The coarse mental map of the breast is anchored on the nipple

Reviewer #1 (Public review):

The authors investigated tactile spatial perception on the breast through discrimination, categorization, and direct localization tasks. They reach three main conclusions:

(1) The breast has poor tactile spatial resolution.
This conclusion is based on comparing just noticeable differences, a marker of tactile spatial resolution, across four body regions, two on the breast. The data compellingly support the conclusion; the study outshines other studies on tactile spatial resolution that tend to use problematic measures of tactile resolution such as two-point-discrimination thresholds. The result will interest researchers in the field and possibly in other fields due to the intriguing tension between the finding and the sexually arousing function of touching the breast.

(2) Larger breasts are associated with lower tactile spatial resolution
This conclusion is based on a strong correlation between participants' JNDs and the size of their breasts. The correlation convincingly supports the conclusion. It is of interest to the field, as it aligns with the hypothesis that nerve fibers are more sparsely distributed across larger body parts.

(3) The nipple is a landmark: perceptually a unit and an attractor for tactile percepts
The data do not support these conclusions. The conclusion that the nipple is perceived as a unit is based on poor performance in tactile categorization for touches on the nipple. This categorization performance may simply mirror the breast's low tactile spatial resolution with JNDs about the size of a nipple.

The conclusion that tactile percepts are drawn towards the nipple is based on tactile localization biases towards the nipple for tactile stimuli on the breast compared to localization biases for tactile stimuli on the back. Currently, the statistical analysis of the data does not match the field, psychophysics, standards. Moreover, any bias towards the nipple could simply be another instance of regression to the mean of the stimulus distribution, given that the tested locations were centered on the nipple. This confound can only be experimentally solved by shifting the distribution of the tested locations. Finally, given that participants indicated the locations on a 3D model of the body part, further experimentation would be required to determine whether there is a perceptual bias towards the nipple or whether the authors merely find a response bias.

Further comments:

- Given that later analyses require regression models, the authors might consider using them throughout.

- The stability of the JND differences between body parts across subjects is already captured in the analysis of the JNDs; the ANOVA and the post-hoc testing would not be significant if the order were not relatively stable across participants. Thus, it is unclear why this is being evaluated again with reduced power due to improper statistics.

- The null hypothesis of an ANOVA is that at least one of the mean values is different from the others; adding participants as a factor does not provide evidence for similarity.

- The pairwise correlations between body parts seem to be exploratory in nature. Like all exploratory analyses, the question arises of how much potential extra insights outweigh the risk of false positives. It would be hard to generate data with significant differences between several conditions and not find any correlations between pairs of conditions. Thus, the a priori chance of finding a significant correlation is much higher than what a correction accounts for.

- If the JND at mid breast (measured with locations centered at the nipple) is roughly the same size as the nipple, it is not surprising that participants have difficulty with the categorical localization task on the nipple but perform better than chance on the significantly larger areola.

- To justify the conclusion that the nipple is a unit, additional data would be required. 1) One could compare psychometric curves with the nipple as the center and psychometric curves with a nearby point on the areola as the center. 2) Performance in the quadrant task could be compared for the nipple and an equally sized portion of the areola. Otherwise, the task "only" provides confirmatory evidence for a low tactile resolution in the midbreast area.

- A localization bias toward the nipple in this context does not show that the nipple is the anchor of the breast's tactile coordinate system. The result might simply be an instance of regression to the mean of the stimulus distribution (also known as experimental prior). To convincingly show localization biases towards the nipple, the tested locations should be centered at another location on the breast.

- Another problem is the visual salience of the nipple, even though Blender models were uniformly grey. With this type of direct localization, it is very difficult to distinguish perceptual from response biases even if the regression to the mean problem is solved. There are two solutions to this problem: 1) Varying the uncertainty of the tactile spatial information, for example, by using a pen that exerts lighter pressure. A perceptual bias should be stronger for more uncertain sensory information; a response bias should be the same across conditions. 2) Measure bias with a 2IFC procedure by taking advantage of the fact that sensory information is noisier if the test is presented before the standard.

- Neither signed nor absolute localization error can be compared to the results of the previous experiments. The JND should be roughly proportional to the variance of the errors.

- The statistically adequate way of testing the biases is a hierarchical regression model (LMM) with a distance of the physical location from the nipple as a predictor, and a distance of the reported location from the nipple as a dependent variable. Either variable can be unsigned or signed for greater power, for example, coding the lateral breast as negative and the medial breast as positive. The bias will show in regression coefficients smaller than 1.

- It does not matter whether distances are calculated based on skin or 3D coordinates, as Euclidean distances or based on polar coordinates. However, there should only be one consistent distance in the text across both independent and dependent variables. Calculating various versions of these measures can create issues in Frequentist Statistics. For transparency, it is good practice to report the results of other methods for calculating the distance in the supplement.

- The body part could be added as a predictor to the LMM, with differences in bias between the body parts showing a significant interaction between the two predictors. The figures suggest such an effect. However, the interpretation should take into account that 1) response biases are more likely to arise at the breast and 2) it might be harder to learn the range of locations on the back given that stimulation is not restricted to an anatomically defined region as it is the case for the breast.

Reviewer #2 (Public review):

The authors tested tactile acuity on the breast of females using several tasks and reported overall low acuity compared to the back, which is typically considered to have the worst acuity of all body parts. Moreover, there was evidence that acuity is worse the larger the breast; this finding mirrors similar findings for the hand and therefore suggests that the number of tactile sensors is fixed and must be distributed across a larger extent of skin when a body part is larger, thus resulting in comparably lower tactile acuity.

Strengths:

I find this an interesting paper with results that are relevant to the tactile community. The authors apply several tasks allowing them to link the paper with previous results. The methodology and psychophysical analysis are sound.

Weaknesses:

The analysis of localization error direction, with the result that the nipple area may be a landmark for tactile localization, is interesting and aligns the paper with some other recent papers that have suggested that such landmarks should exist. However, there are major issues with methodology and statistics, so that currently the conclusions are not supported.

In the following, line numbers refer to the re-formatted manuscript provided by the authors upon request and are mentioned for them to find the relevant passages faster.

(1) Comments on analysis of tactile acuity:

- I had a hard time understanding some parts of the report. What is meant by "broadly no relationship" in line 137?

- It is suggested that spatial expansion (which is correlated with body part size) is related between medial breast and hand - is this to say that women with large hands have large medial breast size? Nipple size was measured, but hand size was not measured, is this correct?

- It is furthermore unclear how the authors differentiate medial breast and NAC. The sentence in lines 140-141 seems to imply the two terms are considered the same, as a conclusion about NAC is drawn from a result about the medial breast. This requires clarification.

- Finally, given that the authors suspect that overall localization ability (or attention) may be overshadowed by a size effect, would not an analysis be adequate that integrates both, e.g. a regression with multiple predictors?

(2) Comments on analysis of "The nipple is a unit":

- Statistics in this section are not adequately described and may be partly false.

- In the paragraph about testing quadrants of the nipple, it is stated that only 3 of 10 participants barely outperformed chance with a p < 0.01. It is unclear how a significant t-test is an indication of "barely above chance".

- The final part of the paragraph on nipple quadrants (starting line 176) explains that there was a trend (4 of 10 participants) for lower tactile acuity being related to the inability to differentiate quadrants. It seems to me that such a result would not be expected: The stated hypothesis is that all participants have the same number of tactile sensors in their nipple and areola, independent of NAC size. In this section, participants determine the quadrant of a single touch. Theoretically, all participants should be equally able to perform this task, because they all have the same number of receptors in each quadrant of nipple and areola. Thus, the result in Figure 2C is curious.

(3) Comments on analysis of "Absolute localization on the breast is anchored to the nipple"

- Again, there are things that are unclear with the statistics and description of the analysis.

- This section reports an Anova (line 193/194) with a factor "participant". This doesn't appear sensible. Please clarify. The factor distance is also unclear; is this a categorical or a continuous variable? Line 400 implies a 6-level factor, but Anovas and their factors, respectively, are not described in methods (nor are any of the other statistical approaches).

- The analysis on imprecision using mean pairwise error (line 199) is unclear: does pairwise refer to x/y or to touch vs. center of the nipple?

- p8, upper text, what is meant by "relative over-representation of the depth axis"? Does this refer to the breast having depth but the equivalent area on the back not having depth? What are the horizontal planes (probably meant to be singular?) - do you simply mean that depth was ignored for the calculation of errors? This seems to be implied in Figure 3AB.

- Lines 232-241, I cannot follow the conclusions drawn here. First, it is not clear to a reader what the aim of the presented analyses is: what are you looking for when you analyze the vectors? Second, "vector strength" should be briefly explained in the main text. Third, it is not clear how the final conclusion is drawn. If there is a bias of all locations towards the nipple, then a point closer to the nipple cannot exhibit a large bias, because the nipple is close-by. Therefore, one would expect that points close to the nipple exhibit smaller errors, but this would not imply higher acuity - just less space for localizing anything. The higher acuity conclusion is at odds with the remaining results, isn't it: acuity is low on the outer breast, but even lower at the NAC, so why would it be high in between the two?

(4) Comments on the Discussion:

The discussion makes some concrete suggestions for sensors in implants (line 283). It is not clear how the stated numbers were computed. Also, why should 4 sensors nipple quadrants receive individual sensors if the result here was that participants cannot distinguish these quadrants?

Additional comments:

I would find it interesting to know whether participants with small breast measurement delta had breast acuity comparable to the back. Alternatively, it would be interesting to know whether breast and back acuity are comparable in men. Such a result would imply that the torso has uniform acuity overall, but any spatial extension of the breast is unaccounted for. The lowest single participant data points in Figure 1B appear similar, which might support this idea.