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.
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.
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

Guan D
(2022)
A new active contraction model for the myocardium using a modified hill model.
in Computers in biology and medicine

Richardson SIH
(2021)
A poroelastic immersed finite element framework for modelling cardiac perfusion and fluid-structure interaction.
in International journal for numerical methods in biomedical engineering

Da Silva L
(2023)
Antibacterial potential of chalcones and its derivatives against Staphylococcus aureus.
in 3 Biotech

Li W
(2021)
Apparent growth tensor of left ventricular post myocardial infarction - In human first natural history study
in Computers in Biology and Medicine

Guan D
(2020)
Effect of myofibre architecture on ventricular pump function by using a neonatal porcine heart model: from DT-MRI to rule-based methods.
in Royal Society open science

Guan D
(2021)
Modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systole
in Journal of Engineering Mathematics

Zhuan X
(2020)
Residual Stress Estimates from Multi-cut Opening Angles of the Left Ventricle.
in Cardiovascular engineering and technology

Cai L
(2021)
The Comparison of Different Constitutive Laws and Fiber Architectures for the Aortic Valve on Fluid-Structure Interaction Simulation.
in Frontiers in physiology

Zhuan X
(2022)
Volumetric growth of soft tissues evaluated in the current configuration
in Biomechanics and Modeling in Mechanobiology
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 |