1
|
Genet M, Diaz J, Chapelle D, Moireau P. Reduced left ventricular dynamics modeling based on a cylindrical assumption. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023; 39:e3711. [PMID: 37203282 DOI: 10.1002/cnm.3711] [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: 09/16/2022] [Revised: 02/11/2023] [Accepted: 04/02/2023] [Indexed: 05/20/2023]
Abstract
Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-order finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, for example, for pre-calibration of full-order models, fast predictions, real-time applications, and so forth. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of Guccione, McCulloch, & Waldman (1991); Guccione, Waldman, & McCulloch (1993), albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel aswell, with consistent spatial (finite element) and time discretizations. Finally, we analyze the sensitivity of the model response to various numerical and physical parameters, and study its physiological response.
Collapse
Affiliation(s)
- Martin Genet
- LMS, École Polytechnique/CNRS/Institut Polytechnique de Paris, Palaiseau, France
- Inria, MΞDISIM Team, Inria Saclay-Ile de France, Palaiseau, France
| | - Jérôme Diaz
- LMS, École Polytechnique/CNRS/Institut Polytechnique de Paris, Palaiseau, France
- Inria, MΞDISIM Team, Inria Saclay-Ile de France, Palaiseau, France
| | - Dominique Chapelle
- LMS, École Polytechnique/CNRS/Institut Polytechnique de Paris, Palaiseau, France
- Inria, MΞDISIM Team, Inria Saclay-Ile de France, Palaiseau, France
| | - Philippe Moireau
- LMS, École Polytechnique/CNRS/Institut Polytechnique de Paris, Palaiseau, France
- Inria, MΞDISIM Team, Inria Saclay-Ile de France, Palaiseau, France
| |
Collapse
|
2
|
Chapelle D, Le Gall A. A biomechanics-based parametrized cardiac end-diastolic pressure-volume relationship for accurate patient-specific calibration and estimation. Sci Rep 2023; 13:11232. [PMID: 37433813 DOI: 10.1038/s41598-023-38196-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 07/05/2023] [Indexed: 07/13/2023] Open
Abstract
A simple power law has been proposed in the pioneering work of Klotz et al. (Am J Physiol Heart Circ Physiol 291(1):H403-H412, 2006) to approximate the end-diastolic pressure-volume relationship of the left cardiac ventricle, with limited inter-individual variability provided the volume is adequately normalized. Nevertheless, we use here a biomechanical model to investigate the sources of the remaining data dispersion observed in the normalized space, and we show that variations of the parameters of the biomechanical model realistically account for a substantial part of this dispersion. We therefore propose an alternative law based on the biomechanical model that embeds some intrinsic physical parameters, which directly enables personalization capabilities, and paves the way for related estimation approaches.
Collapse
Affiliation(s)
- Dominique Chapelle
- Inria, Palaiseau, France.
- LMS, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France.
| | - Arthur Le Gall
- Inria, Palaiseau, France
- LMS, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France
- AP-HP, Hôpital Lariboisière, Paris, France
| |
Collapse
|
3
|
Niklas C, Hölle T, Dugas M, Weigand MA, Larmann J. [The digital twin for perioperative medicine-An exciting look into the future of clinical research]. DIE ANAESTHESIOLOGIE 2023; 72:191-194. [PMID: 36695840 PMCID: PMC9876409 DOI: 10.1007/s00101-023-01251-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 01/02/2023] [Indexed: 06/17/2023]
Affiliation(s)
- Christian Niklas
- Institut für Medizinische Informatik, Universitätsklinikum Heidelberg, Im Neuenheimer Feld 130.3, 69120, Heidelberg, Deutschland.
| | - Tobias Hölle
- Klinik für Anästhesiologie, Universitätsklinikum Heidelberg, Im Neuenheimer Feld 420, 69120, Heidelberg, Deutschland
| | - Martin Dugas
- Institut für Medizinische Informatik, Universitätsklinikum Heidelberg, Im Neuenheimer Feld 130.3, 69120, Heidelberg, Deutschland
| | - Markus A Weigand
- Klinik für Anästhesiologie, Universitätsklinikum Heidelberg, Im Neuenheimer Feld 420, 69120, Heidelberg, Deutschland
| | - Jan Larmann
- Klinik für Anästhesiologie, Universitätsklinikum Heidelberg, Im Neuenheimer Feld 420, 69120, Heidelberg, Deutschland
| |
Collapse
|
4
|
Piccioli F, Valiani A, Alastruey J, Caleffi V. The effect of cardiac properties on arterial pulse waves: An in-silico study. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3658. [PMID: 36286406 DOI: 10.1002/cnm.3658] [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: 04/14/2022] [Revised: 08/29/2022] [Accepted: 10/16/2022] [Indexed: 06/16/2023]
Abstract
This study investigated the effects of cardiac properties variability on arterial pulse wave morphology using blood flow modelling and pulse wave analysis. A lumped-parameter model of the left part of the heart was coupled to a one-dimensional model of the arterial network and validated using reference pulse waveforms in turn verified by comparison with in vivo measurements. A sensitivity analysis was performed to assess the effects of variations in cardiac parameters on central and peripheral pulse waveforms. Results showed that left ventricle contractility, stroke volume, cardiac cycle duration, and heart valves impairment are determinants of central waveforms morphology, pulse pressure and its amplification. Contractility of the left atrium has negligible effects on arterial pulse waves. Results also suggested that it might be possible to infer left ventricular dysfunction by analysing the timing of the dicrotic notch and cardiac function by analysing PPG signals. This study has identified cardiac properties that may be extracted from in vivo central and peripheral pulse waves to assess cardiac function.
Collapse
Affiliation(s)
| | | | - Jordi Alastruey
- School of Biomedical Engineering and Imaging Sciences, King's College London, St Thomas' Hospital, London, UK
| | - Valerio Caleffi
- Department of Engineering, University of Ferrara, Ferrara, Italy
| |
Collapse
|
5
|
Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare. Ann Biomed Eng 2021; 49:3339-3348. [PMID: 34853921 DOI: 10.1007/s10439-021-02895-9] [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: 09/28/2021] [Accepted: 11/12/2021] [Indexed: 10/19/2022]
Abstract
Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient's pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSMpre, and patient-specific models of the same patients created post-PVR (PSMpost)-both created in our previous published work. Using the PSMpre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSMpost, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSMpost model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.
Collapse
|
6
|
Gusseva M, Hussain T, Friesen CH, Moireau P, Tandon A, Patte C, Genet M, Hasbani K, Greil G, Chapelle D, Chabiniok R. Biomechanical Modeling to Inform Pulmonary Valve Replacement in Tetralogy of Fallot Patients After Complete Repair. Can J Cardiol 2021; 37:1798-1807. [PMID: 34216743 PMCID: PMC9810481 DOI: 10.1016/j.cjca.2021.06.018] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Revised: 06/05/2021] [Accepted: 06/26/2021] [Indexed: 01/07/2023] Open
Abstract
BACKGROUND A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health. METHODS Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Qeff) was also compared with expected values. RESULTS RV contractility before PVR (mean 66 ± 16 kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38-48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Qeff-both in line with published data. CONCLUSIONS This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation.
Collapse
Affiliation(s)
- Maria Gusseva
- Inria, Palaiseau, France,LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France
| | - Tarique Hussain
- Division of Pediatric Cardiology, Department of Pediatrics, UT Southwestern Medical Center, Dallas, Texas, USA
| | - Camille Hancock Friesen
- Division of Pediatric Cardiothoracic Surgery, Department of Pediatrics, UT Southwestern Medical Center, Dallas, Texas, USA
| | - Philippe Moireau
- Inria, Palaiseau, France,LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France
| | - Animesh Tandon
- Division of Pediatric Cardiology, Department of Pediatrics, UT Southwestern Medical Center, Dallas, Texas, USA
| | - Cécile Patte
- Inria, Palaiseau, France,LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France
| | - Martin Genet
- Inria, Palaiseau, France,LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France
| | - Keren Hasbani
- Division of Pediatric Cardiology, Department of Pediatrics, Dell Medical School, University of Texas, Austin, Texas, USA
| | - Gerald Greil
- Division of Pediatric Cardiology, Department of Pediatrics, UT Southwestern Medical Center, Dallas, Texas, USA
| | - Dominique Chapelle
- Inria, Palaiseau, France,LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France
| | - Radomír Chabiniok
- Inria, Palaiseau, France,LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France,Division of Pediatric Cardiology, Department of Pediatrics, UT Southwestern Medical Center, Dallas, Texas, USA,School of Biomedical Engineering & Imaging Sciences, St Thomas’ Hospital, King’s College London, London, United Kingdom,Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic
| |
Collapse
|
7
|
Regazzoni F, Chapelle D, Moireau P. Combining data assimilation and machine learning to build data-driven models for unknown long time dynamics-Applications in cardiovascular modeling. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3471. [PMID: 33913623 PMCID: PMC8365699 DOI: 10.1002/cnm.3471] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Revised: 03/12/2021] [Accepted: 04/23/2021] [Indexed: 06/12/2023]
Abstract
We propose a method to discover differential equations describing the long-term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast-scale. Our methodology is based on a synergetic combination of data assimilation (DA), used to estimate the parameters associated with the known fast-scale dynamics, and machine learning (ML), used to infer the laws underlying the slow-scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data-driven models obtained within the black-box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically ill-posed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise-robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods.
Collapse
Affiliation(s)
- Francesco Regazzoni
- MOX—Mathematics DepartmentPolitecnico di MilanoMilanoItaly
- M3DISIMInstitut National de Recherche en Informatique et en AutomatiquePalaiseauFrance
- LMSEcole Polytechnique, CNRS, Institut Polytechnique de ParisPalaiseauFrance
| | - Dominique Chapelle
- M3DISIMInstitut National de Recherche en Informatique et en AutomatiquePalaiseauFrance
- LMSEcole Polytechnique, CNRS, Institut Polytechnique de ParisPalaiseauFrance
| | - Philippe Moireau
- M3DISIMInstitut National de Recherche en Informatique et en AutomatiquePalaiseauFrance
- LMSEcole Polytechnique, CNRS, Institut Polytechnique de ParisPalaiseauFrance
| |
Collapse
|
8
|
Kimmig F, Caruel M. Hierarchical modeling of force generation in cardiac muscle. Biomech Model Mechanobiol 2020; 19:2567-2601. [PMID: 32681201 DOI: 10.1007/s10237-020-01357-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2019] [Accepted: 06/10/2020] [Indexed: 11/25/2022]
Abstract
Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models, however, may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models-from the more refined to the more simplified-that are rigorously and systematically related to each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three model families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation.
Collapse
Affiliation(s)
- François Kimmig
- LMS, CNRS, École polytechnique, Institut Polytechnique de Paris, Paris, France.
- Inria, Inria Saclay-Ile-de-France, Palaiseau, France.
| | | |
Collapse
|