# A Numerical Analysis of the Influence of Oxygen and Glucose in Healthy and Tumour Cells
## 5 Conclusions  
Cancer is one of the deadliest diseases in our society, affecting and killing millions of people every year. It is often associated with the emergence of mutations that promote abnormal proliferation of the affected cells, leading to an imbalance between cell proliferation and cell death. Due to that, the normal functioning of the tissues can be disrupted. To understand this problem, it is necessary to comprehend the mechanism and the species that are involved in the process of proliferation, both in healthy and diseased conditions. In this particular process, cells are strongly dependent on oxygen, nutrients, and growth factors. Therefore, understanding their influence becomes essential. Various methods have been employed to study cancer, including mathematical and computational models, which have emerged as powerful tools to complement more traditional analyses. In the literature, different types of models can be found, and several numerical methods are used to solve them. Among these numerical methods, meshless methods, such as the RPIM, have emerged as an alternative to conventional methods and are currently employed to address more complex problems. However, when it comes to studying cell proliferation and cancer, these methods are less commonly utilized. One of the main reasons to choose this method is that mesh-based methods would require a more complex remeshing procedure since the elements of the mesh would have to be divided to simulate the process of cell division. This reduces the efficiency of the method. Thus, for the study of cell proliferation, which is a nonlinear geometric problem that implies remeshing, meshless methods are a better choice. In contrast to other meshless techniques, the RPIM is able to use structures available in FEM softwares and can perform structural analyses that are not possible with discrete methods that use probabilities and statistical laws, in contrast to other meshless techniques. The objective of the present work was to implement and study the influence of oxygen and glucose concentrations on healthy and tumour cells using a previously created algorithm by the research group. The algorithm simulates the growth and division process of a single cell, which is dependent on oxygen and glucose. To incorporate the influence of these two molecules, five states of concentration were defined for each one (extreme hyperoxia, hyperoxia, normal oxygen concentration, hypoxia,and extreme hypoxia for oxygen, extreme hyperglycaemia, hyperglycaemia, normal glucose concentration, hypoglycaemia, and extreme hypoglycaemia for glucose). The growth of the cell over time was analysed for each combination of oxygen and glucose states. In the end, it was possible to verify that the obtained results were coherent with what was expected, and each case led to satisfactory and adequate results for each one of the twenty-five combinations in terms of volume growth for both types of cells. When normal concentrations were tested, the proliferation process occurred within 24 h for the healthy cell and within 18 h for the tumour cell, which aligns with the normal duration of a human cell cycle. However, when these concentrations were increased or decreased, the process of proliferation was affected, usually resulting in slower volume growth. This behaviour was observed in conditions of hyperoxia, hypoxia, and hypoglycaemia. When extreme states were analysed, the cell maintained the same volume until the initiation of the apoptosis process. Such behaviour is coherent with what occurs in the biological environment since, in extreme cases, cells tend to stop this process in order to protect themselves from the hostile environment and prevent the emergence and spread of mutations. In the case of a healthy cell, under hyperglycaemia, the same behaviour was verified. However, when the tumour cell is subjected to this state, the opposite effect is verified, leading to faster cell growth.