The aim of this article is to study the well-posedness and properties of a fast-slow system which is related with brain lactate kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions and obtain linear stability results. We also give numerical simulations with different values of the small parameter $\varepsilon$ and compare them with experimental data.

BACKGROUND AND PURPOSE: Perfusion and spectroscopic MR imaging provide noninvasive physiologic and metabolic characterization of tissues, which can help in differentiating brain tumors. We investigated the diagnostic role of perfusion and spectroscopic MR imaging using individual and combined classifiers of these modalities and assessed the added performance value that spectroscopy can provide to perfusion using optimal combined classifiers that have the highest differential diagnostic performance to discriminate lymphomas, glioblastomas, and metastases. MATERIALS AND METHODS: From January 2013 to January 2016, fifty-five consecutive patients with histopathologically proved lymphomas, glioblastomas, and metastases were included after undergoing MR imaging. The perfusion parameters (maximum relative CBV, maximum percentage of signal intensity recovery) and spectroscopic concentration ratios (lactate/Cr, Cho/NAA, Cho/Cr, and lipids/Cr) were analyzed individually and in optimal combinations. Differences among tumor groups, differential diagnostic performance, and differences in discriminatory performance of models with quantification of the added performance value of spectroscopy to perfusion were tested using 1-way ANOVA models, receiver operating characteristic analysis, and comparisons between receiver operating characteristic analysis curves using a bivariate χ², respectively. RESULTS: The highest differential diagnostic performance was obtained with the following combined classifiers: maximum percentage of signal intensity recovery–Cho/NAA to discriminate lymphomas from glioblastomas and metastases, significantly increasing the sensitivity from 82.1% to 95.7%; relative CBV–Cho/NAA to discriminate glioblastomas from lymphomas and metastases, significantly increasing the specificity from 92.7% to 100%; and maximum percentage of signal intensity recovery–lactate/Cr and maximum percentage of signal intensity recovery–Cho/Cr to discriminate metastases from lymphomas and glioblastomas, significantly increasing the specificity from 83.3% to 97.0% and 100%, respectively. CONCLUSIONS: Spectroscopy yielded an added performance value to perfusion using optimal combined classifiers of these modalities, significantly increasing the differential diagnostic performances for these common brain tumors.

Three-dimensional surface reconstruction is a well-known task in medical imaging. In procedures for intervention or radiation treatment planning, the generated models should be accurate and reflect the natural appearance. Traditional methods for this task, such as Marching Cubes, use smoothing post processing to reduce staircase artifacts from mesh generation and exhibit the natural look. However, smoothing algorithms often reduce the quality and degrade the accuracy. Other methods, such as MPU implicits, based on adaptive implicit functions, inherently produce smooth 3D models. However, the integration in the implicit functions of both smoothness and accuracy of the shape approximation may impact the precision of the reconstruction. Having these limitations in mind, we propose a hybrid method for 3D reconstruction of MR images. This method is based on a parallel Marching Cubes algorithm called Flying Edges (FE) and Multi-level Partition of Unity (MPU) implicits. We aim to combine the robustness of the Marching Cubes algorithm with the smooth implicit curve tracking enabled by the use of implicit models in order to provide higher geometry precision. Towards this end, the regions that closely fit to the segmentation data, and thus regions that are not impacted by reconstruction issues, are first extracted from both methods. These regions are then merged and used to reconstruct the final model. Experimental studies were performed on a number of MRI datasets, providing images and error statistics generated from our results. The results obtained show that our method reduces the geometric errors of the reconstructed surfaces when compared to the MPU and FE approaches, producing a more accurate 3D reconstruction.

Biotin is thought to improve functional impairment in progressive multiple sclerosis (MS) by upregulating bioenergetic metabolism. We enrolled 19 patients suffering from progressive MS (5 primary and 14 secondary Progressive‐MS). Using cerebral multinuclear magnetic resonance spectroscopy (MMRS) and clinical evaluation before and after 6 months of biotin cure, we showed significant modifications of: PME/PDE, ATP, and lactate resonances; an improvement of EDSS Neuroscore. Our results are consistent with metabolic pathways concerned with biotin action and could suggest the usefulness of MMRS for monitoring.