Task-induced changes in brain entropy

Abstract

Entropy indicates irregularity of a dynamic system, with higher entropy indicating higher irregularity and more transit states. In the human brain, regional brain entropy (BEN) has been increasingly assessed using resting state fMRI (rs-fMRI), while changes of regional BEN during task-based fMRI have been scarcely studied. The purpose of this study is to characterize task-induced regional BEN alterations using the large Human Connectome Project (HCP) data. To control the potential modulation by the block-design, BEN of task-fMRI was calculated from the fMRI images acquired during the task conditions only (task BEN) and then compared to BEN of rs-fMRI (resting BEN). Moreover, BEN was separately calculated from the control blocks of the task-fMRI runs (control BEN) and compared to task BEN. Finally, control BEN was compared to resting BEN to test for residual task effects in the control condition. With respect to resting state, task-performance unanimously induced BEN reduction in the peripheral cortical area and BEN increase in the centric part of the sensorimotor and perception networks. Control compared to resting BEN showed similar entropy alterations, suggesting large residual task effects. Task compared to control BEN was characterized by reduced entropy in occipital, orbitofrontal, and parietal regions.

Graphical_Abstract

Brain entropy (BEN) represents a unique method to characterize brain activity at rest and during task performance. In this study, we compare BEN estimated during resting-state, task performance, and fixation blocks of task-fMRI. Our results provide new insight into BEN modifications during task performance involving higher-level cognitive functions.

Introduction

Entropy indicates the irregularity or uncertainty of a dynamic system (Clausius, 1865). Statistically, entropy can be defined by the number of states that a system can be configured (Boltzmann, 1964) or the information capacity of the dynamic system (Shannon, 1948). In theory, entropy tends to increase with time and extremely high entropy will destroy the organization of a system. Living organisms are characterized by being highly self-organized (Bak et al., 1989; Bak, 1996; Camazine et al., 2020), and counteracting entropy is crucial to keeping their functional order and the corresponding functions (Bergström, 1969; Pinker, 1997; Singer, 2009). As a highly complex and self-organized system, the human brain has a prominent need to suppress entropy in order to maintain its functionality at an adequate level. While it remains elusive how this entropy maintaining operates, monitoring brain entropy (BEN) may open a unique window to observe and evaluate brain function and brain health. In recent years, regional BEN has been increasingly characterized using resting-state fMRI (rs-fMRI) (Sokunbi et al., 2011, 2013; Wang, 2012, 2013; Wang et al., 2014, 2017, 2020; Smith et al., 2014, 2015; Song et al., 2019; Chang et al., 2018; Del Mauro and Wang, 2023). Using rs-fMRI from a large cohort of healthy subjects, we have identified normal resting BEN distributions (Wang et al., 2014) and its associations with age, sex, educations, and neurocognitions (Wang, 2021). The neurocognitive correlates of resting BEN were further supported by the correlations between regional BEN and the magnitude of task activations and task de-activations in the corresponding activated and de-activated brain regions (Lin et al., 2022). Moreover, the translational value of resting BEN has been implicated by its alterations found in various brain diseases (Sokunbi et al., 2013; Zhou et al., 2016; Li et al., 2016; Wang et al., 2017, 2020; Xue et al., 2019; Lin et al., 2019; Jiang et al., 2023). Importantly, we have demonstrated that regional BEN is modifiable through repetitive transcranial magnetic stimulations (Chang et al., 2018; Song et al., 2019), and medication (Liu et al., 2020).

Thus far, the vast majority of BEN mapping research is based on rs-fMRI. Few studies have examined regional BEN changes in response to task activation or deactivations. Based on sensorimotor task fMRI from a small cohort of healthy subjects, we have showed task-induced regional BEN reductions in motor and visual cortex (Wang et al., 2014). Using a subset (n=100) of the Human Connectome Project (HCP) cohort (Van Essen et al., 2013), Nezafati et al. (Nezafati et al., 2020) demonstrated reduced BEN in both cortical and subcortical regions during a working memory task.

In this study, we compared task-based to rs-fMRI based BEN to examine task performance-induced alterations of BEN. BEN was computed for each voxel’s time series using sample entropy (SampEn), which is an approximate formula for the conditional entropy. High BEN values indicate high irregularity or high uncertainty, which corresponds to low regularity or coherence. While this method does not directly address the repertoire of states accessible to the brain, recent findings suggest that these measures are indeed related (Hull & Morton, 2023). Compared to previous works (Wang et al., 2014; Nezafati et al., 2020), we used the entire large cohort from the HCP to gain more statistic power and examined four different tasks to investigate the generalizability and specificity of the task-induced BEN changes. Moreover, while previous studies calculated BEN using the entire task-fMRI time series, here the task fMRI BEN was calculated using only fMRI images extracted from task blocks. We hypothesize that high order cognitive tasks compared to resting state would reduce BEN in task activated regions as well as in the temporal fronto-parietal circuits that are often deactivated by cognitive tasks, which would indicate a more regular brain activity during task performance. In addition, BEN from non-task blocks (i.e., fixation blocks) was separately calculated and compared to task-related BEN to examine the within-session task-induced BEN changes, and to resting BEN to explicitly explore residual task performance-induced BEN alterations on the non-task performing brain state. We predict that task compared to control BEN would be associated with task specific BEN reduction. Moreover, we hypothesize that BEN during control state would not be restored to the resting state in the task-free control condition.

Materials and Methods

Ethics statement

Data acquisition and sharing have been approved by the HCP parent IRB. Written informed consent forms have been obtained from all subjects before any experiments. This study re-analyzed the HCP data and data Use Terms have been signed and approved by the WU-Minn HCP Consortium. Code is available from https://github.com/zewangnew/BENtbx.

Data descriptions

Sample size was determined by downloading participants from the HCP dataset (N = 1206) (Van Essen et al., 2013), and excluding participants with missing neuroimaging or sociodemographic data. The final sample included 1096 healthy young adults (mean age = 28.78 ± 3.69, range: 22 – 37 years old; mean years of education = 14.86 ± 1.82, range = 11–17; male/female: 550/656). Task-fMRI and rs-fMRI data were retrieved from HCP dataset. All MRI data were acquired with a connectome dedicated 3 Tesla (3T) Siemens MR scanner using the following parameters: repetition time (TR) = 720 ms, echo time (TE) = 33.1 ms, resolution = 2×2×2 mm³ (detailed information about acquisition protocols can be found in Van Essen et al., 2013). Task-fMRI and rs-fMRI were pre-processed using the HCP full pre-processing pipeline, which included the following steps: correction for spatial distortions, head motion, and B₀ distortions, registration to T1-weighted structural images, normalization to MNI space, global intensity normalization, and masking out non-brain voxels (Glasser et al., 2013). Then, confounds and non-neuronal artifacts (including physiological signals) were removed using high-pass temporal filtering and independent component analyses (ICA)-based artifact removal (Glasser et al., 2013; Smith et al., 2013).

Task-fMRI

Four task-fMRI experiments were considered in this study: motor (Thomas Yeo et al., 2011; Buckner et al., 2011), social (Castelli et al., 2000; Castelli, 2002; Wheatley et al., 2007; White et al., 2011), working memory (WM) (Barch et al., 2013), and gambling (Delgado et al., 2000; Tricomi et al., 2004; May et al., 2004; Forbes et al., 2009) tasks.

All tasks were presented to the participants in text or video projected to the screen in the back of the MR scanner. Participants saw the screen through the mirror hooked on the head coil. During the motor task, participants were instructed through visual cues to squeeze their left or right toes (LT and RT, respectively), tap left or right fingers (LF and RF, respectively), or move their tongue. In the social cognition task, subjects were presented with short video clips of objects (i.e., squares, circles, triangles) that either interact in some way, or moved randomly on the screen. After the video clip, the participants were asked to judge whether the objects had a mental interaction, not sure, or no interaction. The WM task consisted of pictures of places, tools, faces, and body parts presented in separate blocks. One half of the blocks included a 0-back WM task, and the other half a 2-back WM task. The gambling task consisted in a card game where subjects had to guess the number on a mystery card in order to win or lose money; the task included mostly rewarding and mostly loss trials.

To exclude participants with high motion, the Framewise Displacement (FD) (Power et al., 2012) was calculated for each task, and participants with FD > 0.2 (Gu et al., 2015) were excluded from the sample. The final number of participants of each task, along with the conditions and number of blocks, duration and number of volumes within each task are summarized in Table 1. Detailed task design and imaging parameters can be found in (Barch et al., 2013).

Table 1.

fMRI tasks used to calculate performance-related brain entropy (BEN). For each task, we reported the number of participants that completed that task as well as the task conditions, the number and duration of the blocks within each task. Task-blocks were concatenated and used to compute task BEN, while fixation blocks were used to compute control BEN (see “Conditions” column).

	Conditions	Blocks number (duration, number of volumes)
Motor task (N = 688)	Left toe (Task) Right toe (Task) Left finger (Task) Right finger (Task) Tongue (Task) Fixation (Control)	2 blocks (12s, 16 volumes each) 2 blocks (12s, 16 volumes each) 2 blocks (12s, 16 volumes each) 2 blocks (12s, 16 volumes each) 2 blocks (12s, 16 volumes each) 3 blocks (15s, 20 volumes each)
Social cognition task (N = 755)	Interaction (Task) Random (Task) Fixation (Control)	2 blocks (15s, 20 volumes each) 3 blocks (15s, 20 volumes each) 5 blocks (15s, 20 volumes each)
Working memory task (N = 782)	0-back (Task) 2-back (Task) Fixation (Control)	4 blocks (25s, 34 volumes each) 4 blocks (25s, 34 volumes each) 4 blocks (15s, 20 volumes each)
Gambling task (N = 809)	Mostly rewarding (Task) Mostly loss (Task) Fixation (Control)	2 blocks (15s, 20 volumes each) 2 blocks (15s, 20 volumes each) 4 blocks (15s, 20 volumes each)

BEN mapping

Participants of the HCP completed four rs-fMRI and two task-fMRI runs (i.e., each task was completed twice). For both acquisitions, only the first run was used for BEN mapping. BEN maps were calculated with the BENtbx (Wang et al., 2014) using the preprocessed rs-fMRI and task-fMRI images provided by HCP. The BENtbx was updated to be compatible with the CIFTI image format used by HCP and be able to automatically locate the specific task-block associated images based on the event timing file (EV file). The updated version of BENtbx is available in https://github.com/zewangnew/BENtbx. For each task-fMRI, images from all task blocks were extracted and time concatenated to form a new time series for calculating BEN (i.e., task BEN). Following the same procedure, BEN was calculated from fixation blocks of each task-fMRI (i.e., control BEN). To control for potential residual task-related activations in the fixation blocks, control BEN was computed excluding the first 2 seconds of the fixation blocks. See Table 1 for information about the conditions used to compute task and control BEN in each task. This procedure is consistent with previous findings showing that BEN can be accurately estimated from discontinuous segments (Grandy et al., 2016). However, in contrast with Grandy et al. (2016), in this study entropy was not calculated within each block separately. The rationale of this procedure is that calculating entropy within each block has a severe instability problem because fMRI data often do not have many time points for each block. Finally, BEN was obtained from rs-fMRI sessions (i.e., resting or rest BEN). To prevent any potential systematic entropy value difference caused by the difference of time series length, rs-fMRI time series was truncated to match the length of task and fixation blocks before BEN calculation. Truncation of rs-fMRI runs was performed using the following procedure: blocks of rs-fMRI time series corresponding to start and end times of the task blocks were extracted and concatenated; the same procedure was followed using the start and end times of the fixation blocks as reference. Finally, two rest BEN maps were obtained, one using the concatenated rs-fMRI blocks obtained using task blocks as reference, and the other using the concatenated rs-fMRI blocks obtained using the fixation blocks as reference.

Briefly, entropy values were calculated using SampEn formula, which is the logarithmic likelihood that a small section (within a window of length ‘m’) of the data that “matches” with other sections will still “match” the others if the section window length increases by 1. “Match” is defined by a threshold of r times standard deviation of the entire time series. Window length m is widely set to be from 2 to 3 (Wang et al., 2014). However, a window length of 1 was used here to minimize the potential effects of the time gap and the potential signal abrupt changes at the boundaries of different blocks. The embedding vector matching cut-off should be selected to avoid “no matching” (when it is too small) and “all matching” (when it is too big) (Richman & Moorman, 2000). Based on previous publications (Wang et al., 2014)⁠, a cut-off threshold of 0.6 was adopted in this study.

Statistical Analysis

For each fMRI task, an ANOVA analysis was first performed to detect any difference between the task BEN, control BEN, and the two resting BEN maps. Statistically significant results were defined by a threshold of F > 12.49, corresponding to P < 0.05 corrected for multiple comparisons using the family-wise error (FWE) method (Nichols & Hayasaka, 2003). Moreover, ANOVA analysis was performed between the task BEN of all tasks to investigate for significant differences between task-induced BEN alterations. For this analysis, only participants who completed all four tasks and were not excluded due to excessive motion were included in the sample (N = 491). For this analysis, statistically significant results were defined by a threshold of F > 12.66, corresponding to P < 0.05 corrected for multiple comparisons using the family-wise error (FWE) method (Nichols & Hayasaka, 2003). In addition, the mean task BEN was calculated for each task. Before calculating the mean task BEN, the task BEN map of each participant was normalized by dividing the value of each voxel by the mean of the whole brain. Then, a series of group level BEN comparisons were performed involving task BEN, control BEN, and resting BEN. The comparisons were performed using paired t-test. As mentioned above, for each paired comparison the rs-fMRI time series was truncated to match the length of the task fMRI to avoid the BEN calculation bias caused by the data length difference.

For each fMRI task, three types of comparisons were made: 1) task BEN vs resting BEN. For this analysis, aiming at assessing task-induced BEN changes compared to resting state, we used resting BEN maps calculated from rs-fMRI time series concatenated using task blocks as reference; 2) task BEN vs control BEN. Similar to the standard task activation detection in task fMRI analysis, this comparison aimed at examining the within-session task-induced BEN changes; 3) control BEN vs resting BEN. For this analysis, we used resting BEN maps calculated from rs-fMRI time series concatenated using fixation blocks as reference. This analysis explored the residual task effects in the control condition of the task fMRI scan. Statistically significant BEN changes were defined by a threshold of T > 5.46, corresponding to P-FWE < 0.01.

Results

ANOVA and mean Task BEN

ANOVA analyses between the four BEN maps of each task showed significant group differences (Motor task: F_3,684 > 12.49, n = 688, P-FWE < 0.05; Social cognition task: F_3,751 > 12.49, n = 755, P-FWE < 0.05; WM task: F_3,778 > 12.49, n = 782, P-FWE < 0.05; Gambling task: F_3,805 > 12.49, n = 809, P-FWE < 0.05) (see Figure S1 in Supporting information). ANOVA analysis between the task BEN of each task showed significant differences in occipital and parietal, as well as the OFC cortex (F_3,1003 > 12.66, n = 491, P-FWE < 0.05) (see Figure S2 in Supporting information). The mean task BEN of each task resulted in a very similar pattern, with no difference across task detectable by visual inspection (Figure S3 in Supporting information).

Task BEN vs resting BEN

For all fMRI tasks, the task vs resting BEN comparison resulted in a similar pattern of BEN alterations (Motor task: T₆₈₇ > 5.46, P-FWE < 0.01; Social cognition task: T₇₅₄ > 5.46, P-FWE < 0.01; WM task: T₇₈₁ > 5.46, P-FWE < 0.01; Gambling task: T₈₀₈ > 5.46, P-FWE < 0.01) (Figure 1). Overall, the task performance was characterized by reduced BEN in peripheral brain regions, including bilateral visual and motor cortices, temporal and parietal lobes, and prefrontal cortex, such as lateral and medial orbito-frontal cortex (OFC) and dorso-lateral prefrontal cortex (DLPFC). Moreover, task performance compared to resting-state was related to increased entropy in centric regions of the cerebral cortex and in subcortical areas, including the superior part of the motor network (e.g., supplementary motor area and precentral gyrus), cerebellum, fusiform gyrus, limbic regions (i.e., hippocampus, amygdala, ventral striatum, basal ganglia, insula, thalamus), cingulate cortex, and precuneus.

Figure 1.

Statistically significant difference between task BEN vs resting BEN in the motor task (A), social task (B), working memory task (C), gambling task (D). Higher t-values (hot colors) indicate higher BEN, and lower t-values (cold colors) indicate lower BEN in the task BEN.

Task BEN vs control BEN

For the motor, social, and gambling tasks (Motor task: T₆₈₇ > 5.46, P-FWE < 0.01; Social cognition task: T₇₅₄ > 5.46, P-FWE < 0.01; Gambling task: T₈₀₈ > 5.46, P-FWE < 0.01), the task vs control BEN comparison mainly resulted in BEN reductions located in the OFC, cerebellum, occipital and temporal regions as well as superior parietal cortex (Figure 2A, 2B, and 2D). Small clusters of BEN increase were detected in the ventral temporal cortex, dorsal parietal cortex, and cerebellum in the motor and social tasks. No significant difference was observed in the WM task (WM task: T₇₈₁ > 5.46, P-FWE < 0.01).

Figure 2.

Statistically significant difference between control BEN vs task BEN in the motor task (A), social task (B), working memory task (C), and gambling task (D). Higher t-values (hot colors) indicate higher BEN, and lower t-values (cold colors) indicate lower BEN in the task BEN.

Control BEN vs Resting BEN

For the motor, social, and gambling tasks (Motor task: T₆₈₇ > 5.46, P-FWE < 0.01; Social cognition task: T₇₅₄ > 5.46, P-FWE < 0.01; Gambling task: T₈₀₈ > 5.46, P-FWE < 0.01), the control BEN vs resting BEN comparison resulted in the peripheral BEN reduction and centric BEN increase pattern already described above (Figure 3A, 3B, and 3D; see also Figure 1). The WM was characterized by BEN reduction in the occipital cortex (WM task: T₇₈₁ > 5.46, P-FWE < 0.01) (Figure 3C).

Figure 3.

Statistically significant difference between resting BEN vs control BEN in the A) motor task, B) social task, C) working memory task, D) gambling task, and E) relational task. Color bar is based on t-values. Higher t-values (hot colors) indicate higher BEN, and lower t-values (cold colors) indicate lower BEN in the control BEN.

Discussion

We examined task performance induced BEN changes using four different task fMRI data from HCP. Our major findings are: 1) compared to the resting state, task performance induced BEN change patterns with a clear bifurcation between the peripheral cortical area and the interior cortical and subcortical regions: the peripheral areas showed BEN reduction while the interior brain showed BEN increase; 2) compared to control condition, the motor, social, and gambling tasks showed BEN reductions in occipital, orbitofrontal, and parietal regions; 3) compared to resting state, the control conditions resulted in the same pattern of BEN peripheral reduction and interior increase observed when comparing the task vs resting BEN.

In contrast with our initial hypothesis, we observed task-induced BEN changes not only in the task-activated and task-deactivated brain regions but also in other regions. Task performance was generally related to reduced BEN in peripheral cortical areas mainly located in visual cortex, default mode network (Raichle et al., 2001), and attention network (Damoiseaux et al., 2006). These regions include those showing task activations and deactivations as reported in (Barch, Burgess et al. 2013). This finding indicates a more regular brain activity in these regions during task performance, and possibly reflect a greater involvement of attentive processes, corresponding to narrowed (i.e., more regular) brain activity patterns, during the task performance (Barch et al., 2013). This regularity or organization increase is consistent with our previous finding of lower resting entropy in these regions corresponding to better cognitive functions (Wang, 2021) and stronger task activation and deactivations (Lin et al., 2022). Compared to the resting state, task performance increased BEN in the centric sensorimotor and perception system, which indicates high irregularity and information capacity in these regions (Shannon, 1948). The increased entropy in the sensorimotor network and perception networks may reflect a need of higher information capacity to allow the brain to have more flexibility to adjust the actions in response to the unknown task. Moreover, the mean task BEN was very similar across tasks, with no difference detectable by visual inspection, and the ANOVA analysis between the task BEN of all tasks detected significant differences only in the occipital cortex. These findings suggest that task-related BEN alterations were largely independent of the cognitive domain.

The task vs control BEN comparison is similar to a standard contrast analysis typically used in fMRI to detect the task specific brain activations. However, while the standard contrast analysis is based on mean difference between two contrast conditions, the BEN comparison detects difference in the mean brain activity irregularity between two different conditions. Our results showed task-related (Zhang et al., 2016) BEN reductions in the motor, social, and gambling tasks mainly located in the occipital, orbitofrontal, and parietal regions. As discussed above, BEN reduction in these regions indicates a more organized brain activity and might reflect higher engagement of attentive processes during the task compared to fixation blocks. No difference between task and control BEN was detected for WM task, suggesting that substantial residual task-effects exist in the control condition.

The control vs resting BEN comparison showed the same pattern of peripheral BEN reduction and centric BEN increase described above. This pattern was substantially reduced in the WM and gambling tasks. Overall, this finding might suggest that the duration of the fixation blocks was not sufficient to bring BEN to a base level, as that observed during resting-state. Thus, the broad BEN alterations observed in this contrast for most tasks might still reflect the engagement of attentive and high-level cognitive processes during the task blocks.

A previous study by Nezafati et al. (Nezafati et al., 2020) reported reduced entropy during working memory task in both cortical and subcortical regions, which seems to be contradictory to our findings in the centric brain regions. However, their results were based on 100 participants from the HCP data, and they did not report statistical significance level for that reduction. Moreover, it is worth nothing that the HCP rs-fMRI data include 1200 data points, which is much longer than the task fMRI. As demonstrated by (Wang et al., 2014) using synthetic data, longer time series tends to produce lower SampEn value because of the increased number of time segments available for the matching process. To avoid this confound, we specifically controlled the data length by chopping the rs-fMRI time series to match the length of the task-fMRI run before calculating BEN. In addition, in (Nezafati et al., 2020) task BEN was calculated from the entire task fMRI, including the control condition. Including the control condition may reduce the overall entropy due to the modulation of the systematic on-off task design. To avoid the systematic influence of the low frequency periodic design function, we instead calculated task BEN from the task blocks only after excluding the fixation blocks from the entire fMRI time series. Nevertheless, we still found similar bidirectional BEN change patterns in the resting BEN vs task BEN comparisons even when BEN was calculated from the entire task fMRI time series rather than the task blocks alone (data not shown).

Compared to the standard general linear model (GLM) based activation detection results (Barch et al., 2013), our control vs task BEN difference was spatially less extended. This detection sensitivity difference may be attributed to the fundamental difference between magnitude and entropy. GLM is designed to detect the change of the mean signal, while our study aimed at revealing the change of signal irregularity or equivalently the change of the signal change. Our BEN analysis results showed the task performance induced brain activity irregularity changes, which are complementary to those identified by standard GLM.

Overall, our results provide new insights into how BEN is altered during task performance. One limitation of current study is that task conditions have different number of timepoints making it difficult to compare them. In addition, it is worth noting that the number of volumes for some task conditions (e.g., control BEN of the motor task) was relatively low, thus reducing the stability of BEN calculation. Future research is needed to overcome these limitations and replicate these findings.

Conclusion

In this study, we investigated BEN changes associated with task performance during fMRI, task-fMRI control condition, and rs-fMRI. Overall, our results provide novel insights into how BEN is related to brain activity by suggesting that regional BEN is sensitive to task performance during fMRI. Indeed, compared to resting state, task performance was associated with reduced BEN (i.e., more regular brain activity) in peripheral brain regions, and increased BEN in sensorimotor and perception regions, which might reflect a higher capacity for information processing. The difference between task and control BEN was only moderate, with task compared to control conditions showing lower BEN in occipital, orbitofrontal, and parietal regions. This finding indicates that task and control BEN were substantially similar, with lower task BEN in the regions mentioned above reflecting a greater allocation of cognitive resources during the task blocks. The control compared to resting state was associated to a similar pattern of BEN increase and decrease, indicating a substantial residual effect of task performance during the control condition.

Significance statement.

Brain entropy (BEN) has recently gained increasing interest as a unique signature of brain activity. While this technique has been extensively used to characterize brain activity during resting state, evidence regarding BEN alterations during task performance is still lacking. To address this gap, this study aims at comparing BEN estimated during resting-state, task performance, and control blocks of task-fMRI sessions. Overall, results showed that task performance and control blocks are related to reduced BEN in cortical brain regions involved in attentive and higher-level cognitive processes, and increased BEN in brain regions involved in sensorimotor and perception networks.

Data Accessibility Statement

Data are accessible upon approval of the Human Connectome Project, Wu-Minn Consortium.