Introduction: Functional magnetic resonance imaging (fMRI) often involves long scanning durations to ensure the associated brain activity can be detected. However, excessive experimentation can lead to many undesirable effects, such as from learning and/or fatigue effects, discomfort for the subject, excessive motion artifacts and loss of sustained attention on task. Overly long experimentation can thus have a detrimental effect on signal quality and accurate voxel activation detection. Here, we propose dynamic experimentation with real-time fMRI using a novel statistically driven approach that invokes early stopping when sufficient statistical evidence for assessing the task-related activation is observed.Methods: Voxel-level sequential probability ratio test (SPRT) statistics based on general linear models (GLMs) were implemented on fMRI scans of a mathematical 1-back task from 12 healthy teenage subjects and 11 teenage subjects born extremely preterm (EPT). This approach is based on likelihood ratios and allows for systematic early stopping based on target statistical error thresholds. We adopt a two-stage estimation approach that allows for accurate estimates of GLM parameters before stopping is considered. Early stopping performance is reported for different first stage lengths, and activation results are compared with full durations. Finally, group comparisons are conducted with both early stopped and full duration scan data. Numerical parallelization was employed to facilitate completion of computations involving a new scan within every repetition time (TR).Results: Use of SPRT demonstrates the feasibility and efficiency gains of automated early stopping, with comparable activation detection as with full protocols. Dynamic stopping of stimulus administration was achieved in around half of subjects, with typical time savings of up to 33% (4 min on a 12 min scan). A group analysis produced similar patterns of activity for control subjects between early stopping and full duration scans. The EPT group, individually, demonstrated more variability in location and extent of the activations compared to the normal term control group. This was apparent in the EPT group results, reflected by fewer and smaller clusters.Conclusion: A systematic statistical approach for early stopping with real-time fMRI experimentation has been implemented. This dynamic approach has promise for reducing subject burden and fatigue effects. Analysis of task-based fMRI scans is typically performed with fixed, predetermined experimental designs. As a result, subjects must often endure stimulus protocols that are overly long in order to ensure the neural activity can be statistically discerned in the noisy data. However, this can lead to fatigue, learning effects and excessive motion, such as from agitation, as well as being costlier to administer due to longer scan times and potentially less reliable measurement. Also, the experimenter does not know if the neural activity is detectable until long after the scanning session is over. Real-time functional MRI (RT-fMRI) provides an opportunity to ameliorate these issues. RT-fMRI has been successfully applied in the field of neurofeedback and biofeedback from neural responses, where subjects may be trained to alter their brain activity based on real-time information provided from the fMRI scans. This has been reported in ADHD , healthy) Shorter scan times for fMRI testing: Shorter scan times cannot only save in technology and personnel costs, but fatigue and learning effects can be avoided, improving signal quality. Scanning becomes less burdensome on the subject as well, which is an especially important consideration for children or elderly subjects. (2) Real-time quality control: greater consistency in activation classification error can be obtained, through statistical error-based benchmarks for stopping rules and real-time feedback on classification performance and adjustment of stimulus durations. (3) Richer information: Paradigms can become more complex and sophisticated. With greater time efficiency and flexibility, more variations of a stimulus, such as reflected by a broader range of difficulty levels, can be administered in the same amount of time. (4) Wide applicability: Dynamic adjustment of stimuli based on BOLD response in real-time can be generally applied across a range of focus areas that investigate localization of brain activity, including cognition and motor functioning.The benefits of adaptive RT-fMRI include: . The fMRI stimulus was a mathematical version of the well-known 1-back task. Early stopping was implemented using sequential probability ratio test (SPRT) statistics and our server was a Linux workstation located in a nearby building. Processing of RT-fMRI was completed within 3 s, always before the next scan arrived. We observed time savings of up to 33% based on early stopping when 80% of voxels were classified, which equals up to 4-min savings with a 12-min scan. The impact on activation analysis from the selection of early stopping criteria is assessed, as described in detail below. Finally, as an illustration, we conduct a comparison of group analyses between difficulty levels for EPT and healthy control subjects, to assess the effects of early stopping in this context.t , the GLM takes the form:Briefly, the general linear model involves convolving a double gamma hemodynamic response function (HRF) with task indicator variables that denote timing of administration to reflect expected task-related BOLD responses. Voxel-level task-related regression parameters are estimated and represent the association of the observed response to expected task-activated BOLD signal. Thus, activation is assessed through statistical inference on regression parameters. For a given voxel up to time Yt is a t × 1 vector of observed BOLD signal intensities for the voxel up to time t, Et is a t × 1 vector that represents the error terms, Xt is a t × p design matrix and includes the expected BOLD signal values per condition and β = [b1…bj…bp]′ is a p × 1 regression coefficients vector. In this formulation, a regression parameter bj can represent magnitude of association with condition j. Et is assumed to be distributed as multivariate normal with mean zero and covariance Wt, where Wt is a t × t covariance matrix. Error variances comprise the diagonal elements. For spatial correlation, we conduct spatial smoothing, so do not explicitly model the spatial correlation structure. Yt is assumed to have a multivariate normal probability distribution as follows:where Wt| is the determinant of Wt. At each voxel, the focus is on estimation of cβ, where c is some 1 × p linear contrast. Hence, we consider the more general scenario when inferential interest can also be a linear combination of the task parameters, which includes the single task parameter case. The standard linear estimate for cβ at time t is:where | This estimator is normally distributed and unbiased under (1.2). We fit regression models in parallel for all voxels under consideration in a target region of interest (ROI), which could be a particular structure or include the whole brain. Real-time analysis requires signal and image processing steps, as well as the continual updating of statistical estimates as new scan data are received from the scanner. Hence, given the large number of voxels to be analyzed, real-time fMRI presents “big data” computational challenges.W, which were too slow to estimate for real-time implementations given our available computational resources.In our previous work , we assur^[cβt^] . The san be slow . The appAt the voxel level, we can use the sequential analytic framework of H0: cβ = cβ0 versus Ha: cβ ≥ cβ1, where c(β1 − β0) > 0. Two-sided formulations are described in The general procedure of Wald’s SPRT is as follows. Consider a one-sided hypothesis of the form cβ0 or cβ1 is the true value of the parameter of interest and conditioning on the estimated variance. After Yt is observed up to time point, t, one of three possible decisions is made according to the following rules:where 1.B < Λt < AContinue sampling, if 2.H0, if Λt < BStop sampling and accept 3.aH, if A < ΛtStop sampling and accept where stopping boundaries are:E and βE. Note that both the Type I and Type II error levels are controlled for with SPRT, as opposed to standard hypothesis test formulations that only control for Type I error level. Multiple SPRTs are conducted concurrently across voxels. This can in principle be adjusted for by Bonferroni correction to account for this simultaneous testing. If the specified Type I error levels are too small, however, this can affect the feasibility of early stopping. Although not done here, it is possible to also consider post-hoc multiple comparisons methods after experimentation is completed . Given an estimated value t scans, we solve for the value of θ1 = cβ1 that satisfies:A practical modification of the original SPRT formulation for stopping is to consider the truncated SPRT , which w1 as the alternative hypothesis value for cβ, so that the activation magnitude threshold in the alternative hypothesis is held constant. Note that zt will thus tend to increase across scans, since This value becomes the alternative hypothesis, and it represents the voxel-level targeted activation magnitude threshold. For subsequent scans we fix the value of θcβ parameter values that are “in-between” the null and alternative hypothesis values, the SPRT is indifferent to preferring one hypothesis over the other. This leads to larger numbers of scans needed before a stopping boundary is crossed. So, we have to accept a lack of decisive stopping decisions for these cases in order for overall experimentation to stop early. This can be an acceptable trade-off for shorter experimental scan times and the ability to tailor experimentation.Ultimately, we aggregate the findings of the voxel-level SPRTs to determine whether or not experimentation within a block design should be terminated early. A “global” stopping rule that considers all voxels in a region of interest  that we have adopted is to terminate task administration when a predetermined percentage of voxels have been classified by their respective SPRTs. For instance, we have used 80% as a global stopping criterion. Note that 80% classified means either as active or non-active. We choose this cut-off as it is fairly strict, and yet approximately one half of the participants still stop early. As we will see, it also facilitates correspondence with full scan data results, particularly if the activation threshold is adjusted to recognize longer scan durations. We also consider other global stopping criterion here, 70 and 90%, and assess impact on stopping times and resultant images arising from early stopping. We also choose the SPRT target Type I and Type II error levels that are relatively more stringent for Type I error. Note that for Twelve healthy subjects were recruited, 7 males. They were aged 15–16 years old and 11 were right-handed. They had no known neurological conditions and a normal developmental history. A group of 11 adolescents born EPT were also recruited, 1 male. EPT was defined as being born at <26-week gestation and weighing < 1000 g. All were aged 15–17 years old and 8 were right-handed, 2 left-handed and 1 ambidextrous. All subjects were recruited as part of a larger study to evaluate functional and structural differences associated with mathematical abilities and working memory between those born EPT and those born at normal term. The aim of the larger study is to improve our understanding of mathematics disabilities and potentially lead to improvements in pedagogical practices for young people experiencing problems acquiring mathematics skills. Adolescents were recruited as they can handle the stress of fMRI experimentation, are mathematically advanced enough and have had time to master the subject area compared to younger children. This age range is also an advantageous time to implement interventions to improve mathematical abilities before leaving school, hence adults were not studied. EPT subjects were included to show that differences with patient populations are detectable with our methods. A subsection of the full study is reported here to demonstrate the real-time analysis.The subjects made one two-h visit to the MRI department at University Hospitals Cleveland Medical Center (UHCMC). Ethics approval was obtained from the UHCMC Institutional Review Board office prior to the study and complied with the Declaration of Helsinki for human subject research. Subjects and their parents gave informed consent prior to taking part.1, As part of our wider study, subjects also made another, separate 3-h visit to the study offices to undergo neuropsychological testing and a refresher of fraction calculations. In the interests of brevity, the full neuropsychological testing results are not reported here. One finding that is particularly relevant to the fMRI task considered here is that nearly two thirds (63.6%) of the EPT cohort have lower working memory function, compared to just over one third (35.7%) of controls subjects. Working memory level was determined by sample quartiles of standardized z-scores based on the Wide Range Assessment of Memory and Learning test WRMAL1, . We deno2 (matrix 128 × 128), slice thickness was 4 mm, number of slices = 36 slices and flip angle = 90°. A SENSE P reduction factor of 2 was implemented and scans were acquired in an ascending interleaved fashion.The subjects were positioned head-first supine on the scanner bed with their head fixed in position using inflatable pads. An 8-channel head coil was used for data acquisition. Echo planar imaging scans were acquired on a Philips Ingenuity 3T PET/MR imager at UHCMC. The following fMRI scan parameters were used: TR = 3.0 s, TE = 35 ms, in-plane resolution was 1.797 mm2 (matrix 256 × 256), slice thickness was 1 mm, number of slices = 200 slices and flip angle = 8°.In addition to the fMRI scans, a high-resolution T1-weighted anatomical image of the brain was also acquired. This was taken using a magnetic preparation gradient-echo sequence (3D IR TFE). Imaging parameters were: TR = 7.5 ms, TE = 3.7 ms, in-plane resolution was 1 mmDuring data acquisition subjects were presented with a mathematical version of the well-known 1-back memory task. It involved performing basic addition and subtraction calculations and required the answer to be remembered and compared to the next answer. Two difficulty levels were included. The protocol was developed by our lab as part of a battery to assess mathematical and working memory abilities in 14–17 year olds to evaluate the functional differences between those born EPT and those born at normal term. The stimulus was presented on an MRI compatible LCD monitor  positioned at the end of the bore and viewed via a mirror attached to the head coil. Equations were presented, for example, the subject may see “2 + 3 = ?.” The subject was required to work out the answer and then remember it while working out the next equation, for example “1 + 4 = ?.” If they thought the answers matched, then the subject pressed a button on a response box held in their right hand. If they thought the answers did not match, then they did nothing but remember the new answer to compare to the answer of the next equation. An example sequence is shown in The stimulus was presented in a block design, see Two difficulty levels were included to investigate differences in neural responses associated with increasing task demand. As the brain is ‘pushed’ to solve more complex problems, differential networks may be apparent, and these may be different between normal term and EPT subjects. Additionally, increasing the difficulty level serves to maintain the subject’s attention and, generally, increases their effort. This can have the effect of increasing brain activation cluster sizes and magnitude as well as causing recruitment of additional areas, which is of interest. Incorporating difficulty levels into protocols that can separately be terminated early demonstrates the flexibility of the proposed approach.2) and libraries from PsychoPy - an open source visual presentation program . This is a program integrated into the Philips scanner software and enabled by a research clinical science key. XTC communicates with the reconstruction and scanner processes on the scanner computer and interfaces to a network client application using a minimalistic CORBA (Common Object Request Broker Architecture)  interfac4) and FSL (FMRIB’s Software Library5). The analysis sequence is detailed in the following section. The setup is shown in The Linux computer was a custom-built server equipped with a solid state hard drive and two 8-core Intel Xeon E5-2687W processors running at 3.1 GHz and providing 40 MB L3 cache. It was installed with Centos 7.4 operating system. As the scans were received, custom written Python and Bash scripts implemented the analysis using core-based parallelization to preprocess the data and perform the SPRT statistical analysis. Preprocessing was performed using standard modules from AFNI  was acquired and used for coregistration (motion correction) purposes. In preparation, the skull was removed using FSL’s Brain Extraction Tool (BET)  and a maThe resulting preprocessed images were then converted to ASCII text files for statistical analysis with SPRT producing one .txt file per fMRI scan. The text file contained the grayscale values for every voxel in a 3D image. The conversion was accomplished using ‘fsl2ascii’ command.https://bitbucket.org/tatsuoka-lab.The SPRT analysis was applied using a highly optimized C++ program that used Intel Cilk Plus library for multicore and vector processing of data. BLAS routines from Intel MKL were used to enable instruction-based acceleration for matrix computation. They are available from the Bitbucket repository at ∗2, maximum scan duration, maximum scan duration/1.5, maximum scan duration/2 and maximum scan duration/2.5. It is also possible to include the temporal derivatives of the HRF or other regressors in the design matrix where applicable in studies. Temporal derivatives were not included here due to the long durations of the block design used to present the task. Motion parameters are also frequently used as regressors to remove correlated activations produced by movement. Here motion parameter regressors were not included with the estimation of the discrete cosine transforms due to the limitations of the computational resources.The design matrix was created prior to the scan session and contained 8 columns. One column of ‘1s’ is for the intercept. Two columns represented the easy and hard stimuli. They were created using AFNI’s ‘3dDeconvolve’ command to model the HRF. Easy and hard levels were modeled separately and the contrasts applied post processing were easy or hard versus rest. We also included in the design matrix cosine functions of increasing periodicity to model major sources of noise in fMRI data. These include brain metabolism, physiology, and spontaneous fluctuations . For larImportant design parameters for implementation were selected through analysis of a training sample. For training, each subject underwent the full duration of experimentation. We determined design parameters through the following criteria:(1) First stage duration: It is desirable for the voxel-level error variance and beta parameter estimates to stabilize – we assessed this qualitatively by assessing plots from a sample of voxels. We tested 2 scenarios using either 2-blocks or 4-blocks of easy and hard stimuli first stage administration before allowing early stopping to occur. Where 2-blocks per difficulty level of stimulus administration were used before allowing early stopping, the first 78 scans were used for the first stage of experimentation. Where 4-blocks were used, 154 scans were used for the first stage. Recall, a full-length task protocol comprised 238 scans and lasted 11 min and 54 s.z-score threshold of zt = 3.10 after the first stage since this is a standard threshold value for determining activation of a voxel. We then solved for θ1, as in (1.6). After this first stage, the null and alternative hypotheses at a given voxel are set as H0: cβ = 0 and a: cβH = θ1.(2) Activation threshold: We chose a E = 0.001, βE = 0.1  Target Type I and Type II error levels: Typical values used in the literature were used to test stopping time performance, with αβE = 0.1 . We also(4) Global stopping percentage: We investigate the scenarios of classifying 70, 80, and 90% of voxels. Ideally, early stopping occurs while there is still correspondence in activation patterns to full scan durations, and general concurrence with expected activations from neuroscientific literature.The stopping rules were defined as described in Section “Sequential Probability Ratio Test”:1.B < Λt < AContinue sampling, if 2.H0, if Λt < BStop sampling and accept 3.aH, if A < ΛtStop sampling and accept where stopping boundaries are given in (1.4) and are based on target Type I and II error levels. The error levels are specified before testing begins.Although our goal was to stop scanning early it was necessary to acquire first full length datasets to fully verify our analysis methods and check the feasibility of stopping early. In addition to the subjects reported in the results, we tested early stopping in 2 other subjects to confirm that our procedures worked. Subject details and data are not reported for them as full datasets are not available.This 1-back arithmetic task involves not only number sense and mathematical calculations but also general cognitive skills involving working memory and sustained attention. The brain networks involved with each of these have been well characterized in the literature and lends itself to the evaluation of this real-time analysis method. There is a large amount of overlap for the active brain areas that control each of these functions and they appear as a frontoparietal network . The arepost-hoc analysis and can be processed with different parameters to those specified in SPRT. Raw data was preprocessed with FSL FEAT  , even wiFSL FEAT . Motion FSL FEAT ].p < 0.001). Comparing correctness percentages per subject across birth status groups, there are significant differences with the hard level (Mann-Whitney U-test two-sided p = 0.037), but not with the easy one (two-sided p = 0.401). These results indicate that the difficulty levels have different psychometric properties, and affect the groups differently. We also see this in activation patterns, as discussed in Section “Group Analysis Results” and reflected in the group analysis results.The median control subject response time across both difficulty levels was 1.44 s (SD 0.51 s), and median task accuracy was 90.8% (SD 20.2%). When these are broken down by difficulty level, the easy level median task accuracy was 86.1% (SD 22.6%) with median response time of 1.28 s (SD 0.54 s); and the hard level median task accuracy was 90.0% (SD 18.4%) with median response time of 1.56 s (SD 0.51 s). EPT subjects had a slightly longer overall median response time of 1.91 s (SD 0.48 s) and overall median task accuracy was lower at 65.8% (SD 21.2%). For the easy level, the median accuracy was 72.2% (SD 24.2%) and median response time was 1.63 s (SD 0.49 s). For the hard level the median accuracy was 70.0% (SD 19.8%) with a median response time of 2.10 s (SD 0.54 s). Note that there are statistically significant differences in same subject differences in speed to completion by difficulty level  required 145 s to conduct all SPRT analyses, starting from scan 79. Less than 1 s is required to analyze the first stage data. The subject with the fewest number of voxels  required 79 s for SPRT analyses across the scans. Overall real-time processing times in this workflow were due in most part to pre-processing computations. For the subject with the largest number of voxels, the maximum time to process one scan in real-time would be about 1.6 s . This would be even faster with more computational resources, faster transfer speeds or reducing the number of voxels being analyzed.z-score maps for easy and hard levels for each subject showed that generally, across subjects, the largest activations were centered bilaterally around the inferior and superior parietal areas, taking in the intraparietal sulcus, a region highly associated with mathematical functioning. Further activations were seen in the cuneus. These are most likely correlated with the visual processing associated with the task. Additional activations were seen in the precuneus, bilateral areas in the medial frontal gyrus, anterior cingulate, insula and inferior frontal gyrus. These areas are often associated with attention and memory systems  for 2-block first stage. For 4-block first stage, 7/12 control subjects stopped early for both the easy and hard levels. Among the EPT group, 6/11 subjects stopped early for the easy level and 9/11 subjects stopped early for the hard level. The median stopping duration for both difficulty levels for control subjects was 3 blocks of easy and 2 blocks of hard stimulus administration for 2-blocks first stage. For 4-blocks first stage, the median stopping time was 5 easy, 4 hard for both difficulty levels. In EPT subjects, the median stopping time for 2-block first stage was 3 easy, 2 hard blocks of stimuli. For 4-blocks first stage, the median stopping time was 4 easy and 4 hard for the easy level and 5 easy, 5 hard for the hard level. Depending on the number of first stage blocks, time savings of 1/3 to 2/3 (4 to 8 min on a 12-min scan) can be achieved.post-hoc analyses, and may have some potential advantages for group analysis, as discussed below. Hence, we present results for the more conservative 80% rule, which leads to relatively longer durations even when early stopping occurs.An early stopping rule based on a classification rate of at least 70 or 90% was also tested. Results reported in In summary, these results indicate that early stopping is feasible but that the parameters need to be carefully chosen. The desire for earliest possible stopping must be balanced with selections of a first stage estimation duration and a voxel classification percentage which help insure that the number of active voxels will significantly overlap with those from a full scan, and that a sufficient amount of experimentation has been conducted. Of the parameters we tested, our results indicate that useful results were obtained using 4-blocks first stage with 80% classification. We discuss this further in the Discussion section.The activation maps under the different conditions are shown in 1constant after the first stage, note that the corresponding zt-score associated with the θ1threshold actually increases as the scan durations increase. The decreasing variance of c(X′X)–1c′ . Hence, for the easy level task, a zt-score of 3.1 for 154 scans approximately corresponds to a zt-score of 4.0 for the final scan (238 scans), holding θ1 fixed. At 78 scans, a zt-score of 3.1 corresponds to a zt-score of approximately 8.37 at 238 scans, so there may be less overlap between early stopping and full duration for shorter first stage durations. See By holding the alternative hypothesis threshold θImportantly, the issue of whether early stopping or full duration provide better activation maps is best answered neuro-scientifically, through the support of literature and hypotheses. We used this training sample to assess whether early stopping activation patterns were reasonable, or too early, and compared them with full duration results. In the Supplementary, we add plots for early stopping versus full duration for each subject for which early stopping was invoked. Comparing these plots, we see that in many instances that the cluster peaks are located in the expected anatomical locations.1-values at the end of the 2-block first stage may be too early for correspondence with full duration scans, as the estimated standard deviations are relatively larger and the corresponding θ1-values for z = 3.10 in the alternative hypothesis can be larger as well, compared to a 4-block first stage.In summary, although there are similar rates of early termination between the 2-block and 4-block first stage cases, the detected activation patterns suggest that using 4-blocks of stimulus administration is more suited to determining active voxels. In p = 0.003, two-sided signed rank test). EPT group also has significantly more movement in the first half of scanning , indicating a group-level proclivity for more motion events.Note that in a subset of subjects there was some volatility due to subject movement. This may in part explain why sometimes there is a lower number of active voxels for the easy task for full duration than when stopping early. In most subjects the active voxel count increases with scan duration. Subjects 13, 15 and 17 had the most pronounced decrease of active voxel counts. Subject 13 demonstrates very few active voxels at all and there is almost no consistency in location. Further investigation shows large relative framewise displacement occurs frequently throughout the scan and many of the responses have been missed or have relatively long response times, 60.5% correct overall and 2.08 s (SD 0.97 s) average response time , respectively, satisfy their SPRT-based stopping criterion generally leads to early stopping of stimulus administration, while also leading to comparable activation classification as with the full protocol. The stricter 90% criterion was infrequently satisfied, and did not often lead to early stopping of experimentation at 4-blocks first stage estimation. Recall that when GLM parameter values are “in-between” the null and alternative hypothesis values, SPRT-based stopping is less likely at the voxel level. A 100% stopping rule is thus not feasible, as are values relatively close to 100%. The 80% rule seems conservative in that not all participants are stopped early, but there are high levels of correspondence in individual and group level activation maps with full durations, particularly when the first stage is comprised of 4 blocks. The 70% rule is more aggressive, and early stopping is invoked more frequently. Given that the resultant images from early stopping in many cases appear similar across these two rules, the 70% rule should be considered as well.The SPRT approach was effective at detecting brain activity at the individual level with early stopping in both the control and EPT groups. Note the individual variability among subjects in early stopping performance. Factors that can affect stopping times include the magnitudes of activation, variability in task performance, sustained attention levels, motion, and the noise levels in the BOLD signal. Those born EPT also can have structural abnormalities of the brain which can affect fMRI results and 2 subjects reported here had clear abnormalities that were obvious even in this low-resolution fMRI data (1.8 mm × 1.8 mm × 4.0 mm voxel size). Subtle abnormalities may have been present in some of the other subjects.The EPT group data demonstrated less consistent activity by comparison to control group data across all stopping points. In order to understand this result it is necessary to consider neuropsychological skills and structural and functional brain changes within the group. Working memory is a key skill required for both mathematics and this numerical 1-back task. Recall the lower accuracy and longer response times in the EPT group. fMRI studies on dyscalculia (difficulty in learning and performing mathematics) suggest that there is greater heterogeneity in activations with a more diffuse pattern being apparent . AdditioBased on our analysis of head movements, early stopping of data collection could be particularly useful in populations where attention is problematic, such as with young children or adults with cognitive deficits. We see in our EPT population that head movement became more frequent and had a greater amplitude in the second half of the scans when compared to the control subjects. This may be an indication of attentional fatigue. In In the future, it is possible that the first stage length can be tailored at the voxel level, once it is clear error variance and other GLM parameter estimates are relatively stable, which is expected at some point due to the convergence properties of the estimators. This may facilitate earlier stopping. Alternatively, if local computational resources are limited, note that stopping can be assessed on an interval basis, and not necessarily after every scan. Although not considered here, these BOLD signal-based early stopping rules could also possibly be enriched by incorporating individual motion displacement patterns, as well as behavioral measures such as correctness rates in experimentation.Here we demonstrated full brain analytics with parallelization using MKL Intel libraries for matrix computation with two Xeon E5-2687W 8-core processors. It is also feasible to consider only partial brain volumes where experiments demand more consideration of a particular area. Future directions for the study are to implement the SPRT and Bayesian sequential estimation methods using distributed computing approaches to increase processing speed and allow advance in stopping rule methods under shorter scan TR periods.We introduce a systematic, statistically based approach to dynamic experimentation with real-time fMRI. Saving in scan time and accurate voxel activation detection can be achieved, while redundant experimentation in block design is reduced. We investigate different aspects of how to determine early stopping rules. These analyses can be viewed as intended on a training sample to guide implementation of early stopping in future studies involving the same experiments and study populations. These methods can be particularly useful such as when investigating fragile patients and young children, as shorter scan requirements can enhance patient experience and reduce fatigue effects. Another possible application is in real-time quality control, where it is important to know if sufficient testing has been conducted, or whether more experimentation is needed. These methods lay a foundation for future dynamic experimentation approaches and with real-time fMRI, including for resting state, neurofeedback and presurgical evaluation. Use of high-performance computing will enable the advent of more sophisticated real-time experimental designs and dynamically determined early stopping rules.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by University Hospitals Cleveland Medical Center Institutional Review Board. Written informed consent to participate in this study was provided by the participants’ legal guardian/next of kin.SC and CT contributed to study design, analysis and interpretation of data, and drafting of manuscript. WC contributed to study design, analysis and interpretation of data, software development, and drafting of manuscript. JF contributed to study design and software development. HF contributed to study design and technical support, and drafting of manuscript. JS-G contributed to software development and revision of manuscript. JZ contributed to analysis and interpretation of data, and revision of manuscript. All authors contributed to the article and approved the submitted version.HF was employed by the company Philips Healthcare, USA. JS-G was employed by the company Philips Healthcare, Spain. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The authors declare that this study received funding from Philips Healthcare. The funder had the following involvement in the study: technical support and software development for the real-time output of fMRI files and revision of the manuscript.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Bola-type terpyridine-based ligands (R-L1 and S-L1) comprising R- or S-alanine analogs were synthesized. First, R-L1 dissolved in DMSO/H2O  forms right-handed helical fibers (aggregate I) via supramolecular polymerization. However, after the addition of AgNO3 (0.2–1.1 equiv.) to the R-L1 ligand, in particular, it was found that aggregate II with left-handed helicity is generated from the [R-L1(AgNO3)2] complex through the [R-L1Ag]+ complex via the dissociation of aggregate I by a multistep with an off pathway, thus demonstrating interesting self-sorting properties driven by helicity and shape discrimination. In addition, the [R-L1(AgNO3)2] complex, which acted as a building block to generate aggregate III with a spherical structure, existed as a metastable product during the formation of aggregate II in the presence of 1.2–1.5 equiv. of AgNO3. Furthermore, the AFM and CD results of two samples prepared using aggregates I and III with different volume ratios were similar to those obtained upon the addition of AgNO3 to free R-L1. These findings suggest that homochiral self-sorting in a mixture system occurred by the generation of aggregate II composed of the [R-L1Ag]+ complex via the rearrangement of both, aggregates I and III. This is a unique example of helicity- and shape-driven chiral self-sorting supramolecular polymerization induced by Ag+ starting from one enantiomeric component. This research will improve understanding of homochirality in complex biological models and contribute to the development of new chiral materials and catalysts for asymmetric synthesis.The study of chiral self-sorting is extremely important for understanding biological systems and for developing applications for the biomedical field. In this study, we attempted unprecedented chiral self-sorting supramolecular polymerization accompanying helical inversion with Ag R-L1 and S-L1) comprising R- or S-alanine analogs occurred upon addition of Ag+ in one enantiomeric component.Chiral self-sorting supramolecular polymerization of bola-type terpyridine-based ligands ( A variety of artificial systems, driven by metal–ligand coordination, hydrogen bonding, and solvophobic interaction in a racemic mixture,31–34 have been widely investigated. In particular, metal–ligand coordination interactions are the most widely used for the self-sorted construction of discrete and functional complex structures, including chiral ones at the single crystal level.35–39Self-sorting is one of the high-fidelity self-recognitions or self-discriminations in living systems, in which a complex object is recognizable from non-self into well-organized supramolecular architectures.40,41 Recently, one example for helicity-driven self-sorting in a single component system was reported by the Wurthner group.40 According to the cooling rate, the achiral perylene bisimide derivative formed either a homochiral self-assembly with a columnar structure or a heterochiral self-assembly with a lamellar structure, forming supramolecular polymers. In contrast, no studies have reported helicity-driven self-sorting metallosupramolecular polymerization induced by metal ions in a single component system, because transition metal ions form a variety of coordination geometries with different coordination numbers, and one handedness of supramolecular polymers is mainly determined by chirality of organic building blocks. Thus, a study on metallosupramolecular polymerization with handedness regulation by metal ions in a single component system, as a unique self-sorting system, can offer significant insights into the underlying mechanisms to understand chirality in biological systems, though it is a major challenge.To the best of our knowledge, helicity-driven self-sorting supramolecular polymerization in a single component, is rarely reported.R-L1 and S-L1), possessing either two R- or two S-alanine moieties, toward chiral self-assembly and towards intermolecular hydrogen-bonding interactions for promoting metallosupramolecular polymerization  (R-L1Ag]+ and [S-L1Ag]+) from a single component, but not a racemic mixture.We designed chiral bolaamphiphilic terpyridine-based ligands (rization . The Ag+nd S-L1)  and compi) complexes of R-L1 systemically, a series of the high-resolution electrospray ionization mass spectrometry (HR-ESI-MS) experiments were performed by varying the AgNO3 contents (0–2.0 equiv.). When the molar ratios are in the range of 0.1–0.4 equiv., monosilver complex [R-L1Ag]+ at m/z 885.3002 is predominant except the free R-L1  complex in the presence of the excess Ag+.In order to monitor the molar ratio effect on the formation of silver images of R-L1 and S-L1 in the presence of AgNO3 (0–1.8 equiv.) in DMSO/H2O (1 : 1 v/v). First, R-L1 forms right-handed fibers (aggregate I) with pitch lengths and angles of 55 ± 7 nm and 28 ± 3°, respectively , to our surprise, both right- and left-handed helical fibers were observed, indicating the coexistence of two building blocks at a molecular level. The left-handed helical fiber (aggregate II) had a pitch length of ∼75 ± 5 nm and a pitch angle of ∼30 ± 3°  (+ concentration (0–1.2 equiv.), as shown in R-L1Ag]+ complex. Thus, chiral self-sorting in this supramolecular polymerization can be controlled quantitatively using the concentration of AgNO3. In addition, the AFM image revealed a spherical structure (aggregate III) in the presence of AgNO3 (2.0 equiv.) 2] complex. The right-handed helicity of the free ligand based on bipyridine possessing the alanine moiety was converted to the left-handed helicity upon addition of Ag+ by circular dichroism (CD) observation in our previous study.6 However, AFM revealed one-handed helicity of the self-assemblies although the Ag+ concentration revealed one handedness.6 Thus, the presence of isolated right – and left-handed helical fibers induced by Ag+ in one sample is a unique phenomenon, which indicates a new chiral self-sorting system that occurs due to free ligands and complexes with opposite helicities in a single enantiomeric component.Subsequently, only aggregate II was observed with more than 1.2 equiv. of AgNO(50–100) . Interes Fig. S18, which oS-L1 ligand with and without AgNO3 revealed the opposite behavior to that exhibited by the self-assembled R-L1 with and without AgNO3. In the absence of AgNO3, the self-assembled S-L1 ligand formed a left-handed helical fiber with a pitch length of ∼58 ± 7 nm and a pitch angle of ∼30 ± 5°  self-sorting during supramolecular polymerization. In the presence of 0.6 equiv. of Ag+, again right- and left-handed fibers with approximately 1 : 1 ratio  complexation. Similarly, the left-handed fibers originates from S-L1 and [R-L1Ag]+. These results demonstrate that chiral self-sorting occurs by selective shape-recognition via helicity inversion upon silver(i) complexation: R-L1 and [S-L1Ag]+ form a P-type helical structure .By employing a 1 : 1 mixture of 3, CD spectra of self-assembled R-L1 and S-L1 in a DMSO and H2O mixture (1 : 1 v/v) were recorded. An intense positive CD signal, corresponding to the terpyridine moiety of the free ligand R-L1, was observed at ∼297 nm (R-L1 ligand is inclined toward P-helicity (right-handed),7,8,45 which is consistent with the AFM observations. In contrast, the intensity of the CD signal for self-assembled R-L1 gradually decreased with the concentration of AgNO3, and eventually became negative with 1.2 equiv. of AgNO3 (R-L1 ligand (no AgNO3). The reduction of the positive CD signal occurred due to the coexistence of aggregate I with right-handed (P-type) helicity and aggregate II with left-handed (M-type) helicity,7,8,45 as confirmed by AFM observations. The negative signal at ∼307 nm originated from the terpyridine–Ag+ in the [R-L1Ag]+ complex, which is not a mirror image of the free ligand R-L1. This result indicates that the [R-L1Ag]+ complex exhibited left-handed helicity. Thus, the addition of Ag+ to the free R-L1 ligand produced building blocks with opposite handedness. These helical building blocks aggregated with those exhibiting the same handedness and shapes, resulting in helicity- and shape-driven chiral self-sorting supramolecular polymerization with Ag+. In conclusion, the addition of Ag+ to the free R-L1 ligand (right-handed helicity) induced unique chiral self-sorting through the formation of the [R-L1Ag]+ complex, which has left-handed helicity.To demonstrate self-sorting and helicity inversion upon the addition of AgNO ∼297 nm . A positof AgNO3 , when thR-L1 in the absence and the presence of AgNO3 (1.2 and 2.0 equiv.) under the same conditions as those used for the CD observations  were negligible, indicating that the LD effect did not contribute to the CD signals of the helical supramolecular polymers.To confirm the linear dichroism (LD) effect in the CD signal, we also observed the LD spectra of  Fig. S28. The intS-L1 with and without AgNO3 were completely opposite to those of self-assembled R-L1 without and with AgNO3 (S-L1 with AgNO3 occurred due to helicity inversion when the free S-L1 ligand (left-handed M-type helicity) was converted to the [S-L1Ag]+ complex (right-handed P-type helicity).In contrast, the CD spectra of self-assembled th AgNO3  and S29†R-L1 were obtained in the presence and the absence of AgNO3 in a mixture of DMSO and H2O (1 : 1 v/v)  obtained from the control experiment , as described by Meijer and Takeuchi groups in porphyrin-based supramolecular polymerization with Zn2+ and pyridine.46,47 Based on the ESI-MS results  state is more thermodynamically favorable than that in the aggregate I state in the present system. The free ligand R-L1 is capable of forming the [R-L1Ag]+ complex spontaneously based on the stability constant (K1Ag = 8.51 × 105) obtained from UV-Vis titration.48–50 Finally, the monomer [R-L1Ag]+ complex formed a supramolecular polymer. More interestingly, two step-shaped curves were observed with 0.6 and 0.8 equiv. of AgNO3 2] complexes, as confirmed by HR-ESI-MS observations  of [R-L1Ag]+ was higher than the stability constant (K2Ag = 0.97 × 102) of the [R-L1(AgNO3)2] complex. The lag times at 0.6 and 0.8 equiv. of AgNO3 were due to the intermediate aggregate I. However, the [R-L1(AgNO3)2] complex formed in the presence of AgNO3 (0.5–1.1 equiv.) did not form aggregate III with a spherical structure, according to AFM observations 2] complex was not sufficiently high to induce nucleation. In contrast, the lag times in the self-assembly process with 1.2 and 1.4 equiv. of AgNO3 were clearly observed in the initial stage (R-L1(AgNO3)2] complex 2] complex, upon the addition of 1.2 and 1.4 equiv. of AgNO3. Thus, aggregate II, which is based on the [R-L1Ag]+ complex, was the thermodynamically favored product. The AFM image also showed one-dimensional nanorods with a length of 500–800 nm and nanoparticles 100–300 nm in diameter 2] complex as a metastable product.To demonstrate self-sorting in supramolecular polymerization, time-dependent UV-Vis spectra of the self-assembled : 1 v/v) . The absn 10 min , which in 10 min . With 0.ut AgNO3 . This waut AgNO3 . This ph Fig. S33 and elons Fig. S2, stabilis Fig. S2, we assureaction , becauseof AgNO3 . The abss Fig. S2, and the complex , becauseal stage . The AFMal stage , which o complex , as conf complex . These fR-L1 with and without AgNO3  using different volume ratios of aggregates I and III. With 0.6 equiv. AgNO3, as expected, the AFM image clearly revealed a right-handed helical fiber (aggregate I) and a spherical structure (aggregate III) in the initial stage  were obtained  was added to aggregate I to confirm the self-sorting mechanism for the generation of aggregate II. As shown in Fig. S40,3 was added to aggregate I formed without AgNO3, because aggregate I dissociated quickly to the monomer species, and then formed [R-L1Ag]+ and [R-L1(AgNO3)2] (R-L1(AgNO3)2] complex. After aging for 300 min, the negative CD signal gradually increased and finally reached equilibrium after 1200 min 2] . The iniAgNO3)2] ; this waFig. S40B. This waFig. S40B. The occR-L1, the spectra of aggregates I and II showed a shift in the –NH stretching bands to shorter wavenumbers −1 (pink) and 1355 cm−1 3− and the self-assembled [R-L1Ag]+, respectively.51 In contrast, the NO3− band of aggregate III shifted to a shorter wavenumber, which is indicative of coordination to Ag+.To better understand the intermolecular structures involved in supramolecular polymerization, we analyzed the chiral self-sorting supramolecular polymers by Fourier transform infrared (FTIR) spectroscopy. Compared to the spectrum of the monomer 1H NMR spectra of the two supramolecular polymers were observed by heating  largely shifted to a low field compared to that without AgNO3, indicative of the π–π stacking of R-L1 in the presence of AgNO3. In contrast, the chemical shift of the aromatic proton peaks without AgNO3 is negligible, which means that the π–π stacking of aggregate I was negligible.52,53 Also, the aromatic proton peaks of R-L1 with AgNO3 are broader than those of the free R-L1, mainly due to the formation of the [R-L1Ag]+ complex and the supramolecular polymerization.In addition, temperature-dependent 3  revealed a sharp peak, which corresponds to the Ag–Ag interaction with a distance of 2.8 Å, at 2θ = 32°  measurements of self-assembled samples obtained with AgNO Fig. S44.54,55 Th Fig. S45.+, we optimized the molecular structure of the free ligand R-L1, and the [R-L1(AgNO3)2] complex using density functional theory (DFT) calculations.56 The optimized molecular length of the free ligand R-L1 was 31.9 Å, and the dihedral angle between the two terpyridine moieties of R-L1 was approximately 46.8° (+ and the Ag+ of the [R-L1(AgNO3)2] complex (24.5 Å) was lower than that of the free ligand, and the dihedral angle between terpyridine and terpyridine moieties decreased to 38.7°. In addition, each Ag+ interacted with the three nitrogen atoms from terpyridine and one oxygen atom from NO3−, which resulted in a four-coordinated structure  is coordinated to one nitrogen atom (N1) from the left side of the terpyridine moiety and two nitrogen atoms (N5 and N6) from the right side of the terpyridine moiety. In contrast, Ag+ (2) is coordinated to two nitrogen atoms (N2 and N3) from the left side of the terpyridine moiety and one nitrogen atom (N4) from the right side of the terpyridine moiety. These results led to the left-handed helical structure. The distance between Ag+ and nitrogen atoms was 2.32–2.38 Å. More interestingly, the length of the Ag(1)–Ag(2) bond was 2.82 Å, which was consistent with the WAXD results. The result indicates that the Ag–Ag interaction acted as an additional driving force in the formation of aggregate II. The Ag+ (1) and Ag+ (2) atoms showed a four-coordinated tetrahedral structure involving a Ag–Ag interaction.For the +, and [R-L1(AgNO3)2] 2] via the stepwise complexation equilibria. During the formation of aggregate II, [R-L1(AgNO3)2] is converted to [R-L1Ag]+ because the monosilver complex (K1Ag = 8.51 × 105) is thermodynamically more stable than the disilver one (K2Ag = 0.97 × 102). Finally, aggregate II is generated by a multistep off-pathway.63,64We propose an energy landscape consisting of two competing pathways to confirm the mechanism of self-assembly of AgNO3)2] . As ment+ for a single enantiomeric component. Chiral self-sorting occurred by three different completion reaction pathways, which were largely affected by the Ag+ concentration. The chiral self-sorting supramolecular polymerization was precisely controlled with the addition of Ag+. The unique chiral self-sorting occurred because of the coexistence of R-L1 with right-handed helicity and the [R-L1Ag]+ complex with left-handed helicity. Thus, the present chiral self-sorting was induced by self-discrimination in a mixture of differently shaped building blocks with different helicities. In addition, chiral self-sorting in a mixture system occurred by the generation of aggregate II composed of the [R-L1Ag]+ complex via the rearrangement of aggregates I and III. Two different helical aggregates I and II were thermodynamically favored, and the chiral self-sorted supramolecular polymers were generated by a cooperative pathway with a nucleation–elongation mechanism. With 0.1–1.1 equiv. of AgNO3, the chiral self-sorted supramolecular polymer was formed through an off-pathway mechanism. This system is a significant example of chiral self-sorting supramolecular polymerization starting with one enantiomeric component and Ag+. We believe that this approach will contribute significantly to the development of catalysts for asymmetric synthesis and new materials with intriguing chiral properties. It will also improve understanding of the origin of homochirality in complex biological molecules.In conclusion, we demonstrated unprecedented successive chiral self-sorting in supramolecular polymerization accompanied by helical inversion with AgM. O. and K. Y. K. contributed equally. M. O. and K. Y. K. contributed to the design and performed the preparation and characterization of supramolecular polymers. H. C. contributed to the thermodynamic studies. S. K. and J. C. carried out DFT calculations of complexes. J. H. J. and S. H. J. directed the project. All authors contributed to the discussion and the preparation of the paper.There are no conflicts to declare.SC-013-D1SC06413D-s001


We found that bisulfate ion could efficiently stabilize all the three conformers of H2CO3 and reduce the energy differences of isomers with H2CO3 in three different conformations compared to the isolated H2CO3 molecule. Calculated isomerization pathways and ab initio molecular dynamics simulations suggest that all the optimized isomers of the complex have good thermal stability and could exist at finite temperatures. We also explored the hydrogen bonding properties in this interesting complex and simulated their harmonic infrared spectra to aid future infrared spectroscopic experiments. This work could be potentially important to understand the fate of carbonic acid in certain complex environments, such as in environments where both sulfuric acid (or rather bisulfate ion) and carbonic acid (or rather carbonic dioxide and water) exist.Carbonic acid is an important species in a variety of fields and has long been regarded to be non-existing in isolated state, as it is thermodynamically favorable to decompose into water and carbon dioxide. In this work, we systematically studied a novel ionic complex [H Specifically, M06-2X functional and aug-cc-pVTZ basis set were employed, as previous studies showed that this combination could provide reliable results for hydrogen bonded, bisulfate ion-containing complexes [−4 eV. Quantum theory of atoms in molecules (QTAIM) [2CO3·HSO4]−.Geometry optimizations of all minima and transition states on the potential energy surface of the anionic molecular complex −. To better understand the changes of each component in [H2CO3·HSO4]− upon complexation, we provide the optimized three conformers of carbonic acid, bisulfate ion, and sulfuric acid in 2CO3·HSO4]−, we have obtained six stable isomers, among which isomers 2a and 2b could be considered as enantiomers, and isomers 3a and 3b could also be considered as enantiomers. While isomers 1, 3, and 4 may be regarded as HSO4–·H2CO3, isomer 2 is better recognized as H2SO4·HCO3−, which is only about 2 kJ/mol higher in energy than isomer 1. Isomer 2 is unexpected solely from gas-phase proton affinity prediction and its stability can be attributed to the formation of two strong hydrogen bonds and highly delocalized extra electrons according to previous findings by Hou et al. − and the energy barriers needed to be overcome. The calculations show that the isomerization between isomers 2a and 2b, isomers 3a and 3b involves the rotation of −OH group in bicarbonate or carbonic acid, and the barriers are almost equal to be 45.4 and 46.4 kJ/mol, respectively. Such relatively high energy barriers may preclude the isomerization between the enantiomers of 2 and 3, and they may all exist at finite temperatures. Isomerization between isomers 2a and 3a, isomers 2b and 3b has low barriers of only about 8 kJ/mol, indicating that the proton translocation between the two negatively charged oxygen atoms should not be difficult, as found in HCOO−·H+·HSO4– −, we performed AIMD simulations for isomers 1 and 2a, as presented in 1 and isomer 2a are only about 0.5 eV, confirming their high-temperature stability −, as presented in Temperature-controlled infrared spectroscopy is a useful experimental approach to probe the proton translocation dynamics as demonstrated by Johnson and co-workers ,54 and v−1 corresponding to the O–H stretching of the HSO4– moiety, and the strong vibration at ~3180 cm−1 is the symmetric double O–H stretching of the H2CO3 moiety. The spectra of isomers 2a and 2b are almost identical, as they are enantiomers; the vibrations at ~2230 and 2410 cm−1 are the asymmetric and symmetric stretching of the two shared H+ between SO42– and HCO3– moieties. Similarly, the spectra of isomers 3a and 3b are almost identical; the weak mode at ~3700 cm−1 is the free O–H stretching of the H2CO3 moiety, and the two strong modes at ~1810 and 3270 cm−1 are the shared H+ translocation and hydrogen bonded O–H stretching of the HSO4– moiety. In the simulated spectrum of isomer 4, the vibrations at ~2130, 3590, and 3700 cm−1 are the shared H+ translocation, hydrogen bonded O–H stretching of the HSO4– moiety, and the free O–H stretching of the H2CO3 moiety. Those vibrational vectors are included in In isomer 1, there is a very weak vibrational mode at ~3680 cm2CO3·HSO4]− complex to investigate if bisulfate ion is capable to stabilize the exotic conformers of carbonic acid. Our results showed that compared to the bare H2CO3 molecule, the energy differences between the different isomers of [H2CO3·HSO4]− complex with H2CO3 moiety in the conformation of trans-trans, cis-trans, and cis-cis become smaller, suggesting that bisulfate ion can efficiently stabilize the three conformers of H2CO3. Notably, for bare H2CO3, the cis-cis conformer is the most stable, while in [H2CO3·HSO4]− the isomer with H2CO3 in trans-trans becomes the most stable due to the formation of two strong hydrogen bonds. Combining quantum theory of atoms in molecules topological analysis and a fitted empirical equation, we estimated the strengths of the hydrogen bonds. The calculated isomerization pathways between the different isomers of [H2CO3·HSO4]− and also ab initio molecular dynamics simulations of the first two low-lying isomers revealed that these isomers could coexist at finite temperatures. We further simulated their harmonic infrared spectra to facilitate future infrared spectroscopic experiments to fully understand the proton translocation dynamics in this interesting complex.In summary, we theoretically explored the potential energy surface of the anionic [H


Abdominal wall hernia repair is one of the most commonly performed surgical procedures worldwide, yet despite this, there remains a lack of high-quality evidence to support best management. The aim of the study was to use a modified Delphi process to determine future research priorities in this field.Stakeholders were invited by email, using British Hernia Society membership details or Twitter, to submit individual research questions via an online survey. In addition, questions obtained from a patient focus group (PFG) were collated to form Phase I. Two rounds of prioritization by stakeholders (phases II and III) were then completed to determine a final list of research questions. All questions were analyzed on an anonymized basis.A total of 266 questions, 19 from the PFG, were submitted by 113 stakeholders in Phase I. Of these, 64 questions were taken forward for prioritization in Phase II, which was completed by 107 stakeholders. Following Phase II analysis, 97 stakeholders prioritized 36 questions in Phase III. This resulted in a final list of 14 research questions, 3 of which were from the PFG. Stakeholders included patients and healthcare professionals  from over 27 countries during the 3 phases.The study has identified 14 key research priorities pertaining to abdominal wall hernia surgery. Uniquely, these priorities have been determined from participation by both healthcare professionals and patients. These priorities should now be addressed by well-designed, high-quality international collaborative research.The online version contains supplementary material available at 10.1007/s10029-021-02519-0. Abdominal wall hernias are common and hernia repair is one of the most commonly performed operations in the world, generating huge health care costs. Indeed, the incidence of inguinal hernias, primary ventral hernias and incisional hernias are rising due to an aging population and the world obesity crisis , 2. HoweDelphi methodology is a well-established process used to collate judgements and opinions on a specific topic . The proModified Delphi techniques have also been used within the field of hernia surgery. Recent consensus has helped to provide definitions for loss of domain  and for We, therefore, used a modified Delphi process with the aim to identify and prioritize future research questions in current hernia practice that are deemed to be of greatest clinical importance to patients, surgeons and allied health professionals. The study was undertaken as a collaboration between the Scottish Surgical Research Group (SSRG) and the British Hernia Society (BHS).This study adopted a three-phase modified Delphi technique Fig.  to estabwww.surveymonkey.co.uk®). BHS members include surgeons, nurses, patients and other allied health professionals. A dedicated Twitter® account (@hernia_delphi) was also used to increase the awareness of the study and encourage wider stakeholder participation. Stakeholders were invited to submit as many questions as they wished. The survey remained open for 6 weeks between October and December 2019. Five dedicated hernia Delphi tweets were made from the official hernia Delphi account and two email reminders to the BHS membership were sent during this period.Members of the BHS were invited by email to submit research focused hernia surgery questions via an online survey  of the steering committee patient and public involvement (PPIs) members who helped guide the group discussion. Patients were invited via a Twitter advertisement and through direct invitation via outpatient clinic from members of the steering committee. Recurring themes that were deemed to be important to the majority of PFG participants were identified and collated during the course of the day.The completion of the PFG marked the end of Phase I. Submitted questions were analyzed by a subcommittee. Duplicate questions were removed and recurring theme questions were altered by consensus agreement of the steering committee to ensure that the meaning of the questions were not distorted. The themes identified from the PFG were subsequently converted into research questions and included in the next phase of the Delphi process.During Phase II stakeholders were invited, via email and Twitter, to rank the Phase I questions using a Likert scale from 1 (lowest research priority) to 5 (highest research priority). Five reminders were sent via Twitter and by two emails to the BHS membership over a 6 week period between August and October 2020. The steering committee reviewed the results whilst blinded to the questions and selected a mean ‘cut-off’ score of ≥ 3.60 for inclusion in the final phase of the study.During the final Phase of the study, stakeholders were again invited, via email and Twitter, to rank the questions brought forward from Phase II using the same Likert scale as previously described. The survey remained open for 6 weeks between October and December 2020. Five reminder Tweets were made and two email reminders sent to BHS members. An invitation to complete the survey was also advertised during the BHS 2020 virtual conference. A final mean ‘cut-off’ score of ≥ 4.0 was agreed by the steering committee as described in Phase II.The committee consisted of three SSRG general surgery specialty registrars , an international hernia research fellow (BE), three PPIs  and four general surgeons who perform high-volume hernia surgery  as BHS members. All decisions in relation to methodology and analysis were agreed on a consensus basis.n = 19) and healthcare professionals (n = 94); professor or consultant surgeon (71.3%), surgical trainee/fellow/specialty doctor (25.5%), other (3.2%). Following analysis and categorization by the steering committee, 64 questions were moved forward for prioritization in Phase II.A total of 247 individual research questions were submitted online by 103 stakeholders during Phase I. With the addition of 19 questions proposed by the PFG, the final Phase I cohort totaled 266 research questions from 113 stakeholders  and healthcare professionals (n = 95), professor or consultant surgeon (77.9%), surgical trainee/fellow/specialty doctor (15.8%), other (6.3%). A total of 36 questions were included in Phase III.One hundred and seven stakeholders from 14 countries Fig. B prioritn = 11) and healthcare professionals (n = 86), professor or consultant (74.4%), surgical trainee/fellow/specialty doctor (23.3%), other (2.3%) . Following this final prioritization, 14 questions met the criteria to be defined as high research priority  who did not continue from Phase II to III.To increase participant numbers, each phase was considered as a separate entity and stakeholders were able to enrol in the study during any of the three, thus explaining the variation in participant numbers during the study. The authors attempted to avoid research fatigue by leaving a significant time gap between the phases, however, there was a small number of participants (n = 5) focused on pre-operative information, whether that included peer support groups, pre-operative education, videoing of consent or patient interaction whilst on the waiting list. Interestingly, this is a topic that was not prioritized to the final list of questions, but is perhaps something that as a group of medical professionals we should be spending more time investigating in order to optimize the patient experience.Unique to this Delphi process was a PFG who identified 19 research questions that were deemed to be of greatest importance to patients. Three of these questions were prioritized in the third phase to be included in the final list  hernia registry and whether surgeons should be informed of their recurrence and/or incisional hernia rates.The question “Should the operating surgeon be informed of their recurrence or incisional hernia rate?” is an interesting but potentially contentious one that may generate more questions than answers. Although most surgeons and patients will likely want to know, the practicality of collecting and using this information to change practice may be challenging. Nonetheless, this information may encourage some surgeons to pay more attention during abdominal wall closure and highlight surgeons/units with outlying recurrent incisional hernia rates, which is associated with non-specialists performing hernia surgery . HoweverThe tension-free vaginal tape (TVT) controversy has had a significant impact on patients’ trust in their surgeon who wishes to perform a hernia repair with mesh . These cAt the time of the final prioritization process, there was a paucity of high-quality evidence on the long-term complications associated with IPOM, hence the inclusion of “What are the long-term adverse consequences of IPOM?” in the final list. However, Henriksen et al. have recently published a nationwide database study on the short- and long-term outcomes of IPOM, concluding that IPOM should still be considered for fascial defects between 2 and 6 cm . The autThe primary outcome measure for hernia surgery has traditionally focused on recurrence, but in recent years, there has been a paradigm shift towards a greater focus on patient satisfaction and PROMs following hernia surgery. This is reflected in the number of hernia-specific PROM questions that have featured in the final list of research questions selected during this Delphi process Table .Despite this shift towards patient-centered primary outcome measures in recent years, there remains significant inconsistencies in PROM reporting. This has been highlighted by two well conducted systematic reviews that were designed to examine outcome reporting in both inguinal and ventral hernia surgery , 26. BotThe Core Outcome Measures in Effectiveness Trials (COMET) initiative has been designed to identify which PROMs should be included for both inguinal and incisional hernia repair . This foOnce these outcomes have been developed the next challenge will be to establish how to accurately collect and record them. Appropriate tools for collecting these outcomes will need to be developed to enable seamless integration into current and planned hernia registries. For this reason, the question “What are the most appropriate tools for collecting PROMS before and after hernia surgery?” was prioritized.The development of a COS in incisional hernia is still in its infancy with the systematic review from the first phase of the process just recently published. Harji and colleagues identified a total of 2215 outcomes reported in incisional hernia surgery, which were mapped to eight broad-based domains . It is uIn January 2018, the European Hernia Society (EHS) published comprehensive international guidelines for groin hernia management . These gThe prevalence of CPIP has been quoted to be between 10 and 12% based on several studies dating back to the beginning of the twenty-first century, decreasing over time, with debilitating chronic pain affecting daily activities ranging from 0.5 to 0.6% , 36. HowWhilst this is the first hernia study to seek the views of patient representatives, in collaboration with healthcare providers, the proportion of stakeholders which were patients was still significantly lower than that of surgeons. We believe in order to truly define the key hernia research priorities, it is important to have equal weighting of both service users and surgeon’s views. Is important to acknowledge the selection bias that may have been introduced  during the PFG session as the majority of patients who attended had already undergone their hernia surgery and thus many of the questions initially put forward were related to post-surgery issues, specifically chronic pain. Whilst these are key areas to be researched, less weighting was placed on pre-operative care which is also important and may indeed impact on the long-term outcomes. In addition, despite stakeholders being from over 27 countries during the three phases, they were predominantly from more developed countries. Research priorities may be substantially different in the more developing countries and this was perhaps not relayed entirely in this study.The authors acknowledge that some questions in the final list of research priorities are already being addressed, in particular those relating to hernia registries and PROMS. The initial phase of this study and PFG was undertaken prior to the COVID-19 pandemic, with subsequent phases unfortunately being delayed by almost a year to prioritize the clinical need of the pandemic over research. It is inevitable, therefore, due to the long time period the study ran over, that some of these questions will already have more evidence around them by the time of this study being published.In conclusion, we have undertaken a modified Delphi process to determine a list of abdominal wall hernia research priorities. The study involved a large body of multidisciplinary healthcare professionals across multiple centers worldwide. Unique to this hernia study is the direct involvement of patients during all three phases and the PFG. These priorities should now be addressed by well-designed, high-quality international collaborative research.Supplementary file1 (DOCX 116 kb)Below is the link to the electronic supplementary material.


PEEK appears as an excellent candidate to substitute epoxy resins in carbon fibre laminates for high-performance aeronautical applications. The optimization of the properties and, in particular, of the transition region between the fibres and the matrix appear as a major issue prior to serial production. Graphene, modified with two compatibilizers, has been incorporated in the polymer layer with the purpose of imparting additional functionalities and enhancing the matrix-fibre interaction. It is found that both carbon fibres and modified graphene significantly influence the crystallization behaviour and smaller, and/or more imperfect crystals appear while the degree of crystallinity decreases. Despite this, nanoindentation studies show that the PEEK layer exhibits significant modulus improvements (≈30%) for 5 wt.% of graphene. Most importantly, the study of the local mechanical properties by nanoindentation mapping allows the identification of remarkably high modulus values close to the carbon fibre front. Such a relevant mechanical enhancement can be associated with the accumulation of graphene platelets at the polymer–fibre boundary, as revealed by electron microscopy studies. The results offer a feasible route for interlaminar mechanical improvement based on the higher density of graphene platelets at the fibre front that should promote interfacial interactions. Concerning electrical conductivity, a large anisotropy was found for all laminates, and values in the range ~10 Advanced polymer-based composites have progressively substituted metals for lightweight applications in the aerospace and aeronautical industry ,2. In thAdvanced thermoplastics and, in particular, poly(ether ether ketone) (PEEK) are potential candidates to substitute epoxy resins due to the large chemical resistance and high melting temperature . It has g-CNT as a sizing compound, and it was found that the load transfer across the laminates improved significantly [One critical aspect in the development of new laminar composites is the interlaminar failure. Here, the fibre–polymer interface/interphase plays a crucial role. Preceding work using nanoindentation analysis on PEEK/glass fibre multilaminar systems showed a transition region between the matrix and the fibres, with intermediate properties that were improved with the incorporation of carbon nanotubes (CNT) and with the addition of polysulfone as a compatibilizing agent ,15. Enhaficantly ,19.Graphene has motivated enormous scientific interest for more than a decade as filler in polymer matrices due to its outstanding mechanical, electrical, thermal, and gas barrier properties ,22,23,24The incorporation of graphene to PEEK has taken place at a slower pace than for other polymer matrices ,33,34,35Studies including graphene in PEEK/CF laminates are very limited ,37, desp−2 S cm−1.The present paper approaches the study of the thermal, electrical, and mechanical properties of PEEK/carbon fibre laminates with small quantities of graphene incorporated into the polymer matrix. Graphene is expected to improve the fibre–matrix interfacial interaction and provide additional functionalities to the laminate. The homogeneous dispersion of graphene in the PEEK matrix was approached in a recent paper , and it The objective of the present work is the study of the influence of graphene, modified with PEI and SPEEK compatibilizers, on the structure and properties of PEEK/carbon fibre laminates. The thermal behaviour, electrical conductivity, and mechanical properties are examined, and the results are correlated to structural and morphological studies. Advanced nanoindentation techniques are used to evaluate the mechanical properties of the laminates at a local scale, particularly at the boundary regions between the polymer-based layers and the fibre tows. This technique has been successfully used to probe the transition region between a thermoplastic polymer such as isotactic polypropylene and carbon fibre (CF) fabric .−1). Graphene was purchased from Avanzare Nanotechnology, and the specifications were 1–2 layers, with lateral dimensions of 22 ± 5 μm and 9 ± 2 μm. The plain weave CF fabric (G0904) was provided by Hexcel . The areal weight was 193 g/m2, and the micro-sized fibres had a diameter of ≈7 μm.A commercial powder of PEEK was used  and sulfonated PEEK (SPEEK) . The nomThe nanocomposites were prepared following several mixing steps . Films were fabricated by hot compression, and the final thickness was around 0.35 mm. Graphene content (without the contribution of the compatibilizer) was determined to be 3 wt.% for PEEK-GPEI and 5 wt.% for PEEK-GSPEEK .Tm, and the degree of crystallinity, Xc, determined in our preceding work by differential scanning calorimetry [Details on the preparation of the polymer-modified graphene fillers and the nanocomposites can be found elsewhere . Table 1orimetry .2 with a thickness of 1.8 ± 0.2 mm. The CF content was 70 wt.%, as determined by TGA.The laminates were prepared by alternatively placing nine plies of CF fabric and ten nanocomposite films. Consolidation of the material was made at 390 ± 5 °C in a hot press under high pressure in a two-step process, as shown in 2 immersion pool and different piezelectric sensors for the analysis of carbon composite materials according to Airbus Standards (Airbus AITM 6-0013). Considering that all the laminates had comparable thicknesses and carbon fibre content, changes in the observed ultrasonic signal attenuation can be correlated with differences in void contents. Inspection of the laminates was carried out using ultrasonic C-scan, which represents a useful and non-destructive technique for detecting and quantifying defects in composite materials. ATriton 1500 (Tecnitest) equipment was employed with a 1500 × 800 mm2) using a plastic clip that was introduced in a cylindrical mould. Epoxy resin was used as the embedding medium, and the resin blocks were trimmed using a Leica microtome. The preparation of the surface included a number of polishing steps with decreasing silicon carbide paper grain size  and a microcloth soaked with alumina paste . For nanoindentation studies, the cross section of the laminates was exposed by vertically placing a portion of the laminates .Thermogravimetric analysis under air and nitrogen atmospheres was carried out in a TA Instruments Q50 Thermobalance . The scans covered a temperature interval of 50–800 °C at 10 °C minmT = 156.6 °C, ΔmH = 28.45 kJ·kg−1) and zinc . Samples of ≈10 mg weight were extracted from the central part of the laminates and introduced in aluminium pans. Scans were carried out under an inert nitrogen flow at a rate of 10 °C min−1 over a temperature interval of 50 °C to 380 °C. Tm was determined as the maximum of the melting endotherm, and Xc was obtained by dividing the crystallization enthalpy of the nanocomposites (corrected for the amount of PEEK) by the value for 100% crystalline PEEK, taken to be 130 J·g−1 [Differential scanning calorimetry measurements were performed using a Perkin-Elmer DSC7-7700 calorimeter . Melting temperatures and meting enthalpies were calibrated against indium (30 J·g−1 .Scanning electron microscopy (SEM) images were obtained using a Hitachi SU8000 field emission microscope .−1 was applied, and a small oscillating force of 75 Hz was superimposed to the quasi-static loading. Based on the amplitude and phase of the displacement response to the sinusoidal loading, the contact stiffness S was measured continuously during the loading. The procedure involves the assumption of a simple harmonic oscillator model to describe the instrument–sample contact behaviour [E′, following [Mechanical properties at different locations across the multilaminar material were evaluated using a G200 nanoindenter with a low load resolution head . During the loading cycle, a constant indentation strain rate of 0.05 sehaviour . Finallyollowing ,41:(1)E′ν was assumed to be 0.4 in all cases, and β is a correction factor that can be taken as 1.034 for a Berkovich indenter. The function describing the indenter–sample contact area cA as a function of the contact penetration depth was determined using a fused silica standard [Poisson’s ratio standard .V/I was measured with a DC low-current source (LCS-02) and a digital micro-voltmeter . The conductivity σ was determined as the inverse of the resistivity ρ using the equation: t is the thickness of the sample, f1 is the finite thickness correction for an insulating bottom boundary, and f2 is the finite width correction [The in-plane electrical conductivity was measured using three different laminate pieces for each material (≈6 mm wide and 12 mm long), whereas the out-of-plane electrical conductivity was measured in at least eight points. The samples were previously dried under a vacuum, and silver paint was used to optimize the polymer–lead contacts. For the transverse arrangement, a terminal was placed at the top and bottom surfaces, and the resistance was measured using a digital voltmeter. For the in-plane measurements, a four-probe setup was employed, and the resistance rrection .iT significantly dropped in the nanocomposites. As already discussed in our preceding work, this was a consequence of the lower thermal stability of the compatibilizers [iT values of all laminates were higher than those of the corresponding nanocomposites, regardless of the atmosphere. For example, iT increased by 10 °C in nitrogen and 20 °C in air for the PEEK-GSPEEK/CF laminate compared with the nanocomposite. This can be explained by the higher heat absorption capacity of the CFs with respect to PEEK. Consequently, a higher temperature is required to achieve the threshold energy needed to initiate the degradation process [bilizers . However process . Regarding the crystallization behaviour, the crystallization temperature of all laminates decreases with respect to PEEK, indicating a reduction in the crystallization rate B. This bE′ values (represented by the colour code shown at the bottom of the figure) at an indenter displacement of h = 100 nm. Each location has an associated E′ versus h plot, and E′ behaviour observed. E′ vs. h for three representative locations in the PEEK/CF laminate (indicated by numbers): (1) at the fibre, showing a constant E′ value with indentation depth (E′ ≈ 55 GPa); (2) on the PEEK matrix, also displaying steady E′ values, but significantly lower (E′ ≈ 5 GPa); and (3) on the PEEK matrix at the beginning of the test, but coming into contact with the fibre edge during the loading cycle hence, producing a sudden E′ rise. E′ values are independent of the indentation depth (see for example position number 4 in the fibre and numbers 6 to 8 in the reinforced matrix) and others in which E′ increases rapidly as a consequence of the indenter–fibre contact (see location number 5).Nanoindentation was used to evaluate the local mechanical properties of the laminates. E′ maps resemble the surface topography observed by optical microscopy, and one can clearly distinguish the carbon fibres’ contour as a consequence of their higher modulus compared to PEEK. The second clear observation is that E′ of the polymer layer increases first with the incorporation of 3 wt.% of GPEI and then, more significantly, with the addition of 5 wt.% of GSPEEK. Indeed, it is noteworthy that the E′ map turns from light green colours into dark green ones as the quantity of graphene increases (from top to bottom). Finally, one can also appreciate that the darkest green zones tend to concentrate close to the fibre, as can be clearly discerned for the PEEK-GSPEEK/CF laminate. Let us recall that only E′ values immediately next to the fibre edge were affected by the fibre–indenter contact during the test . Inspection of the results away from CF clearly show that the distribution of E′ data shifts to higher values and widens with graphene addition. The results revealed that graphene reinforced the PEEK matrix and suggested that local variations of the quantity and orientation of graphene layers produce a broadening of the mechanical properties at the sub-micrometre scale. Equivalent portions on the mechanical maps of E′ distribution close to the fibre seemed to slightly shift to higher values with respect to the distribution far away from it. However, such a trend was more apparent for the PEEK-GSPEEK/CF laminate with higher graphene content. In this latter case, the E′ distribution close to the fibre exhibited a tail that extended up to the 15–30 GPa interval. It is noteworthy that the high modulus tail was mostly associated to the dark green values of the mechanical map appearing immediately next to the fibre. In order to better understand the origin of the high modulus values found at the fibre–polymer boundary, electron microscopy images were taken at exactly the same location selected for nanoindentation mapping. Most interesting was the comparison of the counting analysis close and far away from the fibres. For the PEEK/CF laminate, quite similar results were found, and the occurrence of an interphase between the fibre and the polymer layer cannot be distinguished at this scale. For the PEEK-GPEI/CF case, the The accumulation of graphene at the fibre–polymer boundary described by electron microscopy can be associated to the local mechanical enhancement detected at the tow front by indentation mapping. This higher density of graphene platelets could promote enhanced interfacial interaction with the carbon fibres  that, in the end, would appear as most beneficial for the interlaminar properties.E′ values associated to the polymer-based layers within the laminates obtained using the E′ distribution away from CF of E′ values for the free-standing nanocomposite films are also included E’/PEEKE’).The role of graphene in the mechanical reinforcement of PEEK can only be fully understood after taking into account the nanostructural changes taking place in the polymer matrix with graphene addition. eference ). FigureE′ value of neat PEEK was substantially larger when the film forms part of the laminate. This finding suggests that the consolidation of PEEK between the carbon fibre plies introduced heterogeneities at the sub-micrometre scale. This result is in agreement with the broader melting endotherm observed for PEEK/CF with respect to the neat PEEK  is partly counterbalanced by the introduction of CFs. Indeed, the initial degradation temperatures under air drop by ≤15 °C for the nanocomposite laminates with respect to the PEEK laminate, compared to ≤25 °C between the nanocomposites and the PEEK free-standing films.A broader melting endotherm at lower temperatures is found for PEEK sandwiched between CF plies with respect to the PEEK free-standing film. The incorporation of graphene further spreads the melting process over a wider temperature range, and it is suggested that both CFs and modified graphene expand the crystal size distribution to smaller and/or more imperfect crystals. E′ data is significantly higher when the polymer layers are incorporated to the multilaminar system. In addition, mechanical heterogeneities arising from the distribution of graphene throughout the polymer layers also contribute to the enhancement of data dispersion.Enhanced structural heterogeneity has a significant impact on the mechanical properties, and it is found that the dispersion of CFs and modified graphene distort the lamellar assembly, reducing the levels of crystallinity and giving rise to thinner and/or more imperfect crystals, and significant modulus improvements approaching ≈30% can be measured in the PEEK-GSPEEK layer of the CF laminate.Indentation mapping allowed the investigation of the mechanical properties at a local scale and in particular at the polymer–fibre boundary. The study covers a research area of great importance still unexplored for PEEK-graphene/CF laminates, and provides the basis for a comprehensive understanding of the reinforcing mechanism at a macroscopic level. Indeed, a local mechanical enhancement at the polymer–CF boundary region is identified upon graphene addition that can be associated to the accumulation of the filler at the fibre front, as revealed by electron microscopy studies. This higher density of the platelets is expected to be the most beneficial for the interlaminar mechanical properties, and opens up a route for property improvements.−4–3 × 10−4 S/cm), and the dispersion of graphene in the polymer layers does not seem to produce relevant differences, probably due to the poor presence of the filler inside the fibre tows. However, the conductivity levels (~10−4 S/cm) are adequate for a broad range of applications, including sensors, strain sensing materials, electromagnetic shielding, etc.Finally, carbon fibres appear to dominate the in-plane electrical conductivity, and very high values have been attained for all laminates (35–90 S/cm). Transverse conductivity values are significant in all cases (2 × 10