The subjects of this study were seven healthy adults: six males and one female; the mean age was 33.3 ± 8.0 years. The participants had some experience in sports before age 20, but had not received any intensive strength training for at least 1 year.

All participants were identified as being right-handed based on the Edinburgh Handedness Inventory. The study was explained to the subjects in writing and orally, and they provided prior written consent for participation in and reporting of this study.

The experimental procedure complied with the principles of the Declaration of Helsinki. All subjects received full explanation of the procedures and provided written informed consent for participation in the study. This study was reviewed and approved by the Ethics Committee of KatoBrain Co., Ltd. which included outside members.

A multi-channel NIRS apparatus (ETG-100) monitored localized changes in oxyHb and deoxyHb. The scalp was irradiated at each site with two wavelengths of near-infrared light (780 and 830 nm) from a semi-conductor laser using three optical fibers. Three avalanche photodiodes detected light passing through the head. Hb concentration measurements were recorded at a sampling rate of 10 Hz.

Measurements were collected from a total of seven channels (Figure 1). Channel 1 was positioned directly over the left M1, and the remaining six channels were arranged around it: channel 2 lateral to the precentral knob, channel 3 in the premotor area, channel 5 in the SMA, and channels 4, 6, and 7 over the postcentral gyrus. The distance between emitter and detector probes was 30 mm. The M1 was identified using a technique for pre-measurement identification of target cortex sites that utilizes the distance between points of reference on the scalp from the subject's MRI (Murakoshi and Kato, 2006). The right M1 was measured by fNIRS simultaneously with the left M1. However, the analysis was limited to the left-hemisphere channel.

The task used in this study to investigate the effects of the strength of neural activity was a dumbbell-lifting exercise that involved flexing and extending the elbow joints of both arms. It has been reported that movement-related cortical potentials increase more for isometric contractions of the elbow flexors under a heavy load than they do under a light load (Oda et al., 1996). Therefore, there were three different weights: 0 kg (no dumbbell), and dumbbells weighing 4.5 and 9.5 kg. One trial consisted of flexing and extending a given weight 12 times. Repetitions were paced at 3 s (Tamaki et al., 1994), for a total of 36 s per trial, with a 60 s resting period between trials. Each repetition lasted for 1.5 s, for a total of 3 s. Five trials with each weight made up a trial set. After completing a trial set for one weight, the subject went on to the next, heavier weight. The training order was always from lightest to heaviest, with participants always set to be most fatigued on the heaviest trial set.

For the 0 and 4.5 kg tasks, a total of 35 trials performed by the seven subjects were used for analysis. For the 9.5 kg task, one subject completed only one trial and another subject only four because the weight was too heavy, and a total of 30 trials were used for analysis.

The weight of the dumbbells that can be lifted could be different for each individual.

However, the neural activity to M1 and its surrounding sites is expected to be higher with the dumbbell weighing more. Therefore, instead of selecting the dumbbell weight that produces maximal voluntary muscle contraction, a uniform dumbbell weight was set.

Measurements performed over 36 s during a trial and 36 s after a trial were used for analysis. Functional imaging was performed using seven indices: the four-vector components (ΔO, ΔD, ΔCBV, and ΔCOE) of the addition vectors during the tasks, phase (k), the scalar (L), and the oxygen regulation index (Area_kL).

The time-course changes were averaged, with each trial onset set as zero. The time-course changes in ΔCBV and ΔCOE were calculated from the time-course changes in ΔO and ΔD using Equations (1) and (2). Vector tracks were plotted using task onset as the origin and the grand averages calculated for all trials for each component. No baseline normalization or motion correction was performed as a preprocessing step for the analysis, as these may distort the phase of oxygen exchange (Kato, 2021).

CORE addition vectors during and after the tasks were calculated to observe total changes across the task time. The cumulative sums of ΔCBV and ΔCOE grand averages were determined, and the CORE addition vectors were plotted using those values. Imaging of each vector component (ΔO, ΔD, ΔCBV, and ΔCOE) was carried out using the cumulative sums recorded during the task. Imaging of k and L was performed using Equations (3) and (4), with values determined from the CORE addition vectors. Imaging of Area_kL was carried out based on Equation (9) based on the cumulative sums of the area determined from k and L of the single-trial CORE addition vectors.

The phase distribution of a CORE vector was determined by first classifying k for each trial into the appropriate octant and then calculating the ratio of the number of trials in each phase to the total number of trials for analysis for each task. Phase distribution for the sites surrounding the left M1 was calculated by averaging the phase distributions of all surrounding channels.

Spatial concordance between k and L was calculated as the ratio of the number of trials in which the maximum values for k and L coincided with the number of trials in the analysis of each task.

The percent contribution of ΔO and ΔD to L was calculated using Equations (6) and (7). Values for L of the CORE addition vectors and the cumulative sums of ΔD and ΔO were used for the calculation. The contribution rates for the sites surrounding the left M1 were averaged from the contribution rates of all channels. Differences in contribution rates were calculated by subtracting the percentages for ΔO from those for ΔD.

Multiple analysis of variance and post-hoc multiple comparison tests (Scheffe's) were performed using ΔCBV and ΔCOE for all trials to determine the significance of differences between the left M1 and the averages of the surrounding sites. Statistical tests were performed for k, L, and the Area_kL, to determine the significance of differences between the left M1 and the averages of surrounding sites. Independent t-tests were used for L and the Area_kL, and Watson's U2 test was used for k. Differences in phase distribution between the left M1 and the surrounding sites were compared using Fisher's exact test for each phase.

Figure 3A shows the average time courses for each vector component during and after the tasks. Figure 3B is a functional image of the four-vector components during a task. At the left M1 (channel 1), ΔO decreased for the 4.5 and 9.5 kg tasks, whereas ΔD and ΔCBV increased. However, in the surrounding sites, ΔO increased, and ΔD and ΔCOE decreased. The left M1, where the maximum decrease in ΔO occurred, was surrounded by a high oxygen supply (increased ΔO), in a donut-like shape. The sites of maximum increase in ΔD and ΔCOE were the left M1 for the 4.5 and 9.5 kg tasks and the SMA (channel 5) for the 0 kg task. ΔCBV increased in both the left M1 and the surrounding sites, not indicating localization. At 9.5 kg, the rate of the maximum increase of each vector component at the left M1 was 0% for ΔO, 0% for ΔCBV, 56.7% for ΔD, and 63.3% for ΔCOE.

Figure 4 provides functional images of k, L, and the Area_kL. The SMA was the site with the maximum increase in k at 0 kg. At 4.5 and 9.5 kg, the left M1 showed the maximum increase in k, whereas oxygen consumption decreased in the surrounding area. The maximum increase in L appeared not at the left M1, but in the surrounding area. The spatial concordance of the maximum increases in k and L was low; 11.4% at 0 kg, 17.1% at 4.5 kg, and 20.0% at 9.5 kg.

The spatial concordance of the maximum increases in k and Area_kL increased as the dumbbell weight increased; 37.1% at 0 kg, 54.3% at 4.5 kg, and 76.7% at 9.5 kg. Area_kL showed a significantly greater increase at the left M1 compared with the surrounding area (4.5 and 9.5 kg) (P < 0.01), indicating increased oxygen consumption. The site of maximum increase in Area_kL was the SMA at 0 kg. The imaging of Area_kL emphasized the changes at the left M1 and SMA and allowed the detection of a small increase in oxygen consumption at the left M1 that could not be detected in images of the single-vector components or L.

Figure 5 displays the CORE addition vectors during the task (36 s) and after the task (36 s) at each channel.

Table 1 shows the phase distribution of the CORE addition vectors at the left M1 and surrounding sites.

Vectors for the 4.5 and 9.5 kg tasks showed significant differences between the left M1 and the surrounding sites (P < 0.01). The most common phase at the left M1 was Phase 3, indicating hypoxic–hyperemic activation. The percent occurrence of Phase 3 at the left M1 was 31.4% at 0 kg, 54.3% at 4.5 kg, and 46.7% at 9.5 kg, which were all significantly higher than those detected in the surrounding sites (Table 1). At this time, k was 83.9° at 0 kg, 93.8° at 4.5 kg, and 101.6° at 9.5 kg, which were also significantly higher than those detected in the surrounding sites (P < 0.05). Vectors in the surrounding sites were significantly concentrated in Phases −1 and −2, which are non-activation phases. In the surrounding area, k ranged from −118.3° to 135.2° at 0 kg, from −34.0° to 11.6° at 4.5 kg, and from −25.5° to 14.0° at 9.5 kg.

After the tasks, the phase differences between the left M1 and the surrounding sites disappeared. The direction of the vectors changed and moved toward the origin.

During the task, L increased significantly with increased dumbbell weight at both the left M1 and the surrounding area (P < 0.01). In the 4.5 and 9.5 kg tasks, there was no significant difference between L at the left M1 and the surrounding sites. In this way, the CORE vectors showed specific phase distributions according to site and task.

Table 2 reports the relative contributions of ΔO and ΔD to L during the tasks. The contribution percentages from ΔO and ΔD were different for each measurement channel. At the left M1, the contribution of ΔO was small, at < 4.0%, whereas the contribution of ΔD was more than 96%, which represented a difference of ~92%.

At the sites surrounding the left M1, the contribution rate was higher for ΔO than for ΔD. Differences in the contribution rates of ΔO and ΔD increased as the dumbbell weights became heavier: 12.8% at 0 kg, 65.8% at 4.5 kg, and 83.8% at 9.5 kg. Namely, the donut-shaped image surrounding the site of maximum increase in oxygen consumption became clearer as the dumbbell weight increased from 0 to 4.5 kg and then to 9.5 kg, reflecting the increase in oxygen supply (ΔO increase) in the area surrounding the M1 unaccompanied by oxygen consumption as the dumbbell weight increased.

Although at 0 kg L was smaller at the left M1 than it was at the surrounding sites (Figure 5), the contribution of ΔO at the left M1 was lower (1.1%) than it was at the surrounding sites (56.4%).

Differences in the distribution of oxygen consumption are quantifiable using the images of k, which represents the degree of oxygen exchange. During dumbbell exercises, oxygen exchange increased at the left M1, indicating a localized increase in oxygen consumption. In the area surrounding the left M1, oxygen exchange decreased, and oxygen supply increased unaccompanied by oxygen consumption. The spatial concordance between the maximum values for the degree of oxygen exchange during a task and L, which reflects the intensity of Hb changes, was <20%. The contribution rates of ΔO and ΔD differed according to the measurement site. Therefore, the hypothesis that the distribution of oxygen consumption associated with neural activation does not coincide with the distribution of oxygen supply was supported in the motor task study.

Interestingly, an increasing difference in the relative contribution of ΔO and ΔD in the area surrounding the M1 was found as the dumbbell weights increased, which suggests that oxygen supply in the surrounding area is regulated concerning the site of increasing oxygen consumption. Even at sites of increased oxygen consumption, the contribution of ΔO was found to be low. It is believed that neural activity and local cerebral blood flow (CBF) increase or decrease relatively correlatedly. Similarly, local CBF and local CBV are also thought to increase or decrease in correlation. However, it is thought that, in brain regions where COE has increased markedly because of a rapid and sustained increase in oxygen consumption relative to oxygen supply, there is a mechanism of cerebral blood circulation that promotes replenishment from surrounding sites with sufficient oxygen supply.

Neural activity may not always correlate with local CBV or CBF when it has a strong impact on the COE homeostasis for the whole brain, as in the results of this study. The detection of an excessive increase in ΔCBV rather than an increase in ΔCOE around the near regions of rapidly increasing oxygen consumption was not previously known and therefore has not been incorporated into conventional models of cerebral circulation regulation (Roy and Sherrington, 1890; Lassen, 1959). A new model of whole brain circulation regulation is needed that can explain the mechanisms that maintain COE homeostasis for the whole brain.

Using the vector method fNIRS, it is necessary to study further how the oxygen supply in the brain is regulated from the site of increased oxygen exchange in the brain and its surrounding areas. The nature of the mechanisms that regulate the simultaneous oxygen supply at sites of increased oxygen exchange is also an important research topic at the level of whole brain regulation and at the level of more microscopic cell populations. As the weight of dumbbells lifted increases or the subject's muscle fatigue increases, the mechanisms that attempts to maintain COE homeostasis for the whole brain may be more likely to be strongly detected by vector method fNIRS. Thus, the closer to maximal voluntary muscle contraction, the more brain-muscle coordination may be required.

Compared with previous studies using verbal tasks (Kato et al., 2003; Yoshino and Kato, 2012), the present results suggest that, during muscle training, oxygen consumption and oxygen supply are controlled in areas of the cortex within a few centimeters square.

The FORCE, which is an oxygen-consuming response that occurs in a high neuroactivation site, has been observed in invasive human studies using optical imaging (Suh et al., 2006). However, it does not report that the phenomenon of oxygen supply surrounding the FORCE effect in the form of a doughnut has occurred, as obtained in this experiment. The strong and persistent FORCE effect on the homeostasis of oxygen exchange for the whole brain, as obtained in this experiment, may be a different brain mechanism from the temporary FORCE that has been previously reported (Kato, 2004, 2018).

It has been shown that γ-aminobutyric acid (GABA) concentrations during a motor learning task decrease in the left M1 and increase around it (Gudberg et al., 2012).

Studies using proton magnetic resonance spectroscopy have shown interactions between M1 and its surrounding sites in neurotransmitters (Umesawa et al., 2020; Maruyama et al., 2021). Although this method cannot measure intracellular and extracellular GABA separately, it could be used in conjunction with the vector method fNIRS to clarify the relationship between oxygen metabolism and GABA. However, because the dumbbell task is not a motor learning task, it does not necessarily elicit the same response as the strength training task. Further evidence and discussion of the physiological link between GABA and oxygen kinetics are needed.

The CORE model of 2-dimensional analysis of ΔO and ΔD was used to simultaneously generate functional distribution images using seven indices, including oxygen exchange.

The advantage of vector-based fNIRS is that multiple indices with different physiological significance can be compared to understand better neurovascular-coupling mechanisms and neuro-oxygen coupling that accompany neuroactivation. Conversely, these indices cannot be separately detected using the fMRI BOLD signal, which includes the effects of both oxyHb and deoxyHb changes (Yamamoto and Kato, 2002).

Unlike the other component images, the oxygen exchange images were able to indicate both high oxygen exchange sites, such as Phase 3 sites (common in the M1), and reduced oxygen exchange sites, such as Phase −1 (more common in the surrounding area), even though ΔCBV increased in the same way in both types of sites. The fact that the M1 site was most frequently a Phase 3 site (ΔCOE increased more than ΔCBV) reflects the fact that the increase in ΔD attributable to oxygen consumption exceeds the increase in ΔO from oxygen supply. Together with k, the ΔD and ΔCOE indices (reflecting oxygen consumption) increased most at the SMA for 0 kg, and at the M1 for 4.5 and 9.5 kg. However, the sites showing maximum increases in the ΔO, ΔCBV, and L indices (strongly affected by blood supply) did not coincide with the M1. Phase −1 is a non-activation phase, and I also observed that it did not reflect neuroactivation in a language task (Yoshino and Kato, 2012). In Phase −1, ΔO increases and ΔD decreases, which has been considered a typical fNIRS activation pattern; however, oxygen consumption is low in this phase, and it has become clear that it does not indicate a site where activation is strong. Based on our results, an increase in ΔCBV at a site does not necessarily imply an increase in oxygen demand. Variations were found in the oxygen exchange response concerning the amount of increase in ΔO or ΔCBV. For example, it was reported that, during a motor task, CMRO₂ did not increase significantly at the M1, whereas CBF did (Vafaee et al., 2012); conversely, CBF did not increase significantly in the visual cortex, although CMRO₂ did (Mintun et al., 2001).

Area_kL, which combines the indices k and L, proved to be useful for clearly imaging slight neuroactivation at the left M1 and SMA during a 0 kg task. Increased oxygen exchange, rather than the intensity of oxygen supply, coincided with the neuroactivation site. This result shows that the location and intensity of neuroactivation cannot be accurately estimated from the intensity of Hb concentration changes. Mintun et al. (2001) strongly suggested that increased CBF is caused by factors other than oxygen demand. The response at the M1 was in danger of being overlooked, masked by the intensity of ΔO. However, even small Hb changes, such as those from cognitive tasks, can provide dynamic oxygen consumption and oxygen supply images if Area_kL is used.

Because the dumbbell load in our study was sufficient to cause a systemic cardiovascular response, it is possible that systemic circulatory changes or scalp perfusion were included in the ΔO increases in the sites surrounding M1 (Kato et al., 1999). However, the donut-shaped excessive oxygen supply response generated in the area surrounding the neuroactivation site cannot be explained simply by changes in the systemic circulation. The most recent study (Kato, 2021) showed that vector-based fNIRS was less susceptible to artifacts from whole-body cardiovascular responses and motion. In other words, detecting localized increases in k may allow us to discount the broader influence of circulation and the autonomous nervous system.

I also observed an increase in k in a prior study of passive word listening (1.5-s tasks) that was unlikely to cause systemic circulation changes (Yoshino and Kato, 2012). It is important to note that the use of baseline normalization or motion correction to preprocess the data for analysis may distort the phase of oxygen exchange. For a rigorous study, it is interesting to use data from short channels where the distance between probes detects only the scalp. Even in such a comparative study, it may not be possible to conclude that systemic changes are not involved in brain responses.

When describing the exercise during validation, the loads used were 0, 4.5, and 9.5 kg, citing previous research showing that cortical potentials increase more with heavier loads (Tamaki et al., 1994). Due to the lack of information on the maximum voluntary muscle contraction of the participants' biceps curls, it is impossible to determine whether these loads were truly heavy for the participants. Bearability for loads varies from person to person; what may be light for one person may be heavy for another. It is necessary to study the COE distribution when using dumbbells of a weight that cannot be lifted and the relationship between maximal voluntary muscle contraction and oxygen exchange. By focusing on the strong FORCE effect and the surrounding oxygen supply response using the vector-based fNIRS, it may be possible to distinguish whether the subject's inability to lift the dumbbell is due to muscle fatigue or brain fatigue, or whether the patient is capable of lifting the dumbbell but does not intentionally try to do so.