164

Bioinformatics of the Brain

6.5

Impact of Fractional Calculus on Tumor Growth

Models

Complex in nature, cancer is a significant public health issue [1]. Because can-

cer is a chronic disease and current therapies include side effects, it places a

significant load on health care systems. Personalized adaptive radiation treat-

ment has the potential to benefit from the incorporation of mathematical

models into radiation oncology by considering either fractionation or dose

adaptation to patients based on their unique clinical responses. By using

numerical simulations that utilize tumor growth models and person’s gene

expression, predictive oncology may be able to assist in the personalization

of radiation dosages. Research efforts have been focused on applying mathe-

matics and physics to cancer genesis and early growth, as well as tumor and

intercellular interactions, because thorough modeling may possibly improve

the development and implementation of innovative cancer treatments [34].

In fact, the subject of mathematical oncology is founded on the ideas that

biology presents novel mathematical problems that require the development

of improved mathematical tools, and that mathematics may be employed to

advance biological knowledge about the disease. From the investigation of tu-

mor growth to the implementation of tailored treatment plans, mathematical

oncology encompasses the development and use of models for phenomena rel-

evant to cancer. It’s a growing field for research that obtains from the data

produced by the present bioinformatics boom. Given its significance, math-

ematical oncology makes the case for comprehensive theoretical models to

comprehend, organize, or utilize clinical data with an eye toward oncology

decision-making, for example. All solid cancers originate from the formation

of a primary tumor, despite being an extremely complex collection of diseases.

By concentrating on this shared location, we may be able to better understand

key aspects of early tumor development. While the pathways and signals lead-

ing to the emergence of malignant cells have become increasingly clear due to

the sequencing of genes and molecular biology, it is as crucial to comprehend

the phenomenological principles driving the proliferation of tumor population

cells. In terms of general vascular tumor growth, approaches based on ecolog-

ical models and explained via ordinary differential equations (ODE) have the

prospect of expanding notions and insights [34].

Numerous ODE models have been created to characterize dynamic tumor

development by including special adjustments to account for biological par-

ticularities and experimental data. Most of them are based on a sigmoidal

rule that relies on the population’s carrying capacity and growth rate. The

several phases that a primary tumor goes through in relation to the resources

at hand, and like tumor surface area and small heterogeneity, justify this be-

havior. Even though ODE-based approaches are not as complex as cancer

models that include partial differential equations (PDEs), their continued use