title: Taguchi method for partial differential equations with application in tumor growth.
abstract: The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth.
  
  
  METHODS
  Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average.
  
  
  RESULTS
  First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small.
  
  
  CONCLUSIONS
  Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.
authors: M
authors: M
authors: Ilea
authors: M
authors: M
authors: Turnea
authors: M
authors: M
authors: Rotariu
authors: D
authors: D
authors: Arotăriţei
authors: Marilena
authors: M
authors: Popescu
mesh_terms: D000704:Analysis of Variance; D008432:Mathematical Computing; D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply / Q000473:pathology*; D012107:Research Design; D013997:Time Factors