A three-dimensional model of cell movement in multicellular systems
Future Generation Computer Systems - Special issue on particle based modelling methods applied in biology
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Mathematical Models of Avascular Tumor Growth
SIAM Review
Finite element models for mechanical simulation of coronary arteries
FIMH'03 Proceedings of the 2nd international conference on Functional imaging and modeling of the heart
A computational model of cellular morphogenesis in plants
ECAL'05 Proceedings of the 8th European conference on Advances in Artificial Life
Individual-based approaches to birth and death in avascu1ar tumors
Mathematical and Computer Modelling: An International Journal
A model for the volumetric growth of a soft tissue
Mathematical and Computer Modelling: An International Journal
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The biomechanical modeling of growing tissues has recently become an area of intense interest. In particular, the interplay between growth patterns and mechanical stress is of great importance, with possible applications to arterial mechanics, embryo morphogenesis, tumor development, and bone remodeling. This review aims to give an overview of the theories that have been used to model these phenomena, categorized according to whether the tissue is considered as a continuum object or a collection of cells. Among the continuum models discussed is the deformation gradient decomposition method, which allows a residual stress field to develop from an incompatible growth field. The cell-based models are further subdivided into cellular automata, center-dynamics, and vertex-dynamics models. Of these the second two are considered in more detail, especially with regard to their treatment of cell-cell interactions and cell division. The review concludes by assessing the prospects for reconciliation between these two fundamentally different approaches to tissue growth, and by identifying possible avenues for further research.