Contribution of flow state to the discrepancy between perceived exercise intensity and physiological intensity during endurance bike exercise

Abstract

Background

The flow phenomenon, achieving a heightened state of concentration, is characterized by an autotelic experience, which may reduce the perception of physical exertion during sports activities. It has been extensively documented in sports and is associated with exceptional performance. However, despite comprehensive descriptions of the autotelic experience in flow, the physiological mechanisms underlying flow remain elusive, limiting its reproducibility and broader application. This study aimed to elucidate the contribution of flow to the discrepancies between perceived exercise intensity and physiological intensity during endurance exercise using an exercise bike.

Methods

We assessed specific conditions conducive to flow during endurance exercise on a bicycle ergometer. Flow states were evaluated using a shortened version of the Flow State Scale, whereas subjective perceptions of exercise intensity were measured using the Rating of Perceived Exertion (RPE). Physiological responses were monitored by measuring heart rate (HR), oxygen consumption, breathing frequency, ventilation, and oxy- and deoxy-hemoglobin levels for changes in cerebral oxygenation at the prefrontal cortex assessed using near-infrared spectroscopy.

Results

Participants were categorized into RPE alleviation and escalation groups to examine individual differences in perceived exertion. RPE changes significantly differed between the two groups (p = 0.0002), despite no significant difference in HR changes (p = 0.36). The discrepancy ratios between perceived and physiological exercise intensity also significantly differed between groups (p = 0.001) and were negatively correlated with flow state levels (r = − 0.56).

Conclusions

These findings advance our understanding of the physiological and neurological correlates of flow states during physical activity, with potential applications extending beyond sports performance enhancement to domains such as education and arts.

Background

The phenomenon where players in various sports enter a heightened state of concentration has been widely documented as giving rise to distinct performances. This phenomenon has been subtly explained by various concepts such as flow, achievement zone, and runner height [1–6]. Players attaining such states frequently exhibit higher than usual performance. The acquisition of such states is important for augmenting a player’s skill. These studies emphasize the state of flow during physical activities in endurance sports. The concept of flow, coined by Csíkszentmihályi [7, 8], is a characteristic mental state of complete concentration on the activity that a person is performing. This state is characterized by factors such as concentration in the present moment, merging of action and awareness, loss of self-consciousness, sense of control, distortion of temporal experience, clear feedback, clear goal/purpose, engrossment in the experience, and autotelic experience. These factors are considered characteristic properties of the flow state, as well as optimal conditions for entering the flow state. However, despite extensive psychological characterization, the underlying physiological characterization of flow in endurance sports, particularly those contributing to its autotelic nature, remain insufficiently understood. If how its autotelic nature may influence the perception of physical exertion during sustained exercise can be understood, the reproducibility of this autotelic effect in endurance sports could be enhanced using physiological and neural indicators.

The flow state has been reported in various activities, most notably within sports, where instances of its manifestation have been consistently reported [9–13]. Since flow has the potential to maximize innate human potential, it is expected to be utilized in all aspects of daily life beyond sports, such as education and art [14–16]. Specifically, applications of the flow state in athletic competitions have high potential in the field of sports psychophysiology [17, 18]. Indeed, the potential impact of the flow state on performance has been suggested across various athletic populations, including climbing, cycling, figure skating, golf, soccer, swimming, tennis, and volleyball [5, 9]. However, despite consistent reports of the beneficial effects of flow in sports, supported by recent meta-analyses [19], experimental methods to reliably induce flow and measure associated physiological responses remain underdeveloped. Consequently, the practical application of flow states in athletic contexts has not been fully explored or utilized.

This limited utilization is partly because the flow phenomenon is sensed internally and has not been understood as a physiological phenomenon and because physiological indicators have not been utilized to facilitate entry into the flow state. For example, while the transient hypofrontality theory posited that the flow state would be accompanied by reduced prefrontal cortex (PFC) activity, other studies have reported increased PFC activation during flow states [20]. Electroencephalogram (EEG) correlates of the flow state have been suggested, but they have not yet been used for reproducing the flow state [17, 21, 22]. The relationship between heart rate variability and flow has also been studied; however, its application in endurance sports remains technically challenging due to the elevated heart rate and the dominance of sympathetic nervous activity in endurance sports [23]. Therefore, the specific physiological characteristics required to reproduce such states remain ambiguous, thereby impeding the realization of reproducibility and applications of the flow state in endurance sports.

To address the limited understanding of the specific characteristics required to reproduce the flow state in endurance sports, particularly the autotelic component, which may influence perceived exertion, we developed an experimental protocol that integrates both subjective and physiological assessments during endurance cycling. Bike exercise was selected due to its low measurement noise and precise load control. Simultaneous measurements were conducted for key physiological parameters, such as cerebral oxygenation in the PFC, which is associated with concentration [24], perceived exertion, and the flow state. By analyzing the temporal dynamics and interrelationships among these indicators during sustained moderate-intensity exercise, we can examine whether and how flow is linked to discrepancies between subjective and physiological measures of exertion in endurance sports and identify the conditions under which flow emerges as a scientifically measurable phenomenon.

In this study, we hypothesized that the flow state contributes to the discrepancy between perceived and physiological exercise intensity during endurance cycling. Specifically, we posited that participants who report a stronger sense of flow would experience lower perceived tightness, even when their physiological responses are comparable to those of participants with lower flow scores. We also hypothesized that variations in the flow state would be reflected in changes in cerebral oxygenation in the PFC. These hypotheses are to clarify the connection between psychological aspects of flow and physiological indicators, contributing to the understanding of flow as a reproducible and objectively measurable phenomenon during steady-state aerobic exercise.

Methods

Participants

This study involved 21 male participants (age 22.6 ± 3.6 years; height 174.2 ± 5.0 cm; weight 66.0 ± 7.1 kg, mean ± standard deviation [SD]), all of whom were active track and field athletes training 2 to 3 h per day, 3 to 4 times per week. They voluntarily participated in response to recruitment that was open to both male and female individuals under the specified experimental conditions (exercise task, compensation, and time commitment). We excluded one participant due to unexpected irregular experimental conditions, two participants with heart rate (HR) outside the target range, and two participants with unchanging HR, resulting in 16 participants (11 endurance runners and 5 sprinters) whose data were analyzed. The HR outside the target range and unchanging HR were considered to result from limitations in the available load range of the equipment used, which may have been either too light or too heavy for the participants, preventing appropriate load adjustment. Given the nature of the experiment, participants were required to exhibit sufficient physical capacity to complete the task. The 21-min bike exercise session was designed based on pilot experiments to ensure a gradual and appropriate increase in workload, from a safe initial level to the target intensity, while minimizing the time burden on participants and ensuring a sufficient duration to allow the emergence of the flow state. Individuals engaging in regular exercise bike practice or competitive-level cycling were excluded from the study to ensure uniformity in exercise familiarity. Ethical approval for the study was obtained from the Ethics Review Committee of the Health and Physical Education Research Institute at Chuo University (Ethics Committee approval code: 2021-3), and informed consent was obtained from all participants.

Endurance bike exercise

This study aimed to create a situation closely resembling the flow state, with participants engaging in a 21-min pedaling exercise on an exercise bike with varying pedal resistance. The equipment (75XLIII, Konami Sports Life Co Ltd, Japan) comprised typical components, including a saddle, pedals, and handlebars. The positions of the saddle and handlebars were adjusted by height to allow the participants to pedal easily and naturally. A monitor screen on the handlebars displayed the elapsed time, pedal rate, and load in Watts. During the experiment, the participants were instructed to maintain a pace of 60 pedal rotations per min (rpm), as indicated by a rhythmic reference sound from the exercise bike. If the participants deviated from the target pedal cadence of 60 rpm, either below 45 rpm or above 85 rpm, instructions were displayed on the screen to guide them back to the appropriate pace.

A preliminary test, serving as both a warm-up and intensity assessment, was conducted prior to the main experiment to determine the optimal exercise intensity for each participant. During the test, the participants wore an HR sensor (H10, Polar Electro Co Ltd, Finland), and HRs, which were transmitted via Bluetooth to a tablet device, alongside perceived exertion levels (measured through a questionnaire), were recorded every minute.

The preliminary test began with a 2-min resting phase. Over the next 2 min, the pedal load was increased by 20 W every 30 s, followed by a 10 W increment per min. As soon as a “somewhat hard” load (that is assumed to be appropriate for inducing the flow state) was determined through a questionnaire-based assessment of exercise tightness (described below), and an HR of 120–130 bpm was achieved, the participants engaged in a 1-min cooldown at a low load before completing the preliminary test. Flow tends to emerge at an optimal level of difficulty, often characterized by a U-sharp relationship between challenge and skill [23]. In the context of physical exertion, this corresponds to a workload that is neither too easy nor too strenuous but sufficiently demanding to require focused effort while still being sustainable. In endurance exercise, the “somewhat hard” intensity level is considered to approximate the peak of this U curve, making it a suitable target for inducing the flow state. For this reason, the load identified as “somewhat hard” during this preliminary test was set as the pedal somewhat hard load, starting at the 14th min of the main experiment.

The main experiment comprised six distinct phases (Fig. 1). The first phase, lasting 3 min, involved participants remaining as still as possible while seated on the exercise bike (Fig. 1, Rest). The second phase consisted of 2 min of pedaling at the minimum pedal load (Fig. 1, Minimum load). The third phase involved progressively increasing the pedal load by 10 W every minute for 9 min (Increasing load). The fourth phase, lasting 9 min, entailed pedaling at the pedal somewhat hard load, which was determined individually for each participant based on the preliminary test (Fig. 1, Somewhat hard load). Unlike in the preliminary experiment, this phase continued even after a questionnaire-based “somewhat hard” assessment of exercise tightness (described below) and the achievement of a heart rate of 120–130 bpm. The fifth phase, lasting 1 min, involved a gradual reduction in pedal load to facilitate the cooldown process (Fig. 1, Cooldown). The final phase, lasting 3 min, required the participants to minimize movement while seated on the exercise bike (Fig. 1, Recovery). Throughout the experiment, the participants were instructed to maintain a pedal rate of 60 rpm, except during the rest and recovery phases.

Fig. 1.

Loads and assessments during the main experiment − endurance exercise on a bicycle ergometer. The phases of Rest, Minimum load, Increasing load, Somewhat hard load, Cooldown, and Recovery are shown with the timings of Rating of Perceived Exertion (RPE) and Flow State Scale (FSS) questionnaires

Assessment of exercise tightness using a questionnaire

To assess the perceived intensity of exercise, a questionnaire using a 15-point subjective Borg Rating of Perceived Exertion (RPE) scale ranging from 6 to 20, as defined in the original Borg rating [25], was administered. The results of this questionnaire on this scale were later converted and compared with the physiological intensity of the exercise sessions based on the HR during exercise. To implement the exercise tightness questionnaire, a slide displaying the subjective sensory descriptors (“very, very light,” “very light,” “fairly light,” “somewhat hard,” “hard,” “very hard,” and “very very hard”) was projected onto the upper section of a large display screen positioned in front of the exercise bike. This was accompanied by the corresponding range of the Borg values (6–20), with the labels “very very light,” “very light,” “fairly light,” “somewhat hard,” “hard,” “very hard,” and “very very hard” assigned the values of 7, 9, 11, 13, 15, 17, and 19, respectively. The participants were instructed to select a value on the 6–20-point scale that closely corresponded to their perception of exercise intensity. The selected values were recorded using a numeric keypad attached to the handlebar of the exercise bike. A total of 10 records were administered at 2-min intervals, beginning 4 min after the start of the experiment.

Flow state assessment

To evaluate the flow state, we administered a modified version of the conventional Flow State Scale (FSS) [26, 27]. Given the constraints of real-time measurement and the time required to complete the full scale, a shortened version of the FSS [27] was adopted in this study. Specifically, the number of items was reduced to nine, with each item corresponding to one of the nine flow dimensions to minimize the impact of the questionnaire completion time on the experimental procedure. The wording of each item was also adjusted based on participant feedback to ensure suitability for exercise contexts. The modifications to the conventional short FSS were as follows: all questions were translated into Japanese and rephrased in past tense to evoke immediate feelings; additionally, some questions in the original FSS were modified to include expressions that were not suitable for the context of bike exercise. The nine Japanese questions were translated into English as follows:

1. Balance of activity level and ability: “My physical abilities are perfectly suited to this task.”

2. Fusion of activity and consciousness: “My body moves naturally without thinking.”

3. Clear goals and objectives: “I know what I want to achieve.”

4. Clear feedback: “I am aware that I am moving well.”

5. Concentration on the task: “I am completely focused on the task.”

6. Sense of control: “I feel in control of my body.”

7. Loss of self-consciousness: “I am not concerned about what others think of me.”

8. Distortion of temporal experience: “I am feeling as though time is moving faster or slower.”

9. Autotelic experience: “Going through the menu makes me feel really good.”

A simplified version of the response options, consisting of a trichotomous selection between “Yes,” “Neither,” and “No,” was used for the questionnaire. Similar to the RPE assessment, the participants provided their responses to the displayed items projected onto a screen in front of the exercise bike. The responses were recorded by inputting the corresponding numerical value—1, 2, or 3—for “No,” “Neither,” and “Yes,” respectively. The questionnaire was administered five times at 4-min intervals, starting 3 min after the beginning of the exercise.

Physiological indicators

Physiological changes during the exercise (HR, pulmonary oxygen uptake [VO2], breathing frequency [Bf], pulmonary ventilation [VE], oxygenated hemoglobin [oxy-Hb], and deoxygenated hemoglobin [deoxy-Hb]) were measured over a 27-min period. HR was monitored using an HR sensor (H10, Polar Electro Co Ltd, Finland). VO2, Bf, and VE were assessed using a pulmonary exercise monitoring system (AE-310 S, Minato Medical Science Co., Ltd. Japan). Gas exchange variables were calibrated using a standard gas mixture (O₂: 15.11%, CO₂: 5.160%, N₂: balance) with a built-in calibration function, and data were collected using the breath-by-breath method. The light source of the near-infrared spectroscopy (NIRS) system consisted of three-wavelength light-emitting diodes (735 nm, 810 nm, and 850 nm), and the detector was a photodiode. Measurements were performed using the Modified Beer-Lambert Law, with a source-detector separation of 3 cm. Oxy-Hb and deoxy-Hb levels were measured at the frontopolar midline (Fpz) in the 10–20 system using a portable near-infrared tissue oxygen monitor (PocketNIRS Duo, DynaSense, Japan).

Data analysis

Time-series changes in physiological indicators recorded over the 21-min session under varying pedal loads were synchronized and presented for easy comparison (Figs. 2 and 6a). The measured values were averaged per min: the measured values from 1 min to 0 s to 1 min and 59 s were averaged and reported as the value at 1 min in the text and shown at 1 min and 30 s in the figures. Participants were divided into the RPE alleviation and escalation groups to highlight individual variations in subjective perceptions of exercise tightness. The RPE alleviation group included participants whose RPE either increased or remained stable between the 14- and 18-min intervals, followed by a decrease or consistent level between the 18- and 22-min intervals (Fig. 3, middle panel). Participants who did not meet these criteria were categorized into the RPE escalation group (Fig. 3, lower panel), where RPE exhibited a trend of increase in response to the rising HR, as anticipated. To further illustrate the distinct trends between these two groups, HR and RPE values were plotted on a scatter plot at the 14-, 18-, and 22-min marks during both constant pedal load at somewhat hard periods (Fig. 3). Additional indicators were also plotted on scatter plots at the 18- and 22-min intervals across the same load conditions (Figs. 4 and 5, and 6b).

Fig. 2.

Physiological indicators during the bike exercise. Heart rate (HR), pulmonary oxygen uptake (VO2), breathing frequency (Bf), pulmonary ventilation (VE), oxygenated hemoglobin (oxy-Hb), deoxygenated hemoglobin (deoxy-Hb), Rating of Perceived Exertion (RPE), and flow state scale (FSS) during the exercise protocol in Fig. 1 are illustrated from top to bottom

Fig. 3.

Alleviation and escalation of RPE during the pedal exercise at a constant somewhat hard load. The HR and RPE are shown as mean and standard deviation (top, black). The results for those with a decrease (middle, blue) and those with an increase (lower, red) are shown with the means in dark colors and individual results in light colors. HR, heart rate; RPE, Rating of Perceived Exertion

Fig. 4.

Alleviation effect of flow state on RPE between the 18- and 22-min intervals during the pedal exercise at a constant somewhat hard load. The changes in FSS and RPE are shown as mean and standard deviation (top, black). The results for those with a decrease (middle, blue) and those with an increase (lower, red) are shown with the means in dark colors and individual results in light colors. FSS, flow state scale; RPE, Rating of Perceived Exertion

Fig. 5.

Effect of FSS on the discrepancy between subjective perceived tightness and physical tightness during the pedal exercise at a constant somewhat hard load. The changes in FSS and discrepancy ratio are shown as mean and standard deviation (top, black). The results for those with a decrease (middle, blue) and those with an increase (lower, red) are shown with the means in dark colors and individual results in light colors. FSS, flow state scale; RPE, Rating of Perceived Exertion; HR, heart rate

Fig. 6.

Physiological indicators during the bike exercise for the alleviation and escalation groups. (a) Time courses of HR, VO2, VE, RPE, FSS, oxy-Hb, and deoxy-Hb during the bike exercise are shown with the mean values and standard deviations (colored bands) for the two groups. (b) The changes in FSS and oxy-Hb for all participants (black) and for participants based on the increase or decrease in RPE (blue and red) are shown with mean and standard deviation and individual results in empty circles. FSS, flow state scale; HR, heart rate, VO2, pulmonary oxygen uptake; Bf, breathing frequency; VE, pulmonary ventilation; oxy-Hb, oxygenated hemoglobin; deoxy-Hb, deoxygenated hemoglobin

Statistical analyses

The average values and SDs were calculated, with SDs presented as bars (Figs. 2 − 5 and 6b) or colored zones (Fig. 6a). Two-tailed t-test p-values were also calculated and presented in the text. Statistical analyses were performed using Microsoft Excel (Microsoft Corp., USA). The required sample size was estimated using G*Power 3.1.9.7 (Heinrich Heine University, Germany) for a two-tailed paired t-test, comparing physiological and FSS variables between high-flow and low-flow conditions within participants. Previous studies reported markedly higher FSS subscale scores under flow-inducing exergaming conditions compared to traditional exercise, with between-condition differences corresponding to large effect sizes (Cohen’s d ≈ 0.8–1.4) [28]. Similarly, a significant group × time interaction for FSS scores was observed in a randomized controlled trial of flow-enhancing vs. non-adaptive tasks, with a between-group effect size of d = 0.82 [29]. The effect size (Cohen’s d = 0.90) was determined based on these previous studies reporting large differences in FSS scores between flow-inducing and control conditions. Using α = 0.05 and statistical power (1–β) = 0.95, the required sample size was calculated to be 21 participants.

Results

Physiological indicators during endurance bike exercise

Cardiorespiratory variables (HR, VO2, Bf, and VE), oxy- and deoxy Hb at the PFC, RPE, and FSS during the 21-min pedaling session on an exercise bike with varying pedal loads are shown in Fig. 2. HR, VO2, Bf, and VE linearly increased as the pedal load increased. However, these indicators exhibited distinct patterns during the maintained somewhat hard load period (Fig. 2, HR, VO2, Bf, and VE). Following a steady increase in response to the rising pedal load, the HR and Bf slightly increased during the constant pedal somewhat hard load exercise, whereas the VO2 and VE remained relatively stable under the same conditions.

In contrast, the oxy-Hb levels remained unchanged until the 8th min of the load-increasing phase, began to rise from the 9th min, and continued to increase throughout the period of constant somewhat hard load (Fig. 2, oxy-Hb). The deoxy-Hb levels showed minimal change during the entire session (Fig. 2, deoxy-Hb). These results suggest that progressive increases in pedal resistance elicited corresponding elevations in various physiological indicators. In line with the minimal pedal load phase, the RPE scores showed a consistent elevation as the pedal load increased compared with the RPE at 4 min. During the constant somewhat hard load pedal exercise session (at 16-, 18-, 20-, and 22-min intervals), the RPE scores remained relatively stable until a noticeable decrease was observed at 22 min. The FSS score (Fig. 2, FSS) increased during the load-increasing period (at 6-, 10-, and 14-min intervals) and remained relatively stable throughout the sustained pedal somewhat hard load exercise period (at 18- and 22-min intervals).

Alleviation and escalation of subjective perceptions of exercise tightness

To examine the differences between physiological responses and subjective perceptions of exercise tightness, we further analyzed HR, as an indicator of physical exertion tightness, and RPE scores, which reflect perceived tightness, during the constant somewhat hard load periods (Fig. 3). The mean and standard deviation values for the HR and RPE across all participants were plotted on a scatter plot at 14, 18, and 22 min during the constant somewhat hard load periods (Fig. 3, top). The arrow from 14 to 18 min indicates an increase in RPE scores, corresponding to the elevation in HR. However, from 18 to 22 min, the HR continued to increase, while the RPE score remained unchanged.

To further elucidate the discordant trend observed between the averaged RPE and HR, the participants were classified into two distinct groups based on the RPE changes between the 18- and 22-min intervals (Fig. 3, middle and lower). The RPE alleviation group included individuals whose RPE either increased or remained stable between the 14- and 18-min intervals, followed by a reduction or stable level between the 18- and 22-min intervals (Fig. 3, middle). In the latter half of the somewhat hard load period, RPE showed a downward trend. The participants who did not meet these criteria were assigned to the RPE escalation group (Fig. 3, lower). In this group, the RPE score tended to increase in response to the increasing HR.

Eight participants were included in the RPE alleviation group (Fig. 3, middle, light blue arrow). Of these, seven participants demonstrated an increase in RPE scores between the 14- and 18-min intervals, whereas one participant maintained a steady RPE score, concurrently experiencing an increase in HR across the 14-, 18-, and 22-min intervals. However, the RPE alleviation group exhibited a contrasting RPE pattern between the 18- and 22-min intervals. The group’s mean RPE score declined during the latter half of the somewhat hard load period between the 18- and 22-min intervals, with six participants demonstrating a decrease and two maintaining a constant RPE score, in contrast to the elevation observed between the 14- and 18-min intervals. The mean RPE score in this group indicates a tendency to decline (Fig. 3, middle, dark blue arrow). Contrary to the expected elevation in exercise intensity, as indicated by the rise in HR, a decrease in perceived exercise intensity was observed within the RPE alleviation group.

The RPE escalation group comprised eight individuals who did not meet the criteria for inclusion in the RPE alleviation group and showed increases in HRs between the 14- and 18-min intervals and between 18- and 22-min intervals (Fig. 3, bottom). In this group, four participants demonstrated an accelerated increase in RPE scores, whereas the other four showed a consistent increase in RPE scores. Between the 18- and 22-min intervals, the RPE increased in six participants but remained constant in two participants (Fig. 3, bottom, light red arrow). The averaged RPE showed a more pronounced escalation between the 18- and 22-min intervals than between the 14- and 18-min intervals (Fig. 3, bottom, dark red arrow).

RPE changes between the 18- and 22-min intervals significantly differed among the RPE alleviation and escalation groups (p = 0.0002). In contrast, HR changes between the two groups, which indicates physiological tightness, were not significantly different during the same period (p = 0.36). Within the RPE escalation group, the HR and RPE exhibited sustained increases, so the RPE escalation group showed similar increases in the subjective perception of physical tightness and the objective physiological tightness.

Alleviation effect of flow state on subjective perceived tightness

A comparative analysis was conducted to examine the relationship between the two groups in terms of the effect of the flow state on RPE scores (Fig. 4). The averaged changes between the 18- and 22-min intervals in the RPE alleviation and escalation groups (Fig. 4, black arrow) showed minimal changes in both the RPE and FSS scores; however, substantial standard deviations indicated pronounced variations across participants. The RPE alleviation group showed a decrease in RPE scores and an increase in FSS scores (Fig. 4, blue), as reflected by a shift toward the upper left quadrant in the distribution plot (ΔRPE = − 1.25, ΔFSS = + 2.75). Within the RPE escalation group, RPE increased and FSS decreased, yielding average changes in ΔRPE = + 1.00 and ΔFSS = − 2.38. A negative correlation (r = − 0.53) was observed between the RPE and FSS scores across both groups.p.

Effect of FSS scores on the discrepancy between subjective perceived tightness and physiological tightness

Furthermore, we examined whether the FSS scores could explain the discrepancy between subjective perceived tightness and physiological tightness (Fig. 5). To quantify this discrepancy, the discrepancy ratios were calculated using the formula 10 × RPE / HR [25]. The averaged changes in discrepancy ratios and FSS scores between the 18- and 22-min intervals for both the RPE alleviation and escalation groups (Fig. 5, black arrow) indicated minimal group-level change (Fig. 5, black arrow). However, the discrepancy ratios differed significantly between the two groups (p = 0.001). In the RPE alleviation group, the FSS scores tended to increase, whereas the discrepancy ratio decreased (ΔFSS = + 2.75 and ΔRPE × 10/HR = − 0.13) (Fig. 5, blue). In the RPE escalation group, the FSS scores tended to decrease, whereas the discrepancy ratio increased (FSS = − 2.38 and Δ(10× RPE /HR) = + 0.04). A negative correlation (r=-0.56) was also found between the changes in the discrepancy ratio and FSS scores.

RPE behavior-based Temporal analysis of the physiological indicators

The temporal characteristics of the physiological indicators were examined separately for the RPE alleviation and escalation groups (Fig. 6). Following the initiation of exercise, the HR, VO2, and VE were slightly higher in the RPE escalation group than in the RPE alleviation group, whereas Bf remained at a similar level between the two groups.” (Fig. 6a). The RPE alleviation group demonstrated a more moderate RPE response to the increasing load than the RPE escalation group (Fig. 6a, RPE). During the somewhat hard load period, the RPE score continued to increase in the RPE escalation group but gradually declined sharply in the RPE alleviation group by the end of the period. By contrast, both groups displayed an overall temporal FSS trend that opposed the RPE trajectory (Fig. 6a, FSS). At the beginning of the load-increasing period, the FSS of the RPE escalation group was lower than that of the RPE alleviation group; however, it increased until the middle of the somewhat hard load period and decreased at the end of the period. By contrast, the FSS score of the RPE alleviation group remained stable throughout the session and increased again at the end of the somewhat hard period, possibly contributing to the observed decrease in RPE.

Finally, we examined the temporal behavior of oxy- and deoxy-Hb in the two groups separately (Fig. 6a, oxy-Hb and deoxy-Hb). The RPE alleviation group demonstrated a delayed onset of oxy-Hb increase in response to the increasing load, followed by a continuous increase during the load at the somewhat hard period and stabilization during the cooldown period (Fig. 6a, oxy-Hb, blue line). In the RPE escalation group, the oxy-Hb levels began to rise earlier but remained stable during the middle of the somewhat hard load period and were lower than those of the RPE alleviation group after this period and even during the cooldown period (Fig. 6a, oxy-Hb, red line). In both groups, the deoxy-Hb levels showed similarly minimal change throughout the entire session (Fig. 6, deoxy-Hb).

We investigated the effects of temporal changes in oxy-Hb levels across the two groups by re-analyzing the relationship between oxy-Hb and FSS score changes from the 18- to 22-min intervals, dividing the participants into two groups based on RPE scores (Fig. 6b). Although the overall average FSS score showed minimal change between the 18- and 22-min intervals, the oxy-Hb levels moderately increased (Fig. 6b, black), resulting in no clear correlation between oxy-Hb levels and FSS score changes. In the RPE alleviation group, the FSS scores and oxy-Hb levels increased relative to the overall average between the 18- and 22-min intervals (Fig. 6b, blue). In the RPE escalation group, the FSS scores and oxy-Hb levels decreased relative to the overall average between the 18- and 22-min intervals (Fig. 6b, red). Although no significant differences were observed in the temporal oxy-Hb changes between the two groups (p = 0.3), a weak positive correlation (0.21) was observed between oxy-Hb changes and FSS scores in both groups. Notably, when participants with minimal oxy-Hb increases (< 20)—who exhibited high variability in FSS score changes (0.4 ± 7.9 (SD))—were excluded from the analysis, a stronger positive correlation (0.48) was observed.

Discussion

This study examined the flow state and the discrepancy between perceived and physiological exercise intensity during endurance cycling. By analyzing physiological responses alongside subjective ratings of exertion and flow, we found that individuals who experienced a stronger flow state reported lower perceived exertion despite sustained or increasing physiological load. Given that HR is generally regarded as a measure of physiological intensity [25, 30], the inconsistency between HR-based physical exertion tightness and perceived tightness was evident in the averaged HR and RPE values between 18- and 22-min intervals. The analysis indicated that, within the RPE alleviation group, the HR exhibited a sustained increase, whereas the RPE tended to transition from increasing to decreasing, which corresponds to the difference between the reduced subjective perception of physical tightness and the increased objective physiological tightness. A lower flow state corresponded with a heightened perception of tightness and vice versa. Notably, this reduction in perceived tightness was accompanied by increased oxygenated hemoglobin levels in the PFC. These findings suggest that individuals with a higher flow state experienced a reduced perception of tightness relative to physiological load, implying that differences in flow engagement may underlie the discrepancy between perceived and physiological exercise intensity. The flow state in endurance sports may modulate subjective experience during physical activity, potentially through neural mechanisms involving prefrontal brain activity.

A previous study utilizing an exercise bike found that pedaling reduced negative mood and tended to increase engagement in vigorous activity afterward [31]. By contrast, the present study did not observe a reduction in negative mood based on the average RPE and FSS scores. However, the categorization analysis revealed individual differences. The participants were divided into the RPE alleviation group—comprising participants who experienced reduced perceived tightness as the flow increased—and the RPE escalation group, comprising participants who reported an increase in perceived tightness as the flow decreased. This analysis elucidated inverse correlations between the flow state and perceived tightness within the two groups. This result indicates that the autotelic effects on perceived tightness were not consistently and robustly reproduced across participants but were evident on an individual level, potentially obscured in the averaged data.

Regarding the underlying mechanisms, previous studies on long-distance running and endurance sports have discussed the role of motivation in facilitating flow or flow-like phenomena [10, 12, 13]. The phenomenon known as the runners’ high has been attributed to endocannabinoid and opioidergic mechanisms [3, 4]. In a previous study using an exercise bike, pedaling led to a significant increase in oxy-Hb levels in the ventral and dorsal PFC, and it was hypothesized that the observed mood changes were induced by the activation of the ventral PFC [31]. Other studies involving video games have shown that flow conditions, characterized by an optimal level of difficulty, led to increased oxy-Hb levels in the lateral PFC [32, 33]. Similarly, in this study, changes in FSS scores were dependent on oxy-Hb levels. Another previous study indicated a significant increase in whole blood serotonin levels after pedaling exercise [31]. Given that the activation of the serotonin system through rhythmic gum chewing demonstrated analgesic effects [34] and transcranial stimulation in the PFC induced the flow state [35], oxy-Hb levels in the PFC may play an important role in the autotelic aspect of flow.

This study elucidated the differences in the temporal characteristics of RPE scores by dividing the participants into two groups based on the significant inter-individual variability observed among the participants. Although no differences in HR, VO2, and VE were observed between the two groups prior to the exercise, these measures were slightly higher in the RPE escalation group following the initiation of exercise (Fig. 6). Therefore, the exercise load in the RPE escalation group may have been higher than expected, potentially leading to an early peak in FSS scores (Fig. 6a, FSS). The excessive exercise load in the RPE escalation group may have induced an early induced flow peak at 18 min and attenuated flow at 22 min. Owing to the excessive load setting, a decrease in the RPE was not evident at 18 min, and the RPE scores subsequently increased at 22 min (Fig. 6a, RPE). This finding aligns with the observation that the RPE escalation group had higher initial RPE scores and experienced an increase in RPE scores during the higher load phase. Additionally, the variability in load settings likely influenced the oxy-Hb levels. In the RPE escalation group, the oxy-Hb levels began to increase earlier than in the RPE alleviation group, likely due to the higher load; however, the increase plateaued at an intermediate point during the load at the somewhat hard period (Fig. 6a, oxy-Hb).

In the RPE alleviation group, the oxy-Hb levels continued to increase even during the load at the somewhat hard period. Interestingly, even after the exercise ended, the RPE alleviation group, which likely experienced a relatively smaller load, showed higher levels of oxy-Hb. This suggests that the increase in oxy-Hb levels, associated with the flow state, persisted beyond the exercise period, indicating that the increase in oxy-Hb levels observed in this study cannot be solely explained by the metabolic demands of the exercise.

One limitation of this study is the relatively small number of participants. Although the number of participants in the present study did not reach this threshold as in similar experimental studies, the results of the present study showed statistically significant differences. The weak positive correlation between oxy-Hb changes and FSS scores in Fig. 6(b) may be attributable to the limited number of participants.

Another limitation of the present study is that the frontal lobe NIRS measurements used to assess cerebral blood oxygenation may be influenced by extracerebral blood. NIRS detects changes in local oxy-Hb and deoxy-Hb based on differences in near-infrared light absorbance. An increase in oxy-Hb and a slight decrease in deoxy-Hb had been measured as presumed typical task-evoked cerebral hemodynamic responses extracted from the fNIRS signals; however, oxy-Hb and deoxy-Hb measured at the frontal lobe by NIRS could be influenced by skin blood flow, potentially preventing a pure evaluation of cerebral blood oxygenation [36]. Previous flow studies have reported inconsistencies in the dynamics of oxygenation measured from these brain regions during flow states [37]. These consistencies may partly reflect oxygenation changes from extracerebral blood. However, previous studies primarily involved static exercises or computer games, which were less influenced by extracerebral blood. This discrepancy may be explained by the stronger positive correlations observed when participants with minimal oxy-Hb increases and deoxy-Hb decreases were excluded from the correlation analysis in the present study. A positive correlation may exist in participants who experience oxy-Hb increases and slight deoxy-Hb decreases; however, some participants may show varying FSS scores without a corresponding oxy-Hb increase and slight deoxy-Hb decrease. In exercise tasks such as those in the present study, it is challenging to exclude the influence of NIRS signals caused by extracerebral blood. Despite likely lower extracerebral circulation in the RPE alleviation group, their oxy-Hb levels were higher, suggesting that cerebral blood oxygenation in the frontal lobe increased in the opposite direction to the extracerebral blood changes associated with increased exercise load. Thus, cerebral blood significantly contributes to the observed NIRS signal increase, supporting the conclusion that discrepancies between perceived exercise intensity and physiological intensity stem from differences in flow state levels, potentially reflected in cerebral oxygenation changes.

Conclusions

The flow state significantly contributes to the discrepancy between perceived and physiological exercise intensity during endurance cycling. Higher flow levels corresponded with lower perceived exertion despite maintaining similar physiological workloads. These findings enhance the understanding of the physiological correlates of the flow state, with potential applications in sports, education, and other domains requiring sustained performance.

Abbreviations

FSS

Flow State Scale

RPE

Rating of Perceived Exertion

HR

Heart rate

VO2

Oxygen consumption

Bf

Breathing frequency

VE

Ventilation

PFC

Prefrontal cortex

bpm

Beats per minute

SD

Standard deviation

NIRS

Near-infrared spectroscopy

Author contributions

AT, YN, and SM conceptualized the study. ST and YN collected the data; AT and SM wrote the original draft. YN and YO reviewed and edited the draft. All authors read and approved the final manuscript.

Funding

This work was supported by the Chuo University Joint Research Grant, Chuo University Grant for Research Cluster Formation, and Chuo University Personal Research Grant.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Ethical approval was granted by the Ethics Review Committee of the Health and Physical Education Research Institute at Chuo University (Ethics Committee approval code: 2021-3), and informed consent was obtained from all participants. The study was conducted in accordance with the Declaration of Helsinki.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.