Experimental diagram of this study.

The upper sub-graph illustrates the whole multiple sessions tDCS neuromodulation pipeline including seven sessions (days) and eight task-demanded days. Here, the “flash” icon indicates conducting tDCS neuromodulation (active anodal stimulation for active NM group and sham stimulation for sham NM group). This “+” label means a task-demanded day, where no stimulation is required for participants but all the covariates of interests should be measured by experience sampling methods. The bottom sub-graph reflect specific pipeline in task-demanded days. Participants were required to provide response at five progressive time moments nearing deadline for task aversiveness and outcome value in task-demanded days. In this diagram, the icon of “clock” symbolize ecological momentary assessment for measuring instant task willingness and outcome value. In addition, twice tests for daily emotions (labeled by “+”) were added for participants at 10:00 and 16:00 as covariates of no interests to be adjusted.

Flow diagram of CONSORT (A) and partial details of randomized groups (B-D) and neural locations of electric pole (E).

B plots the distribution of all the participants procrastination scores (GPS = general procrastination scale). C detailed what the full randomized block design is. D shows the comparison between active neuromodulation group and sham control for procrastination scores. E indicates the pipeline to determine the location of electric pole. The 10-20 EEG standard lead is used to locate the left dorsolaterial prefrontal cortex (DLPFC) initially, and the neuronavigation is further utilized to locate the exact location of this targeting region (i.e., left DLPFC).

Demographic information for included participants.

NM represents active neuromodulation group and sham indicates sham-control group. Anxiety symptoms were measured by State-Trait Anxiety Inventory (STAI). Depression symptoms were tested by Self-Rating Depression Scale (SDS). BF10 describes the Bayesian evidence strength to support alternative hypothesis, with > 3 for a strong evidence.

Results of neuromodulation effects to task-execution willingness and procrastination rates (PR).

A shows the effects of neuromodulation to increase task-execution willingness for both active group and sham control across sessions that included in formal analysis (session 0 (baseline), 2, 3, 5, 6, 7). B illustrates the effects of whole neuromodulation round to task-execution willingness for both group. C plots the changes of task-execution willingness for both group after neuromodulation. D provides a line chart to show the changes of task-execution willingness across each session that included in formal analysis. E shows the effects of neuromodulation to reduce PR for both active group and sham control across sessions that included in formal analysis. F illustrates the effects of whole neuromodulation round to PR for both group. G plots the absolute changes of PR for both group after neuromodulation. H provides a line chart to show the changes of PR across these sessions that included in formal analysis. Pie graph for each comparison represent the corresponding result of Bayesian factor inference, with brown piece for supporting H1 evidence and white piece for supporting H0 evidence. Each bar indicates mean value, and each line placed onto the bar reflects standard deviation (SD).

Results of neuromodulation effects to task aversiveness and outcome value.

A shows the effects of neuromodulation to increase AUC of task aversiveness for both active group and sham control across sessions that included in formal analysis (session 0 (baseline), 2, 3, 5, 6, 7). B plots the changes of AUC of task aversiveness for both group after neuromodulation. C shows the effects of neuromodulation to increase outcome value for both active group and sham control across sessions that included in formal analysis. D plots the changes of outcome value for both group after neuromodulation. E provides a line chart to show the changes of AUC of task aversiveness across these sessions that included in formal analysis. F provides a line chart to show the changes of outcome value in the same manner. Pie graph for each comparison represent the corresponding result of Bayesian factor inference, with brown piece for supporting H1 evidence and white piece for supporting H0 evidence. Each bar indicates mean value, and each line placed onto the bar reflects standard deviation (SD).

Summary for general linear model in predicting changes of task aversiveness and outcome value to actual procrastination.

S.E. means standard error. * p < .05.

Results of Quasi-Bayesian causal model for the medicated role of increased task outcome value in the association between neuromodulation and task-execution willingness (A) and actual procrastination rates (B).

ADE = averaged direct effect, ACME = averaged causal mediated effect, CI = confident interval.

Changes of actual procrastination rates among pre-test, post-test and 6-month follow-up for active neuromodulation group and sham-control group.

Pre-test means to test the actual procrastination rates before first HD-tDCS neuromodulation. Post-test means to test the actual procrastination rates after last neuromodulation. The 6-month follow means to re-investigate the actual procrastination rates after last neuromodulation for 6 months.

The number of reporting additional side effects in both group across all the session.

Here, we conducted a post-neuromodulation investigation to require participants to report whether their performance for completing task was influenced by additional impacts outside normal conditions, such as “get a flu”, “get a fever”, “mandatory assignment for other tasks” and “unexpected emergency events”. If in this case, they should report what additional side effects occur. In the S1, all the 44 participants reported expected effects from the neuromodulation. In the S1, one participant reported to be in flu. In the S3, both participants in NM group reported a mandatory meeting assignment, whist one participant in the SC reported a bicycle accident and additional two reported mandatory meeting assignment. In the S4, all the 39 participants reported that their task performances are fully disrupted by the weekends. S5-7 reported the similar additional AE mentioned previously.

Summary of NMSE for all the machine learning algorithms.

KNN = K-nearest neighbor; SVM = support machine learning

Summary of JM for longitudinal process and event process by using outcome value as independent variable.

Summary of JM for longitudinal process and event process by using task aversiveness as independent variable.

Summary for linear probability panel model in predicting task-execution willingness by using task aversiveness and outcome value.

S.E. means standard error.

Summary for causal mediation model in predicting task-execution willingness by using treatment (active ms-tDCS vs sham) from medicated effect of increased task outcome.

Summary for causal mediation model in predicting actual procrastination by using treatment (active ms-tDCS vs sham) from medicated effect of increased task outcome.

Statistical power estimation by using ANOVA model and power contours according to experimental design

Density of intercept and group-between effect from MCMC sampling for the task-execution willingness.

Density of intercept and individual-within effect from MCMC sampling for the task-execution willingness.

Density of intercept and group-between effect from MCMC sampling for the actual PR.

Density of intercept and individual-within effect from MCMC sampling for the actual PR.

Density of intercept and individual-within effect from MCMC sampling for the task aversiveness.

Density of intercept and group-between effect from MCMC sampling for the task aversiveness.

Density of intercept and group-between effect from MCMC sampling for the outcome value.

Density of intercept and individual-within effect from MCMC sampling for the outcome value.

Summary for causal mediation model in predicting task aversiveness by using treatment (active ms-tDCS vs sham) from medicated effect of increased task outcome.