Growth and Remodelling in the Porcine Heart-- Pushing Mathematics through Experiments

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

Abstract

Cardiovascular disease (CVD) is the leading cause of disability and death in the UK and worldwide, with an estimated £19bn annual economic impact. The prevalence of acquired heart disease (e.g. coronary heart disease, which can lead to myocardial infarction), particularly in the elderly population, means that this is the dominant public health problem in our society. Scope remains for more effective clinical management of CVDs, in part due to the poor correlation between symptoms and causation. Significant potential exists in developing novel and innovative solutions to lead towards patient-specific interventions, which have already achieved enhanced outcomes within other clinically-demanding specialities.
Computational modelling provides a platform for forward and inverse analysis of cardiac mechanics. Soft tissue modelling enables integration of multi-scalar structure-function and FSI, and presents an emerging opportunity for investigating CVD-based, patient-specific interventions and is already being exploited to improve knowledge of myocardial infarction, evaluation of novel graft materials and assessing the vulnerabilities of atherosclerotic arteries to the plaque. The value of such simulations is a function of accurately representing tissue behaviour, via constitutive models. Existing models consider the tissue's anisotropic, hyperelastic response, but with limited studies on growth and remodelling (G&R) and data derived age-specific behaviour. Recent adult myocardium experimental studies also demonstrated the importance of viscoelastic tissue properties, which are generally ignored in heart modelling. This study will deliver experimentally based G&R laws with viscoelasticity that increase the accuracy of age-specific, cardiac tissue-behaviour simulations. Twinned with increasing computational capabilities, this is an important next-step towards realising patient-specific cardiac treatments.
We have designed an experimental programme that provides data for generating new G&R constitutive laws, from porcine tissue across 6 G&R stages. We will measure critical structural parameters including collagen and cardiomyocyte fibre orientation and dispersion, and biomechanical parameters including bi-axial, simple shear and stress-relaxation. We will also biochemically and biologically analysis these tissues, to allow cross-mapping to human studies. These data will then enable generation of new constitutive models, based on the framework developed by the Glasgow group. These have been used successfully to simulate the 3D dynamic finite strain LV mechanics, using the structure-based HO constitutive law, coupled with cardiac active contraction and FSI. We will hypothesis-test the new G&R laws by acquiring in vivo porcine ultrasound data, to allow derivation of p-v curves, blood flow rate and pressure. We will also map this behaviour to equivalent phases of human maturation.
The experimentally based G&R laws will represent significant progress versus the existing international capabilities of modelling in cardiac tissues. It should bring nearer the ambition of achieving patient-specific surgeries to enable more effective treatment of acquired heart disease and other CVDs. Our work will also set a foundation and reference for subsequent studies focused on G&R in disease progressions and potential clinical intervention. Our approach will provide a platform for others to exploit these principles and methodologies across a broader research area, which could include monitoring and managing progression of general heart diseases. Our work will also contribute towards worldwide academic basic and applied sciences, as well as the translational (healthcare) domain. We will provide the first combined experimental and theoretical approach to G&R of a natural porcine heart, establishing a database of structural and biomechanical changes mapped to human physiology, which will be available for interrogation to support further research.

Planned Impact

The research proposed here would have a combination of short- and long-term beneficiaries, and with continued effort, will offer long-term social and economic benefit.

Academic impact: The most direct impact will be the training of the two PDRAs, as well as training of PhD, MSc and final year undergraduate project students across the three universities. This research, defining viscoelastic G&R laws for the healthy heart, will also provide a valuable reference that scientists and clinicians can use to plan and develop new intervention strategies. For example, our work will provide a valuable database of the key changes in geometry and material properties associated with growth and, by modelling, we can show: how this evolution will affect the stress and strain distributions within the heart; what drives the growth laws; and what parameters changes (e.g. myocyte alignment) are strongly associated with ageing. Using such a multidisciplinary approach for such a topical medical problem, the project will broaden the base of researchers engaged in CVD treatment and diagnostics through a combination of project-associated seminar programme, and SofTMech bi-monthly meetings. Outside the three universities, researchers engaged in heart research will gain access to our open source software, as well as journal publications and conference presentations.

Socio-Economic impact: CVDs and chronic heart disease, in particular, cause nearly 74k deaths each year in the UK, equivalent to an average of nearly 200 people dying every day. They also cause a £19bn annual economic impact. Myocardial infarction in younger adults, particularly in women is currently a hot topic in cardiovascular medicine. The current proposal aims to provide new insights into the consequences of, and patient-specific interventions to assist, ageing myocardial tissue. Identification of specific G&R laws in healthy and diseased hearts can result in novel treatments. This is because cells within the tissue are balanced in homeostasis. Ageing or diseases disturb this, and cells remodel to reach a new state of homeostasis. One questions is when the fibroblast cells deposit and remodel collagen, do they act as over-stretched (strain-driven), or over-stressed (stress-driven)? These different scenarios are the same for a linear elastic material but not for the anisotropic myocardium. Clarifying the two mechanisms will lead to novel treatments: for strain-driven processes, therapies that restrain deformation are crucial; for stress-driven processes, control of pressure and stiffness are more effective. Our work will lay the foundation for future work on heart diseases, e.g. myocardial infarction in young and aged-subjects. We will organize a special Heart-day meeting at which our clinical collaborators, as well as researchers from other user groups (e.g. from Golden Jubilee National Hospital Glasgow Royal Infirmary, Vascutek, Wolfram Research), will be invited to participate, with the aim to identify new partners for further research.

User engagement: The team is ideally placed to maximise the impact generated from the research, with clinical input hardwired into the project. Prof Berry, a clinical academic and Consultant Cardiologist, is a co-investigator and will ensure that this work remains grounded within clinical reality. Strong clinical links also exist between the applicants and the other clinical groups at theBHF Glasgow Cardiovascular Research Centre and the Golden Jubilee Hospital, via the GlasgowHeart project. The project proposed here also draws upon a substantial body of UK and international expertise outside Glasgow.

Other public engagement will include Glasgow Science Festival activities, School open days, Family/Patient groups, production of YouTube videos, displaying posters and animations in lay language in the Glasgow Kelvingrove Museum, and broadcasting our work in the University of Glasgow Research Radio show.

Publications

10 25 50
 
Description The heart evolves with time; this process is faster when diseased. Modelling this requires a new mathematical theory. One approach is to introduce a so-called growth tensor in the framework of the volumetric growth theory. However, most existing theories evaluate the growth tensor in the undeformed and unloaded configuration, which is not appropriate as tissues adapt to changes in real-time. We have developed a new theory that allows the growth tensor to be defined in the currently loaded configuration, and able to produce a residual strain that is consistent with experimental observation.
Exploitation Route The outcome has been published and presented at conferences.
Sectors Education,Healthcare

 
Description Cardiovascular disease (CVD) is the leading cause of disability and death in the UK and worldwide, with an estimated £19bn annual economic impact. The incidence of heart failure, such as after heart attack, has remained persistently high due to the maladaptive growth and remodelling (G&R). Nowadays there are more heart disease survivors, leading to a subsequent rise in heart failure. This study will deliver experimentally based G&R laws with viscoelasticity that increase the accuracy of age-specific, cardiac tissue-behaviour simulations. Twinned with increasing computational capabilities, this is an important next-step towards realising patient-specific cardiac prognosis and treatment planning. Currently, we are developing two novel growth laws, one is the volumetric growth from the current configuration, and the other law is the constrained mixture theory based G&R. The experimentally informed G&R laws will represent significant progress versus the existing international capabilities of modelling in cardiac tissues. In parallel, we have developed a procedure for estimating the growth tensor in myocardial infarction patients for the first time purely based on longitudinal conventional cardiac magnetic resonance imaging, which is now integrated into the Glasgow Cardiac Mechanics Platform (https://github.com/HaoGao/GlasgowHeart) and freely available. Together with the newly developed G&R laws, it should bring nearer the ambition of achieving patient-specific diagnosis to enable more effective treatment of acquired heart disease and other CVDs. To explore G&R in other scenarios, we have further established a new collaboration with a team from the University of Strathclyde to study G&R in rat right ventricle under pulmonary hypertension, a proposal has been submitted to SULSA's (Scottish Universities Life Science Alliance) Innovation Seed Funding to carry out essential experiments for informing the G&R modelling. The virtual Human Modelling team (Dassault Systemes) has agreed to contribute to this project through in-kind support with matched funding. Our work will also set a foundation and reference for subsequent studies focused on G&R in disease progressions and potential clinical intervention. Our approach will provide a platform for others to exploit these principles and methodologies across a broader research area, which could include monitoring and managing the progression of general heart diseases. Our work will also contribute towards worldwide academic basic and applied sciences, as well as the translational (healthcare) domain. We will provide the first combined experimental and theoretical approach to G&R of a natural porcine heart, establishing a database of structural and biomechanical changes mapped to human physiology, which will be available for interrogation to support further research.
First Year Of Impact 2021
Sector Digital/Communication/Information Technologies (including Software),Education,Healthcare,Manufacturing, including Industrial Biotechology
Impact Types Economic

 
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 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 GlasgowHeart: A Magnetic Resonance Imaging-derived 'virtual twin' cardiac mechanics platform 
Description A personalized biomechanical cardiac modelling framework, aimed at the mechanistic understanding of individual patients' cardiac remodelling in the longer-term and risk-stratification. Our long-term aim is to be able to revolutionise clinical practice through accurate risk-stratification and virtual testing. Four modules are currently available in GlasgowHeart: 1) image processing, 2) biomechanics modelling, 3) personalization, inference and machine learning of left ventricular (LV) mechanics and 4) statistical emulation as shown in Figure 1. Modules 1, 2 and 3 have been developed in MATLAB by the co-authors, and module 4 is programmed in Python using Tensor Flow, Scikit-learn, XGBoost to use advanced machine-learning methods. For computational modelling in module 2, we further use LibMesh, IBAMR, Fenics for solving nonlinear systems, Visit and Paraview for 3D visualization. Module 2 can also work with other commercial packages for biomechanics simulations (ABAQUS, FEAP). 
Type Of Material Computer model/algorithm 
Year Produced 2021 
Provided To Others? Yes  
Impact This framework has been developed over the last ten years and contributed to various projects and funding applications. Recently it was presented in SCMR 2021 conference in the open-source software demo session. 
URL https://github.com/HaoGao/GlasgowHeart
 
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. 
 
Description BAMC minisymposium on Soft Tissue Growth and Remodelling 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact I organized a BAMC mini-symposium on Soft Tissue Growth and Remodelling with colleagues, which has attracted more than 50 audience
Year(s) Of Engagement Activity 2022
 
Description Interview for BBC Scotland News, 12th November 2020: Colin Berry 
Form Of Engagement Activity A broadcast e.g. TV/radio/film/podcast (other than news/press)
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact Colin Berry discussing the effects of long COVID on BBC News on the 12th November, 2020. The purpose was to make the general public aware that some people who become infected with COVID suffer long lasting effects.
Year(s) Of Engagement Activity 2020
URL https://twitter.com/UofGMVLS/status/1326844312525606914
 
Description Plenary talk at the International Forum on coompuational heart modelling 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Up to 100 people attended this event, organized by the North-West Polytechnic University
Year(s) Of Engagement Activity 2021
URL http://xygg.nwpu.edu.cn
 
Description Presentation of GlasgowHeart Platform in SCMR 2021 meeting 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact This is the first time to present the Glasgow heart modelling framework to clinicians in one of the largest meetings in the cardiac magnetic resonance imaging community, SCMR 2021. The audiences consist of clinicians, imaging experts, industry partners, etc. The presentation was given in the first software demo session of the SCMR meeting, which brings the mechanic model one step closer to clinicians. The meeting committee believes that biomechanical biomarkers shall be included in the diagnosis guideline, and encourage more open-source software within the society of cardiac magnetic resonance.
Year(s) Of Engagement Activity 2021
URL https://scmr2021.process.y-congress.com/scientificProcess/Schedule/?setLng=en
 
Description Research visits and seminars at the University of Auckland, Auckland Bioengineering Institute, and Department of Maths, University of Canterbury, Christchurch 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Both students and researchers, including other international visitors, attended the talks during the visits, which sparkled questions and discussion afterwards, and laid the foundation for future collaborations.
Year(s) Of Engagement Activity 2020
 
Description Talk at 9th International Biofluid Mechanics And Vascular Mechanobiology Symposium 
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 Maintain the tradition of excellence and the spirit of the International Bio-fluid Mechanics and Vascular Mechano-Biology Symposia that have evolved to be a unique opportunity for reviewing recent major milestones and achievements in all areas of biofluid mechanics, experimental and computational, from molecule and cell to organ levels and corresponding mechano-biological processes, therapeutics, and cardiovascular devices.

The event gathered scientists, clinicians, and practitioners from around the world to explore and assess the latest frontiers of Bio-Fluid Mechanics and Vascular Mechano-Biology, and set important directions for further research and development, and education. The symposium provided an opportunity for investigators to interact with peers, young and seniors, for development of new collaborations, as well as enhancement of existing ones.
Year(s) Of Engagement Activity 2020
URL https://9thbiofluids.com/
 
Description Twitter Account 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact SofTMech Twitter Account which covers a number of SofTMech and SofTMech related grants. Main purpose to give information on research activities, events including social, advertise job opportunities to a wide audience, and announce graduations, prizes and achievements of the group. In addition to use the Re-tweet feature of Twitter to advertise information from partner groups or followers. The account has 201 followers and follows 171 other Twitter accounts. Impacts arising from the Account are quick dissemination of material.
Year(s) Of Engagement Activity 2020,2021,2022
URL https://twitter.com/home