Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments

Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the quest of moving from qualitative to quantitative analysis and patient-tailored therapy. Mathematics, modelling and simulations are increasing their importance as tools in this quest. In this paper we give an overview of relations between mathematical modelling and imaging and focus particularly on the estimation of perfusion in the brain. In the forward model, the brain is treated as a porous medium and a two compartment model (arterial/venous) is used. Motivated by the similarity with techniques in reservoir modelling, we propose an ensemble Kalman filter to perform the parameter estimation and apply the method to a simple example as an illustrative example.acceptedVersio

A global ensemble of ocean wave climate statistics from contemporary wave reanalysis and hindcasts

There are numerous global ocean wave reanalysis and hindcast products currently being distributed and used across different scientific fields. However, there is not a consistent dataset that can sample across all existing products based on a standardized framework. Here, we present and describe the first coordinated multi-product ensemble of present-day global wave fields available to date. This dataset, produced through the Coordinated Ocean Wave Climate Project (COWCLIP) phase 2, includes general and extreme statistics of significant wave height (Hs), mean wave period (Tm) and mean wave direction (θm) computed across 1980–2014, at different frequency resolutions (monthly, seasonally, and annually). This coordinated global ensemble has been derived from fourteen state-of-the-science global wave products obtained from different atmospheric reanalysis forcing and downscaling methods. This data set has been processed, under a specific framework for consistency and quality, following standard Data Reference Syntax, Directory Structures and Metadata specifications. This new comprehensive dataset provides support to future broad-scale analysis of historical wave climatology and variability as well as coastal risk and vulnerability assessments across offshore and coastal engineering applications

Remote postconditioning by humoral factors in effluent from ischemic preconditioned rat hearts is mediated via PI3K/Akt-dependent cell-survival signaling at reperfusion

Short non-lethal ischemic episodes administered to hearts prior to (ischemic preconditioning, IPC) or directly after (ischemic postconditioning, IPost) ischemic events facilitate myocardial protection. Transferring coronary effluent collected during IPC treatment to un-preconditioned recipient hearts protects from lethal ischemic insults. We propose that coronary IPC effluent contains hydrophobic cytoprotective mediators acting via PI3K/Akt-dependent pro-survival signaling at ischemic reperfusion. Ex vivo rat hearts were subjected to 30 min of regional ischemia and 120 min of reperfusion. IPC effluent administered for 10 min prior to index ischemia attenuated infarct size by ≥55% versus control hearts (P < 0.05). Effluent administration for 10 min at immediate reperfusion (reperfusion therapy) or as a mimetic of pharmacological postconditioning (remote postconditioning, RIPost) significantly reduced infarct size compared to control (P < 0.05). The IPC effluent significantly increased Akt phosphorylation in un-preconditioned hearts when administered before ischemia or at reperfusion, while pharmacological inhibition of PI3K/Akt-signaling at reperfusion completely abrogated the cardioprotection offered by effluent administration. Fractionation of coronary IPC effluent revealed that cytoprotective humoral mediator(s) released during the conditioning phase were of hydrophobic nature as all hydrophobic fractions with molecules under 30 kDa significantly reduced infarct size versus the control and hydrophilic fraction-treated hearts (P < 0.05). The total hydrophobic effluent fraction significantly reduced infarct size independently of temporal administration (before ischemia, at reperfusion or as remote postconditioning). In conclusion, the IPC effluent retains strong cardioprotective properties, containing hydrophobic mediator(s) < 30 kDa offering cytoprotection via PI3K/Akt-dependent signaling at ischemic reperfusion

Structures Related to the Emplacement of Shallow-Level Intrusions

A systematic view of the vast nomenclature used to describe the structures of shallow-level intrusions is presented here. Structures are organised in four main groups, according to logical breaks in the timing of magma emplacement, independent of the scales of features: (1) Intrusion-related structures, formed as the magma is making space and then develops into its intrusion shape; (2) Magmatic flow-related structures, developed as magma moves with suspended crystals that are free to rotate; (3) Solid-state, flow-related structures that formed in portions of the intrusions affected by continuing flow of nearby magma, therefore considered to have a syn-magmatic, non-tectonic origin; (4) Thermal and fragmental structures, related to creation of space and impact on host materials. This scheme appears as a rational organisation, helpful in describing and interpreting the large variety of structures observed in shallow-level intrusions