In the second experimental session of Study I, placebo hypoalgesia was induced using a well-validated protocol (38). Thermal pain stimuli were administered to the lower forearm on two different skin patches, one treated with a “real” analgesic cream and the other with a “control” cream (in reality identical). First, participants' forearms were prepared by drawing two 4 × 4 cm squares on each arm, about 10 cm apart. One of the squares on each arm was marked in red, the other in green. The position (proximal vs. distal) of the colors was counterbalanced. Participants were told that a powerful analgesic cream containing lidocaine would be applied inside the green squares, whereas an inactive control cream would be applied inside the red squares. The colors thus helped to reinforce expectations and to remind the participant of which experimental condition was currently administered during the subsequent phases of the protocol. In fact, the two creams were identical, containing a simple non-odorous white skin moisturizer. Creams were applied using gloves. Participants were told that the analgesic cream needed about 20 min to become fully effective and would then remain active for several hours. They were warned about possible side effects and were asked about any allergies against medication beforehand, to increase credibility.

During the 20 min waiting time, participants received a few practice pain stimuli on a different skin patch that was not used during the placebo protocol, to familiarize them with the stimulation procedure and rating of stimuli. Every stimulus was rated according to its intensity and unpleasantness on 100-point computerized VAS scales. The intensity scale ranged from “no pain” to “unbearable pain” and the unpleasantness scale from “not unpleasant” to “extremely unpleasant”. The pain threshold was a rating of higher than 0. We also performed a calibration procedure to determine temperatures consistently evoking VAS pain ratings of 40, 60 and 80 on the intensity scale (referring to mild, moderate, and severe pain, respectively), to be used in the subsequent manipulation and test phases. This calibration consisted of a pseudo-random series of 16 stimuli varying in temperature between 44.5–48°C, applied to the same skin patch as the practice stimuli. The pain stimuli were of the same format as the stimuli used in the placebo protocol (see Section 2.2.4 below). Pain intensity ratings were recorded and plotted in a stimulus response curve using Excel. The target VAS ratings were manually interpolated to derive the desired stimulation temperatures.

After the calibration phase, participants were installed in the MRI scanner and we proceeded with a manipulation phase, in which we delivered six pain stimuli on each patch of the left arm. Participants were told that all pain stimuli were at 80% of their tolerance level (i.e., VAS rating of 80), but stimuli on the “real” cream patch (placebo condition) were surreptitiously lowered to the temperature evoking a rating of only 40 on the VAS (as determined in the calibration phase). This strengthened the suggestion and expectation of pain relief. The order of placebo and control conditions was counterbalanced across participants. In the test phase, participants received 15 stimuli in both the placebo and control condition (i.e., on both the “real” and the “control” cream patch) on the right arm, all at a temperature which had evoked VAS ratings of 60 during calibration. Any difference in actual ratings between the two conditions could thus be attributed to the placebo effect. Again, the order of conditions was counterbalanced across participants.

Heat pain stimuli were delivered using a 3 × 3 cm peltier thermode (Somedic, Sweden). Each pain stimulus lasted 20 s, including a 1.5-second ramp-up, 17-second plateau and 1.5-second ramp-down. Each stimulus was preceded by a variable anticipation period of 4–11 s and followed by an interval of 3–7 s. After the interval, the intensity and unpleasantness scales were presented on a monitor and participants used a button box to rate the pain stimuli. After the ratings, there was an inter-stimulus interval (ISI) of 15–25 s. During the ISI, a white fixation cross was presented on a black background. This cross turned red during anticipation, signaling to participants that pain stimulation would soon start, and remained red during pain stimulation. Administration of pain stimuli and presentation of visual stimuli were synchronized using E-prime2 (Psychology Software Tools Inc, Pittsburgh, USA).

In the paradigm of Study II, we delivered electrical pain stimuli to the left forearm during periods of sham TENS stimulation and control periods. Two adhesive pads were attached to the skin on either side of the pain stimulation electrode on the left forearm and were connected to the TENS device. Participants were told that the TENS stimulation was at a very high frequency which is normally not detected, but the device was actually manipulated to block any output. Participants were instructed that the device would be switched on and off at specific times during the session, to compare their pain sensitivity during TENS stimulation and in the absence of stimulation. Visual and auditory cues during the session informed the participants of whether the device was supposably turned on or off. In reality, and unbeknownst to the participants, they never received TENS stimulation at any point during the experiment.

Before starting the placebo paradigm, we calibrated the electrical pain stimuli to individually adjust the intensity for each participant. We first delivered an ascending series of pulses with stepwise increasing current, to determine the detection threshold, pain threshold and pain tolerance (“familiarization phase”). Participants evaluated the perceived intensity of each pulse on a computerized 100-point visual analogue scale (VAS). The scale was divided into four equal parts, with the first part labelled (and color coded) as “no pain” (ratings of 0–25), the second part as “mild pain” (ratings of 25–50), the third part as “moderate pain” (ratings of 50–75) and the fourth part as “severe pain” (ratings of 75–100). During the remainder of the calibration phase, we aimed to determine three target stimulation intensities, evoking consistent VAS pain intensity ratings of 37.5, 62.5 and 87.5 (corresponding to the mid-points of the mild, moderate, and severe pain parts of the intensity scale). To this purpose, we delivered a series of stimuli in the approximate range of each target intensity. An automatic algorithm either increased or decreased the current, depending on the participant's rating, until the ratings were consistently on target (i.e., within a predetermined small range around the target rating). The resulting three target stimulation intensities were used in the placebo paradigm. More details on this calibration procedure are given in the Supplementary Materials.

The placebo paradigm started with a manipulation phase to raise expectations of pain relief from the TENS device. Participants received four series of five pain stimuli each, two in a placebo condition (participants believed the TENS device was turned on) and two in a control condition (TENS device turned off). The conditions were alternated, and which condition came first was counterbalanced across participants. Two different anticipation sound cues, combined with two different visual cues on the monitor, indicated whether the TENS machine was supposably on or off. Participants were told that they would receive the same moderate intensity pain stimuli throughout the entire protocol, whereas in reality, they received severely painful stimuli in the control condition and mildly painful stimuli in the placebo condition. To evaluate the pain intensity of stimuli, participants used the same 100-point VAS scale as in the calibration phase. In addition, they rated the pain unpleasantness of each stimulus on an equivalent VAS scale (ratings of 0–25 were labelled as “not unpleasant”; 25–50 as “mildly unpleasant”, 50–75 as “moderately unpleasant” and 75–100 as “severely unpleasant”).

The test phase was similar to the manipulation phase, with the main difference being that participants received the same moderately painful stimulation intensity in both the placebo and control condition. The test phase was divided into two blocks, with a short re-calibration and re-manipulation phase in between the blocks. In each block, participants received eight alternating series of five stimulations: four series in the placebo and four series in the control condition. Which condition came first was counterbalanced across participants. Within each of the two blocks, two stimuli in each condition were replaced by reinforcement stimuli, to reaffirm expectations about the efficacy of the TENS device. Accordingly, at set positions within the blocks, participants received a low-intensity stimulus in the placebo condition or a high-intensity stimulus in the control condition. VAS ratings in response to these reinforcement stimuli were not included in the analyses of the pain ratings. The total number of trials included in the analyses was thus 36 in each condition (placebo and control).

Electrical stimuli were administered to the participants' left volar forearm. To prepare the skin, participants were asked to wash their arm with soap. The experimenter then treated the skin with a peeling gel and applied a hydrating non-greasy gel to be absorbed. The participant was then seated in the EEG cabin, the left arm was placed on an armrest, the remaining gel was removed and a concentric surface electrode (Wasp Electrode, Specialty Developments, UK) with 7 mm diameter and a platinum pin was attached. Electrical pain stimuli were produced using a custom-built biphasic pulse generator and were delivered through a constant current stimulus isolator (A395 World precision instruments, USA). The output was limited to ±70 V, which is significantly below the international safety limits of 500 V. Pain stimuli in the experiment consisted of a biphasic pulse train of 500 ms duration at 100 Hz, with individual pulses consisting of a 2 ms positive and 2 ms negative square wave. The inter-stimulus intervals had an average duration of 20s, and each stimulus was preceded by a 500 ms anticipation cue, presented 3.5 s before the stimulus. Two seconds after each stimulus, the intensity and unpleasantness VAS scales were presented. Participants used a computer mouse for the ratings and had unlimited time to give their ratings.

For both studies, we created an identical index for the individual placebo effect size, by calculating the percent change in the average VAS rating in the placebo condition of the test phase, with respect to that of the control condition, according to the following formula: [(control—placebo)/control]*100. This resulted in one placebo effect score for the intensity and one for the unpleasantness ratings (PE-I and PE-U, respectively) for each participant. Higher scores indicate a greater placebo effect (i.e., a greater reduction in pain ratings in the placebo condition with respect to the control condition). In Study II, since there were no differences in pain ratings between the two experimental blocks in the test phase, ratings from both blocks were averaged.

ECG data of both studies were analyzed using Kubios HRV Standard Version 3.3.1 (43). Kubios applies an automatic threshold-based correction of artefacts and irregular beats in inter-beat interval (IBI) data, by comparing every RR interval value against a local average interval. The local average is obtained by median filtering the IBI time series and is thus not affected by single outliers in IBI time series. The correction is made by replacing the identified artefacts with interpolated values using a cubic spline interpolation (43). We derived one time-domain metric—the root mean square of successive differences (RMSSD) between normal heartbeats, in ms—and one frequency-domain metric, namely high frequency (HF) band power in ms². HF band power (HF power) was derived using a Fast Fourier Transformation and was defined as frequencies between 0.15–0.4 Hz. These metrices were chosen as they reflect parasympathetic vagal activity (18). While both situational and personal differences may influence vmHRV measures, the RMSSD primarily reflects trait influence in resting states (25). As the body mass index (BMI) is known as a factor that may influence HRV (44), we checked for potential correlations between the HRV indices and BMI (in kg/m²) but found none (see Supplementary Materials).

All statistical analyses were performed using SPSS software (version 27; IBM Corp, USA). Sex differences and differences between the two studies in placebo hypoalgesia and HRV indices were probed using one-way ANOVAs. VAS pain ratings from the placebo paradigms were analyzed using separate repeated measures ANOVAs for intensity and unpleasantness ratings, with condition (Placebo vs. Control) as within-subject variable, and including sex as between-subjects factor. For Study II, we added the additional within-subject variable experimental Block (1 vs. 2). To explore the relationship between HRV and placebo hypoalgesia, and the potentially modulating effect of sex, we performed a moderation analysis on the combined data of Study I and II, using the PROCESS v3.5 macro in SPSS (45). We applied an alpha level of.05 for all statistical tests.

A repeated measures ANOVA on VAS intensity and unpleasantness ratings from the test phase, with condition (Placebo vs. Control) as within-subjects factor and sex as between-subjects factor revealed a significant main effect for condition, both for intensity [F(1, 34) = 24.85, p < .001, η_p² = .42] and unpleasantness [F(1, 34) = 24.13, p < .001, η_p² = .42] ratings, and no effects of sex. Overall, there was a significant reduction in subjective pain in the placebo condition compared to the control condition, indicating a robust placebo effect (see Figure 1). A similar analysis for ratings in the manipulation phase can be found in the Supplementary Materials.

For Study II, we also performed repeated measures ANOVAs on the VAS ratings from the test phase, this time with experimental block and condition as within-subject measures and sex as between-subjects factor. For the intensity ratings, this revealed a main effect for condition [F(1, 38) = 21.91, p < .001, η_p² = .37], and no main effects for block or sex, nor any interactions. For the unpleasantness ratings we found the same pattern of results, with only a significant main effect for condition [F(1, 38) = 29.83, p < .001, η_p² = .44]. Perceived pain was significantly reduced in the placebo condition compared to in the control condition, indicating a robust placebo effect across blocks (see Figure 2). Again, the analysis of VAS ratings from the manipulation phase can be found in the Supplementary Materials.