia Römer * and Bernd Wolfarth
Department of Sports Medicine, Charité—Universitätsmedizin Berlin, Humboldt-University of Berlin,
10117 Berlin, Germany
* Correspondence: claudia.roemer@charite.de
Abstract: Background: Active exercise therapy plays an essential role in tackling the global burden
of obesity. Optimizing recommendations in individual training therapy requires that the essential
parameters heart rate HR(IAT) and work load (W/kg(IAT) at individual anaerobic threshold (IAT)
are known. Performance diagnostics with blood lactate is one of the most established methods for
these kinds of diagnostics, yet it is also time consuming and expensive. Methods: To establish a
regression model which allows HR(IAT) and (W/kg(IAT) to be predicted without measuring blood
lactate, a total of 1234 performance protocols with blood lactate in cycle ergometry were analyzed.
Multiple linear regression analyses were performed to predict the essential parameters (HR(IAT))
(W/kg(IAT)) by using routine parameters for ergometry without blood lactate. Results: HR(IAT) can
be predicted with an RMSE of 8.77 bpm (p < 0.001), R2 = 0.799 (|R| = 0.798) without performing
blood lactate diagnostics during cycle ergometry. In addition, it is possible to predict W/kg(IAT) with
an RMSE (root mean square error) of 0.241 W/kg (p < 0.001), R2 = 0.897 (|R| = 0.897). Conclusions: It
is possible to predict essential parameters for training management without measuring blood lactate.
This model can easily be used in preventive medicine and results in an inexpensive yet better training
management of the general population, which is essential for public health.
Keywords:
performance diagnostics; blood lactate; individual anaerobic threshold; training
recommendation
1. Introduction
Reluctance to undertake physical activity and obesity are associated with an increase
in cardiovascular diseases, in particular in coronary heart disease, diabetes mellitus and
a higher level of inﬂammation [1–3]. Research has demonstrated that engaging in regu-
lar physical activity leads to a reduction in both morbidity and mortality rates [4,5]. As
our society continues to face an increasing burden of disease from conditions such as
diabetes mellitus, arterial hypertension, and obesity, the cost of treating these cardiovas-
cular diseases will also become a growing ﬁnancial strain on the healthcare system in the
future [6–11]. Especially, during the COVID-19 pandemic, regular exercising decreased
signiﬁcantly [12]. Consequences may be not only increasing obesity and cardiovascular
diseases but also mental health conditions [13,14]. The WHO Guidelines recommend
regular activity (150–300 min per week of moderate intensity, or 150 min per week of
intensive physical activity) [15]. In order to achieve comprehensive prevention, simple
and inexpensive training recommendations and the prescription of physical activity are
required [16]. Optimizing training intensity recommendations in cardiopulmonary training
requires that the essential parameters heart rate (HR) and training load (W/kg) at individ-
ual anaerobic threshold (IAT) are known [17]. It is necessary to deﬁne individual training
parameters, as several studies have conﬁrmed that training adherence depends on training
intensity [18,19]. Adherence to physical activity is one of the most relevant factors to better
health [20]. Realization of exercise recommendations by health workers is reported to be
insufﬁcient [21,22], which might be caused by the lack of personalized trainings programs.
Int. J. Environ. Res. Public Health 2023, 20, 4641. https://doi.org/10.3390/ijerph20054641
https://www.mdpi.com/journal/ijerph
Int. J. Environ. Res. Public Health 2023, 20, 4641
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Overexertion, deﬁned as the transition from the aerobic to the anaerobic metabolism [23],
may therefore reduce training adherence. To perform optimal training, knowing the heart
rate at the individual anaerobic threshold is essential for better training control. Measuring
these important parameters (HR(IAT) and W/kg(IAT)) is largely limited to competitive
athletes in dedicated sports medicine centers. Performance diagnostics with blood lactate
is one of the most established methods for these kinds of diagnostics [24,25], but it is time-
and cost-intensive [26].
The prediction of IAT was early performed by Conconi et al. by determining heart
rate threshold which shows a high correlation in runners [27]. There are only a few studies
using linear regression models to predict anaerobic threshold on cycling ergometry in the
general population. Mostly athletes were examined, and the number of examined subjects
is low [27–30]. Simple methods for measuring performance are crucial for allowing the gen-
eral population access to the appropriate training parameters, particularly for individuals
who are new to sports. There is a lack of studies examining prediction models for essential
training parameters in the general population using non-invasive methods [31–34]. The
aim of this study was to assess HR(IAT) and W/kg(IAT) by linear regression models to
establish an easy access training recommendation for the general population, as physical
inactivity is an important predictor of mortality [35].
2. Methods
In this study, a retrospective analysis was performed. Secondary data of the Sports
Medicine Institute of the University Medical Center Charité Berlin were analyzed for the
prediction of HR(IAT) and W/kg(IAT) without lactate measurement. All of the ergometry
protocols conducted between 2015 and 2017 were obtained from the institutional sports
medicine information system. Patients who were not included in the study were excluded
for speciﬁc reasons: For the present analysis, the following inclusion criteria were applied:
patients (I) with missing lactate data, (II) with missing heart rate data, and (III) with
insufﬁcient protocols and implausible data. Exclusion criteria were cardio-pulmonary and
musculoskeletal diseases. The study was conducted in accordance with the Declaration of
Helsinki and with the approval of the local ethics committee of Humboldt University Berlin.
2.1. Peak Performance Test
The performance test on the cycle ergometer started at 50 Watt (W) and was raised in
25 W steps after 3 min. Resting heart rate, blood pressure and blood lactate were measured
before the lactate step test was initiated. During the test, heart rate was continuously
measured by electrocardiogram. Blood pressure, blood lactate and RPE (rate of perceived
exertion) were measured in the last thirty seconds of each step. Determination of lactate
threshold (LT = ﬁrst signiﬁcant increase in blood lactate during exercise test starting from
the resting lactate values) and individual lactate threshold (IAT = second signiﬁcant increase
in blood lactate and transition from aerobic to anaerobic metabolism) were assessed using
the method of Dickhuth et al. [36].
2.2. Statistical Analysis
The Kolmogorov–Smirnov test was used to determine whether the continuous vari-
ables were normally distributed, and a descriptive analysis was carried out. The power per
kilogram body weight at the individual anaerobic threshold (W/kg(IAT)) was used as a
measure of individual physical performance. The Pearson correlation coefﬁcient and root
mean square error (RMSE) were used to assess correlation. A two-sided signiﬁcance level of
α = 0.001 was set as the threshold for determining statistical signiﬁcance. Before performing
multiple regression analysis of HR (IAT), all parameters were checked individually for
their respective correlation and linear regression with a very high level of signiﬁcance
p < 0.001. Descriptive analysis was performed and is shown in Table 1. Minimum, mean
and maximum HR and HR after one-, three- and ﬁve-minutes post-workout were examined.
All parameters with a signiﬁcance level p > 0.001 were removed. All statistical analyses
Int. J. Environ. Res. Public Health 2023, 20, 4641
3 of 12
were performed using the SPSS software (IBM Corp. Released 2016. IBM SPSS Statistics
for Windows, Version 25.0. Armonk, NY, USA: IBM Corp.) and Matlab (MATLAB and
Statistics Toolbox Release 2022b, The MathWorks, Inc., Natick, MA, USA).
Table 1. Descriptive characteristics of female and male individuals.
Female (n = 469)
Male (n = 765)
Mean ± SD
Mean ± SD
Age (years)
48.24 ± 19.36
46.61 ± 18.60
Height (cm)
166.25 ± 7.79
180.33 ± 7.93
Weight (kg)
67.12 ± 12.37
84.77 ± 13.53
Pmax/kg (W/kg)
2.16 ± 0.91
2.78 ± 1.02
Pmean (W)
Mean power
89.85 ± 35.44
141.19 ± 48.68
HRmin
Minimum HR
73.30 ± 12.53
70.38 ± 12.41
HRmean
Mean HR
124.00 ± 16.83
123.32 ± 15.94
HRmax
Maximum HR
166.99 ± 20.93
170.13 ± 20.78
HRpw1
HR 1 min post workout
142.43 ± 22.63
144.85 ± 20.04
HRpw3
HR 3 min post workout
115.66 ± 20.04
119.26 ± 17.44
HRpw5
HR 5 min post workout
103.80 ± 18.57
108.59 ± 16.60
HRR
delta HRmax − HRpw5
63.19 ± 14.04
61.54 ± 15.02
P/kg(IAT) (W/kg)
1.58 ± 0.64
1.98 ± 0.77
HR(IAT)
143.99 ± 18.66
141.12 ± 19.46
Study Population
The population consisted of 188 competitive athletes (football, handball, athletics,
volleyball, etc.), 226 prevention and rehabilitation athletes (with various chronic diseases,
e.g., orthopedic, rheumatological or other autoimmune diseases) and 820 recreational
athletes. None of the athletes had known coronary artery disease or heart failure. A total
of 579 had a BMI greater than 25. Overall, 141 individuals of the 226 prevention and
rehabilitation athletes had a BMI greater than 25, 52 individuals in this subgroup had a
BMI greater than 30, and 13 individuals had a BMI greater than 35. Descriptive analysis is
shown in Table 1.
3. Results
We performed multiple linear regression analyses for both HR(IAT) and W/kg(IAT)
using personal parameters such as gender, age, height and weight as well as performance
measurements such as heart rate and power as input parameters.
After each multiple regression analysis, we removed one parameter with the highest
p-value until the desired signiﬁcance level of p < 0.001 was met by all remaining input
parameters.
After completing this process, the following input parameters are included in the multi-
ple linear regression analysis for determining the HR(IAT); see equation in Figure 1: gender;
weight; mean power (Pmean); maximum power (Pmax); mean HR (HRmean); and minimal
HR (HRmin). Using these parameters in multiple linear regression, the determination of
HR(IAT) is possible with an RMSE = 8.77 bpm. The adjusted R-squared is 0.798.
The proposed linear regression model for determining HR at IAT was compared to the
Karvonen formula (Figure 2). The proposed method shows a lower RMSE (8.77 bpm) than
the Karvonen formula (RMSE of 11.2 bpm), and HR determination at IAT is more exact
using linear regression.
The essential parameter W/kg(IAT), which is especially important for determining
changes in performance, was also examined. As explained above, the respective input
parameters were iteratively removed unless they met a level of signiﬁcance p < 0.001. This
includes the removal of the heart rate recovery (HRR = HRmax-HR after 5 min of recovery)
parameter, as its signiﬁcance level was p = 0.057. As a result, only the following four
parameters were included for multiple linear regression analysis to determine W/kg(IAT):
gender; body weight (kg); mean power (Pmean); maximum power (Pmax); maximum HR
Int. J. Environ. Res. Public Health 2023, 20, 4641
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(HRmax). Using these parameters in multiple linear regression (Figure 3), the determination
of W/kg(IAT) is possible with a root mean square error, RMSE = 0.241 W/kg. The adjusted
R-squared was 0.897. Figure 3 shows the comparison between W/kg(IAT) values on the
horizontal axis determined by means of blood lactate values and the W/kg(IAT) values on
the vertical axis determined by means of multiple linear regression.
Int. J. Environ. Res. Public Health 2023, 20, x FOR PEER REVIEW 
4 of 12 
 
 
 
HRS(IAS) = 25.464 
+ 1.0302 × HRmean [bpm] 
− 0.11889×HRmin [bpm] 
− 0.23561 × Pmean [W] 
+ 0.16634 × Pmax [W] 
+ 3.8084 × gender [f = 1, m = 0] 
− 0.09512 × weight [kg] 
Figure 1. The comparison between HR(IAT) values on the horizontal axis determined by means of 
blood lactate values and the HR(IAT) values on the vertical axis determined by means of multiple 
linear regression. 
The proposed linear regression model for determining HR at IAT was compared to 
the Karvonen formula (Figure 2). The proposed method shows a lower RMSE (8.77 bpm) 
than the Karvonen formula (RMSE of 11.2 bpm), and HR determination at IAT is more 
exact using linear regression. 
 
Figure 2. Comparison between regression model and Karvonen formula. 
The essential parameter W/kg(IAT), which is especially important for determining 
changes in performance, was also examined. As explained above, the respective input pa-
rameters were iteratively removed unless they met a level of significance p < 0.001. This 
includes the removal of the heart rate recovery (HRR = HRmax-HR after 5 min of recov-
ery) parameter, as its significance level was p = 0.057. As a result, only the following four 
parameters were included for multiple linear regression analysis to determine W/kg(IAT): 
gender; body weight (kg); mean power (Pmean); maximum power (Pmax); maximum HR 
(HRmax). Using these parameters in multiple linear regression (Figure 3), the determination 
of W/kg(IAT) is possible with a root mean square error, RMSE = 0.241 W/kg. The adjusted 
R-squared was 0.897. Figure 3 shows the comparison between W/kg(IAT) values on the 
horizontal axis determined by means of blood lactate values and the W/kg(IAT) values on 
the vertical axis determined by means of multiple linear regression. 
70
90
110
130
150
170
190
210
70
90
110
130
150
170
190
210
HR(IAT) determined using multiple linear regression
HR(IAT) determined by blood lactate values
70
90
110
130
150
170
190
210
70
90
110
130
150
170
190
210
HR(IAT) determined using Karvonen formula
HR(IAT) determined by blood lactate values
70
90
110
130
150
170
190
210
70
90
110
130
150
170
190
210
HR(IAT) determined using multiple linear regression
HR(IAT) determined by blood lactate values
Karvonen formula
Proposed method
Figure 1. The comparison between HR(IAT) values on the horizontal axis determined by means of
blood lactate values and the HR(IAT) values on the vertical axis determined by means of multiple
linear regression.
Int. J. Environ. Res. Public Health 2023, 20, x FOR PEER REVIEW 
4 of 12 
 
 
 
HRS(IAS) = 25.464 
+ 1.0302 × HRmean [bpm] 
− 0.11889×HRmin [bpm] 
− 0.23561 × Pmean [W] 
+ 0.16634 × Pmax [W] 
+ 3.8084 × gender [f = 1, m = 0] 
− 0.09512 × weight [kg] 
Figure 1. The comparison between HR(IAT) values on the horizontal axis determined by means of 
blood lactate values and the HR(IAT) values on the vertical axis determined by means of multiple 
linear regression. 
The proposed linear regression model for determining HR at IAT was compared to 
the Karvonen formula (Figure 2). The proposed method shows a lower RMSE (8.77 bpm) 
than the Karvonen formula (RMSE of 11.2 bpm), and HR determination at IAT is more 
exact using linear regression. 
 
Figure 2. Comparison between regression model and Karvonen formula. 
The essential parameter W/kg(IAT), which is especially important for determining 
changes in performance, was also examined. As explained above, the respective input pa-
rameters were iteratively removed unless they met a level of significance p < 0.001. This 
includes the removal of the heart rate recovery (HRR = HRmax-HR after 5 min of recov-
ery) parameter, as its significance level was p = 0.057. As a result, only the following four 
parameters were included for multiple linear regression analysis to determine W/kg(IAT): 
gender; body weight (kg); mean power (Pmean); maximum power (Pmax); maximum HR 
(HRmax). Using these parameters in multiple linear regression (Figure 3), the determination 
of W/kg(IAT) is possible with a root mean square error, RMSE = 0.241 W/kg. The adjusted 
R-squared was 0.897. Figure 3 shows the comparison between W/kg(IAT) values on the 
horizontal axis determined by means of blood lactate values and the W/kg(IAT) values on 
the vertical axis determined by means of multiple linear regression. 
70
90
110
130
150
170
190
210
70
90
110
130
150
170
190
210
HR(IAT) determined using multiple linear regression
HR(IAT) determined by blood lactate values
70
90
110
130
150
170
190
210
70
90
110
130
150
170
190
210
HR(IAT) determined using Karvonen formula
HR(IAT) determined by blood lactate values
70
90
110
130
150
170
190
210
70
90
110
130
150
170
190
210
HR(IAT) determined using multiple linear regression
HR(IAT) determined by blood lactate values
Karvonen formula
Proposed method
Figure 2. Comparison between regression model and Karvonen formula.
Int. J. Environ. Res. Public Health 2023, 20, x FOR PEER REVIEW 
5 of 12 
 
 
W/kg(IAS) = 2.2306 
− 3.8992 ×10−3 × HRmax [bpm] 
−5.0916 × 10−3 × Pmean [W] 
+ 6.5394 × 10−3 × Pmax [W] 
+ 71.384 × 10−3 × gender [f = 1, m = 0] 
− 21.407 × 10−3 × weight [kg] 
Figure 3. Impact of the individual input parameters on the W/kg (IAT). 
To better understand the impact of individual input parameters on the W/kg (IAT), 
we have visualized the regression parameters using an effect plot in Figure 4. For this, we 
multiplied the weights of the formula in Figure 3 with the actual values in our database. 
The latter are normalized by subtracting their respective mean values, as this offset is al-
ready modeled in linear regressions in our case 2 2306 W/kg
0
1
2
3
4
5
0
1
2
3
4
5
W/kg(IAT) determined using multiple linear regression
W/kg(IAT) determined by blood lactate values
Figure 3. Impact of the individual input parameters on the W/kg(IAT).
Int. J. Environ. Res. Public Health 2023, 20, 4641
5 of 12
To better understand the impact of individual input parameters on the W/kg(IAT),
we have visualized the regression parameters using an effect plot in Figure 4. For this, we
multiplied the weights of the formula in Figure 3 with the actual values in our database.
The latter are normalized by subtracting their respective mean values, as this offset is
already modeled in linear regressions, in our case 2.2306 W/kg.
 
 
 21.407  10   weight [kg] 
Figure 3. Impact of the individual input parameters on the W/kg (IAT). 
To better understand the impact of individual input parameters on the W/kg (IAT), 
we have visualized the regression parameters using an effect plot in Figure 4. For this, we 
multiplied the weights of the formula in Figure 3 with the actual values in our database. 
The latter are normalized by subtracting their respective mean values, as this offset is al-
ready modeled in linear regressions, in our case 2.2306 W/kg. 
 
Figure 4. Effect plot for individual input parameters on W/kg (IAT) with parameter values normal-
ized to a mean of zero for better comparison. 
4. Discussion 
This retrospective analysis of this dataset was examined to predict heart rate at IAT 
as well as training load (W/kg) at IAT without measuring blood lactate values for cycle 
ergometry. Both heart rate and the number of watts at the individual anaerobic threshold 
are essential parameters for training control. These parameters are currently best deter-
mined via blood lactate diagnostics during ergometry performance testing. A total of 1234 
performance protocols with blood lactate in cycle ergometry were analyzed. Multiple lin-
ear regression analyses were performed to predict the essential parameters heart rate at 
individual anaerobic threshold (HR(IAT)) and workload at individual anaerobic thresh-
old (W/kg(IAT)) by using routine parameters for ergometry without blood lactate. 
HR(IAT) can be predicted with a root mean square error, RMSE of 8.77 bpm (p < 0.001). 
The intention of this regression model is the acceleration of preventive medicine by using 
0
1
0
1
2
3
4
5
W/kg(IAT)
W/kg(IAT) determined by blood lactate values
Figure 4. Effect plot for individual input parameters on W/kg(IAT) with parameter values normalized
to a mean of zero for better comparison.
4. Discussion
This retrospective analysis of this dataset was examined to predict heart rate at IAT
as well as training load (W/kg) at IAT without measuring blood lactate values for cycle
ergometry. Both heart rate and the number of watts at the individual anaerobic threshold
are essential parameters for training control. These parameters are currently best deter-
mined via blood lactate diagnostics during ergometry performance testing. A total of
1234 performance protocols with blood lactate in cycle ergometry were analyzed. Multi-
ple linear regression analyses were performed to predict the essential parameters heart
rate at individual anaerobic threshold (HR(IAT)) and workload at individual anaerobic
threshold (W/kg(IAT)) by using routine parameters for ergometry without blood lactate.
HR(IAT) can be predicted with a root mean square error, RMSE of 8.77 bpm (p < 0.001).
The intention of this regression model is the acceleration of preventive medicine by using
every ergometry to compile an individual training recommendation in primary and sec-
ondary prevention. At once, the greatest challenge and the utmost beneﬁt is a continuous
training adherence. To avoid overexertion, knowing the individual anaerobic threshold is
necessary. This applies for preventive medicine as well as for pre-habilitation to meet the
proposed exercise recommendation of 150–300 min per week by the WHO. Future work
implies to supervise pre-habilitation patients with the recommended regression model, as
standard cycle ergometry can be performed by every general practitioner, and patients can
be examined close to the place of residence.
There is a need for more research in preventive medicine that focuses on developing
better preventive training control methods for the general population. The main leverage
point is the prevention of cardiovascular diseases, which is one of the most causes of
morbidity and mortality. Furthermore, as societies are becoming older, frailty amongst the
elderly population is a growing ﬁnancial burden [37]. Increasing frailty goes in line with a
decrease in quality of life. Regular physical activity can reduce frailty [38], and research
has also shown an improvement for quality of life [39]. This challenge for health systems
needed to be addressed by establishing easy access methods for training control parameters
and training programs for the main population.
Int. J. Environ. Res. Public Health 2023, 20, 4641
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Although lactate performance diagnostics is a well-established method for recording
performance, methodological errors must be considered. Due to constantly increasing blood
lactate values and only intermittently measured lactate values by using the capillary blood
of the earlobe, measurement inaccuracy must be assumed. Furthermore, certain nutritional
methods (e.g., low-carb) are associated with an altered lactate curve [40]. Due to glycogen
depletion, incorrect low blood lactate is measured, which can lead to a misinterpretation of
the lactate curve. A large number of studies examined different threshold models, whereby
an exact determination of the aerobic and anaerobic threshold is better to be regarded as
an aerobic and anaerobic transition [41,42]. The earlier assumption of ﬁxed aerobic and
anaerobic thresholds soon showed individual differences in further investigations and
the need to consider individual threshold methods. Despite these challenges of metabolic
threshold models, the lactate determination for training recommendation was established
as daily routine in contrast to other methods, in the last decades. The cardio-pulmonary
exercise test (CPET), which is applied to determine VO2max and ventilatory thresholds, is
also a method of assessing an individual’s physical ﬁtness. For the collection of respiratory
and metabolic parameters, this is a complex measurement, and expensive equipment
with regular calibration is needed. This method is signiﬁcantly more time-consuming,
requires special trained nurses or sport scientists, and is therefore primarily reserved for
patients with cardiac and pulmonary diseases. The RPE and the walking test are simple
methods to avoid overexertion in preventive and recreational sports. Nevertheless, the
application of RPE is difﬁcult for people who are inexperienced in sports and can easily lead
to overexertion or unchallenged activity. In preventive medical examination, an individual
training recommendation is increasingly demanded by patients.
It could be shown that the lactate accumulation shows inter-individual differences [43–45],
and fixed submaximal threshold concepts (of 2 mmol/and 4 mmol/l) should not be applied for
individual training recommendations. The lactate concentration in the aerobic–anaerobic tran-
sition range is also dependent on muscle recruitment in different movement patterns [46,47].
Individual training recommendations should therefore be specific to the sport. Several studies
have been able to prove the training effect of exercise based on the individual anaerobic
threshold. The determination of the HR(IAT) during the ergometry without lactate diag-
nostics can be used for recommendations of basic endurance and interval training and for
prevention programs.
Lactate measurement examination is an expensive, as lactate measurement equipment
and special trained nurses are required, and time-consuming examination and has until
now rarely been covered by health insurance companies. Depending on the individual,
the test takes forty to ﬁfty minutes, including warm-up, measuring resting heart rate and
recovery time in the end. In various studies, the lactate transition range and the maxi-
mum lactate steady state showed a connection with hormonal and immunological changes,
which at least supports the assumption of an upper anaerobic threshold [48–50]. Therefore,
the individual anaerobic threshold should be considered when making training recom-
mendations for the general population, since long-term training with a disproportionate
increase in lactate can lead to training non-adherence and vulnerability for infections or
injuries, thus bringing the known advantages of regular physical activity [49,50]. Our
regression model allows a good prediction of HR(IAT) with an RSME 8.77 bpm and a
prediction of W/kg(IAT) with a deviation of 0.241 W/kg. Shen et al. examined the velocity
at lactate threshold on a treadmill by using several prediction models with different heart
rates [31]. As with the data in this study, age was not a signiﬁcant parameter and was
excluded in the regression models. However, body mass index was excluded [31], and this
study only included body weight for predicting W/kg(IAT). Interestingly, women seem
to show a slightly higher W/kg unless body height is considered to be negative, in which
case these effects neutralize each other. Differences between the results of Shen et al. also
might be attributed to different physical activity on a treadmill and a cycle ergometry [31].
Sport-speciﬁc differences for HR(IAT) and W/kg(IAT) needed to be considered [51–53],
Int. J. Environ. Res. Public Health 2023, 20, 4641
7 of 12
and further research on regression models for running and rowing should be addressed in
future studies.
The exclusion of heart rate recovery for the prediction of W/kg(IAT) was justiﬁed by
not meeting the signiﬁcance level of p < 0.001. This suggests that HRR may not be a singular
predictor for evaluating physical ﬁtness [54]. As research results are inconclusive and the
evidence is weak [55–57], further research should be performed in larger studies. However,
HRR should be recorded as a longitudinal parameter [54], since changes in HRR showed
good results in recognizing cardiopulmonary diseases [58,59]. In this context, HRR is an
essential parameter, which should be monitored regularly to detect changes in autonomic
function [60].
The Karvonen formula is mainly used for training control in popular sports. The
Karvonen formula uses the heart rate reserve, and it requires that the maximum heart rate
and resting heart rate are determined to apply the formula [61]. By multiplication with a
ﬁtness level factor (0.8 for athletes; 0.6 for recreational athletes; and 0.3 for untrained people),
the heart rate at the anaerobic threshold can be calculated [61]. The Karvonen formula
was applied to the examined measurement protocol results in this study. The results of
using the Karvonen formula with a factor of 0.7, due to the predominantly athletic clientele
of the sports medicine university outpatient clinic, are shown in Figure 2. In comparison
to the measured heart rate at IAT, the scatter diagram reveals a good correlation with a
higher RMSE of 11.2 bpm in comparison to the regression model of this study (RMSE
8.77 bpm). The shape of the curve indicates an overestimation of the low values and an
underestimation of the high HR values at the IAT. The Karvonen formula also uses resting
HR and maximum heart rate to determine HR(IAT). Both heart rates are individual values,
and maximum heart rate is especially difﬁcult to determine for the general population,
especially as maximum heart rate changes with age [62–64]. Thus, an initial determination
of maximum heart rate is also required for the Karvonen formula and should be acquired
under medical supervision, especially for individuals > 35 years to cardiovascular adverse
events. Due to the improved prediction based on a regression model determined in this
study, we recommend cycle ergometry in medical supervision with the regression model
identiﬁed in Figure 1.
In preventive medicine, ergometry is also recommended for every sports beginner and
returner over the age of 40 (for men) and over 55 (for women), according to the German
guideline for preventive medical check-ups in sports. In contrast to lactate performance
diagnostics, ergometry can be carried out by almost any general practitioner or as part of
an occupational medical examination. However, an individual training recommendation
is usually only given by sports physicians, since a respective specialization for individual
training advice is missing. Due to the increasing number of cardiovascular events, obesity
and an increasingly aging population, there is a health gap to reach the general population
with individual training recommendations and to examine the full scope of preventive
medicine. The proposed regression model differs from other studies with a signiﬁcantly
higher number of study protocols examined in a heterogeneous population [27,28]. In
addition, further research should examine whether shorter exercise tests, such as the 6-MWT
(6-min walking test), can be used for a regression model prediction of essential parameters
for training control [65]. Studies in obese individuals demonstrated promising potential
to assess individual respiratory threshold [65–67]. Especially obese and older subjects or
individuals with other disabilities which rule out cycle ergometry might beneﬁt [65]. Thus,
a regression model for cycle ergometry with a shortened protocol should be addressed in
future studies, as these shorter tests can be performed more regularly to examine training
improvement and address the changed HR(IAT) after consistent training [66]. Considering
the results of this retrospective study, we recommend the output of a training program with
an individual training heart rate at IAT and watt range at IAT, provided after every check-up
examination using cycle ergometry in medical supervision, including the recommendation
of the WHO [15].
Int. J. Environ. Res. Public Health 2023, 20, 4641
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Future Work
As it is known that also children and adolescent obesity has been continuously rising
during the last few years [68], there is a need to ﬁnd approaches for physical activity
in these age groups, since chronic diseases will start in early ages and will have a huge
impact on GNP. Further studies are necessary to establish regression models for HF(IAT)
for adolescents to teach them a healthy and adequate regular exercise program with a
potentially better exercise adherence, since exercise adherence is one of the most encourag-
ing parameters for health [20]. These exercise programs should be established in schools
under supervision and with regular physical examinations. Furthermore, research has
shown that pre-habilitation can be a relevant beneﬁt prior to chemotherapy or extensive
operations [69,70]. As neoadjuvant chemotherapy is associated with decreasing aerobic
endurance [70,71], there is a need for easy access training therapy not only in primary but
also in secondary and tertiary prevention. Measuring HF(IAT) at routine secondary and
tertiary preventive examinations may improve exercise adherence; further research in these
subgroups is necessary.
Further goals of these examinations are an establishment of pre-habilitation offers close
to home, besides the expansion of the preventive individual training recommendations
for the general population. An individual training recommendation for pre-habilitation
could therefore be made directly by the attending general practitioner or cardiologist. A
gap in care, of mostly only a few sports medicine offers, could thus be closed. Further
examinations with other ergometer types (rowing ergometer, elliptical) are planned in
order to enable a conversion of HR(IAT) and different ergometer types in prevention and
pre-habilitation.
5. Limitations
Incorrect entries during the manual transmission of the lactate values must be consid-
ered. These were minimized in advance by means of a plausibility check of the entire data
set. The sample size in this study is appropriate for generating a valuable prediction in
comparison to other studies [31,72]. The age and gender distribution may vary in compari-
son to the general population, as the examined population includes more physically active
individuals, especially in the younger age groups. Furthermore, a heart rate deviation of
8.77 bpm is not appropriate for athletes in professional sports, although a blood lactate test
or cardiopulmonary exercise test (CPET) is still recommended for this clientele. This regres-
sion model is suitable for cardiorespiratory endurance sports. It should be noticed that it is
not applicable for resistance or interval training; individual training recommendations for
these kinds of training should be considered.
At the same time, ergometry offers a simple and inexpensive measuring method that
can be performed in the outpatient and inpatient sector and represents a suitable procedure
for popular sports and preventive medicine to monitor cardiorespiratory training.
6. Conclusions
In conclusion, it is possible to derive relevant parameters for training control after
a standard cycle ergometry without performing a blood lactate test by using regression
models to predict HR(IAT) and W/kg(IAT) for the general population. This enables training
control without blood lactate diagnostics or CPET and does achieve enormous time and
ﬁnancial savings for active exercise therapy as well as for preventive and rehabilitative
medicine. Regular individual test repetition allows the consideration of short-term training
adaption and supports continuous training progress.
Author Contributions: Conceptualization, C.R. and B.W.; Methodology, C.R.; Formal analysis, C.R.;
Investigation, C.R.; Writing—original draft, C.R.; Writing—review and editing, B.W.; Supervision,
B.W.; Project administration, B.W. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Int. J. Environ. Res. Public Health 2023, 20, 4641
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Institutional Review Board Statement: The study was conducted in accordance with the Declaration
of Helsinki and approved by the Institutional Review Board (or Ethics Committee) of Humboldt
University (protocol code HU-KSBF_EK_2018_0004; date of approval 2018/05/09).
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: The data presented in this study are available on request from the
corresponding author. The data are not publicly available due to data privacy regulations.
Conﬂicts of Interest: The authors declare no conﬂict of interest regarding this publication.
Abbreviations
CPET
cardiopulmonary exercise test
HR
heart rate
HR (IAT)
heart rate at individual anaerobic threshold
HRmax
maximum heart rate
HRR
heart rate recovery = HRmax-HR after 5 min of recovery
Pmax
maximum power output
W/kg(IAT)
Watt per kg at individual anaerobic threshold
RMSE
root mean square error
W
Watt
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Prediction of Relevant Training Control Parameters at Individual Anaerobic Threshold without Blood Lactate Measurement.
Römer, Claudia,Wolfarth, Bernd