Localized energy for wave equations with degenerate trapping

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of regularity is a common way to incorporate such. When trapping is sufficiently weak, a logarithmic loss of regularity suffices. Here, by studying a warped product manifold introduced by Christianson and Wunsch, we encounter the first explicit example of a situation where an estimate with an algebraic loss of regularity exists and this loss is sharp. Due to the global-in-time nature of the estimate for the wave equation, the situation is more complicated than for the Schr\"{o}dinger equation. An initial estimate with sub-optimal loss is first obtained, where extra care is required due to the low frequency contributions. An improved estimate is then established using energy functionals that are inspired by WKB analysis. Finally, it is shown that the loss cannot be improved by any power by saturating the estimate with a quasimode.Comment: 18 page

State-of-the-art imaging for glioma surgery.

Diffuse gliomas are infiltrative primary brain tumors with a poor prognosis despite multimodal treatment. Maximum safe resection is recommended whenever feasible. The extent of resection (EOR) is positively correlated with survival. Identification of glioma tissue during surgery is difficult due to its diffuse nature. Therefore, glioma resection is imaging-guided, making the choice for imaging technique an important aspect of glioma surgery. The current standard for resection guidance in non-enhancing gliomas is T2 weighted or T2w-fluid attenuation inversion recovery magnetic resonance imaging (MRI), and in enhancing gliomas T1-weighted MRI with a gadolinium-based contrast agent. Other MRI sequences, like magnetic resonance spectroscopy, imaging modalities, such as positron emission tomography, as well as intraoperative imaging techniques, including the use of fluorescence, are also available for the guidance of glioma resection. The neurosurgeon's goal is to find the balance between maximizing the EOR and preserving brain functions since surgery-induced neurological deficits result in lower quality of life and shortened survival. This requires localization of important brain functions and white matter tracts to aid the pre-operative planning and surgical decision-making. Visualization of brain functions and white matter tracts is possible with functional MRI, diffusion tensor imaging, magnetoencephalography, and navigated transcranial magnetic stimulation. In this review, we discuss the current available imaging techniques for the guidance of glioma resection and the localization of brain functions and white matter tracts

Connectivity in MEG resting-state networks increases after resective surgery for low-grade glioma and correlates with improved cognitive performance☆

Purpose Low-grade glioma (LGG) patients often have cognitive deficits. Several disease- and treatment related factors affect cognitive processing. Cognitive outcome of resective surgery is unpredictable, both for improvement and deterioration, especially for complex domains such as attention and executive functioning. MEG analysis of resting-state networks (RSNs) is a good candidate for presurgical prediction of cognitive outcome. In this study, we explore the relation between alterations in connectivity of RSNs and changes in cognitive processing after resective surgery, as a stepping stone to ultimately predict postsurgical cognitive outcome. Methods: Ten patients with LGG were included, who had no adjuvant therapy. MEG recording and neuropsychological assessment were obtained before and after resective surgery. MEG data were recorded during a no-task eyes-closed condition, and projected to the anatomical space of the AAL atlas. Alterations in functional connectivity, as characterized by the phase lag index (PLI), within the default mode network (DMN), executive control network (ECN), and left- and right-sided frontoparietal networks (FPN) were compared to cognitive changes. Results: Lower alpha band DMN connectivity was increased after surgery, and this increase was related to improved verbal memory functioning. Similarly, right FPN connectivity was increased after resection in the upper alpha band, which correlated with improved attention, working memory and executive functioning. Discussion Increased alpha band RSN functional connectivity in MEG recordings correlates with improved cognitive outcome after resective surgery. The mechanisms resulting in functional connectivity alterations after resection remain to be elucidated. Importantly, our findings indicate that connectivity of MEG RSNs may be used for presurgical prediction of cognitive outcome in future studies

The patients' experience of neuroimaging of primary brain tumors: a cross-sectional survey study

PURPOSE: To gain insight into how patients with primary brain tumors experience MRI, follow-up protocols, and gadolinium-based contrast agent (GBCA) use. METHODS: Primary brain tumor patients answered a survey after their MRI exam. Questions were analyzed to determine trends in patients' experience regarding the scan itself, follow-up frequency, and the use of GBCAs. Subgroup analysis was performed on sex, lesion grade, age, and the number of scans. Subgroup comparison was made using the Pearson chi-square test and the Mann-Whitney U-test for categorical and ordinal questions, respectively. RESULTS: Of the 100 patients, 93 had a histopathologically confirmed diagnosis, and seven were considered to have a slow-growing low-grade tumor after multidisciplinary assessment and follow-up. 61/100 patients were male, with a mean age ± standard deviation of 44 ± 14 years and 46 ± 13 years for the females. Fifty-nine patients had low-grade tumors. Patients consistently underestimated the number of their previous scans. 92% of primary brain tumor patients did not experience the MRI as bothering and 78% would not change the number of follow-up MRIs. 63% of the patients would prefer GBCA-free MRI scans if diagnostically equally accurate. Women found the MRI and receiving intravenous cannulas significantly more uncomfortable than men (p = 0.003). Age, diagnosis, and the number of previous scans had no relevant impact on the patient experience. CONCLUSION: Patients with primary brain tumors experienced current neuro-oncological MRI practice as positive. Especially women would, however, prefer GBCA-free imaging if diagnostically equally accurate. Patient knowledge of GBCAs was limited, indicating improvable patient information

Connectomic profile and clinical phenotype in newly diagnosed glioma patients.

Gliomas are primary brain tumors, originating from the glial cells in the brain. In contrast to the more traditional view of glioma as a localized disease, it is becoming clear that global brain functioning is impacted, even with respect to functional communication between brain regions remote from the tumor itself. However, a thorough investigation of glioma-related functional connectomic profiles is lacking. Therefore, we constructed functional brain networks using functional MR scans of 71 glioma patients and 19 matched healthy controls using the automated anatomical labelling (AAL) atlas and interregional Pearson correlation coefficients. The frequency distributions across connectivity values were calculated to depict overall connectomic profiles and quantitative features of these distributions (full-width half maximum (FWHM), peak position, peak height) were calculated. Next, we investigated the spatial distribution of the connectomic profile. We defined hub locations based on the literature and determined connectivity (1) between hubs, (2) between hubs and non-hubs, and (3) between non-hubs. Results show that patients had broader and flatter connectivity distributions compared to controls. Spatially, glioma patients particularly showed increased connectivity between non-hubs and hubs. Furthermore, connectivity distributions and hub-non-hub connectivity differed within the patient group according to tumor grade, while relating to Karnofsky performance status and progression-free survival. In conclusion, newly diagnosed glioma patients have globally altered functional connectomic profiles, which mainly affect hub connectivity and relate to clinical phenotypes. These findings underscore the promise of using connectomics as a future biomarker in this patient population

A quantitative comparison of cognitive performance and patient-reported symptoms in preoperative lower-grade glioma patients from two Dutch Hospitals

Background Protocols for assessment of (neuro)psychological outcomes in lower-grade glioma patients vary between hospitals. This potentially complicates generalization of these outcomes. We compared standardized scores on tests of two frequently impaired cognitive domains (attention and executive functioning (EF)), and two relevant patient-reported outcomes (PROs; depression and fatigue) of two neuro-oncological hospitals that use different measurement instruments. Material and Methods Data were used from preoperative assessments of patients with (IDH-mut) WHO grade II/III glioma tested between 2007 and 2021 at Amsterdam UMC (AMS) or at Elisabeth-Tweesteden Hospital Tilburg (ETZ). AMS patients were referred for (neuro)psychological assessment based on physician and patient preference (paper and pencil tests), whereas all ETZ patients routinely undergo screening (computerized tests). To compare scores of the different attention and EF tests we converted patients’ performances to z-scores based on normative data. For cognitive performance, we compared scores of different cognitive flexibility tests (CST vs SAT), processing speed tests (SDC vs LDMT), and Stroop tests (Stroop I and Stroop III). PROs included the CES-D vs HADS-D and the CIS-fatigue vs MVI-general fatigue (AMS vs ETZ, resp.). Differences were tested using Fisher's, χ 2, and Mann-Whitney U tests. Results Assessments were done median 4 weeks (AMS, n=97, range 19-0 weeks) and 1 day (ETZ, n=106; range 14-0 days) preoperatively. Age, sex, tumor location and histology were comparable between cohorts (p>0.05), but the AMS cohort showed significantly more grade III tumors (36% vs 16%) and more awake surgeries (84% vs 46%). Z-scores measuring attention and EF (n=94 and n=95, AMS vs ETZ) were not significantly different (CST vs SAT, percentage with a disorder (z <-1.5SD) 15% vs 13%; SDC vs LDMT 13% vs 14%; Stroop I 11% vs 18%; Stroop III 13% vs 16% at AMS and ETZ, resp.). Percentages of patients with possible depression (CES-D≥16, n=88 and HADS-D≥8, n=106) did not differ significantly between hospitals (28% vs 26%), nor did percentages of patients with severe fatigue (CIS-fatigue≥35, n=88 and MVI-general fatigue (z <-1.5SD), n=38, 42% vs 24% at AMS and ETZ, resp.). Conclusion Standardized scores of glioma patients on cognitive domains (attention and EF) and PROs (depression and fatigue) did not differ between two centers with slightly different samples using different testing protocols. This cautiously suggests that study findings on cognitive functioning and symptoms could be generalized. For research purposes, conjoint use of pooled populations for outcome evaluation could be explored with different samples from other centers using different instruments