Publications
Talks, contributed
Functional Analysis of Healthy and Heart Failure Tissue Populations using 3D Cardiac Electromechanical Models
In 15th World Congress on Computational Mechanics (virtual), 2022.Status: Accepted
Functional Analysis of Healthy and Heart Failure Tissue Populations using 3D Cardiac Electromechanical Models
Computer modelling and simulation of the beating heart must reflect on electrical activation of cells and tissue, mechanical properties of tissue, and their interaction. Electrophysiological properties of the heart have been simulated abundantly and applied to increase mechanistic understanding of disease and improve treatment development. Recent maturity in cardiac mechanical modelling increased quantitative predictive power. However, tight coupling of cardiac mechanics with the underlying electrophysiological properties of the tissue makes modelling clinical mechanical phenomena such as cardiac disease and drug effects difficult. A combination of uncertainty quantification through populations of models and fully coupled electromechanics models provide greater predictive power on cardiac mechanisms and aid treatment development for cardiac diseases.
A fully coupled electromechanics model of ventricular tissue is developed by coupling the O’Hara-Rudy[1] electrophysiology model and the Land[2] mechanics model. A population of models was created by varying 16 electrophysiological and 11 mechanical parameters at the cell level. The population was calibrated from 1000 to 187 models based on biomarkers derived from the action potential shape, calcium transient and active tension. This calibrated population was altered in 11 parameters of the cell model to represent heart failure (based on [3]). A geometry of 20x7x3 mm is simulated with 1.0 or 0.5 mm spatial resolution for mechanics or electrophysiology respectively, with free movement in the fibre direction on one side. Results are extracted at the centre of the tissue, as well as tissue shortening on the free-contracting side.
Relative to the healthy population, heart failure manifests in both electrophysiological and mechanics biomarkers. The action potential takes ~20% longer to recover from activation and peak calcium concentration in the cell is reduced by 50.9%. In a similar trend, mechanical biomarkers show 42.2% reduction in peak active force, slower contraction and more variation in recovery times across the heart failure tissue population. The peak tissue shortening in the fibre direction as a result of free contraction is reduced from 0.68±0.07mm to 0.45±0.07mm (-33.2%) and its peak is delayed by 112ms (38.6%) in heart failure.
These simulations indicate strong effects on electrophysiological and mechanical heart function by population variation and disease such as heart failure. Therefore, strongly coupled 3D models are necessary to assess the impact of biological variation, cardiac vulnerability as well as safe and effective treatment development.
REFERENCES
[1] O’Hara, T. et al.; PLoS Comput. Biol. 2011 [doi:10.1371/journal.pcbi.1002061]
[2] Land, S. et al.; J. Mol. Cell. Cardiol. 2017 [doi:10.1016/J.YJMCC.2017.03.008]
[3] Gomez, J. et al; PLoS ONE 2014 [doi:10.1371/journal.pone.0106602]
| Afilliation | Scientific Computing |
| Project(s) | Department of Computational Physiology, Simulation of Cardiac Devices and Drugs for In-Silico Testing and Certification (SimCardioTest) |
| Publication Type | Talks, contributed |
| Year of Publication | 2022 |
| Location of Talk | 15th World Congress on Computational Mechanics (virtual) |
| Keywords | Cardiac biomechanics, Cardiac disease, Uncertainty quantification |
Proceedings, refereed
Population of Computational Cell and Tissue Cardiac Electromechanical Models for functional analysis
In World Congress of Biomechanics. 9th ed, 2022.Status: Accepted
Population of Computational Cell and Tissue Cardiac Electromechanical Models for functional analysis
Introduction
Cardiac computational models can fill important gaps in understanding the cardiomyocyte or cardiac tissue properties. Recent maturity in cardiac mechanical modelling enables quantitative predictive power across a range of applications. One challenge however is the tight coupling of cardiac mechanics with the underlying electrophysiological properties of the tissue, which makes modelling clinical mechanical phenomena such as drug effects difficult. More robust predictions can be achieved by modelling populations of models, which incorporate stochastic parameter variability to represent biological variation. For cardiac computational models to live up to their potential in developing safe and efficient treatments for increasingly prevalent cardiac disease, such populations of fully coupled electromechanics models will provide greater predictive power on mechanics and physiology of the heart.
Methods
A fully coupled electromechanics model of ventricular tissue is developed by coupling the O’Hara-Rudy[1] electrophysiology model and the Land[2] mechanics model. A population of models was created by varying 16 electrophysiological and 11 mechanical parameters at the cell level. The population was calibrated from 1000 to 187 models based on biomarkers derived from the action potential shape, calcium transient and active tension. The electromechanics solver is implemented by combining existing solvers for electrophysiology[3] and mechanics[4], which are both based on the open-source framework FEniCS[5]. A geometry of 20x7x3 mm is simulated with 1.0 or 0.5 mm spatial resolution for mechanics or electrophysiology respectively, with free movement in the fibre direction on one side.
Results
Traces from all population models were extracted at the center of the tissue in all directions (green star in top left panel) for further analysis (see figure). Electrophysiological biomarkers, such as action potential duration and systolic calcium concentration remain within calibrated and cell population model range. The maximum active tension in tissue is reduced by 65% compared to cell simulations. This reduction can be attributed to the free contraction in tissue versus fixed stretch in calibration and cell simulations. The magnitude and especially the recovery duration of active stretch varies widely across the population (see table for average±SD). This range of timing and force of contraction reinforce the need to assess cardiac function and drug effects in populations of electromechanical models.
Discussion
We present a pipeline for creating populations of strongly coupled 3D excitation-contraction models for ventricular tissue. The tissue model includes bidirectional coupling and biological variation, facilitating further investigation into the multifactorial effect of variation and drugs on the in silico human heart. This enables simulation of both mechanical and physiological function of the heart to aid development of safe and efficient treatment based on population statistics.
References
O’Hara, T. et al.; PLoS Comput Biol 2011 [doi:10.1371/journal.pcbi.1002061]
Land, S. et al.; J. Mol. Cell. Cardiol. 2017 [doi:10.1016/J.YJMCC.2017.03.008]
Logg, A. et al.; Springer 2012 [doi:10.1007/978-3-642-23099-8]
Rognes, M. E. et al.; Journal of Open Source Software, 2017 [doi:10.21105/joss.00224]
Finsberg, H. N. T.; Journal of Open Source Software, 2019 [doi:10.21105/joss.01539]
| Afilliation | Scientific Computing |
| Project(s) | Department of Computational Physiology, Simulation of Cardiac Devices and Drugs for In-Silico Testing and Certification (SimCardioTest) |
| Publication Type | Proceedings, refereed |
| Year of Publication | 2022 |
| Conference Name | World Congress of Biomechanics |
| Edition | 9th |
Journal Article
Regional Left Ventricular Fiber Stress Analysis for Cardiac Resynchronization Therapy Response
Annals of Biomedical Engineering (2022).Status: Published
Regional Left Ventricular Fiber Stress Analysis for Cardiac Resynchronization Therapy Response
Cardiac resynchronization therapy (CRT) is an effective treatment for a subgroup of heart failure (HF) patients, but more than 30% of those selected do not improve after CRT implantation. Imperfect pre-procedural criteria for patient selection and optimization are the main causes of the high non-response rate. In this study, we evaluated a novel measure for assessing CRT response. We used a computational modeling framework to calculate the regional stress of the left ventricular wall of seven CRT patients and seven healthy controls. The standard deviation of regional wall stress at the time of mitral valve closure (SD_MVC) was used to quantify dyssynchrony and com- pared between patients and controls and among the patients. The results show that SD_MVC is significantly lower in controls than patients and correlates with long-term response in patients, based on end-diastolic volume reduction. In contrast to our initial hypothesis, patients with lower SD_MVC respond better to therapy. The patient with the highest SD_MVC was the only non-responder in the patient cohort. The distribution of fiber stress at the beginning of the isovolumetric phase seems to correlate with the degree of response and the use of this measurement could potentially improve selection criteria for CRT implantation. Further studies with a larger cohort of patients are needed to validate these results.
| Afilliation | Scientific Computing |
| Project(s) | Department of Computational Physiology |
| Publication Type | Journal Article |
| Year of Publication | 2022 |
| Journal | Annals of Biomedical Engineering |
| Date Published | 07/2022 |
| Publisher | Springer |
| Keywords | Cardiac resynchronization therapy, Computational cardiology, electrophysiology, Heart failure |
| URL | https://doi.org/10.1007/s10439-022-03030-y |
| DOI | 10.1007/s10439-022-03030-y |
Journal Article
Heart Muscle Microphysiological System for Cardiac Liability Prediction of Repurposed COVID-19 Therapeutics
Frontiers in Pharmacology 12 (2021): 684252.Status: Published
Heart Muscle Microphysiological System for Cardiac Liability Prediction of Repurposed COVID-19 Therapeutics
| Afilliation | Scientific Computing |
| Project(s) | IdentiPhy |
| Publication Type | Journal Article |
| Year of Publication | 2021 |
| Journal | Frontiers in Pharmacology |
| Volume | 12 |
| Pagination | 684252 |
| Publisher | Frontiers Media SA |
| URL | doi.org/10.3389/fphar.2021.684252 |
| DOI | 10.3389/fphar.2021.684252 |
In vitro safety “clinical trial” of the cardiac liability of drug polytherapy
Clinical and Translational Science 14, no. 3 (2021): 1155-1165.Status: Published
In vitro safety “clinical trial” of the cardiac liability of drug polytherapy
| Afilliation | Scientific Computing |
| Project(s) | IdentiPhy |
| Publication Type | Journal Article |
| Year of Publication | 2021 |
| Journal | Clinical and Translational Science |
| Volume | 14 |
| Issue | 3 |
| Pagination | 1155-1165 |
| Date Published | 03/2021 |
| Publisher | Wiley Online Library |
| URL | https://ascpt.onlinelibrary.wiley.com/doi/full/10.1111/cts.13038 |
| DOI | 10.1111/cts.13038 |
Journal Article
Improved computational identification of drug response using optical measurements of human stem cell derived cardiomyocytes in microphysiological systems
Frontiers in Pharmacology 10 (2020).Status: Published
Improved computational identification of drug response using optical measurements of human stem cell derived cardiomyocytes in microphysiological systems
Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) hold great potential for drug screening applications. However, their usefulness is limited by the relative immaturity of the cells’ electrophysiological properties as compared to native cardiomyocytes in the adult human heart. In this work, we extend and improve on methodology to address this limitation, building on previously introduced computational procedures which predict drug effects for adult cells based on changes in optical measurements of action potentials and calcium transients made in stem cell derived cardiac microtissues. This methodology quantifies ion channel changes through the inversion of data into a mathematical model, and maps this response to an adult phenotype through the assumption of functional invariance of fundamental intracellular and membrane channels during maturation. Here we utilize an updated action potential model to represent both hiPSC-CMs and adult cardiomyocytes, apply an IC50-based model of dose-dependent drug effects, and introduce a continuation-based optimization algorithm for analysis of dose escalation measurements using five drugs with known effects. The improved methodology can identify drug induced changes more efficiently, and quantitate important metrics such as IC50 in line with published values. Consequently, the updated methodology is a step towards employing computational procedures to elucidate drug effects in adult cardiomyocytes for new drugs using stem cell-derived experimental tissues.
| Afilliation | Scientific Computing |
| Project(s) | Department of Computational Physiology, IdentiPhy |
| Publication Type | Journal Article |
| Year of Publication | 2020 |
| Journal | Frontiers in Pharmacology |
| Volume | 10 |
| Number | 1648 |
| Date Published | 02/2020 |
| Publisher | Frontiers |
| DOI | 10.3389/fphar.2019.01648 |
In Vitro Safety “Clinical Trial” of the Cardiac Liability of Hydroxychloroquine and Azithromycin as COVID19 Polytherapy
Clinical Pharmacology & Therapeutics (2020).Status: Published
In Vitro Safety “Clinical Trial” of the Cardiac Liability of Hydroxychloroquine and Azithromycin as COVID19 Polytherapy
| Afilliation | Scientific Computing |
| Project(s) | Department of Computational Physiology, IdentiPhy |
| Publication Type | Journal Article |
| Year of Publication | 2020 |
| Journal | Clinical Pharmacology & Therapeutics |
| Publisher | Wiley |
Regional Left Ventricular Fiber Stress Analysis for Cardiac Resynchronization Therapy Response
Journal of Cardiovascular Electrophysiology (2020).Status: Submitted
Regional Left Ventricular Fiber Stress Analysis for Cardiac Resynchronization Therapy Response
| Afilliation | Scientific Computing |
| Project(s) | Department of Computational Physiology |
| Publication Type | Journal Article |
| Year of Publication | 2020 |
| Journal | Journal of Cardiovascular Electrophysiology |
| Publisher | Wiley |
Journal Article
Computational quantification of patient-specific changes in ventricular dynamics associated with pulmonary hypertension
American Journal of Physiology-Heart and Circulatory Physiology 31711911, no. 6 (2019): H1363-H1375.Status: Published
Computational quantification of patient-specific changes in ventricular dynamics associated with pulmonary hypertension
| Afilliation | Scientific Computing |
| Project(s) | Department of Computational Physiology |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Journal | American Journal of Physiology-Heart and Circulatory Physiology |
| Volume | 31711911 |
| Issue | 6 |
| Pagination | H1363 - H1375 |
| Publisher | American Journal of Physiology |
pulse: A python package based on FEniCS for solving problems in cardiac mechanics
Journal of Open Source Software 4, no. 41 (2019): 1539.Status: Published
pulse: A python package based on FEniCS for solving problems in cardiac mechanics
| Afilliation | Scientific Computing |
| Project(s) | inHeart: In Silico Heart Failure - Tools for Accelerating Biomedical Research |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Journal | Journal of Open Source Software |
| Volume | 4 |
| Issue | 41 |
| Pagination | 1539 |
| Date Published | Jan-09-2019 |
| Publisher | The Journal of Open Source Software, Open Source Initiative |
| URL | http://www.theoj.org/joss-papers/joss.01539/10.21105.joss.01539.pdf |
| DOI | 10.21105/joss.01539 |
Talks, contributed
Adjoint Based Data Assimilation for Quantification of Dynamic Mechanical Behavior of the Heart
In World Congress of Biomechanics, New York, USA, 2018.Status: Published
Adjoint Based Data Assimilation for Quantification of Dynamic Mechanical Behavior of the Heart
| Afilliation | Scientific Computing |
| Publication Type | Talks, contributed |
| Year of Publication | 2018 |
| Location of Talk | World Congress of Biomechanics, New York, USA |
Adjoint based data assimilation for quantifying mechanical properties in clinical cardiac mechanics
In Computer Methods in Biomechanics and Bioengineering, Lisbon, Portugal, 2018.Status: Published
Adjoint based data assimilation for quantifying mechanical properties in clinical cardiac mechanics
| Afilliation | Scientific Computing |
| Publication Type | Talks, contributed |
| Year of Publication | 2018 |
| Location of Talk | Computer Methods in Biomechanics and Bioengineering, Lisbon, Portugal |
Poster
Adjoint Based Personalization of Mechanical Models for Quantification of Right Ventricular Failure in Pulmonary Hypertension
Heart by Numbers Conference, Berlin, Germany, 2018.Status: Published
Adjoint Based Personalization of Mechanical Models for Quantification of Right Ventricular Failure in Pulmonary Hypertension
| Afilliation | Scientific Computing |
| Publication Type | Poster |
| Year of Publication | 2018 |
| Place Published | Heart by Numbers Conference, Berlin, Germany |
Journal Article
Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization
International Journal for Numerical Methods in Biomedical Engineering 34, no. 7 (2018).Status: Published
Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization
| Afilliation | Scientific Computing |
| Project(s) | inHeart: In Silico Heart Failure - Tools for Accelerating Biomedical Research |
| Publication Type | Journal Article |
| Year of Publication | 2018 |
| Journal | International Journal for Numerical Methods in Biomedical Engineering |
| Volume | 34 |
| Issue | 7 |
| Publisher | John Wiley & Sons |
| DOI | 10.1002/cnm.2982 |
In vivo estimation of elastic heterogeneity in an infarcted human heart
Biomechanics and Modeling in Mechanobiology 17, no. 5 (2018): 1317-1329.Status: Published
In vivo estimation of elastic heterogeneity in an infarcted human heart
In myocardial infarction, muscle tissue of the heart is damaged as a result of ceased or severely impaired blood flow. Survivors have an increased risk of further complications, possibly leading to heart failure. Material properties play an important role in determining post-infarction outcome. Due to spatial variation in scarring, material properties can be expected to vary throughout the tissue of a heart after an infarction. In this study we propose a data assimilation technique that can efficiently estimate heterogeneous elastic material properties in a personalized model of cardiac mechanics. The proposed data assimilation is tested on a clinical dataset consisting of regional left ventricular strains and in vivo pressures during atrial systole from a human with a myocardial infarction. Good matches to regional strains are obtained, and simulated equi-biaxial tests are carried out to demonstrate regional heterogeneities in stress–strain relationships. A synthetic data test shows a good match of estimated versus ground truth material parameter fields in the presence of no to low levels of noise. This study is the first to apply adjoint-based data assimilation to the important problem of estimating cardiac elastic heterogeneities in 3-D from medical images.
| Afilliation | Scientific Computing |
| Project(s) | Department of Numerical Analysis and Scientific Computing |
| Publication Type | Journal Article |
| Year of Publication | 2018 |
| Journal | Biomechanics and Modeling in Mechanobiology |
| Volume | 17 |
| Issue | 5 |
| Pagination | 1317–1329 |
| Date Published | May-05-2019 |
| Publisher | Springer |
| Place Published | Berlin Heidelberg |
| ISSN | 1617-7959 |
| URL | http://link.springer.com/10.1007/s10237-018-1028-5 |
| DOI | 10.1007/s10237-018-1028-5 |
I am a computer scientist with a background in artificial intelligence and biophysics. I previously developed methods for determining the risk of sudden cardiac death based on MRI analysis, and models of electrical propagation in damaged heart tissue at King's College London. Afterwards, I worked with bioinformatics and machine learning for two years at the University of Oslo. In 2017, I completed my PhD at Simula Research Laboratory/UiO on the topic of cardiac mechanics.
PhD Thesis
Patient-Specific Computational Modeling of Cardiac Mechanics
In The University of Oslo. Vol. PhD. Norway: University of Oslo, 2018.Status: Published
Patient-Specific Computational Modeling of Cardiac Mechanics
| Afilliation | Scientific Computing |
| Project(s) | inHeart: In Silico Heart Failure - Tools for Accelerating Biomedical Research |
| Publication Type | PhD Thesis |
| Year of Publication | 2018 |
| Degree awarding institution | The University of Oslo |
| Degree | PhD |
| Publisher | University of Oslo |
| Place Published | Norway |
| URL | http://urn.nb.no/URN:NBN:no-64609 |
Talks, contributed
Assessment of regional myocardial work through adjoint-based data assimilation
In Oslo, Norway, 2017.Status: Published
Assessment of regional myocardial work through adjoint-based data assimilation
Assessment of regional myocardial work through adjoint-based data assimilation
Introduction
To achieve efficient pumping of blood to the body, the healthy heart contracts in a synchronous manner. However, heart disease can alter how the heart is activated during a beat, and dyssynchronous contraction can occur, reducing the overall pumping efficiency. Advanced treatments exist for such cases, but selecting patients likely to respond can be challenging. The existing selection criteria, based on organ level measures of activation and contraction, have relatively low specificity. It is therefore of interest to extract new biomarkers to help better identify potential responders. Here we explore one example of a potential biomarker, the regional myocardial work [1], a measure of cardiac efficiency, using a computational model of cardiac mechanics optimized to patient specific data using a high level adjoint based data assimilation method.
Methods
Left ventricular (LV) geometry was obtained from 4D echocardiography, and the segmented chamber was modelled as an incompressible, continuous hyperelastic body described via an transversely isotropic material law[2]. Active force development was modeled through additively decomposing stress into passive and active stresses, the latter added along the cardiac fiber direction, defined by a rule based architecture.
The model was fit to 4D imaging of the LV through the cardiac cycle using an adjoint-based data assimilation technique, which automatically solves for the gradient of the solution with respect to local active stress, for highly efficient minimization of model misfit against collected data. Simulations were optimized both globally and regionally in 17 delineated segments[3]. With these simulations, the amount of mechanical work performed between time point tm and tn could be regionally calculated through -
W(tm, tn) = ∫ S: ∂tE dt = ∑i S(ti-½): dE(ti-½)
where
S(ti-½) = 0.5*(S(ti)+S(ti-1))
and
dE(ti-½) = E(ti)-E(ti-1)
Here subscript t indicates the time point, S is the Second Piola-Kirchhoff stress tensor and E is the Green-Lagrange strain tensor.
Results
We tested the method on healthy control subjects and patients suffering from left bundle branch block (LBBB). The results show an excellent fit between measured and simulated strain (R^2 = 0.8) and volume (R^2 = 1.0). The estimated regional myocardial work, assessed in these segments, shows clear differences between the healthy and diseased patients (e.g Mid Septal longitudinal wasted work ratio[1]: 1.45 (LBBB), 0.24(Healthy)) and can potentially be used as a biomarker to map regional cardiac dysfunction.
References
[1] doi:10.1152/ajpheart.00191.2013
[2] doi:10.1098/rsta.2009.0091
[3] doi:10.1002/cnm.2863
| Afilliation | Scientific Computing |
| Project(s) | inHeart: In Silico Heart Failure - Tools for Accelerating Biomedical Research |
| Publication Type | Talks, contributed |
| Year of Publication | 2017 |
| Location of Talk | Oslo, Norway |
| Type of Talk | International Conference on Computational Science and Engineering, In memory of Hans Petter Langtangen |
| URL | https://cseconf2017.files.wordpress.com/2017/09/2017-09-28-cseconf2017-c... |
Journal Article
Estimating cardiac contraction through high resolution data assimilation of a personalized mechanical model
Journal of Computational Science 24 (2017): 85-90.Status: Published
Estimating cardiac contraction through high resolution data assimilation of a personalized mechanical model
| Afilliation | Scientific Computing |
| Project(s) | inHeart: In Silico Heart Failure - Tools for Accelerating Biomedical Research |
| Publication Type | Journal Article |
| Year of Publication | 2017 |
| Journal | Journal of Computational Science |
| Volume | 24 |
| Pagination | 85-90 |
| Publisher | Elsevier |
| ISSN | 1877-7503 |
| Keywords | Adjoint Method, Cardiac Mechanics, Contractility, Data assimilation, PDE-constrained optimization |
| URL | http://www.sciencedirect.com/science/article/pii/S1877750317308190 |
| DOI | 10.1016/j.jocs.2017.07.013 |
High resolution data assimilation of cardiac mechanics
International journal for numerical methods in biomedical engineering 33 (2017): e2863.Status: Published
High resolution data assimilation of cardiac mechanics
| Afilliation | Scientific Computing |
| Project(s) | Center for Biomedical Computing (SFF) |
| Publication Type | Journal Article |
| Year of Publication | 2017 |
| Journal | International journal for numerical methods in biomedical engineering |
| Volume | 33 |
| Number | 11 |
| Pagination | e2863 |
| Date Published | 04/2017 |
| Publisher | John Wiley & Sons, Ltd |
| DOI | 10.1002/cnm.2863 |
Poster
Mechanical Analysis of Pulmonary Hypertension via Adjoint based Data Assimilation of a Finite Element Model
Summer Biomechanics, Bioengineering, and Biotransport Conference, Tuscon, USA, 2017.Status: Published
Mechanical Analysis of Pulmonary Hypertension via Adjoint based Data Assimilation of a Finite Element Model
| Afilliation | Scientific Computing |
| Project(s) | inHeart: In Silico Heart Failure - Tools for Accelerating Biomedical Research, Center for Biomedical Computing (SFF) |
| Publication Type | Poster |
| Year of Publication | 2017 |
| Date Published | 06/2017 |
| Place Published | Summer Biomechanics, Bioengineering, and Biotransport Conference, Tuscon, USA |
I currently work on the IdentiPhy project where I am hired as a senior research engineer to develop tools and software to analyse and model heart-on-chip systems.
Sensitivity Analysis of Cardiac Growth Models
FEniCS 2017 conference, Luxembourg, 2017.Status: Published
Sensitivity Analysis of Cardiac Growth Models
Introduction The heart is a dynamic organ capable of changing its shape in response to the body’s demands. For example, the human heart continuously adapts in size and geometry to meet greater blood flow needs of the growing body during normal development. In this case, a gradually imposed volume overload leads to progressive chamber enlargement. Another example of a normal physiological growth can be found in the athlete’s heart, where a sustained elevated chamber pressure results in the chamber wall thickening and an overall increase in cardiac mass. Growth processes, however, can also be maladaptive as found in many cardiovascular diseases where structural changes in the heart progressively decompensate cardiac function.
In order to better understand this balance between adaptive and maladaptive cardiac growth, we examine the effect of known growth stimuli using a mechanical model of the heart. We perform a sensitivity analysis of existing growth models in order to assess the relative importance of model parameters and respective mechanisms. This work can eventually lead to simplifications in the model systems for prediction of growth, or help in localizing shortcomings that need to be addressed in the existing modeling frameworks.
Methods In order to simulate the motion of the heart throughout the cardiac cycle, we use a nonlinear finite element (FE) model of a realistic left ventricle (LV) coupled to a lumped-parameter model of the systemic circulation. Under the quasi-static assumption, this problem is reduced to finding the displacement u, hydrostatic pressure p and LV pressure p LV that minimize the incompressible strain energy functional Π parameterised by the LV volume V LV [1]: The muscular tissue of the heart is modeled as a transversely isotropic hyperelastic material via the strain energy density Ψ [2]:
where m = (a, b, a f , b f ) is a set of passive material parameters, C e is the elastic right Cauchy-Green. By introducing an activation parameter γ representing the active tensor, I1 = trC e and I shortening in the fiber direction f 0 at zero-load, the model incorporates muscle contraction using the active strain approach, which is based on a multiplicative decomposision of the deformation gradient F = I + Grad(u) into an elastic and an active parts F = F e F a with F a defined as:
The dynamic changes in the ventricular blood pressure and volume over the entire cardiac cycle are modeled by a three-element Windkessel model described by a system of ordinary differential equations [3]. At each time step, the coupling between the FE model and the circulatory model is achieved through an additional Lagrange multiplier p LV which represents the LV cavity pressure. The problem (1) is solved such that the simulated LV cavity volume V (u) matches the target volume value V LV obtained from the circulatory model.
Growth process in the heart wall is modeled by deforming the reference unloaded geometry to a new grown configuration, again through a multiplicative decomposition of F into an elastic and, this time, a growth part, where F = F e F g . The constitutive laws for finite growth can be expressed using a generic format for the growth tensor F g = θ f f 0 ⊗ f 0 + θ s s 0 ⊗ s 0 + θ n n 0 ⊗ n 0. The evolution of the local tissue growth parameter θ g = [θ f , θ s , θ n ] T can be defined in terms of a growth activation function φ (F e ) and a growth rate function k(θ θ g ) which specifies the speed and nonlinearity of the growth process [4].
Using the above described model it is possible to simulate various physiological conditions together with the associated structural adaptation of the heart walls in response to change in loadings. In each case, a growth model can be chosen depending on the nature of the considered physiology. The sensitivity of the system’s grown state to the prescribed growth model can then be estimated. For this, we define an objective functional J(u), the model output of interest, which is to serve as a qualitative and/or quantitative measure of how well the growth model reproduces the expected behavior. More specifically, if we are to compare the model response to a real measurement, then the objective functional can be defined as the mismatch between the simulated u and the measured u exp grown states at a reference time tref :
Finally, the sensitivities of J to θ , where θ is a set of growth parameters specific to a given model, are defined as dJ(u)dθ.
The solver has been developed within the FEniCS [5] framework and the functional gradients are computed by solving an automatically derived adjoint equations [6].
Results We first focus on implementing and testing a strain-driven growth law to simulate a volume overload state of the left ventricle. To achieve this, the initial physiological equilibrium of the heart is altered by increasing a diastolic filling pressure. This initiates cardiac growth that continues until a new equilibrium state is reached. The model is able to reproduce qualitatively experimental observations reported in the literature, such as LV cavity dilation due to fiber over-stretching and a gradual increase in myocardium volume. At the next step, we perform a sensitivity analysis of the model with respect to the growth model parameters and evaluate its performance in reproducing the expected growth behavior.
| Afilliation | Scientific Computing |
| Project(s) | OptCutCell: Simulation-based optimisation with dynamic domains, Center for Biomedical Computing (SFF) |
| Publication Type | Poster |
| Year of Publication | 2017 |
| Place Published | FEniCS 2017 conference, Luxembourg |
| URL | http://easychair.org/smart-program/FEniCS'17/2017-06-12.html#talk:45748 |
Proceedings, non-refereed
Optimization of a Spatially Varying Cardiac Contraction parameter using the Adjoint Method
In FEniCS'16, 2016.Status: Published
Optimization of a Spatially Varying Cardiac Contraction parameter using the Adjoint Method
A cardiac computational model is constrained using clinical measurements such as pressure, volume and regional strain. The problem is formulated as a PDE-constrained optimisation problem where the objective functional represents the misfit between measured and simulated data. The control parameter for the active phase is a spatially varying contraction parameter defined at every vertex in the mesh. This makes gradient calculations using the adjoint approach computationally advantageous over standard finite difference approximations.
| Afilliation | Scientific Computing, , Scientific Computing, Scientific Computing |
| Project(s) | Center for Biomedical Computing (SFF) |
| Publication Type | Proceedings, non-refereed |
| Year of Publication | 2016 |
| Conference Name | FEniCS'16 |
| Keywords | Adjoint Method, Cardiac Mechanics, parameter estimation, PDE-constrained optimization |
Poster
Patient Specific Modeling of Cardiac Mechanics using the Active Strain Formulation
In Geilo Winter School, 2016.Status: Published
Patient Specific Modeling of Cardiac Mechanics using the Active Strain Formulation
| Afilliation | Scientific Computing |
| Project(s) | Center for Biomedical Computing (SFF) |
| Publication Type | Poster |
| Year of Publication | 2016 |
| Secondary Title | Geilo Winter School |
I currently work on the IdentiPhy project where I am hired as a senior research engineer to develop tools and software to analyse and model heart-on-chip systems.
Proceedings, refereed
Personalized Cardiac Mechanical Model using a High Resolution Contraction Field
In VPH16 Translating VPH to the Clinic, 2016.Status: Published
Personalized Cardiac Mechanical Model using a High Resolution Contraction Field
| Afilliation | Scientific Computing, , Scientific Computing, Scientific Computing |
| Project(s) | Center for Biomedical Computing (SFF) |
| Publication Type | Proceedings, refereed |
| Year of Publication | 2016 |
| Conference Name | VPH16 Translating VPH to the Clinic |
I currently work on the IdentiPhy project where I am hired as a senior research engineer to develop tools and software to analyse and model heart-on-chip systems.
Talks, invited
Dyssynchronous Left Ventricular Stress Estimation
In Workshop on Advanced Numerical Techniques in Biomedical Computing: Simula Research Laboratory, 2015.Status: Published
Dyssynchronous Left Ventricular Stress Estimation
The heart is a muscular pump that moves approximatly 8,000 litres per day through the human body. It manages to this by a combination of contraction/relaxation along muscle fibers and elastic recoil. These two effects are indistinguishable in a medical image, but can be estimated using a computational model.
In our work we use adjoint based optimization techniques in order to determine muscle contraction and elastic recoil in a patient specific left ventricular geometry based on echocardiography and pressure catheter data. Possible applications of the technique include mechanical stress estimation and hypothesis testing in cardiac resynchronization therapy research.
| Afilliation | Scientific Computing, , Scientific Computing |
| Project(s) | Center for Biomedical Computing (SFF) |
| Publication Type | Talks, invited |
| Year of Publication | 2015 |
| Location of Talk | Workshop on Advanced Numerical Techniques in Biomedical Computing: Simula Research Laboratory |
Talks, contributed
Patient Constrained Ventricular Stress Mapping
In Lugano Switzerland, 2015.Status: Published
Patient Constrained Ventricular Stress Mapping
Abnormal stresses are hypothesized to be a key driver in remodelling processes associated with heart failure
However, it is currently impossible to measure stresses safely in vivo in a human heart. This necessitates the use of computational models
in cardiac stress calculation.
A key step to making simulated stresses useful for clinical practice is patient specificity. This means that the simulated stresses should
come from a computational model that has been calibrated to behave in the same way as a patient's heart.
Doing this typically involves first creating a patient specific geometry, and then using available clinical data to personalize the mechanics of a computational model.
One source of mechanical data that is currently available is dynamic left ventricular strain, which can be
obtained cheaply and efficiently using 4D echocardiography methods. In our study, we combine such strain data
with left ventricular pressure and volume measurements in order to match simulated bi-ventricular mechanics to those observed in the ventricles of a patient.
We formulate this matching as a mathematical optimization problem in which the least squares difference between
simulated and measured strains and volumes is minimized. This minimization is carried out using a gradient based optimization algorithm and an automatically
derived adjoint equation. As a result, we obtain patient specific stress maps that can be used
to improve the treatment of cardiac conditions in which stress plays a significant role.
| Afilliation | Scientific Computing, Scientific Computing, , Scientific Computing, Scientific Computing |
| Project(s) | Center for Biomedical Computing (SFF) |
| Publication Type | Talks, contributed |
| Year of Publication | 2015 |
| Location of Talk | Lugano Switzerland |
| Type of Talk | Conference Presentation at MALT 2015 |
Proceedings, non-refereed
Personalization of a Cardiac Compuational Model using Clinical Measurements
In 28th Nordic Seminar on Computational Mechanics. Vol. 28. Tallin, Estonia: Proceedings of NSCM-28, 2015.Status: Published
Personalization of a Cardiac Compuational Model using Clinical Measurements
Important features in cardiac mechanics that cannot easily be measured in the clinic, can be computed using a computational model that is calibrated to behave in the same way as a patient’s heart. To construct such a model, clinical measurements such as strain, volume and cavity pressure are used to personalize the mechanics of a cardiac computational model. The problem is formulated as a PDE-constrained optimization problem where the minimization functional represents the misfit between the measured and simulated data. The target parameters are material parameters and a spatially varying contraction parameter. The minimization is carried out using a gradient based optimization algorithm and an automatically derived adjoint equation. The method has been tested on synthetic data, and is able to reproduce a prescribed contraction pattern on the left ventricle.
| Afilliation | Scientific Computing, , Scientific Computing, Scientific Computing |
| Project(s) | Center for Biomedical Computing (SFF) |
| Publication Type | Proceedings, non-refereed |
| Year of Publication | 2015 |
| Conference Name | 28th Nordic Seminar on Computational Mechanics |
| Volume | 28 |
| Pagination | 47-50 |
| Date Published | 10/2015 |
| Publisher | Proceedings of NSCM-28 |
| Place Published | Tallin, Estonia |
I currently work on the IdentiPhy project where I am hired as a senior research engineer to develop tools and software to analyse and model heart-on-chip systems.