Estimation of tumor size by diffusion equation
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fereshteh rouygar,1 zohreh rouygar,2,* Ahmad Shirzadi,3
1. Birjand University
2. Bushehr University
3. ph.D Aplied mathematics university persian gulf bushehr
- Introduction: Tumors in the early stages of formation are without arteries (they do not have their own source of blood supply) and depend on diffusion from the surrounding arteries to receive oxygen and nutrients, as well as to excrete waste products. As the tumor grows, the demand for nutrients increases until the flux of nutrients through the tumor surface is insufficient for all cells in the tumor area.
Therefore, tumor growth continues only when the tumor is permeable to a network of capillaries.
- Methods: By considering the slope of nutrients around the tumor and the size of the tumor, we can determine the extent of angiogenesis as a result of the size of the tumor at a later time.
In this article, the diffusion method is used to estimate the volume of the tumor at different times and matlab software is used to implement it in the personal system.
- Results: The system determines the rate of angiogenesis and ultimately the size of the tumor based on the amount of material accumulation. By doing this, we can determine the rate of tumor growth and its risk to the patient (especially in brain tumor samples).
- Conclusion: Accordingly, estimating the size of the tumor at the desired time by the system has accelerated our work for surgery and drug delivery and treatment of people with cancer. The use of this system will also give us the coordinates of how the tumor will orient and grow in a predictable way at the time we want, which makes the treatment of such diseases easier.
- Keywords: Tumor, mathematical model, diffusion equation, MATLAB software, angiogenesis, surgery
