Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures

Co-Deletion of Chromosome 1p/19q and IDH1/2 Mutation in Glioma Subsets of Brain Tumors in Chinese Patients

OBJECTIVE: To characterize co-deletion of chromosome 1p/19q and IDH1/2 mutation in Chinese brain tumor patients and to assess their associations with clinical features. METHODS: In a series of 528 patients with gliomas, pathological and radiological materials were reviewed. Pathological constituents of tumor subsets, incidences of 1p/19q co-deletion and IDH1/2 mutation in gliomas by regions and sides in the brain were analyzed. RESULTS: Overall, 1p and 19q was detected in 339 patients by FISH method while the sequence of IDH1/2 was determined in 280 patients. Gliomas of frontal, temporal and insular origin had significantly different pathological constituents of tumor subsets (P<0.001). Gliomas of frontal origin had significantly higher incidence of 1p/19q co-deletion (50.4%) and IDH1/2 mutation (73.5%) than those of non-frontal origin (27.0% and 48.5%, respectively) (P<0.001), while gliomas of temporal origin had significantly lower incidence of 1p/19q co-deletion (23.9%) and IDH1/2 mutation (41.7%) than those of non-temporal origin (39.9% and 63.2%, respectively) (P = 0.013 and P = 0.003, respectively). Subgroup analysis confirmed these findings in oligoastrocytic and oligodendroglial tumors, respectively. Although the difference of 1p/19q co-deletion was not statistically significant in temporal oligodendroglial tumors, the trend was marginally significant (P = 0.082). However, gliomas from different sides of the brain did not show significant different pathological constituents, incidences of 1p/19q co-deletion or IDH1/2 mutation. CONCLUSION: Preferential distribution of pathological subsets, 1p/19q co-deletion and IDH1/2 mutation were confirmed in some brain regions in Chinese glioma patients, implying their distinctive tumor genesis and predictive value for prognosis

Genomic aberrations associated with outcome in anaplastic oligodendroglial tumors treated within the EORTC phase III trial 26951

Despite similar morphological aspects, anaplastic oligodendroglial tumors (AOTs) form a heterogeneous clinical subgroup of gliomas. The chromosome arms 1p/19q codeletion has been shown to be a relevant biomarker in AOTs and to be perfectly exclusive from EGFR amplification in gliomas. To identify new genomic regions associated with prognosis, 60 AOTs from the EORTC trial 26951 were analyzed retrospectively using BAC-array-based comparative genomic hybridization. The data were processed using a binary tree method. Thirty-three BACs with prognostic value were identified distinguishing four genomic subgroups of AOTs with different prognosis (p < 0.0001). Type I tumors (25%) were characterized by: (1) an EGFR amplification, (2) a poor prognosis, (3) a higher rate of necrosis, and (4) an older age of patients. Type II tumors (21.7%) had: (1) loss of prognostic BACs located on 1p tightly associated with 19q deletion, (2) a longer survival, (3) an oligodendroglioma phenotype, and (4) a frontal location in brain. Type III AOTs (11.7%) exhibited: (1) a deletion of prognostic BACs located on 21q, and (2) a short survival. Finally, type IV tumors (41.7%) had different genomic patterns and prognosis than type I, II and III AOTs. Multivariate analysis showed that genomic type provides additional prognostic data to clinical, imaging and pathological features. Similar results were obtained in the cohort of 45 centrally reviewed–validated cases of AOTs. Whole genome analysis appears useful to screen the numerous genomic abnormalities observed in AOTs and to propose new biomarkers particularly in the non-1p/19q codeleted AOTs