I am interested in studying tumor growth in cancer using both fractal calculus and fractional calculus. Can it be done? If yes, what could be the possible rationale and biophysical significance for choosing the mentioned approaches, respectively?
I hope for your kind consideration and positive response.
Thank you.
Dear Abhijeet Das
In the context of tumor growth, fractal calculus and fractional calculus offer different perspectives.
Fractal calculus focuses on the geometrical complexity of the tumor, especially its irregular and self-similar structures, such as the vascular networks and the tumor boundary. Tumors often grow in a way that resembles fractals, with patterns that repeat at different scales. Fractal calculus helps to characterize these complex, irregular shapes and quantify the heterogeneity of the tumor, which can be important for understanding its aggressiveness, potential for invasion, and ability to metastasize.
On the other hand, fractional calculus is more concerned with the dynamic and temporal aspects of tumor growth. It helps model processes that involve long-range interactions, memory effects, and non-local behaviors. These are common in tumor biology, where growth and spread don't just depend on local conditions but are influenced by the surrounding microenvironment, past interactions, and diffusion processes. Fractional calculus can capture these history-dependent effects and model complex processes like nutrient diffusion, drug delivery, and metastatic spread, which can't be accurately described using traditional integer-order calculus.
Together, these two approaches offer a complete understanding of tumor growth. Fractal calculus helps explain the spatial irregularities of the tumor, while fractional calculus models the dynamic, long-range interactions and memory effects that govern tumor behavior and its response to treatment.
Best Regards....
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