Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation

By O. Clatz, Maxime Sermesant, P. Bondiau, H. Delingette, Simon Keith Warfield, Grégoire Malandain, Nicholas Ayache. IEEE Transactions on Medical Imaging, 2005

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A class of time‐fractional reaction‐diffusion equation with nonlocal boundary condition (2018, background): “It is obvious to understand that the above form of FODE (2) equivalent to the following form of integral equation31: u(t) = u(0) + 1 Γ(α) ∫ t”
Spatial normalization of lesioned brains: Performance evaluation and impact on fMRI analyses (2007, neutral): “The importance of these issues is reflected on the large body of work modeling the effect of lesions on anatomy (Cuadra et al., 2004; Mohamed et al., 2006; Xue et al., 2006; Dawant et al., 2002; Clatz et al., 2005).”
Deformable Medical Image Registration: A Survey (2013, methodology): “In [181], after an initial a ne registration between a normal atlas and the patient's image, a coupled model that predicts the anisotropic evolution of the tumor as well as its mass-e ect was applied.”