Combined Application of CAR-T Cells and Chlorambucil for CLL Treatment: Insights from Nonlinear Dynamical Systems and Model-Based Design for Dose Finding

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors In the current in silico study, Valle and colleagues developed a mechanistic nonlinear mathematical model that can be used to simulate the dynamics of the response of chronic lymphocytic leukemia (CLL) cells to treatment with CAR-T cells combined with the alkylating agent chlorambucil in the clinic. The authors formulated three ordinary differential equations describing this treatment according to two schemes, short-term and long-term. Using a set of nonlinear system algorithms with the implementation of the localization of compact invariant sets (LCIS), Lyapunov's direct and indirect methods, as well as the Lipschitz condition, the developed dynamic model was analyzed in detail and its performance was proven. Using this algorithm, the authors compared dose-escalation and dose-de-escalation protocols and revalidated a number of important findings, including a high probability of achieving effective antitumor dynamics at lower total treatment doses in the dose-de-escalation protocol. In addition, the authors demonstrated the possibility of remission, either complete or partial, when doses are selected that do not lead to eradication of minimal residual disease, confirming the realistic in silico results. This mathematical model, after some modifications, can be integrated into clinical practice to select optimal treatment regimens for CLL, which confirms the relevance and practical importance of this study. In my opinion, this work can be published in Hemato after some minor revisions. (a) Line 161 - the authors determined the growth rate of CLL within the interval based on murine CLL data. Given the peculiarities of cancer development in laboratory mice, which do not always correlate with patients, please provide references to published work that shows similarity of leukemia cell growth rates in humans and mice. (b) In their model, the authors did not consider a possible multidrug resistance phenotype of CLL cells. Could you please include this in your mathematical model? (c) Line 471 - Dear authors, please explain why a factor of 1.1 was used for kappa1*psi1/kappa3. (d) line 246 - please add a comma before where

Author Response

Please see the attached pdf file addressing all of your concerns.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The present paper brings a nonlinear-dynamical model that describes interaction of chemoterapeutic agents, immunotherapeutic agents and their combination with CLL cells. The model is based on three differential equations which describe time dependence of CLL cells, immunotherapy cells and anticancer drug concentration. The parameters defined within the model were estimated using the literature data.

The approach is very interesting and attractive, deserves attention and further development. However, the model is unphysical, so that it is difficult to distinguish artefacts from real results. The function of bare CLL cell growth is described by an exponential function bounded with the plateau – maximal physiological number of lymphocytes in the bloodstream.

 

I have the following suggestions that I hope could help in improvement of the model:

 

1. In real systems, exponential growth is decreased by the functions of the intrinsic immune response and natural cell death (if any). Immune response is quite complex – it consists of nonspecific and specific response. Nonspecific is early onset and low intensity, while specific is delayed onset and high and sharp growth, but more or less disturbed in leukemias. Thus, the function would be highly dependent on the type of pathology considered and will include large number of parameters (time delays, rate constants, efficiency coefficients etc). Please, check if any literature is available to model intrinsic immune response in CLL with a reasonable number of parameters. Approximation of real system with in situ detected exponential growth is too rough.

 

2. Also, the definition of the plateau as the physiological total number of lymphocites in the bloodstream is also rough and physiologically unrealistic. The CLL is limited only to the fraction of lymphocytes that is malignant. On the other hand, the number of target malignant lymphocites increases enormously, by a few orders of magnitude above the physiological level. Not all of them are in the bloodstream – the significant fraction is in the bones and metastatic tissues. Defining of any plateau without analysis of CLL-specific parameters from literature (for example, maximal number of cancer cells in the living organism specific for CLL, instead all lymphocytes in the bloodstream) bears a risk of serious artefacts in the model.

 

I recommend the revision of the model, if any of the suggested can be included.

Author Response

Please see the attached pdf file addressing all of your concerns.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Review for Hemato

Manuscript ID: hemato-3447443
Type of manuscript: Article

 

In the manuscript presented to me for review entitled "Combined application of CAR-T cells and chlorambucil for CLL treatment: Insights from nonlinear dynamical systems and model-based design for dose finding" a set of three first-order ordinary differential equations was used to present the short-term and long-term effects of chemoimmunotherapy with CAR-T cells and chlorambucil in the treatment of chronic lymphocytic leukemia. The number of leukemic cells, CAR-T cells, and doses of chlorambucil were assessed. This is presented in a simple pictorial way in Figure 1, and then extensively in the form of mathematical proofs of individual cases in the results.

 

The discussion discussed in silico experiments, which took into account each case on specific clinical data, taking into account the time of treatment and their dynamics, presented in Tables and Figures. Extensive conclusions were written, which are a summary of the capabilities of the applied algorithm.

 

My comments:

The paper is written in a very mathematically extensive manner, but it was submitted to a medical journal that is read by clinicians.

I believe that both the abstract and conclusions need to be revised to emphasize the useful application of this model in hematology.

Author Response

Please see the attached pdf file addressing all of your concerns.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript "Combined Application of CAR-T Cells and Chlorambucil for CLL Treatment" develops a mathematical model to optimize chemoimmunotherapy using nonlinear dynamical systems and in silico simulations. Through a system of Ordinary Differential Equations (ODEs), it explores conditions for tumor eradication, CAR-T cell persistence, and chemotherapy effects, comparing dose-escalation and dose de-escalation strategies.

While the study is mathematically rigorous, its focus on theoretical modeling makes it better suited for a journal specializing in mathematical biology or computational oncology rather than a clinical hematology journal like Hemato. 

In my opinion, in its current form, this work would be best appreciated in a mathematical or systems biology journal, where its theoretical advancements can be further explored.

If the authors are set on publishing in Hemato, they should strengthen the clinical perspective, making the work more relatable to hematologists and oncologists who may not have expertise in nonlinear dynamical systems.

A more interdisciplinary approach—linking mathematical insights to real-world treatment decisions—would enhance its potential for publication in a clinical journal.

Author Response

Please see the attached pdf file addressing all of your concerns.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

 

I agree that substantial reconstruction of the model is difficult, so I agree that the model is published as is. Strengths and weaknesses of the model should be then described in the discussion.

You can use the parts of your response to me to make discussion stronger. The main strength of the model is that it is the first step towards mathematical description of such complex system as chemoimmunotherapy of CLL is. It can be the basic model for further improvements and you can emphasize this. The weaknesses are mentioned potential sources of artefacts, that also can be pointed in the discussion. You can keep the potential practical aspects, but in this phase your model has prevalently a theoretical significance.

Author Response

Following the reviewer’s valuable advice, we have strengthened our discussion section by adding the following closing paragraph:

Our model captures key interactions between CLL cells, CAR-T cells, and chlorambucil, providing a mechanistic framework to explore short-term chemoimmunotherapy effects and inform dose-finding strategies. Although we describe leukemia growth with a sigmoidal logistic law, commonly used to approximate tumor expansion in solid cancers [47]. Hence, it is important to recognize the need for long-term clinical data to further refine this assumption. Additionally, while our model considers CLL cells in the bloodstream, a large fraction of malignant cells may reside in bone marrow and metastatic tissues, which could introduce artifacts or simplifications in the system dynamics. Nonetheless, we believe this work represents a significant step toward a more comprehensive mathematical characterization of CLL under combined chemoimmunotherapy, offering a valuable foundation for future model refinements and clinical applications.

Reviewer 4 Report

Comments and Suggestions for Authors

I am sorry but, in my opinion, this paper can be better placed in a different journal. t

Author Response

We sincerely appreciate the time and effort the reviewer dedicated to evaluating our manuscript and providing thoughtful feedback. We understand that our work may still have areas of opportunity to further bridge the gap between dynamical systems modeling and blood cancer research. We remain committed to refining our approach to enhance its relevance and applicability to the clinical hematology community.