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Mathematics at the service of health

Mathematical model assists in the prognostic analysis of kidney cancer

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Master's thesis developed by Cristina Sacilotto at the Department of Applied Mathematics, of the Institute of Mathematics, Statistics and Scientific Computing (Imecc) at Unicamp, supervised by professor Laércio Luis Vendite, presents the construction of two mathematical models developed to predict the risks of metastasis and death in patients with kidney cancer of the most common subtype, called conventional, characterized by clear cells.

Renal cell carcinoma is a heterogeneous disease with a widely variable prognosis and responsible for 2% of malignant neoplasms. A more accurate diagnosis of the risk of disease progression and mortality after treatment is essential for patient guidance, treatment decision-making and selection of appropriate follow-ups. In Brazil, neoplasms are the second cause of death, surpassed only by diseases of the circulatory system.

As the discussion and understanding of the factors that determine the prognosis of kidney tumors are fundamental for establishing their approach, the research analyzes some of them and their importance in patients' survival. Today, the Fuhrman Grading System is used, with considerable prognostic value, which classifies the nuclear pattern of the neoplasm into four grades, determined according to the difference between the cell nucleus of a cancerous cell and a healthy one. Grade 1 tumors are considered to have a favorable prognosis, grade 4 tumors are considered to have a dismal and intermediate prognosis, and grades 2 and 3 are considered to have a favorable prognosis. However, in the medical community, there is a question regarding this classification, which appears to be incompatible with certain real cases, suggesting that it is not enough to take into account only the degree of cell involvement for the diagnosis.

Available in: https://www.auanet.org/education/modules/pathology/kidneycarcinomas/fuhrman-grade.cfm
 

Photo: Reproduction
Figure - Clear cell renal cell carcinoma. A: Nuclear grade 1 tumor with round or uniform nuclei; nucleoli not discernible or absent. B: Nuclear grade 2 carcinoma with slightly irregular nuclear contours and discrete nucleoli. C: Grade 3 nuclear neoplasia has large, irregular nuclei. D: Grade 4 nuclear carcinoma with bizarre nuclei and large, prominent nucleoli

The study, in addition to an analysis of this univariate criterion, also considers other factors, resulting in a multivariate analysis, so that, by combining them with the Fuhrman classification, they can lead to more accurate results for the prognosis of the neoplasia, allowing verify the relationship between Fuhrman grade and survival. Advances in diagnoses and treatments and the impact they can have on patient survival are relevant for defining prognosis in individuals with the disease. The intention of the research is to assist the specialist in making decisions regarding the stage of the neoplasia.


Mathematical model

In fact, any grading system accepted today in pathological practice, such as Fuhrman's, presents a certain degree of subjectivity, as diseases are generally described in linguistic terms, which are vague and difficult to translate quantitatively. Hence the advantage of a mathematical model, such as the one using Fuzzy Set Theory, used in doubtful and uncertain situations. This theory combines the precision of mathematics and impressions of the real world, so that uncertain data and expert opinion are taken into account and incorporated into mathematical models.

By the way, the researcher states: “The subjectivity of information in the study of kidney cancer motivated us to use Fuzzy Set Theory to treat the problem. Given the uncertainties in the information, we believe that the use of this theory is appropriate. It is a language of logical thinking, increasingly necessary in the health sector”.

Photo: Scarpa
Professor Laércio Luis Vendite, dissertation advisor: “Our work formalizes and organizes this evidence, facilitating an accurate diagnosis and, consequently, a more appropriate treatment”

In fact, in the mathematical literature there are several works that use set theory fuzzy to analyze biological events, in particular neoplasms. The mathematical models developed have largely contributed to a greater understanding of medical events, their diagnoses, prognoses and the efficiency of treatments.

The work is part of Professor Laércio's line of research, who has been dedicated to biomathematics for almost thirty years, and his references included studies on prostate and bladder cancer also supervised by him. His focus was the construction of two mathematical models fuzzy to predict the risks of metastasis and death for individuals with kidney tumors and analyze the relationship between Fuhrman grading and the prognosis of patients with this neoplasm.

The model fuzzy used to predict the risk of metastasis combines the patient's tumor data - Fuhrman grade, presence of necrosis, tumor size and staging, that is, the patient's clinical status, which depends on the considerations passed by clinicians. The model used to predict death uses the same data as the first model, only exchanging the tumor size factor for the presence of metastasis. The two models make use of a set of rules, of a linguistic nature, drawn up with the help of specialists, research into literature in the area and statistical data from patients at the Hospital de Clínicas (HC) at Unicamp. The statistical analysis of these data made it possible to identify the most determining variables to be considered, such as the presence of necrosis and staging, contributing to the adjustment of the weights of the rules established for each model. “We created rules with information from experts with the weights assigned and support from statistical analysis”, explains the professor.

Photo: Scarpa
Cristina Sacilotto, author of the research: “The subjectivity of information in the study of kidney cancer motivated us to use Fuzzy Set Theory to treat the problem”

Finally, simulations were carried out with data collected from HC patients to verify the compatibility of the model with reality. According to the researcher, the results can be considered satisfactory and compatible with what was observed in real patients.

The researchers considered the collaboration of urologists Ubirajara Ferreira and Wagner Eduardo Matheus to be of fundamental importance in developing the work; pathologists Athanase Billis and Larissa Eloy; and resident doctor Eduardo Azevedo, all from the University's HC.


Ponderations

The models were tested in concrete situations of Brazilian patients, with a known history. Properly operationalized, they provide the doctor with information in terms of possibility and not probability, therefore not requiring a large database to indicate the chances of the tumor developing metastasis and the individual's survival.

The model provides the clinician with the best possible diagnosis at any given time. Laercio explains: “Today the doctor makes the diagnosis based on medical evidence and his experiences. Our work formalizes and organizes this evidence, facilitating an accurate diagnosis and, consequently, more appropriate treatment. As the model is built based on information from experts, it incorporates medical experiences and the software built based on it provides answers according to clinical concepts.”

For the researcher, the proposed model allows for a more accurate diagnosis in relation to the evolution of the tumor. But as the conclusions arise from the use of the Unicamp HC database, she issues a warning: “As simulations are limited to a restricted universe, there is a need for new experiments so that the results can be confirmed and consolidated”.

Professor Laércio concludes: “It is important that this mathematical treatment is debated by the medical community, as our procedure has no parallel in other research with international impact. We proved, through a mathematical model, that there is very strong evidence that the Fuhrman classification has a limited scope.”

 

 

JU-online cover image
Researcher Cristina Sacilotto, author of the research, and professor Laércio Luis Vendite, advisor | Photo: Antonio Scarpinetti

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