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A new method to estimate parameters of the growth model for metastatic tumours.

Journal article
Authors Esmaeil Mehrara
Eva Forssell-Aronsson
Viktor Johanson
Lars Kölby
Ragnar Hultborn
Peter Bernhardt
Published in Theoretical biology & medical modelling
Volume 10
Pages Article number: 31
ISSN 1742-4682
Publication year 2013
Published at Institute of Clinical Sciences, Department of Radiation Physics
Institute of Clinical Sciences, Department of Surgery
Institute of Clinical Sciences, Department of Oncology
Pages Article number: 31
Language en
Links dx.doi.org/10.1186/1742-4682-10-31
https://gup.ub.gu.se/file/104394
Keywords Modelling tumour growth, Metastasis, Dissemination, Gompertzian
Subject categories Cancer and Oncology, Radiological physics

Abstract

PURPOSE: Knowledge of natural tumour growth is valuable for understanding tumour biology, optimising screening programs, prognostication, optimal scheduling of chemotherapy, and assessing tumour spread. However, mathematical modelling in individuals is hampered by the limited data available. We aimed to develop a method to estimate parameters of the growth model and formation rate of metastases in individual patients. MATERIALS AND METHODS: Data from one patient with liver metastases from a primary ileum carcinoid and one patient with lung metastases from a primary renal cell carcinoma were used to demonstrate this new method. Metastatic growth models were estimated by direct curve fitting, as well as with the new proposed method based on the relationship between tumour growth rate and tumour volume. The new model was derived from the Gompertzian growth model by eliminating the time factor (age of metastases), which made it possible to perform the calculations using data from all metastases in each patient. Finally, the formation time of each metastasis and, consecutively, the formation rate of metastases in each patient were estimated. RESULTS: With limited measurements in clinical studies, fitting different growth curves was insufficient to estimate true tumour growth, even if patients were followed for several years. Growth of liver metastases was well described with a general growth model for all metastases. However, the lung metastases from renal cell carcinoma were better described by heterogeneous exponential growth with various growth rates. CONCLUSION: Analysis of the regression of tumour growth rate with the logarithm of tumour volume can be used to estimate parameters of the tumour growth model and metastasis formation rates, and therefore the number and size distribution of metastases in individuals.

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