Data Output and Visualization

For computer-based modeling and simulation, simulation data collection and visualiza- tion are important. One may do data analysis during the running of simulations and outputs the statistical results directly. For small and simple problems, this method works ne, since it usually would not increase the computational cost too much. How- ever, it isn't proper to do so for problems involving complex statistics collections, since it may signicantly drag simulations down. For this kind of problems, the values of variables of interest are usually written into les as raw simulation results, which allows one to analyze them exibly without changing the original source code of models. The disadvantage is that outputting large data sets is very time-consuming.

Data visualization is necessary since it gives modelers the rst impression of simulation results and it is needed for result presentation. Run-time data visualization is ne if visualization is to show the raw result les but not to directly access the memory of model variables. However, this may be not feasible for programs with a large amount of data sets, since accessing them may take long then that of the simulation itself. TUGME provides methods to collect the information of models during the running of simulations. The information covers almost every model aspect, in which the modelers may be interested. First, one can access the basic information of single tumor cells, including the position (the spherical center), the radius, the type (tumor of healthy cells), the stem cell marker (yes or no), the cell cycle phase, the polyhedral volume and the number of neighbors etc. Second, cells can be visualized using currently two tools, namelyParaview[144] andPov-Ray. As it is shown in gure4.28, these two tools show some distinguish ideas for rendering objects. Paraview integrates the VTKfor viewing the VTK format les, where points is the basic building unit of lines. Linking line seg- ments end to end gives planes or polygons in two dimensions and connecting polygons in three dimensions produces polyhedra. However, curved surfaces, for example, a 3D sphere, are constructed by points in Paraview. The number of points used depends on the image resolution specied by users, which results in large les for high quality (resolution) images. Besides, it allows to generate videos directly with a set of gures whose names are ordered. In contrast, Pov-Ray supports dening a sphere by specify- ing its center and its radius, which allows users to create very high quality images with curved surfaces without substantially increasing its size. The interface of Paraview is much more user friendly, for example, it is easy to change the viewing orientation in Paraview, while the viewing orientation has to be specied by users in the input le of Pov-Ray and changes usually have to be made manually. Details about these two viewing tools are out of the discussion of this thesis. Finally, the concentration of bio- chemical molecules modeled by RDEs can also visualized by Paraview. Our molecular

Figure 4.28: Visualization of the radical Voronoi polyhedra and the distribution of biochemical molecules using Paraview (above) and Pov-Ray (below) in three dimen- sions. Blue line segments in this gure are the edges of the radical Voronoi polyhedra. Colors of the above right panel indicate the concentration gradient (from red (high) to blue (low)) of biochemical molecules within simulation domain. Three panels below from left to right are tumor cell spheres, corresponding radical Voronoi polyhedra and

the merger of them.

concentration le writer wraps the VTK format le writer (VTKWriter) provided by DUNE.

Case Study: Modeling the Growth

of the EMT6/Ro MTSs

This chapter introduces how to construct a concrete tumor model using TUGME. Fur- thermore, a series of simulations are carried out based on the models established by us to investigate the inuences of biochemical and biomechanical factors on the overall growth of a multicellular tumor by treating them as the main cell cycle controllers. The parameters of our models are set specically according to the EMT6/Ro mammary car- cinoma cell line, since abundant experimental data about this cell line are available. We look at the population, the distribution of biochemical molecules as well as the morphol- ogy of tumor tissues under dierent oxygen and glucose conditions. Our simulations are compared with the experiments in the laboratory. In general, good agreements between our simulation results and the experimental data indicate the applicability of TUGME as well as the validity of our models.

5.1 Introduction

The ultimate goal of creating a computer model is to replace the real system which is dicult or impossible to study directly. Computer-model-based system research is generally to uncover the working mechanisms of the investigated system so that its behavior can be predicted. How well a computer model representing the physical system from the point of view of supporting its intended use indicates the delity of the model. Obviously, model delity is the key thing that concerns a modeler, since it directly inuences the quality of simulation results.

In general, a set of standard programmes have been established for model quality control in computer-based modeling and simulation. These standards are termed VV&A [1, 177, 178]. VV&A is the abbreviation of (model) verication, validation and accreditation. Verication is mainly to check whether a model is correctly imple- mented as what it is designed by the modeler. Validation corresponds to the delity control of a model. Finally, accreditation is the process to decide based on both veri- cation and validation information whether a model is practically useful according to the acceptability criteria.

Tumor model VV&A is still very challenging currently from the point of view of both model validation and accreditation. Validation is very hard for cancer modeling because of the shortage of the experimental data that can be actually used by cancer modelers, since most experimental oncologists seem to be more interested in the molecular working mechanisms within single cells. Besides, cells of dierent tumors usually show distinct phenotypes. Consequently, most current cancer modelers can only study few types of tumors. For cancer model accreditation, the problem is even worse, since there are hardly any criteria to the best of our knowledge. In a word, the VV&A of cancer computer models still in its very infant stage.

In order to validate our models, we simulate the growth of the EMT6/Ro mammary carcinoma, more specically, the avascular growth of EMT6/Ro MTSs, since abundant experimental data are available about this cell line [7,175,176,179186].