Discrete Geometric Structures in Homogenization and Inverse Homogenization with application to EIT

We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients $\sigma(x)$ in dimension two. We show that conductivity coefficients are in one-to-one correspondence with divergence-free matrices and convex functions $s(x)$ over the domain $\Omega$. Although homogenization is a non-linear and non-injective operator when applied directly to conductivity coefficients, homogenization becomes a linear interpolation operator over triangulations of $\Omega$ when re-expressed using convex functions, and is a volume averaging operator when re-expressed with divergence-free matrices. Using optimal weighted Delaunay triangulations for linearly interpolating convex functions, we obtain an optimally robust homogenization algorithm for arbitrary rough coefficients. Next, we consider inverse homogenization and show how to decompose it into a linear ill-posed problem and a well-posed non-linear problem. We apply this new geometric approach to Electrical Impedance Tomography (EIT). It is known that the EIT problem admits at most one isotropic solution. If an isotropic solution exists, we show how to compute it from any conductivity having the same boundary Dirichlet-to-Neumann map. It is known that the EIT problem admits a unique (stable with respect to $G$-convergence) solution in the space of divergence-free matrices. As such we suggest that the space of convex functions is the natural space in which to parameterize solutions of the EIT problem

The effect of heavy rain on an airfoil at high lift

No serious studies of the relationship of heavy rain to aircraft safety were made until 1981 when it was suggested that the torrential rain which often occurs at the time of severe wind shear might substantially increase the danger to aircraft operating at slow speeds and high lift in the vicinity of airports. While these data were not published until early 1983, appropriate measures were taken by NASA to study the effect of heavy rain on the lift of wings typical of commercial aircraft. One of the aspects of these tests that seemed confirmed by the data was the existence of a velocity effect on the lift data. The data seemed to indicate that when all the normal non-dimensional aerodynamic parameters were used to sort out the data, the effect of velocity was not accounted for, as it usually is, by the effect of dynamic pressure. Indeed, the measured lift coefficients at high lift indicated a dropoff in lift coefficient for the same free-stream water content as velocity was increased. indicated a drop-off in lift coefficient for the same free-stream water content as velocity was increased

Key challenges in simulated patient programs: An international comparative case study

<p>Abstract</p> <p>Background</p> <p>The literature on simulated or standardized patient (SP) methodology is expanding. However, at the level of the program, there are several gaps in the literature. We seek to fill this gap through documenting experiences from four programs in Australia, Canada, Switzerland and the United Kingdom. We focused on challenges in SP methodology, faculty, organisational structure and quality assurance.</p> <p>Methods</p> <p>We used a multiple case study method with cross-case synthesis. Over eighteen months during a series of informal and formal interactions (focused meetings and conference presentations) we documented key characteristics of programs and drew on secondary document sources.</p> <p>Results</p> <p>Although programs shared challenges in SP methodology they also experienced differences. Key challenges common to programs included systematic quality assurance and the opportunity for research. There were differences in the terminology used to describe SPs, in their recruitment and training. Other differences reflected local conditions and demands in organisational structure, funding relationships with the host institution and national trends, especially in assessments.</p> <p>Conclusion</p> <p>This international case study reveals similarities and differences in SP methodology. Programs were highly contextualised and have emerged in response to local, institutional, profession/discipline and national conditions. Broader trends in healthcare education have also influenced development. Each of the programs experienced challenges in the same themes but the nature of the challenges often varied widely.</p

Primary sclerosing cholangitis

Primary sclerosing cholangitis (PSC) is a chronic cholestatic liver disease of unknown aetiology characterised by inflammation and fibrosis of the biliary tree. The mean age at diagnosis is 40 years and men are affected twice as often as women. There is a reported annual incidence of PSC of 0.9–1.31/100,000 and point prevalence of 8.5–13.6/100,000. The onset of PSC is usually insidious and many patients are asymptomatic at diagnosis or have mild symptoms only such as fatigue, abdominal discomfort and pruritus In late stages, splenomegaly and jaundice may be a feature. In most, the disease progresses to cirrhosis and liver failure. Cholangiocarcinoma develops in 8–30% of patients. PSC is thought to be immune mediated and is often associated with inflammatory bowel disease, especially ulcerative colitis. The disease is diagnosed on typical cholangiographic and histological findings and after exclusion of secondary sclerosing cholangitis. Median survival has been estimated to be 12 years from diagnosis in symptomatic patients. Patients who are asymptomatic at diagnosis, the majority of whom will develop progressive disease, have a survival rate greater than 70% at 16 years after diagnosis. Liver transplantation remains the only effective therapeutic option for patients with end-stage liver disease from PSC, although high dose ursodeoxycholic acid may have a beneficial effect

Effects of sleep disturbance on dyspnoea and impaired lung function following hospital admission due to COVID-19 in the UK:a prospective multicentre cohort study

BACKGROUND: Sleep disturbance is common following hospital admission both for COVID-19 and other causes. The clinical associations of this for recovery after hospital admission are poorly understood despite sleep disturbance contributing to morbidity in other scenarios. We aimed to investigate the prevalence and nature of sleep disturbance after discharge following hospital admission for COVID-19 and to assess whether this was associated with dyspnoea. METHODS: CircCOVID was a prospective multicentre cohort substudy designed to investigate the effects of circadian disruption and sleep disturbance on recovery after COVID-19 in a cohort of participants aged 18 years or older, admitted to hospital for COVID-19 in the UK, and discharged between March, 2020, and October, 2021. Participants were recruited from the Post-hospitalisation COVID-19 study (PHOSP-COVID). Follow-up data were collected at two timepoints: an early time point 2-7 months after hospital discharge and a later time point 10-14 months after hospital discharge. Sleep quality was assessed subjectively using the Pittsburgh Sleep Quality Index questionnaire and a numerical rating scale. Sleep quality was also assessed with an accelerometer worn on the wrist (actigraphy) for 14 days. Participants were also clinically phenotyped, including assessment of symptoms (ie, anxiety [Generalised Anxiety Disorder 7-item scale questionnaire], muscle function [SARC-F questionnaire], dyspnoea [Dyspnoea-12 questionnaire] and measurement of lung function), at the early timepoint after discharge. Actigraphy results were also compared to a matched UK Biobank cohort (non-hospitalised individuals and recently hospitalised individuals). Multivariable linear regression was used to define associations of sleep disturbance with the primary outcome of breathlessness and the other clinical symptoms. PHOSP-COVID is registered on the ISRCTN Registry (ISRCTN10980107). FINDINGS: 2320 of 2468 participants in the PHOSP-COVID study attended an early timepoint research visit a median of 5 months (IQR 4-6) following discharge from 83 hospitals in the UK. Data for sleep quality were assessed by subjective measures (the Pittsburgh Sleep Quality Index questionnaire and the numerical rating scale) for 638 participants at the early time point. Sleep quality was also assessed using device-based measures (actigraphy) a median of 7 months (IQR 5-8 months) after discharge from hospital for 729 participants. After discharge from hospital, the majority (396 [62%] of 638) of participants who had been admitted to hospital for COVID-19 reported poor sleep quality in response to the Pittsburgh Sleep Quality Index questionnaire. A comparable proportion (338 [53%] of 638) of participants felt their sleep quality had deteriorated following discharge after COVID-19 admission, as assessed by the numerical rating scale. Device-based measurements were compared to an age-matched, sex-matched, BMI-matched, and time from discharge-matched UK Biobank cohort who had recently been admitted to hospital. Compared to the recently hospitalised matched UK Biobank cohort, participants in our study slept on average 65 min (95% CI 59 to 71) longer, had a lower sleep regularity index (-19%; 95% CI -20 to -16), and a lower sleep efficiency (3·83 percentage points; 95% CI 3·40 to 4·26). Similar results were obtained when comparisons were made with the non-hospitalised UK Biobank cohort. Overall sleep quality (unadjusted effect estimate 3·94; 95% CI 2·78 to 5·10), deterioration in sleep quality following hospital admission (3·00; 1·82 to 4·28), and sleep regularity (4·38; 2·10 to 6·65) were associated with higher dyspnoea scores. Poor sleep quality, deterioration in sleep quality, and sleep regularity were also associated with impaired lung function, as assessed by forced vital capacity. Depending on the sleep metric, anxiety mediated 18-39% of the effect of sleep disturbance on dyspnoea, while muscle weakness mediated 27-41% of this effect. INTERPRETATION: Sleep disturbance following hospital admission for COVID-19 is associated with dyspnoea, anxiety, and muscle weakness. Due to the association with multiple symptoms, targeting sleep disturbance might be beneficial in treating the post-COVID-19 condition. FUNDING: UK Research and Innovation, National Institute for Health Research, and Engineering and Physical Sciences Research Council

Effects of sleep disturbance on dyspnoea and impaired lung function following hospital admission due to COVID-19 in the UK: a prospective multicentre cohort study

BACKGROUND: Sleep disturbance is common following hospital admission both for COVID-19 and other causes. The clinical associations of this for recovery after hospital admission are poorly understood despite sleep disturbance contributing to morbidity in other scenarios. We aimed to investigate the prevalence and nature of sleep disturbance after discharge following hospital admission for COVID-19 and to assess whether this was associated with dyspnoea. METHODS: CircCOVID was a prospective multicentre cohort substudy designed to investigate the effects of circadian disruption and sleep disturbance on recovery after COVID-19 in a cohort of participants aged 18 years or older, admitted to hospital for COVID-19 in the UK, and discharged between March, 2020, and October, 2021. Participants were recruited from the Post-hospitalisation COVID-19 study (PHOSP-COVID). Follow-up data were collected at two timepoints: an early time point 2-7 months after hospital discharge and a later time point 10-14 months after hospital discharge. Sleep quality was assessed subjectively using the Pittsburgh Sleep Quality Index questionnaire and a numerical rating scale. Sleep quality was also assessed with an accelerometer worn on the wrist (actigraphy) for 14 days. Participants were also clinically phenotyped, including assessment of symptoms (ie, anxiety [Generalised Anxiety Disorder 7-item scale questionnaire], muscle function [SARC-F questionnaire], dyspnoea [Dyspnoea-12 questionnaire] and measurement of lung function), at the early timepoint after discharge. Actigraphy results were also compared to a matched UK Biobank cohort (non-hospitalised individuals and recently hospitalised individuals). Multivariable linear regression was used to define associations of sleep disturbance with the primary outcome of breathlessness and the other clinical symptoms. PHOSP-COVID is registered on the ISRCTN Registry (ISRCTN10980107). FINDINGS: 2320 of 2468 participants in the PHOSP-COVID study attended an early timepoint research visit a median of 5 months (IQR 4-6) following discharge from 83 hospitals in the UK. Data for sleep quality were assessed by subjective measures (the Pittsburgh Sleep Quality Index questionnaire and the numerical rating scale) for 638 participants at the early time point. Sleep quality was also assessed using device-based measures (actigraphy) a median of 7 months (IQR 5-8 months) after discharge from hospital for 729 participants. After discharge from hospital, the majority (396 [62%] of 638) of participants who had been admitted to hospital for COVID-19 reported poor sleep quality in response to the Pittsburgh Sleep Quality Index questionnaire. A comparable proportion (338 [53%] of 638) of participants felt their sleep quality had deteriorated following discharge after COVID-19 admission, as assessed by the numerical rating scale. Device-based measurements were compared to an age-matched, sex-matched, BMI-matched, and time from discharge-matched UK Biobank cohort who had recently been admitted to hospital. Compared to the recently hospitalised matched UK Biobank cohort, participants in our study slept on average 65 min (95% CI 59 to 71) longer, had a lower sleep regularity index (-19%; 95% CI -20 to -16), and a lower sleep efficiency (3·83 percentage points; 95% CI 3·40 to 4·26). Similar results were obtained when comparisons were made with the non-hospitalised UK Biobank cohort. Overall sleep quality (unadjusted effect estimate 3·94; 95% CI 2·78 to 5·10), deterioration in sleep quality following hospital admission (3·00; 1·82 to 4·28), and sleep regularity (4·38; 2·10 to 6·65) were associated with higher dyspnoea scores. Poor sleep quality, deterioration in sleep quality, and sleep regularity were also associated with impaired lung function, as assessed by forced vital capacity. Depending on the sleep metric, anxiety mediated 18-39% of the effect of sleep disturbance on dyspnoea, while muscle weakness mediated 27-41% of this effect. INTERPRETATION: Sleep disturbance following hospital admission for COVID-19 is associated with dyspnoea, anxiety, and muscle weakness. Due to the association with multiple symptoms, targeting sleep disturbance might be beneficial in treating the post-COVID-19 condition. FUNDING: UK Research and Innovation, National Institute for Health Research, and Engineering and Physical Sciences Research Council

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio