Cancer is a group of diseases that are characterized by uncontrolled growth with the ability to spread around the body. According to the World Health Organization (WHO), cancer is considered the leading cause of death worldwide causing millions of deaths every year [1]. It is important to note that many but not all cancers are curable if detected early. This is because cancer is usually localized in one place in the early stage, which makes it more amenable to treatment options such as surgery, radiation therapy, or chemotherapy. 

Cancer’s complexity, stemming from factors such as heterogeneity, genetic mutations, tumor microenvironment, and metastasis, presents significant challenges for researchers attempting to overcome the disease. In response, they have increasingly turned to mathematical modeling as a novel powerful tool to enhance understanding, make predictions, and ultimately help in controlling cancer progression.

The Need for Mathematical Modeling in Cancer Biology

Mathematical modeling has been used in various fields of Biology for decades, including the famous Lotka-Volterra equation also known as a prey-predator model used to describe the dynamic relationship between the prey distribution and its effect on the predator, within an ecosystem. However, only in the mid-20^th century, researchers implemented mathematical modeling to explore cancer biology for the first time. 

One of the earliest groundbreaking achievements in mathematical modeling for cancer research dates back to the 1950s when researchers began employing mathematical techniques to describe the kinetics of solid tumor growth[4]. This pioneering work laid the foundation for future advancements in the field, with mathematical modeling evolving to encompass a wide range of aspects related to cancer biology.

Over the years, researchers have used mathematical models to investigate tumor invasion, which explores how cancer cells infiltrate surrounding tissues[5]. Additionally, they have applied these models to study angiogenesis, the process by which tumors develop new blood vessels to support their growth and metastasis, the complex process through which cancer cells spread from the primary tumor site to distant organs.

Mathematical models have also been instrumental in understanding treatment response and resistance in cancer. These models can help identify the optimal therapeutic strategies and predict the likely success of various interventions. Furthermore, by analyzing experimental data from genomics and proteomics studies, researchers have been able to pinpoint critical genes and molecular pathways that can serve as potential drug targets.

Another significant application of mathematical modeling in cancer research is the estimation of survival rates based on various factors, such as genetic profiles, clinical characteristics, and treatment response. By integrating real patient data into these models, researchers can generate more accurate and personalized predictions of cancer outcomes.

This multidisciplinary approach, which combines expertise from fields such as mathematics, fundamental biology, and oncology, enables the integration of real patient data with the prediction of complex interactions at the molecular, cellular, and tissue levels. As a result, mathematical modeling has become an indispensable tool in cancer research, providing valuable insights into the underlying mechanisms of cancer development and progression, and paving the way for more effective diagnostic and therapeutic strategies. By integrating diverse data sources into predictive frameworks, mathematical models can guide experimental research, inform the design of novel therapies, and pave the way for personalized medicine. As our understanding of cancer biology continues to grow, mathematical modeling will remain a critical component in the quest to conquer this devastating multifaced disease.

Editorial Board’s Note: The Polish medical market recognizes the value that mathematical modeling brings to cancer research as an essential tool in understanding this complex disease and in developing personalized therapeutic approaches. Its role is becoming increasingly significant in the context of personalized medicine development, opening new perspectives for cancer treatment.

References

1. World Health Organization. “Cancer.” World Health Organization. Accessed May 14, 2023. https://www.who.int/news-room/fact-sheets/detail/cancer.

2. Chakraborty, S., and T. Rahman. 2012. “The Difficulties in Cancer Treatment.” Ecancermedicalscience 6 (November 14): ed16. https://doi.org/10.3332/ecancer.2012.ed16.

3. Hernández-Bermejo, B., and V. Fairén. 1997. “Lotka-Volterra Representation of General Nonlinear Systems.” Mathematical Biosciences 140, no. 1 (February): 1-32. https://doi.org/10.1016/s0025-5564(96)00131-9.

4. Yin, A., D.J.A.R. Moes, J.G.C. van Hasselt, J.J. Swen, and H.J. Guchelaar. 2019. “A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors.” CPT Pharmacometrics & System Pharmacology 8, no. 10 (October): 720-737. https://doi.org/10.1002/psp4.12412.

5. Jóźwiak, P., Formanowicz, P., & Blazewicz, J. 2021. “Mathematical modeling in oncology: a comprehensive review.” Journal of Cancer Research and Clinical Oncology 147, no. 7 (July): 1841-1868. https://doi.org/10.1007/s00432-021-03657-9.

6. Leder, K., Pitter, K., LaPlant, Q., and Hambardzumyan, D. 2014. “Mathematical Modeling of PDGF-Driven Glioblastoma Reveals Optimized Radiation Dosing Schedules.” Cell 156, no. 3 (February 6): 603-616. https://doi.org/10.1016/j.cell.2013.12.029.

7. Agur, Z., and Halevi-Tobias, K. 2020. “A Biomarker-Stratified Dynamic Model for Predicting the Response of Metastatic Colorectal Cancer Patients to Chemotherapy.” NPJ Systems Biology and Applications 6, no. 1 (February 12): 1-7. https://doi.org/10.1038/s41540-020-0132-2.

Konstancja Urbaniak

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Jako Postdoctoral Fellow w dziedzinie medycyny obliczeniowej i komputerowej, obecnie prowadzę pionierskie badania związane z analizami sekwencjonowania RNA na poziomie pojedynczych komórek. Moja praca polega na rozwijaniu i wykorzystywaniu innowacyjnych metodologii obliczeniowych i komputerowych, które mają na celu podniesienie jakości i głębokości analizy biologicznej. Ostatnio moje zainteresowania skierowały się w stronę modelowania matematycznego, stosując te techniki do symulacji i zrozumienia środowisk biologicznych. To przedsięwzięcie dostarczyło mi unikalnych spostrzeżeń i fascynujących odkryć, które nadal podsycają moją pasję do tej dziedziny. W 2022 roku miałam zaszczyt zdobycia doktoratu na programie A*STAR na prestiżowym Uniwersytecie w Manchesterze. A*STAR program dał mi możliwość prowadzenia części moich badań w Singapurze, w renomowanym Instytucie Bioinformatyki A*STAR. Moje studia doktoranckie były interdyscyplinarnym badaniem biochemii i bioinformatyki, w ramach którego badałem kluczową rolę rodziny białek SUMO. To unikalne połączenie dyscyplin pozwoliło mi zrozumieć złożone zjawiska biologiczne. Zanim zdobyłam tytuł doktora, moja akademicka podróż zaprowadziła mnie na Uniwersytet w Bristolu w 2018 roku, gdzie zdobyłam tytuł magistra nauk medycznych przez badania w dziedzinie medycyny molekularnej i komórkowej. Doświadczenie to pozwoliło mi zagłębić się w złożony świat procesów komórkowych i mechanizmów molekularnych, wzbogacając moje zrozumienie złożonych wzajemnych powiązań stojących u podstaw medycyny i biologii. Moja edukacja na poziomie wyższym rozpoczęła się na Kingston University, gdzie w 2017 roku ukończyłam studia licencjackie z wyróżnieniem z nauk biomedycznych. Tam zostały zacementowane moje akademickie podstawy, dając mi solidne podłoże w interdyscyplinarnym charakterze nauki biomedycznej. Te doświadczenia, wraz z moją późniejszą pracą, kształtowały moje podejście i wiedzę specjalistyczną w tej dziedzinie, dostarczając kompleksowego i wieloaspektowego podejścia do moich badań w dziedzinie medycyny obliczeniowej i komputerowej.