The RSS Glasgow local group hosted an event on 9 February with three speakers working on cardiovascular modelling at the University of Glasgow. Alan Lazarus, Agnieszka Borowska and Mihaela Paun presented their PhD and post-doc research to an audience of approximately 45 people.
The event focused on the application of pulmonary hypertension, which is high blood pressure in the pulmonary arteries. Pulmonary hypertension can be diagnosed using invasive procedures that risk excessive bleeding and partial lung collapse. The speakers introduced Bayesian methodology to model the left ventricular chamber of a human heart using MRI imagining to avoid such invasive risky procedures.
The event started with Mihaela’s talk discussing the importance of allowing for model mismatch in cardiovascular modelling. She presented a Bayesian approach that improves on uncertainty quantification by considering the discrepancy between the mathematical model and the reality. These additional sources of uncertainty lead the conventional least squares approach to be overly confident and furthermore introduces biased parameter estimates. Mihaela’s method is based on Gaussian processes and achieves to produce a more realistic uncertainty measure and corrects the bias introduced by the conventional method.
Mihaela's slides (PDF)
Alan addressed the problem of computational time when estimating model parameters and quantifying their uncertainty. He proposes to use a statistical emulator that can be trained before the patient arrives in the clinic. The emulator is a neural network that uses ex-vivo data that is incorporated as prior information. The difficulty here lies in the left ventricular geometry, which is substantially different between patients. That makes training the neural network before in-vivo data is obtained difficult. The talk introduces a low dimensional representation of the left ventricular chamber to address these problems.
Alan's slides (PDF)
Agnieszka Borowska improves computational times by using Bayesian optimisation to find the optimum of an unknown black-box function. This method aims to improve efficiency and accuracy of the state-of-the-art algorithm by using a statistical surrogate-model. The surrogate model is used to select the next query point at which to evaluate the expensive black box-function. The method was tested on two studies and performs well. While it does improve computational time, the speaker points out that further research is needed to make these models applicable in a clinical setting. Multi-task BO was suggested to be explored for that purpose.
Agnieszka's slides (PDF)
The talks were followed by a discussion that focused on the clinical application of this work and the importance of it for personalised medicine in general. The speakers acknowledged that this is very much an active area of research and it is not yet used in a clinical setting, however patient-specific models are promising research to advance personalised medicine. Modelling the left ventricular chamber has the potential to inform clinicians about the patient’s pulmonary blood pressure, fibre stiffness, stretch-stress relations, etc without the need for invasive procedures.
Michael Waltenberger is a PhD student and MacLaurin scholar at the University of Glasgow working on spatial statistics.