2.1. Sample recruitment and characterization
Seventy healthy participants, with a mean age of 24.0 ± 4.7 and a gender proportion of 46% women, were recruited through notices at Aalborg University, University College Nordjylland, on public noticeboards in Northern Jutland and on social media. Participants were included if they were healthy, aged 18–60 years and could speak, read, and understand English or Danish. Individuals were excluded in the case of pregnancy, current substance, opioids, antipsychotics, and benzodiazepines misuse and previous or current neurological, musculoskeletal, rheumatic, malignant, inflammatory, or mental illnesses. Also, volunteers with current or prior chronic pain conditions were excluded. The recruitment and conduction of this study was designed to comply with the Declaration of Helsinki and the protocol was approved by the North Denmark Region Committee on Health Research Ethics (VN-20180078).
2.2. Experimental procedure
Each participant was informed about the study in a meeting prior to the experimental session. The session began with an introduction by the investigator and obtaining informed consent. Firstly, the demographic questionnaire was completed. Then, the mechanical pain detection protocol (pin-prick) was performed on both arms over the testing site for the NPP-task (volar forearm). Afterwards, the NPP-task protocol was conducted on the non-dominant arm. The NPP-task was described briefly by the investigator. All other instructions were presented on the monitor during the protocol. The investigator was present in the room but did not interact with the participant unless necessary. After the NPP-task, the mechanical pain detection procedure was performed a second time to investigate whether the NPP-task induced any sensitization of the test area. Then, the thresholds for perceived pain detection and pain tolerance (PDT & PTT), as well as temporal summation (TSP) and conditioned pain modulation (CPM), were assessed on the legs by cuff algometry.
2.3. Mechanical pain detection protocol
To investigate potential changes in sensation at the test area, the mechanical detection threshold was measured using seven weighted pinprick stimulators (8–512 mN). The threshold was determined for the test and control arm (volar forearm) both before and after the NPP-task. The intensity (represented by the exerted force of the individual pinpricks in mN), was applied in an alternating ascending and descending manner until three “Yes” (a pricking sensation was felt) and two “No” (no pricking sensation was felt) responses were obtained from the participant32.
2.4. Nociceptive predictive processing task
Based on a computational modelling approach of learning under uncertainty30,31, and inspired by the Conditioned Hallucination task from Powers et al.33, we developed a NPP-task assessing the relative weight of the prior versus the sensory input during perception of nociceptive stimuli. All nociceptive stimuli during the NPP-task were induced by bipolar cutaneous electrical stimulation to the forearm causing an intensity-dependent sensation from a non-painful to a painful pricking sensation. The NPP-task essentially comprised three steps: In the first step, maximum likelihood threshold estimation procedures (QUEST) 34 were used to determine the individual perceptual threshold for nociceptive stimuli. In the second step, aberrant pain perceptions were elicited using a probabilistic Pavlovian conditioning paradigm (see below). For this purpose, all participants were asked to report whether they felt an electrical stimulus as a pricking sensation during the stages of the paradigm. The conditioning stage comprised of a high percentage of trials with intensities slightly above the perceptual threshold along a visual conditioning cue. Subsequently, the testing stage was comprised of a gradual decrease in association strength presenting sub-threshold intensities along with a progressive increase in the rate of zero-intensity trials. In the third step, the perceptual learning and unlearning of this association were modelled using Hierarchical Gaussian Filters (HGF) and the relative weight (\({\nu }\)) of the prior versus the sensory input during perception was estimated.
The experimental paradigm was comprised of the determination of the nociceptive threshold (method of limits and QUEST) and probabilistic Pavlovian conditioning with a visual cue (main body of the NPP-task; Fig. 1a) as inspired and utilized in the works of Powers et al.35–37.
All stimuli were presented in trials and participants’ responses were recorded with MATLAB Psychtoolbox 3.0. A visual fixation cross was present throughout each trial, white on a black background and the visual conditioning stimulus consisted of a checkerboard image (Fig. 1b). Visual stimuli were presented concurrently with target electrical stimuli, if present, for one second.
Determination of the nociceptive threshold: Stimulus intensities were determined using the QUEST maximum-likelihood procedure for threshold determination (Psychtoolbox 3.0, MATLAB 2018b). The QUEST is a Bayesian adaptive psychometric method used to determine individual stimulus intensities eliciting sensory perceptions with a sufficient degree of perceptual uncertainty in the individual34. First, the QUEST assesses the threshold for electrical stimuli for which the participants are 75% likely to report detection. This is accomplished via two independent, 40-trial-long ascending and descending series of stimulus intensities (stimulus staircases) determined by the QUEST program based upon participant responses (Fig. 1c) with a subsequent derivation of the mean threshold value from the posterior distribution of threshold intensities35. Prior to the QUEST, a coarse threshold paradigm is conducted using a method of limits approach with five detections to determine a starting value for the QUEST. After the QUEST paradigm, individual psychometric curves were fitted to participant responses using a log-Weibull curve from which stimulus intensities, at which participants are 75%, 50% and 25% likely to detect stimulus presentations, were derived. The beta, gamma and delta parameters of the log-Weibull model for the psychometric curve were set to values of 3.5, 0.01 and 0.01, respectively35.
Probabilistic Pavlovian conditioning: During the main body of the NPP-task (Fig. 1a), participants were implicitly taught the association between the target electrical stimulus and a concurrently presented visual conditioning cue stimulus (checkerboard image; Fig. 1b). Subsequently, they were tested on the strength of this association over the course of 12 blocks of 30 trials each (Fig. 1d). Following each trial, participants were asked to indicate whether the target electrical stimulus was present (in form of a pricking sensation) using a button press. The likelihood of threshold-level electrical stimulus presentations decreased non-linearly over the course of the 12 blocks with concomitant overrepresentation of subthreshold and zero-intensity trials (Fig. 1e and e). Trial-type relative likelihoods were determined by block number, and trial type presentation was pseudorandomized within blocks. To avoid habituation or sensitization to the electrical stimuli, the presentations were separated by a fixed time of 4 seconds, in which the participants were allowed to give a response. Participants were prompted to take a short break of up to 2 minutes after every three blocks.
Computational modelling using Hierarchical Gaussian Filters: A Bayesian framework with a Hierarchical Gaussian Filter (HGF) was used to model the integration of sensory input with prior beliefs during perception to yield in a posterior belief about the states causing the sensory inputs30,31. This modelling approach is based on the theory of agents that are learning about their world by perceiving sensory inputs, constantly updating their model of hidden states that caused these, and taking actions based on their new beliefs2,4,38. As inspired by Behrens et al. 2007, hidden states of the world are represented by a generative model of hierarchically coupled Gaussian random walks that evolve in time39. The HGF approach allows for the utilization of a dynamic and adaptive learning rate, which tackles the process of learning under uncertainty in a changing environment. Each higher level in the hierarchy represents the dynamic structure of the world and each step size of the random walk is influenced by the next-higher state in the hierarchy. By inverting this generative model with variational approximation, we can derive update rules for the expectation of hidden states that the agent has at any given time. Furthermore, the introduction of prior parameters that govern the coupling between levels in the hierarchy, allows for the extraction of learning characteristics that vary between individuals and allows for learning that is subjectively optimal, but objectively erroneous – as is expected with strong priors. The model was defined by three levels of environmental states: Level 1, representing the belief about whether a stimulus was present. Level 2, describing the belief about the strength of association between nociceptive stimuli and visual cue. Level 3, describing the volatility of level 2. By fitting the HGF to our behavioral data from the NPP-task, a weighting parameter (\({\nu }\)) between prior expectations and sensory evidence could be extracted.
2.5. Electrical stimulation
Due to ethical reasons, an intraepidermal electrode for the stimulation of A-δ fibers, as recommended in the work of Inui et al., could not be implemented in this study40. As a workaround, a bipolar electrode with two steel balls for skin contact (7 mm stimulation points at 28 mm distance) was secured 5 cm distal to the elbow on the volar forearm. The total signal duration was set to one second with a pulse train of 15 bipolar waves, with a frequency of 50 Hz, starting at 200 milliseconds. There was no intensity (0 milliamperes; mA) before and after the pulse train. The pulse waves were rectangular as suggested by Inui et al., whereas the remaining parameters had to be adjusted (polarity, frequency and duration), to achieve a pricking like sensation upon stimulation40. For stimulus presentation, this signal was sent to the data acquisition board (National Instruments; Model: USB-6341) and further to a DS-5 (Digitimer, United Kingdom) electrical stimulation device with the attached electrode. The electrical signal was defined in MATLAB.
2.6. Cuff algometry
A computerized pressure cuff system (Nocitech, Denmark) was used to investigate the perceived pain detection (PDT) and pain tolerance thresholds (PTT) as well as temporal summation of pain (TSP) and conditioned pain modulation (CPM)41. The protocol included a ramp to assess PDT and PTT on the dominant leg, a TSP paradigm on the dominant leg, a ramp to assess PDT and PTT on the non-dominant leg, and a CPM paradigm with the test stimulus on the dominant and conditioning stimulus on the non-dominant leg. The cuffs were placed over the widest portion of the gastrocnemius muscle on each lower leg with participants in a reclined long sitting position with a pillow under the knees. Participants were asked to rate the intensity of pain felt during the pressure application using an electronic visual analogue scale (VAS). The VAS score for pain ranged from 0 cm (no perceived pain) to 10 cm (maximum tolerable pain). The maximum cuff pressure was limited to 100 kPa and participants were able to immediately deflate the cuffs by pushing a button. Each subject was familiarized with the cuff algometry device during a training phase in the start of the session, with the subject seated and the cuff placed around the upper arm. Subjects were trained on how to use the electronic VAS and how to stop cuff inflation.
Ramps conducted to assess PDT and PTT used steadily increasing pressure (1 kPa/s) to a maximum of 100 kPa. The VAS was used by the subjects to provide continuous VAS ratings of their pain intensity during cuff inflation. When the VAS reached 1 cm, the corresponding cuff pressure was taken as the subject's PDT41. Once the pressure reached the subject's tolerance limit, they pushed the stop button on the VAS device to deflate the cuffs and this was taken as their PTT. For subjects who reached the maximum pressure of 100 kPa, this was taken as a conservative estimate of their PTT42.
TSP was assessed by ten cuff stimuli at PTT intensity with 1 s duration and 1 s interstimulus interval 41,43. The participants were instructed to rate their pain from the first stimulus immediately on the VAS, then to adjust their rating up as necessary on subsequent stimuli without returning the dial to zero. The rating for the first stimulus was used as a normalization factor (subtracted from the VAS scores related to the 2nd to the 10th stimuli). The TSP-effect ratio was calculated as the average of the pain ratings of the last three pulses, divided by the average of the pain ratings during the first three pulses.
The CPM protocol included rapidly increasing pressure on the nondominant leg to 70% of PTT (conditioning stimulus), which then remained constant throughout. A steadily increasing pressure (as per initial PTT determination) was then applied to the dominant leg to capture the conditioned PTT (test stimulus). The CPM effect was calculated as the difference between the PTT of the dominant leg during conditioning and the PTT measured at baseline.
2.7. Computational modelling
HGF modelling was used to quantify the influence of prior beliefs about sensory inputs on perception at the individual level. In line with Powers et al.’s implementation of the HGF using a very similar procedure in audition, an observation model was implemented where decision noise was applied to the probability of a detection, where the “belief” of the participant, i.e., the posterior probability of a stimulation, is given by the participant’s prior and the strength of the observed stimulation. This was formalized as the Bayesian posterior of a beta distribution:
$$belief=prior+ \frac{1}{1+v}(observation-prior)$$
1
where observation is the stimulus intensity of the trial, prior is the learning prior from the HGF’s level 1, and ν is a parameter indicating the relative weight of the prior vs the sensory input so that for values greater than 1 the prior has more weight than the observation and values lower than 1 indicate greater weighting of the observation. The logistic sigmoid is:
$$f\left(x\right)=\frac{1}{{e}^{(-\beta *({V}_{1}-{V}_{0})}}$$
2
where β is a positive parameter that determines the slope, and V1 and V0 are the values of detection vs non-detection, respectively. In this study, there will be focus on the ν-parameter, given the likely importance of prior weighting in the perceptual computation of pain in chronic pain conditions. Here, \({\nu }\)<1 indicates a stronger weighting of prior expectations over sensory information, whereas \({\nu }\)>1 indicates a stronger weighting of sensory information over prior expectations.
The initial parameter states of the HGF were set to default as defined in the TAPAS toolbox (MATLAB and Statistics Toolbox Release Version 5.0.0, The MathWorks, Inc., Natick, Massachusetts, United States). During the fitting of the HGF, we observed issues achieving a fit for several participants, which was corrected by altering the initial state for the Ω2 parameter, which forms part of the linking function between the first and second level of the HGF. A systematic search of parameter values from the initial prior of -3 up to -10 revealed optimal fit at an initial value of -4.2, in that the model was able to converge on a fit for all participants but without inducing outliers in the ν parameter or fit indices (LME/AIC). To prevent undue influence of outliers in the ν-parameter fit, a robust regression approach was undertaken (elaborated further below).
2.8. Statistical analysis
Inferential Models: All statistical analyses were carried out in R (version 4.1.1), using Bayesian estimation in brms which acts as a high-level interface to Stan to implement a no-U-turn sampler variant of Hamiltonian Monte Carlo (HMC)44–46. For all models fitted, four chains were run using 5000 iterations at a warm-up of 1000. The models were specified with mildly informative priors to achieve regularization. Outcome parameters were estimated using Student’s t-distributions rather than Gaussian normal distributions for all models, which are more robust to outliers47. All predictors were scaled and centered. Two main models were fitted, with the specifications:
![](data:image/png;base64,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)
Where\({\gamma }_{i }\)is the outcome,\({\alpha }_{i}\)the intercepts of pre- and post-task thresholds, \({\beta }_{j}\) a vector of coefficients for the vector of covariates \({X}_{j}\) (gender & QUEST threshold),\(\sigma\) is the initial value of the scaling parameter, and \({\nu }\) the degrees of freedom of the t (not to be confused with the \({\nu }\)-parameter from the HGF).
First, a robust regression model was fitted to assess whether the task induced systematic sensitization/habituation in the test area, with mechanical pain detection threshold assessed via pinprick as the outcome and pre- and post-task timepoint as the primary predictor. Additionally, gender and QUEST threshold were entered as covariates. The model was set up to estimate individual intercepts for pre- and post-task.
Second, a robust regression model was fitted to assess whether the weighting of prior to likelihood in the NPP-task, instantiated in the ν-parameter, was linearly associated with TSP-effect, CPM-effect, PDT, PTT and QUEST threshold. The three parameters showed no evidence of multicollinearity and were therefore entered into the same model. Again, gender was entered as a covariate to control for its potential influence on outcome and predictors.
HMC chain convergence was assessed using the Rhat value, reliability of posterior quantiles was evaluated in the bulk- and tail-Effective Sample Size (ESS), and predictive accuracy was evaluated using the leave-one-out cross-validation information criterion (LOO-IC) to estimate the expected log predictive density48,49. Further, Bayesian R2 estimates (which define R2 based on the variance of estimated prediction errors) are provided50. To provide measures of uncertainty, 95% highest probability density intervals (HDI) around the mode were evaluated for parameter estimates.
NPP-task specific statistical analysis: For the mechanical pain detection threshold, the geometric mean and the standard deviation were calculated based on the five collected intensities for “Yes” and “No” responses. The statistics were calculated for the test and control arm both before and after the NPP-task.
To validate the method of nociceptive stimulation and test for potential habituation or sensitization effects, we analyzed participants’ responses during the QUEST and main body of the NPP-task. A convergence between the QUEST stimulus staircases was calculated with a difference in intensity values between staircases and chronologically searching for the trial number, at which all subsequent trials yield intensity differences that are in average lower than 5% of the estimated threshold by QUEST.
A Student’s t test was performed to test for differences in QUEST threshold values between female and male participants. A difference in counts between female and male participants with a ν > 1 was tested with a chi-square test of independence with a significance test level of 0.05.
To check if the participants were able to detect the intensities of the different trial types during the main body of the task, the detection rate was calculated by dividing the number of perceived trials with the total count of trials for each specific type.