Journal of Physics and Medicine

¶ … Journal of Physics and Medicine in Biology: Manuscript 653

"A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density" by Webb and Nahum (1993)

The following paper critically evaluates the basis of the article entitled Re: "A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density" by Webb and Nahum (1993). This article seeks to contribute to the knowledge base by expanding on a tumour control probability model that incorporates a variable clonogenic cell density throughout radiation treatment. The following areas are covered in discrete sections: article overview, accuracy, scientific quality, scientific content, and interpretation.

Article Overview

In their manuscript, Webb and Nahum generate a tumour control probability (TCP) model for a non-uniform clonogenic cell density during radiation treatment. They posit that TCP is typically only measured with an assumption that clonogenic cell density is uniform; the authors state that this is not the case in actuality, and that a new model is needed. The investigators use equations in their new model to demonstrate the complexity between tumour probability control and clonogenic cell density during radiation. The data the researchers use is based on existing TCP models, to which they add the additional variable of non-uniform clonogenic cell density. The resulting equations appear to be of a high level and in accurate to the mathematical principles they reflect. The results of the equation offer a different view on the value of TCP in radiation that is dependent upon the assumptions made on the uniformity of clonogenic cell density (uniform or non-uniform). The conclusion does posit that the proof exists for such a model given the dynamics of the equation. This research offers a novel approach to calculating TCP during radiation treatment with the additional variable of clonogenic cell density. For a clinical application, this model provides a way to adjust radioactive chemotherapy doses based on a TCP model which takes into account the variability of clonogenic cell density.

Major Comments:

The abstract of the article that the authors provide does not give a clear indication of the clinical relevance to the considered audience. This point should be included for revision to allow for the breadth and variability of readership for the journal Physics in Biology and Medicine. The journal subscribers include those in the field of medical physics, and while the abstract introduction is technical in nature, it lacks conceptual application data, prima facie, to the clinician.

The introduction does relate to the clinical application, yet this is a major point of the research and should be included in the abstract in clear understandable technically appropriate language. The entire idea of the research relates around the issue of targeting tumours with the least radiation possible. TCP models allow for this to happen.

Minor Comments

The article is very technical yet it regards a very real clinical application. The overall tone of the article should reflect that fact.

Accuracy

The investigators use several mathematical-based models of TCP to explain the theory of the concept; they run through the proofs of each theorem and as such the accuracy is expected to be high. The inclusion of a the new variable in the mathematical model can similarly be run through the proofing process, and as such is likewise found to be of high accuracy. In technical terms, the equation is accurate.

Major Comments

As the investigators are attempting to validate their new mathematical model with the new variable included, the forms in which they offer proof are appropriate for their research. However the majority of the article is offered through mathematical proofs; this may be relevant to their new model yet lack interest for the clinician. The clinician that is attempting to destroy a cancerous tumour of a patient is not likely to desire to wade through multiple mathematical equations. The end result is the true validation of the research. The article would be strengthened by advocating that the proof is sound for clinical application.

Minor Comments

While the authors chose to build their article around mathematical models, the meaning of these could be made more widely available with less technical proofing language.

Scientific Quality

The study has offered a potentially new and powerful model by which to measure tumour control probabilities. This in itself is a unique finding. The authors have expanded on a theory of TCP using uniform clonogenic cell density which is often used to ascertain the amount of radiation needed to dose a tumour with for cell kill. The nature of the material in the article is of high scientific quality, from the description of the TCP model to the description of clonogenic cells. The additional material of very high quality mathematical models to support the science is of strength in validating the results of the article.

Major Comments

The issue, again, lays not with the quality of the material offered. The issue lays with the highly technical and almost exclusive offerings of the mathematical equations. The flow of the article is interrupted from imparting the clinical application and usefulness of the new model because of the exclusivity of the high-end math without the inclusion of a less technical translation. While the journal is geared toward those in medical physics, this includes many areas of the specialty that may not always be efficacious if resting entirely on the slow and laborious interpretation of math models. The article quality in terms of the science is high; the accuracy is high; the application is muddled however.

Minor Comments

The article would be strengthened by the inclusion of using TCP in tumour control in the clinical setting. This aspect leaves the entire experience of reading it somewhat dry and hard to internalize. If the material is hard to internalize, it will be difficult to apply.

Scientific Content

The relevance of the content is important. The content itself is directly applicable to dosing patients who have cancerous tumours. The authors show the differences that exist between different mathematical models of TCP, and use graphs to represent the failings of the models that assume uniform clonogenic cell density. The assumption of uniform clonogenic cell density in TCP models does has resulted in an approach by radiotherapists to use uniform radiotherapy, thereby raising the chance that non-cancerous health cells may be killed during the radiotherapy process. As such, the authors note the use of resulting targeted radiotherapy, which is a non-uniform approach to target tumours. However, the radiotherapists are still relying on those older TCP models which use uniform assumptions of clonogenic cell density. The reality, is that cancer cells are often not uniform, and that variable needs to be taken into account in the new approach of targeted non-uniform radiotherapy. The scientific content of the article is high in offering the distinction between older models of TCP and the mathematical proofs of their failings.

Major Comments

The graphs and equations offered as the content of the article should be explained by words, not just equations and strings of theorems.

Interpretation

The article flows with a procession of mathematical proofs to hold up the validation of the authors inclusion of an extra variable to use for the TCP model in dosing tumours with radiation. The interpretation of the results is given through graphs and further equations. The authors posit that the outcome of the math proves their theory that using the additional variable is more in line with the new practice of targeted radiotherapy for cancer patients. The last two paragraphs of the article are the actual supporting acknowledgement by the authors of the outcome of their research. The authors have interpreted the data as demonstrating that their new TCP model is more in line with variable clonogenic cells, and provide a recommendation for future studies on elucidating the nature of clonogenic cells. If such data existed, the authors posit, then along with their new model more targeted radiotherapy could be done that would benefit the patient. Ultimately, the goal of the research is to add to the knowledge base of tumour control therapies; the authors offer their interpretation that this is a complex matter to which they provide one aspect of the solution.

Major Comments