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Atherosclerosis is a chronic inflammatory disease of the artery wall. The early stages of atherosclerosis are driven by interactions between lipids and monocyte-derived-macrophages (MDMs). The mechanisms that govern the spatial distribution of lipids and MDMs in the lesion remain poorly understood. In this paper, we develop a spatially-resolved and lipid-structured model for early atherosclerosis. The model development and analysis are guided by images of human coronary lesions by Nakashima et al. 2007. Consistent with their findings, the model predicts that lipid initially accumulates deep in the intima due to a spatially non-uniform LDL retention capacity. The model also qualitatively reproduces the global internal maxima in the Nakashima images only when the MDM mobility is sufficiently sensitive to lipid content, and MDM lifespan sufficiently insensitive. Introducing lipid content-dependence to MDM mobility and mean lifespan produced minimal impact on model behaviour at early times, but strongly impacted lesion composition at steady state. Increases to the sensitivity of MDM lifespan to lipid content yield lesions with fewer MDMs, less total lesion lipid content and reduced mean MDM infiltration depth. Increases to the sensitivity of MDM mobility to lipid content also reduces the MDM infiltration depth, but increases the proportion of lipid-laden MDMs. We find that MDM lipid content increases with spatial depth, regardless of blood LDL and HDL content. These results shed light on the mechanisms that drive spatial variation in the composition of early atherosclerotic lesions, and the role of macrophage lipid content in disease progression.

Smooth muscle cells (SMCs) play a fundamental role in the development of atherosclerotic plaques. SMCs may ingest lipids in a similar way to monocyte-derived macrophages (MDMs) in the plaque. This can stimulate SMCs to undergo a phenotypic switch towards a macrophage-like phenotype. We formulate an ordinary differential equation (ODE) model for the populations of SMCs, MDMs and smooth muscle cell-derived macrophages (SDMs) and the internalised lipid load in each population. We use this model to explore the effect on plaque fate of SMC phenotype switching. We find that when SMCs switch to a macrophage-like phenotype, the total lipid contained in cells in the plaque increases. Additionally, removal of SMCs from the plaque via phenotype switching reduces the fibrous plaque cap, increases the lipid in the necrotic core, and increases plaque inflammation. This makes the plaque more vulnerable to rupture, which can lead to heart attacks and strokes. When SDMs are highly proliferative and resistant to cell death, the plaque grows rapidly and becomes highly pathological. The model suggests that plaque dynamics, driven by the switch of SMCs to a macrophage-like phenotype, may drive the development of unstable, vulnerable and pathological plaques.

Macrophages in atherosclerotic lesions exhibit a spectrum of behaviours or phenotypes. The phenotypic distribution of monocyte-derived macrophages (MDMs), its correlation with MDM lipid content, and relation to blood lipoprotein densities are not well understood. Of particular interest is the balance between low density lipoproteins (LDL) and high density lipoproteins (HDL), which carry bad and good cholesterol respectively. To address these issues, we have developed a mathematical model for early atherosclerosis in which the MDM population is structured by phenotype and lipid content. The model admits a simpler, closed subsystem whose analysis shows how lesion composition becomes more pathological as the blood density of LDL increases relative to the HDL capacity. We use asymptotic analysis to derive a power-law relationship between MDM phenotype and lipid content at steady-state. This relationship enables us to understand why, for example, lipid-laden MDMs have a more inflammatory phenotype than lipid-poor MDMs when blood LDL lipid density greatly exceeds HDL capacity. We show further that the MDM phenotype distribution always attains a local maximum, while the lipid content distribution may be unimodal, adopt a quasi-uniform profile or decrease monotonically. Pathological lesions exhibit a local maximum in both the phenotype and lipid content MDM distributions, with the maximum at an inflammatory phenotype and near the lipid content capacity respectively. These results illustrate how macrophage heterogeneity arises in early atherosclerosis and provide a framework for future model validation through comparison with single-cell RNA sequencing data.

We present the Extragalactic Serendipitous Swift Survey (ExSeSS), providing a new well-defined sample constructed from the observations performed using the Swift X-ray Telescope. The ExSeSS sample consists of 79,342 sources detected in the medium (1-2 keV), hard (2-10 keV) or total (0.3-10 keV) energy bands, covering 2086.6 deg$^{2}$ of sky across a flux range of $f_\mathrm{0.3-10keV}\sim10^{-15}-10^{-10}$ erg s$^{-1}$ cm$^{-2}$. Using the new ExSeSS sample we present measurements of the differential number counts of X-ray sources as a function of 2-10 keV flux that trace the population of Active Galactic Nuclei (AGN) in a previously unexplored regime. We find that taking the line-of-sight absorption column density into account has an effect on the differential number count measurements and is vital to obtain agreement with previous results. In the hard band, we obtain a good agreement between the ExSeSS measurements and previous, higher energy data from NuSTAR and Swift/BAT when taking into account the varying column density of the ExSeSS sample as well as the X-ray spectral parameters of each of the samples we are comparing to. We also find discrepancies between the ExSeSS measurements and AGN population synthesis models, indicating a change in the properties of the AGN population over this flux range that is not fully described by current models at these energies, hinting at a larger, moderately obscured population at low redshifts ($z\lesssim0.2$) that the models are not currently taking into account., Comment: 14 pages, 11 figures, accepted for publication by MNRAS. Supplementary data provided at https://www.swift.ac.uk/2SXPS/exsess/

We extend the lipid-structured model for atherosclerotic plaque development of Ford et al. (2019) to account for macrophage proliferation. Proliferation is modelled as a non-local decrease in the lipid structural variable that is similar to the treatment of cell division in size-structured models (e.g. Efendiev et al. (2018)). Steady state analysis indicates that proliferation assists in reducing eventual necrotic core size and acts to spread the lipid load of the macrophage population amongst the cells. The relative contribution of plaque macrophages by proliferation and recruitment from the bloodstream is also examined. The model suggests that a more proliferative plaque differs from an equivalent (same lipid content and cell count) recruitment-dominant plaque only in the way lipid is distributed amongst the macrophages., Comment: 29 pages, 8 figures

X-ray luminosity functions (XLFs) of Active Galactic Nuclei (AGN) trace the growth and evolution of supermassive black hole populations across cosmic time, however, current XLF models are poorly constrained at redshifts of z>6, with a lack of spectroscopic constraints at these high redshifts. In this work we \redit{place limits} on the bright-end of the XLF at z=5.7-6.4 using high-redshift AGN identified within the Extragalactic Serendipitous Swift Survey (ExSeSS) catalogue. Within ExSeSS we find one serendipitously X-ray detected z>6 AGN, ATLAS J025.6821-33.4627, with an X-ray luminosity of $L_\mathrm{X}=8.47^{+3.40}_{-3.13}\times10^{44}\mathrm{erg.s^{-1}}$ and $z=6.31\pm0.03$ making it the highest redshift, spectroscopically confirmed, serendipitously X-ray detected quasar known to date. We also calculate an upper limit on the space density at higher luminosities where no additional sources are found, enabling us to place constraints on the shape of the XLF. Our results are consistent with the rapid decline in the space densities of high-luminosity AGN toward high redshift as predicted by extrapolations of existing parametric models of the XLF. We also find that our X-ray based measurements are consistent with estimates of the bolometric quasar luminosity function based on UV measurements at $z\gtrsim6$, although they require a large X-ray to bolometric correction factor at these high luminosities., Comment: 10pages, 6 figures. Resubmitted to MNRAS, following referee comments

Atherosclerosis is characterised by the growth of fatty plaques in the inner (intimal) layer of the artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from the adjacent medial layer to deposit a cap of fibrous collagen over the fatty plaque core. The fibrous cap isolates the thrombogenic content of the plaque from the bloodstream and prevents the formation of blood clots that cause myocardial infarction or stroke. Despite the important protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why certain caps become stable, while others become vulnerable to rupture. We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to growth factor signals from the endothelium. Diffusible platelet-derived growth factor (PDGF) stimulates SMC migration, proliferation and collagen degradation, while diffusible transforming growth factor (TGF)-$\beta$ stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using a range of in vivo and in vitro experimental data, reproduces several observations from studies of plaque growth in atherosclerosis-prone mice. Numerical simulations and model analysis demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGF-$\beta$ in effective cap formation and maintenance. These findings provide unique insight into the cellular and biochemical mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque.

The enhanced oil recovery technique of low-salinity (LS) water flooding is a topic of substantial interest in the petroleum industry. Studies have shown that LS brine injection can increase oil production relative to conventional high-salinity (HS) brine injection, but contradictory results have also been reported and an understanding of the underlying mechanisms remains elusive. We have recently developed a steady-state pore network model to simulate oil recovery by LS brine injection in uniformly wetted pore structures (Watson et al., Transp. Porous Med. 118, 201-223, 2017). We extend this approach here to investigate the low-salinity effect (LSE) in heterogeneously wetted media. We couple a model of capillary force-driven fluid displacement to a novel tracer algorithm and track the salinity front in the pore network as oil and HS brine are displaced by injected LS brine. The wettability of the pore structure is modified in regions where water salinity falls below a critical threshold, and simulations show that this can have significant consequences for oil recovery. For networks that contain spanning clusters of both water-wet and oil-wet (OW) pores prior to flooding, our results demonstrate that the OW pores contain the only viable source of incremental oil recovery by LS brine injection. Moreover, we show that a LS-induced increase in microscopic sweep efficiency in the OW pore fraction is a necessary, but not sufficient, condition to guarantee additional oil production. Simulations suggest that the fraction of OW pores in the network, the average network connectivity and the initial HS brine saturation are key factors that can determine the extent of any improvement in oil recovery in heterogeneously wetted networks following LS brine injection. This study highlights that the mechanisms of the LSE can be markedly different in uniformly wetted and non-uniformly wetted porous media.

Atherosclerotic plaque growth is characterised by chronic inflammation that promotes accumulation of cellular debris and extracellular fat in the inner artery wall. This material is highly thrombogenic, and plaque rupture can lead to the formation of blood clots that occlude major arteries and cause myocardial infarction or stroke. In advanced plaques, vascular smooth muscle cells (SMCs) migrate from deeper in the artery wall to synthesise a cap of fibrous tissue that stabilises the plaque and sequesters the thrombogenic plaque content from the bloodstream. The fibrous cap provides crucial protection against the clinical consequences of atherosclerosis, but the mechanisms of cap formation are poorly understood. In particular, it is unclear why certain plaques become stable and robust while others become fragile and vulnerable to rupture. We develop a multiphase model with non-standard boundary conditions to investigate early fibrous cap formation in the atherosclerotic plaque. The model is parameterised using a range of in vitro and in vivo data, and includes highly nonlinear mechanisms of SMC proliferation and migration in response to an endothelium-derived chemical signal. We demonstrate that the model SMC population naturally evolves towards a steady-state, and predict a rate of cap formation and a final plaque SMC content consistent with experimental observations in mice. Parameter sensitivity simulations show that SMC proliferation makes a limited contribution to cap formation, and highlight that stable cap formation relies on a critical balance between SMC recruitment to the plaque, SMC migration within the plaque and SMC loss by apoptosis. The model represents the first detailed in silico study of fibrous cap formation in atherosclerosis, and establishes a multiphase modelling framework that can be readily extended to investigate many other aspects of plaque development.

We present the most up-to-date X-ray luminosity function (XLF) and absorption function of Active Galactic Nuclei (AGNs) over the redshift range from 0 to 5, utilizing the largest, highly complete sample ever available obtained from surveys performed with Swift/BAT, MAXI, ASCA, XMM-Newton, Chandra, and ROSAT. The combined sample, including that of the Subaru/XMM-Newton Deep Survey, consists of 4039 detections in the soft (0.5--2 keV) and/or hard ($>2$ keV) band. We utilize a maximum likelihood method to reproduce the count-rate versus redshift distribution for each survey, by taking into account the evolution of the absorbed fraction, the contribution from Compton-thick (CTK) AGNs, and broad band spectra of AGNs including reflection components from tori based on the luminosity and redshift dependent unified scheme. We find that the shape of the XLF at $z \sim 1-3$ is significantly different from that in the local universe, for which the luminosity dependent density evolution model gives much better description than the luminosity and density evolution model. These results establish the standard population synthesis model of the X-Ray Background (XRB), which well reproduces the source counts, the observed fractions of CTK AGNs, and the spectrum of the hard XRB. The number ratio of CTK AGNs to the absorbed Compton-thin (CTN) AGNs is constrained to be $\approx$0.5--1.6 to produce the 20--50 keV XRB intensity within present uncertainties, by assuming that they follow the same evolution as CTN AGNs. The growth history of supermassive black holes is discussed based on the new AGN bolometric luminosity function., Comment: 33 pages including 48 figures and 6 tables, accepted for publication in ApJ

We present the X-ray source catalog in the Subaru/XMM-Newton deep survey. A continuous area of 1.14 deg^2 centered at R.A. = 02h18m and Dec. = -05d is mapped by seven pointings with XMM-Newton covering the 0.2-10 keV band. From the combined images of the EPIC pn and MOS cameras, we detect 866, 1114, 645, and 136 sources with sensitivity limits of 6x10^{-16}, 8x10^{-16}, 3x10^{-15}, and 5x10^{-15} erg cm^{-2} s^{-1} in the 0.5-2, 0.5-4.5, 2-10, and 4.5-10 keV bands, respectively, with detection likelihood >= 7 (corresponding to a confidence level of 99.91%). The catalog consists of 1245 sources in total including 32 extended-source candidates. The averaged log N-log S relations are in good agreement with previous results, bridging the flux range between Chandra deep surveys and brighter surveys. The log N-log S relations show significant spatial variation among pointings on a scale of 0.2 deg^2. Analyzing the auto correlation function, we detect significant clustering signals from the 0.5-2 keV band sample, which can be fit with a power law form (\theta/\theta_c)^{-0.8} with a correlation length of \theta_c=5.9^{+1.0}_{-0.9} arcsec when the integral constraint term is included. In the 2-10 keV band, however, the clustering is not significant with a 90% upper limit of \theta_c < 1.5 arcsec., Comment: 17 pages, 32 figures, accepted for publication in ApJS