Background and objective: The present study investigates the transport of drugs in the proximity of the glioblastoma multiforme, a brain neoplasm which is regarded to be the most aggressive type of cancer. In such a small distance from the tumor, diffusion dominates and is driven by the concentration gradient of drug that acquires its maximum at regions where the drugs are released and its minimum at the cancer cell boundary. Undoubtedly, the morphology of the aforementioned boundary is going to play a crucial role in the drug delivery and should be taken into account for the optimal design of the treatment. As first step in order to simulate the topography of glioblastoma multiforme, a fractal boundary is examined which mimics an acceptable model-problem for prognosis and diagnosis of a number of cancer tumors in breast, lungs and brain.
Methods: The drug diffusion is investigated for two concentrations, namely a strong and a mild diffusion, while the outer boundary of the glioblastoma multiforme is approximated via triangular Von Koch shapes. Besides, a Finite Element Method is utilized via FEniCS, which is a Python-based open-source computing platform. Finally, after ascertaining the accuracy of the present numerical model, the concentration of the drug, the entropy production and the mass fluxes in the horizontal and vertical directions are estimated up to the fifth order of Von Koch fractal iterations.
Results: It is ascertained that as the boundaries become more and more irregular, the entropy production in specific areas increases and as a consequence the delivery of the drug is facilitated. Hence, the mass fluxes in these sites appear to be larger comparing to the rest of the boundary and increase, as expected, for the case of strong diffusion.
Conclusions: These active regions, which are referred as "hot spots", are of great importance since they seem to be the sites where the drug ultimately penetrates the glioblastoma. This first-principles investigation is anticipated to shed light on a very significant part of drug delivery, which deals with the vicinity of the glioblastoma multiforme, stress the importance of the topography and give rise to future studies to be conducted based on subject-specific geometries.
Keywords: Drug diffusion; Entropy production; Finite elements; Fractal-shaped curve; Glioblastoma multiforme.
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