L3

Cardiac fibrosis plays a significant role in the disruption of healthy electrical signalling in the heart, creating structural heterogeneities that induce and stabilise arrhythmia.  However, a proper understanding of the consequences of cardiac fibrosis must take into account the complex and highly variable patterns of its spatial localisation in the heart, which significantly affects the extent and manner of its impacts on cardiac wave propagation. In this work we present a methodology for the algorithmic generation of fibrotic patterns via Perlin noise, a technique for computationally efficient generation of textures in computer graphics.

Our approach works directly from image data to create populations of pattern realisations that all resemble the target image under a set of metrics. Our technique thus serves as a type of data enrichment, enabling analysis of how variability in the precise placement of fibrotic structures modulates their electrophysiological impact. We demonstrate our method, and the types of analysis it can enable, using a widely referenced histological image of four different types of microfibrotic structure. Our generator and Bayesian tuning method prove flexible enough to successfully capture each of these very distinct patterns.

We demonstrate the importance of this tool, by presenting 2D simulations overlayed on the generated images that highlight the effects of microscopic variability on the electrophysiological impact of fibrosis. Finally, we discuss the application of our methodology to the increasingly available imaging data of fibrotic patterning on a more macroscopic scale, and indeed to other areas of science underpinned by image based modelling and simulation.    

Competition between peptides for binding and presentation by MHC class I molecules decides the immune response to foreign or tumor antigens. Many previous studies have attempted to classify the immunogenicity of a peptide using machine learning algorithms to predict the affinity, or half-life, of the peptide binding to MHC. However immunopeptidome analyses have shown a poor correlation between sequence based predictions and the abundance on the cell surface of the experimentally identified peptides. Such metrics are, for instance, only comparable when the abundance of competing peptides can be accurately quantified. We have developed a model for predicting the relative presentation of competing peptides that takes into account off-rate, source protein abundance and turnover and cofactor-assisted MHC assembly with peptides. This model is mechanism based so that it can accommodate complex biology phenomena such as inflammation, up or downregulation of peptide loading complex chaperones, appearance of a mutanome. We have used aspects of the model to drive an investigation of the precise molecular mechanism of peptide selection by MHC I and its associated intracellular cofactors.

Despite their tiny size, microorganisms play a huge role in many biological, medical, and engineering phenomena. For example, massive plankton blooms are an integral part of the oceanic ecosystem. Algal cells incorporate carbon dioxide, which affects global warming. In industry, microorganisms are used in bioreactors to produce food and medicines and to treat sewage. The human body hosts hundreds of microorganism species, and the number of microorganisms in the human body is roughly double the number of cells in the body. In the intestine, approximately 1 kg of enterobacteria form a unique ecosystem, called the gut flora, which plays important roles in digestion and in relation to infection. Because of the considerable influence that microorganisms have on human life, the study of their behavior and function is important.

Recent research has demonstrated the importance of biomechanics in understanding the behavior and functions of microorganisms. For example, red tides can be induced by the interplay between the background flow and swimming cells. A dense suspension of bacteria can generate a coherent structure, which strongly enhances mass transport in a suspension. These phenomena show that the physical environments around cells alter their behavior and biological functions. Such a biomechanical understanding is still lacking in microbiology, and we believe that biomechanics can provide new perspectives on future microbiology.

In this talk, we first introduce some of our studies of the behavior of individual swimming microorganisms near surfaces. We show that hydrodynamic forces can trap cells at liquid–air or liquid–solid interfaces. We then introduce interactions between a pair of swimming microorganisms, because a two-body interaction is the simplest many-body interaction. We show that our mathematical models can describe the interactions between two nearby swimming microorganisms. Collective motions formed by a group of swimming microorganisms are also introduced. We show that some collective motions of microorganisms, such as coherent structures of bacterial suspensions, can be understood in terms of fluid mechanics. We then discuss how cellular-level phenomena can change the rheological and diffusion properties of a suspension. The macroscopic properties of a suspension are strongly affected by mesoscale flow structures, which in turn are strongly affected by the interactions between cells. Hence, a bottom-up strategy, i.e., from a cellular level to a continuum suspension level, represents a natural approach to the study of a suspension of swimming microorganisms. Finally, we discuss whether our understanding of biological functions can be strengthened by the application of biomechanics, and how we can contribute to the future of microbiology.

Snapshot mosaic multispectral imagery acquires an undersampled data cube by acquiring a single spectral measurement per spatial pixel. Sensors which acquire p frequencies, therefore, suffer from severe 1/p undersampling of the full data cube.  We show that the missing entries can be accurately imputed using non-convex techniques from sparse approximation and matrix completion initialised with traditional demosaicing algorithms.

Atom Probe Tomography is a powerful 3D mass spectrometry technique. By pulsing the sample apex with an electric field, surface atoms are ionised and collected by a detector. A 3D image of estimated initial ion positions is constructed via an image reconstruction protocol. Current protocols assume ion trajectories follow a stereographic projection. However, this method assumes a hemispherical sample apex that fails to account for varying material ionisation rates and introduces severe distortions into atomic distributions for complex material systems.

We aim to develop continuum models and use this to derive a time-dependent mapping describing how ion initial positions on the sample surface correspond to final impact positions on the detector. When correctly calibrated with experiment, such a mapping could be used for performing reconstruction.

Currently we track the sample surface using a level set method, while the electric field is solved via BEM or a FEM-BEM coupling. These field calculations must remain accurate close to the boundary. Calibrating unknown evaporation parameters with experiment requires an ensemble of models per experiment. Therefore, we are also looking to maximise model efficiency via BEM compression methods i.e. fast multipole BEM. Efficiently constructing and reliably interpolating the non-bijective trajectory mapping, while accounting for ion trajectory overlap and instabilities (at sample surface corners), also presents intriguing problems.

This project is in collaboration with Cameca, the leading manufacturer of commercial atom probe instruments. If successful in minimising distortions such a technique could become valuable within the semiconductor industry.

In this talk we will show how the floating point errors in the simulation of SDEs (stochastic differential equations) can be modelled as stochastic. Furthermore, we will show how these errors can be corrected within a multilevel Monte Carlo approach which performs most calculations with low precision, but a few calculations with higher precision. The same procedure can also be used to correct for errors in converting from uniform random numbers to approximate Normal random numbers. Numerical results will be generated on both CPUs (using single/double precision) and GPUs (using half/single precision).