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Most biological tissues grow by the synthesis of new material close to thetissue's interface, where spatial interactions can exert strong geometricinfluences on the local rate of growth. These geometric influences may bemechanistic, or cell behavioural in nature. The control of geometry on tissuegrowth has been evidenced in many in-vivo and in-vitro experiments, includingbone remodelling, wound healing, and tissue engineering scaffolds. In thispaper, we propose a generalisation of a mathematical model that captures themechanistic influence of curvature on the joint evolution of cell density andtissue shape during tissue growth. This generalisation allows us to simulateabrupt topological changes such as tissue fragmentation and tissue fusion, aswell as three dimensional cases, through a level-set-based method. Thelevel-set method developed introduces another Eulerian field than the level-setfunction. This additional field represents the surface density of tissuesynthesising cells, anticipated at future locations of the interface. Numericaltests performed with this level-set-based method show that numericalconservation of cells is a good indicator of simulation accuracy, particularlywhen cusps develop in the tissue's interface. We apply this new model toseveral situations of curvature-controlled tissue evolutions that includefragmentation and fusion.

A level-set method for the evolution of cells and tissue during curvature-controlled growth