Block diagonalisation of four-dimensional metrics

It is shown that, in 4-dimensions, it is possible to introduce coordinates so that an analytic metric locally takes block diagonal form. i.e. one can find coordinates such that g = 0 for (, ) 2 S where S = {(1, 3), (1, 4), (2, 3), (2, 4)}. We call a coordinate system in which the metric takes this form a ‘doubly biorthogonal coordinate system’. We show that all such coordinate systems are determined by a pair of coupled second-order partial differential equation

The wave equation on singular space-times

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.Comment: Latex, 19 pages, 1 figure. Discussion of class of metrics covered by our results and some examples added. Conclusion more detailed. Version to appear in Communications in Mathematical Physic

Dissociation between exercise-induced reduction in liver fat and changes in hepatic and peripheral glucose homoeostasis in obese patients with non-alcoholic fatty liver disease.

Non-alcoholic fatty liver disease (NAFLD) is associated with multi-organ (hepatic, skeletal muscle, adipose tissue) insulin resistance (IR). Exercise is an effective treatment for lowering liver fat but its effect on IR in NAFLD is unknown. We aimed to determine whether supervised exercise in NAFLD would reduce liver fat and improve hepatic and peripheral (skeletal muscle and adipose tissue) insulin sensitivity. Sixty nine NAFLD patients were randomized to 16 weeks exercise supervision (n=38) or counselling (n=31) without dietary modification. All participants underwent MRI/spectroscopy to assess changes in body fat and in liver and skeletal muscle triglyceride, before and following exercise/counselling. To quantify changes in hepatic and peripheral insulin sensitivity, a pre-determined subset (n=12 per group) underwent a two-stage hyperinsulinaemic euglycaemic clamp pre- and post-intervention. Results are shown as mean [95% confidence interval (CI)]. Fifty participants (30 exercise, 20 counselling), 51 years (IQR 40, 56), body mass index (BMI) 31 kg/m(2) (IQR 29, 35) with baseline liver fat/water % of 18.8% (IQR 10.7, 34.6) completed the study (12/12 exercise and 7/12 counselling completed the clamp studies). Supervised exercise mediated a greater reduction in liver fat/water percentage than counselling [Δ mean change 4.7% (0.01, 9.4); P<0.05], which correlated with the change in cardiorespiratory fitness (r=-0.34, P=0.0173). With exercise, peripheral insulin sensitivity significantly increased (following high-dose insulin) despite no significant change in hepatic glucose production (HGP; following low-dose insulin); no changes were observed in the control group. Although supervised exercise effectively reduced liver fat, improving peripheral IR in NAFLD, the reduction in liver fat was insufficient to improve hepatic IR

SARS-CoV-2-specific nasal IgA wanes 9 months after hospitalisation with COVID-19 and is not induced by subsequent vaccination

BACKGROUND: Most studies of immunity to SARS-CoV-2 focus on circulating antibody, giving limited insights into mucosal defences that prevent viral replication and onward transmission. We studied nasal and plasma antibody responses one year after hospitalisation for COVID-19, including a period when SARS-CoV-2 vaccination was introduced. METHODS: In this follow up study, plasma and nasosorption samples were prospectively collected from 446 adults hospitalised for COVID-19 between February 2020 and March 2021 via the ISARIC4C and PHOSP-COVID consortia. IgA and IgG responses to NP and S of ancestral SARS-CoV-2, Delta and Omicron (BA.1) variants were measured by electrochemiluminescence and compared with plasma neutralisation data. FINDINGS: Strong and consistent nasal anti-NP and anti-S IgA responses were demonstrated, which remained elevated for nine months (p < 0.0001). Nasal and plasma anti-S IgG remained elevated for at least 12 months (p < 0.0001) with plasma neutralising titres that were raised against all variants compared to controls (p < 0.0001). Of 323 with complete data, 307 were vaccinated between 6 and 12 months; coinciding with rises in nasal and plasma IgA and IgG anti-S titres for all SARS-CoV-2 variants, although the change in nasal IgA was minimal (1.46-fold change after 10 months, p = 0.011) and the median remained below the positive threshold determined by pre-pandemic controls. Samples 12 months after admission showed no association between nasal IgA and plasma IgG anti-S responses (R = 0.05, p = 0.18), indicating that nasal IgA responses are distinct from those in plasma and minimally boosted by vaccination. INTERPRETATION: The decline in nasal IgA responses 9 months after infection and minimal impact of subsequent vaccination may explain the lack of long-lasting nasal defence against reinfection and the limited effects of vaccination on transmission. These findings highlight the need to develop vaccines that enhance nasal immunity. FUNDING: This study has been supported by ISARIC4C and PHOSP-COVID consortia. ISARIC4C is supported by grants from the National Institute for Health and Care Research and the Medical Research Council. Liverpool Experimental Cancer Medicine Centre provided infrastructure support for this research. The PHOSP-COVD study is jointly funded by UK Research and Innovation and National Institute of Health and Care Research. The funders were not involved in the study design, interpretation of data or the writing of this manuscript

Large-scale phenotyping of patients with long COVID post-hospitalization reveals mechanistic subtypes of disease

One in ten severe acute respiratory syndrome coronavirus 2 infections result in prolonged symptoms termed long coronavirus disease (COVID), yet disease phenotypes and mechanisms are poorly understood1. Here we profiled 368 plasma proteins in 657 participants ≥3 months following hospitalization. Of these, 426 had at least one long COVID symptom and 233 had fully recovered. Elevated markers of myeloid inflammation and complement activation were associated with long COVID. IL-1R2, MATN2 and COLEC12 were associated with cardiorespiratory symptoms, fatigue and anxiety/depression; MATN2, CSF3 and C1QA were elevated in gastrointestinal symptoms and C1QA was elevated in cognitive impairment. Additional markers of alterations in nerve tissue repair (SPON-1 and NFASC) were elevated in those with cognitive impairment and SCG3, suggestive of brain–gut axis disturbance, was elevated in gastrointestinal symptoms. Severe acute respiratory syndrome coronavirus 2-specific immunoglobulin G (IgG) was persistently elevated in some individuals with long COVID, but virus was not detected in sputum. Analysis of inflammatory markers in nasal fluids showed no association with symptoms. Our study aimed to understand inflammatory processes that underlie long COVID and was not designed for biomarker discovery. Our findings suggest that specific inflammatory pathways related to tissue damage are implicated in subtypes of long COVID, which might be targeted in future therapeutic trials

Multiorgan MRI findings after hospitalisation with COVID-19 in the UK (C-MORE): a prospective, multicentre, observational cohort study

Introduction: The multiorgan impact of moderate to severe coronavirus infections in the post-acute phase is still poorly understood. We aimed to evaluate the excess burden of multiorgan abnormalities after hospitalisation with COVID-19, evaluate their determinants, and explore associations with patient-related outcome measures. Methods: In a prospective, UK-wide, multicentre MRI follow-up study (C-MORE), adults (aged ≥18 years) discharged from hospital following COVID-19 who were included in Tier 2 of the Post-hospitalisation COVID-19 study (PHOSP-COVID) and contemporary controls with no evidence of previous COVID-19 (SARS-CoV-2 nucleocapsid antibody negative) underwent multiorgan MRI (lungs, heart, brain, liver, and kidneys) with quantitative and qualitative assessment of images and clinical adjudication when relevant. Individuals with end-stage renal failure or contraindications to MRI were excluded. Participants also underwent detailed recording of symptoms, and physiological and biochemical tests. The primary outcome was the excess burden of multiorgan abnormalities (two or more organs) relative to controls, with further adjustments for potential confounders. The C-MORE study is ongoing and is registered with ClinicalTrials.gov, NCT04510025. Findings: Of 2710 participants in Tier 2 of PHOSP-COVID, 531 were recruited across 13 UK-wide C-MORE sites. After exclusions, 259 C-MORE patients (mean age 57 years [SD 12]; 158 [61%] male and 101 [39%] female) who were discharged from hospital with PCR-confirmed or clinically diagnosed COVID-19 between March 1, 2020, and Nov 1, 2021, and 52 non-COVID-19 controls from the community (mean age 49 years [SD 14]; 30 [58%] male and 22 [42%] female) were included in the analysis. Patients were assessed at a median of 5·0 months (IQR 4·2–6·3) after hospital discharge. Compared with non-COVID-19 controls, patients were older, living with more obesity, and had more comorbidities. Multiorgan abnormalities on MRI were more frequent in patients than in controls (157 [61%] of 259 vs 14 [27%] of 52; p&lt;0·0001) and independently associated with COVID-19 status (odds ratio [OR] 2·9 [95% CI 1·5–5·8]; padjusted=0·0023) after adjusting for relevant confounders. Compared with controls, patients were more likely to have MRI evidence of lung abnormalities (p=0·0001; parenchymal abnormalities), brain abnormalities (p&lt;0·0001; more white matter hyperintensities and regional brain volume reduction), and kidney abnormalities (p=0·014; lower medullary T1 and loss of corticomedullary differentiation), whereas cardiac and liver MRI abnormalities were similar between patients and controls. Patients with multiorgan abnormalities were older (difference in mean age 7 years [95% CI 4–10]; mean age of 59·8 years [SD 11·7] with multiorgan abnormalities vs mean age of 52·8 years [11·9] without multiorgan abnormalities; p&lt;0·0001), more likely to have three or more comorbidities (OR 2·47 [1·32–4·82]; padjusted=0·0059), and more likely to have a more severe acute infection (acute CRP &gt;5mg/L, OR 3·55 [1·23–11·88]; padjusted=0·025) than those without multiorgan abnormalities. Presence of lung MRI abnormalities was associated with a two-fold higher risk of chest tightness, and multiorgan MRI abnormalities were associated with severe and very severe persistent physical and mental health impairment (PHOSP-COVID symptom clusters) after hospitalisation. Interpretation: After hospitalisation for COVID-19, people are at risk of multiorgan abnormalities in the medium term. Our findings emphasise the need for proactive multidisciplinary care pathways, with the potential for imaging to guide surveillance frequency and therapeutic stratification

Accelarated immune ageing is associated with COVID-19 disease severity

Background The striking increase in COVID-19 severity in older adults provides a clear example of immunesenescence, the age-related remodelling of the immune system. To better characterise the association between convalescent immunesenescence and acute disease severity, we determined the immune phenotype of COVID-19 survivors and non-infected controls. Results We performed detailed immune phenotyping of peripheral blood mononuclear cells isolated from 103 COVID-19 survivors 3–5 months post recovery who were classified as having had severe (n = 56; age 53.12 ± 11.30 years), moderate (n = 32; age 52.28 ± 11.43 years) or mild (n = 15; age 49.67 ± 7.30 years) disease and compared with age and sex-matched healthy adults (n = 59; age 50.49 ± 10.68 years). We assessed a broad range of immune cell phenotypes to generate a composite score, IMM-AGE, to determine the degree of immune senescence. We found increased immunesenescence features in severe COVID-19 survivors compared to controls including: a reduced frequency and number of naïve CD4 and CD8 T cells (p < 0.0001); increased frequency of EMRA CD4 (p < 0.003) and CD8 T cells (p < 0.001); a higher frequency (p < 0.0001) and absolute numbers (p < 0.001) of CD28−ve CD57+ve senescent CD4 and CD8 T cells; higher frequency (p < 0.003) and absolute numbers (p < 0.02) of PD-1 expressing exhausted CD8 T cells; a two-fold increase in Th17 polarisation (p < 0.0001); higher frequency of memory B cells (p < 0.001) and increased frequency (p < 0.0001) and numbers (p < 0.001) of CD57+ve senescent NK cells. As a result, the IMM-AGE score was significantly higher in severe COVID-19 survivors than in controls (p < 0.001). Few differences were seen for those with moderate disease and none for mild disease. Regression analysis revealed the only pre-existing variable influencing the IMM-AGE score was South Asian ethnicity ( = 0.174, p = 0.043), with a major influence being disease severity ( = 0.188, p = 0.01). Conclusions Our analyses reveal a state of enhanced immune ageing in survivors of severe COVID-19 and suggest this could be related to SARS-Cov-2 infection. Our data support the rationale for trials of anti-immune ageing interventions for improving clinical outcomes in these patients with severe disease