Evaluation of Classical Mathematical Models of Tumor Growth Using an On-Lattice Agent-Based Monte Carlo Model†
, Mercedes Villalobos 3,4,5 and Antonio M. Lallena 3,6,*Round 1
Reviewer 1 Report
The authors considered the classical mathematical models of tumor growth such as exponential, logistic, potential, von Bertalanffy and Gompertz in order to describe multicellular spheroids. For their simulations they used an already validated on-lattice agent-based Monte Carlo model that previously been developed by the authors. It is a very well written article with interesting results on modelling tumor growth that could have the potential to be used to analyse clinical data.
However, I would like to bring to the authors attention a very recent study at Physical Review E , by Azimzade, Youness and Saberi, Abbas Ali and Gatenby, Robert A, that showed that the Allee effect is the most suitable mechanism for tumor growth (not for MTS) (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.042405). The Allee effect model was originated from ecology and it has been used by several researchers in tumor growth modeling. I was wondering if the authors apart from the logistic growth model could consider an Allee effect growth model and what kind of results could take in comparison with the rest of the models that have already considered and justified.
In my personal view it is worth mentioning and even taking into consideration the Allee effect model. I think that the inclusion of the Allee effect model will increase the originality as well as the significance of their results.
Minnor comments:
Line 17: magnitude
Line 268 : "add space between" figure 4
Author Response
See enclosed pdf.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors presented in this contribution an assessment of mathematical models (exponential, Gompertz, logistic, etc.) pertinent to describe the evolution of tumour spheroids. To achieve this, they compared the growth dynamics (tumour spheroid volume) with respect to predictions produced viA an agent-based model (ABM), and analysed the results using statistics. The work presented in this manuscript is interesting though it has some serious flaws - major points of criticism presented below in no special order:
The novelty and value of this paper is not clear. What's the point assessing those "classic" mathematical models for tumour growth when elaborate ABM have already been established in the cancer modelling field (even the authors have published one before), and have shown their capacity to simulate (single- or/and multi-)cellular behaviour dynamics and their underlying mechanisms? What is the true value of this approach here?
The thesis of this paper is to analyse different mathematical models pertinent to describing growth of multicellular tumour spheroids. Unfortunately, the presentation focuses here only on experiments of a single cancer cell line: MCF-7! Therefore, the reviewer cannot see how this work could encompass the dynamics of multicellular populations - the statement in the Abstract's "Purpose" sounds like an overstretch. This is a serious flaw of this work and requires major reconsideration in the paper.
The Introduction is very long-winded! The authors should build their story around review articles like the following: DOI:10.1088/1478-3975/ab1a09, DOI:10.1016/j.ymeth.2020.02.010, DOI:10.1200/CCI.18.00068, DOI:10.1016/j.semcancer.2014.04.001
The authors have already published their ABM elsewhere (reference [47] in the manuscript). Despite of this, the description of the on-lattice method is very poor in section 2.1; it fails to give a clear and concise description of the rules associated with MCF-7 cell proliferation, differentiation, etc. - they are simply mentioned! Also, specifically in lines 127-129 and 130-133, the authors fail to provide evidence that their ABM model reproduces experimental results and so on. Arguments are presented here with no data to support their case. The same in lines 135-136, there is no evidence provided in this manuscript about the "ratio of the number of hypoxic plus proliferative cells to the MTS volume" and how it agrees with experimental results.
Text in paragraph between lines 136-146 seems more appropriate to go in the beginning of the Methods - it seems to the reviewer that the authors attempt to describe the ABM rules, is that correct? Also, the statement in lines 142-143 is very vague and unclear, please rephrase.
Text in paragraph between lines 147-150 seems more appropriate to fit in the Intro rather than the Method, unless the authors want to convey a different message here.
The argument in lines 152-153 is vague and unclear, please rephrase. In the same paragraph, in lines 156-157, the authors seem to present the results from their previous paper (citation [47]), why?
Figure 1 shows line plots of the MTS volume against time; nevertheless, it is unclear how tumour spheroid volume was measured in their ABM and how it compares with how it is measured in the experiments as well - in other words is the volume measurement approach consistent across the board? Please clarify this in the paper.
In the Abstract, the statement "Overall, the predictive power ... was discrete." is not clear to the reviewer. Also, the statement between lines 226-227 needs rephrasing, it's not clear.
Author Response
See enclosed pdf.
Author Response File: Author Response.pdf
Reviewer 3 Report
Review of the manuscript applsci-1189691
May 13, 2021
This is a review of the manuscript “Evaluation of Classical Mathematical Models of Tumor Growth Using an on-Lattice Agent-based Monte Carlo Model” by S. Ruiz-Arrebola, D. Guirado, M. Villalobos, A. M. Lallena
Many real situations that are determined by statistical processes can be simulated in a computer with the aid of random numbers. Now, it is well-known that, not only processes of interest following statistical laws can be simulated with the Monte Carlo (the use of random numbers in computer programs) method, but also the measurement errors which occur in every measurement. Monte Carlo techniques can be applied to complex dynamic models and do not require extensive mathematical analysis. Two important practical problems arise when implementing a Monte Carlo analysis of error. First, we must decide what probability distribution from which to choose the parameters. The second practical concern is to ensure that our scheme for sampling from the probability distribution(s) adequately represents the tails of the distributions. This is especially important if we do not wish to use a large sample size. On the other hand, there are three broad areas in which Monte Carlo simulation is useful in biological simulation: 1) statistical hypotheses; 2) differential and difference equations; 3) Markov processes.
In the reviewed manuscript, the authors used Monte Carlo method to perform a quantitative evolution of the of the predictive power of the exponential, Gompertz, logistic, potential and Bertalanffy models. These models have been fitted to the volume vs. time data set obtained with on-lattie Monte Carlo ABM (agent-based models) for each one of the simulated MTS (multicellular tumor spheroid). In my opinion, the manuscript does not introduce new theory or methods, nor does it discover new phenomena.
Major comments:
It is biologically not clear why the fitting procedure is in the interval i=[1-60]. Thus, the importance of that work is not well described.
The list of reference requires extension. In a fast-moving area, this can be an issue. You can read a nice survey in: i) Nikolov, S., Dimitrov, A., Vera, J., Hierarchical levels of biological systems and their integration as a principal cause for tumour occurrence, Nonlinear Dynamics, Psychology, and Life Sciences, 23(3), pp. 315-329, 2019; 2) Vera, J., Lischer, Ch., Nenov, M., Nikolov, S., Lai, X., Eberhardt, M., Mathematical modelling in biomedicine: A primer for the curious and the skeptic, Int. J. of Molecular Sciences, 22(2), art. No 547, 1-16, 2021.
Minor comments:
Figure 2 and 3 are not well prepared and are unclear.
In general the manuscript is well-written and it is interesting. I would like the authors implement my improvements before of accepting it.
Comments for author File: Comments.pdf
Author Response
See enclosed pdf.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors have responded to all of my comments.
