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Optimal Combined Radio- and Anti-Angiogenic Cancer Therapy
A mathematical model for combination of radio- and anti-angiogenic therapy is considered as optimal control problem with the objective of minimizing...
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Modelling HIF-PHD Dynamics and Related Downstream Pathways
Hypoxia can represent a challenging condition for survival at different biological scales, from cells to organisms. The efficiency of the response to...
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A Fokker–Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis
In this paper, a new framework for obtaining personalized optimal treatment strategies in colon cancer-induced angiogenesis is presented. The...
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A Hybrid Discrete–Continuum Modelling Approach to Explore the Impact of T-Cell Infiltration on Anti-tumour Immune Response
We present a spatial hybrid discrete–continuum modelling framework for the interaction dynamics between tumour cells and cytotoxic T cells, which...
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Mathematical Oncology: Tumor Evolution Models
Cancer is the second leading cause of death globally, accounting for an estimated nine million deaths per year. Mathematical oncology, modeling the...
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Bacillus Calmette Guerin (BCG) Immunotherapy for Bladder Cancer: A Control and Mathematical Analysis
In this manuscript, Immunotherapy with Bacillus Calmette Guerin (BCG) vaccine is devised for treating spherical bladder cancer. We considered the...
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Modeling of Mouse Experiments Suggests that Optimal Anti-Hormonal Treatment for Breast Cancer is Diet-Dependent
Estrogen receptor positive breast cancer is frequently treated with anti-hormonal treatment such as aromatase inhibitors (AI). Interestingly, a high...
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Modeling LSD1-Mediated Tumor Stagnation
LSD1 (KDMA1) has gained attention in the last decade as a cancer biomarker and drug target. In particular, recent work suggests that LSD1 inhibition...
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A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma
Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this...
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Mathematical modeling of cancer treatment with radiation and PD-L1 inhibitor
Radiation therapy is a longstanding cancer treatment. More recently, it has been demonstrated that radiation therapy (RT) elicits anti-cancer immune...
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Tumor Evolution Models of Phase-Field Type with Nonlocal Effects and Angiogenesis
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models...
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On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies
We review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We discuss various...
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A mathematical model of angiogenesis and tumor growth: analysis and application in anti-angiogenesis therapy
The purpose of this paper is to develop a new coupled mathematical model of angiogenesis (new blood vessel growth) and tumor growth to study cancer...
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Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative
In this work, optimal control for a fractional-order nonlinear mathematical model of cancer treatment is presented. The suggested model is determined...
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Predictive Modeling of Neuroblastoma Growth Dynamics in Xenograft Model After Bevacizumab Anti-VEGF Therapy
Neuroblastoma is the leading cause of cancer death in young children. Although treatment for neuroblastoma has improved, the 5-year survival rate of...
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Cholesterol Regulation in Age-Related Macular Degeneration: A Framework for Mathematical Modelling of Drusen Biogenesis
In age-related macular degeneration (AMD), there is, in common with many other age-related diseases, the need to distinguish between changes in the...
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Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment
Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a...
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Mathematical Models of Cancer: When to Predict Novel Therapies, and When Not to
The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US...
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Optimization of Combined Antitumor Chemotherapy with Bevacizumab by Means of Mathematical Modeling
Unlike traditional tumor treatment which kills proliferating cells, antiangiogenic therapy is aimed at blocking of angiogenesis, i.e., new blood...
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Mathematical Modeling of Cellular Cross-Talk Between Endothelial and Tumor Cells Highlights Counterintuitive Effects of VEGF-Targeted Therapies
Tumor growth and progression are critically dependent on the establishment of a vascular support system. This is often accomplished via the...
