10:30 Arrival and coffee
11:00 Prof. Catherine Powell (University of Manchester)
Title: Numerical Methods for Forward UQ in PDE Models with Uncertain
12:00 Dr. Dimitris Kalogiros (University of Nottingham)
Title: Combining in vitro Data and Mathematical Models to Understand
Chemokine Biology: An Integrated Pipeline Using a Bayesian
Parameter Inference Approach.
Abstract: All protective and pathogenic immune and inflammatory responses rely heavily on leukocyte migration and localisation. Chemokines are secreted chemoattractants that orchestrate the positioning and migration of leukocytes through concentration gradients. However, understanding how these gradients are formed, maintained and regulated remains unclear.
We present a mathematical and computational framework that integrates experimental, computational and modelling approaches. It accounts for dynamic interactions between physical, biological and biochemical processes modelled through diffusion, advection, binding kinetics and cellular uptake leading to the establishment of spatio-temporal chemokine gradients. Reduced modelling frameworks and computational bayesian methods are implemented to infer underlying parameters as well as to quantify uncertainty of the computational model.
This study shows how a synergistic approach between experimental and computational modelling benefits from the Bayesian approach to provide a robust analysis of chemokine transport, chemokine-cell interactions and cell migration. It provides a building block for a larger research effort to gain holistic insight and generate novel and testable hypotheses in chemokine biology and leukocyte trafficking.
13:30 Dr. Tony Shardlow (University of Bath)
Title: Mathematical techniques for modelling bone-shape variation in arthritic hands.
14:30 Thomas Pak (University of Oxford)
Title: Pakman: a modular and efficient software tool for approximate Bayesian inference.
Abstract: The amount of data generated in the biological sciences has rise sharply due to the development of high-throughput experimental techniques. Bayesian statistics provides a framework for data-driven parameter estimation and model selection, even when dealing with complicated mathematical models. In particular, inferring model parameters from observed data is possible with approximate Bayesian computation (ABC) methods, even when the likelihood function is analytically or computationally intractable.
Certain ABC methods, such as the ABC rejection and sequential Monte Carlo (SMC) method, involve a simulation workload that can be parallelised across many computational nodes. A parallel implementation can thus dramatically reduce the time needed to run these methods. In this talk, we introduce Pakman, a tool for parallel ABC that is designed to be modular, efficient and portable. Pakman is modular at the systems-level, which means that any executable application can be used with Pakman in a "plug and play" manner. This modular framework allows researchers to use their existing software in ABC workloads, without the need to rewrite their code. Moreover, the use of the Message Passing Interface (MPI) standard for parallelisation means that Pakman can be built and used on virtually any parallel computing platform. Thus, Pakman enables researchers to leverage all the computational resources at their disposal to fit mathematical models to experimental data in a convenient and efficient manner.
15:00 Luminita Maxim (VU Amsterdam)
Title: Removing bias in functional connectivity estimation from MEG recordings
Abstract: Neural oscillations have been the focus of many studies in Neuroscience since it was demonstrated that they are involved in cognitive and motor functions. In the human brain, non-invasive methods are required, with high temporal resolution and large coverage. One such method is MEG, which records the magnetic fields produced by the electric activity of groups of activated neurons. However, its spatial resolution is limited by the ill-posed nature of the inverse problem we need to solve in order to obtain the brain functional connectivity from the recordings. Mapping a possibly large number of active sources in the brain to a relatively low number of sensors in the MEG device is generating spurious correlations. The methods to solve this issue have been usually conservative, removing not only false connections, but also true ones.
In this talk, I discuss some mathematical aspects of the MEG forward and inverse problems, and I present a method to remove statistical bias from the cross-spectral matrix of the brain activity. The bias correction corresponds to removing spurious correlations, while largely preserving the true ones. I also present simulation results used to compare the performance of this method to existing methods in the MEG community.
16:00 Dr. Deirdre McGrath (University of Nottingham)
Title:Advanced Inverse Problem Solving for Magnetic Resonance
Abstract: Magnetic Resonance Elastography (MRE) is a powerful diagnostic imaging technique that measures changes in the biomechanical properties of biological tissue caused by disease. MRE works by delivering mechanical waves to the tissue, which are measured using MRI, and these wave measurements are converted into estimated biomechanical properties using specialised reconstruction algorithms, generally termed “inversion algorithms”. These algorithms solve an inverse problem: starting from MR imaging data, they estimate tissue biomechanical properties, thereby allowing the differentiation of healthy and diseased tissue. The accurate identification of the disease location and boundaries is a main challenge for current inversion algorithms which are required to assimilate a large amount of noisy MRI data.
In this collaboration between the NIHR Nottingham Biomedical Research Centre and the Department of Mathematics at the University of Nottingham, we are developing novel inversion algorithms for MRE data, using Bayesian inversion approaches. The algorithms are validated with simulated MRE data and will be applied to data acquired at the Sir Peter Mansfield Imaging Centre, University of Nottingham, and in particular for the clinical application of diagnosing liver fibrosis. The development of these methods has the potential to improve significantly MRE-based diagnosis, by assimilating MRI data into a general class of heterogeneous and anisotropic biomechanical models.
17:00 Dr. Igor Chernyavsky (University of Manchester)
Title: Reverse-engineering complex microvascular systems: structural
determinants of transport in placental capillary networks.
Abstract: Across mammalian species, solute transport takes place in complex microvascular networks. However, despite recent advances in three-dimensional (3D) imaging, there has been poor understanding of geometric and physical factors that determine solute exchange and link the structure and function. Here, we use an example of the human placenta, a vital fetal life-support system, where the primary functional exchange units, terminal villi, contain disordered networks of fetal capillaries and are surrounded externally by maternal blood. We show how the irregular internal structure of a terminal villus determines its exchange capacity for a wide range of solutes. Integrating 3D image-based geometric and transport features into new non-dimensional parameters, we characterise the structure-function relationship of terminal villi via a simple and robust algebraic approximation, revealing transitions between flow- and diffusion-limited transport at vessel and network levels. The developed theory accommodates for nonlinear blood rheology and tissue metabolism and offers an efficient method for multi-scale modelling. Our results show how physical estimates of transport, based on scaling arguments and carefully defined geometric statistics, provide a useful tool for understanding solute exchange in placental and other complex microvascular systems.
Erlich A, Pearce P, et al. (2019) Sci Adv 5:eaav6326 (doi.org/10.1126/sciadv.aav6326).
Erlich A, et al. (2019) Interface Focus 9:0190021 (doi.org/10.1098/rsfs.2019.0021).