A Simplified Mathematical Framework for Pulse Wave Velocity Alterations in Neonatal Aortic Coarctation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The scientific writing should be revised using a passive voice throughout the manuscript.
2. The abstract lacks sufficient numerical and statistical data to clearly demonstrate the study outcomes; therefore, key digital results should be added.
3. The keyword list should include “alteration in aortic coarctation” to improve indexing and searchability.
4. The introduction section is excessively long and should be shortened to focus more directly on the study rationale and objectives.
5. The Methods section does not clearly describe the PICO analysis; the Population, Intervention, Comparison, and Outcome components should be explicitly reported.
6. Figure titles should be positioned below the figures according to standard manuscript formatting guidelines.
7. The limitations of the study are not adequately reported and should be included in a dedicated subsection.
8. The figure illustrating the theoretical relationship between PWV ratio and pressure lacks both a figure number and a descriptive title; these should be added.
9. The Discussion section is too brief and requires further elaboration, particularly regarding study limitations and the impact of different variables on the findings.
10. The reference list should be updated with more recent and relevant literature.

Author Response

Dear Reviewer,

please find our answers to your comments below.

1. The scientific writing has been revised using a passive voice throughout the manuscript

2. Our article hasn’t the scope to demonstrate empirically on neonate the relationship between the ratio of velocities and pressure changes but to validate a theorical applicable model confirmed from the latest mathematical results in the Moens–Korteweg equation (so mathematically proven)

3. The word “alteration in aortic coarctation” has been added to keyword list

4-5  The article focus on the mathematical development on a model that underline the importance of the measurement in future clinical studies of PWV and pressure oscillation before and after aortic coarctation. The PICO analysis can’t be applicated to this work because has been developed for empirical data and not for theoretical models. The introduction explain the necessity to have possibly a new parameter/ device to screen newborns and finally to have a safe hospital discharge avoiding the lost of unrecognized neonatal aortic coarctation. Moreover in the introduction we find the conceptual link between PWV, blood pressure and pathophysiology of aortic coarctation.

6. The titles have been positioned below the figures.

7. Limitations have been reported in a separated subsection

8. Correction Done of figure

9 Discussion has been modified and in particular is underlined the small loss of energy lost by turbulent flow transformed to heat.

Thanks for considerating out article.

Kind regards,

Alessandro Messina

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for the opportunity to review this manuscript that presents a simplified mathematical framework for pulse wave velocity (PWV) alterations in neonatal aortic coarctation (CoA). The topic is clinically relevant, as early non-invasive detection of CoA before hemodynamic deterioration remains an unmet need. The theoretical approach is interesting, but several concerns need to be addressed before this manuscript is suitable for publication.

Below are my comments

1. The energy conservation framework (Section 2.1) contains several gaps and unjustified steps. Specifically, the transition from pressure-volume work to kinetic energy is not adequately justified. The assumption that all stored elastic work converts to kinetic propagation energy (L1=K1) is an oversimplification that requires explicit mathematical justification or acknowledgment as a major limitation. The derivation leading to v2/v1 = sqrt(p2/p1) needs more rigorous algebraic steps and physical interpretation.

2. The assumption of negligible viscous and turbulent losses is particularly problematic given that coarctation is characterized by turbulent post-stenotic flow. This assumption should be discussed in greater depth, and its effect on model validity should be quantified or at least qualitatively assessed. Similarly, neglecting reflected waves in a stenotic setting significantly limits the model's physiological validity.

3. The manuscript lacks any clinical or computational validation. While the authors acknowledge this as a limitation, the Discussion section would benefit from a more structured presentation of what specific experiments or clinical studies would be needed to validate the model, including measurable parameters, patient populations, and diagnostic thresholds.

4. The quadratic relationship shown between PWV ratio and pressure excursion ratio requires explicit mathematical derivation in the text. It is currently not clear how this curve was generated from the model equations.

5. The reference to a patent (Patent WO 2015142603) in the Conclusions section appears out of place. If it is relevant, its relevance should be explained clearly within the text.

Author Response

Dear Reviewer,

please find our answers to your comments below.

1. The conversion from L to K is direct because in our simple model we assume that the vessel are elastic perfectly like an ideal mechanical compression spring. If you imagine an ideal compression spring mounted in a piston and the opposite side the piston is filled of water with a nozzle and a valve at the end, charging the spring you have an initial pressure. Opening the valve there is the conversion form the potential energy to kinetic. This is the base of hydroelectric power plants. ( U converted to K). In our case there is the obvious previous step where the work of the spring (L) is converted to potential energy (U) end you can see the hydraulic pressure p.

2. The turbulent losses characterized by turbulent post-stenotic flow have been added in the discussion. The entity of these losses must be very low because obviously in the opposite situation we shoud have a significative rise in temperature blood flow( losses must convert in heat) not compatible with human temperatures.

3. In the Discussion, we describe two noninvasive clinical methods for measuring pulse wave velocity (PWV) and arterial pressure in newborns.

4. The Curve is the final equation:

  = where is plotted on the x axis and the  is plotted on the y axis.

5. The patent reference has been linked to the text.

Thanks for considerating our article.

Kind regards,

Alessandro Messina

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thanks for doing modifications 

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have adequately addressed the concerns raised in the previous review round. The revised manuscript presents a simplified but physiologically coherent mathematical framework for describing pulse wave velocity alterations in neonatal aortic coarctation. The energy conservation-based derivation is clearly articulated, the conceptual consistency with the Moens–Korteweg formulation is well demonstrated, and the limitations of the model are transparently acknowledged. The scope of the work is appropriately defined as a theoretical approximation rather than a clinically validated predictive tool. The manuscript is acceptable for publication in its current form.