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De Florio M, Zou Z, Schiavazzi DE, Karniadakis GE. Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology. ARXIV 2024:arXiv:2408.07201v1. [PMID: 39184536 PMCID: PMC11343238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 08/27/2024]
Abstract
When predicting physical phenomena through simulation, quantification of the total uncertainty due to multiple sources is as crucial as making sure the underlying numerical model is accurate. Possible sources include irreducible aleatoric uncertainty due to noise in the data, epistemic uncertainty induced by insufficient data or inadequate parameterization, and model-form uncertainty related to the use of misspecified model equations. In addition, recently proposed approaches provide flexible ways to combine information from data with full or partial satisfaction of equations that typically encode physical principles. Physics-based regularization interacts in nontrivial ways with aleatoric, epistemic and model-form uncertainty and their combination, and a better understanding of this interaction is needed to improve the predictive performance of physics-informed digital twins that operate under real conditions. To better understand this interaction, with a specific focus on biological and physiological models, this study investigates the decomposition of total uncertainty in the estimation of states and parameters of a differential system simulated with MC X-TFC, a new physics-informed approach for uncertainty quantification based on random projections and Monte-Carlo sampling. After an introductory comparison between approaches for physics-informed estimation, MC X-TFC is applied to a six-compartment stiff ODE system, the CVSim-6 model, developed in the context of human physiology. The system is first analyzed by progressively removing data while estimating an increasing number of parameters, and subsequently by investigating total uncertainty under model-form misspecification of non-linear resistance in the pulmonary compartment. In particular, we focus on the interaction between the formulation of the discrepancy term and quantification of model-form uncertainty, and show how additional physics can help in the estimation process. The method demonstrates robustness and efficiency in estimating unknown states and parameters, even with limited, sparse, and noisy data. It also offers great flexibility in integrating data with physics for improved estimation, even in cases of model misspecification.
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Affiliation(s)
- Mario De Florio
- Division of Applied Mathematics, Brown University, Providence, 02906 RI, USA
| | - Zongren Zou
- Division of Applied Mathematics, Brown University, Providence, 02906 RI, USA
| | - Daniele E. Schiavazzi
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, 46556 IN, USA
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Colebank MJ, Oomen PA, Witzenburg CM, Grosberg A, Beard DA, Husmeier D, Olufsen MS, Chesler NC. Guidelines for mechanistic modeling and analysis in cardiovascular research. Am J Physiol Heart Circ Physiol 2024; 327:H473-H503. [PMID: 38904851 PMCID: PMC11442102 DOI: 10.1152/ajpheart.00766.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Revised: 06/07/2024] [Accepted: 06/16/2024] [Indexed: 06/22/2024]
Abstract
Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.
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Affiliation(s)
- Mitchel J Colebank
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
| | - Pim A Oomen
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
| | - Colleen M Witzenburg
- Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, Wisconsin, United States
| | - Anna Grosberg
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
| | - Daniel A Beard
- Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, Michigan, United States
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina, United States
| | - Naomi C Chesler
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States
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Rumbell T, Parikh J, Kozloski J, Gurev V. Novel and flexible parameter estimation methods for data-consistent inversion in mechanistic modelling. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230668. [PMID: 38026012 PMCID: PMC10646445 DOI: 10.1098/rsos.230668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Accepted: 10/18/2023] [Indexed: 12/01/2023]
Abstract
Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g. ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric families of mechanistic models (MMs). Two classes of methodologies, based on Bayesian inference and population of models, currently prevail in parameter estimation for physical systems. However, in Bayesian analysis, uninformative priors for MM parameters introduce undesirable bias. Here, we propose how to infer parameters within the framework of stochastic inverse problems (SIPs), also termed data-consistent inversion, wherein the prior targets only uncertainties that arise due to MM non-invertibility. To demonstrate, we introduce new methods to solve SIPs based on rejection sampling, Markov chain Monte Carlo, and generative adversarial networks (GANs). In addition, to overcome limitations of SIPs, we reformulate SIPs based on constrained optimization and present a novel GAN to solve the constrained optimization problem.
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Affiliation(s)
- Timothy Rumbell
- IBM Research, Hybrid Biological-AI Modeling, Yorktown Heights, NY, USA
| | - Jaimit Parikh
- IBM Research, Hybrid Biological-AI Modeling, Yorktown Heights, NY, USA
| | - James Kozloski
- IBM Research, Hybrid Biological-AI Modeling, Yorktown Heights, NY, USA
| | - Viatcheslav Gurev
- IBM Research, Hybrid Biological-AI Modeling, Yorktown Heights, NY, USA
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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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Colebank MJ, Chesler NC. An in-silico analysis of experimental designs to study ventricular function: A focus on the right ventricle. PLoS Comput Biol 2022; 18:e1010017. [PMID: 36126091 PMCID: PMC9524687 DOI: 10.1371/journal.pcbi.1010017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 09/30/2022] [Accepted: 09/07/2022] [Indexed: 11/19/2022] Open
Abstract
In-vivo studies of pulmonary vascular disease and pulmonary hypertension (PH) have provided key insight into the progression of right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are practically identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct a practical identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for practical identifiability using profile likelihood-based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from practical identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure-volume data reveals that at least some quantitative data from both ventricles should be included for future experimental studies.
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Affiliation(s)
- Mitchel J. Colebank
- University of California, Irvine–Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
| | - Naomi C. Chesler
- University of California, Irvine–Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
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Arduini M, Pham J, Marsden AL, Chen IY, Ennis DB, Dual SA. Framework for patient-specific simulation of hemodynamics in heart failure with counterpulsation support. Front Cardiovasc Med 2022; 9:895291. [PMID: 35979018 PMCID: PMC9376255 DOI: 10.3389/fcvm.2022.895291] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2022] [Accepted: 07/13/2022] [Indexed: 11/17/2022] Open
Abstract
Despite being responsible for half of heart failure-related hospitalizations, heart failure with preserved ejection fraction (HFpEF) has limited evidence-based treatment options. Currently, a substantial clinical issue is that the disease etiology is very heterogenous with no patient-specific treatment options. Modeling can provide a framework for evaluating alternative treatment strategies. Counterpulsation strategies have the capacity to improve left ventricular diastolic filling by reducing systolic blood pressure and augmenting the diastolic pressure that drives coronary perfusion. Here, we propose a framework for testing the effectiveness of a soft robotic extra-aortic counterpulsation strategy using a patient-specific closed-loop hemodynamic lumped parameter model of a patient with HFpEF. The soft robotic device prototype was characterized experimentally in a physiologically pressurized (50–150 mmHg) soft silicone vessel and modeled as a combination of a pressure source and a capacitance. The patient-specific model was created using open-source software and validated against hemodynamics obtained by imaging of a patient (male, 87 years, HR = 60 bpm) with HFpEF. The impact of actuation timing on the flows and pressures as well as systolic function was analyzed. Good agreement between the patient-specific model and patient data was achieved with relative errors below 5% in all categories except for the diastolic aortic root pressure and the end systolic volume. The most effective reduction in systolic pressure compared to baseline (147 vs. 141 mmHg) was achieved when actuating 350 ms before systole. In this case, flow splits were preserved, and cardiac output was increased (5.17 vs. 5.34 L/min), resulting in increased blood flow to the coronaries (0.15 vs. 0.16 L/min). Both arterial elastance (0.77 vs. 0.74 mmHg/mL) and stroke work (11.8 vs. 10.6 kJ) were decreased compared to baseline, however left atrial pressure increased (11.2 vs. 11.5 mmHg). A higher actuation pressure is associated with higher systolic pressure reduction and slightly higher coronary flow. The soft robotic device prototype achieves reduced systolic pressure, reduced stroke work, slightly increased coronary perfusion, but increased left atrial pressures in HFpEF patients. In future work, the framework could include additional physiological mechanisms, a larger patient cohort with HFpEF, and testing against clinically used devices.
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Affiliation(s)
- Mattia Arduini
- Department of Radiology, Stanford University, Palo Alto, CA, United States
| | - Jonathan Pham
- Mechanical Engineering, Stanford University, Palo Alto, CA, United States
| | - Alison L. Marsden
- Department of Bioengineering, Stanford University, Palo Alto, CA, United States
- Department of Pediatrics, Stanford University, Palo Alto, CA, United States
| | - Ian Y. Chen
- Cardiovascular Institute, Stanford University, Palo Alto, CA, United States
- Division of Medicine (Cardiology), Veterans Affairs Health Care System, Palo Alto, CA, United States
| | - Daniel B. Ennis
- Department of Radiology, Stanford University, Palo Alto, CA, United States
- Cardiovascular Institute, Stanford University, Palo Alto, CA, United States
- Division of Radiology, Veterans Affairs Health Care System, Palo Alto, CA, United States
| | - Seraina A. Dual
- Department of Radiology, Stanford University, Palo Alto, CA, United States
- Cardiovascular Institute, Stanford University, Palo Alto, CA, United States
- *Correspondence: Seraina A. Dual
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Villalobos Lizardi JC, Baranger J, Nguyen MB, Asnacios A, Malik A, Lumens J, Mertens L, Friedberg MK, Simmons CA, Pernot M, Villemain O. A guide for assessment of myocardial stiffness in health and disease. NATURE CARDIOVASCULAR RESEARCH 2022; 1:8-22. [PMID: 39196108 DOI: 10.1038/s44161-021-00007-3] [Citation(s) in RCA: 27] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 11/10/2021] [Indexed: 08/29/2024]
Abstract
Myocardial stiffness is an intrinsic property of the myocardium that influences both diastolic and systolic cardiac function. Myocardial stiffness represents the resistance of this tissue to being deformed and depends on intracellular components of the cardiomyocyte, particularly the cytoskeleton, and on extracellular components, such as collagen fibers. Myocardial disease is associated with changes in myocardial stiffness, and its assessment is a key diagnostic marker of acute or chronic pathological myocardial disease with the potential to guide therapeutic decision-making. In this Review, we appraise the different techniques that can be used to estimate myocardial stiffness, evaluate their advantages and disadvantages, and discuss potential clinical applications.
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Affiliation(s)
- José Carlos Villalobos Lizardi
- Division of Cardiology, Department of Pediatrics, The Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada
| | - Jerome Baranger
- Division of Cardiology, Department of Pediatrics, The Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada
| | - Minh B Nguyen
- Division of Cardiology, Department of Pediatrics, The Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada
| | - Atef Asnacios
- Laboratoire Matière et Systèmes Complexes, CNRS UMR 7057, Université de Paris, Paris, France
| | - Aimen Malik
- Division of Cardiology, Department of Pediatrics, The Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada
| | - Joost Lumens
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht (CARIM), Maastricht University, Maastricht, the Netherlands
| | - Luc Mertens
- Division of Cardiology, Department of Pediatrics, The Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada
| | - Mark K Friedberg
- Division of Cardiology, Department of Pediatrics, The Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada
| | - Craig A Simmons
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
| | - Mathieu Pernot
- Physics for Medicine Paris, INSERM U1273, ESPCI Paris, CNRS UMR 8063, PSL Research University, Paris, France
| | - Olivier Villemain
- Division of Cardiology, Department of Pediatrics, The Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada.
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