HSD method and rationale#

The Heartbeat Synchrony Discrimination task (HSD) asks when, relative to the ECG R-wave, a participant experiences their heartbeat. Participants judge whether a sequence of tones feels synchronous with it. By varying the delay, the task estimates where synchronous responses are most likely and how broadly they are distributed across the cardiac cycle.

This page explains the measurement logic, the adaptive procedure, and the timing constraints. For session setup, use the HSD task page. The companion validation page presents the simulations, hardware demonstration, and remaining validation work.

Important

HSD is in beta. Simulations and a hardware demonstration have been completed, but the task has not been validated in a participant study. The reported simulation results use marginal estimates of heartbeat timing; the current stopping rule uses conditional estimates. Their implications are distinguished on the validation page.

Why a new task#

Heartbeat sensations do not occur at the same delay after the R-wave in every person. A task that compares only two fixed delays can therefore miss a clearly perceived heartbeat whose timing falls between them. Across heartbeat discrimination tasks with two fixed delays, Brener and Ring estimate that only about one in three or four people reliably discriminate [Brener and Ring, 2016]. Whitehead and colleagues, who introduced the procedure, set no detector criterion [Whitehead et al., 1977].

The original procedure flashed a light 128 or 384 ms after each R-wave; later versions mostly use tones, and the delays vary between laboratories.

The method of constant stimuli addresses this problem by sampling several delays across the cardiac cycle [Brener et al., 1993]. Each participant’s responses reveal a preferred delay and a spread of delays judged synchronous. A standard session takes about 35 minutes, including familiarization. HSD retains this multi-interval approach and uses adaptive sampling to obtain information about the preferred delay in fewer trials.

The theory page explains the measurement problem in more detail. The literature and the relationship to the Phase Adjustment Task are reviewed under background evidence.

The model#

The model links the probability of a synchronous response to the tone delay \(d\) through a Gaussian response envelope:

\[P(\text{synchronous} \mid d) = \mathrm{floor} + (\mathrm{peak} - \mathrm{floor}) \exp\left[-\frac{1}{2}\left(\frac{d-\mu}{\sigma}\right)^2\right].\]

The centre, \(\mu\), is the delay at which synchronous responses are most likely. The width, \(\sigma\), describes how quickly that probability falls as tones move away from the centre. The floor and peak set the baseline and maximum response probabilities. They allow the model to represent occasional inconsistent responses and a general tendency to answer yes or no.

These are properties of the response pattern. In particular, \(\sigma\) can reflect variability in both perception and stimulus timing. A narrow envelope is consistent with precise judgements only to the extent that the recording and audio system deliver the intended delays reliably.

The task can express delays in milliseconds after the R-wave or as fractions of the cardiac period. In either case it updates a discrete posterior over the four parameters after each valid response. The absolute-axis parameter grids and priors are given below.

Parameter grids and priors

Parameter	Meaning	Default grid
`mu`	Where in the cardiac cycle the sensation is felt, in ms after the R-wave	0 to 600 ms in 10 ms steps (61 values)
`sigma`	Width of the sensation, in ms	20 to 300 ms, log-spaced (20 values)
`floor`	Rate of “yes” far from the sensation: lapses towards “yes”	0.03, 0.1, 0.2, 0.35, 0.5, 0.65, 0.8, 0.9, 0.97
`peak`	Rate of “yes” at the sensation: one minus the lapse rate towards “no”. Equal to `floor` for a flat responder	The same grid as `floor`, at or above it

The parameter grids extend beyond the published range of heartbeat timing estimates [Brener and Ring, 2016, Brener and Kluvitse, 1988], allowing the model to represent a wide range of response patterns. The simulations offer candidate delays from 0 to 600 ms in 20 ms steps and the task runner from 80 to 600 ms. With the 130 ms floor of the current hardware the shortest delay presented is 140 ms, the first candidate above it, and the ceiling of about 0.68 of the heart period allows 600 ms only at periods over 0.89 s (see delay limits). The posterior is discrete on the outer product of the four grids, 98,820 points, of which the 54,900 with the peak at or above the floor carry prior mass; one stimulus selection takes about 20 ms.

Prior. Uniform over mu by default, or any non-negative weights over the mu grid. Uniform over the sigma grid points, which is log-uniform because the grid is log-spaced. Uniform over the 45 pairs of floor and peak with the peak at or above the floor, and zero mass where it would lie below (an inverted envelope). The 9 pairs with the peak equal to the floor, the flat responders, carry 0.2 of the prior.

Choosing the next delay#

After each response, the task evaluates the information expected from each available delay. By default, it chooses the delay expected to reduce uncertainty about \(\mu\) most. This is the Psi-marginal approach [Prins, 2013]: \(\sigma\), floor, and peak remain in the model, but the objective averages over their uncertainty rather than targeting them directly. Targeting all four parameters instead gives the joint objective of the original Psi method [Kontsevich and Tyler, 1999].

The task also selects a delay at random on 10 percent of trials. This exploration helps sample parts of the response pattern that the adaptive objective might otherwise visit rarely. The underlying engine defaults to no exploration; the task configuration sets explore=0.1.

Adaptive sampling can concentrate observations within a limited stimulus range, a concern raised for non-monotonic psychometric functions by García-Pérez [García-Pérez, 2014]. HSD addresses this through the location objective, random exploration, and retention of the full trial history for later fitting. The validation study also checks which delays were actually sampled.

PsychoPy’s PsiHandler assumes a monotonic cumulative Gaussian function, as used in HRD. Synchrony responses instead rise towards a preferred delay and fall beyond it. HSD therefore uses its own grid-based estimation engine, cardioception.HSD.psi.

Evidence for a timing-dependent response#

A participant may answer synchronous at roughly the same rate at every delay. The model represents this with peak equal to floor. Such a flat response pattern provides no information about a preferred timing, whether the participant answers yes frequently, rarely, or about half the time.

The task consequently reports both a timing estimate and evidence that responses vary with delay. Detection evidence is the posterior probability that the model’s largest and smallest response probabilities differ by more than 0.2 over the range of delays presented. This is distinct from peak - floor: a peak outside the sampled range, or an extremely broad envelope, may produce little variation within that range. Before two distinct delays have been presented, the candidate range is used.

The prior probability of this event is about 0.47 over 140 to 500 ms and 0.55 over 80 to 600 ms. The task also reports a Bayes factor, calculated as posterior odds divided by prior odds, to express how the observations change the evidence. This is a monitoring measure. The simulation results do not establish it as a classifier of individual participants.

Timing estimates and the stopping rule#

A flat envelope leaves \(\mu\) unidentified. If it retains posterior probability, the marginal posterior for \(\mu\) includes a diffuse component, even when the location of a possible rise is fairly well constrained.

The current task reports \(\mu\) and \(\sigma\) conditional on a rise greater than 0.2 over the presented range. These estimates answer: where and how broad is the response pattern, given that such a rise exists? The estimates of floor and peak remain marginal. Detection evidence must be read alongside the conditional estimates to assess support for their premise.

If the posterior probability of a rise falls below 0.01, the task falls back to marginal estimates and sets MuConditional to False. Delay selection always uses the marginal posterior of \(\mu\), so trials continue to inform both location and the evidence for a rise.

The session may stop after at least 15 valid updates when the 95 percent interval for \(\mu\) is no wider than 100 ms, or 0.17 of a cardiac period on the phase axis. Otherwise it ends at the maximum of 60 trials. These defaults are provisional. The session-length results were calculated from marginal intervals and do not establish the stopping behaviour of the current conditional rule.

Realized delays and per-trial constraints#

The recording and audio system restrict which delays can be presented. At the short end, the task must detect an R-wave and schedule a tone before its target time. At the long end, the tone must remain sufficiently far from the next heartbeat to avoid ambiguity about which beat it accompanies.

The default minimum delay is 130 ms, making 140 ms the first available candidate. On the absolute axis, the upper limit is 0.675 of the anticipated heart period: a 0.75 limit with a 10 percent margin. Thus, a 600 ms candidate requires a period longer than about 0.89 s. If no candidate falls within the limits, the engine raises an error.

The minimum must be checked on the actual recording setup. The hardware demonstration recorded some beats too late to deliver a 140 ms tone. Delays below the minimum are not sampled; an earlier preferred timing can only be inferred from the accessible portion of the response envelope. This is a major source of error for early sensations in the simulations.

The model updates from the mean reported delay of the tones delivered on a trial, with latencyBias added back, rather than simply using the requested delay. This accommodates real-valued delays. However, driver-reported onset is not a direct measurement of sound reaching the participant. Constant latency and timing variability must be assessed separately. The timing measurements explain these quantities and the default 50 ms correction.

Trial structure and saved data#

This section describes the task as cardioception.HSD.task runs it. The HSD page lists the files a session writes.

Five tones, each at the chosen delay after a detected R-wave.
A “synchronous” or “not synchronous” judgement on the keyboard.
A confidence rating on the existing confidence scale, reusing the HRD’s keyboard rating and cardioception.scales.ConfidenceScale.

Confidence is recorded alongside the judgement. It is not part of the likelihood and does not affect stimulus placement.

Saved for every trial:

Column group	Contents
Stimulus	Requested delay; realized delay, the trial’s mean (each tone’s is in `*_tones.txt`); interbeat intervals during the train; trial type (adaptive or explore)
Response	Decision; response time; confidence
Online estimates	Posterior mean, median and credible interval for `mu` and `sigma`; posterior mean of `floor` and `peak`; detection evidence and Bayes factor

As with the HRD, the online estimates are a monitoring aid. They are not an analysis, and the trial history is what a later model should be fitted to.

Background evidence#

The following sections retain the literature supporting the task’s design and its relationship to adjustment methods.

What the classical task established#

Multi-interval studies and their implications

Measuring cardiac interoception already covers what fixed-delay synchrony tasks can establish and why the MCS is a stronger measure of heartbeat timing. This section adds the findings that shaped the HSD design. It follows the review by Brener and Ring [Brener and Ring, 2016].

Study	Procedure	Finding
Yates et al. [Yates et al., 1985]	Six delays, 0 to 500 ms, one light flash per trial	Only 25 percent met detector criteria, later attributed to a single stimulus per trial giving too little data
Brener and Kluvitse [Brener and Kluvitse, 1988]	Participants switched freely among tones at the six delays	Preferred intervals from 100 to 400 ms; standard deviations of the preferred interval from 43 to 167 ms
Brener, Liu and Ring [Brener et al., 1993]	MCS: ten tones per trial at each of the six delays	54 percent classified as detectors, against 50 percent (Brener-Kluvitse method) and 33 percent (Whitehead variant). Tones at 100 to 300 ms most often judged simultaneous. Median preferred intervals 152 to 373 ms; interquartile ranges 118 to 362 ms
Brener, Ring and Liu [Brener et al., 1994]	MCS with fewer tones per trial	Five tones per trial did not impair reliability
Ring and Brener [Ring and Brener, 2018]	MCS at six fixed delays, 48 participants, alongside heartbeat counting	Each task gave reliable scores; heartbeat detection was unrelated to heartbeat counting

The standard MCS is 20 trials at each of six delays, 120 trials in all. With a 30-trial exteroceptive familiarization it takes about 35 minutes. It yields two measures: the median of the delays judged simultaneous (the location of the sensation in the cardiac cycle) and their interquartile range (its precision).

These findings motivate three features of the HSD. The location of the sensation must be estimated because it varies between people by hundreds of milliseconds. Its width also varies and requires a separate parameter. Finally, each trial presents several tones to support a more reliable judgement.

Relation to the Phase Adjustment Task#

Validation and further reading#

The validation and technical details page presents the simulation results, hardware demonstration, and implementation history.

Simulation study#

See the simulation design and results, including accuracy, detection evidence, and session length.

Hardware dry run#

See the hardware demonstration for timing measurements and the recorded session figure.

What comes next#

See the remaining validation work for the hardware improvements and planned exteroceptive validation.

References#

Full citation details are on the references page.