# A Numerical Analysis of the Influence of Oxygen and Glucose in Healthy and Tumour Cells
## 5 Conclusions
Hyperglycaemia tends to favour the proliferation of tumour cells, highlighting one of the main differences between tumour cells and healthy cells. In summary, the main differences between healthy and tumour cells lie in the proliferation time and the impact of hyperglycaemia. In tumour cells, the double of the initial cell volume is achieved earlier, and in healthy cells, the state of hyperglycaemia negatively affects the growth of the healthy cell. Both behaviours were successfully implemented and simulated using the proposed algorithm. Furthermore, the implementation of the RPIM as a discretization technique yielded accurate and satisfactory results. However, it should be noted that alternative methods can be considered. The literature offers various discretization techniques that may potentially enhance efficiency. Therefore, this research topic holds potential for further exploration. Note that the proliferation of tumour cells is dependent on a huge number of parameters that can influence their progression and aggressiveness, often involving complex mechanisms. Therefore, considering only the concentrations of oxygen and glucose as factors influencing cell growth is a simplified approach. Future work should focus on several improvements to enhance the algorithm. For instance, the inclusion of a larger number of cells in the domain would enable the study of cell populations and their interactions. The process of angiogenesis, which strongly influences tumour cells, should also be incorporated. Additionally, other parameters affecting tumour cell proliferation, such as pH levels, should be taken into account. These could open up new potential applications for our research, such as predicting the cellular behaviour of distinct cell types and the dynamics of various cell populations by applying this methodology with tailored parameters. It may also be applied to model the progression of diseases characterised by abnormal cell proliferation to obtain insights into disease dynamics and potential intervention points, enhancing our understanding of cellular behaviours in pathological contexts. Moreover, it can be considered for applications in a broader range of scenarios, from optimising cell culture conditions in laboratories to predicting responses in complex biological systems. Conceptualization, J.B. and M.I.B. ; methodology, J.B. and M.I.B. ; validation, M.I.B. ; formal analysis, M.I.B. ; investigation, M.I.B. ; data curation, M.I.B. ; writing--original draft preparation, M.I.B. ; writing--review and editing, M.I.B., J.B., R.N.J. and A.X.d.C. ; supervision, J.B., R.N.J. and A.X.d.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the Ministerio da Ciencia, Tecnologia e Ensino Superior--Fundacao para a Ciencia e a Tecnologia, grant number SFRH/BD/146272/2019, and by LAETA under the project UIDB/50022/2020. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. **Acknowledgments:** The authors truly acknowledge the funding provided by Ministerio da Ciencia, Tecnologia e Ensino Superior--Fundacao para a Ciencia e a Tecnologia (Portugal), under Grant SFRH/BD/146272/2019. Additionally, the authors acknowledge the funding provided by LAETA under the project UIDB/50022/2020. **Conflicts of Interest:** The authors declare no conflicts of interest.