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May RW, Maso Talou GD, Clark AR, Mynard JP, Smolich JJ, Blanco PJ, Müller LO, Gentles TL, Bloomfield FH, Safaei S. From fetus to neonate: A review of cardiovascular modeling in early life. WIREs Mech Dis 2023:e1608. [DOI: 10.1002/wsbm.1608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2022] [Revised: 01/31/2023] [Accepted: 03/03/2023] [Indexed: 04/03/2023]
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Nolte D, Bertoglio C. Inverse problems in blood flow modeling: A review. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3613. [PMID: 35526113 PMCID: PMC9541505 DOI: 10.1002/cnm.3613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Revised: 12/29/2021] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.
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Affiliation(s)
- David Nolte
- Bernoulli InstituteUniversity of GroningenGroningenThe Netherlands
- Center for Mathematical ModelingUniversidad de ChileSantiagoChile
- Department of Fluid DynamicsTechnische Universität BerlinBerlinGermany
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Ventre J, Politi MT, Fernández JM, Ghigo AR, Gaudric J, Wray SA, Lagaert JB, Armentano R, Capurro C, Fullana JM, Lagrée PY. Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3261. [PMID: 31617333 DOI: 10.1002/cnm.3261] [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: 01/03/2019] [Accepted: 09/01/2019] [Indexed: 06/10/2023]
Abstract
Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R2 > .95) with experimental blood pressure data.
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Affiliation(s)
- Jeanne Ventre
- Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris, France
| | - M Teresa Politi
- Universidad de Buenos Aires, Facultad de Medicina. Departamento de Ciencias Fisiológicas, Laboratorio de Biomembranas, Buenos Aires, Argentina
- CONICET-Universidad de Buenos Aires, Instituto de Fisiologíay Biofísica "Bernardo Houssay", Buenos Aires, Argentina
| | - Juan M Fernández
- Universidad de Buenos Aires, Facultad de Medicina. Departamento de Ciencias Fisiológicas, Laboratorio de Biomembranas, Buenos Aires, Argentina
- CONICET-Universidad de Buenos Aires, Instituto de Fisiologíay Biofísica "Bernardo Houssay", Buenos Aires, Argentina
| | - Arthur R Ghigo
- Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS
| | - Julien Gaudric
- Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris, France
- Service de Chirurgie Vasculaire, Hôpitaux Universitaires La Pitié-Salpêtriêre, Paris, France
| | - Sandra A Wray
- Instituto de Medicina Traslacional, Trasplante y Bioingeniería, Universidad Favaloro-CONICET, Buenos Aires, Argentina
| | | | - Ricardo Armentano
- Departamento de Ingeniería Biológica, Universidad de la República, Montevideo, Uruguay
| | - Claudia Capurro
- Universidad de Buenos Aires, Facultad de Medicina. Departamento de Ciencias Fisiológicas, Laboratorio de Biomembranas, Buenos Aires, Argentina
- CONICET-Universidad de Buenos Aires, Instituto de Fisiologíay Biofísica "Bernardo Houssay", Buenos Aires, Argentina
| | - José Maria Fullana
- Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris, France
| | - Pierre-Yves Lagrée
- Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, Paris, France
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Fevola E, Ballarin F, Jiménez‐Juan L, Fremes S, Grivet‐Talocia S, Rozza G, Triverio P. An optimal control approach to determine resistance-type boundary conditions from in-vivo data for cardiovascular simulations. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3516. [PMID: 34337877 PMCID: PMC9285750 DOI: 10.1002/cnm.3516] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 07/26/2021] [Indexed: 06/01/2023]
Abstract
The choice of appropriate boundary conditions is a fundamental step in computational fluid dynamics (CFD) simulations of the cardiovascular system. Boundary conditions, in fact, highly affect the computed pressure and flow rates, and consequently haemodynamic indicators such as wall shear stress (WSS), which are of clinical interest. Devising automated procedures for the selection of boundary conditions is vital to achieve repeatable simulations. However, the most common techniques do not automatically assimilate patient-specific data, relying instead on expensive and time-consuming manual tuning procedures. In this work, we propose a technique for the automated estimation of outlet boundary conditions based on optimal control. The values of resistive boundary conditions are set as control variables and optimized to match available patient-specific data. Experimental results on four aortic arches demonstrate that the proposed framework can assimilate 4D-Flow MRI data more accurately than two other common techniques based on Murray's law and Ohm's law.
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Affiliation(s)
- Elisa Fevola
- Department of Electronics and TelecommunicationsPolitecnico di TorinoTorinoItaly
| | - Francesco Ballarin
- MathLab, Mathematics areaSISSA ‐ International School for Advanced StudiesTriesteItaly
- Department of Mathematics and PhysicsCatholic University of the Sacred HeartBresciaItaly
| | - Laura Jiménez‐Juan
- Department of Medical ImagingSt Michael's Hospital and Sunnybrook Research Institute, University of TorontoTorontoCanada
| | - Stephen Fremes
- Schulich Heart CentreSunnybrook Health Sciences Center and Sunnybrook Research Institute, University of TorontoTorontoCanada
| | | | - Gianluigi Rozza
- MathLab, Mathematics areaSISSA ‐ International School for Advanced StudiesTriesteItaly
| | - Piero Triverio
- Department of Electrical & Computer EngineeringInstitute of Biomedical Engineering, University of TorontoTorontoCanada
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Rapadamnaba R, Ribatet M, Mohammadi B. Global sensitivity analysis for assessing the parameters importance and setting a stopping criterion in a biomedical inverse problem. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3458. [PMID: 33759369 DOI: 10.1002/cnm.3458] [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] [Received: 04/02/2020] [Revised: 01/27/2021] [Accepted: 03/12/2021] [Indexed: 06/12/2023]
Abstract
This paper shows how to obtain in addition to the standard deviations available after a data assimilation procedure based on the ensemble Kalman filter, an apportioning of the total uncertainty in the outputs of a patient-specific blood flow model into small portions of uncertainty due to input parameters. Statistical indicators generally used for identifying the importance of numerical parameters, namely the Sobol' first order and total indices, are introduced and discussed. These allow the identification of the importance rank of the different input parameters for the patient-specific blood flow model, as well as the influence of the interactions between these parameters on the model output variance. The results show that knowing the importance rank of the model input parameters during the assimilation procedure is useful to avoid unnecessary over-solving and to find a suitable stopping criterion in clinical situations where faster diagnosis is always requested. Indeed, the work permits to reduce typically by a factor of six the time to solution and most importantly with very limited extra calculation using already available information.
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Affiliation(s)
- Robert Rapadamnaba
- Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CNRS, Montpellier, France
| | - Mathieu Ribatet
- Département Informatique et Mathématiques, Ecole Centrale de Nantes, Nantes Cedex, France
| | - Bijan Mohammadi
- Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CNRS, Montpellier, France
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Arthurs CJ, Xiao N, Moireau P, Schaeffter T, Figueroa CA. A flexible framework for sequential estimation of model parameters in computational hemodynamics. ADVANCED MODELING AND SIMULATION IN ENGINEERING SCIENCES 2020; 7:48. [PMID: 33282681 PMCID: PMC7717067 DOI: 10.1186/s40323-020-00186-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2020] [Accepted: 11/06/2020] [Indexed: 06/02/2023]
Abstract
A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A "Netlist" implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.
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Affiliation(s)
| | - Nan Xiao
- Dept. of Biomedical Engineering, King’s College London, London, UK
| | - Philippe Moireau
- Inria, Inria Saclay-Ile de France, 91128 Palaiseau, France
- LMS, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, 91128 Palaiseau, France
| | - Tobias Schaeffter
- Physikalisch-Technische Bundesanstalt, Berlin, Germany
- Technical University Berlin, Berlin, Germany
| | - C. Alberto Figueroa
- Depts. of Surgery and Biomedical Engineering, University of Michigan, 2800 Plymouth Rd, Ann Arbor, MI 48109 USA
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Rapadamnaba R, Nicoud F, Mohammadi B. Backward sensitivity analysis and reduced-order covariance estimation in noninvasive parameter identification for cerebral arteries. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3170. [PMID: 30426715 DOI: 10.1002/cnm.3170] [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: 05/03/2018] [Revised: 11/02/2018] [Accepted: 11/03/2018] [Indexed: 06/09/2023]
Abstract
Using a previously developed inversion platform for functional cerebral medical imaging with ensemble Kalman filters, this work analyzes the sensitivity of the results with respect to different parameters entering the physical model and inversion procedure, such as the inlet flow rate from the heart, the choice of the boundary conditions, and the nonsymmetry in the network terminations. It also proposes an alternative low complexity construction for the covariance matrix of the hemodynamic parameters of a network of arteries including the circle of Willis. The platform takes as input patient-specific blood flow rates extracted from magnetic resonance angiography and magnetic resonance imaging (dicom files) and is applied to several available patients data. The paper presents full analysis of the results for one of these patients, including a sensitivity study with respect to the proximal and distal boundary conditions. The results notably show that the uncertainties on the inlet flow rate led to uncertainties of the same order of magnitude in the estimated parameters (blood pressure and elastic parameters) and that three-lumped parameters boundary conditions are necessary for a correct retrieval of the target signals.
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Affiliation(s)
| | - Franck Nicoud
- IMAG, Université de Montpellier, CC051, Montpellier, France
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Lal R, Nicoud F, Bars EL, Deverdun J, Molino F, Costalat V, Mohammadi B. Non Invasive Blood Flow Features Estimation in Cerebral Arteries from Uncertain Medical Data. Ann Biomed Eng 2017; 45:2574-2591. [DOI: 10.1007/s10439-017-1904-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2016] [Accepted: 08/12/2017] [Indexed: 11/30/2022]
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