Modelling and Estimating Dynamics of Tumor Shrinkage with BlenX and Kinfer

Lecca, Paola; Kahramanoullari, O.; Morpurgo, Daniele; Priami, Corrado; Soo, Ross A.

doi:10.1109/uksim.2011.24

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…The diffusion coefficient of gemcitabine is automatically calculated by Redi as a function of space and time according to the formula (25). The efficacy of the gemcitabine ( k 2 ), the rate constant for resistance appearance ( k 3 ), and the tumor growth rate ( k 4 ) have been inferred with KInfer (a maximum likelihood parameter estimator recently developed by Lecca et al [ 38 , 39 ]) from the tumor size shrinkage curves observed in 56 patients treated with gemcitabine [ 18 ]. The 56 patients have been categorized by their age, sex and smoke history, and in our simulations we considered the average values of k 2 , k 3 , and k 4 (see in Tables 1 and 2 the average values and the standard deviations of these three parameters).…”

Section: Resultsmentioning

confidence: 99%

Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth

Lecca

Morpurgo

2012

BMC Bioinformatics

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BackgroundReaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel.MethodsWe present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non-homogeneous media. The diffusion coefficient is explicitly expressed as a function depending on the local conditions of the medium, such as the concentration of molecular species, the viscosity of the medium and the temperature. We incorporated this generalized law in a reaction-based stochastic simulation framework implementing an efficient version of Gillespie algorithm for modeling the dynamics of the interactions between tumor cell, nutrients and gemcitabine in a spatial domain expressing a nutrient and drug concentration gradient.ResultsUsing the mathematical framework of model we simulated the spatial growth of a 2D spheroidal tumor model in response to a treatment with gemcitabine and a dynamic gradient of oxygen and glucose. The parameters of the model have been taken from recet literature and also inferred from real tumor shrinkage curves measured in patients suffering from non-small cell lung cancer. The simulations qualitatively reproduce the time evolution of the morphologies of these tumors as well as the morphological patt...

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Section: Resultsmentioning

confidence: 99%

Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth

Lecca

Morpurgo

2012

BMC Bioinformatics

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“…Our modelling approach to describe prostate cancer is based on stochastic Concurrent Constraint Programming (sCCP, [5]) a modelling language belonging to the class of stochastic Process Algebras (SPA) applied to Systems Biology [12]. SPA have been applied in modelling many aspects of biological systems, including tumour growth [22,23].…”

Section: Introductionmentioning

confidence: 99%

Programmable models of growth and mutation of cancer-cell populations

Bortolussi

Policriti

2011

Electron. Proc. Theor. Comput. Sci.

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In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint Programming, a flexible stochastic modelling language. The methodology is tested on (and partially motivated by) the study of prostate cancer. In particular, we prove how our method is suitable to systematically reconstruct different mathematical models of prostate cancer growth –together with interactions with different kinds of hormone therapy– at different levels of refinement

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