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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Mathematical and Computer Modelling, Volume 54, Issues 9–10, November 2011, Pages 1989–2006
Prior to an eventual clinical adaptation and validation of any clinically oriented model, a thorough study of its dynamic behavior is a sine qua non. Such a study can also elucidate aspects of the interplay of the involved biological mechanisms. Toward this goal, the paper focuses on an in-depth investigation of the free growth behavior of a macroscopically homogeneous malignant tumor system, using a discrete model of tumor growth. We demonstrate that when a clinical tumor grows exponentially, the following preconditions must be fulfilled: (a) time- and space-independent tumor dynamics, in terms of the transition rates among the considered cell categories and the duration of the cell cycle phases, and (b) a tumor system in a state of population equilibrium. Moreover, constant tumor dynamics during the simulation are assumed. In order to create a growing tumor, a condition that the model parameters must fulfill has been derived based on an analytical treatment of the model’s assumptions. A detailed parametric analysis of the model has been performed, in order to determine the impact and the interdependences of its parameters with focus on the free growth rate and the composition of cell population. Constraining tumor cell kinetics, toward limiting the number of possible solutions (i.e., sets of parameters) to the problem of adaptation to the real macroscopic features of a tumor, is also discussed. After completing all parametric studies and after adapting and validating the model on clinical data, it is envisaged to end up with a reliable tool for supporting clinicians in selecting the most appropriate pattern, extracted from several candidate therapeutic schemes, by exploiting tumor- and patient-specific imaging, molecular and histological data.
Over the past decades, a considerable effort has been made by the research community to reveal and elucidate the fundamental mechanisms that govern cancer initiation and progression. Despite considerable progress, many biological aspects still remain obscure. The mathematical modeling of tumor growth and response to treatment could serve as a powerful tool for studying cancer in a more systematic way. Models can help to better comprehend the underlying biological processes, verify or discard assumptions about the natural mechanisms involved and guide the next research steps. The great diversity that characterizes tumors, even those of the same type, creates the need for sophisticated models that encompass biological phenomena on a multiscale basis. A number of models have been proposed in the literature trying to incorporate findings, derived from cumulative experimental or clinical observations and knowledge, regarding mechanisms such as cell cycling, quiescence, differentiation, loss, as well as avascular and vascular phases of growth, angiogenesis, tumor interaction with the surrounding tissue(s), invasion and metastasis. Simulation models can be categorized into two main groups: predominantly continuous and predominantly discrete.
نتیجه گیری انگلیسی
Nowadays a core scientific question is how to exploit the cumulative data from experimental and clinical observations toward the design of personalized medicine . Simulation models of cancer dynamics constitute an imperative tool toward this direction. Such a model must initially undergo an in-depth parametric investigation, for a number of reasons, including: detecting biologically irrelevant virtual tumor behavior, narrowing the acceptable value range of the model parameters, correlating these parameters with kinetic and other quantities reported in the literature (e.g. doubling time, growth fraction, differentiation grade, etc.) and determining the sensitivity or robustness of the output in relation to uncertainties in the input data. Only then an efficient methodology for the adaptation of model input parameters to patient- and tumor-specific data can be defined and the credibility of the model results can be increased. In the present paper, an advanced, discrete-state simulation model of untreated tumor growth was parametrically investigated. The model incorporates the underlying biological mechanisms of cell cycle, quiescence, differentiation and loss and adopts the distinction of proliferating cells into stem cells of infinite mitotic potential and cells of limited proliferative capacity, modeling the path toward terminal differentiation. Depending on the spatiotemporal distribution of the values assigned to the model input parameters, different tumor growth patterns can be demonstrated.