The concept involved designing a U-shaped buckle (Figure 1A) that is both water- and pressure-proof and equipped with integrated strain gauges. These gauges enable the detection of pulling forces exerted on the buckle, facilitating the monitoring of alterations in chest circumference during underwater activities (Figure 1C). The description of this force sensor has been previously documented (Sieber et al., 2022). The custom buckle was crafted through a conventional biomechanical engineering design process employing machine drawing techniques. The choice of stainless steel as the buckle material was made to ensure its suitability for use in saltwater environments. The sensor was calibrated by applying a force of 10 N to one of its legs, producing a slight bending of the section connecting the two legs (Figure 1A). The applied force was correlated with the electrical signal from the sensor. To ensure water resistance, the entire buckle, including the strain gauges, was coated with a multipurpose rubber coating (Plasti Dip International, Blaine, MN). The strap from a commercially available Polar heart rate belt (Polar T34, Polar Electro, OY, Finland) was used to place the buckle on the chest (Figure 1B).

An improved version of a data logger, constructed by our laboratory previously, was used to read out the signals of the sensor-equipped buckle (Mulder et al., 2021; Figures 1A, D). Due to the low amplitude of the signals of the sensor-equipped buckle, it was necessary to employ an amplifier and a high-resolution analog-to-digital converter. We opted for the AD7192 analog-to-digital converter by Analog Devices, which is specifically designed for strain gauge signal acquisition. This integrated circuit combines a programmable gate array with a maximum 128x amplification, a 24-bit sigma–delta ADC, and a filtering stage, which effectively suppresses noise, particularly from 50 or 60 Hz power lines. Further improvements to the data logger included a USB port, a Bluetooth module, a digital pressure sensor, and a 3 × 16 character LC display.

The calibration procedure aimed to test the accuracy of the force sensor to estimate the vital capacity (VC). Details about the VC calibration are presented in Supplementary Material. The equation for the predicted VC was VC = 1.6 + (0.4396 × amplitude). The difference between the measured VC and the predicted VC was 0.00 ± 0.7 L (Supplementary Figure S1B).

The study included 21 participants (5 female and 16 male) with a mean ± SD age of 44 ± 7 years, a height of 178 ± 9 cm, a weight of 73 ± 10 kg, and a lung vital capacity of 5.82 ± 1.22 L. All participants were trained freedivers. Their training load was 5 ± 7 h per week. The study was conducted during two freediving national competitions. The divers competed in four pool disciplines. The participants received written and oral information on the protocol, after which they signed an informed consent document. The protocol was approved by the Swedish Research Ethics Authorities (EPM; #2019-05147) and complied with the Helsinki Declaration of 2004, apart from preregistration in a database.

The study involved a dry static apnea ramp test with durations of 1, 2, and 3 min, respectively, spaced by 2 min of recovery (Figure 2).

A field laboratory was setup within the same pool area where the competitions took place. Participants were required to have a minimum of 12 h of rest following maximal performance and at least 2 h of fasting before initiating the test. Height, weight, and slow vital capacity were measured in triplicate in standing conditions, and the largest volume was used (Compact Expert, Vitalograph, Buckingham, United Kingdom). The participants filled out a questionnaire with information on the training load and personal best achievements in different freediving disciplines in the last 12 months. The participants performed a series of three apneas with fixed duration in dry conditions and the seated position (Figure 2). A researcher carried out a 2-min countdown before starting. At 30 s before apnea, a nose clip was applied, and 20 s before apnea, a mouthpiece was offered to breathe through. Ten seconds before the apnea, the countdown continued second by second.

Participants were instructed to exhale completely and then take a large, but not maximal, inhalation before starting the apnea voluntarily; this technique results in a volume of approximately 80 - 85% of the vital capacity (Schagatay and Holm, 1996). The participants were instructed to avoid hyperventilation. An experimenter closely monitored peripheral arterial oxygen saturation S_pO₂ and was ready to interrupt the apnea should it fall below 65%. The room temperature was 26.9°C ± 2.0°C.

P _ETCO₂ was measured before and after every apnea via an infrared-based gas measurement module (LifeSense LS1-9R, Nonin Medical Inc., Plymouth, United States). The diver breathed through a disposable mouthpiece with a bacterial filter connected to a T-valve with two one-way valves (AFT21, Biopac Systems, Goleta, United States). S_pO₂ and heart rate (HR) were measured using a reflectance sensor (800R, Nonin Medical Inc., Plymouth, United States) placed on the forehead 1 cm over the left eye and connected to a clinical monitor (LifeSense, Nonin Medical Inc., Plymouth, United States). Breathing movements were measured continuously using the prototype force sensor (Sieber et al., 2022).

Six male freedivers were also outfitted with the prototype force sensor prior to engaging in their freediving competition performances. This was done to assess the signal quality in the underwater environment.

P _ETCO₂ used was the highest value measured after the last exhalation before the apnea. The data from the data logger were extracted and analyzed with custom-made scripts using MATLAB (R2022b, MathWorks Inc., Natick, United States). Within the final minute leading up to the last exhalation before commencing the breath-hold, both breathing frequency and signal amplitude were extracted for analysis. The number of peaks in the respiratory signal represented the RR, and the prominence of the signal was used as the surrogate of Vt. With those values, the estimated minute ventilation (eMv) was calculated as the product of the RR and the amplitude of the prominence (RR x prominence; Figure 3).

The statistical analysis was carried out using SPSS 27 software (IBM Corp, Armonk, United States). The data were tested for normality using Shapiro–Wilk test and are reported as the mean ± SD. Outliers were defined as cases with a studentized deleted residual greater than three standard deviations (SD). A Spearman’s correlation test was run to assess the relationship between VC and P _ETCO₂ and the amplitude of the signal from the force sensor. A one-way repeated measures analysis of variance (ANOVA) was used to compare VC and amplitude of the respiratory signal and compare P _ETCO₂, amplitude, and eMv before every apnea. The Bonferroni correction for multiple comparisons was applied. Significance was observed at p < 0.05. A linear regression was run to predict PE_TCO₂ from the eMV before every apnea. The Bland–Altman method was used to assess the agreement between the measured VC and predicted VC and between measured PE_TCO₂ and predicted PE_TCO₂ (Bland and Altman, 1986). The accepted clinical limits of agreement (LOA) for capnography are ≤5 mmHg (Wu et al., 2003), but the LOA between PE_TCO₂ and PaCO₂ could be as large as + 31 mmHg (İşat et al., 2023). When comparing two methods for measuring PE_TCO₂, the LOA could be 11 mmHg (Tamashiro et al., 2023). We set the accepted LOA to ≤10 mmHg. Effect sizes were estimated by the partial eta squared ( η p 2 ) and the generalized eta squared ( η G 2 ) and are presented with a 90% confidence interval (CI). An effect size of 0.01–0.05 was considered small, 0.06–0.13 was considered medium, and 0.14 and above was considered large (Cohen, 1988; Bakeman, 2005; Lakens, 2013).

End-tidal carbon dioxide (P _ETCO₂) data before the first apnea were missing for one participant; therefore, analyses for apnea 1 were conducted with data from 20 participants, as indicated in the results.

P _ETCO₂ was lower before the last apnea (A3) than before the first apnea (A1, p = 0.034, η p 2 = 0.16, 90% CI [0.01–0.31], and η G 2 = 0.03; Table 1). The RR was lower in A2 than in A1 (p = 0.034, η p 2 = 0.20, 90% CI [0.02–0.34], and η G 2 = 0.05; Table 1).

The signal from the device was clear, and RR and amplitude were easily detectable (Figure 3). The amplitude was larger in A2 and A3 than in A1 (p < 0.001, η p 2 = 0.36, 90% CI [0.12–0.52], and η G 2 = 0.05; Table 1). The product of the amplitude and the respiratory rate (eMV) was higher in A3 than in A1 (p < 0.001, η p 2 = 0.35, 90% CI [0.14–0.49], and η G 2 = 0.04; Table 1).

For A1, the correlation did not reach significance (r _s = −0.371 and p = 0.054, Figure 4A), while there was a moderate negative correlation for A2 (r _s = −0.500 and p = 0.010; Figure 4B) and for A3 (r _s = −0.512 and p = 0.009; Figure 4C).

A linear regression analysis revealed a significant predictive relationship between eMv and P _ETCO₂ in A1 (F (1, 18) = 6.629 and p = 0.019; Figure 4A), A2 (F (1, 19) = 13.994 and p = 0.001; Figure 4B), and A3 (F (1, 19) = 9.600 and p = 0.006; Figure 4C). eMv accounted for 27% of the explained variability in A1, 42% in A2, and 34% in A3. The linear regression equation for every apnea (Figure 4) was used to calculate the predicted P _ETCO₂ (predP _ETCO₂) before the three apneas (Table 1). The difference between P _ETCO₂ and predP _ETCO₂ was −0.00 ± 4.5 mmHg for A1, −1.15 ± 5.0 mmHg for A2, and −0.00 ± 5.2 mmHg for A3 (Figure 5).

The quality of the respiratory signal recorded in water before starting apneic performance was satisfactory (Figure 6).

We also found that freedivers hyperventilate without noticing as they keep RR within normal or even in the lower range of normal values, which explains the previous observations in our group (unpublished work). The hyperventilation is, thus, solely due to increasing Vt. This emphasizes the challenge of quantifying the depth of breathing, a parameter that is less easily observed than RR both by the diver and observer. Quantifying the extent of hyperventilation is critical as severe hypocapnia correlates with reduced cerebral blood flow. In healthy participants, a 31% decrease in cerebral blood flow at a PaCO₂ level of 26 ± 2 mmHg has been reported (Fortune et al., 1995). Even moderate hyperventilation can cause a 20% reduction in brain blood flow (Reivich, 1964). Additionally, patients with brain hypertension also demonstrated up to a 34% increase in brain tissue hypoxia when P _ETCO₂ values fell below 25 mmHg (Carrera et al., 2010). Some participants in our study, particularly before the third apnea, experienced severe hypocapnia (PE_TCO₂ ≤ 25 mmHg), and divers who initiate a dive with severe hypocapnia could be at a higher risk of BO. Hyperventilation alone could be a contributing factor to a transient loss of consciousness (Immink et al., 2014). At present, the relationship between the severity of hypocapnia and BO remains unclear.

During quiet breathing, Vt is mainly determined by the diaphragm contraction, which induces small changes in the vertical volume of the lung (West and Luks, 2021). As the force sensor detects changes in the circumference of the thorax, it is expected to be less sensitive at lower Vt, such as in A1. However, hyperventilation typically entails a more pronounced movement of the diaphragm and accessory muscles. Consequently, this amplifies the thoracic diameter, thereby enhancing the potential to detect an increase in chest circumference using the force sensor. In our study, the estimated Vt constituted nearly 58% of the VC. We acknowledge the limitation at low volumes, which explains why we cannot estimate VC or Vt with 100% accuracy and why the correlation with P _ETCO₂ was not significant in A1. This limitation applies to all the techniques used to estimate Vt from wearables as estimating it based on the movements of the chest wall is challenging (Monaco and Stefanini, 2021). As our intention is not to use it in a clinical setting but to monitor athletes for high respiratory activity, we consider that our results are suitable for exploring practical applications in different freediving situations, including saltwater and depth. This study acts as a proof-of-concept for applying breath analysis to estimate P _ETCO₂ levels during various underwater performances.

Additionally, the respiratory signal proved instrumental in detecting thoracic changes associated with “lung packing”—a maneuver employed by freedivers to enhance their total lung capacity (Örnhagen et al., 1998; Figure 6). This maneuver was initially described as glossopharyngeal breathing in post-polio patients (Dail et al., 1955).

Our results apply only to dry static apneas in the sitting position, so the device should be further tested in underwater scenarios.

Additionally, despite most of the measurements being within the limits of agreement, there was a tendency to underpredict P _ETCO₂ when it was close to normal values. This means that during normal ventilation, the changes in the thoracic circumference were small and did not exert enough force in the sensor, so the amplitude of the signal was lower than expected. As we measured the changes in chest circumference in only one place, we could have missed information when ventilation was shallow or was only affecting the upper part of the chest.