Glioblastomas are among the most lethal cancers, with a 5 year survival rate below 25%. Temozolomide is typically used in glioblastoma treatment; however, the enzymes alkylpurine-DNA-N-glycosylase (APNG) and methylguanine-DNA-methyltransferase (MGMT) efficiently mediate the repair of DNA damage caused by temozolomide, reducing treatment efficacy. Consequently, APNG and MGMT inhibition has been proposed as a way of overcoming chemotherapy resistance. Here, we develop a mechanistic mathematical model that explicitly incorporates the effects of chemotherapy on tumour cells, including the processes of DNA damage induction, cell arrest and DNA repair. Our model is carefully parametrized and validated, and then used to virtually recreate the response of heteroclonal glioblastomas to dual treatment with temozolomide and inhibitors of APNG/MGMT. Using our mechanistic model, we identify four combination treatment strategies optimized by tumour cell phenotype, and isolate the strategy most likely to succeed in a pre-clinical and clinical setting. If confirmed in clinical trials, these strategies have the potential to offset chemotherapy resistance in patients with glioblastoma and improve overall survival.

Vascular endothelial growth factor (VEGF) is the most studied family of soluble, secreted mediators of endothelial cell migration, survival, and proliferation. VEGF exerts its function by binding to specific tyrosine kinase receptors on the cell surface and transducing the effect through downstream signaling. In order to study the influence of VEGF binding on endothelial cell motion, we develop a hybrid model of VEGF-induced angiogenesis, based on the theory of reinforced random walks. The model includes the chemotactic response of endothelial cells to angiogenic factors bound to cell-surface receptors, rather than approximating this as a function of extracellular chemical concentrations. This allows us to capture biologically observed phenomena such as activation and polarization of endothelial cells in response to VEGF gradients across their lengths, as opposed to extracellular gradients throughout the tissue. We also propose a novel and more biologically reasonable functional form for the chemotactic sensitivity of endothelial cells, which is also governed by activated cell-surface receptors. This model is able to predict the threshold level of VEGF required to activate a cell to move in a directed fashion as well as an optimal VEGF concentration for motion. Model validation is achieved by comparison of simulation results directly with experimental data.

Due to its dependence on androgens, metastatic prostate cancer is typically treated with continuous androgen ablation. However, such therapy eventually fails due to the emergence of castration-resistance cells. It has been hypothesized that intermittent androgen ablation can delay the onset of this resistance. In this paper, we present a biochemically-motivated ordinary differential equation model of prostate cancer response to anti-androgen therapy, with the aim of predicting optimal treatment protocols based on individual patient characteristics. Conditions under which intermittent scheduling is preferable over continuous therapy are derived analytically for a variety of castration-resistant cell phenotypes. The model predicts that while a cure is not possible for androgen-independent castration-resistant cells, continuous therapy results in longer disease-free survival periods. However, for androgen-repressed castration-resistant cells, intermittent therapy can significantly delay the emergence of resistance, and in some cases induce tumor regression. Numerical simulations of the model lead to two interesting cases, where even though continuous therapy may be non-viable, an optimally chosen intermittent schedule leads to tumor regression, and where a sub-optimally chosen intermittent schedule can initially appear to result in a cure, it eventually leads to resistance emergence. These results demonstrate the model's potential impact in a clinical setting.

Agent-based modeling (ABM) is a powerful computational approach for studying complex biological and biomedical systems, yet its widespread use remains limited by significant computational demands. As models become increasingly sophisticated, the number of parameters and interactions rises rapidly, exacerbating the so-called “curse of dimensionality” and making comprehensive parameter exploration and uncertainty analyses computationally prohibitive. A growing body of work points to surrogate modeling as a powerful approach for approximating the dynamics of agent-based models, providing computationally efficient pathways for tasks such as parameter estimation, sensitivity analysis, and uncertainty quantification. In this review, we examine traditional approaches for performing these tasks directly within ABMs-providing a baseline for comparison-and then synthesize recent developments in surrogate-assisted methodologies for biological and biomedical applications. We cover statistical, mechanistic, and machine-learning-based approaches, emphasizing emerging hybrid strategies that integrate mechanistic insights with machine learning to balance interpretability and scalability. Finally, we discuss current challenges and outline directions for future research, including the development of standardized benchmarks to enhance methodological rigor and facilitate the broad adoption of surrogate-assisted ABMs in biology and medicine.