A multi-layered hybrid model for cancer cell invasion.

In this article, a hybrid model is developed based on multi-scale concept for solid  tumour cell invasion into a healthy tissue. Our aim is to study the tumour heterogeneity due to the geometry of a growing tumour caused by the phenotypic transformations of cells. In this context, an early vascular growth is considered after angiogenesis. Hence, the microenvironment of the solid tumour is rich of oxygen and nutrients. It is also considered that epidermal growth factor (EGF) is distributed into the surrounding extracellular matrix (ECM) of the tumour. The developed multi-layered model consists of three layers: intracellular or subcellular, cellular, and extracellular or tissue layer. The model integrates the events that occur simultaneously in these three layers to identify the underlying diversity. Here, every cell is represented as an agent. Characteristics of an agent are controlled by its intracellular protein expressions and its surrounding microenvironment. A mature proliferative or migratory or hybrid cell agent spawn two indistinguishable children unless it may convert into other phenotype due to influence of the microenvironment. Further, a simple cell cycle model is adapted which is influenced by EGF-EGFR signalling pathway and the external oxygen and nutrients. Moreover, migratory and hybrid cells secrete several matrix degrading enzymes (MDEs) which remodel the ECM for tumour invasion locally. Several biomechanical forces are considered that simultaneously act on the cancer cells. The outcome of the model is very similar to the results reported in earlier studies. The model shows the characteristics of cancer invasion that include sustainable proliferation by ignoring growth suppressor signals and reproduction of cancer cells at abnormal proportion, restrict apoptosis, and invade into the surrounding tissue. As the simulation parameters get modified due to different biochemical and biophysical processes, the robustness of the model is determined. It is found that only a number of proliferative cells are moderately sensitive to the parameters and others are less-sensitive.

A multi-scale agent-based model for avascular tumour growth.

In this paper, we have developed a multi-scale, lattice-free, agent based model of avascular tumour growth in epithelial tissue. The model integrates different events to identify the underlying diversity within intracellular, cellular, and extracellular layer dynamics. The model considers every cell as an agent. A cellular agent may proliferate, spawns two identical daughter agents, or it may be transformed into other phenotypes during its life time depending on its internal proteins' activity as well as its external microenvironment. In this context, a simplified age-structured cell cycle model is adopted from the existing literature. The model considers that the intracellular events are regulated by p27 gene expression. In this model, p27 protein controls the overall tumour growth dynamics. Moreover, p27 is controlled by the external oxygen and nutrients that are modelled with the reaction-diffusion equations. The model also considers several biophysical forces which directly effect on the tumour growth dynamics. This modelling framework offers biologically realistic outcomes and also covers important criteria of the hallmarks of cancer which include oxygen and nutrient consumptions, micro-environmental heterogeneity, tumour cell proliferation by avoiding growth suppressor signals, replication of tumour cells at an abnormally faster rate, and resistance of apoptosis. The avascular tumour growth model is validated with immunohistochemistry and histopathology data. The outcome of the proposed model is very close to the range of the patient data, which concludes that the model is capable enough to mimic these complex biophysical phenomena.

Avascular tumour growth models based on anomalous diffusion.

In this study, we model avascular tumour growth in epithelial tissue. This can help us to understand that how an avascular tumour interacts with its microenvironment and what type of physical changes can be observed within the tumour spheroid before angiogenesis. This understanding is likely to assist in the development of better diagnostics, improved therapies, and prognostics. In biological systems, most of the diffusive processes are through cellular membranes which are porous in nature. Due to its porous nature, diffusion in biological systems are heterogeneous. The fractional diffusion equation is well suited to model heterogeneous biological systems, though most of the early studies did not use this fact. They described tumour growth with simple diffusion-based model. We have developed a spherical model based on simple diffusion initially, and then the model is upgraded with fractional diffusion equations to express the anomalous nature of biological system. In this study, two types of fractional models are developed: one of fixed order and the other of variable order. The memory formalism technique is also included in these anomalous diffusion models. These three models are investigated from phenomenological point view by measuring some parameters for characterizing avascular tumour growth over time. Tumour microenvironment is very complex in nature due to several concurrent molecular mechanisms. Diffusion with memory (fixed as well as variable) formation may be an oversimplified technique, and does not reflect the detailed view of the tumour microenvironment. However, it is found that all the models offer realistic and insightful information of the tumour microenvironment at the macroscopic level, and approximate well the physical phenomena. Also, it is observed that the anomalous diffusion based models offer a closer description to clinical facts than the simple model. As the simulation parameters get modified due to different biochemical and biophysical processes, the robustness of the model is determined. It is found that the anomalous diffusion models are moderately sensitive to the parameters.