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Mathematical modelling of solid tumour growth: a Dynamical Density Functional Theory-based model

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posted on 30.10.2018, 16:23 by Hayder M. Al-Saedi
We present a theoretical framework based on an extension of Dynamical Density Functional Theory (DDFT) to describe the structure and dynamics of cells in living tissues and tumours. DDFT is a microscopic statistical mechanical theory for the time evolution of the density distribution of interacting many-particle systems. The theory accounts for cell pair-interactions, different cell types, phenotypes and cell birth and death processes (including cell division), in order to provide a biophysically consistent description of processes bridging across the scales, including the description of the tissue structure down to the level of the individual cells. Analysis of the model is presented for a single species and a two-species cases, the latter describing competition between a cancerous and healthy cells. In suitable parameter regimes, model results are consistent with biological observations. Of particular note, divergent tumour growth behaviour, mirroring metastatic and benign growth characteristics, are shown to be dependent on the cell pair-interaction parameters.


Iraq, Ministry of Higher Education and Scientific Research.



  • Science


  • Mathematical Sciences


© H.M. Al-Saedi

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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at:

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A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.