# A Numerical Analysis of the Influence of Oxygen and Glucose in Healthy and Tumour Cells
###### Abstract  
Cancer is widely regarded as a critical health issue in modern society. Tumour cells are usually associated with abnormal proliferation that disrupts the normal behaviour of the body. All cells depend on the availability of oxygen and nutrients present in the extracellular environment, which can enhance or decrease their ability to proliferate. Therefore, to comprehend the influence of these factors, it is helpful to understand the proliferation process of both healthy and tumour cells. Computational models are powerful tools used to study biomedical problems, and several models have been presented in the literature. Different numerical methods have been proposed to solve these models. Among them, meshless methods can be highlighted, as they are used to solve complex problems with accurate results. However, in the case of cell proliferation, this is still an area that has not yet been fully explored. The aim of this work is to implement and study the influence of oxygen and glucose during the proliferation of healthy and tumour cells using a novel algorithm. This is an iterative discrete algorithm that employs a meshless numerical and uses a new phenomenological law to describe cell growth. In the end, the algorithm was capable of generating satisfactory results, in accordance with the literature. cell proliferation; oxygen; glucose; meshless methods; numerical simulation +
Footnote †: journal: Medical Engineering and Industrial Management  
M.I.B. Regarding oxygen, it is essential for both healthy and tumour cells. Oxygen has a significant impact on cell proliferation, as cells require adequate oxygenation for proper metabolic processes and cellular functions to occur [8; 9; 10]. When oxygen concentrations exceed normal levels (i.e., hyperoxia), cells experience a toxic effect. Under such conditions, cells are prone to oxidative damage caused by the production of reactive oxygen species, which can induce apoptosis and necrosis depending on the duration and level of hyperoxic exposure [11; 12]. Under hypoxia (i.e., low oxygen concentrations), the rate of cell proliferation decreases, and the process of apoptosis can be activated to prevent the emergence and progression of mutations in subsequent cell generations, thereby attempting to prevent the formation of tumour cells [13; 14]. When this condition becomes severe, respiration is impaired, and cells die within a short period, typically ranging from 10 to 48 h [15]. In the case of tumour cells, hypoxia influences tumour progression, aggressiveness, metastasis, and resistance to apoptosis, treatments, and radiation [9; 16; 17]. However, hypoxia alone is usually insufficient to neutralise tumour cells [17; 18]. Initially, cells tend to decrease their proliferation rate; however, this leads to excessive resource consumption and abnormal angiogenesis, which, in turn, promote tumour motility in search of a new oxygen source, ultimately increasing the proliferation rate [18]. However, similar to what occurs in healthy cells, when this condition becomes severe and extreme, tumour cells stop proliferation and die [7; 19]. Within 24 h, cell proliferation may stop, and approximately 20% to 30% of the affected cells are prone to die under these conditions [17]. On the other hand, hypoxia can also increase glucose consumption in tumour cells [16]. When comparing the metabolism of tumour cells to healthy cells, tumour cells tend to consume glucose at higher rates [20; 21]. Glucose serves as the primary molecule utilised in their metabolism, facilitating their proliferation [22; 23]. Therefore, under conditions of glucose deprivation, tumour cells tend to halt their proliferation due to ATP depletion [7], leading to metabolic disturbances, oxidative stress, alteration of the redox status, and cellular death [24; 25].