The growth of a tumoral multicellular spheroid is considered in the framework of Continuum Mechanics, describing the body as a specific growing soft tissue. The volumetric growth and the mechanical response are ideally decoupled by an algebraic decomposition of the gradient of deformation tensor. The model is then applied to describe the volumetric growth of a multicell spheroid embedded in a gel under a non-homogeneous availability of nutrients. Thanks to spherical symmetry, the equations read as two sets of ordinary differential equations defined on subdomains separated by a moving interface. The equations are numerically integrated by an implicit finite difference scheme, the interface conditions being satisfied by a Dirichlet-Neumann iterative procedure. The numerical results confirm that residual stresses are generated because of the inhomogeneous growth.
Numerical simulation of the growth of a multicellular spheroid
MOLLICA, Francesco
2003
Abstract
The growth of a tumoral multicellular spheroid is considered in the framework of Continuum Mechanics, describing the body as a specific growing soft tissue. The volumetric growth and the mechanical response are ideally decoupled by an algebraic decomposition of the gradient of deformation tensor. The model is then applied to describe the volumetric growth of a multicell spheroid embedded in a gel under a non-homogeneous availability of nutrients. Thanks to spherical symmetry, the equations read as two sets of ordinary differential equations defined on subdomains separated by a moving interface. The equations are numerically integrated by an implicit finite difference scheme, the interface conditions being satisfied by a Dirichlet-Neumann iterative procedure. The numerical results confirm that residual stresses are generated because of the inhomogeneous growth.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
