Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables

Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems, namely Hamilton-Jacobi, Helmholtz and time-independent Schrödinger equations with potential on N-dimensional Riemannian and pseudo-Riemannian manifolds, but with a linear side condition, where more structure is available. We show that the requirement of N−1 commuting second-order symmetry operators, modulo a second-order linear side condition corresponds to nonregular separation of variables in an orthogonal coordinate system, characterized by a generalized Stäckel matrix. The coordinates and solutions obtainable through true nonregular separation are distinct from those arising through regular separation of variables. We develop the theory for these systems and provide examples

Characterizing Sensitive Cardiac Substructure Excursion Due to Respiration

PURPOSE: Whole-heart dose metrics are not as strongly linked to late cardiac morbidities as radiation doses to individual cardiac substructures. Our aim was to characterize the excursion and dosimetric variation throughout respiration of sensitive cardiac substructures for future robust safety margin design. METHODS AND MATERIALS: Eleven patients with cancer treatments in the thorax underwent 4-phase noncontrast 4-dimensional computed tomography (4DCT) with T2-weighted magnetic resonance imaging in end-exhale. The end-exhale phase of the 4DCT was rigidly registered with the magnetic resonance imaging and refined with an assisted alignment surrounding the heart from which 13 substructures (chambers, great vessels, coronary arteries, etc) were contoured by a radiation oncologist on the 4DCT. Contours were deformed to the other respiratory phases via an intensity-based deformable registration for radiation oncologist verification. Measurements of centroid and volume were evaluated between phases. Mean and maximum dose to substructures were evaluated across respiratory phases for the breast (n = 8) and thoracic cancer (n = 3) cohorts. RESULTS: Paired t tests revealed reasonable maintenance of geometric and anatomic properties (P \u3c .05 for 4/39 volume comparisons). Maximum displacements \u3e5 mm were found for 24.8%, 8.5%, and 64.5% of the cases in the left-right, anterior-posterior, and superior-inferior axes, respectively. Vector displacements were largest for the inferior vena cava and the right coronary artery, with displacements up to 17.9 mm. In breast, the left anterior descending artery D(mean) varied 3.03 ± 1.75 Gy (range, 0.53-5.18 Gy) throughout respiration whereas lung showed patient-specific results. Across all patients, whole heart metrics were insensitive to breathing phase (mean and maximum dose variations \u3c0.5 Gy). CONCLUSIONS: This study characterized the intrafraction displacement of the cardiac substructures through the respiratory cycle and highlighted their increased dosimetric sensitivity to local dose changes not captured by whole heart metrics. Results suggest value of cardiac substructure margin generation to enable more robust cardiac sparing and to reduce the effect of respiration on overall treatment plan quality

Diffusion tensor imaging of post mortem multiple sclerosis brain.

Magnetic resonance imaging (MRI) is being used to probe the central nervous system (CNS) of patients with multiple sclerosis (MS), a chronic demyelinating disease. Conventional T(2)-weighted MRI (cMRI) largely fails to predict the degree of patients' disability. This shortcoming may be due to poor specificity of cMRI for clinically relevant pathology. Diffusion tensor imaging (DTI) has shown promise to be more specific for MS pathology. In this study we investigated the association between histological indices of myelin content, axonal count and gliosis, and two measures of DTI (mean diffusivity [MD] and fractional anisotropy [FA]), in unfixed post mortem MS brain using a 1.5-T MR system. Both MD and FA were significantly lower in post mortem MS brain compared to published data acquired in vivo. However, the differences of MD and FA described in vivo between white matter lesions (WMLs) and normal-appearing white matter (NAWM) were retained in this study of post mortem brain: average MD in WMLs was 0.35x10(-3) mm(2)/s (SD, 0.09) versus 0.22 (0.04) in NAWM; FA was 0.22 (0.06) in WMLs versus 0.38 (0.13) in NAWM. Correlations were detected between myelin content (Tr(myelin)) and (i) FA (r=-0.79, p<0.001), (ii) MD (r=0.68, p<0.001), and (iii) axonal count (r=-0.81, p<0.001). Multiple regression suggested that these correlations largely explain the apparent association of axonal count with (i) FA (r=0.70, p<0.001) and (ii) MD (r=-0.66, p<0.001). In conclusion, this study suggests that FA and MD are affected by myelin content and - to a lesser degree - axonal count in post mortem MS brain

ADvanced IMage Algebra (ADIMA): a novel method for depicting multiple sclerosis lesion heterogeneity, as demonstrated by quantitative MRI.

BACKGROUND: There are modest correlations between multiple sclerosis (MS) disability and white matter lesion (WML) volumes, as measured by T2-weighted (T2w) magnetic resonance imaging (MRI) scans (T2-WML). This may partly reflect pathological heterogeneity in WMLs, which is not apparent on T2w scans. OBJECTIVE: To determine if ADvanced IMage Algebra (ADIMA), a novel MRI post-processing method, can reveal WML heterogeneity from proton-density weighted (PDw) and T2w images. METHODS: We obtained conventional PDw and T2w images from 10 patients with relapsing-remitting MS (RRMS) and ADIMA images were calculated from these. We classified all WML into bright (ADIMA-b) and dark (ADIMA-d) sub-regions, which were segmented. We obtained conventional T2-WML and T1-WML volumes for comparison, as well as the following quantitative magnetic resonance parameters: magnetisation transfer ratio (MTR), T1 and T2. Also, we assessed the reproducibility of the segmentation for ADIMA-b, ADIMA-d and T2-WML. RESULTS: Our study's ADIMA-derived volumes correlated with conventional lesion volumes (p < 0.05). ADIMA-b exhibited higher T1 and T2, and lower MTR than the T2-WML (p < 0.001). Despite the similarity in T1 values between ADIMA-b and T1-WML, these regions were only partly overlapping with each other. ADIMA-d exhibited quantitative characteristics similar to T2-WML; however, they were only partly overlapping. Mean intra- and inter-observer coefficients of variation for ADIMA-b, ADIMA-d and T2-WML volumes were all < 6 % and < 10 %, respectively. CONCLUSION: ADIMA enabled the simple classification of WML into two groups having different quantitative magnetic resonance properties, which can be reproducibly distinguished

Transcriptional profiling of leukocytes in critically ill COVID19 patients: implications for interferon response and coagulation

BACKGROUND: COVID19 is caused by the SARS-CoV-2 virus and has been associated with severe inflammation leading to organ dysfunction and mortality. Our aim was to profile the transcriptome in leukocytes from critically ill patients positive for COVID19 compared to those negative for COVID19 to better understand the COVID19-associated host response. For these studies, all patients admitted to our tertiary care intensive care unit (ICU) suspected of being infected with SARS-CoV-2, using standardized hospital screening methodologies, had blood samples collected at the time of admission to the ICU. Transcriptome profiling of leukocytes via ribonucleic acid sequencing (RNAseq) was then performed and differentially expressed genes as well as significantly enriched gene sets were identified. RESULTS: We enrolled seven COVID19 + (PCR positive, 2 SARS-CoV-2 genes) and seven age- and sex-matched COVID19- (PCR negative) control ICU patients. Cohorts were well-balanced with the exception that COVID19- patients had significantly higher total white blood cell counts and circulating neutrophils and COVID19 + patients were more likely to suffer bilateral pneumonia. The mortality rate for this cohort of COVID19 + ICU patients was 29%. As indicated by both single-gene based and gene set (GSEA) approaches, the major disease-specific transcriptional responses of leukocytes in critically ill COVID19 + ICU patients were: (i) a robust overrepresentation of interferon-related gene expression; (ii) a marked decrease in the transcriptional level of genes contributing to general protein synthesis and bioenergy metabolism; and (iii) the dysregulated expression of genes associated with coagulation, platelet function, complement activation, and tumour necrosis factor/interleukin 6 signalling. CONCLUSIONS: Our findings demonstrate that critically ill COVID19 + patients on day 1 of admission to the ICU display a unique leukocyte transcriptional profile that distinguishes them from COVID19- patients, providing guidance for future targeted studies exploring novel prognostic and therapeutic aspects of COVID19

A cyclic nucleotide-gated channel (CNGC16) in pollen is critical for stress tolerance in pollen reproductive development

Cyclic nucleotide-gated channels (CNGCs) have been implicated in diverse aspects of plant growth and development, including responses to biotic and abiotic stress, as well as pollen tube growth and fertility. Here, genetic evidence identifies CNGC16 in Arabidopsis (Arabidopsis thaliana) as critical for pollen fertility under conditions of heat stress and drought. Two independent transfer DNA disruptions of cngc16 resulted in a greater than 10-fold stress-dependent reduction in pollen fitness and seed set. This phenotype was fully rescued through pollen expression of a CNGC16 transgene, indicating that cngc16-1 and 16-2 were both loss-of-function null alleles. The most stress-sensitive period for cngc16 pollen was during germination and the initiation of pollen tube tip growth. Pollen viability assays indicate that mutant pollen are also hypersensitive to external calcium chloride, a phenomenon analogous to calcium chloride hypersensitivities observed in other cngc mutants. A heat stress was found to increase concentrations of 3′,5′-cyclic guanyl monophosphate in both pollen and leaves, as detected using an antibody-binding assay. A quantitative PCR analysis indicates that cngc16 mutant pollen have attenuated expression of several heat-stress response genes, including two heat shock transcription factor genes, HsfA2 and HsfB1. Together, these results provide evidence for a heat stress response pathway in pollen that connects a cyclic nucleotide signal, a Ca(2+)-permeable ion channel, and a signaling network that activates a downstream transcriptional heat shock response

Fully automated segmentation of the cervical cord from T1-weighted MRI using PropSeg: Application to multiple sclerosis.

Spinal cord (SC) atrophy, i.e. a reduction in the SC cross-sectional area (CSA) over time, can be measured by means of image segmentation using magnetic resonance imaging (MRI). However, segmentation methods have been limited by factors relating to reproducibility or sensitivity to change. The purpose of this study was to evaluate a fully automated SC segmentation method (PropSeg), and compare this to a semi-automated active surface (AS) method, in healthy controls (HC) and people with multiple sclerosis (MS). MRI data from 120 people were retrospectively analysed; 26 HC, 21 with clinically isolated syndrome, 26 relapsing remitting MS, 26 primary and 21 secondary progressive MS. MRI data from 40 people returning after one year were also analysed. CSA measurements were obtained within the cervical SC. Reproducibility of the measurements was assessed using the intraclass correlation coefficient (ICC). A comparison between mean CSA changes obtained with the two methods over time was performed using multivariate structural equation regression models. Associations between CSA measures and clinical scores were investigated using linear regression models. Compared to the AS method, the reproducibility of CSA measurements obtained with PropSeg was high, both in patients and in HC, with ICC > 0.98 in all cases. There was no significant difference between PropSeg and AS in terms of detecting change over time. Furthermore, PropSeg provided measures that correlated with physical disability, similar to the AS method. PropSeg is a time-efficient and reliable segmentation method, which requires no manual intervention, and may facilitate large multi-centre neuroprotective trials in progressive MS

Wolbachia and DNA barcoding insects: patterns, potential and problems

Wolbachia is a genus of bacterial endosymbionts that impacts the breeding systems of their hosts. Wolbachia can confuse the patterns of mitochondrial variation, including DNA barcodes, because it influences the pathways through which mitochondria are inherited. We examined the extent to which these endosymbionts are detected in routine DNA barcoding, assessed their impact upon the insect sequence divergence and identification accuracy, and considered the variation present in Wolbachia COI. Using both standard PCR assays (Wolbachia surface coding protein – wsp), and bacterial COI fragments we found evidence of Wolbachia in insect total genomic extracts created for DNA barcoding library construction. When >2 million insect COI trace files were examined on the Barcode of Life Datasystem (BOLD) Wolbachia COI was present in 0.16% of the cases. It is possible to generate Wolbachia COI using standard insect primers; however, that amplicon was never confused with the COI of the host. Wolbachia alleles recovered were predominantly Supergroup A and were broadly distributed geographically and phylogenetically. We conclude that the presence of the Wolbachia DNA in total genomic extracts made from insects is unlikely to compromise the accuracy of the DNA barcode library; in fact, the ability to query this DNA library (the database and the extracts) for endosymbionts is one of the ancillary benefits of such a large scale endeavor – for which we provide several examples. It is our conclusion that regular assays for Wolbachia presence and type can, and should, be adopted by large scale insect barcoding initiatives. While COI is one of the five multi-locus sequence typing (MLST) genes used for categorizing Wolbachia, there is limited overlap with the eukaryotic DNA barcode region