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A Genuinely Hybrid, Multiscale 3D Cancer Invasion and Metastasis Modelling Framework
We introduce in this paper substantial enhancements to a previously proposed hybrid multiscale cancer invasion modelling framework to better reflect...
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Exact Traveling Wave Solutions of One-Dimensional Models of Cancer Invasion
AbstractIn this paper, we obtain exact analytical solutions of equations of continuous mathematical models of tumor growth and invasion based on the...
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Stochastic differential equation modelling of cancer cell migration and tissue invasion
Invasion of the surrounding tissue is a key aspect of cancer growth and spread involving a coordinated effort between cell migration and matrix...
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The Tumor Invasion Paradox in Cancer Stem Cell-Driven Solid Tumors
Cancer stem cells (CSCs) are key in understanding tumor growth and tumor progression. A counterintuitive effect of CSCs is the so-called tumor growth...
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Mathematical Modelling of Cancer Invasion: A Review
A defining feature of cancer is the capability to spread locally into the surrounding tissue, with cancer cells spreading beyond any normal...
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Modelling microtube driven invasion of glioma
Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of...
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The Search for Cancer Drivers
During the past decade, significant technological and computational advances have provided unprecedented opportunities for gaining a better...
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The First Step Towards the Mathematical Understanding of the Role of Matrix Metalloproteinase-8 in Cancer Invasion
The role of matrix metalloproteinases-8 (MMP-8) in the cancer progression is quite complex, with contradictory indications as to whether it...
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Cancer Fingerprints by Topological Data Analysis
Topological data analysis has arisen has a promising tool to extract information on the structure of a wide variety of datasets. We analyze here its...
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Numerical analysis of a chemotaxis model for tumor invasion
This paper is devoted to the study of a time-discrete scheme and its corresponding fully discretization approximating a d -dimensional chemotaxis...
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Optimal Control of HPV Infection and Cervical Cancer Cells with Beddington–DeAngelis Functional Response
The uncontrollable proliferation of human papillomavirus (HPV) can cause severe cervical cancer. The objective of this work is to study the optimal...
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Breast Cancer Exosomal microRNAs Facilitate Pre-Metastatic Niche Formation in the Bone: A Mathematical Model
Pre-metastatic niche is a location where cancer cells, separating from a primary tumor, find “fertile soil” for growth and proliferation, ensuring...
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Free Boundary Problem of Cell Deformation and Invasion
A novel approach of free boundary problem of invadopodia formation and invasion is proposed in this paper. The modeling of invadopodia formation and...
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Existence of solutions of cancer invasion parabolic system with integrable data
In this work, we consider the model which describes the interactions of cancer cells with healthy cells and matrix degrading enzymes. This model...
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Modelling Cell Invasion: A Review of What JD Murray and the Embryo Can Teach Us
Cell invasion and cell plasticity are critical to human development but are also striking features of cancer metastasis. By distributing a...
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Blow-Up Phenomena of a Cancer Invasion Model with Nonlinear Diffusion and Haptotaxis Term
In this paper, we consider a nonlinear cancer invasion mathematical model with proliferation, growth and haptotaxis effects. We obtain lower bounds...
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Directionality of Macrophages Movement in Tumour Invasion: A Multiscale Moving-Boundary Approach
Invasion of the surrounding tissue is one of the recognised hallmarks of cancer (Hanahan and Weinberg in Cell 100: 57–70, 2000.
https://doi.org/10.1016/S0092-8674(00)81683-9... 
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Global Solvability and Optimal Control to a Haptotaxis Cancer Invasion Model with Two Cancer Cell Species
This paper deals with an optimal control problem for a haptotaxis model which describes two types of cancer cell invading the surrounding healthy...
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Cell-Scale Degradation of Peritumoural Extracellular Matrix Fibre Network and Its Role Within Tissue-Scale Cancer Invasion
Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. During the complex interaction...
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Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion
Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired...
