# A Numerical Analysis of the Influence of Oxygen and Glucose in Healthy and Tumour Cells
## 4 Results and Discussion
Figure 6: (**a**) Schematic representation of the section of the domain used to present the (**b**) nodal mesh and (**c**) integration mesh used in all the analyses. For visual reference and since the domain is symmetric, only a quarter of the domain is shown (Adapted with permission from Ref. [46]. Copyright 2022 ELSEVIER). Figure 8: Evolution of the volume of the tumour cell, when the five states of oxygen were combined with extreme hyperglycemia. Figure 7: Evolution of the volume of the healthy cell, taking into account the five states of oxygen combined with extreme hyperglycemia. Figure 9: Evolution of the volume of the healthy cell, taking into account the five states of oxygen combined with hyperglycemia. Figure 11: Evolution of the volume of the healthy cell, taking into account the five states of oxygen combined with a normal level of glucose. Figure 12: Evolution of the volume of the tumour cell, when the five states of oxygen were combined with a normal level of glucose. Figure 10: Evolution of the volume of the tumour cell, when the five states of oxygen were combined with hyperglycaemia. Figure 14: Evolution of the volume of the tumour cell, when the five states of oxygen were combined with hypoglycaemia. Figure 13: Evolution of the volume of the healthy cell, taking into account the five states of oxygen, combined with hypoglycaemia. Figure 6:0 Evolution of the volume of the healthy cell, taking into account the five states of oxygen, combined with extreme hypoglycaemia. In Figure 7 (healthy cell) and Figure 8 (tumour cell), the concentration of glucose was assumed to be within the extreme hyperglycaemia range, while the concentration of oxygen was varied among the five possible ranges. For all curves and both types of cells, the cell size remained constant for a period of time (as indicated in Tables 2 and 3). After this, the cell initiated the process of apoptosis, resulting in a reduction of the cell volume by up to 40% of its initial volume. This behaviour can be attributed to the extreme hyperglycaemia condition, which was present in all cases and defined in the algorithm as the only possible outcome. However, it is important to note that the duration of the constant volume period and the initiation of apoptosis varied for each combination. More aggressive combinations, such as extreme hyperglycaemia combined with extreme hypoxia, resulted in shorter analysis times, leading to earlier cell death. The combination with normal concentrations of oxygen took 24 h to initiate the apoptosis process, as defined in the algorithm. Figure 9 illustrates the volume variation of the healthy cell over time for different oxygen concentration states, considering hyperglycaemia. Once again, when extreme conditions of oxygen are considered, the cell presents a similar behaviour as the one presented in Figure 6:1 In the remaining three cases, the growth of the cell is slower, as expected, since in each one there is at least one case of an abnormal concentration of glucose and oxygen. These conditions always have a negative impact on the proliferation process. However, in these three cases, the cell managed to grow and double its initial volume before undergoing the process of division. The tumour cell (Figure 10) analysed under the same combinations once again led to the cell maintaining a constant volume for a period of time before entering apoptosis. When hyperglycaemia and normal levels of oxygen are combined, the process of proliferation is enhanced, so the cell achieves double its volume in less than 18 h (the defined time for a tumour cell to complete the cell cycle). This acceleration can be attributed to the fact that hyperglycaemia promotes tumour cell proliferation. In combination with hyperoxia or hypoxia, as defined in the algorithm, the cell is allowed to grow and double its volume, but at a slower rate. However, since these states are combined with hyperglycaemia, their aggressiveness is mitigated.