Mathematically Modelling Metabolism with Hyperpolarised MRI (360G-Wellcome-211767_Z_18_Z)

Nuclear Magnetic Resonance has traditionally provided much information about metabolism in living systems ranging from enzymes to humans, owing to its unique chemical specificity. Due to the Boltzmann distribution, conventional magnetic resonance is inherently insensitive and resolving many metabolic reactions is impossible in vivo. Hyperpolarised Magnetic Resonance with Dynamic Nuclear Polarisation (DNP) provides a way to overcome the Boltzmann distribution by using low temperature quantum mechanics. A 13C-labelled metabolite is prepared at 0.8K, rapidly melted, and then injected into a living system in an MRI scanner. The 13C labelled molecule can then be briefly tracked through space, time and biochemistry before relaxing back to thermodynamic equilibrium. Currently, the field quantifies DNP data poorly because it estimates pseudo-first-order metabolic rate constants and neglects physical facts such as membrane transport. My project would propose differential equations that model the underlying biology and physics, solve them using advanced Bayesian methods and produce quantitative estimates of metabolic rate constants with bounded uncertainty. The aim is to quantify unidirectional metabolic fluxes on data acquired in vivo in the human heart, with external validation. The key goals would be the production of mathematical models, comparison of fitting algorithms and in vitro enzymatic comparison.