Measuring the Time-Scale-Dependent Information Flow Between Maternal and Fetal Heartbeats During the Third Trimester: Impact of Fetal Sex and Maternal Chronic Stress

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The rationale to study maternal-fetal heart rate/beat linkages is still not developed in the introduction.  How are these two systems connected and why would it be important to know?  Clearly among the auditory and pressure signals the fetus is exposed to, maternal heart beats together with digestive and respiratory sounds are dominant.  They are inescapable to the captive fetus.  Of course, as the authors speculate, there is the possibility that the fetal movements and physiological changes influence the mother and her heart rate.  If there is synchronization between mother and fetus, is it evidence of entrainment to these physical signals?

There are other signals traveling both ways in the maternal/fetal dyad, including biochemical messages.  How would these influence coupling of maternal-fetal heart rate?  Suggesting that this could be a marker of chronic stress that may be useful in a clinical setting is unconvincing.  There are many direct ways that chronic stress can be assessed that are much less labor intensive and technically challenging.  And the available methods for assessing prenatal stress are probably much more reliable (and therefore more valid) than heart rate coupling.  The authors obviously agree because they use the PSS as a validation instrument, and it is much more tractable in a clinical setting than assessment of heart rate.

The findings and methods are impressive.  As written, this is an outstanding technical paper, but It remains very difficult to read.  The narrative is choppy and ideas are not fully developed.  Perhaps too much is presented. I would suggest a separate paper describing the methods and the evidence of coupling and a second paper on the developmental significance of coupling.

The differences in coupling between stressed and control dyads presented in the graphs are very interesting but it was not possible to parse these differences from what is presented the text.  Another paper focused just on the prenatal stress relations would be an additional interesting paper.  The authors are to be congratulated on this fine analytical and methodological accomplishment.  Moreover, it is honorable that they have attempted to fit all their findings into a single paper, but in this case there is too much to digest and not enough depth for each of the questions raised.

Author Response

Please view the enclosed PDF for a cleanly formatted response letter.

 

Note on Track Changes and Structural Reorganization

A central concern raised by all reviewers was that the manuscript was excessively technical

for a biology-oriented readership. In response, we have reorganized the manuscript by moving

all mathematical definitions, model specifications, and technical analyses to a comprehensive

Supplementary Materials document. The main text now focuses on physiological context, key

findings, and biological interpretation. No content was removed—it was reorganized to improve

accessibility while maintaining full reproducibility.

Throughout the revised manuscript and supplementary materials, we use the following color

coding:

• Red text: New or edited content in the main manuscript

• Blue text: Content moved verbatim from the main manuscript to the Supplementary

Materials

• Purple text: Content that was both edited and moved to the Supplementary Materials

During data reconciliation, we identified and excluded three participants: FS-004 (no clinical

record), FS-144 (missing PSS score), and FS-124 (excluded from Table 2 only due to extreme

outlier net TE, z-score = 23.7). The final analytical sample comprises 118 mother-fetus dyads

(59 stressed, 59 control; 49 male, 69 female), with n = 117 for Table 4.

 

REVIEWER: The rationale to study maternal-fetal heart rate/beat linkages is still not

developed in the introduction. How are these two systems connected and why would it be

important to know? Clearly among the auditory and pressure signals the fetus is exposed to,

maternal heart beats together with digestive and respiratory sounds are dominant. They are

inescapable to the captive fetus. Of course, as the authors speculate, there is the possibility

that the fetal movements and physiological changes influence the mother and her heart rate. If

there is synchronization between mother and fetus, is it evidence of entrainment to these physical

signals?

RESPONSE: We have substantially expanded the Introduction to cover the autonomic,

hemodynamic, and mechanical mechanisms underlying maternal-fetal heart rate coupling, evi-

dence from normal pregnancies, alterations in pathological conditions, and short- and long-term

developmental implications.

REVIEWER: There are other signals traveling both ways in the maternal/fetal dyad, in-

cluding biochemical messages. How would these influence coupling of maternal-fetal heart rate?

Suggesting that this could be a marker of chronic stress that may be useful in a clinical setting

is unconvincing. There are many direct ways that chronic stress can be assessed that are much

less labor intensive and technically challenging. And the available methods for assessing prenatal

stress are probably much more reliable (and therefore more valid) than heart rate coupling. The

authors obviously agree because they use the PSS as a validation instrument, and it is much

more tractable in a clinical setting than assessment of heart rate.

RESPONSE: We and others published on this topic [1, 2, 3, 4, 5, 6, 7, 8]. While biochem-

ical pathways were not our focus here, the Discussion now includes a broader integration with

the prenatal stress programming literature (Section 5.3), covering autonomic, hemodynamic,

and neuroendocrine pathways. A new subsection “From Information Metrics to Physiological

Meaning” (Section 5.7) explicitly bridges mathematical metrics and their biological significance.

REVIEWER: The findings and methods are impressive. As written, this is an outstanding

technical paper, but it remains very difficult to read. The narrative is choppy and ideas are not

fully developed. Perhaps too much is presented. I would suggest a separate paper describing the

methods and the evidence of coupling and a second paper on the developmental significance of

coupling.

RESPONSE: We thank the reviewer for the positive reception. We consulted with the

Journal and do not see a viable path for splitting the paper. However, we agree completely that

the manuscript needed to be tailored to the audience. We moved all mathematical definitions,

model specifications, and technical analyses to a comprehensive Supplementary Materials docu-

ment, reducing the main manuscript by∼39% (from∼1,600 to∼1,000 lines) while preserving

full reproducibility. The main text now focuses on physiology and biological interpretation.

REVIEWER: The differences in coupling between stressed and control dyads presented in

the graphs are very interesting but it was not possible to parse these differences from what is

presented the text. Another paper focused just on the prenatal stress relations would be an

additional interesting paper. The authors are to be congratulated on this fine analytical and

methodological accomplishment. Moreover, it is honorable that they have attempted to fit all

their findings into a single paper, but in this case there is too much to digest and not enough

depth for each of the questions raised.

RESPONSE: We thank the reviewer again for the very thoughtful and supportive comments. As the reviewer sees in our responses to the other two colleagues, we have expanded each section of the manuscript, especially deepening the connections between the methods used and the physiology.

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

This manuscript investigates maternal–fetal heart rate coupling under prenatal stress using information-theoretical approaches, including entropy rate, sample entropy, and transfer entropy, in a cohort of third-trimester pregnancies. The study aims to extend the previously described Fetal Stress Index framework by identifying short- and long-term coupling mechanisms and their modulation by stress and fetal sex. The topic is potentially interesting and clinically relevant. However, several conceptual, methodological, and structural issues limit the clarity, interpretability, and suitability of the manuscript for a biologically oriented readership.

The Introduction would benefit from a stronger physiological and clinical contextualization. At present, it does not sufficiently describe the current understanding of how maternal and fetal heartbeats are coupled, including the autonomic, hemodynamic, and neuroendocrine mechanisms that may underlie synchronization. Additionally, the short- and long-term implications of altered coupling are not adequately discussed. The manuscript would be strengthened by integrating what is already known about maternal–fetal heart rate coupling in normal pregnancies and in pathological conditions such as gestational diabetes, pre-eclampsia, or other maternal stress-related disorders. Without this context, it is difficult to fully appreciate the biological and clinical relevance of the reported entropy-based findings.

The clinical characterization of the pregnancy cohort appears incomplete. Important maternal variables such as BMI, pre-existing diseases, development of gestational complications (including gestational diabetes or hypertensive disorders), and medication use are not clearly detailed. These factors could represent relevant confounders and, at minimum, gestational age and maternal age should be incorporated as covariates in the mixed models. If these variables were considered and found not to influence the results, this should be explicitly stated. Otherwise, the absence of such adjustments limits confidence in the robustness of the associations reported.

There is also ambiguity in the description of clinical data collected at delivery. The manuscript states that pH was recorded, but it is not specified whether this refers to umbilical arterial pH, venous pH, or another measurement. This should be clarified to avoid confusion.

From a structural perspective, the manuscript is excessively long and analytically dense. Large portions of the Methods section provide detailed explanations and definitions of the entropy-based algorithms that appear unnecessary for the readership of a biological or clinical journal. While methodological transparency is important, the level of mathematical detail resembles a computational methods paper rather than a physiology-focused study. The organization of the manuscript is unconventional, with topic-based subsections and limited linear narrative development. This makes the logical flow difficult to follow and obscures the main biological message. In addition, certain elements currently presented in the Methods would be more appropriately placed in the Results, and the statistical reporting does not follow standard conventions typically used in the field, further complicating interpretation.

The Discussion relies heavily on the authors’ previous publication and frames the current work primarily as an extension of that framework. A broader integration into the existing literature on maternal–fetal physiology and stress-related pregnancy outcomes is needed. More importantly, the manuscript does not sufficiently bridge the gap between mathematical metrics and physiological meaning. While changes in transfer entropy or entropy rate are statistically described, the biological implications of these changes remain insufficiently articulated. The reader is left uncertain about how these findings translate into meaningful alterations in fetal development or long-term health risk.

Overall, although the analytical approach is sophisticated, substantial revision would be required to improve biological contextualization, clarify cohort characterization and potential confounders, simplify and reorganize the structure, and better articulate the physiological relevance of the findings. In its current form, the manuscript is difficult to follow and does not clearly communicate its contribution to maternal–fetal physiology or stress research.

Author Response

Please view the enclosed PDF for a cleanly formatted response letter.

 

Note on Track Changes and Structural Reorganization

A central concern raised by all reviewers was that the manuscript was excessively technical

for a biology-oriented readership. In response, we have reorganized the manuscript by moving

all mathematical definitions, model specifications, and technical analyses to a comprehensive

Supplementary Materials document. The main text now focuses on physiological context, key

findings, and biological interpretation. No content was removed—it was reorganized to improve

accessibility while maintaining full reproducibility.

Throughout the revised manuscript and supplementary materials, we use the following color

coding:

• Red text: New or edited content in the main manuscript

• Blue text: Content moved verbatim from the main manuscript to the Supplementary

Materials

• Purple text: Content that was both edited and moved to the Supplementary Materials

During data reconciliation, we identified and excluded three participants: FS-004 (no clinical

record), FS-144 (missing PSS score), and FS-124 (excluded from Table 2 only due to extreme

outlier net TE, z-score = 23.7). The final analytical sample comprises 118 mother-fetus dyads

(59 stressed, 59 control; 49 male, 69 female), with n = 117 for Table 4.

 

REVIEWER: This manuscript investigates maternal–fetal heart rate coupling under pre-

natal stress using information-theoretical approaches, including entropy rate, sample entropy,

and transfer entropy, in a cohort of third-trimester pregnancies. The study aims to extend the

previously described Fetal Stress Index framework by identifying short- and long-term coupling

mechanisms and their modulation by stress and fetal sex. The topic is potentially interesting and

clinically relevant. However, several conceptual, methodological, and structural issues limit the

clarity, interpretability, and suitability of the manuscript for a biologically oriented readership.

RESPONSE: We thank the reviewer for the overall positive reception and constructive

criticisms. We focused on improving the Introduction, Methods, and Results, as recommended

by the reviewer, and responded in the following point-by-point manner.

REVIEWER: The Introduction would benefit from a stronger physiological and clinical

contextualization. At present, it does not sufficiently describe the current understanding of

how maternal and fetal heartbeats are coupled, including the autonomic, hemodynamic, and

neuroendocrine mechanisms that may underlie synchronization. Additionally, the short- and

long-term implications of altered coupling are not adequately discussed. The manuscript would

be strengthened by integrating what is already known about maternal–fetal heart rate coupling

in normal pregnancies and in pathological conditions such as gestational diabetes, pre-eclampsia,

or other maternal stress-related disorders. Without this context, it is difficult to fully appreciate

the biological and clinical relevance of the reported entropy-based findings.

RESPONSE: We thank the reviewer for this constructive critique. We agree that the Intro-

duction was insufficiently grounded in the physiological and clinical context. We have substan-

tially expanded the Introduction to cover: (1) autonomic, hemodynamic, and mechanical mech-

anisms underlying maternal-fetal heart rate coupling; (2) evidence from normal pregnancies; (3)

alterations in pathological conditions; and (4) short- and long-term developmental implications.

REVIEWER: The clinical characterization of the pregnancy cohort appears incomplete.

Important maternal variables such as BMI, pre-existing diseases, development of gestational

complications (including gestational diabetes or hypertensive disorders), and medication use

are not clearly detailed. These factors could represent relevant confounders and, at minimum,

gestational age and maternal age should be incorporated as covariates in the mixed models. If

these variables were considered and found not to influence the results, this should be explicitly

stated. Otherwise, the absence of such adjustments limits confidence in the robustness of the

associations reported.

There is also ambiguity in the description of clinical data collected at delivery. The manuscript

states that pH was recorded, but it is not specified whether this refers to umbilical arterial pH,

venous pH, or another measurement. This should be clarified to avoid confusion.

RESPONSE: We appreciate this important methodological concern. We have added Table

1, which includes all cohort characteristics. Stressed mothers were matched 1:1 with controls

on parity, maternal age, and gestational age at study entry (Section 3.1). Exclusion criteria

included fetal growth restriction, fetal malformations, maternal severe illness, and maternal drug

or alcohol abuse.

We conducted sensitivity analyses incorporating gestational age at birth, maternal age, and

pre-gestational BMI as covariates in all mixed linear models. No originally significant effects

changed significance status, with maximum coefficient changes of 7% (ER), 6% (SE), and 18%

(TE). Details are in Supplementary Methods, Section S1.7.

Table 4 reports p-values quantifying the probability of observing zero or negative net TE

under a Gaussian assumption (see Supplementary Methods, Section S1.8)—a within-subject

4metric inherently less susceptible to between-subject confounders.

During data reconciliation, we identified and excluded three participants: FS-004 (no clinical

record), FS-144 (missing PSS score), and FS-124 (excluded due to extreme outlier net TE, z-

score = 23.7). The final analytical sample comprises 118 mother-fetus dyads (n = 117 for Table

2).

We now specify that pH was obtained from the umbilical artery.

REVIEWER: From a structural perspective, the manuscript is excessively long and analyt-

ically dense. Large portions of the Methods section provide detailed explanations and definitions

of the entropy-based algorithms that appear unnecessary for the readership of a biological or

clinical journal. While methodological transparency is important, the level of mathematical

detail resembles a computational methods paper rather than a physiology-focused study. The

organization of the manuscript is unconventional, with topic-based subsections and limited lin-

ear narrative development. This makes the logical flow difficult to follow and obscures the main

biological message. In addition, certain elements currently presented in the Methods would be

more appropriately placed in the Results, and the statistical reporting does not follow standard

conventions typically used in the field, further complicating interpretation.

RESPONSE: We thank the reviewer for the thoughtful comments and suggestions. This

was the central structural change in this revision. We created a comprehensive Supplementary

Materials document containing all mathematical definitions, model specifications, and technical

analyses. The main manuscript was reduced by∼39% while retaining all key findings with brief

intuitive summaries referencing the supplement. The supplement includes a table of contents for

easy navigation.

REVIEWER: The Discussion relies heavily on the authors’ previous publication and frames

the current work primarily as an extension of that framework. A broader integration into the ex-

isting literature on maternal–fetal physiology and stress-related pregnancy outcomes is needed.

More importantly, the manuscript does not sufficiently bridge the gap between mathematical

metrics and physiological meaning. While changes in transfer entropy or entropy rate are sta-

tistically described, the biological implications of these changes remain insufficiently articulated.

The reader is left uncertain about how these findings translate into meaningful alterations in

fetal development or long-term health risk.

RESPONSE: We thank the reviewer for this important observation. We have revised the

Discussion to strengthen its integration with the broader literature on maternal-fetal physiology

and to better articulate the biological significance of our information-theoretical findings. We

revised the Discussion in two ways:

(1) We added a new subsection “From Information Metrics to Physiological Meaning” (Section

5.7) that explicitly translates each finding into biological terms: what reduced fetal entropy

during maternal decelerations means for autonomic regulation, how stress-modulated transfer

entropy may relate to altered fetal programming, and what the null neurodevelopmental FDR

results imply.

(2) We broadened literature integration throughout the Discussion, including references to

recent work on maternal-fetal heart rate coupling [9, 10, 11] and the broader prenatal program-

ming literature [12, 13, 14, 15]. The Discussion opening now leads with this broader context

before framing the FSI extension.

 

Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Before beginning this review, I congratulate all the authors for their work examining the flow of information between maternal and fetal heartbeats and the effects of maternal stress using information theory approaches. This study briefly investigates the directional flow of information and physiological coupling between maternal and fetal heart rates in 120 mother-fetus pairs in the third trimester. The authors expanded upon previous BPRSA-based Fetal Stress Index studies by using information theory metrics such as TE, SE, and ER. The most important finding of the study is the revelation of a stress-invariant universal physiological coupling mechanism that limits maternal heart rate deceleration and fetal heart rate complexity by 60%. In the following section of my review, I will add the strengths of the study and my suggestions for improving it.

__Strengths__

**I consider the use of Transfer Entropy and a three-tiered conditioning framework to capture complex physiological dependencies, rather than classical linear metrics, to be a strong methodological approach.

**I believe that dividing the coupling mechanism into two parts—stress-sensitive temporal information flow and stress-independent state-dependent synchronization—will make a very valuable contribution to the fetal programming literature.

**The demonstration that a 4 Hz sampling rate is sufficient for these analyses opens the way for the integration of these findings into existing clinical ultrasound devices and wearable equipment.

__Recommendations__

1. It is stated that sample entropy fails due to short event windows (2-10 seconds), resulting in zero values ​​in 87-100% of cases. I suggest adding a more emphatic explanation to the Discussion section suggesting that methods like Multi-scale Entropy or Permutation Entropy, which may be more robust in such short medical signal segments, could be used in future studies.

2. I believe the negative CV R-squared values ​​in the section using Elastic Net, PCA, PLS, and Random Forest models are statistically unreliable due to overfitting and underpowering. To avoid weakening the main message of the paper, instead of presenting these 50-feature machine learning experiments (Section 3.5) as a main finding, I recommend moving them to the Supplementary Material section and presenting them as a proof-of-concept for larger cohorts in the future.

3. The time interval between 0.5 and 2.5 seconds was chosen based on a data-driven observation where clear TE was positive. I suggest including a description in the signal processing steps of how this interval overlaps with known physiological time constants such as RSA or baroreflex responses of the maternal and fetal autonomic nervous systems.

4. In the discussion section, maternal heart rate slowing is correlated with the expiratory phase and vagal tone. However, respiratory data was not directly collected?In the limitations, I have suggested including a proposed algorithm on how this variable can be controlled in future studies.

5. The threshold value was kept at zero (mu=0) to ensure maximum data points are used while calculating acceleration and deceleration. To ensure that the 60% strong matching rate is not just because of microscopic noise, I think that conducting a sensitivity analysis on the data set with a very small physiologically significant threshold value would enhance the article and convince the researchers.

6. In the current study, it was noted that none of the exploratory correlations passed the correction. Instead of Benjamini-Hochberg correction, which can be overly conservative in studies with highly correlated metrics (VIF > 10), including a suggestion on the potential utility of hierarchical clustering in reducing the size of the metrics in future studies can greatly enhance your research.

7. We know that male and female fetuses have different maturation curves. Prior to interpreting the sex-stress interaction effect in the current study, I think it would be useful to include whether there is a significant difference at baseline in terms of basal heart rate variability between male and female fetuses.

8. It was noted in the current study that neurodevelopmental follow-up data was only available in 55% of the cohort. It would be useful to include a brief analysis on whether there is selection bias in terms of sociodemographics and basal stress levels between those patients who dropped out of the study and those who completed the study.I believe that mentioning this practical hardware potential in a single sentence in the Clinical Implications section of the discussion will enhance the impact of the article.

Author Response

Please view the enclosed PDF for a cleanly formatted response letter.

 

Note on Track Changes and Structural Reorganization

A central concern raised by all reviewers was that the manuscript was excessively technical

for a biology-oriented readership. In response, we have reorganized the manuscript by moving

all mathematical definitions, model specifications, and technical analyses to a comprehensive

Supplementary Materials document. The main text now focuses on physiological context, key

findings, and biological interpretation. No content was removed—it was reorganized to improve

accessibility while maintaining full reproducibility.

Throughout the revised manuscript and supplementary materials, we use the following color

coding:

• Red text: New or edited content in the main manuscript

• Blue text: Content moved verbatim from the main manuscript to the Supplementary

Materials

• Purple text: Content that was both edited and moved to the Supplementary Materials

During data reconciliation, we identified and excluded three participants: FS-004 (no clinical

record), FS-144 (missing PSS score), and FS-124 (excluded from Table 2 only due to extreme

outlier net TE, z-score = 23.7). The final analytical sample comprises 118 mother-fetus dyads

(59 stressed, 59 control; 49 male, 69 female), with n = 117 for Table 4.

 

REVIEWER: Strengths: I consider the use of Transfer Entropy and a three-tiered condi-

tioning framework to capture complex physiological dependencies, rather than classical linear

metrics, to be a strong methodological approach. I believe that dividing the coupling mech-

anism into two parts—stress-sensitive temporal information flow and stress-independent state-

dependent synchronization—will make a very valuable contribution to the fetal programming

literature. The demonstration that a 4 Hz sampling rate is sufficient for these analyses opens the

way for the integration of these findings into existing clinical ultrasound devices and wearable

equipment.

RESPONSE: We thank the reviewer for the encouragement.

REVIEWER (1): It is stated that sample entropy fails due to short event windows (2-10

seconds), resulting in zero values in 87-100% of cases. I suggest adding a more emphatic explana-

tion to the Discussion section suggesting that methods like Multi-scale Entropy or Permutation

Entropy, which may be more robust in such short medical signal segments, could be used in

future studies.

RESPONSE: We thank the reviewer for this constructive suggestion. In this revision, sam-

ple entropy was recomputed with an improved algorithm, yielding 99.5% non-zero observations

across all conditioning types (2,348 total observations vs. the previous 286). With adequate data,

the SE MLM now had full statistical power. Importantly, sample entropy still did not detect the

bivariate cross-signal coupling (β = -0.034, p = 0.073), whereas entropy rate did (β = -0.123,

p = 0.012). This confirms that the null result reflects a genuine difference between what these

metrics capture, not insufficient data.

We updated the Discussion (Section 5.8, “Sample entropy vs. entropy rate”) and added the

suggestion regarding multi-scale entropy and permutation entropy as future directions.

REVIEWER (2): I believe the negative CV R-squared values in the section using Elastic

Net, PCA, PLS, and Random Forest models are statistically unreliable due to overfitting and

underpowering. To avoid weakening the main message of the paper, instead of presenting these

50-feature machine learning experiments (Section 3.5) as a main finding, I recommend moving

them to the Supplementary Material section and presenting them as a proof-of-concept for larger

cohorts in the future.

RESPONSE: We followed this recommendation. The multivariate modeling section is now

in Supplementary Results (Section S2.3), with a brief summary in the main text presenting these

as a proof-of-concept for future larger cohorts.

REVIEWER (3): The time interval between 0.5 and 2.5 seconds was chosen based on a

data-driven observation where clear TE was positive. I suggest including a description in the

signal processing steps of how this interval overlaps with known physiological time constants

such as RSA or baroreflex responses of the maternal and fetal autonomic nervous systems.

RESPONSE: We thank the reviewer for this excellent suggestion to ground our data-driven

time-scale selection in established autonomic physiology. We added a paragraph in Section 3.5.1,

grounding the time-scale selection in established autonomic physiology, noting the overlap with

respiratory sinus arrhythmia (∼0.5–1.5 s) and baroreflex response times (∼1–3 s).

REVIEWER (4): In the discussion section, maternal heart rate slowing is correlated with

the expiratory phase and vagal tone. However, respiratory data was not directly collected? In

the limitations, I have suggested including a proposed algorithm on how this variable can be

controlled in future studies.

RESPONSE: This is an excellent suggestion. We added to the Limitations section 5.9 that

ECG-derived respiration based on respiratory sinus arrhythmia can be extracted retrospectively

from the existing RR interval data, and that conditioning TE on maternal respiratory phase is

planned as a follow-up study.

REVIEWER (5): The threshold value was kept at zero (µ= 0) to ensure maximum data

points are used while calculating acceleration and deceleration. To ensure that the 60% strong

matching rate is not just because of microscopic noise, I think that conducting a sensitivity

analysis on the data set with a very small physiologically significant threshold value would

enhance the article and convince the researchers.

RESPONSE: We applied the threshold to low-pass-filtered HR data, where microscopic

noise is unlikely to alter the sign of the time derivative. We conducted a ”first level” sensitivity

analysis: as the threshold increases from zero (reported in the Supplementary Materials, Figure

S2) and observed that the number of points in accelerations and decelerations diminishes as the

threshold is increased, as expected, but the ratio of decelerations/accelerations remains constant,

confirming that the coupling pattern is not an artifact of the zero threshold.

REVIEWER (6): In the current study, it was noted that none of the exploratory corre-

lations passed the correction. Instead of Benjamini-Hochberg correction, which can be overly

conservative in studies with highly correlated metrics (VIF >10), including a suggestion on the

potential utility of hierarchical clustering in reducing the size of the metrics in future studies can

greatly enhance your research.

RESPONSE: We thank the reviewer for this methodologically insightful suggestion. The

reviewer correctly identifies that our 50 entropy features are highly correlated (91-94% with

VIF > 10), meaning the effective number of independent tests is substantially lower than 144.

While we retain BH correction for transparency, we note this conservatism in the Discussion and

emphasize that the null FDR results do not prove absence of relationships. We added this in

Discussion, Section 5.9.

REVIEWER (7): We know that male and female fetuses have different maturation curves.

Prior to interpreting the sex-stress interaction effect in the current study, I think it would be

useful to include whether there is a significant difference at baseline in terms of basal heart rate

variability between male and female fetuses.

RESPONSE: We thank the reviewer for this important suggestion. We compared baseline

fetal entropy between male and female fetuses. There were no significant sex differences in either

hmax (p = 0.490, Cohen’s d = -0.13) or hmean (p = 0.370, Cohen’s d = -0.17). Maternal entropy

likewise did not differ by fetal sex (both p >0.57). We have added this clarification to the revised

manuscript, in Section 4.3.2.

REVIEWER (8): It was noted in the current study that neurodevelopmental follow-up

data was only available in 55% of the cohort. It would be useful to include a brief analysis on

whether there is selection bias in terms of sociodemographics and basal stress levels between

those patients who dropped out of the study and those who completed the study. I believe that

mentioning this practical hardware potential in a single sentence in the Clinical Implications

section of the discussion will enhance the impact of the article.

RESPONSE: We compared baseline characteristics between participants with and without

Bayley follow-up data. No significant differences were found in maternal age, gestational age at

birth, PSS score, stress group distribution, fetal sex, or birth weight (all p > 0.05), suggesting

that attrition was not systematically related to the variables under study. We added this in

Results, Section 4.1 and as Table 2.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The authors have substantially revised the manuscript in response to the previous comments. While some of my original concerns regarding structure and journal fit remain, these ultimately fall within the editor’s remit. From a reviewer’s perspective, the manuscript can be considered suitable for publication.

 

 

Author Response

We thank the reviewer for the thoughtful and positive feedback regarding the submitted manuscript.

We agree and will follow the editor's guidance as to the fit. We are committed to working with the editorial team to achieve consensus and make any necessary changes. Just let us know.

With best regards,

Dr. Martin Frasch

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

I congratulate all the authors on their efforts in this round.

My decision: Acceptable.

Author Response

We thank the reviewer for the positive feedback!

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

It is difficult to fully assess/appreciate this manuscript. It appears to be a draft requiring
editing. The analytical strategy is difficult to comprehend. It has the appearance of
statistical sophistication but without an equal amount of sophisticated rationale. In that
regard the narrative in the results sections is dense and sterile. However, the overall
question of the linkage between mother and fetus is significant and timely. There may be
some critical new findings reported in this manuscript, but I cannot accept the conclusions
in the discussion without a clearer presentation in the results.

There are several papers that have discussed the significance of understanding the linkage
between the mother and her fetus and how that relation may influence later infant
development or even the relationship between mother and infant. The paper does address
the di'erence in mother-fetal “communication” as a function of maternal stress, but the
rationale for this potential influence is not developed. For instance, how is the stress from
mother communicated in this dyad? Is it from stress-related biological factors? If so, why
not assess them directly? The assessment of cortisol in maternal hair is evidence that the
authors are thinking about this, but the presentation of the findings are indiscernible. There
is overwhelming evidence that the placenta (a fetal organ) synthesizes and releases stress
hormones and immune factors. Even if it is beyond the scope of this paper to assess this
possibility, some consideration of plausible pathways would broaden the interest of this
paper.

The sex differences reported is consistent with other reports of these differences, both in
terms of interactions with stress and more directly with patterns of fetal heart rate in
response to stimulation. Although these reports are not specifically connected to the
present findings, they do justify the inclusion of sex differences in the analysis and should
be considered in developing the rationale.

The beautiful figures are bewildering. Not sure what Figure 2 is illustrating. Is the message
that time/filters and accelerations do not make a di'erence in determining mHR? If so, that
di'ers from the conclusions. Without detailing each figure, some thought should be given
about describing the figures in the legend but especially the text.

Finally, the discussion that this sophisticated analysis of mother-fetal communication will
find its way into clinical assessment requires more strong evidence that there are
developmental consequences for the strength and direction of the communication. It
would be more edifying at this point if the paper concluded with the scientific significance
of this approach.

Author Response

REVIEWER: It is difficult to fully assess/appreciate this manuscript. It appears to be a
draft requiring editing.

RESPONSE: We apologize for this embarassing oversight. MDPI compiled the PDF from
the overleaf ZIP. We failed to catch that it picked the older tex file, as the final PDF was not
shown. We then submitted a correct version to arxiv (https://arxiv.org/abs/2512.22270) and
have now submitted here the proper final version carefully responding to all reviewer comments.

REVIEWER: The analytical strategy is difficult to comprehend. It has the appearance
of statistical sophistication but without an equal amount of sophisticated rationale. In that
regard the narrative in the results sections is dense and sterile. However, the overall question
of the linkage between mother and fetus is significant and timely. There may be some critical
new findings reported in this manuscript, but I cannot accept the conclusions in the discussion
without a clearer presentation in the results.

 

RESPONSE: We appreciate the interest of the reviewer and the chance to make good with
a properly formatted correct version of our manuscript which we hope addresses the concerns.

REVIEWER: There are several papers that have discussed the significance of understanding
the linkage between the mother and her fetus and how that relation may influence later infant
development or even the relationship between mother and infant. The paper does address the
difference in mother-fetal “communication” as a function of maternal stress, but the rationale
for this potential influence is not developed.

For instance, how is the stress from mother communicated in this dyad? Is it from stressrelated
biological factors? If so, why not assess them directly? The assessment of cortisol in
maternal hair is evidence that the authors are thinking about this, but the presentation of the
findings are indiscernible. There is overwhelming evidence that the placenta (a fetal organ)
synthesizes and releases stress hormones and immune factors. Even if it is beyond the scope of
this paper to assess this possibility, some consideration of plausible pathways would broaden the
interest of this paper.

 

RESPONSE: We and others did publish on this topic [1, 2, 3, 4, 5, 6, 7, 8]. This topic was
not our focus here. Rather, we aimed to use information-theoretical principles to analyze the
information flow between the mother and the fetus as gauged by their heart beat interactions.
We also evaluated if and how chronic stress (and fetal sex) impact these interactions.

 

REVIEWER: The sex differences reported is consistent with other reports of these differences,
both in terms of interactions with stress and more directly with patterns of fetal heart rate
in response to stimulation. Although these reports are not specifically connected to the present
findings, they do justify the inclusion of sex differences in the analysis and should be considered
in developing the rationale.

 

RESPONSE: We thank the reviewer for the suggestion. In the updated version, in Introduction,
we added references [3, 5] to the existing evidence on how stress exerts sex-specific
effects; we also discuss the sex differences in section 3.4.4. and 3.4.5 (pages 20-22) and 4.4.

 

REVIEWER: The beautiful figures are bewildering. Not sure what Figure 2 is illustrating.
Is the message that time/filters and accelerations do not make a difference in determining mHR?
If so, that differs from the conclusions. Without detailing each figure, some thought should be
given about describing the figures in the legend but especially the text.

RESPONSE: Figure 2 illustrates several effects. First, the raw HR is piece-wise constant,
which implies that there is no relevant information at smaller time-scales corresponding to R-R
intervals and smaller. Filtering smoothes the HR data, but the resulting data depends on the
time-scale: blue and purple curves in Figure 2 are thus different. In particular, the accelerations
and decelerations are not the same. As a consequence, both the entropy rate and the TE depend
on the time-scale, which is discussed later in the article. What we emphasize later in the article
is also that our results do not depend on the sampling rate (we use 20Hz but show various other
values in Figure 10): the sampling rate should not be confused with the time-scale. While we
vary the time-scale, we always down-sample the filtered data from 1kHz down to 20Hz.

 

REVIEWER: Finally, the discussion that this sophisticated analysis of mother-fetal communication
will find its way into clinical assessment requires more strong evidence that there are
developmental consequences for the strength and direction of the communication. It would be
more edifying at this point if the paper concluded with the scientific significance of this approach.

 

RESPONSE: We added a discussion of these aspects. Here and elsewhere we already
presented paradigms of antepartum care using ECG wearables to track chronic stress levels and
help parents mitigate the stress effects via non-pharmacological interventions such as yoga [9].
We and others also published extensively on the chronic impact of early life stress exposure on
fetal and postnatal neurodevelopment [2, 3, 4, 5, 6, 7, 8].

 

References

[1] Silvia M. Lobmaier, Maureen Mensing, Andrea M¨uller, Elisabeth Lorenz, Susanne Bechtold-

Dalla Pozza, Beatrice H¨uner, Bjoern Kuschel, Uta Nennstiel, Pauline Wimberger, and Celia Antonelli. Fetal heart rate variability responsiveness to maternal stress, noninvasively

detected from maternal transabdominal ECG. Archives of Gynecology and Obstetrics,

301(2):405–414, 2020.

[2] M.G. Frasch, S.M. Lobmaier, T. Stampalija, P. Desplats, M.E. Pallar´es, V. Pastor, M.A.

Brocco, H.Wu, J. Schulkin, C.L. Herry, A.J.E. Seely, G.A.S. Metz, Y. Louzoun, and MC Antonelli.

Non-invasive biomarkers of fetal brain development reflecting prenatal stress: An

integrative multi-scale multi-species perspective on data collection and analysis. Neuroscience

& Biobehavioral Reviews, 117:165–183, 10 2020.

[3] V. Treidel, Shani, Silvia M. Lobmaier, Ritika Sharma, Nimrod Madrer, Dana Shulman,

Pnina Greenberg, Estelle R. Bennett, David S. Greenberg, Adi Turjeman, Camilla Zelgert,

Peter Zimmermann, Martin G. Frasch, Liran Carmel, Marta C. Antonelli, and Hermona

Soreq. Maternal prenatal stress induces sex-dependent changes in trna fragment families

and cholinergic pathways in newborns. bioRxiv, 2024.

[4] Marta C. Antonelli, Martin G. Frasch, Mercedes Rumi, Ritika Sharma, Peter Zimmermann,

Maria S. Molinet, and Silvia M. Lobmaier. Early biomarkers and intervention programs for

the infant exposed to prenatal stress. Curr. Neuropharma., 20:94–106, 2022.

[5] P. Zimmermann, M.C. Antonelli, R. Sharma, A. M¨uller, C. Zelgert, B. Fabre, N Wenzel,

H-T. Wu, M.G. Frasch, and Lobmaier S.M. Prenatal stress perturbs fetal iron homeostasis

in a sex specific manner. Sci Rep, 12:9341, 6 2022.

[6] R. Sharma, M.G. Frasch, C. Zelgert, P. Zimmermann, B. Fabre, R. et al. Wilson, M.Waldenberger,

J.W. MacDonald, T.K. Bammler, S.M. Lobmaier, and M.C. Antonelli. Maternalfetal

stress and dna methylation signatures in neonatal saliva: an epigenome-wide association

study. Clin Epigenet, 14(87), 7 2022.

[7] M.G. Frasch, B.J. Yoon, D.L. Helbing, G. Snir, M.C. Antonelli, and R. Bauer. Autism spectrum

disorder: A neuro-immunometabolic hypothesis of the developmental origins. Biology,

12(7):914, 6 2023.

[8] F. Cerritelli, M.G. Frasch, M.C. Antonelli, C. Viglione, S. Vecchi, M. Chiera, and A. Manzotti.

A review on the vagus nerve and autonomic nervous system during fetal development:

Searching for critical windows. Front Neurosci, 15:721605, 9 2021.

[9] C. Becker, M.J.E. Mayer, M.G. Frasch, D. Gonzalez, B. Fabre, M.C. Antonelli, and S.M.

Lobmaier. Prenatal yoga for stress reduction: results from the felicity-2 quasi-randomized

controlled trial. preprint, 12 2025.

Reviewer 2 Report

Comments and Suggestions for Authors

Title  

Since stress is a key factor in the criteria, the title and main objective of the study must be corrected to reflect the role of stress and its implications on transfer entropy metrics.

Introduction

The introduction is insufficient. It lacks adequate background and references that justify the motivation for the study. Two out of three paragraphs in the introduction do not include citations.

The main results of the bPRSA approach and the SAVEr algorithm for fetal/maternal ECG and R-peak extraction should be described to justify the use of these methodologies in the present study.

References should specifically address transfer entropy in the study of maternal-fetal cardiac dynamics.

A brief comment on transfer entropy and its application in cardiac dynamics is necessary, including the main results of previous studies with proper citations.

Prior work on entropy dynamics and maternal-fetal interactions should be discussed.

The mention of wearables is not appropriate at this stage of the study. This section should be removed.

If the results are reliable, the clinical application must be clearly stated and sufficient to justify the development of the study. 

Methods

 

The experimental design must be explicitly described and illustrated with a figure, rather than narrated "briefly".

Include details about the Cohen Perceived Stress Scale.

Was the transabdominal ECG recorded with the AN24 device?
Why did the deconvolution algorithm use a higher sampling rate than the raw recording (900 Hz)?
Explain if AN24 customized software was used for data analysis, and specify the applications and data extracted with the tool.

The origin of the “0.5 bpm” noise is unclear. Please clarify and include a figure if possible.

Add a figure showing the electrode configuration for abdominal ECG recordings.

Improve the technical language and clarity in the statistical analysis section.

Line 66:

Describe the “relevant guidelines and regulations” and add citations if applicable.

Line 89:
Explain how ECG recordings were standardized “as much as possible.”

Line 93:
Clarify what kind of “screening” was performed on participants 2.5 weeks before recording.

The statement in line 111:
“raw heart rate X signal is derived from the successive time positions of the R-peaks of the ECG signal” is not correct and must be revised.

Line 197:
Remove unrelated text.

 

Comments on the Quality of English Language

This manuscript is not ready for publication. The version reviewed appears incomplete and contains annotations from the authors, indicating it is not the final draft. Due to the poor quality of the text and lack of methodological clarity, I did not proceed to review the results section.

Author Response

REVIEWER: Since stress is a key factor in the criteria, the title and main objective of

the study must be corrected to reflect the role of stress and its implications on transfer entropy

metrics.

RESPONSE: We have changed the title to “Measuring the time-scale-dependent information

flow between maternal and fetal heartbeats during the third trimester: impact of fetal sex

and maternal chronic stress”.

Introduction

REVIEWER: The introduction is insufficient. It lacks adequate background and references

that justify the motivation for the study. Two out of three paragraphs in the introduction do

not include citations.

The main results of the bPRSA approach and the SAVEr algorithm for fetal/maternal ECG

and R-peak extraction should be described to justify the use of these methodologies in the present

study.

RESPONSE: We thank the reviewer for the opportunity to improve the manuscript.

- To provide a more compelling rationale for the present study, we now revised and expanded

the references in the Introduction as the reviewer pointed out.

- The bPRSA approach (also referred to as FSI, fetal stress index) and the SAVEr algorithm

have been characterized and cited. We did not use bPRSA nor SAVEr in this work. We relied

on SAVEr-processed maternal and fetal ECG/heart beat data extracted with SAVEr previously

and published in several prior works. We refer to these facts in the Methods section.

REVIEWER: References should specifically address transfer entropy in the study of maternalfetal

cardiac dynamics.

RESPONSE: We have added references [2, 3, 4] in the introduction.

REVIEWER: A brief comment on transfer entropy and its application in cardiac dynamics

is necessary, including the main results of previous studies with proper citations.

RESPONSE:We have added a brief summary of important results in section 2.5.3 dedicated

to transfer entropy definition.

REVIEWER: Prior work on entropy dynamics and maternal-fetal interactions should be

discussed.

RESPONSE: Entropy (or entropy rate) is mono-variate in the sense that it only depends on

a single variable (either mHR or fHR); to our knowledge, it was never used to explore maternalfetal

interactions per se. We propose here to make it bi-variate by conditioning it on the other

variable. This is detailed in section 2.5.4. ”Conditioning Framework” of the new manuscript.

REVIEWER The mention of wearables is not appropriate at this stage of the study. This

section should be removed.

If the results are reliable, the clinical application must be clearly stated and sufficient to

justify the development of the study.

RESPONSE: We thank the reviewer for this insight and removed the mention of wearables

from the Introduction as advised.

Methods

REVIEWER The experimental design must be explicitly described and illustrated with a

figure, rather than narrated “briefly”.

RESPONSE: We provided the complete experimental design.

REVIEWER: Include details about the Cohen Perceived Stress Scale.

RESPONSE: This is an established psychometric test for chronic stress levels. We reference

it accordingly on line 121 [5] and 146 [1]. We added more detail about what the PSS-10 measures.

REVIEWER: Was the transabdominal ECG recorded with the AN24 device?

RESPONSE: Yes. We state it in Methods on Line 158.

REVIEWER: Why did the deconvolution algorithm use a higher sampling rate than the

raw recording (900 Hz)? Explain if AN24 customized software was used for data analysis, and

specify the applications and data extracted with the tool.

RESPONSE: As we mentioned above, we did not do any new work on the aECG data. We

only used the aECG dataset on which we already published elsewhere [1, 6, 7]. The aECG

device AN-24, for reasons not known to us, outputs aECG at 900Hz, not at 1000 Hz as is the

standard otherwise. For SAVEr pipeline, we process this signal at 900 Hz as input and after

separation into mECG and fECG output those at 1000 Hz as reported in [7].

REVIEWER: The origin of the “0.5 bpm” noise is unclear. Please clarify and include a

figure if possible.

RESPONSE: We added a detailed derivation in the text (line 172) and corrected the value

to 0.2 bpm.

REVIEWER: Add a figure showing the electrode configuration for abdominal ECG recordings.

RESPONSE: The electrode placement is following the Monica Healthcare AN24 documentation,

as depicted below:

REVIEWER: Improve the technical language and clarity in the statistical analysis section.

RESPONSE: The updated version should be clearer.

REVIEWER: Line 66 (now line 131): Describe the “relevant guidelines and regulations”

and add citations if applicable.

RESPONSE: We updated the text to make this clear.

REVIEWER: Line 89 (now line 155): Explain how ECG recordings were standardized “as

much as possible.”

RESPONSE: This is detailed in the next sentence (line 156). We want the experimental

conditions (electrodes placement, time of day) to be all as close as possible.

REVIEWER: Line 93: Clarify what kind of “screening” was performed on participants 2.5

weeks before recording.

RESPONSE: This is detailed on lines 141-143.

REVIEWER: The statement in line 111: “raw heart rate X signal is derived from the

successive time positions of the R-peaks of the ECG signal” is not correct and must be revised.

RESPONSE: Thank you. We agree that this was too short an explanation. The text now

details the intermediate step (R-R interval estimation) (section 2.2, lines 163+ 212+).

REVIEWER: Line 197: Remove unrelated text.

RESPONSE: The final version has been carefully cleaned. We apologize for this embarassing

oversight.

 

References

[1] Silvia M. Lobmaier, Maureen Mensing, Andrea M¨uller, Elisabeth Lorenz, Susanne Bechtold-

Dalla Pozza, Beatrice H¨uner, Bjoern Kuschel, Uta Nennstiel, Pauline Wimberger, and Celia Antonelli. Fetal heart rate variability responsiveness to maternal stress, noninvasively

detected from maternal transabdominal ECG. Archives of Gynecology and Obstetrics,

301(2):405–414, 2020.

[2] Marzbanrad F, Kimura Y, Palaniswami M, and Khandoker AH. Quantifying the interactions

between maternal and fetal heart rates by transfer entropy. PLoS ONE, 10(12):e0145672,

2015.

[3] R. Avci, D. Escalona-Vargas, E.R. Siegel, C.L. Lowery, and H. Eswaran. Coupling analysis

of fetal and maternal heart rates via transfer entropy using magnetocardiography. In 40th

Annual International Conference of the IEEE Engineering in Medicine and Biology Society

(EMBC), Honolulu, HI, USA, pages 1–4, 2018.

[4] Nichting TJ, Bester M, Joshi R, Mischi M, van der Ven M, van der Woude DAA, Oei SG,

J.O.E.H. van Laar, and R. Vullings. Evidence and clinical relevance of maternal-fetal cardiac

coupling: A scoping review. PLoS ONE, 18(7):e0287245, 2023.

[5] S. Cohen, T. Kamarck, and R. Mermelstein. A global measure of perceived stress. J. Health

Soc. Behav., 24:385–396, 1983.

[6] P. Sarkar, S. Lobmaier, B. Fabre, et al. Detection of maternal and fetal stress from the

electrocardiogram with self-supervised representation learning. Sci. Rep., 11:24146, 2022.

[7] R. Li, M. G. Frasch, and H.-T. Wu. Efficient fetal-maternal ECG signal separation from

two channel maternal abdominal ECG via diffusion-based channel selection. Front. Physiol.,

8:277, 2017.