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Estimation of maximal lactate 
steady state using the sweat 
lactate sensor
Yuki Muramoto 
1, Daisuke Nakashima 
2, Tsubasa Amano 3, Tomota Harita 3, 
Kazuhisa Sugai 4, Kyohei Daigo 5, Yuji Iwasawa 5, Genki Ichihara 5, Hiroki Okawara 
2, 
Tomonori Sawada 
2, Akira Kinoda 1, Yuichi Yamada 1, Takeshi Kimura 1, Kazuki Sato 1 & 
Yoshinori Katsumata 
1,5*
A simple, non-invasive algorithm for maximal lactate steady state (MLSS) assessment has not been 
developed. We examined whether MLSS can be estimated from the sweat lactate threshold (sLT) using 
a novel sweat lactate sensor for healthy adults, with consideration of their exercise habits. Fifteen 
adults representing diverse fitness levels were recruited. Participants with/without exercise habits 
were defined as trained/untrained, respectively. Constant-load testing for 30 min at 110%, 115%, 
120%, and 125% of sLT intensity was performed to determine MLSS. The tissue oxygenation index 
(TOI) of the thigh was also monitored. MLSS was not fully estimated from sLT, with 110%, 115%, 
120%, and 125% of sLT in one, four, three, and seven participants, respectively. The MLSS based on 
sLT was higher in the trained group as compared to the untrained group. A total of 80% of trained 
participants had an MLSS of 120% or higher, while 75% of untrained participants had an MLSS of 
115% or lower based on sLT. Furthermore, compared to untrained participants, trained participants 
continued constant-load exercise even if their TOI decreased below the resting baseline (P < 0.01). 
MLSS was successfully estimated using sLT, with 120% or more in trained participants and 115% or 
less in untrained participants. This suggests that trained individuals can continue exercising despite 
decreases in oxygen saturation in lower extremity skeletal muscles.
Exercise with appropriate frequency and intensity is paramount to maintaining good health in all generations 
and improving exercise performance in athletes. Maximal lactate steady state (MLSS) is the intensity at which 
constant-workload exercise can be performed for 40–60 min without lactate  accumulation1,2. Above the MLSS 
intensity, blood lactate shows an identifiable increase during constant-workload exercise, with a concomitant 
decrease in oxygen saturation in the vastus lateralis in the  thigh3. MLSS has been utilized as a measure of train-
ing intensity in endurance sports, such as track and  field4,  cycling5, and  swimming6,7. MLSS assessment requires 
several constant submaximal load tests performed on separate days and frequent blood lactate measurements 
during exercise, which are complicated and physically strenuous for the  participants8. Therefore, the lactate 
threshold (LT) and blood lactate accumulation onset time (OBLA) are frequently used instead of MLSS as 
measures of training  intensity8. More specifically, LT and OBLA are thought to reflect  low9 and  high10 intensity, 
respectively, relative to MLSS. However, there are limitations to the use of LT and OBLA for MLSS. Recently, 
several algorithms for MLSS estimation from LT or OBLA have been developed, mainly for use with  athletes4,11,12.
Despite being simple indices for determining training intensity, LT and OBLA require frequent blood lactate 
measurements and exercise cessation to collect blood samples. Since these methods are somewhat invasive, they 
are impractical, particularly for non-athletes or those with no exercise habits. To overcome this limitation, we 
developed a sweat lactate sensor for real-time, non-invasive measurement of sweat lactate. The sweat lactate 
threshold (sLT) is reportedly consistent with the anaerobic metabolic  threshold13. Therefore, we expected that 
sLT could be utilized to estimate MLSS with minimal stress on participants. Additionally, this simple and non-
invasive algorithm may be applicable to non-athletes as well as athletes.
OPEN
1Institute for Integrated Sports Medicine, Keio University School of Medicine, Tokyo, Japan. 2Department of 
Orthopaedic Surgery, Keio University School of Medicine, Tokyo, Japan. 3Keio University School of Medicine, 
Tokyo, Japan. 4School of Veterinary Nursing and Technology, Faculty of Veterinary Science, Nippon Veterinary 
and Life Science University, Tokyo, Japan. 5Department of Cardiology, Keio University School of Medicine, Tokyo, 
Japan. *email: goodcentury21@keio.jp
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This study aimed to verify whether MLSS could be estimated from sLT using a sweat lactate sensor for healthy 
adults, with consideration of their exercise habits, and to investigate whether a decrease in oxygen saturation in 
the vastus lateralis is a factor contributing to the difference in MLSS based on sLT.
Results
In-vitro characterization of the lactate sensor under simulated sweat environments. 
Figure 1 
showed the amperometric response of the lactate sensor to increasing lactate concentrations in 0, 2.5, 5, 10, and 
20 mM. In our sensors, a significant difference was observed in sensor responses to several lactate solutions (2.5, 
5, 10, and 20 mM) with different pH (5, 6, 7, and 8) and different temperatures (25, 31, and 36 °C) (Fig. 1A and 
Online Figs. 1–4). Secondly, a significant response in the sensor to 10 mM lactate solution was observed even in 
the presence of NaCl (10, 25, 50, 100 mM) and KCl (2.5, 5, 10 mM) (Fig. 1B, C). These findings indicated that 
the lactate values (current values) of sweat obtained from this sensor could show a significant enough difference 
to determine the inflection point under various sweat environments.
Characteristics of participants. 
The fifteen participants (14 male, 1 female) had a mean age of 26 ± 6 years, 
mean height of 173 ± 9 cm, mean weight of 67 ± 10 kg, mean skeletal muscle mass of 52 ± 18 kg, mean body fat 
percentage of 18 ± 7%, mean peak  VO2 of 41 ± 5 mL/min/kg, and mean HRmax of 175 ± 9 beats per min (bpm). 
Eleven participants engaged in regular exercise (Table 1).
MLSS based on sLT. 
The sLT was correlated with the VT (r = 0.70) (Online Fig. 5). The Bland–Altman plot 
described no bias between the mean values (mean differences: −3.0 W, respectively) (Online Fig. 6). Constant-
load exercises at 125%, 120%, 115%, and 110% of sLT load were performed in that order, and completed by 8, 
10, 14, and 15 participants, respectively (Table 2, Online Fig. 7). Each result shows the values of participants who 
were able to perform 30 min of exercise. Blood lactate levels at the end of exercise at each load in the aforemen-
tioned order were 6.5 ± 3.7 mM, 4.4 ± 1.1 mM, 4.1 ± 1.2 mM, and 3.7 ± 1.7 mM (Table 2, Fig. 2).  VO2 values (% 
peak  VO2) at the end of exercise were 36.3 ± 4.0 mL/min/kg (84.5 ± 7.2%), 32.8 ± 5.5 mL/min/kg (76.9 ± 8.0%), 
30.7 ± 6.7 mL/min/kg (71.1 ± 11.1%), and 29.0 ± 6.6 mL/min/kg (68.8 ± 13.1%). HR values (% HRmax) at the end 
of exercise were 168.6 ± 14.1 bpm (84.8 ± 6.8%), 158.1 ± 14.8 bpm (79.9 ± 7.4%), 152.6 ± 16.2 bpm (77.5 ± 7.8%), 
and 144.4 ± 15.2 bpm (73.2% ± 7.3%). Among the participants who completed the constant-load exercise at 125% 
of sLT load, one had an increase in blood lactate > 1 mM at the end of the exercise (30 min). Therefore, MLSS 
was 125% of sLT in seven participants, 120% in three, 115% in four, and 110% in one, suggesting that estimating 
MLSS based on sLT was difficult (Table 2). MLSS data obtained from 15 participants were calculated (Table 3, 
35
30
25
20
15
10
5
0
(C) KCL
0
2
4
Current (uA)
Lactate + NaCL
6
Time (min)
10mM
50mM
25mM
100mM
25
20
15
10
5
0
PBS
aCL
N
(B) NaCL
Current (uA)
0
5
10
15
20
25
30
35
0
2.5
5
10
20
(mM)
36٦
31٦
25٦
(A)
PBS
0
2
4
Lactate + KCL
6
Time (min)
PBS
KCL
PBS
2.5mM
10mM
5.0mM
Figure 1.  In-vitro characterization of the lactate sensor under imitated sweat environments. (A) The graph 
shows the corresponding calibration plots of the sensor with pH 7 under different temperature (25, 31, and 
36 °C) conditions. The interference study for individual lactate (B,C). The presence of non-target electrolytes; 
Na, K, and Cl cause negligible interference to the response of our lactate sensors. Applied voltage = 0.16 V versus 
Ag/AgCl. The data were obtained from three samples.
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Table 1.  Characteristics of participants (mean ± standard deviation). P-values refer to the significance of 
differences between the trained and untrained groups. MLSS > 120%: number and percentage of participants 
whose MLSS was 120% or higher. bpm beats per min, HRmax maximal heart rate, peak VO2/kg peak oxygen 
uptake/weight, MLSS maximal lactate steady state, sLT sweat lactate threshold. *p < 0.05.
Measures
All (n = 15)
Trained (n = 11)
Untrained (n = 4)
Mean difference
p-value
95% CI
Cohen’d
Age (year)
26 ± 6
22 ± 4
33 ± 4
−11.3
0.01*
−18.6 to −3.9
2.5
Height (cm)
173 ± 9
173 ± 10
172 ± 7
1.4
0.79
−10.0 to 12.7
0.14
Weight (kg)
67 ± 10
65 ± 8
72 ± 16
−7.6
0.43
−32.1 to 16.9
0.70
Skeletal muscle mass 
(kg)
52 ± 18
52 ± 8
50 ± 10
1.8
0.76
−12.9 to 16.6
0.21
Body fat percentage (%)
18 ± 7
15 ± 6
25 ± 4
−10.0
0.01*
−16.6 to −3.2
1.59
PeakVO2/kg (mL/min/
kg)
41 ± 5
43 ± 3
36 ± 6
6.9
0.13
−3.5 to 17.2
1.72
HRmax (bmp)
175 ± 9
174 ± 8
177 ± 7
−2.3
0.61
−12.3 to 7.7
0.27
MLSS (% of sLT)
120 ± 5
122 ± 4
115 ± 4
7.3
0.03*
1.3 to 13.3
1.78
MLSS > 120% (n,%)
10.67%
9.82%
1.25%
0.03*
Table 2.  Exercise data of participants at each load (mean ± standard deviation). Exercise completion: number 
of participants who were able to achieve 30 min of constant-load exercise. MLSS: number of participants who 
were greatest load among the loads in which blood lactate values at the end of exercise (30 min) increased 
within 1 mM, compared to those at 10 min after exercise initiation. The value of “measures at the end of 
the exercise” is exercise completion. % HRmax heart rate/maximal heart rate, % peak VO2 oxygen uptake/
peak oxygen uptake, bpm beats per min, HR heart rate, MLSS maximal lactate steady state, sLT sweat lactate 
threshold, VO2/kg oxygen uptake/weight.
Relative load based on sLT (%)
125%
120%
115%
110%
Exercise completion (n, %)
8 (53%)
10 (66%)
14 (93%)
15 (100%)
MLSS (n, %)
7 (47%)
3 (20%)
4 (27%)
1 (6%)
Measures at the end of the exercise
 Blood lactate (mM)
6.5 ± 4.4
4.4 ± 1.1
4.1 ± 1.2
3.6 ± 1.7
  VO2/kg (mL/min/kg)
36.3 ± 4.0
32.8 ± 5.5
30.7 ± 6.7
29.0 ± 6.6
 % peak  VO2 (%)
84.5 ± 7.2
76.9 ± 8.0
71.1 ± 11.1
68.8 ± 13.1
 HR (bpm)
168.6 ± 14.1
158.1 ± 14.8
152.6 ± 16.2
144.4 ± 15.2
 % HRmax (%)
84.8 ± 6.8
79.9 ± 7.4
77.5 ± 7.8
73.2 ± 7.3
Figure 2.  Blood lactate for participants who were able to exercise at each load.
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Fig. 3). Blood lactate, % peak  VO2, and % HRmax at the end of exercise at the MLSS load in the full sample were 
4.6 ± 1.3 mM, 77.2 ± 12.7%, and 83.3 ± 6.9%, respectively.
MLSS based on sLT in participants with daily exercise. 
Next, the effect of daily exercise on MLSS 
based on sLT was investigated. The MLSS based on sLT in trained participants was higher than in untrained 
participants (Table 1). The MLSS for the trained group accounted for more than 120% of the sLT, while the 
untrained group accounted for less than 115% of the sLT (P = 0.03, φ = 0.55). These findings suggested that MLSS 
was 120% or more of sLT in regularly trained participants and 115% or less of sLT in untrained participants. To 
determine a physiological contributor to the difference in MLSS based on sLT between regularly trained and 
untrained participants, we investigated the relationship between blood lactate accumulation during constant 
loading tests and a decrease in oxygen saturation in intra-skeletal muscles.
ΔTOI and blood lactate levels in participants with daily exercise. 
ΔTOI strongly correlated with 
blood lactate level at the end of exercise (trained: r = −0.7, untrained: r = −0.8, Fig. 4 and Online Fig. 8). The plot 
revealed that the constant-load exercise was discontinued in the untrained group only when ΔTOI was lower 
than the resting value (Fig. 4, red triangle). In contrast, in regularly trained participants, the exercise continued 
until up to a 15% decrease in ΔTOI, as compared to the resting value (Fig. 4, black circle). Moreover, a steeper 
increase in blood lactate was associated with a decrease in ΔTOI in untrained participants as compared to the 
trained group, suggesting that a slight decrease in ΔTOI immediately contributed to the increase in blood lactate 
(regression line: trained = −0.286, untrained = −0.479). Further, trained participants continued constant-load 
exercise even if their ΔTOI decreased (Fig. 5) (mean difference: −7.4, 95% confidence interval [CI]: −11.4 to 
−3.4, P < 0.01). The optimal cut-off value for completion of the constant-load exercise was estimated to occur at 
ΔTOI of −17% (sensitivity: 0.97, specificity: 1.00) and −2.6% (sensitivity: 0.88, specificity: 1.00) in trained and 
untrained participants, respectively, by the ROC curve analysis (Online Fig. 9).
Table 3.  Exercise data of participants at MLSS (mean ± standard deviation). % HRmax heart rate/maximal 
heart rate, % peak VO2 oxygen uptake/peak oxygen uptake, bpm beats per min, HR heart rate, MLSS maximal 
lactate steady state, VO2/kg oxygen uptake/weight.
Measures at the end of exercise (n = 15)
 Blood lactate (mM)
4.63 ± 1.21
  VO2/kg (mL/min/kg)
32.6 ± 7.1
 % peak  VO2 (%)
77.2 ± 12.7
 HR (bpm)
164.3 ± 15.4
 % HRmax (%)
83.3 ± 6.9
 125%:120%:115%:110% (n)
7:3:4:1
Figure 3.  Blood lactate, heart rate,  VO2/kg at the MLSS in all participants (n = 15). Blood lactate (red), heart 
rate (gray), and oxygen uptake-adjusted weight (blue) at the MLSS in each participant. MLSS maximal lactate 
steady state, VO2/kg oxygen uptake/weight.
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Figure 4.  Correlation between change in tissue oxygenation index (TOI) and blood lactate. The black 
circle represents trained participants, who showed a good correlation between ΔTOI and blood lactate level 
(y = −0.2859x + 3.035, r = −0.7, P < 0.01). The red triangle represents untrained participants, who showed a 
good correlation between ΔTOI and blood lactate (y = −0.479x + 5.2349, r = −0.8, P < 0.01). A steeper increase 
in blood lactate level was associated with a decrease in ΔTOI in untrained participants as compared to trained 
participants. ΔTOI TOI (pre-post).
Figure 5.  Difference in ΔTOI between trained and untrained participants in the completed exercise. Trained 
participants continued constant-load exercise even if their ΔTOI decreased (mean difference: −7.4, 95% 
confidence interval: −11.4 to −3.4, P < 0.01). ΔTOI TOI (pre-post); *: P < 0.05.
Figure 6.  Flowchart of the study protocol. NIRS near-infrared spectrometer, VO2 oxygen uptake.
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Discussion
This prospective study provided novel evidence of successful MLSS estimation via sLT calculation by a wearable 
and non-invasive sweat lactate sensor, with consideration of daily exercise. sLT can be determined independ-
ent of the amount of sweating using a sweat lactate sensor on the upper  arm13. The device also determines the 
inflection point but not the absolute sweat lactate  value13–15. The most significant result was that MLSS approxi-
mated 120–125% of sLT in regularly trained participants and 115% or less of sLT in untrained participants. The 
difference in the physiological response to the decrease in oxygen saturation in lower limb skeletal muscle may 
contribute to this relationship between MLSS and sLT.
Determining MLSS requires multiple constant-load exercise tests. MLSS was defined as the greatest load 
among the loads in which blood lactate values at the end of exercise (30 min) increased within 1 mM, compared 
to those at 10 min after exercise  initiation4,11,12 Therefore, methods have been developed to estimate MLSS 
using LT and OBLA, with MLSS of 124–127% of LT  load4,11 and 90% of OBLA  load12, mainly for  athletes4,11,12. 
Additionally, the Functional Threshold Power (FTP) used by cyclists has been determined through several 
constant submaximal load tests performed on separate days as well as  MLSS16. FTP is a non-invasive method 
for measuring training intensity, which correlates well with  MLSS17. However, LT and OBLA require frequent 
blood lactate measurements and exercise cessation to collect blood samples. FTP is an index specific to cyclists 
that requires several constant submaximal load tests performed on separate days and frequent blood lactate 
measurements during exercise. Therefore, although exercise with appropriate dosage and intensity is essential 
for maintaining good health in all generations, MLSS measurements are impractical, particularly in non-athletes 
or those without exercise habits.
A sweat sensor was developed to monitor sweat lactate values in real-time during progressive exercise in a 
clinical setting and for sports use. Our sensor is highly flexible and can be smoothly adjusted to curved surfaces 
using PET substrates. The upper arm and forehead are appropriate sites to monitor the lactate levels in sweat 
due to a high-sweat rate during exercise, smooth skin surfaces for sensor placement, and noninterference during 
pedaling  tasks13–15. Especially in healthy subjects, the upper arm has been used because of its simplicity of attach-
ment and minimal interference. sLT defined as the first significant increase in sweat lactate concentration above 
baseline based on graphical plots, is consistent with LT calculated from blood samples and ventilatory threshold 
assessed with exhaled gas  analysis13. In this study, MLSS was successfully estimated via sLT, with 120–125% of 
sLT in regularly trained participants and 115% or less in untrained participants. Blood lactate, % peak  VO2, and 
% HRmax at the end of exercise at MLSS load were consistent with data from previous  reports1,2,8,17,18. Report-
edly, 124–127% of blood LT intensity at the running speed was the MLSS intensity in track and field athletes or 
 cyclists4,11. These previous findings were consistent with MLSS load based on sLT in participants who regularly 
exercised. In untrained participants, MLSS approximated 115% or less of sLT. Assessment of appropriate exercise 
dosage and intensity should be further targeted for the well-being of non-athletes. MLSS, estimated in a simple 
and non-invasive manner using a sweat lactate sensor, could be used for health maintenance in non-athletes.
To determine a physiological contributor to the difference in MLSS based on sLT between regularly trained 
and untrained participants, we investigated the relationship between blood lactate accumulation during constant 
loading tests and a decrease in oxygen saturation in intra-skeletal muscles. The constant-load exercise was com-
pleted for 30 min in trained participants without blood lactate accumulation, even with substantial decreases 
in oxygen saturation in lower limb skeletal muscles. This finding suggests that training enables constant-load 
exercise for long periods, even at loads relatively greater than an anaerobic threshold, at which oxygen saturation 
in intra-skeletal muscles can be preserved. In contrast, a steeper increase in blood lactate was associated with a 
decrease in ΔTOI in the untrained group as compared to the trained group, suggesting that a slight decrease in 
ΔTOI immediately contributes to blood lactate accumulation. Exercise tolerance improves through biological 
responses, such as increased blood flow in skeletal  muscles19, improved mitochondrial  function20, and a shift 
from IIb to IIa in skeletal muscle  subsets21. These biological responses are induced by the activation of hypoxic 
response signals following oxygen saturation reduction in skeletal muscles during  exercise22–27. Therefore, the 
extent and variability of oxygen saturation reduction during exercise may be related to training effectiveness. 
Training results in the acquisition of hypoxic tolerance in skeletal muscles, causing increases in exercise endur-
ance and enabling exercise with stronger intensity. Positive feedback between the decrease in oxygen saturation 
in skeletal muscles and improvement in exercise tolerance could maximize training benefits.
Limitations. 
Our findings should be interpreted with consideration of the following limitations. First, 
because of the observational study design, we cannot exclude the influence of selection bias. Second, our study 
included a relatively small number of cases, particularly for the untrained group, and primarily healthy college-
age male individuals. Further research should include untrained participants and women. Third, constant-load 
exercises at 130% of sLT load were not performed in this study. Finally, there was a possibility of non-response 
in the sweat lactate sensor owing to a lack of sweat during exercise. Particularly, older adults and women sweat 
 less28. Therefore, in such cases, adjusting exercise parameters to promote sweating is necessary. However, sLT 
could be clearly determined in all participants in this study.
Conclusions
By dividing the participants into trained and untrained groups, MLSS was successfully estimated using sLT, with 
120% or more of the sLT load in trained participants and 115% or less in untrained participants. This finding 
may involve the ability of an individual to continue exercising despite a decrease in oxygen saturation in the 
lower extremity skeletal muscles. This novel actualized measurement of sLT is expected to enable non-invasive 
MLSS estimation. This simple and non-invasive algorithm can be used as a convenient indicator of good health 
maintenance for non-athletes and a potential guide for training athletes.
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Methods
Participants. 
Fifteen healthy adults representing a broad spectrum of fitness levels, regardless of exercise 
habits, were recruited between May and September 2022. Participants with/without exercise habits were defined 
as “trained”, and “untrained,” respectively. Exercise habit was defined as > 75 min per week of exercise at vigor-
ous  intensity29. The inclusion criteria were as follows: no underlying or pre-existing cardiovascular, respiratory, 
or metabolic diseases; no athletic injuries; non-smokers; and no dietary supplements or medication habits of 
any type. The study protocol was approved by the Institutional Review Board of the Keio University School of 
Medicine (approval number: 20190229) and conducted in accordance with the principles of the Declaration of 
Helsinki. All participants provided informed consent because the Institutional Review Board approved the use 
of oral consent, in accordance with the Japanese guidelines for clinical research.
Experimental procedure
A flowchart of the study protocol is shown in Fig. 6. First, the Ramp stress test was performed using an electro-
magnetically braked ergometer (StrengthErgo8 V2; Fukuda Denshi Co., Ltd., Tokyo, Japan) with a sweat lactate 
sensor (Grace Imaging Inc., Tokyo, Japan), an exhaled gas analyzer (Aeromonitor AE-301S; Minato Medical 
Science Co., Ltd., Osaka, Japan), and a heart rate (HR) monitor (POLAR H10 N; Polar Electro Japan, Tokyo, 
Japan). Subsequently, constant-load exercise was performed for 30 min at 125%, 120%, 115%, and 110% of sLT 
intensity in this order. An electromagnetically-braked ergometer was used during the exercise to determine 
 MLSS12. At least 24 h were allowed between each test (mean: 7.0 ± 2.9 days)5. During constant-load exercise, an 
exhaled gas analyzer, HR monitor, and near-infrared spectroscopy (NIRS) monitor (NIRO-200NX; Hamamatsu 
Photonics K.K., Hamamatsu, Japan) were attached. Blood lactate values were obtained via auricular pricking 
and gentle squeezing of the ear lobe using a blood lactate analyzer (Lactate Pro 2, ARKRAY Inc., Kyoto, Japan). 
Blood lactate levels were measured before exercise and every 5 min during exercise.
Exercise test protocol. 
Participants avoided caffeine and alcohol consumption, which would cause fatigue, 
the day before testing. After measuring resting data for 2 min, participants performed a warm-up exercise for 
2 min at a 50-W load and then exercised at increasing intensities until they could no longer maintain the pedal-
ing rate (volitional exhaustion). The resistance was increased in 25-W increments from 50-W at 1-min intervals. 
Rotational speed was maintained at 70 rotations per min (rpm).
sLT determination. 
A sweat lactate sensor quantifies sweat lactate concentration as a value of current 
because it reacts with sweat lactate and generates an electric current. The value of current can be obtained as 
continuous data within 0.1–80 μA in 0.1-μA  increments13. Further, we investigated whether the lactate values 
(current values) of sweat obtained from this sensor could show a relative difference significant enough to deter-
mine this inflection point under various sweat environments (pH, temperature, and ionic conductivity) with 
several solutions that were close in composition to actual sweat. Regarding the pH and temperature of human 
sweat, it has been reported that sweat has a pH of 5–7 and a skin temperature of 25–37 °C30–32. Therefore, the 
electrochemical characterization of the lactate sensor chip was performed using L-lactic acid solutions in 0, 
2.5, 5, 10, and 20 mM prepared in 0.1 mol/L phosphate buffer solution (PBS) under different temperatures (25, 
31, 36 °C) and pH (5, 6, 7, and 8). Then, the three lactate sensor tips were evaluated in each condition using 
chronoamperometry at an applied voltage of 0.16 V (versus Ag/AgCl). Next, the major electrolytes in sweat are 
Na, K, and Cl. Generally, NaCl varies from 10 to 90 mM and KCl from 2 to 8 mM during  exercise30. Therefore, 
the sensor evaluated a significant response to l-lactic acid solution in 10 mM even in the presence of NaCl (10, 
25, 50, 100 mM) and KCl (2.5, 5, 10 mM).
After calibration using saline for 2 or 3 min, the sensor chip connected to the sensor device was attached to 
the superior right upper limb of the  participant13,14, which was cleaned with an alcohol-free cloth. The upper arm 
has a high-sweat rate during physical  excursions33. In addition, it is a site that does not interfere with exercise 
during pedaling tasks. Additionally, data were recorded at a 1-Hz sampling frequency for mobile applications 
with a Bluetooth connection. Recorded data were converted to moving average values over 13-s intervals and 
individually underwent zero correction using the baseline value. sLT was defined as the first significant increase 
in sweat lactate concentration above baseline based on a graphical plot (Fig. 7)13–15,34.
MLSS determination. 
Blood lactate was measured before exercise and every 5 min during constant-load 
exercise for 30 min at 110%, 115%, 120%, and 125% of sLT intensity. The rotational speed was set at 70 rpm. The 
criteria that did not achieve the exercise and exceeded the MLSS included participants who could not finish the 
trial due to fatigue, but could not maintain bicycle pedaling at 70 rpm, as well as participants who could finish 
30 min of exercise but had an increase in blood lactate of more than 1 mM from 10 min after exercise initiation 
to the end of the exercise. MLSS was defined as the greatest load among the loads in which blood lactate values 
at the end of exercise (30 min) increased within 1 mM, compared to those at 10 min after exercise  initiation12 
(Fig. 8).
Measurement data. 
On the first day of measurement, body weight, body fat, and skeletal muscle mass were 
measured using In-Body (InBody470; InBody Japan Inc., Tokyo, Japan). Expired gas flow was measured using 
a breath-by-breath automated system. Three calibration processes were performed on the system: flow volume 
sensor, gas analyzer, and delay time calibration. Parameters of respiratory gas exchange, including ventilation 
(VE), oxygen uptake  (VO2), and carbon dioxide production  (VCO2), were continuously monitored and meas-
ured using a 10-s average. Skeletal muscle oxygenation in the right thigh was measured using NIRS spectroscopy. 
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The monitor consists of a light-sending probe and a light-receiving probe. Near-infrared light emitted from the 
light-sending unit is absorbed by skeletal muscle tissue, and changes in the intensity of the light returned to the 
light-receiving unit enable tissue oxygenation  measurement35. A pair of probes was attached 4 cm apart on the 
skin over the vastus lateralis muscle in the distal third of the  thigh36,37 and then covered and secured with  tape38. 
In this study, tissue hemoglobin oxygen saturation (tissue oxygenation index [TOI]), calculated using the spa-
tially resolved spectroscopy method, was  assessed39,40.
Statistical analyses. 
All data are presented as means and standard deviations. The obtained HR and  VO2 
were calculated as a percentage of the maximal HR (% HRmax) and peak  VO2 (% peak  VO2). The relationships 
between the sLT and ventilatory threshold (VT) were investigated using Pearson’s correlations. Additionally, the 
Bland and Altman technique was applied to verify the similarities among the different methods. This compari-
son is a graphical representation of the difference between the methods and the average of these methods. As 
previous reports have shown that MLSS is 120% or more of LT intensity, we divided our cohort into two groups 
using the cut-off of 120% of sLT  intensity4,11,12. Unpaired t-tests and Chi-squared tests were used to compare 
participant characteristics between the two groups.
The correlation value was used to determine the relationship between the relative change in TOI from baseline 
(ΔTOI) and blood lactate at the end of the exercise. Unpaired t-tests were used to compare ΔTOI across trained 
and untrained participants.
Figure 7.  Sweat lactate levels during ramp exercise. HR heart rate, VO2/W oxygen uptake/weight.
Figure 8.  Imaging of the constant-load exercise. HR heart rate, VO2/W oxygen uptake/weight, BLt blood 
lactate.
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Receiver operating characteristic (ROC) curve analysis was used to determine the ΔTOI cut-off value for the 
completed constant exercise test. All analyses were performed using SPSS version 28 software (IBM Japan Ltd., 
Tokyo, Japan). Statistical significance was set at P < 0.05.
Data availability
All data from these studies are contained within this manuscript or are available from the corresponding author 
upon reasonable request. Source data are provided in this paper.
Received: 27 February 2023; Accepted: 13 June 2023
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Acknowledgements
We are grateful to Editage for editing this manuscript.
Author contributions
The author contributions are stated as follows; Y.M. and Y.K. drew the manuscript. Y.M., D.N., T.S., H.O., and 
Y.K. prepared the images. Y.M., D.N., T.S., H.O., T.A., T.H., K.S., D.K., Y.I., G.I., and Y.K. collected the patient 
information. A.K., Y.Y., T.K., K.S., and Y.K. provided a critical revision of the manuscript for the key intellectual 
content and supervision. All of the authors have approved all aspects of our work, and have read and approved 
the manuscript.
Competing interests 
No funding was received to conduct this study. Daisuke Nakashima is the shareholder and CEO of Grace Imaging 
Inc., which provided the lactate sensor equipment. The other authors declare no competing interests.
Additional information
Supplementary Information The online version contains supplementary material available at https:// doi. org/ 
10. 1038/ s41598- 023- 36983-8.
Correspondence and requests for materials should be addressed to Y.K.
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© The Author(s) 2023

Estimation of maximal lactate steady state using the sweat lactate sensor.
Muramoto, Yuki,Nakashima, Daisuke,Amano, Tsubasa,Harita, Tomota,Sugai, Kazuhisa,Daigo, Kyohei,Iwasawa, Yuji,Ichihara, Genki,Okawara, Hiroki,Sawada, Tomonori,Kinoda, Akira,Yamada, Yuichi,Kimura, Takeshi,Sato, Kazuki,Katsumata, Yoshinori