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Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…
This paper deals with the cellular biological network analysis of the tumor-growth model, consisting of multiple spaces and time scales. In this paper, we present a model in graph simulation using ABM for tumor growth. In particular, we…
Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the…
Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding…
The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that…
Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer…
Recent advances in cancer research largely rely on new developments in microscopic or molecular profiling techniques offering high level of detail with respect to either spatial or molecular features, but usually not both. Here, we present…
I begin with a brief history of N-body simulation and visualization and then go on to describe various methods for creating images and animations of modern simulations in cosmology and galactic dynamics. These techniques are incorporated…
At present it is still quite difficult to match the vast knowledge on the behavior of individual tumor cells with macroscopic measurements on clinical tumors. On the modeling side, we already know how to deal with many molecular pathways…
In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors with radiotherapy influence. Under certain assumptions on the given data in the model, we prove existence and uniqueness of a weak…
We study multicellular tumor spheroids by introducing a new three-dimensional agent-based Voronoi/Delaunay hybrid model. In this model, the cell shape varies from spherical in thin solution to convex polyhedral in dense tissues. The next…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…
Brain injuries resulting from mechanical trauma represent an ongoing global public health issue. Several $\textit{in vitro}$ and $\textit{in vivo}$ models for traumatic brain injury (TBI) continue to be developed for delineating the various…
The use of high-fidelity computational simulations promises to enable high-throughput hypothesis testing and optimisation of cancer therapies. However, increasing realism comes at the cost of increasing computational requirements. This…
A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a…
Computational pathology is part of precision oncology medicine. The integration of high-throughput data including genomics, transcriptomics, proteomics, metabolomics, pathomics, and radiomics into clinical practice improves cancer treatment…
A computational model of aquaporin regulation in cancer cells has been constructed as a Qualitative Network in the software BioModelAnalyzer (BMA). The model connects some important aquaporins expressed in human cancer to common phenotypes…
Fully immersive virtual reality (VR) has the potential to improve neurosurgical planning. For example, it may offer 3D visualizations of relevant anatomical structures with complex shapes, such as blood vessels and tumors. However, there is…
This paper investigates cells proliferation dynamics in small tumor cell aggregates using an individual based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as…
Computational models and simulations are not just appealing because of their intrinsic characteristics across spatiotemporal scales, scalability, and predictive power, but also because the set of problems in cancer biomedicine that can be…