Finite element-immersed boundary method and its application to mitral valves

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

Abstract

Each year, about 225,000 valve replacements in the heart are performed worldwide. In particular, mitral valve (MV) diseases such as mitral regurgitation (leakage) may lead to left ventricle (LV) dilation, decreased LV function, and increased rates of atrial fibrillation. Mathematical modelling can help us to understand MV diseases and their relationship with LV functions. However, compared to the aortic valves, the MV has been significantly understudied due to its more complex anatomical structure. We will deliver Magnetic Resonance Image based dynamic MV models which will include important features such as fluid-structure interaction and nonlinear soft tissue modelling. This will be achieved by developing novel numerical methods; i.e. a new finite element version of immersed boundary method with adaptive mesh refinement (IBAMR). The work will be carried out through an interdisciplinary collaboration between Mathematics at Glasgow, the Institute of Cardiovascular and Medical Science, and the primary developer of the IBAMR software, Prof. Boyce Griffith from NYU. IBAMR represents the state of the art immersed boundary methods, and is gaining increasing popularity in the USA due to its accuracy. Prof. Luo is one of the leading developers of this software. One of the important strengths of this project is the direct involvement of the Cardiovascular Research centre, which has the most advanced MRI facilities in the UK, and is linked to Golden Jubilee National Hospital and Western Infirmary. Thus we will have access to valve geometries from healthy and diseased patients. Most importantly, we will obtain 3D temporal displacement and strain vector field of the MV in vivo using the state of the art imaging techniques. This will tie the computational simulations with clinical applications together and allow us to identify key elements and parameters in our models.Modelling the dynamics of the MV to understand its mechanical performance in health and disease offers exciting new opportunities. Apart from addressing important physiological and pathological questions about the MV functions, our findings will serve as springboard for further research on other valvular heart disease. Improved understanding of the basic mechanisms of heart valve function will result in improved clinical therapies and therefore has clear social benefit. Ultimately, our aim is to delay or prevent progression of valvular disease, for example, by modulating transvalvular blood flow or engaging pharmacological approaches to modify cardiac output and valve elasticity. The framework to be developed from this project will also be used immediately to multi-scale models of the whole heart aiming at understanding acute myocardial infarction.

Planned Impact

Our application will have several impacts: (a) Young researchers: The project will provide the ideal environment to train a PhD student and a highly skilled post-doc RA. (b) Academic community in fundamental research: The science is cutting edge and the computational framework is at the state of the art in the bio-computational community. The proposed work will be fundamental to the fluid and solid mechanics. (c) Mitral valve research community: The application of this framework will address important questions on MV mechanics. The application of modelling the mitral valve so as to understand its mechanical performance in healthy and diseased states offers exciting new challenges. (d) Knowledge base: The research will develop an open source library with state of the art fluid-structure interactions and soft tissue constitutive modelling, which will be beneficial to a large number of research groups both inside the UK and worldwide. (e) Clinical Sector and NHS: Modelling to understand heart valve diseases and other physiological problems will enhance diagnosis, treatment, and prevention. (f) Patients: In the longer term, the collective effort in the research area will directly benefit patients and improve their quality of life.

Publications

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Feng L (2018) On the chordae structure and dynamic behaviour of the mitral valve. in IMA journal of applied mathematics

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Gao H (2017) Modelling mitral valvular dynamics-current trend and future directions. in International journal for numerical methods in biomedical engineering

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Gao H (2014) A finite strain nonlinear human mitral valve model with fluid-structure interaction. in International journal for numerical methods in biomedical engineering

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Gao H (2014) Quasi-static image-based immersed boundary-finite element model of left ventricle under diastolic loading. in International journal for numerical methods in biomedical engineering

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Gao H (2015) Parameter estimation in a Holzapfel-Ogden law for healthy myocardium. in Journal of engineering mathematics

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Griffith BE (2017) Hybrid finite difference/finite element immersed boundary method. in International journal for numerical methods in biomedical engineering

 
Title YouTube 
Description Our events are recorded and published in youtube: https://youtu.be/Ydo4G5VmSOo https://youtu.be/mH8CgNYvRw8 We also have updated animations of our modelling posted on YouTube since 2015 https://www.youtube.com/watch?v=JcUNUmbCJSI https://www.youtube.com/watch?v=Qko55MsoX8k https://www.youtube.com/watch?v=dAX8xnykZJM 
Type Of Art Film/Video/Animation 
Year Produced 2016 
Impact This is hard to assess. 
URL https://www.youtube.com/watch?v=JcUNUmbCJSI
 
Description Our work has been published at International Journals and presented at various conferences. People are already citing our results in their work. From 2016-2018, we organized annual outreach activities in the "European Researchers' Night" on the last Friday of Septembers, where thousands of parents and school pupils attended. We demonstrated what our mathematical models can do to help with heart diseases. In 2015, we organized two outreach activities, one at the Explore Glasgow West End Festival, July 2015, and one at "Meet the Expert" at the Glasgow Science Festival, Nov, 2015. We have shown the general public of what we do, and why our models can be important in disease treatment of mitral valves
Sector Digital/Communication/Information Technologies (including Software),Healthcare
Impact Types Cultural,Societal,Policy & public services

 
Description A whole-heart model of multiscale soft tissue mechanics and fluid structure interaction for clinical applications (Whole-Heart-FSI)
Amount £1,304,759 (GBP)
Funding ID EP/S020950/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 09/2019 
End 09/2024
 
Description EPSRC Maths Centre for Healthcare
Amount £1,998,909 (GBP)
Funding ID EP/N014642/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 04/2016 
End 03/2020
 
Description Effect of vasomotion on efficient flow delivery in microvascular network
Amount HK$500,000 (HKD)
Organisation Research Grants Council Hong Kong 
Sector Public
Country China
Start 10/2013 
End 08/2016
 
Description Feasibility study on the Predictive Modelling of Extruder Design and Behaviour upon Fibre Orientation in an extruder Collagen Tube
Amount £40,000 (GBP)
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 10/2012 
End 09/2013
 
Description First steps towards computed modelling of myocardial infarction (an MI Physiome): A case-control study of novel biomechanical parameters in acute MI survivors with left ventricular dysfunction
Amount £104,456 (GBP)
Funding ID G/14/64/31043 
Organisation British Heart Foundation (BHF) 
Sector Charity/Non Profit
Country United Kingdom
Start 04/2014 
End 03/2016
 
Description Initiating new transformative ideas to heart remodelling (Pump-Priming)
Amount £20,173 (GBP)
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 10/2012 
End 04/2013
 
Description Mechanical and Finite Element Modelling of Collagen Casing Manufacture and Application
Amount £50,000 (GBP)
Organisation Government of Scotland 
Department Scottish Funding Council
Sector Public
Country United Kingdom
Start 10/2013 
End 09/2014
 
Description Myocardial strain measurements in survivors of acute ST-elevation myocardial infarction: implementation and prognostic significance of novel magnetic resonance imaging methods
Amount £118,075 (GBP)
Funding ID CRTF09-31639 
Organisation British Heart Foundation (BHF) 
Sector Charity/Non Profit
Country United Kingdom
Start 10/2015 
End 09/2018
 
Description POEMS Network
Amount £17,500 (GBP)
Organisation University of Sheffield 
Sector Academic/University
Country United Kingdom
Start 04/2016 
End 03/2017
 
Description SofTMech with MIT and POLIMI (SofTMechMP)
Amount £1,599,530 (GBP)
Funding ID EP/S030875/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 06/2019 
End 06/2023
 
Description The Leverhulme Research Fellowship
Amount £50,000 (GBP)
Funding ID RF-2015-510 
Organisation The Leverhulme Trust 
Sector Charity/Non Profit
Country United Kingdom
Start 10/2015 
End 09/2017
 
Description Work on the Predictive Modelling of Extruded Collagen Tube Fund from IAA-EPSRC and Devro LTD
Amount £20,000 (GBP)
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 10/2012 
End 04/2013
 
Title Computational models and methodology 
Description We developed finite element immersed boundary methods and used these to develop new models for mitral valve, left ventricle and various coupled systems. 
Type Of Material Model of mechanisms or symptoms - human 
Provided To Others? No  
Impact Our publications are cited by a number of other research groups, and we are invited to give talks at conferences/workshops 
URL http://www.glasgowheart.org/
 
Title Open Source software, https://github.com/IBAMR/IBAMR 
Description This open source software can be used by any research groups who are interested in modelling fluid-structure interaction and soft tissues 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact We contributed to the develpment of this open source. 
URL https://github.com/IBAMR/IBAMR
 
Description New academic collabrations 
Organisation Heriot-Watt University
Country United Kingdom 
Sector Academic/University 
PI Contribution Our research enabled us to establish new collabrations with three other Universities (St. Andrews, Heriot-Watt, Sheffield), and together we successfully secured 2M funding for an EPSRC Maths centre for Heathcare (SofTMech).
Collaborator Contribution Our collabrators (Mark Chaplain, Steve McDougall, Paul Watton) work extensively cancer research and agent-based modelling, which opened up an exciting new route of multi-scale modelling of soft tissues applied to heart and cancer.
Impact These are new collabrations, so too early to tell.
Start Year 2015
 
Description New academic collabrations 
Organisation University of Sheffield
Country United Kingdom 
Sector Academic/University 
PI Contribution Our research enabled us to establish new collabrations with three other Universities (St. Andrews, Heriot-Watt, Sheffield), and together we successfully secured 2M funding for an EPSRC Maths centre for Heathcare (SofTMech).
Collaborator Contribution Our collabrators (Mark Chaplain, Steve McDougall, Paul Watton) work extensively cancer research and agent-based modelling, which opened up an exciting new route of multi-scale modelling of soft tissues applied to heart and cancer.
Impact These are new collabrations, so too early to tell.
Start Year 2015
 
Description New academic collabrations 
Organisation University of St Andrews
Country United Kingdom 
Sector Academic/University 
PI Contribution Our research enabled us to establish new collabrations with three other Universities (St. Andrews, Heriot-Watt, Sheffield), and together we successfully secured 2M funding for an EPSRC Maths centre for Heathcare (SofTMech).
Collaborator Contribution Our collabrators (Mark Chaplain, Steve McDougall, Paul Watton) work extensively cancer research and agent-based modelling, which opened up an exciting new route of multi-scale modelling of soft tissues applied to heart and cancer.
Impact These are new collabrations, so too early to tell.
Start Year 2015
 
Description New clinical collabration 
Organisation NHS Royal Hospital for Children
Department Department of Cardiac Surgery
Country United Kingdom 
Sector Hospitals 
PI Contribution Our model simulations have raised the keen interests of the cardiologists and they start to approach us and suggesting new collabrations.
Collaborator Contribution We have made new reserach collabration with Mr. Mark Danton Consultant Cardiac Surgeon, and Dr. Patrick Noonan Consultant Cardiologist, who are helping us to develop clinical cases for mitral valve study.
Impact We have submitted a HRUK grant application, which has passed the first round.
Start Year 2015
 
Description New industrial collabration 
Organisation Dassault Systemes UK Ltd
Country United Kingdom 
Sector Private 
PI Contribution Our modelling activities and publications attracted this group, and we are invited to be an academic member of their "Living Heart Project"
Collaborator Contribution DASSAULT SYSTÈMES UK LTD agreed to provide 75k in-kind support to our bid for an EPSRC Maths-centre for Healthcare, which was successful.
Impact Success of the £2M bid for the EPSRC Centre for Multiscale Soft Tissue Mechanics - with application to heart & cancer
Start Year 2016
 
Description 2nd International workshop on Soft Tissue Modelling 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact 60 researchers in the area attended this workshop, including the international leading experts. Selected talks followed by poster sessions sparked questions and discussions afterwards. The meeting finished by a lively research forum led by the plenary speakers on future directions of the soft tissue modelling.
Year(s) Of Engagement Activity 2015
URL http://www.gla.ac.uk/schools/mathematicsstatistics/events/conferences/softtissuemodelling2/
 
Description Explore Glasgow West End Festival 
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 This is a large scale joint event by sevearl Universities/Schools at Glasgow Science Centre. It lasted for two days. We set up a stand and made book markers and leaflets, as well as posters and videos. We have attracted a lot of audience
Year(s) Of Engagement Activity 2015
 
Description Outreach 
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 Meet the Expert at the Glasgow Science Festival
Year(s) Of Engagement Activity 2015