On the Adjoint Operator in Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems

Integer polyhedra for program analysis

Polyhedra are widely used in model checking and abstract interpretation. Polyhedral analysis is effective when the relationships between variables are linear, but suffers from imprecision when it is necessary to take into account the integrality of the represented space. Imprecision also arises when non-linear constraints occur. Moreover, in terms of tractability, even a space defined by linear constraints can become unmanageable owing to the excessive number of inequalities. Thus it is useful to identify those inequalities whose omission has least impact on the represented space. This paper shows how these issues can be addressed in a novel way by growing the integer hull of the space and approximating the number of integral points within a bounded polyhedron

Testing systems of identical components

We consider the problem of testing sequentially the components of a multi-component reliability system in order to figure out the state of the system via costly tests. In particular, systems with identical components are considered. The notion of lexicographically large binary decision trees is introduced and a heuristic algorithm based on that notion is proposed. The performance of the heuristic algorithm is demonstrated by computational results, for various classes of functions. In particular, in all 200 random cases where the underlying function is a threshold function, the proposed heuristic produces optimal solutions

The epigenetic clock is correlated with physical and cognitive fitness in the Lothian Birth Cohort 1936

Background: The DNA methylation-based 'epigenetic clock' correlates strongly with chronological age, but it is currently unclear what drives individual differences. We examine cross-sectional and longitudinal associations between the epigenetic clock and four mortality-linked markers of physical and mental fitness: lung function, walking speed, grip strength and cognitive ability. Methods: DNA methylation-based age acceleration (residuals of the epigenetic clock estimate regressed on chronological age) were estimated in the Lothian Birth Cohort 1936 at ages 70 (n=920), 73 (n=299) and 76 (n=273) years. General cognitive ability, walking speed, lung function and grip strength were measured concurrently. Cross-sectional correlations between age acceleration and the fitness variables were calculated. Longitudinal change in the epigenetic clock estimates and the fitness variables were assessed via linear mixed models and latent growth curves. Epigenetic age acceleration at age 70 was used as a predictor of longitudinal change in fitness. Epigenome-wide association studies (EWASs) were conducted on the four fitness measures. Results: Cross-sectional correlations were significant between greater age acceleration and poorer performance on the lung function, cognition and grip strength measures (r range: -0.07 to -0.05, P range: 9.7 x 10 to 0.024). All of the fitness variables declined over time but age acceleration did not correlate with subsequent change over 6 years. There were no EWAS hits for the fitness traits. Conclusions: Markers of physical and mental fitness are associated with the epigenetic clock (lower abilities associated with age acceleration). However, age acceleration does not associate with decline in these measures, at least over a relatively short follow-up

Photoevaporation of protoplanetary discs I: hydrodynamic models

In this paper we consider the effect of the direct ionizing stellar radiation field on the evolution of protoplanetary discs subject to photoevaporative winds. We suggest that models which combine viscous evolution with photoevaporation of the disc (e.g. Clarke, Gendrin & Sotomayor 2001) incorrectly neglect the direct field after the inner disc has drained, at late times in the evolution. We construct models of the photoevaporative wind produced by the direct field, first using simple analytic arguments and later using detailed numerical hydrodynamics. We find that the wind produced by the direct field at late times is much larger than has previously been assumed, and we show that the mass-loss rate scales as $R_{in}^{1/2}$ (where $R_{in}$ is the radius of the instantaneous inner disc edge). We suggest that this result has important consequences for theories of disc evolution, and go on to consider the effects of this result on disc evolution in detail in a companion paper (Alexander, Clarke & Pringle 2006b).Comment: 13 pages, 9 figures. Accepted for publication in MNRA

The positions of primary and secondary schools in the English school field: a case of durable inequality

In interviews as part of a research study of structural reform in England, some tension between primary head teachers and their secondary peers was evident. This was symptomatic of a long-standing difference in status between the two phases. At a time when relations between stakeholders in local systems are subject to change, we seek to understand anew why that might be the case and how the tension we found was evidence of a current difference of power within interactions between representatives of the phases. We analyse differences of size, resources, workforce, pedagogy and history, and how they have resulted in different, and differently valued, practices and professional identities. We explore how attributes of the two phases have been counterposed and how, in complex interaction with wider discourses of politics, gender and age, this process has invested the differences with meanings and values that tend to relegate attributes associated with primary school. By focusing on the activation of cumulative inequality in interactions, we contribute a complementary perspective to studies of perceived relative status and highlight the implications for understanding school positioning in local arenas as the role of local authorities is reduced

Dynamic Rearrangement of Cell States Detected by Systematic Screening of Sequential Anticancer Treatments

Signaling networks are nonlinear and complex, involving a large ensemble of dynamic interaction states that fluctuate in space and time. However, therapeutic strategies, such as combination chemotherapy, rarely consider the timing of drug perturbations. If we are to advance drug discovery for complex diseases, it will be essential to develop methods capable of identifying dynamic cellular responses to clinically relevant perturbations. Here, we present a Bayesian dose-response framework and the screening of an oncological drug matrix, comprising 10,000 drug combinations in melanoma and pancreatic cancer cell lines, from which we predict sequentially effective drug combinations. Approximately 23% of the tested combinations showed high-confidence sequential effects (either synergistic or antagonistic), demonstrating that cellular perturbations of many drug combinations have temporal aspects, which are currently both underutilized and poorly understood

Mediterranean-type diet and brain structural change from 73 to 76 years in a Scottish cohort

STUDY FUNDING The data were collected by a Research into Ageing programme grant; research continues as part of the Age UK–funded Disconnected Mind project. The work was undertaken by The University of Edinburgh Centre for Cognitive Ageing and Cognitive Epidemiology, part of the cross-council Lifelong Health and Wellbeing Initiative (MR/K026992/1), with funding from the BBSRC and Medical Research Council. Imaging and image analysis was performed at the Brain Research Imaging Centre (sbirc.ed.ac.uk/), Edinburgh, supported by the Scottish Funding Council SINAPSE Collaboration. Derivation of mean cortical thickness measures was funded by the Scottish Funding Council’s Postdoctoral and Early Career Researchers Exchange Fund awarded by SINAPSE to David Alexander Dickie. L.C.A.C. acknowledges funding from the Scottish Government's Rural and Environment Science and Analytical Services (RESAS) division.Peer reviewedPublisher PD

Steps in the right direction for physical frailty research

In this issue of The Lancet Digital Health, Rongtao Jiang and colleagues present a broad and well powered observational study of the correlates of physical frailty among nearly half a million middle-aged and older adults in the UK Biobank. Using a modification of the Fried frailty phenotype (based on weakness, walking speed, inactivity, exhaustion, and weight loss), the strongest correlates of participants' mainly self-reported frailty status were other aspects of self-reported health and wellbeing, as well as neuroticism, anxiety, and depression. Importantly, many of the associations reported were of relatively small effect size. These results were similar between the sexes and across much of the age range, with the exception of mental health measures, which were more strongly associated with frailty in middle age than in older adults. In longitudinal analyses, stronger associations were found between baseline health (particularly mental health) and frailty measured 9 years later than for the converse specification. The results also show widespread but small brain structural correlates of frailty, which mediated less than 2% of the association between physical frailty and the top ten frailty-related phenotypes