The SofTMech Statistical Emulation and Translation Hub

Lead Research Organisation: University of Glasgow
Department Name: School of Mathematics & Statistics

Abstract

There have recently been impressive developments in the mathematical modelling of physiological processes. As part of a previously EPSRC-funded research centre (SofTMech), we have developed mathematical models for the mechanical and electrophysiological processes of the heart, and the flow in the blood vessel network. This allows us to gain deeper insight into the state of a variety of serious cardiovascular diseases, like hypoxia (a condition in which a region of the body is deprived of adequate oxygen supply), angina (reduced blood flow to the heart), pulmonary hypertension (high blood pressure in the lungs) and myocardial infarction (heart attack). A more recent extension of this work to modelling blood flow in the eye also provides novel indicators to assess the degree of traumatic brain injury.
What all these models have in common is a complex mathematical description of the physiological processes in terms of differential equations that depend on various material parameters, related e.g. to the stiffness of the blood vessels or the contractility of the muscle fibres. While knowledge of these parameters would be of substantial benefit to the clinical practitioner to help them improve their diagnosis of the disease status, most of the parameters cannot be measured in vivo, i.e. in a living patient. For instance, the determination of the stiffness and contractility of the cardiac tissue would require the extraction of the heart from a patient and its inspection in a laboratory, which can only be done in a post mortem autopsy.
It is here that our mathematical models reveal their diagnostic potential. Our equations of the mechanical processes in the heart predict the movement of the heart muscle and how its deformations change in time. These movements can also be observed with magnetic resonance image (MRI) scans, and they depend on the physiological parameters. We can thus compare the predictions from our model with the patterns found in the MRI scans, and search for the parameters that provide the best agreement. In a previous proof-of-concept study we have demonstrated that the physiological parameters identified in this way lead to an improved understanding of the cardiac disease status, which is important for deciding on appropriate treatment options.
Unfortunately, the calibration procedure described above faces enormous computational costs. We typically have a large number of physiological parameters, and an exhaustive search in a high-dimensional parameter space is a challenging problem. In addition, every time we change the parameters, our mathematical equations need to be solved again. This requires the application of complex numerical procedures, which take several minutes to converge. The consequence is that even with a high-performance computer, it takes several weeks to determine the physiological parameters in the way described above. It therefore appears that despite their enormous potential, state of the art mathematical modelling techniques can never be practically applied in the clinical practice, where diagnosis and decisions on alternative treatment option have to be made in real time.
Addressing this difficulty is the objective of our proposed research. The idea is to approximate the computationally expensive mathematical model by a computationally cheap surrogate model called an emulator. To create this emulator, we cover the parameter space with an appropriate design, solve the mathematical equations in parallel numerically for the chosen parameters, and then fit a non-linear statistical regression model to this training set. After this initial computational investment, the emulator thus created gives predictions for new parameter values practically instantaneously, allowing us to carry out the calibration procedure described above in real time. This will open the doors to harnessing the diagnostic potential of state-of-the art mathematical models for improved decision support in the clinic.

Planned Impact

According to the British Heart Foundation (BHF), heart and circulatory diseases cause more than a quarter of all deaths in the UK, that is nearly 170,000 deaths each year, an average of 460 deaths each day or one every three minutes in the UK. There are around 7.4 million people living with heart and circulatory disease in the UK: 3.9 million men and 3.5 million women.

Mathematical modelling in cardiovascular physiology is a topical research area and has in principle paradigm-shifting potential for improving our understanding of a patient's cardio-vascular disease status, elucidating the nature of pathophysiological processes, improving patient-specific disease prognostication, and providing more accurate decision support for alternative treatment options. However, a major obstacle is the exorbitant computational cost of model calibration, as discussed in the "Summary" section. These are typically in the order of several weeks even on a high-performance computer, which currently renders state of the art mathematical models completely for the clinical practice.

The general impact of the proposed research hub is the fact that methodological improvements in statistical emulation will provide a decisive stepping stone towards enabling the use of state-of-the-art soft-tissue, electro-physiological and fluid-dynamic models for real-time decision making in the clinic and thereby harness their enormous potential for patient-specific disease prognostication. The emulation of soft-tissue mechanical models of the left ventricle of the heart will help assess the risk and treatment options for myocardial infarction (heart attack). The emulation of cardio-electrophysiological models will allow the monitoring of post-infarction scars to prevent sudden cardiac death. The emulation of fluid dynamic models for the pulmonary circulation system linked to the right ventricle of the heart will enable the non-invasive diagnosis of pulmonary hypertension, which is a major risk factor for stroke, heart failure and coronary artery disease. Endovascular drug delivery will be made more effective by emulating the patient-specific device-tissue-fluid interactions. And an extension of the cardiovascular modelling to the emulation of fluid dynamics in the human eye will allow the fast identification of traumatic brain injury, which will provide e.g. a clinical indicator for the "shaken baby syndrome".

To make specific progress towards these objectives, we will closely engage with the Scottish Pulmonary Vascular Unit at the Golden Jubilee Hospital in Clydebank, with the Cardiology Department at Queen Elizabeth University Hospital in Glasgow, and with NHS Scotland, as described in more detail in the "Pathways to Impact" section of this proposal.

The proposed research will also be relevant to companies that aim to deliver realistic simulation applications to explore real-world behaviour of complex systems particularly related to physiology, in that it will allow them to substantially reduce the computational complexity of inference and uncertainty quantification and thereby make their simulation systems applicable to decision-making in real time. A particular example is Dassault Systems, with whom the proposed research hub will closely engage. Moreover, the proposed research is relevant to companies that manufacture endovascular devices, like stents and drug-coated balloons, in that mathematical models of device-tissue-fluid interactions allow improvement of device design, and emulation is critical for fast patient-specific decisions. As a specific first step, the proposed hub will establish a collaboration with Terumo Aortic.

Statistical emulation is not only relevant to healthcare, but to the mathematical modelling of complex systems for safety-critical situations more generally. This includes e.g. early warning systems for tsunamis and volcanic activities, which will benefit from the methodological advancements made in the proposed research.

Publications

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Al Sariri T (2022) Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours. in Mathematical medicine and biology : a journal of the IMA

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Borowska A (2022) Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle. in International journal for numerical methods in biomedical engineering

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Borowska A (2022) Semi-Complete Data Augmentation for Efficient State Space Model Fitting in Journal of Computational and Graphical Statistics

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Cai L (2022) Fluid-structure interaction simulation of calcified aortic valve stenosis. in Mathematical biosciences and engineering : MBE

 
Title Optimizing Cardio-Mechanic Models for Diagnosis and Treatment of Heart Disease 
Description Video summarising the main findings and potential impact of the paper Lazarus, A., Gao, H. , Luo, X. and Husmeier, D. (2022) Improving cardio-mechanic inference by combining in vivo strain data with ex vivo volume-pressure data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 71(4), pp. 906-931. (doi: 10.1111/rssc.12560) 
Type Of Art Film/Video/Animation 
Year Produced 2022 
Impact The impact is described in the video itself. 
URL https://www.youtube.com/watch?v=W79XGCXH6Sg
 
Description CARDIAC MECHANICS
While there have been impressive advancements in the mathematical modelling of cardiac mechanic processes in recent years, getting these models into the clinic for patient-specific diagnosis and suggestion of treatment options following a heart attack is extremely challenging. The reason is that these models depend on a variety of patient-specific physiological parameters that cannot be measured in vitro, and statistical inference based on a comparison between model predictions and clinical measurements is practically infeasible due to the high computational complexity of repeated numerical solutions of the mathematical models. To address this difficulty, we have developed a statistical surrogate model of the cardiac mechanics model to emulate the original mathematical model at substantially reduced computational costs. To make this approach feasible, we have developed an effective dimension reduction technique and systematically integrated physiological prior knowledge from the literature into our inference. In this way we have reduced the computational costs from several weeks to the order of an hour at negligible loss of accuracy. We have also developed a global sensitivity analysis method for eliminating parameters from the model that have no influence on the clinical quantities of interest, and we have developed a method for quantifying the uncertainty of our physiological parameter estimation.

PULMONARY HYPERTENSION
Pulmonary hypertension (high blood pressure in the main pulmonary artery of the lungs) is a serious medical condition that can ultimately lead to heart failure. Standard diagnostic procedures are based on right-heart catheterization, where a catheter is inserted into the pulmonary artery to directly measure the pressure inside the heart and pulmonary arteries. This is an invasive technique, which comes with a series of potentially fatal side effects. Recent fluid dynamics models of the pulmonary blood circulation system have the potential to predict the blood pressure based on non-invasive measurements of the blood flow. However, these models depend on various patient specific biophysical parameters, like the vessel stiffness, which cannot be measured in vivo. We have developed a novel procedure for estimating these parameters from the available clinical data. This includes a framework for uncertainty quantification, which does not only take measurement errors but also a potential mismatch between the mathematical model and the real cardio-physiological system into account. We have also developed a correction for the closed-loop effect that arises when making medical interventions based on predictions from the mathematical model. This could potentially leave the model mis-calibrated, and we have developed a correction mechanism for automatic re-calibration.

MEDICAL DEVICE OPTIMISATION
One of our goals is patient specific device design of drug eluting-stents for the treatment of coronary artery disease, by optimising the drug dose and release rate. If these parameters are too low, the drug is not sufficiently effective in preventing tissue growth and ultimately vessel occlusion; if they are too high, the drug can be toxic. The optimal values of these parameters depend on patient-specific differences in lesion composition, fluid flow, drug release and tissue uptake, which are computationally expensive to model mathematically. We have developed a novel constrained optimisation method, to maximise the effectiveness of the drug in a patient-specific manner while preventing toxicity. Our approach addresses the challenge of computational complexity by building an emulator, quantifying its uncertainty, and use both to minimise the number of expensive forward simulations from the mathematical model.

LESION DETECTION IN CARDIAC MAGNETIC RESONANCE IMAGES
We have developed a novel method for automatically classifying myocardial (heart) tissue into normal (healthy) and hypoperfused (lesion) regions based on cardiac magnetic resonance images. This promises novel opportunities for the diagnosis of coronary heart disease and for advancing our understanding of the aetiology of this highly prevalent disease.
Exploitation Route There have been impressive advancements in the mathematical modelling of complex systems in the last few decades, increasingly covering areas that until recently have been regarded as elusive for the quantitative sciences. The potential national benefits of what has become known as "digital twins" are enormous. However, complex mathematical models depend on a variety of parameters. If these parameters are not estimated properly, predictions made with a digital twin can be dangerously misleading. If the intrinsic uncertainty of this estimation is not quantified accurately, any risk assessment will be flawed, leading to wrong decisions with potentially serious consequences, particularly in safety-critical applications. The methods we have developed address exactly this challenge: robust and efficient parameter estimation in complex mathematical models with sound uncertainty quantification. While our particular focus in on cardiovascular systems, the methodological insights we have gained will be of interest to developers and users of digital twins in general.

We are confident that our methodological developments will be used by clinicians in the near future. Our pulmonary hypertension models are still in the development phase and have so far only been applied to mouse data, but the ultimate objective is their application to the detection of human hypertension. Our work on automatic lesion detection in cardiac MRI scans can be used by clinicians as part of a clinical decision support system. Our work on cardiac mechanics is still at an early development stage, but will ultimately help clinicians to base their suggestion of treatment options after a heart attack on deeper pathophysiological insights. Our work on medical device optimisation lays the groundwork for improving the design of drug-eluting stents in a patient-specific manner.
Sectors Healthcare

URL https://www.youtube.com/watch?v=W79XGCXH6Sg
 
Description SofTMEch-SET has been running for two years, i.e. it is in the middle of its funding period and translation of the method developments and research findings into clinical applications would not be expected at this stage yet. Our work on cardiac mechanics and medical device design is still in its development phase, and our methods for the detection of pulmonary hypertension have so far only been tested on mouse data. However, the large number of research outputs and publications in renowned international journals is encouraging. We have been in regular contact and discussion with clinicians to disseminate our findings, as summarised in the following dissemination video: https://www.youtube.com/watch?v=W79XGCXH6Sg This has been successful in that it has broadened their views on how mathematical modelling and data science can have a potential impact in the clinic. Our next engagement meeting with clinicians from the Golden Jubilee Hospital is scheduled for March 20th, where we will seek further feedback and input from them. In developing our methods we have been mindful of their implementation in the clinic, taking into account the closed-loop feedback effects caused when clinical interventions are based on mathematical model predictions. We have shown that such interventions may leave the mathematical model miscalibrated, and we have specifically advised how the models have to be recalibrated to avoid biased predictions. The importance of our work has been honoured with the "Best Paper Award" at ICSTA 2022.
First Year Of Impact 2022
Sector Healthcare
Impact Types Societal

 
Description 1 year EPSRC Fellowship at UoG 2022/23 A. Lazarus
Amount £83,330 (GBP)
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 02/2022 
End 02/2023
 
Description A Digital Twin for Designing Bladder Treatment informed by Bladder Outlet Obstruction Mechanobiology (BOOM)
Amount $3,500,000 (USD)
Funding ID R01 DK133434 
Organisation National Institutes of Health (NIH) 
Sector Public
Country United States
Start 07/2023 
End 06/2028
 
Description A modelling study of right ventricular function in repaired tetralogy of fallot for predicting outcome and impact of pulmonary valve replacement
Amount £185,505 (GBP)
Funding ID PG/22/10930 
Organisation British Heart Foundation (BHF) 
Sector Charity/Non Profit
Country United Kingdom
Start 09/2022 
End 10/2025
 
Title Cardiac Modelling with dispersed myofibre and collagen structures 
Description It is the accompanying dataset and model the paper "modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systole", accepted in the Journal of Engineering Mathematics. It implements two different fibre dispersion models within two ventricular finite element models: a bi-ventricular rabbit heart and a human left ventricular model. 
Type Of Material Computer model/algorithm 
Year Produced 2021 
Provided To Others? Yes  
Impact This study highlights the importance of fibre dispersion in cardiac mechanics, and for the first time to investigate how to incorporate a complex fibre dispersion distribution into a cardiac mechanics model. This work has been presented in the Living Heart Project Seminar, and we are working with the Virtual Human Team from Dassault System to implement it in the Living Heart Project. 
URL https://github.com/HaoGao/DispersedFibresMyocardiumModelling
 
Title Cardiovascular Modelling Subject to Medical Interventions 
Description This GitHub repository contains data and code to reproduce the results reported in the paper 'Inference in Cardiovascular Modelling Subject to Medical Interventions' by L. Mihaela Paun, Agnieszka Borowska, Mitchel J. Colebank, Mette S. Olufsen and Dirk Husmeier, published in the Proceedings of ICSTA 2021. 
Type Of Material Computer model/algorithm 
Year Produced 2021 
Provided To Others? Yes  
Impact The software allows the results of the above-mentioned paper to be reproduced, and it can be used more widely to correct closed-loop effects in cardiovascular modelling and inference subject to medical interventions. 
URL https://github.com/LMihaelaP/Cardio_Vasodilation.git
 
Title Code for Estimation of Parameters for an Archetypal Model of Cardiomyocyte Membrane Potentials 
Description This is a suite of MATLAB/Octave functions for numerical solution of and for estimation of the parameter values of the cardiomyocyte membrane potential model of Biktashev et al. (Bull Math Biol, 70(2), 2008,doi:10.1007/s11538-007-9267-0) - "the archetypal model". In particular, the code can be used determine parameter values for the archetypal model such that its solutions approximate the action potential traces and the action potential duration restitution curves of (a) other electrophysiologically detailed mathematical models of the transmembrane ionic currents of single cardiac myocytes - "target models", as well as (b) traces and curves measured experimentally - "target data". Data and functions for several detailed ionic models from the CellML physiological model repository (cellml.org) are included as examples of usage. 
Type Of Material Database/Collection of data 
Year Produced 2021 
Provided To Others? Yes  
Impact N/A 
URL https://zenodo.org/record/4568662
 
Title Codes from Improving cardio-mechanic inference by combining in-vivo strain data with ex-vivo volume-pressure data 
Description Codes to run the model published in Improving cardio-mechanic inference by combining in-vivo strain data with ex-vivo volume-pressure data 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact Codes can be used to improve parameter estimation of material parameters in the HO model. 
URL https://github.com/lazarusal/klotz-codes
 
Title Data From: Emulation of Cardiac Mechanics using Graph Neural Networks 
Description Data from the publication "Emulation of Cardiac Mechanics using Graph Neural Networks" 
Type Of Material Database/Collection of data 
Year Produced 2022 
Provided To Others? Yes  
Impact The dataset has been downloaded and applied to develop the state of the art in statistical emulation of soft-tissue mechanics 
URL https://zenodo.org/record/7075055#.ZAju1x_P25c
 
Title Fibre Dispersion Myocardial Mechanics 
Description It contains the computational models for the following two papers 1. Guan, D., Mei, Y., Xu, L., Cai, L., Luo, X., & Gao, H. (2022). Effects of dispersed fibres in myocardial mechanics, Part I: passive response. Mathematical Biosciences and Engineering, 19(4), 3972-3993. 2. Guan, D., Wang, Y., Xu, L., Cai, L., Luo, X., & Gao, H. (2022). Effects of dispersed fibres in myocardial mechanics, Part II: active response. Mathematical Biosciences and Engineering, 19(4), 4101-4119. Published Year: 2022 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact This work has attracted interest from the Virtual Human Team from Dassault System. It will further improve the cardiac modelling by including detailed fibre dispersion, in particular in fibrosis modelling. 
URL https://github.com/HaoGao/FibreDispersionMyocardialMechanics
 
Title HBM for myocardial perfusion modelling data and algorithms 
Description The data and algorithms are for the publication, Classification of myocardial blood flow based on dynamic contrast-enhanced magnetic resonance imaging using hierarchical Bayesian models. 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact This model has been developed to estimate and classify the myocardial blood flow using myocardial perfusion DCE-MRI. 
URL https://github.com/YaleiYangGlagsow/JRSSC
 
Title Improving cardio-mechanic inference by combining in vivo strain data with ex vivo volume-pressure data 
Description GitHub repository with the software and data needed to reproduce the results of the following article: Alan Lazarus, Hao Gao, Xiaoyu Luo and Dirk Husmeier (2022): ``Improving cardio-mechanic inference by combining in vivo strain data with ex vivo volume-pressure data", Journal of the Royal Statistical Society, Series C, accepted for publication. 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact The software and data allow the user to reproduce the results of the above paper. The user can use the code for cardiac mechanics applications more generally, by systematically integrating in vivo strain data, extracted from cardiac magnetic resonance images, with ex-vivo volume-pressure data. 
URL https://github.com/lazarusal/klotz-codes
 
Title Neural Network-Based Left Ventricle Geometry Prediction from Cardiac Magnetic Resonance Images 
Description Github repository including the software and data for the paper by Lukasz Romaszko, Agnieszka Borowska, Alan Lazarus, David Dalton, Colin Berry, Xiaoyu Luo, Dirk Husmeier and Hao Gao (2021): ``Neural network-based left ventricle geometry prediction from CMR images with application in biomechanics", Artificial Intelligence in Medicine, Volume 119, September 2021, 102140, doi: https://doi.org/10.1016/j.artmed.2021.102140 In particular, the Github repository contains pre-processed data (a subset of re-scaled and cropped original CMR images as well as segmented images and LV geometries), as well as the code (two-stage CNN: segmentation network and geometry prediction network). 
Type Of Material Computer model/algorithm 
Year Produced 2021 
Provided To Others? Yes  
Impact The Github repository allows readers to reproduce the results reported in the above paper and to use the software to automatically predict the shape of the left ventricle of the heart from their own cardiac magnetic resonance images. This is a prerequisite for any subsequent cardiac mechanic modelling. 
URL https://github.com/aborowska/LVgeometry-prediction
 
Title Parameter estimation and uncertainty quantification in differential equation models 
Description Github repository containing the software and the data for the article by L. Mihaela Paun and Dirk Husmeier (2022): Emulation-accelerated Hamiltonian Monte Carlo algorithms for parameter estimation and uncertainty quantification in differential equation models,Statistics and Computing, volume 32, Article number: 1. https://link.springer.com/article/10.1007/s11222-021-10060-4 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact The software and the data of the Github repository allow the user to reproduce the results reported in the above paper. The software can be applied to other differential equation models to infer the model parameters and quantify the estimation uncertainty. 
URL https://github.com/LMihaelaP/Hamiltonian-Monte-Carlo-with-emulation.git
 
Title Sensitivity Analysis and Inverse Uncertainty Quantification for the Left Ventricular Passive Mechanic 
Description It contains the codes and data for the paper 'Sensitivity Analysis and Inverse Uncertainty Quantification for the Left Ventricular Passive Mechanics'. This work performs structural identifiability and practical identifiability analysis for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis to assess structural identifiability, and inverse-uncertainty quantification to assess practical identifiability. 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact It elucidates the dependence of parameter identifiability on external factors for the first time in a nonlinear cardiomechanic model, with a particular focus on the H-O myocardial model. 
URL https://github.com/HaoGao/ho-uncertainty-quantification
 
Title Sensitivity Analysis and Inverse Uncertainty Quantification for the Left Ventricular Passive Mechanics 
Description GitHub repository with the software and the data needed to reproduce the results reported in the following article: Alan Lazarus, David Dalton, Dirk Husmeier, Hao Gao (2022), ``Sensitivity Analysis and Inverse Uncertainty Quantification for the Left Ventricular Passive Mechanics", Biomechanics and Modelling in Mechanobiology Accepted for publication 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact The software and data allow the user to reproduce the results reported in the above paper. The user can adapt the software to use it for global sensitivity analysis and uncertainty quantification more generally. 
URL https://github.com/HaoGao/ho-uncertainty-quantification
 
Title StentsOptimisation 
Description Code reproducing results in the paper "Statistical Inference for Optimisation of Drug Delivery from Stents" by LM Paun, AF Schmidt, S McGinty, D Husmeier. 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact The code can be used by researchers interested in medical device optimisation. 
URL https://github.com/LMihaelaPaun/StentsOptimisation.git
 
Title Code for Estimation of Parameters for an Archetypal Model of Cardiomyocyte Membrane Potentials 
Description This is a suite of MATLAB/Octave functions for numerical solution of and for estimation of the parameter values of the cardiomyocyte membrane potential model of Biktashev et al. (Bull Math Biol, 70(2), 2008,doi:10.1007/s11538-007-9267-0) - "the archetypal model". In particular, the code can be used determine parameter values for the archetypal model such that its solutions approximate the action potential traces and the action potential duration restitution curves of (a) other electrophysiologically detailed mathematical models of the transmembrane ionic currents of single cardiac myocytes - "target models", as well as (b) traces and curves measured experimentally - "target data". Data and functions for several detailed ionic models from the CellML physiological model repository (cellml.org) are included as examples of usage. 
Type Of Technology Software 
Year Produced 2021 
Open Source License? Yes  
Impact NA 
URL https://zenodo.org/record/4568662
 
Title GlasgowHeart 
Description GlasgowHeart platform for personalized modelling of the human heart. It is organized into 4 modules, and each can be run separately. Currently, MatLab is the main programming language and using scripts for run, this will require certain knowledge of Matlab. In the future, we will develop a GUI package for easy use. The four modules are image processing, biomechanics modelling, personalization, and parameter inference of left ventricular (LV) mechanics and statistical emulation. 
Type Of Technology Software 
Year Produced 2021 
Open Source License? Yes  
Impact The package is actively being used by the researchers from the SofTMech Centre and supports a few cardiac research projects. 
 
Title passive-lv-gnn-emul 
Description The software allows for graph neural network emulator to trained and applied to a specified quasi-static mechanics problem, with emphasis on the passive mechanics of the left ventricle. The software is implemented in Python 
Type Of Technology Software 
Year Produced 2022 
Open Source License? Yes  
Impact The software is being used within SofTMech and being developed to more sophisticated applications. 
 
Description CHIMERA ECR Conference 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact The activity involved a series of talks by experienced researchers and medical practitioners, and shorter presentations by early career researchers in the broad area of mathematics applied to healthcare
Year(s) Of Engagement Activity 2022
 
Description CardiARC Zone 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact At the end of May 2022, We organized the CardiARC Zone at the ARCADIA festival, including a hands-on table with heart competitions and a VR suite in which a virtual heart was rotated moved and sliced as it popped up within the virtual laboratory. The CardiaARC Zone has attracted 100+ participants from school kids to the general public, to professionals and to the patient group. It has sparked many questions and discussions afterwards.
Year(s) Of Engagement Activity 2022
URL http://www.softmech.org/newsround/headline_872341_en.html
 
Description Cardiac Digital Twin Workshop 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact It is a one-day workshop to provide a forum on cardiac digital twins with presentations from clinicians, industry representatives, and academic researchers. Challenges and opportunities have been discussed extensively in the workshop.
Year(s) Of Engagement Activity 2023
 
Description Effective parameter inference for a mathematical model of the left ventricle 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited talk at ASCE Engineering Mechanics Institute International Conference 2021 (EMI 2021)
Year(s) Of Engagement Activity 2021
URL https://emi2020-ic.webspace.durham.ac.uk
 
Description IAA impact festival 2022 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact We have shown the research carried out in the SofTMech centre on mathematical modelling of the heart, in particular the projects funded by IAA, including the recent one on the investigation of cardiac injury in relation to COVID-19, to target mechanism understanding of both the short and long term effects of COVID-19. We have met researchers from different fields and industry representatives which have sparked some very interesting questions, in particular the potential commercialization of mathematical models developed in SofTMech.
Year(s) Of Engagement Activity 2022
URL https://impactfestival.hw.ac.uk/
 
Description Inference in Cardiovascular Modelling Subject to Medical Interventions 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk at the International Conference on Statistics: Theory and Applications (ICSTA 2021), given by Dirk Husmeier
Year(s) Of Engagement Activity 2021
URL https://avestia.com/ICSTA2021_Proceedings/files/papers.html
 
Description Inference in blood circulation pulmonary models 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Mihaela Paun was an invited speaker in the largest statistics conference, JSM'22, presenting her work on statistical inference in cardiovascular mathematical models. This has helped increase the visibility of the work done in our research hub.
Year(s) Of Engagement Activity 2022
URL https://ww2.amstat.org/meetings/jsm/2022/onlineprogram/AbstractDetails.cfm?abstractid=322068
 
Description Invited lecture 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited lecture for ECMINT 4.2 Cerebral aneurysms (European Course of Minimal Invasive Therapy). Intense theoretical course (University of Oxford) contributing to neuroradiology training and education, focusing on neuroendovascular therapy/repair (https://www.esmint.eu/ecmint/)
Year(s) Of Engagement Activity 2021
 
Description Invited presentation at the Isaac Newton Institute 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Presentation entitled "Probabilistic Calibration of Personalised Heart Models from Sparse and Noisy Measurements" invited as part of work programme on "The Role of Uncertainty in Mathematical Modelling of Pandemics" at the Isaac Newton Institute in Cambridge.
Year(s) Of Engagement Activity 2022
URL https://gateway.newton.ac.uk/event/tgm110/programme
 
Description Invited talk "A Novel Excitation-Contraction Model Based on Classical Hill Model" 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited talk on "A Novel Excitation-Contraction Model Based on Classical Hill Model", given by Hao Gao at the fourth international meeting on computational cardiology, NPU, XiAn China.
Year(s) Of Engagement Activity 2021
 
Description Invited talk ``Constrained Mixture Based-cardiac Growth and Remodelling" 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited talk on " Constrained Mixture Based-cardiac Growth and Remodelling", given by Hao Gao at the7th international symposium: virtual twin of human & living heart, organized by Dassault Systemes.
Year(s) Of Engagement Activity 2021
URL https://events.3ds.com/sites/default/files/international-symposium-2021-agenda.pdf
 
Description Invited talk at the University of Edinburgh which was live-streamed and recorded 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk entitled "Gaussian process enhanced semi-automatic ABC for inference in a stochastic differential equation system for chemotaxis" by Dirk Husmeier's post-doc Agnieszka Borowska at a Statistics seminar of the University of Edinburgh on the 8th of November 2021. The talk questions afterwards, including a follow-up discussion on gather.town. The recording of the talk can be accessed here:
https://ed-ac-uk.zoom.us/rec/play/f-leD9akIBpTJCiF9ZIlKdq2QEYByLsP79lV4ZwPtaXA3iv0L12TYBLI8cRgoJiWvuIowPSt_Necyekm.YwhHusq0ucFvlT0S?continueMode=true&_x_zm_rtaid=9RE7lTR9SviipSXtp58ZrQ.1637266969453.752b91c756c02a3426d923e4580c6e85&_x_zm_rhtaid=330
Year(s) Of Engagement Activity 2021
URL https://www.maths.ed.ac.uk/school-of-mathematics/events/statistics
 
Description Medical device optimisation 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact Mihaela Paun gave a talk in a small-scale conference attended by members of other UK research hubs working on healthcare modelling (CHIMERA ECR conference). The conference led to initial discussions on method overlap, possibly leading to future collaborations.
Year(s) Of Engagement Activity 2022
 
Description Mini-symposium "Progress and Trends in Mathematical Modelling of Cardiac Function" at BMC BAMC 2021 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Mini-symposium "Progress and Trends in Mathematical Modelling of Cardiac Function" at BMC BAMC 2021 organised by Hao Gao
Year(s) Of Engagement Activity 2021
URL https://sites.google.com/view/bmcbamc2021/home
 
Description Mini-symposium "Stochastic models in biology informed by data" at BMC BAMC 2021 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk entitled "Parameter estimation and uncertainty quantification in a stochastic differential equation model of cell movement and chemotaxis" given by Dirk Husmeier's post-doc Agnieszka Borowska at the Mini-symposium "Stochastic models in biology informed by data" at the British Applied Mathematics Colloquium on the 6th of April 2021, which sparked questions and discussion afterwards, including follow-up emails.
Year(s) Of Engagement Activity 2021
URL https://sites.google.com/view/bmcbamc2021/home
 
Description Optimisation of drug delivery from stents 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Mihaela Paun presented her work on optimisation of drug delivery from stents in an international statistics conference (ICSTA'22), which sparked questions and a discussion on the methodology applied.
Year(s) Of Engagement Activity 2022
URL https://avestia.com/ICSTA2022_Proceedings/files/paper/ICSTA_138.pdf
 
Description Oral talk "A hybrid active contraction for myocardium" 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Oral talk by Hao Gao on "A hybrid active contraction for myocardium" at the 26th Congress of the European Society of Biomechanics, Milano, Italy.
Year(s) Of Engagement Activity 2021
URL https://esbiomech.org/conference/esb2021/
 
Description Oral talk "Constitutive Modelling of Soft Biological tissue from ex vivo to in vivo" 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Oral talk by Hao Gao on "Constitutive Modelling of Soft Biological tissue from ex vivo to in vivo" at 25th International Congress of Theoretical and Applied Mechanics, Milano, Italy.
Year(s) Of Engagement Activity 2021
URL https://ima.org.uk/15361/25th-international-congress-of-theoretical-and-applied-mechanics/#:~:text=T...
 
Description Presentation: Emulation and Uncertainty Quantification in Cardiac Modelling 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact This was an academic engagement event organised by the Cambridge Mathematics of Information in Healthcare Hub. Around 50 researchers attended this event, and I have given a talk on emulation and uncertainty quantification in cardiac modelling. Questions, discussion afterwards and potential collaborations were sparked.
Year(s) Of Engagement Activity 2022
URL https://gateway.newton.ac.uk/event/tgm126
 
Description SofTMech Soft Tissue workshop 2021 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact The 5th Soft Tissue workshop took place from 1st-3rd June 2021. The workshop focused on the most recent advances in the field of soft tissue mechanics, with a clear vision of the landscape of multiscale soft tissue modelling and both fundamental and translational research.
Year(s) Of Engagement Activity 2021
 
Description SofTMech Training Programme Event: Figure Making Workshop 09.03.23 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact This was an interactive workshop designed to help students make better figures; topics included figure design, taking into account your audience, use of software packages, use of colour. For each topic students were able to submit their answers and ideas to the presenter's questions and for these answers to appear on the screen. Feedback on the workshop was also collected and was very positive.
Year(s) Of Engagement Activity 2023
URL http://www.softmech.org/trainingtheleadersoftomorrow/#d.en.910377
 
Description SofTMech Training Programme event (14th-28th November): PhD Course: An Introduction to Nonlinear Solid Mechanics led by Anna Pandolfi from the Politecnico di Milano 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Rigorous introduction to nonlinear solid mechanics, especially addressing finite kinematics, material frame
indifference, constitutive models within a thermodynamic framework. Analysis of nonlinear material behaviors.
Specific topics:
1. Mathematical preliminaries. Dual basis. Tensors.
2. Kinematics of deformations. Motions, kinematics of local deformation. Polar decomposition.
3. Conservation laws (mass, linear & angular momentum, energy). Thermodynamics. Virtual work principle.
4. Constitutive theories. Coleman-Noll's theory. Material frame indifference. Thermodynamic potentials. Kinetic
relations. Material classification.
5. Hyperelasticity. Elasticity symmetry. Internal constraints. Elastic materials: isotropic, transversally isotropic,
anisotropic materials.
6. Finite Plasticity. Multiplicative decomposition of the deformation gradient. Exponential and logarithmic mapping.
J2 plasticity. Pressure dependent plasticity.
7. Special materials: fiber reinforced tissues, liquid crystals
Year(s) Of Engagement Activity 2022
URL http://www.softmech.org/media/Media_894442_smxx.pdf
 
Description SofTMech Training Programme event (24.3.22): Attending an Academic Conference & Networking 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact This half day informal training event was aimed at Early Career Researchers; its aim was to prepare them for attending an in person academic conference. Having been unable to attend in person due to COVID this was especially valuable.
The following topics were covered:
what actually happens at an academic conference?
what can I hope to get out it?
how do I network effectively?
The event also included a practical exercise on preparing an elevator pitch for networking with senior academics.
Several of the students have gone on to attend in person workshops and conferences.
Year(s) Of Engagement Activity 2022
URL http://www.softmech.org/trainingtheleadersoftomorrow/#d.en.835979
 
Description SofTMech Training Programme event (31.5.22): PhD Poster Competition 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact The event was an in-person Poster competition open to PhD students from SofTMech and CMALS. Prior to the event two videos on Effective Poster Presentations were posted on the SofTMech website for any potential competitors to study. 28 people registered for the event; 17 presented posters.
After two years of the pandemic this event gave a valuable opportunity to at last ask questions in person, for discussion and perhaps just as importantly to meet some colleagues for the first time. Students participated in the event from the University of Glasgow Schools of Mathematics and Statistics, Biomedical Engineering, Ultrasonic Engineering and Computational Mechanics. Students came from the University of Strathclyde departments of Mathematics & Statistics and Biomedical Engineering.
Prior to the event the students arrived early to set up their posters. The event was opened by Dr Sean McGinty, Director of CMAL (Centre of Mathematics & Life Sciences at University of Glasgow)) A series of 1 min flash presentations, where each student had to give an overview of their poster by displaying a maximum of 2 PowerPoint slides, set the scene for the poster viewing. One of the students even gave directions to where his poster was; it worked as he finished 2nd !
The posters were judged by a combination of a panel of members of staff and also by the students themselves, who were each allowed one vote for their favourite poster. The standard of posters was high across the board. Certificates and vouchers were awarded to the best three posters.
We hope the experience of this event will help all the students as they progress in their careers.
Year(s) Of Engagement Activity 2022
URL http://www.softmech.org/trainingtheleadersoftomorrow/#d.en.848318
 
Description SofTMech Training Workshop Scientific Computation 2022 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact Training day for PhD students on Scientific Computation, held on 28th January 2022. The event attracted more than 40 participants from Maths-in-Healthcare centres from around the UK. Sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2022
 
Description Special Interest Group on the Fluid Mechanics of the Eye 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Since the COVID lockdown, Peter Stewart has organised virtual study groups on the fluid mechanics of the eye. The first event took place on 30th November 2020 and there have been 6 subsequent meetings across 2021 and 2022. These events have gathered clinicians and modellers (including some PhD students) to derive mathematical models pertinent to the eye. In particular, we have modelled:
(1) uveoscleral flow as a drug delivery platform to the macula
(2) formation of macular holes in aging eyes.
Several publications are in preparation.
We are hosting a follow up conference in Bath in June 2022, funded by the Macular Society.
Year(s) Of Engagement Activity 2020,2021,2022
URL https://eyefluidssig.wordpress.com/history/
 
Description Talk at the "ML in PL 2021" conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk entitled "Neural network-based left ventricle geometry prediction from CMR images with application in biomechanics" given by Dirk Husmeier's post-doc Agnieszka Borowska at the "ML in PL 2021" conference (online) on the 7th of November 2021. The talk sparked questions afterwards, including requests for further information.
Year(s) Of Engagement Activity 2021
URL https://conference2021.mlinpl.org/
 
Description Talk at the Newton Gateway workshop on ``The Role of Uncertainty in Mathematical Modelling of Pandemics" 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Richard Clayton giving a talk on ``Probabilistic Calibration of Personalised Heart Models from Sparse and Noisy Measurements" which has been recorded and is publicly available: https://gateway.newton.ac.uk/presentation/2022-02-09/34658
Year(s) Of Engagement Activity 2022
URL https://gateway.newton.ac.uk/event/tgm110/programme
 
Description Talk on "Forward and Inverse Uncertainty Quantification in Cardiac Mechanics" at ICSTA 2022 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk at ICSTA 2022 (International Conference on Statistics: Theory and Applications) on "Forward and Inverse Uncertainty Quantification in Cardiac Mechanics"
Year(s) Of Engagement Activity 2022
URL https://2022.icsta.net/
 
Description Talk on Graph Neural Network Emulation of Cardiac Mechanics 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Contributed talk given by David Dalton at the 3rd International Conference on Statistics: Theory and Applications (ICSTA'21).
The outcome was making the larger community aware of the potential of graph-based emulation methods in soft tissue mechanics.
Year(s) Of Engagement Activity 2021
URL https://avestia.com/ICSTA2021_Proceedings/
 
Description invited talk "An initial experience of constrained mixture based cardiac growth and remodelling" 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited talk "An initial experience of constrained mixture based cardiac growth and remodelling", given by Hao Gao at SIAM MS21 "Multi-scale modelling in Biomechanics".
Year(s) Of Engagement Activity 2021
URL https://wp.bcamath.org/siamms21/