A Stochastic Fluid Model Approach to the Stationary Distribution of the Maximum Priority Process

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in situations where a performance target in terms of the tails of the class-dependent waiting time distributions has to be met, such models of priority queueing may not be satisfactory. In fact, there could be situations where high priority classes easily meet their performance target for the maximum waiting time, while lower classes do not. Here, we are interested in the stationary distribution at the times of commencement of service of this maximum priority process. Until now, there has been no explicit expression for this distribution. We construct a mapping of the maximum priority process to a tandem fluid queue, which enables us to find expressions for this stationary distribution. We derive the results for the stationary distribution of the maximum priority process at the times of the commencement of service.Comment: The Eleventh International Conference on Matrix-Analytic Methods in Stochastic Models (MAM11), 2022, Seoul, Republic of Kore

Clinical relevance of the radiation dose bath in lower grade glioma, a cross-sectional pilot study on neurocognitive and radiological outcome

AIM: To investigate the clinical relevance of the radiotherapy (RT) dose bath in patients treated for lower grade glioma (LGG). METHODS: Patients (n = 17) treated with RT for LGG were assessed with neurocognitive function (NCF) tests and structural Magnetic Resonance Imaging (MRI) and categorized in subgroups based on tumour lateralisation. RT dose, volumetric results and cerebral microbleed (CMB) number were extracted for contralateral cerebrum, contralateral hippocampus, and cerebellum. The RT clinical target volume (CTV) was included in the analysis as a surrogate for focal tumour and other treatment effects. The relationships between RT dose, CTV, NCF and radiological outcome were analysed per subgroup. RESULTS: The subgroup with left-sided tumours (n = 10) performed significantly lower on verbal tests. The RT dose to the right cerebrum, as well as CTV, were related to poorer performance on tests for processing speed, attention, and visuospatial abilities, and more CMB. In the subgroup with right-sided tumours (n = 7), RT dose in the left cerebrum was related to lower verbal memory performance, (immediate and delayed recall, r = −0.821, p = 0.023 and r = −0.937, p = 0.002, respectively), and RT dose to the left hippocampus was related to hippocampal volume (r = −0.857, p = 0.014), without correlation between CTV and NCF. CONCLUSION: By using a novel approach, we were able to investigate the clinical relevance of the RT dose bath in patients with LGG more specifically. We used combined MRI-derived and NCF outcome measures to assess radiation-induced brain damage, and observed potential RT effects on the left-sided brain resulting in lower verbal memory performance and hippocampus volume

Voxel based morphometry-detected white matter volume loss after multi-modality treatment in high grade glioma patients.

BackgroundRadiotherapy (RT) and chemotherapy are components of standard multi-modality treatment of high grade gliomas (HGG) aimed at achieving local tumor control. Treatment is neurotoxic and RT plays an important role in this, inducing damage even distant to the RT target volume.PurposeThis retrospective longitudinal study evaluated the effect of treatment on white matter and gray matter volume in the tumor-free hemisphere of HGG patients using voxel based morphometry (VBM).Method3D T1-weighted MR images of 12 HGG patients at multiple timepoints during standard treatment were analyzed using VBM. Segmentation of white matter and gray matter of the tumor-free hemisphere was performed. Multiple general linear models were used to asses white matter and gray matter volumetric differences between time points. A mean RT dose map was created and compared to the VBM results.ResultsDiffuse loss of white matter volume, mainly throughout the frontal and parietal lobe, was found, grossly overlapping regions that received the highest RT dose. Significant loss of white matter was first noticed after three cycles of chemotherapy and persisted after the completion of standard treatment. No significant loss of white matter volume was observed between pre-RT and the first post-RT follow-up timepoint, indicating a delayed effect.ConclusionThis study demonstrated diffuse and early-delayed decreases in white matter volume of the tumor-free hemisphere in HGG patients after standard treatment. White matter volume changes occurred mainly throughout the frontal and parietal lobe and grossly overlapped with areas that received the highest RT dose