  The growth of several biological tissues is known to be controlled in part by
local geometrical features, such as the curvature of the tissue interface. This
control leads to changes in tissue shape that in turn can affect the tissue's
evolution. Understanding the cellular basis of this control is highly
significant for bioscaffold tissue engineering, the evolution of bone
microarchitecture, wound healing, and tumour growth. While previous models have
proposed geometrical relationships between tissue growth and curvature, the
role of cell density and cell vigor remains poorly understood. We propose a
cell-based mathematical model of tissue growth to investigate the systematic
influence of curvature on the collective crowding or spreading of
tissue-synthesising cells induced by changes in local tissue surface area
during the motion of the interface. Depending on the strength of diffusive
damping, the model exhibits complex growth patterns such as undulating motion,
efficient smoothing of irregularities, and the generation of cusps. We compare
this model with in-vitro experiments of tissue deposition in bioscaffolds of
different geometries. By accounting for the depletion of active cells, the
model is able to capture both smoothing of initial substrate geometry and
tissue deposition slowdown as observed experimentally.
