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El Moçayd N, Belhamadia Y, Seaid M. Unsupervised stochastic learning and reduced order modeling for global sensitivity analysis in cardiac electrophysiology models. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2024; 255:108311. [PMID: 39032242 DOI: 10.1016/j.cmpb.2024.108311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2024] [Revised: 06/25/2024] [Accepted: 06/26/2024] [Indexed: 07/23/2024]
Abstract
BACKGROUND AND OBJECTIVE Numerical simulations in electrocardiology are often affected by various uncertainties inherited from the lack of precise knowledge regarding input values including those related to the cardiac cell model, domain geometry, and boundary or initial conditions used in the mathematical modeling. Conventional techniques for uncertainty quantification in modeling electrical activities of the heart encounter significant challenges, primarily due to the high computational costs associated with fine temporal and spatial scales. Additionally, the need for numerous model evaluations to quantify ubiquitous uncertainties increases the computational challenges even further. METHODS In the present study, we propose a non-intrusive surrogate model to perform uncertainty quantification and global sensitivity analysis in cardiac electrophysiology models. The proposed method combines an unsupervised machine learning technique with the polynomial chaos expansion to reconstruct a surrogate model for the propagation and quantification of uncertainties in the electrical activity of the heart. The proposed methodology not only accurately quantifies uncertainties at a very low computational cost but more importantly, it captures the targeted quantity of interest as either the whole spatial field or the whole temporal period. In order to perform sensitivity analysis, aggregated Sobol indices are estimated directly from the spectral mode of the polynomial chaos expansion. RESULTS We conduct Uncertainty Quantification (UQ) and global Sensitivity Analysis (SA) considering both spatial and temporal variations, rather than limiting the analysis to specific Quantities of Interest (QoIs). To assess the comprehensive performance of our methodology in simulating cardiac electrical activity, we utilize the monodomain model. Additionally, sensitivity analysis is performed on the parameters of the Mitchell-Schaeffer cell model. CONCLUSIONS Unlike conventional techniques for uncertainty quantification in modeling electrical activities, the proposed methodology performs at a low computational cost the sensitivity analysis on the cardiac electrical activity parameters. The results are fully reproducible and easily accessible, while the proposed reduced-order model represents a significant contribution to enhancing global sensitivity analysis in cardiac electrophysiology.
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Affiliation(s)
- Nabil El Moçayd
- College of Agriculture and Environmental Sciences, University Mohammed VI Polytechnique, Ben Guerir, Morocco.
| | - Youssef Belhamadia
- Department of Mathematics and Statistics, American University of Sharjah, United Arab Emirates.
| | - Mohammed Seaid
- Department of Engineering, University of Durham, South Road, Durham DH1 3LE, United Kingdom.
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2
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Ding CCA, Dokos S, Bakir AA, Zamberi NJ, Liew YM, Chan BT, Md Sari NA, Avolio A, Lim E. Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review. Biomed Eng Online 2024; 23:24. [PMID: 38388416 PMCID: PMC10885508 DOI: 10.1186/s12938-024-01206-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 01/11/2024] [Indexed: 02/24/2024] Open
Abstract
Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.
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Affiliation(s)
- Corina Cheng Ai Ding
- Department of Biomedical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia
- Graduate School of Biomedical Engineering, Faculty of Engineering, University of New South Wales, Sydney, NSW, 2052, Australia
| | - Socrates Dokos
- Graduate School of Biomedical Engineering, Faculty of Engineering, University of New South Wales, Sydney, NSW, 2052, Australia
| | - Azam Ahmad Bakir
- University of Southampton Malaysia Campus, 79200, Iskandar Puteri, Johor, Malaysia
| | - Nurul Jannah Zamberi
- Department of Biomedical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia
- Graduate School of Biomedical Engineering, Faculty of Engineering, University of New South Wales, Sydney, NSW, 2052, Australia
| | - Yih Miin Liew
- Department of Biomedical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Bee Ting Chan
- Department of Mechanical, Materials and Manufacturing Engineering, Faculty of Science and Engineering, University of Nottingham Malaysia, 43500, Selangor, Malaysia
| | - Nor Ashikin Md Sari
- Department of Medicine, Faculty of Medicine, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Alberto Avolio
- Macquarie Medical School, Faculty of Medicine, Health and Human Sciences, Macquarie University, Sydney, NSW, 2109, Australia
| | - Einly Lim
- Department of Biomedical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.
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3
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Lu L, Zhu T, Morelli D, Creagh A, Liu Z, Yang J, Liu F, Zhang YT, Clifton DA. Uncertainties in the Analysis of Heart Rate Variability: A Systematic Review. IEEE Rev Biomed Eng 2024; 17:180-196. [PMID: 37186539 DOI: 10.1109/rbme.2023.3271595] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Heart rate variability (HRV) is an important metric with a variety of applications in clinical situations such as cardiovascular diseases, diabetes mellitus, and mental health. HRV data can be potentially obtained from electrocardiography and photoplethysmography signals, then computational techniques such as signal filtering and data segmentation are used to process the sampled data for calculating HRV measures. However, uncertainties arising from data acquisition, computational models, and physiological factors can lead to degraded signal quality and affect HRV analysis. Therefore, it is crucial to address these uncertainties and develop advanced models for HRV analysis. Although several reviews of HRV analysis exist, they primarily focus on clinical applications, trends in HRV methods, or specific aspects of uncertainties such as measurement noise. This paper provides a comprehensive review of uncertainties in HRV analysis, quantifies their impacts, and outlines potential solutions. To the best of our knowledge, this is the first study that presents a holistic review of uncertainties in HRV methods and quantifies their impacts on HRV measures from an engineer's perspective. This review is essential for developing robust and reliable models, and could serve as a valuable future reference in the field, particularly for dealing with uncertainties in HRV analysis.
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4
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Barahona J, Sahli Costabal F, Hurtado DE. Machine learning modeling of lung mechanics: Assessing the variability and propagation of uncertainty in respiratory-system compliance and airway resistance. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2024; 243:107888. [PMID: 37948910 DOI: 10.1016/j.cmpb.2023.107888] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 10/12/2023] [Accepted: 10/25/2023] [Indexed: 11/12/2023]
Abstract
BACKGROUND AND OBJECTIVE Traditional assessment of patient response in mechanical ventilation relies on respiratory-system compliance and airway resistance. Clinical evidence has shown high variability in these parameters, highlighting the difficulty of predicting them before the start of ventilation therapy. This motivates the creation of computational models that can connect structural and tissue features with lung mechanics. In this work, we leverage machine learning (ML) techniques to construct predictive lung function models informed by non-linear finite element simulations, and use them to investigate the propagation of uncertainty in the lung mechanical response. METHODS We revisit a continuum poromechanical formulation of the lungs suitable for determining patient response. Based on this framework, we create high-fidelity finite element models of human lungs from medical images. We also develop a low-fidelity model based on an idealized sphere geometry. We then use these models to train and validate three ML architectures: single-fidelity and multi-fidelity Gaussian process regression, and artificial neural networks. We use the best predictive ML model to further study the sensitivity of lung response to variations in tissue structural parameters and boundary conditions via sensitivity analysis and forward uncertainty quantification. Codes are available for download at https://github.com/comp-medicine-uc/ML-lung-mechanics-UQ RESULTS: The low-fidelity model delivers a lung response very close to that predicted by high-fidelity simulations and at a fraction of the computational time. Regarding the trained ML models, the multi-fidelity GP model consistently delivers better accuracy than the single-fidelity GP and neural network models in estimating respiratory-system compliance and resistance (R2∼0.99). In terms of computational efficiency, our ML model delivers a massive speed-up of ∼970,000× with respect to high-fidelity simulations. Regarding lung function, we observed an almost matched and non-linear behavior between specific structural parameters and chest wall stiffness with compliance. Also, we observed a strong modulation of airways resistance with tissue permeability. CONCLUSIONS Our findings unveil the relevance of specific lung tissue parameters and boundary conditions in the respiratory-system response. Furthermore, we highlight the advantages of adopting a multi-fidelity ML approach that combines data from different levels to yield accurate and efficient estimates of clinical mechanical markers. We envision that the methods presented here can open the way to the development of predictive ML models of the lung response that can inform clinical decisions.
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Affiliation(s)
- José Barahona
- Department of Structural and Geotechnical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, 7820436, Chile; Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santiago, 7820436, Chile
| | - Francisco Sahli Costabal
- Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santiago, 7820436, Chile; Department of Mechanical and Metallurgical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, 7820436, Chile
| | - Daniel E Hurtado
- Department of Structural and Geotechnical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, 7820436, Chile; Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santiago, 7820436, Chile; Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, 02140, USA.
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Cicci L, Fresca S, Manzoni A, Quarteroni A. Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024; 40:e3783. [PMID: 37921217 DOI: 10.1002/cnm.3783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2023] [Revised: 08/14/2023] [Accepted: 09/22/2023] [Indexed: 11/04/2023]
Abstract
Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.
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Affiliation(s)
- Ludovica Cicci
- MOX-Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Stefania Fresca
- MOX-Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Andrea Manzoni
- MOX-Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Alfio Quarteroni
- MOX-Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
- Mathematics Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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6
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Colunga AL, Colebank MJ, Olufsen MS. Parameter inference in a computational model of haemodynamics in pulmonary hypertension. J R Soc Interface 2023; 20:20220735. [PMID: 36854380 PMCID: PMC9974303 DOI: 10.1098/rsif.2022.0735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2022] [Accepted: 01/31/2023] [Indexed: 03/02/2023] Open
Abstract
Pulmonary hypertension (PH), defined by a mean pulmonary arterial pressure (mPAP) greater than 20 mmHg, is characterized by increased pulmonary vascular resistance and decreased pulmonary arterial compliance. There are few measurable biomarkers of PH progression, but a conclusive diagnosis of the disease requires invasive right heart catheterization (RHC). Patient-specific cardiovascular systems-level computational models provide a potential non-invasive tool for determining additional indicators of disease severity. Using computational modelling, this study quantifies physiological parameters indicative of disease severity in nine PH patients. The model includes all four heart chambers, the pulmonary and systemic circulations. We consider two sets of calibration data: static (systolic and diastolic values) RHC data and a combination of static and continuous, time-series waveform data. We determine a subset of identifiable parameters for model calibration using sensitivity analyses and multi-start inference and perform posterior uncertainty quantification. Results show that additional waveform data enables accurate calibration of the right atrial reservoir and pump function across the PH cohort. Model outcomes, including stroke work and pulmonary resistance-compliance relations, reflect typical right heart dynamics in PH phenotypes. Lastly, we show that estimated parameters agree with previous, non-modelling studies, supporting this type of analysis in translational PH research.
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Affiliation(s)
- Amanda L. Colunga
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Mitchel J. Colebank
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
- University of California, Irvine—Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, CA, USA
| | - REU Program
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Mette S. Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
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7
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Sala L, Golse N, Joosten A, Vibert E, Vignon-Clementel I. Sensitivity Analysis of a Mathematical Model Simulating the Post-Hepatectomy Hemodynamics Response. Ann Biomed Eng 2023; 51:270-289. [PMID: 36326994 PMCID: PMC9832106 DOI: 10.1007/s10439-022-03098-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 09/30/2022] [Indexed: 11/06/2022]
Abstract
Recently a lumped-parameter model of the cardiovascular system was proposed to simulate the hemodynamics response to partial hepatectomy and evaluate the risk of portal hypertension (PHT) due to this surgery. Model parameters are tuned based on each patient data. This work focuses on a global sensitivity analysis (SA) study of such model to better understand the main drivers of the clinical outputs of interest. The analysis suggests which parameters should be considered patient-specific and which can be assumed constant without losing in accuracy in the predictions. While performing the SA, model outputs need to be constrained to physiological ranges. An innovative approach exploits the features of the polynomial chaos expansion method to reduce the overall computational cost. The computed results give new insights on how to improve the calibration of some model parameters. Moreover the final parameter distributions enable the creation of a virtual population available for future works. Although this work is focused on partial hepatectomy, the pipeline can be applied to other cardiovascular hemodynamics models to gain insights for patient-specific parameterization and to define a physiologically relevant virtual population.
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Affiliation(s)
- Lorenzo Sala
- Inria Saclay Ile-de-France, 91120 Palaiseau, France
| | - Nicolas Golse
- Université Paris-Saclay, Inserm Physiopathogénèse et traitement des maladie du foie, UMR-S 1193, 94800 Villejuif, France
| | - Alexandre Joosten
- Université Paris-Saclay, Inserm Physiopathogénèse et traitement des maladie du foie, UMR-S 1193, 94800 Villejuif, France
| | - Eric Vibert
- Université Paris-Saclay, Inserm Physiopathogénèse et traitement des maladie du foie, UMR-S 1193, 94800 Villejuif, France
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Local thermal effect of power-on setting on monopolar coagulation: a three-dimensional electrothermal coupled finite element study. Med Biol Eng Comput 2022; 60:3525-3538. [DOI: 10.1007/s11517-022-02689-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 10/02/2022] [Indexed: 11/07/2022]
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9
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A Computationally Efficient Approach to Simulate Heart Rate Effects Using a Whole Human Heart Model. Bioengineering (Basel) 2022; 9:bioengineering9080334. [PMID: 35892747 PMCID: PMC9331290 DOI: 10.3390/bioengineering9080334] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Revised: 07/12/2022] [Accepted: 07/20/2022] [Indexed: 11/17/2022] Open
Abstract
Computational modeling of the whole human heart has become a valuable tool to evaluate medical devices such as leadless pacemakers, annuloplasty rings and left ventricular assist devices, since it is often difficult to replicate the complex dynamic interactions between the device and human heart in bench-top and animal tests. The Dassault Systèmes Living Heart Human Model (LHHM) is a finite-element model of whole-human-heart electromechanics that has input parameters that were previously calibrated to generate physiological responses in a healthy heart beating at 60 beat/min (resting state). This study demonstrates that, by adjusting only six physiologically meaningful parameters, the LHHM can be recalibrated to generate physiological responses in a healthy heart beating at heart rates ranging from 90−160 beat/min. These parameters are as follows: the sinoatrial node firing period decreases from 0.67 s at 90 bpm to 0.38 s at 160 bpm, atrioventricular delay decreases from 0.122 s at 90 bpm to 0.057 s at 160 bpm, preload increases 3-fold from 90 bpm to 160 bpm, body resistance at 160 bpm is 80% of that at 90 bpm, arterial stiffness at 160 bpm is 3.9 times that at 90 bpm, and a parameter relating myofiber twitch force duration and sarcomere length decreases from 238 ms/mm at 90 bpm to 175 ms/mm at 160 bpm. In addition, this study demonstrates the feasibility of using the LHHM to conduct clinical investigations in AV delay optimization and hemodynamic differences between pacing and exercise. AV delays in the ranges of 40 ms to 250 ms were simulated and stroke volume and systolic blood pressure showed clear peaks at 120 ms for 90 bpm. For a heart during exercise, the increase in cardiac output continues to 160 bpm. However, for a heart during pacing, those physiological parameter adjustments are removed that are related to changes in body oxygen requirements (preload, arterial stiffness and body resistance). Consequently, cardiac output increases initially with heart rate; as the heart rate goes up (>100 bpm), the increasing rate of cardiac output slows down and approaches a plateau.
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10
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Longobardi S, Sher A, Niederer SA. Quantitative mapping of force-pCa curves to whole heart contraction and relaxation. J Physiol 2022; 600:3497-3516. [PMID: 35737959 PMCID: PMC9540007 DOI: 10.1113/jp283352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Accepted: 06/21/2022] [Indexed: 11/17/2022] Open
Abstract
Abstract The force–pCa (F–pCa) curve is used to characterize steady‐state contractile properties of cardiac muscle cells in different physiological, pathological and pharmacological conditions. This provides a reduced preparation in which to isolate sarcomere mechanisms. However, it is unclear how changes in the F–pCa curve impact emergent whole‐heart mechanics quantitatively. We study the link between sarcomere and whole‐heart function using a multiscale mathematical model of rat biventricular mechanics that describes sarcomere, tissue, anatomy, preload and afterload properties quantitatively. We first map individual cell‐level changes in sarcomere‐regulating parameters to organ‐level changes in the left ventricular function described by pressure–volume loop characteristics (e.g. end‐diastolic and end‐systolic volumes, ejection fraction and isovolumetric relaxation time). We next map changes in the sarcomere‐regulating parameters to changes in the F–pCa curve. We demonstrate that a change in the F–pCa curve can be caused by multiple different changes in sarcomere properties. We demonstrate that changes in sarcomere properties cause non‐linear and, importantly, non‐monotonic changes in left ventricular function. As a result, a change in sarcomere properties yielding changes in the F–pCa curve that improve contractility does not guarantee an improvement in whole‐heart function. Likewise, a desired change in whole‐heart function (i.e. ejection fraction or relaxation time) is not caused by a unique shift in the F–pCa curve. Changes in the F–pCa curve alone cannot be used to predict the impact of a compound on whole‐heart function.
![]() Key points The force–pCa (F–pCa) curve is used to assess myofilament calcium sensitivity after pharmacological modulation and to infer pharmacological effects on whole‐heart function. We demonstrate that there is a non‐unique mapping from changes in F–pCa curves to changes in left ventricular (LV) function. The effect of changes in F–pCa on LV function depend on the state of the heart and could be different for different pathological conditions. Screening of compounds to impact whole‐heart function by F–pCa should be combined with active tension and calcium transient measurements to predict better how changes in muscle function will impact whole‐heart physiology.
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Affiliation(s)
- Stefano Longobardi
- Cardiac Electromechanics Research Group, School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Anna Sher
- Pfizer Worldwide Research, Development and Medical, Cambridge, MA, USA
| | - Steven A Niederer
- Cardiac Electromechanics Research Group, School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
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Santiago A, Butakoff C, Eguzkitza B, Gray RA, May-Newman K, Pathmanathan P, Vu V, Vázquez M. Design and execution of a verification, validation, and uncertainty quantification plan for a numerical model of left ventricular flow after LVAD implantation. PLoS Comput Biol 2022; 18:e1010141. [PMID: 35696442 PMCID: PMC9232142 DOI: 10.1371/journal.pcbi.1010141] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Revised: 06/24/2022] [Accepted: 04/26/2022] [Indexed: 11/18/2022] Open
Abstract
Background
Left ventricular assist devices (LVADs) are implantable pumps that act as a life support therapy for patients with severe heart failure. Despite improving the survival rate, LVAD therapy can carry major complications. Particularly, the flow distortion introduced by the LVAD in the left ventricle (LV) may induce thrombus formation. While previous works have used numerical models to study the impact of multiple variables in the intra-LV stagnation regions, a comprehensive validation analysis has never been executed. The main goal of this work is to present a model of the LV-LVAD system and to design and follow a verification, validation and uncertainty quantification (VVUQ) plan based on the ASME V&V40 and V&V20 standards to ensure credible predictions.
Methods
The experiment used to validate the simulation is the SDSU cardiac simulator, a bench mock-up of the cardiovascular system that allows mimicking multiple operation conditions for the heart-LVAD system. The numerical model is based on Alya, the BSC’s in-house platform for numerical modelling. Alya solves the Navier-Stokes equation with an Arbitrary Lagrangian-Eulerian (ALE) formulation in a deformable ventricle and includes pressure-driven valves, a 0D Windkessel model for the arterial output and a LVAD boundary condition modeled through a dynamic pressure-flow performance curve. The designed VVUQ plan involves: (a) a risk analysis and the associated credibility goals; (b) a verification stage to ensure correctness in the numerical solution procedure; (c) a sensitivity analysis to quantify the impact of the inputs on the four quantities of interest (QoIs) (average aortic root flow Q A o a v g, maximum aortic root flow Q A o m a x, average LVAD flow Q V A D a v g, and maximum LVAD flow Q V A D m a x); (d) an uncertainty quantification using six validation experiments that include extreme operating conditions.
Results
Numerical code verification tests ensured correctness of the solution procedure and numerical calculation verification showed a grid convergence index (GCI)95% <3.3%. The total Sobol indices obtained during the sensitivity analysis demonstrated that the ejection fraction, the heart rate, and the pump performance curve coefficients are the most impactful inputs for the analysed QoIs. The Minkowski norm is used as validation metric for the uncertainty quantification. It shows that the midpoint cases have more accurate results when compared to the extreme cases. The total computational cost of the simulations was above 100 [core-years] executed in around three weeks time span in Marenostrum IV supercomputer.
Conclusions
This work details a novel numerical model for the LV-LVAD system, that is supported by the design and execution of a VVUQ plan created following recognised international standards. We present a methodology demonstrating that stringent VVUQ according to ASME standards is feasible but computationally expensive.
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Affiliation(s)
- Alfonso Santiago
- Barcelona Supercomputing Center (BSC), Barcelona, Spain
- ELEM biotech, Barcelona, Spain
| | | | | | - Richard A. Gray
- US Food and Drug Administration (FDA), Silver Spring, Maryland, United States of America
| | - Karen May-Newman
- Department of Mechanical Engineering, San Diego State University (SDSU), San Diego, California, United States of America
| | - Pras Pathmanathan
- US Food and Drug Administration (FDA), Silver Spring, Maryland, United States of America
| | - Vi Vu
- Department of Mechanical Engineering, San Diego State University (SDSU), San Diego, California, United States of America
| | - Mariano Vázquez
- Barcelona Supercomputing Center (BSC), Barcelona, Spain
- ELEM biotech, Barcelona, Spain
- * E-mail:
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12
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Lazarus A, Dalton D, Husmeier D, Gao H. Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics. Biomech Model Mechanobiol 2022; 21:953-982. [PMID: 35377030 PMCID: PMC9132878 DOI: 10.1007/s10237-022-01571-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 02/28/2022] [Indexed: 01/08/2023]
Abstract
Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.
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Affiliation(s)
- Alan Lazarus
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - David Dalton
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Hao Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
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13
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Stimm J, Guenthner C, Kozerke S, Stoeck CT. Comparison of interpolation methods of predominant cardiomyocyte orientation from in vivo and ex vivo cardiac diffusion tensor imaging data. NMR IN BIOMEDICINE 2022; 35:e4667. [PMID: 34964179 PMCID: PMC9285076 DOI: 10.1002/nbm.4667] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Revised: 11/25/2021] [Accepted: 11/26/2021] [Indexed: 06/14/2023]
Abstract
Cardiac electrophysiology and cardiac mechanics both depend on the average cardiomyocyte long-axis orientation. In the realm of personalized medicine, knowledge of the patient-specific changes in cardiac microstructure plays a crucial role. Patient-specific computational modelling has emerged as a tool to better understand disease progression. In vivo cardiac diffusion tensor imaging (cDTI) is a vital tool to non-destructively measure the average cardiomyocyte long-axis orientation in the heart. However, cDTI suffers from long scan times, rendering volumetric, high-resolution acquisitions challenging. Consequently, interpolation techniques are needed to populate bio-mechanical models with patient-specific average cardiomyocyte long-axis orientations. In this work, we compare five interpolation techniques applied to in vivo and ex vivo porcine input data. We compare two tensor interpolation approaches, one rule-based approximation, and two data-driven, low-rank models. We demonstrate the advantage of tensor interpolation techniques, resulting in lower interpolation errors than do low-rank models and rule-based methods adapted to cDTI data. In an ex vivo comparison, we study the influence of three imaging parameters that can be traded off against acquisition time: in-plane resolution, signal to noise ratio, and number of acquired short-axis imaging slices.
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Affiliation(s)
- Johanna Stimm
- Institute for Biomedical EngineeringUniversity and ETH ZurichZurichSwitzerland
| | - Christian Guenthner
- Institute for Biomedical EngineeringUniversity and ETH ZurichZurichSwitzerland
| | - Sebastian Kozerke
- Institute for Biomedical EngineeringUniversity and ETH ZurichZurichSwitzerland
| | - Christian T. Stoeck
- Institute for Biomedical EngineeringUniversity and ETH ZurichZurichSwitzerland
- Division of Surgical ResearchUniversity Hospital ZurichUniversity ZurichSwitzerland
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14
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Borowska A, Gao H, Lazarus A, Husmeier D. Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3593. [PMID: 35302293 PMCID: PMC9285944 DOI: 10.1002/cnm.3593] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 03/12/2022] [Indexed: 06/14/2023]
Abstract
We consider parameter inference in cardio-mechanic models of the left ventricle, in particular the one based on the Holtzapfel-Ogden (HO) constitutive law, using clinical in vivo data. The equations underlying these models do not admit closed form solutions and hence need to be solved numerically. These numerical procedures are computationally expensive making computational run times associated with numerical optimisation or sampling excessive for the uptake of the models in the clinical practice. To address this issue, we adopt the framework of Bayesian optimisation (BO), which is an efficient statistical technique of global optimisation. BO seeks the optimum of an unknown black-box function by sequentially training a statistical surrogate-model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off. To guarantee that the estimates based on the in vivo data are realistic also for high-pressures, unobservable in vivo, we include a penalty term based on a previously published empirical law developed using ex vivo data. Two case studies based on real data demonstrate that the proposed BO procedure outperforms the state-of-the-art inference algorithm for the HO constitutive law.
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Affiliation(s)
| | - Hao Gao
- School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
| | - Alan Lazarus
- School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
| | - Dirk Husmeier
- School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
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15
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Stimm J, Nordsletten DA, Jilberto J, Miller R, Berberoğlu E, Kozerke S, Stoeck CT. Personalization of biomechanical simulations of the left ventricle by in-vivo cardiac DTI data: Impact of fiber interpolation methods. Front Physiol 2022; 13:1042537. [PMID: 36518106 PMCID: PMC9742433 DOI: 10.3389/fphys.2022.1042537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 11/14/2022] [Indexed: 11/29/2022] Open
Abstract
Simulations of cardiac electrophysiology and mechanics have been reported to be sensitive to the microstructural anisotropy of the myocardium. Consequently, a personalized representation of cardiac microstructure is a crucial component of accurate, personalized cardiac biomechanical models. In-vivo cardiac Diffusion Tensor Imaging (cDTI) is a non-invasive magnetic resonance imaging technique capable of probing the heart's microstructure. Being a rather novel technique, issues such as low resolution, signal-to noise ratio, and spatial coverage are currently limiting factors. We outline four interpolation techniques with varying degrees of data fidelity, different amounts of smoothing strength, and varying representation error to bridge the gap between the sparse in-vivo data and the model, requiring a 3D representation of microstructure across the myocardium. We provide a workflow to incorporate in-vivo myofiber orientation into a left ventricular model and demonstrate that personalized modelling based on fiber orientations from in-vivo cDTI data is feasible. The interpolation error is correlated with a trend in personalized parameters and simulated physiological parameters, strains, and ventricular twist. This trend in simulation results is consistent across material parameter settings and therefore corresponds to a bias introduced by the interpolation method. This study suggests that using a tensor interpolation approach to personalize microstructure with in-vivo cDTI data, reduces the fiber uncertainty and thereby the bias in the simulation results.
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Affiliation(s)
- Johanna Stimm
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
| | - David A Nordsletten
- Department of Biomedical Engineering and Cardiac Surgery, University of Michigan, Ann Arbor, MI, United States.,School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
| | - Javiera Jilberto
- Department of Biomedical Engineering and Cardiac Surgery, University of Michigan, Ann Arbor, MI, United States
| | - Renee Miller
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
| | - Ezgi Berberoğlu
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
| | - Sebastian Kozerke
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
| | - Christian T Stoeck
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland.,Division of Surgical Research, University Hospital Zurich, University Zurich, Zurich, Switzerland
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16
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Maher GD, Fleeter CM, Schiavazzi DE, Marsden AL. Geometric Uncertainty in Patient-Specific Cardiovascular Modeling with Convolutional Dropout Networks. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2021; 386:114038. [PMID: 34737480 PMCID: PMC8562598 DOI: 10.1016/j.cma.2021.114038] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We propose a novel approach to generate samples from the conditional distribution of patient-specific cardiovascular models given a clinically aquired image volume. A convolutional neural network architecture with dropout layers is first trained for vessel lumen segmentation using a regression approach, to enable Bayesian estimation of vessel lumen surfaces. This network is then integrated into a path-planning patient-specific modeling pipeline to generate families of cardiovascular models. We demonstrate our approach by quantifying the effect of geometric uncertainty on the hemodynamics for three patient-specific anatomies, an aorto-iliac bifurcation, an abdominal aortic aneurysm and a sub-model of the left coronary arteries. A key innovation introduced in the proposed approach is the ability to learn geometric uncertainty directly from training data. The results show how geometric uncertainty produces coefficients of variation comparable to or larger than other sources of uncertainty for wall shear stress and velocity magnitude, but has limited impact on pressure. Specifically, this is true for anatomies characterized by small vessel sizes, and for local vessel lesions seen infrequently during network training.
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Affiliation(s)
- Gabriel D. Maher
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
| | - Casey M. Fleeter
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
| | - Daniele E. Schiavazzi
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA
| | - Alison L. Marsden
- Departments of Pediatrics and Bioengineering, Stanford University, Stanford, CA, USA
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17
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Miller R, Kerfoot E, Mauger C, Ismail TF, Young AA, Nordsletten DA. An Implementation of Patient-Specific Biventricular Mechanics Simulations With a Deep Learning and Computational Pipeline. Front Physiol 2021; 12:716597. [PMID: 34603077 PMCID: PMC8481785 DOI: 10.3389/fphys.2021.716597] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 08/06/2021] [Indexed: 02/04/2023] Open
Abstract
Parameterised patient-specific models of the heart enable quantitative analysis of cardiac function as well as estimation of regional stress and intrinsic tissue stiffness. However, the development of personalised models and subsequent simulations have often required lengthy manual setup, from image labelling through to generating the finite element model and assigning boundary conditions. Recently, rapid patient-specific finite element modelling has been made possible through the use of machine learning techniques. In this paper, utilising multiple neural networks for image labelling and detection of valve landmarks, together with streamlined data integration, a pipeline for generating patient-specific biventricular models is applied to clinically-acquired data from a diverse cohort of individuals, including hypertrophic and dilated cardiomyopathy patients and healthy volunteers. Valve motion from tracked landmarks as well as cavity volumes measured from labelled images are used to drive realistic motion and estimate passive tissue stiffness values. The neural networks are shown to accurately label cardiac regions and features for these diverse morphologies. Furthermore, differences in global intrinsic parameters, such as tissue anisotropy and normalised active tension, between groups illustrate respective underlying changes in tissue composition and/or structure as a result of pathology. This study shows the successful application of a generic pipeline for biventricular modelling, incorporating artificial intelligence solutions, within a diverse cohort.
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Affiliation(s)
- Renee Miller
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
| | - Eric Kerfoot
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
| | - Charlène Mauger
- Auckland MR Research Group, University of Auckland, Auckland, New Zealand
| | - Tevfik F. Ismail
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
| | - Alistair A. Young
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
- Auckland MR Research Group, University of Auckland, Auckland, New Zealand
| | - David A. Nordsletten
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
- Department of Biomedical Engineering and Cardiac Surgery, University of Michigan, Ann Arbor, MI, United States
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18
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Kovacheva E, Gerach T, Schuler S, Ochs M, Dössel O, Loewe A. Causes of altered ventricular mechanics in hypertrophic cardiomyopathy: an in-silico study. Biomed Eng Online 2021; 20:69. [PMID: 34294108 PMCID: PMC8296558 DOI: 10.1186/s12938-021-00900-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 06/08/2021] [Indexed: 11/22/2022] Open
Abstract
BACKGROUND Hypertrophic cardiomyopathy (HCM) is typically caused by mutations in sarcomeric genes leading to cardiomyocyte disarray, replacement fibrosis, impaired contractility, and elevated filling pressures. These varying tissue properties are associated with certain strain patterns that may allow to establish a diagnosis by means of non-invasive imaging without the necessity of harmful myocardial biopsies or contrast agent application. With a numerical study, we aim to answer: how the variability in each of these mechanisms contributes to altered mechanics of the left ventricle (LV) and if the deformation obtained in in-silico experiments is comparable to values reported from clinical measurements. METHODS We conducted an in-silico sensitivity study on physiological and pathological mechanisms potentially underlying the clinical HCM phenotype. The deformation of the four-chamber heart models was simulated using a finite-element mechanical solver with a sliding boundary condition to mimic the tissue surrounding the heart. Furthermore, a closed-loop circulatory model delivered the pressure values acting on the endocardium. Deformation measures and mechanical behavior of the heart models were evaluated globally and regionally. RESULTS Hypertrophy of the LV affected the course of strain, strain rate, and wall thickening-the root-mean-squared difference of the wall thickening between control (mean thickness 10 mm) and hypertrophic geometries (17 mm) was >10%. A reduction of active force development by 40% led to less overall deformation: maximal radial strain reduced from 26 to 21%. A fivefold increase in tissue stiffness caused a more homogeneous distribution of the strain values among 17 heart segments. Fiber disarray led to minor changes in the circumferential and radial strain. A combination of pathological mechanisms led to reduced and slower deformation of the LV and halved the longitudinal shortening of the LA. CONCLUSIONS This study uses a computer model to determine the changes in LV deformation caused by pathological mechanisms that are presumed to underlay HCM. This knowledge can complement imaging-derived information to obtain a more accurate diagnosis of HCM.
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Affiliation(s)
- Ekaterina Kovacheva
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany
| | - Tobias Gerach
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany
| | - Steffen Schuler
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany
| | - Marco Ochs
- Department of Cardiology, Theresienkrankenhaus, Academic Teaching Hospital of Heidelberg University, Bassermannstr.1, 68165, Mannheim, Germany
| | - Olaf Dössel
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany
| | - Axel Loewe
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany.
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19
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Pagani S, Manzoni A. Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3450. [PMID: 33599106 PMCID: PMC8244126 DOI: 10.1002/cnm.3450] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Revised: 02/05/2021] [Accepted: 02/07/2021] [Indexed: 06/12/2023]
Abstract
We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.
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Affiliation(s)
- Stefano Pagani
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
| | - Andrea Manzoni
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
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20
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Fedele M, Quarteroni A. Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3435. [PMID: 33415829 PMCID: PMC8244076 DOI: 10.1002/cnm.3435] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Revised: 01/01/2021] [Accepted: 01/02/2021] [Indexed: 06/05/2023]
Abstract
In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh-size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms-implemented in the open-source software vmtk-can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.
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Affiliation(s)
- Marco Fedele
- MOX, Department of MathematicsPolitecnico di MilanoMilanItaly
| | - Alfio Quarteroni
- MOX, Department of MathematicsPolitecnico di MilanoMilanItaly
- Institute of MathematicsÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
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21
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Prud'homme C, Sala L, Szopos M. Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:2010-2032. [PMID: 33892535 DOI: 10.3934/mbe.2021105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We propose an uncertainty propagation study and a sensitivity analysis with the Ocular Mathematical Virtual Simulator, a computational and mathematical model that predicts the hemodynamics and biomechanics within the human eye. In this contribution, we focus on the effect of intraocular pressure, retrolaminar tissue pressure and systemic blood pressure on the ocular posterior tissue vasculature. The combination of a physically-based model with experiments-based stochastic input allows us to gain a better understanding of the physiological system, accounting both for the driving mechanisms and the data variability.
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Affiliation(s)
| | - Lorenzo Sala
- Centre de recherche INRIA de Paris, Paris 75012, France
| | - Marcela Szopos
- MAP5 UMR CNRS 8145, Université de Paris, Paris 75006, France
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22
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Cai L, Ren L, Wang Y, Xie W, Zhu G, Gao H. Surrogate models based on machine learning methods for parameter estimation of left ventricular myocardium. ROYAL SOCIETY OPEN SCIENCE 2021; 8:201121. [PMID: 33614068 PMCID: PMC7890479 DOI: 10.1098/rsos.201121] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 12/15/2020] [Indexed: 05/12/2023]
Abstract
A long-standing problem at the frontier of biomechanical studies is to develop fast methods capable of estimating material properties from clinical data. In this paper, we have studied three surrogate models based on machine learning (ML) methods for fast parameter estimation of left ventricular (LV) myocardium. We use three ML methods named K-nearest neighbour (KNN), XGBoost and multi-layer perceptron (MLP) to emulate the relationships between pressure and volume strains during the diastolic filling. Firstly, to train the surrogate models, a forward finite-element simulator of LV diastolic filling is used. Then the training data are projected in a low-dimensional parametrized space. Next, three ML models are trained to learn the relationships of pressure-volume and pressure-strain. Finally, an inverse parameter estimation problem is formulated by using those trained surrogate models. Our results show that the three ML models can learn the relationships of pressure-volume and pressure-strain very well, and the parameter inference using the surrogate models can be carried out in minutes. Estimated parameters from both the XGBoost and MLP models have much less uncertainties compared with the KNN model. Our results further suggest that the XGBoost model is better for predicting the LV diastolic dynamics and estimating passive parameters than other two surrogate models. Further studies are warranted to investigate how XGBoost can be used for emulating cardiac pump function in a multi-physics and multi-scale framework.
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Affiliation(s)
- Li Cai
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Lei Ren
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Yongheng Wang
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Wenxian Xie
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Guangyu Zhu
- School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
| | - Hao Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, UK
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23
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Wisneski AD, Guccione JM. Commentary: Fast and accurate surrogate of finite-element analysis: For bench to bedside, we need it now! JTCVS Tech 2020; 4:48-49. [PMID: 34317962 PMCID: PMC8308617 DOI: 10.1016/j.xjtc.2020.10.026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2020] [Revised: 10/18/2020] [Accepted: 10/20/2020] [Indexed: 11/29/2022] Open
Affiliation(s)
- Andrew D Wisneski
- Division of Adult Cardiothoracic Surgery, Department of Surgery, UCSF, San Francisco, Calif
| | - Julius M Guccione
- Division of Adult Cardiothoracic Surgery, Department of Surgery, UCSF, San Francisco, Calif
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24
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Mirams GR, Niederer SA, Clayton RH. The fickle heart: uncertainty quantification in cardiac and cardiovascular modelling and simulation. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20200119. [PMID: 32448073 PMCID: PMC7287327 DOI: 10.1098/rsta.2020.0119] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Affiliation(s)
- Gary R. Mirams
- School of Mathematical Sciences, University of Nottingham, Mathematical Sciences Building, University Park, Nottingham, Nottinghamshire NG7 2RD, UK
- e-mail:
| | - Steven A. Niederer
- Division of Imaging Sciences and Biomedical Engineering, Kings College London, The Rayne Institute, 4th Floor, Lambeth Wing, St Thomas’ Hospital, London SE1 7EH, UK
| | - Richard H. Clayton
- Computer Science, University of Sheffield, Regent Court, 211 Portobello, Sheffield S1 4DP, UK
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