Mathematical Modeling for Patient-specific Assessment of Tumor Margins for Glioma

Malignant glioma make up about half of all primary brain tumors in adults. These rapidly growing neoplasms are characterized by direct invasion of the neighboring brain tissue and occur in all age classes, being most frequent in later life. Due to their high proliferation rate and diffusive tumor infiltration it is actually impossible to achieve an exhaustive resection, which leads to clinical challenges and high mortality of the affected patients. The most frequent and aggressive form of these tumors, glioblastoma multiforme (GBM), has a median survival time of 60 weeks, in spite of state of the art treatment including resection, radio-, and chemotherapy.

Noninvasive medical imaging like MRI and CT offer valuable diagnostic tools, however they inherently provide only a macroscopic classification of active and necrotic tumor areals and surrounding edema; the microscopic tumor extent remains invisible. Together with the diffusive spread of cancer cells and the patient-specific tumor evolution, this renders a personalized approach to diagnose and therapy necessary. While resection has to be guided by the macroscopic tumor and the surrounding brain regions to be spared, and while chemotherapy is a systemic approach, radiotherapy would greatly benefit from the personalized planning relying on patient-specific microscopic tumor spread and infiltration.


(Picture by Dr. Y. Dzierma, UKS Homburg )

Mathematical models using this incomplete MRI/CT information about individual tumors in order to predict their spread in healthy tissue can contribute decisively towards diagnose and treatment enhancement. They offer the means to account in silicofor highly complex biological and biomedical processes, the study of which would be in vivotoo expensive – if at all feasible. Such processes include acid-mediated invasion, hypoxia-driven angiogenesis, tissue degradation and remodeling by tumor cells, intrinsic and extrinsic uncertainties, multiscality, sensitivity towards various therapy approaches.

The overarching goal of the GlioMaTh project „Glioma, Mathematical Models, and Therapy“ funded by the German Federal Ministry of Education and Research is to offer model- and simulation based prognoses of glioma spread in individual brain structures assessed via diffusion tensor imaging (DTI), in order to facilitate enhanced therapy strategies. Thus the focus lies on one of the most important aspects of the highly complex therapy optimization process: the mathematically obtained prognoses are supposed to lead to more precise CTVs (clinical target volumes) and PTVs (planning target volumes), which are to be used as an input for the medical planning software available in the clinic, thereby supporting the medical specialists in establishing the actual contours of brain tumors and correspondingly adapting the therapy.


(3D Simulations of glioma spread from a mathematical model, Engwer, Hunt, Surulescu, Math. Med. Biol. 2015)

Project partners: TU Kaiserslautern, WWU Münster, Universitätsklinikum des Saarlandes, Klinik für Strahlentherapie und Radioonkologie (Prof. Dr. Ch. Rübe), Klinik für Diagnostische und Interventionelle Neuroradiologie (Prof. Dr. W. Reith), Precisis AG.

For more information please visit the project website:

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