In silico tumor growth: application to glioblastomas Olivier Clatz 1 , Pierre-Yves Bondiau 1 , Herv´ e Delingette 1 , Gr´ egoire Malandain 1 , Maxime Sermesant 1 , Simon K. Warfield 2 , and Nicholas Ayache 1 1 Epidaure - INRIA Sophia Antipolis | 2 CRL - Harvard Medical School Abstract. We propose a new model to simulate the growth of glioblastomas multiforma (GBM), the most aggressive glial tumors. This model relies upon an anatomical atlas including white fibers diffusion tensor information and the delineation of cerebral structures having a distinct response to the tumor aggression. We simulate both the invasion of the GBM in the brain parenchyma and its mechanical interaction (mass effect) with the invaded structures. The former effect is modeled with a reaction-diffusion equation while the latter is based on a linear elastic brain constitutive equation. In addition, we propose a new equation taking into account the mechanical influence of the tumor cells on the invaded tissues. This tumor growth model is assessed by comparing the virtual GBM growth with the real GBM growth observed between two MRIs of a patient acquired with six months difference. 1 Introduction 1.1 Motivation The majority of the primitive tumors of the central nervous system are from glial origin, among which the glioblastomas multiforma (GBM) are the most aggressive. Without therapy, patients with GBMs usually die within 10 months. Despite the sub- stantial research effort for improving tumors treatment, patients treated with state- of-the-art therapy have a median survival of approximately 1.5 year. Relatively little progress has been made toward the construction of a general model describing the growth of these tumors. The interest to carry out a simulation of the tumoral growth for improving the treatment is twofold. First, it could provide addi- tional information about the tumor invasion and help determining the local treatment margins. Second, by quantifying the malignant cell concentration in low contrast areas of MR images, it could also be useful in the selection of the radiotherapy dose. 1.2 Contributions We propose a patient-specific simulator of glioblastoma growth, including the induced brain deformation (mass effect). The simulation relies upon a Finite Element Model (FEM) initialized from the patient MRIs. Additional information has been included into the patient model to take into account the behavior of different structures with respect to tumor invasion, such as the white matter fiber directions (see [3] for de- tails about the atlas construction). Furthermore, we propose to link the classification of tumors in Gross Tumor Volumes (GTV) proposed in protocols for radiotherapy treatment with different tumor invasion behaviour: