Multi-Scale Modeling and Oxygen Impact on Tumor Temporal Evolution: Application on Rectal Cancer During Radiotherapy.

We present a multi-scale approach of tumor modeling in order to predict its evolution during radiotherapy. Within this context we focus on three different scales of tumor modeling: microscopic (individual cells in a voxel), mesoscopic (population of cells in a voxel) and macroscopic (whole tumor), with transition interfaces between these three scales. At the cellular level, the description is based on phase transfer probabilities in the cellular cycle. At the mesoscopic scale we represent populations of cells according to different stages in a cell cycle. Finally, at the macroscopic scale, the tumor description is based on the use of FDG PET image voxels. These three scales exist naturally: biological data are collected at the macroscopic scale, but the pathological behavior of the tumor is based on an abnormal cell-cycle at the microscopic scale. On the other hand, the introduction of a mesoscopic scale is essential in order to reduce the gap between the two extreme, in terms of resolution, description levels. It also reduces the computational burden of simulating a large number of individual cells. As an application of the proposed multi-scale model, we simulate the effect of oxygen on tumor evolution during radiotherapy. Two consecutive FDG PET images of 17 rectal cancer patients undergoing radiotherapy are used to simulate the tumor evolution during treatment. The simulated results are compared with those obtained on a third FDG PET image acquired two weeks after the beginning of the treatment.

A Viability Approach for Robustness Measurement, Organizational Autopoiesis, and Cell Turnover in a Multicellular System.

In this article, we use the potential of computational biology to highlight the key role of cell apoptosis for studying some tissue's properties through in silico experiments of morphogenesis. Our morphogenesis model is a new approach focusing on the deterministic program within cells that controls their placement and their differentiation at the beginning of the embryogenesis. Indeed, when the tissue is made by just a few pair of cells, we consider that cellular mechanisms are related neither to the influence of mechanical forces nor to the spread of chemicals. Dynamics are based on spatial and logical choices, the other factors being involved when the tissue contains a large number of cells. We had established a mathematical formulation of such a model and had enlightened the link between phenotype (cell placement and cell differentiation) and genotype (cell program) at the early embryogenesis. Indeed, that work allowed for generating any early tissue and the associated program that designs it. We propose now to study and assess some properties of these tissues for further selection and classification purposes. More precisely, we present in this article novel methods to measure tissue robustness based on the backward morphogenesis of our model. We also show some implementations of their self-maintenance properties, on the one hand to deal with environment disturbances through autopoiesis and on the other hand to achieve a dynamical steady state which ensures tissue renewal.

Large Scale Tissue Morphogenesis Simulation on Heterogenous Systems Based on a Flexible Biomechanical Cell Model.

The complexity of biological tissue morphogenesis makes in silico simulations of such system very interesting in order to gain a better understanding of the underlying mechanisms ruling the development of multicellular tissues. This complexity is mainly due to two elements: firstly, biological tissues comprise a large amount of cells; secondly, these cells exhibit complex interactions and behaviors. To address these two issues, we propose two tools: the first one is a virtual cell model that comprise two main elements: firstly, a mechanical structure (membrane, cytoskeleton, and cortex) and secondly, the main behaviors exhibited by biological cells, i.e., mitosis, growth, differentiation, molecule consumption, and production as well as the consideration of the physical constraints issued from the environment. An artificial chemistry is also included in the model. This virtual cell model is coupled to an agent-based formalism. The second tool is a simulator that relies on the OpenCL framework. It allows efficient parallel simulations on heterogenous devices such as micro-processors or graphics processors. We present two case studies validating the implementation of our model in our simulator: cellular proliferation controlled by cell signalling and limb growth in a virtual organism.

A software architecture for multi-cellular system simulations on graphics processing units.

The first aim of simulation in virtual environment is to help biologists to have a better understanding of the simulated system. The cost of such simulation is significantly reduced compared to that of in vivo simulation. However, the inherent complexity of biological system makes it hard to simulate these systems on non-parallel architectures: models might be made of sub-models and take several scales into account; the number of simulated entities may be quite large. Today, graphics cards are used for general purpose computing which has been made easier thanks to frameworks like CUDA or OpenCL. Parallelization of models may however not be easy: parallel computer programing skills are often required; several hardware architectures may be used to execute models. In this paper, we present the software architecture we built in order to implement various models able to simulate multi-cellular system. This architecture is modular and it implements data structures adapted for graphics processing units architectures. It allows efficient simulation of biological mechanisms.

Computational energetic model of morphogenesis based on multi-agent Cellular Potts Model.

The Cellular Potts Model (CPM) is a cellular automaton (CA), developed by Glazier and Graner in 1992, to model the morphogenesis. In this model, the entities are the cells. It has already been improved in many ways; however, a key point in biological systems, not defined in CPM, is energetic exchange between entities. We integrate this energetic concept inside the CPM. We simulate a cell differentiation inside a growing cell tissue. The results are the emergence of dynamic patterns coming from the consumption and production of energy. A model described by CA is less scalable than one described by a multi-agent system (MAS). We have developed a MAS based on the CPM, where a cell agent is implemented from the cell of CPM together with several behaviours, in particular the consumption and production of energy from the consumption of molecules.