Evolution of Hemodynamic Parameters Simulated by Means of Diffusion Models
Round 1
Reviewer 1 Report
Please see the report in the attached file
Comments for author File: 
Comments.pdf
Author Response
The answer to review no.1
(convention: part from review – next answer)
In the setup, it is not clear what the stochastic variable x is
Answer: x denotes value of TFC _ now it is pointed out immediately in the text
What is the passage from the raw data (i.e., the TFC vales of single patients) to the stochastic variable x?
Answer: measured stochastic value of TFC in equations is denoted as x
How are the “TFC slots” defined?
Answer: it is explained in the text now
What is the meaning of the abscissa axis in Fig. 1 and what are the physical units?
Answer: Axes in the figure 1 and other figures are described now. Physical unit of TFC is presented in the text.
In the present case, the TFC measures derive from many different patients, hence a heterogeneity is inevitably present to some extent. How could this heterogeneity affect (and spoil) the soundness of the analysis? This has to be commented.
Answer: It can be explained by an example. When You observe stochastic process e.g. Brownian motion population od particles are completely different and each particle has its own velocity different in each time moment. Here each measurement of the TFC is treated in the same manner as velocity of particle in mentioned example. There is nothing to be commented.
In stochastic motion there is no identical replicas od system. We observe fluctuations of the measured values. It is the basic knowledge.
why should the stochastic process be a Markov stationary process of the Ornstein-Uhlenbeck type?
Answer: we do not discuss if observed process is markovian or not. The only assumptions in diffusion equation are the simplest known in diffusion phenomena: liner component of drift and constant value of diffusion coefficient D. The Ornstein-Uhlenbeck process is a result not an a priori assumption.
Presented diffusion is just model of diffusion nothing more.
Why should the process be Markovian?
Answer: such assumption is not present in our article. It must by misunderstanding.
Why should the process be of Ornstein-Uhlenbeck type?
Answer: explained above
Even presuming that the Ornstein-Uhlenbeck process can be motivated, the authors here determine drift and diffusion coefficient only from the stationary distribution. In my opinion, this is not the correct way of validating and parametrizing a dynamical model.
Answer: I can not agree. We have presented basic Green function approach. Such approach is common way of dynamical system analysis.
Rather, the authors should present and exploit the full dynamical content of their data, that is, by considering for instance time correlation functions and try to fit them.
Answer: time correlation function are useless in the case od medical data which are generally irregular in time and strongly fluctuated. On the other hand cumulation of medical data in an uniform measurement, controlled in clinical regime is very expensive, time consuming and rather rare for that reason. So proper data for time correlation function are really hard to obtain in medical measurements and usually are not properly verified.
Reviewer 2 Report
The authors presented a manuscript on a possible use of diffision equation to validate preditive model in medicine. The idea is worthy of interest but some isseissues need to be addressed
- in method it is indicated many parameters evaluated in the AMULET study. Reading the manuscript I understand they are not used in this manuscript. Thus, I I suggest to remove them indicating just what is useful for this study
- The arbitrary decision to divide into 15 value slots may be questionable. Please give more reasons for this choice
- this study results like a proof of concept for the use of diffusion equation in medicine. The parallel between physics and medicine may be interesting but it remains an interesting idea that need a prospective validation. Please indicate it in discussion
- There are no limitations and strengths of the study indicated. Please address
- There is no units for measurements in figures. I suggest to include them
As minor issue, a native English revision may improve the manuscript
Author Response
The answer to review no.2
(convention: part from review – next answer)
- Reading the manuscript I understand they are not used in this manuscript. Thus, I I suggest to remove them indicating just what is useful for this study
Answer: the TFC as measured and analysed example has been pointed out immediately in the text so we decided to leave information on measurement method as a whole
- The arbitrary decision to divide into 15 value slots may be questionable. Please give more reasons for this choice
Answer: now reasons has been placed in the text
- study results like a proof of concept for the use of diffusion equation in medicine. The parallel between physics and medicine may be interesting but it remains an interesting idea that need a prospective validation. Please indicate it in discussion
Answer: we mention in discussion that prospective validation is continued now
- are no limitations and strengths of the study indicated. Please address
Answer: we indicate in text that limitation will be analysed during further validation. Evident strength of the model is continuous, differential model of disease evolution. As far as authors know it seems to be new approach.
- is no units for measurements in figures. I suggest to include tchem
Answer: units are placed in the text
Author Response File: 
Author Response.docx
Reviewer 3 Report
The manuscript is well written and presented even if more attention should be paid to English grammar and structure. The topic is appealable, but the present stage of the paper will impede any publication here or elsewhere. The aims should be clarified and better highlighted in the abstract and the introduction. The latter should be rephrased; at the current stage seems more abstract than an introduction. I suggest deleting "background, conclusions" headings. The introduction should be structured giving a background that paves the basis of the hypothesis explored in the study.
Author Response
The answer to review no.3
(convention: part from review – next answer)
The aims should be clarified and better highlighted in the abstract and the introduction.
Answer: now aims are clearly indicated in the introduction
the current stage seems more abstract than an introduction. I suggest deleting "background, conclusions" headings
Answer: it was done now
introduction should be structured giving a background that paves the basis of the hypothesis explored in the study
Answer: we indicate directly that stage of the art do not allow to obtain repetitive and verifiable result on disease evolution, and this is a reason to prepare such investigation as presented in our article
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
I am afraid to say again that, in my opinion, this paper is not suitable for publication. The idea is good, but it must be developed in a more sound way to meet scientific standards. Moreover, the authors have consider in superficial way my criticisms. I must reject the manuscript again.
Author Response
The answer to review no.1 round 2
(convention: part from review – next answer, next explanation in round2, summary)
Dear Sir,
Below my opinion as answer to You second review. The answer is placed inside the first answer for clarity of explanation.
In the setup, it is not clear what the stochastic variable x is
Answer: x denotes value of TFC _ now it is pointed out immediately in the text
Round 2: Considered, improved in text
What is the passage from the raw data (i.e., the TFC vales of single patients) to the stochastic variable x?
Answer: measured stochastic value of TFC in equations is denoted as x
Round 2: Considered, improved in text
How are the “TFC slots” defined?
Answer: it is explained in the text now
Round 2: Considered, improved in text
What is the meaning of the abscissa axis in Fig. 1 and what are the physical units?
Answer: Axes in the figure 1 and other figures are described now. Physical unit of TFC is presented in the text.
Round 2: Considered, improved in text
In the present case, the TFC measures derive from many different patients, hence a heterogeneity is inevitably present to some extent. How could this heterogeneity affect (and spoil) the soundness of the analysis? This has to be commented.
Answer: It can be explained by an example. When You observe stochastic process e.g. Brownian motion population od particles are completely different, and each particle has its own velocity different in each time moment. Here each measurement of the TFC is treated in the same manner as velocity of particle in mentioned example. There is nothing to be commented.
In stochastic motion there is no identical replicas od system e.g. in Brownian motion particles often evaporate, each of them undergoes different collisions, glue together, etc.. So no identical replicas are observed. The heterogeneity is a feature of real observation. We observe fluctuations of the measured values. It is the basic knowledge.
Round 2: Explained. No possibility to improve in text because of comment in review is improper
why should the stochastic process be a Markov stationary process of the Ornstein-Uhlenbeck type?
Answer: we do not discuss if observed process is Markov process or not. The only assumptions in diffusion equation as the simplest known in diffusion phenomena: liner component of drift and constant value of diffusion coefficient D. The Ornstein-Uhlenbeck process is a result not an a priori assumption.
Presented diffusion is just model of diffusion and nothing more.
Round 2: Explained. No possibility to improve in text because of comment in the review is improper as if addressed to another article
Why should the process be Markovian?
Answer: such assumption is not present in our article. It must by misunderstanding.
Round 2: Explained. No possibility to improve in text because of comment in the review is improper as if addressed to another article
Why should the process be of Ornstein-Uhlenbeck type?
Answer: explained above
Round 2: Explained, no possibility to be improved in proposed article. You are simply wrong.
Even presuming that the Ornstein-Uhlenbeck process can be motivated, the authors here determine drift and diffusion coefficient only from the stationary distribution. In my opinion, this is not the correct way of validating and parametrizing a dynamical model.
Answer: I can not agree. We have presented basic Green function approach. Such approach is common way of dynamical system analysis.
Round 2: Explained. No possibility to improve in text because of comment in the review is improper. You are simply wrong.
Rather, the authors should present and exploit the full dynamical content of their data, that is, by considering for instance time correlation functions and try to fit them.
Answer: time correlation functions are useless in the case od medical data which are generally irregular in time and strongly fluctuated. On the other hand cumulation of medical data in a uniform measurement, controlled in clinical regime is very expensive, time consuming and rather rare for that reason. So proper data for time correlation function are hard to obtain in medical measurements and usually are not properly verified.
Round 2: Explained. No possibility to improve in text because of comment in the review is improper.
Summary
I disagree that our answer is superficial. It was explained step by step during the first round. You are generally in the position “not, because of not”. There is no place to any content-related discussion.
Author Response File: Author Response.docx
Reviewer 2 Report
The authors reply to the required issues. The manuscript is very technical but it is intelligible most. It is a good proof-of-concept and a good idea to start evaluation in more specific and proper prospective model. About the manuscript itself I suggest again to include in figures (at least in caption) the unit of measurement used to this evaluation.
Author Response
The answer to review no.2 round 2
(convention: part from review – next answer)
Captions in figures are improved and units for TFC are added. Some revisions have been done in results presentation as well as in conclusions. Thank You for Your time and attention. I assure that English language was reviewed by the native speaker but additively will be send to verification in MDPI .
Author Response File: Author Response.docx
Reviewer 3 Report
I have no further comments or edits.
Author Response
The answer to review no.3 round 2
(convention: part from review – next answer)
Thank You for Your time and attention. I assure that English was reviewed by the native speaker but additively will be send to verification in MDPI
Author Response File: Author Response.docx
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.
