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Dirix P, Buoso S, Kozerke S. Optimizing encoding strategies for 4D Flow MRI of mean and turbulent flow. Sci Rep 2024; 14:19897. [PMID: 39191846 DOI: 10.1038/s41598-024-70449-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2024] [Accepted: 08/16/2024] [Indexed: 08/29/2024] Open
Abstract
For 4D Flow MRI of mean and turbulent flow a compromise between spatiotemporal undersampling and velocity encodings needs to be found. Assuming a fixed scan time budget, the impact of trading off spatiotemporal undersampling versus velocity encodings on quantification of velocity and turbulence for aortic 4D Flow MRI was investigated. For this purpose, patient-specific mean and turbulent aortic flow data were generated using computational fluid dynamics which were embedded into the patient-specific background image data to generate synthetic MRI data with corresponding ground truth flow. Cardiac and respiratory motion were included. Using the synthetic MRI data as input, 4D Flow MRI was subsequently simulated with undersampling along pseudo-spiral Golden angle Cartesian trajectories for various velocity encoding schemes. Data were reconstructed using a locally low rank approach to obtain mean and turbulent flow fields to be compared to ground truth. Results show that, for a 15-min scan, velocity magnitudes can be reconstructed with good accuracy relatively independent of the velocity encoding scheme ( S S I M U = 0.938 ± 0.003 ) , good accuracy ( S S I M U ≥ 0.933 ) and with peak velocity errors limited to 10%. Turbulence maps on the other hand suffer from both lower reconstruction quality ( S S I M TKE ≥ 0.323 ) and larger sensitivity to undersampling, motion and velocity encoding strengths ( S S I M TKE = 0.570 ± 0.110 ) when compared to velocity maps. The best compromise to measure unwrapped velocity maps and turbulent kinetic energy given a fixed 15-min scan budget was found to be a 7-point multi- V enc acquisition with a low V enc tuned for best sensitivity to the range of expected intra-voxel standard deviations and a high V enc larger than the expected peak velocity.
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Affiliation(s)
- Pietro Dirix
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland.
| | - Stefano Buoso
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
| | - Sebastian Kozerke
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
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Nath R, Kazemi A, Callahan S, Stoddard MF, Amini AA. 4Dflow-VP-Net: A deep convolutional neural network for noninvasive estimation of relative pressures in stenotic flows from 4D flow MRI. Magn Reson Med 2023; 90:2175-2189. [PMID: 37496183 PMCID: PMC10615364 DOI: 10.1002/mrm.29791] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2022] [Revised: 06/15/2023] [Accepted: 06/19/2023] [Indexed: 07/28/2023]
Abstract
PURPOSE To estimate relative transvalvular pressure gradient (TVPG) noninvasively from 4D flow MRI. METHODS A novel deep learning-based approach is proposed to estimate pressure gradient across stenosis from four-dimensional flow MRI (4D flow MRI) velocities. A deep neural network 4D flow Velocity-to-Presure Network (4Dflow-VP-Net) was trained to learn the spatiotemporal relationship between velocities and pressure in stenotic vessels. Training data were simulated by computational fluid dynamics (CFD) for different pulsatile flow conditions under an aortic flow waveform. The network was tested to predict pressure from CFD-simulated velocity data, in vitro 4D flow MRI data, and in vivo 4D flow MRI data of patients with both moderate and severe aortic stenosis. TVPG derived from 4Dflow-VP-Net was compared to catheter-based pressure measurements for available flow rates, in vitro and Doppler echocardiography-based pressure measurement, in vivo. RESULTS Relative pressures calculated by 4Dflow-VP-Net and in vitro pressure catheterization revealed strong correlation (r2 = 0.91). Correlations analysis of TVPG from reference CFD and 4Dflow-VP-Net for 450 simulated flow conditions showed strong correlation (r2 = 0.99). TVPG from in vitro MRI had a correlation coefficient of r2 = 0.98 with reference CFD. 4Dflow-VP-Net, applied to 4D flow MRI in 16 patients, showed comparable TVPG measurement with Doppler echocardiography (r2 = 0.85). Bland-Altman analysis of TVPG measurements showed mean bias and limits of agreement of -0.20 ± 2.07 mmHg and 0.19 ± 0.45 mmHg for CFD-simulated velocities and in vitro 4D flow velocities. In patients, overestimation of Doppler echocardiography relative to TVPG from 4Dflow-VP-Net (10.99 ± 6.77 mmHg) was observed. CONCLUSION The proposed approach can predict relative pressure in both in vitro and in vivo 4D flow MRI of aortic stenotic patients with high fidelity.
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Affiliation(s)
- Ruponti Nath
- Medical Imaging Lab, Department of Electrical and Computer Engineering, University of Louisville, Louisville, Kentucky, USA
- Robley Rex Veterans Affairs Medical Center, Louisville, Kentucky, USA
| | - Amirkhosro Kazemi
- Medical Imaging Lab, Department of Electrical and Computer Engineering, University of Louisville, Louisville, Kentucky, USA
- Robley Rex Veterans Affairs Medical Center, Louisville, Kentucky, USA
| | - Sean Callahan
- Medical Imaging Lab, Department of Electrical and Computer Engineering, University of Louisville, Louisville, Kentucky, USA
- Robley Rex Veterans Affairs Medical Center, Louisville, Kentucky, USA
| | - Marcus F. Stoddard
- Robley Rex Veterans Affairs Medical Center, Louisville, Kentucky, USA
- Cardiovascular Division, University of Louisville School of Medicine, Louisville, Kentucky, USA
| | - Amir A. Amini
- Medical Imaging Lab, Department of Electrical and Computer Engineering, University of Louisville, Louisville, Kentucky, USA
- Robley Rex Veterans Affairs Medical Center, Louisville, Kentucky, USA
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Haslund LE, Jorgensen LT, Bo Stuart M, Traberg MS, Jensen JA. Precise Estimation of Intravascular Pressure Gradients. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2023; 70:393-405. [PMID: 37028315 DOI: 10.1109/tuffc.2023.3255791] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
This study presents a method for noninvasive pressure gradient estimation, which allows the detection of small pressure differences with higher precision compared to invasive catheters. It combines a new method for estimating the temporal acceleration of the flowing blood with the Navier-Stokes equation. The acceleration estimation is based on a double cross-correlation approach, which is hypothesized to minimize the influence of noise. Data are acquired using a 256-element, 6.5-MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner. A synthetic aperture (SA) interleaved sequence with 2 ×12 virtual sources evenly distributed over the aperture and permuted in emission order is used in combination with recursive imaging. This enables a temporal resolution between correlation frames equal to the pulse repetition time at a frame rate of half the pulse repetition frequency. The accuracy of the method is evaluated against a computational fluid dynamic simulation. Here, the estimated total pressure difference complies with the CFD reference pressure difference, which yields an R -square of 0.985 and an RMSE of 3.03 Pa. The precision of the method is tested on experimental data, measured on a carotid phantom of the common carotid artery. The volume profile used during measurement was set to mimic flow in the carotid artery with a peak flow rate of 12.9 mL/s. The experimental setup showed that the measured pressure difference changes from -59.4 to 31 Pa throughout a single pulse cycle. This was estimated with a precision of 5.44% (3.22 Pa) across ten pulse cycles. The method was also compared to invasive catheter measurements in a phantom with a 60% cross-sectional area reduction. The ultrasound method detected a maximum pressure difference of 72.3 Pa with a precision of 3.3% (2.22 Pa). The catheters measured a maximum pressure difference of 105 Pa with a precision of 11.2% (11.4 Pa). This was measured over the same constriction and with a peak flow rate of 12.9 mL/s. The double cross-correlation approach revealed no improvement compared to a normal differential operator. The method's strength, thus, lies primarily in the ultrasound sequence, which allows precise and accurate velocity estimations, at which acceleration and pressure differences can be acquired.
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Park J, Kim J, Lee J. Multivariable Technique for the Evaluation of the Trans-stenotic Pressure Gradient. Cardiovasc Eng Technol 2023; 14:104-114. [PMID: 35879586 DOI: 10.1007/s13239-022-00638-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 06/09/2022] [Indexed: 11/28/2022]
Abstract
PURPOSE This study establishes a reliable image-based multivariable technique for measuring the trans-stenotic pressure gradient. METHODS A self-made in vitro steady flow model based on adjustable velocities and stenotic properties were used as the experimental subject. The pre-stenotic flow velocity, severity, and length of the stenosis were used as the input variables. Based on equations used to fit the plots of the physically measured pressure gradient values versus each input variable, a multivariable formula for the pressure gradient measurement could then be derived. The flow model was scanned using velocity-encoded phase-contrast magnetic resonance imaging (PC-MRI) to validate the derived formula while simultaneously measuring the trans-stenotic pressure gradient. The correlation between the physically-measured pressure gradient values and the pressure gradient values calculated using the new formula were subsequently analyzed. RESULTS The results of linear regression analysis using the physically measured pressure gradient values for the new method were compared to values obtained using the simplified Bernoulli equation (R2, 0.991, and 0.975, respectively). In a paired t-test, no statistically significant difference was found between the new method and the physical measurements. CONCLUSIONS The derived multivariable technique was found to reliably measure the trans-stenotic pressure gradient, with better performance than a traditional procedure based on the simplified Bernoulli equation.
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Affiliation(s)
- Jieun Park
- Nonlinear Dynamics Research Center, Kyungpook National University, Daegu, Republic of Korea
| | - Junghun Kim
- Bio-Medical Research Institute, Kyungpook National University & Hospital, Daegu, Korea
| | - Jongmin Lee
- Department of Radiology, Kyungpook National University & Hospital, 50, Samduk 2-ga, Jung Gu, Daegu, 700-721, Republic of Korea.
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Fernandes JF, Gill H, Nio A, Faraci A, Galli V, Marlevi D, Bissell M, Ha H, Rajani R, Mortier P, Myerson SG, Dyverfeldt P, Ebbers T, Nordsletten DA, Lamata P. Non-invasive cardiovascular magnetic resonance assessment of pressure recovery distance after aortic valve stenosis. J Cardiovasc Magn Reson 2023; 25:5. [PMID: 36717885 PMCID: PMC9885657 DOI: 10.1186/s12968-023-00914-3] [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: 09/02/2022] [Accepted: 01/05/2023] [Indexed: 01/31/2023] Open
Abstract
BACKGROUND Decisions in the management of aortic stenosis are based on the peak pressure drop, captured by Doppler echocardiography, whereas gold standard catheterization measurements assess the net pressure drop but are limited by associated risks. The relationship between these two measurements, peak and net pressure drop, is dictated by the pressure recovery along the ascending aorta which is mainly caused by turbulence energy dissipation. Currently, pressure recovery is considered to occur within the first 40-50 mm distally from the aortic valve, albeit there is inconsistency across interventionist centers on where/how to position the catheter to capture the net pressure drop. METHODS We developed a non-invasive method to assess the pressure recovery distance based on blood flow momentum via 4D Flow cardiovascular magnetic resonance (CMR). Multi-center acquisitions included physical flow phantoms with different stenotic valve configurations to validate this method, first against reference measurements and then against turbulent energy dissipation (respectively n = 8 and n = 28 acquisitions) and to investigate the relationship between peak and net pressure drops. Finally, we explored the potential errors of cardiac catheterisation pressure recordings as a result of neglecting the pressure recovery distance in a clinical bicuspid aortic valve (BAV) cohort of n = 32 patients. RESULTS In-vitro assessment of pressure recovery distance based on flow momentum achieved an average error of 1.8 ± 8.4 mm when compared to reference pressure sensors in the first phantom workbench. The momentum pressure recovery distance and the turbulent energy dissipation distance showed no statistical difference (mean difference of 2.8 ± 5.4 mm, R2 = 0.93) in the second phantom workbench. A linear correlation was observed between peak and net pressure drops, however, with strong dependences on the valvular morphology. Finally, in the BAV cohort the pressure recovery distance was 78.8 ± 34.3 mm from vena contracta, which is significantly longer than currently accepted in clinical practise (40-50 mm), and 37.5% of patients displayed a pressure recovery distance beyond the end of the ascending aorta. CONCLUSION The non-invasive assessment of the distance to pressure recovery is possible by tracking momentum via 4D Flow CMR. Recovery is not always complete at the ascending aorta, and catheterised recordings will overestimate the net pressure drop in those situations. There is a need to re-evaluate the methods that characterise the haemodynamic burden caused by aortic stenosis as currently clinically accepted pressure recovery distance is an underestimation.
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Affiliation(s)
- Joao Filipe Fernandes
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK.
| | - Harminder Gill
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Amanda Nio
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Alessandro Faraci
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | | | - David Marlevi
- Department of Molecular Medicine and Surgery, Karolinska Institutet, Solna, Sweden
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Malenka Bissell
- Department of Biomedical Imaging Science, Leeds Institute of Cardiovascular and Metabolic Medicine, University of Leeds, Leeds, UK
| | - Hojin Ha
- Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, Korea
| | - Ronak Rajani
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
- Cardiovascular Directorate, Guy's and St Thomas' NHS Foundation Trust, London, UK
| | | | - Saul G Myerson
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, Oxford Centre for Clinical Magnetic Resonance Research, University of Oxford, Oxford, UK
| | - Petter Dyverfeldt
- Department of Health, Medicine and Caring Sciences, Linköping University, Linköping, Sweden
- Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden
| | - Tino Ebbers
- Department of Health, Medicine and Caring Sciences, Linköping University, Linköping, Sweden
- Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden
| | - David A Nordsletten
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
- Department of Biomedical Engineering and Cardiac Surgery, University of Michigan, Ann Arbor, MI, USA
| | - Pablo Lamata
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
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Gill H, Fernandes J, Chehab O, Prendergast B, Redwood S, Chiribiri A, Nordsletten D, Rajani R, Lamata P. Evaluation of aortic stenosis: From Bernoulli and Doppler to Navier-Stokes. Trends Cardiovasc Med 2023; 33:32-43. [PMID: 34920129 DOI: 10.1016/j.tcm.2021.12.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Revised: 12/07/2021] [Accepted: 12/07/2021] [Indexed: 02/01/2023]
Abstract
Uni-dimensional Doppler echocardiography data provide the mainstay of quantative assessment of aortic stenosis, with the transvalvular pressure drop a key indicator of haemodynamic burden. Sophisticated methods of obtaining velocity data, combined with improved computational analysis, are facilitating increasingly robust and reproducible measurement. Imaging modalities which permit acquisition of three-dimensional blood velocity vector fields enable angle-independent valve interrogation and calculation of enhanced measures of the transvalvular pressure drop. This manuscript clarifies the fundamental principles of physics that underpin the evaluation of aortic stenosis and explores modern techniques that may provide more accurate means to grade aortic stenosis and inform appropriate management.
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Affiliation(s)
- Harminder Gill
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK.
| | - Joao Fernandes
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Omar Chehab
- Cardiology Department, Guy's and St. Thomas's Hospital NHS Foundation Trust, London, UK
| | - Bernard Prendergast
- Cardiology Department, Guy's and St. Thomas's Hospital NHS Foundation Trust, London, UK
| | - Simon Redwood
- Cardiology Department, Guy's and St. Thomas's Hospital NHS Foundation Trust, London, UK
| | - Amedeo Chiribiri
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - David Nordsletten
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK; Department of Surgery and Biomedical Engineering, University of Michigan, 2800 Plymouth Rd, 48109, Ann Arbor, MI, USA
| | - Ronak Rajani
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK; Cardiology Department, Guy's and St. Thomas's Hospital NHS Foundation Trust, London, UK
| | - Pablo Lamata
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
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7
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Kazemi A, Padgett DA, Callahan S, Stoddard M, Amini AA. Relative pressure estimation from 4D flow MRI using generalized Bernoulli equation in a phantom model of arterial stenosis. MAGMA (NEW YORK, N.Y.) 2022; 35:733-748. [PMID: 35175449 DOI: 10.1007/s10334-022-01001-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2021] [Revised: 01/07/2022] [Accepted: 01/09/2022] [Indexed: 06/14/2023]
Abstract
OBJECTIVE Arterial stenosis is a significant cardiovascular disease requiring accurate estimation of the pressure gradients for determining hemodynamic significance. In this paper, we propose Generalized Bernoulli Equation (GBE) utilizing interpolated-based method to estimate relative pressures using streamlines and pathlines from 4D Flow MRI. METHODS 4D Flow MRI data in a stenotic phantom model and computational fluid dynamics simulated velocities generated under identical flow conditions were processed by Generalized Bernoulli Equation (GBE), Reduced Bernoulli Equations (RBE), as well as the Simple Bernoulli Equation (SBE) which is clinically prevalent. Pressures derived from 4D flow MRI and noise corrupted CFD velocities were compared with pressures generated directly with CFD as well as pressures obtained using Millar catheters under identical flow conditions. RESULTS It was found that SBE and RBE methods underestimated the relative pressure for lower flow rates while overestimating the relative pressure at higher flow rates. Specifically, compared to the reference pressure, SBE underestimated the maximum relative pressure by 22[Formula: see text] for a pulsatile flow data with peak flow rate [Formula: see text] and overestimated by around 40[Formula: see text] when [Formula: see text]. In contrast, for GBE method the relative pressure values were overestimated by 15[Formula: see text] with [Formula: see text]and around 10[Formula: see text] with [Formula: see text]. CONCLUSION GBE methods showed robust performance to additive image noise compared to other methods. Our findings indicate that GBE pressure estimation over pathlines attains the highest level of accuracy compared to GBE over streamlines, and the SBE and RBE methods.
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Affiliation(s)
- Amirkhosro Kazemi
- Electrical and Computer Engineering, University of Louisville, Louisville, KY, USA
- Robley Rex VA Medical Center, Louisville, KY, USA
| | | | - Sean Callahan
- Electrical and Computer Engineering, University of Louisville, Louisville, KY, USA
- Robley Rex VA Medical Center, Louisville, KY, USA
| | - Marcus Stoddard
- Cardiovascular Division, University of Louisville, Louisville, KY, USA
- Robley Rex VA Medical Center, Louisville, KY, USA
| | - Amir A Amini
- Electrical and Computer Engineering, University of Louisville, Louisville, KY, USA.
- Robley Rex VA Medical Center, Louisville, KY, USA.
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8
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Dirix P, Buoso S, Peper ES, Kozerke S. Synthesis of patient-specific multipoint 4D flow MRI data of turbulent aortic flow downstream of stenotic valves. Sci Rep 2022; 12:16004. [PMID: 36163357 PMCID: PMC9513106 DOI: 10.1038/s41598-022-20121-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 09/08/2022] [Indexed: 11/09/2022] Open
Abstract
We propose to synthesize patient-specific 4D flow MRI datasets of turbulent flow paired with ground truth flow data to support training of inference methods. Turbulent blood flow is computed based on the Navier-Stokes equations with moving domains using realistic boundary conditions for aortic shapes, wall displacements and inlet velocities obtained from patient data. From the simulated flow, synthetic multipoint 4D flow MRI data is generated with user-defined spatiotemporal resolutions and reconstructed with a Bayesian approach to compute time-varying velocity and turbulence maps. For MRI data synthesis, a fixed hypothetical scan time budget is assumed and accordingly, changes to spatial resolution and time averaging result in corresponding scaling of signal-to-noise ratios (SNR). In this work, we focused on aortic stenotic flow and quantification of turbulent kinetic energy (TKE). Our results show that for spatial resolutions of 1.5 and 2.5 mm and time averaging of 5 ms as encountered in 4D flow MRI in practice, peak total turbulent kinetic energy downstream of a 50, 75 and 90% stenosis is overestimated by as much as 23, 15 and 14% (1.5 mm) and 38, 24 and 23% (2.5 mm), demonstrating the importance of paired ground truth and 4D flow MRI data for assessing accuracy and precision of turbulent flow inference using 4D flow MRI exams.
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Affiliation(s)
- Pietro Dirix
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland.
| | - Stefano Buoso
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
| | - Eva S Peper
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
| | - Sebastian Kozerke
- Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
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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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10
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Marlevi D, Mariscal-Harana J, Burris NS, Sotelo J, Ruijsink B, Hadjicharalambous M, Asner L, Sammut E, Chabiniok R, Uribe S, Winter R, Lamata P, Alastruey J, Nordsletten D. Altered Aortic Hemodynamics and Relative Pressure in Patients with Dilated Cardiomyopathy. J Cardiovasc Transl Res 2022; 15:692-707. [PMID: 34882286 PMCID: PMC9622552 DOI: 10.1007/s12265-021-10181-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 10/20/2021] [Indexed: 12/05/2022]
Abstract
Ventricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol.
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Affiliation(s)
- David Marlevi
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Biomedical Engineering and Health Systems, KTH Royal Institute of Technology, Huddinge, Sweden
- Department of Clinical Sciences, Karolinska Institutet, Danderyd, Sweden
| | - Jorge Mariscal-Harana
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | | | - Julio Sotelo
- School of Biomedical Engineering, Universidad de Valparaíso, Valparaíso, Chile
- Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, Chile
- Millennium Nucleus in Cardiovascular Magnetic Resonance, Santiago, Cardio MR, Chile
| | - Bram Ruijsink
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Myrianthi Hadjicharalambous
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
- Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
| | - Liya Asner
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Eva Sammut
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
- Faculty of Health Science, Bristol Heart Institute and Translational Biomedical Research Centre, University of Bristol, Bristol, UK
| | - Radomir Chabiniok
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
- Inria, Palaiseau, France
- LMS, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, Paris, France
- Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, , Prague, Czech Republic
| | - Sergio Uribe
- Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, Chile
- Millennium Nucleus in Cardiovascular Magnetic Resonance, Santiago, Cardio MR, Chile
- Department of Radiology, School of Medicine, Pontifica Universidad Católica de Chile, Santiago, Chile
| | - Reidar Winter
- Department of Clinical Sciences, Karolinska Institutet, Danderyd, Sweden
| | - Pablo Lamata
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Jordi Alastruey
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
- World-Class Research Center "Digital Biodesign and Personlized Healthcare", Sechenov University, Moscow, Russia
| | - David Nordsletten
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK.
- Department of Cardiac Surgery and Biomedical Engineering, University of Michigan, Plymouth Rd, Ann Arbor, MI, 48109, USA.
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11
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Pacheco DRQ. On the numerical treatment of viscous and convective effects in relative pressure reconstruction methods. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3562. [PMID: 34873867 PMCID: PMC9286393 DOI: 10.1002/cnm.3562] [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: 10/20/2021] [Revised: 11/29/2021] [Accepted: 12/01/2021] [Indexed: 06/13/2023]
Abstract
The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single-point data. Alternatively, relative pressure fields can be reconstructed from imaging-based velocity measurements by considering viscous and inertial forces. Both contributions can be potential troublemakers in pressure reconstruction: the former due to its higher-order derivatives, and the latter because of the quadratic nonlinearity in the convective acceleration. Viscous and convective terms can be treated in various forms, which, although equivalent for ideal measurements, can perform differently in practice. In fact, multiple versions are often used in literature, with no apparent consensus on the more suitable variants. In this context, the present work investigates the performance of different versions of relative pressure estimators. For viscous effects, in particular, two new modified estimators are presented to circumvent second-order differentiation without requiring surface integrals. In-silico and in-vitro data in the typical regime of cerebrovascular flows are considered, allowing a systematic noise sensitivity study. Convective terms are shown to be the main source of error, even for flows with pronounced viscous component. Moreover, the conservation (often integrated) form of convection exhibits higher noise sensitivity than the standard convective description, in all three families of estimators considered here. For the classical pressure Poisson estimator, the present modified version of the viscous term tends to yield better accuracy than the (recently introduced) integrated form, although this effect is in most cases negligible when compared to convection-related errors.
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Affiliation(s)
- Douglas R. Q. Pacheco
- Institute of Applied MathematicsGraz University of TechnologyGrazAustria
- Present address:
Graz Center of Computational EngineeringGraz University of TechnologyGrazAustria
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12
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de Vecchi A, Faraci A, Fernandes JF, Marlevi D, Bellsham-Revell H, Hussain T, Laji N, Ruijsink B, Wong J, Razavi R, Anderson D, Salih C, Pushparajah K, Nordsletten D, Lamata P. Unlocking the Non-invasive Assessment of Conduit and Reservoir Function in the Aorta. J Cardiovasc Transl Res 2022; 15:1075-1085. [PMID: 35199256 PMCID: PMC9622527 DOI: 10.1007/s12265-022-10221-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Accepted: 02/14/2022] [Indexed: 11/06/2022]
Abstract
Aortic surgeries in congenital conditions, such as hypoplastic left heart syndrome (HLHS), aim to restore and maintain the conduit and reservoir functions of the aorta. We proposed a method to assess these two functions based on 4D flow MRI, and we applied it to study the aorta in pre-Fontan HLHS. Ten pre-Fontan HLHS patients and six age-matched controls were studied to derive the advective pressure difference and viscous dissipation for conduit function, and pulse wave velocity and elastic modulus for reservoir function. The reconstructed neo-aorta in HLHS subjects achieved a good conduit function at a cost of an impaired reservoir function (69.7% increase of elastic modulus). The native descending HLHS aorta displayed enhanced reservoir (elastic modulus being 18.4% smaller) but impaired conduit function (three-fold increase in peak advection). A non-invasive and comprehensive assessment of aortic conduit and reservoir functions is feasible and has potentially clinical relevance in congenital vascular conditions.
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Affiliation(s)
- Adelaide de Vecchi
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - Alessandro Faraci
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - Joao Filipe Fernandes
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - David Marlevi
- Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Hannah Bellsham-Revell
- Department of Congenital Heart Disease, Evelina London Children's Hospital, Guy's & St Thomas' Hospitals, London, SE1 7EH, UK
| | - Tarique Hussain
- Pediatric Cardiology, UT Southwestern, Children's Medical Center Dallas, 1935 Medical District Dr, Dallas, TX, 75235, USA
| | - Nidhin Laji
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - Bram Ruijsink
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - James Wong
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - Reza Razavi
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - David Anderson
- Department of Congenital Heart Disease, Evelina London Children's Hospital, Guy's & St Thomas' Hospitals, London, SE1 7EH, UK
| | - Caner Salih
- Department of Congenital Heart Disease, Evelina London Children's Hospital, Guy's & St Thomas' Hospitals, London, SE1 7EH, UK
| | - Kuberan Pushparajah
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK
| | - David Nordsletten
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK.,Department of Biomedical Engineering and Cardiac Surgery, University of Michigan, Ann Arbor, MI, USA
| | - Pablo Lamata
- School of Biomedical Engineering and Imaging Sciences, King's College London, 5th Floor Becket House, Lambeth Palace Road, London, SE1 7EU, UK.
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13
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Ha H, Huh HK, Park KJ, Dyverfeldt P, Ebbers T, Kim DH, Yang DH. In-vitro and In-Vivo Assessment of 4D Flow MRI Reynolds Stress Mapping for Pulsatile Blood Flow. Front Bioeng Biotechnol 2021; 9:774954. [PMID: 34950643 PMCID: PMC8691458 DOI: 10.3389/fbioe.2021.774954] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 11/16/2021] [Indexed: 02/03/2023] Open
Abstract
Imaging hemodynamics play an important role in the diagnosis of abnormal blood flow due to vascular and valvular diseases as well as in monitoring the recovery of normal blood flow after surgical or interventional treatment. Recently, characterization of turbulent blood flow using 4D flow magnetic resonance imaging (MRI) has been demonstrated by utilizing the changes in signal magnitude depending on intravoxel spin distribution. The imaging sequence was extended with a six-directional icosahedral (ICOSA6) flow-encoding to characterize all elements of the Reynolds stress tensor (RST) in turbulent blood flow. In the present study, we aimed to demonstrate the feasibility of full RST analysis using ICOSA6 4D flow MRI under physiological conditions. First, the turbulence analysis was performed through in vitro experiments with a physiological pulsatile flow condition. Second, a total of 12 normal subjects and one patient with severe aortic stenosis were analyzed using the same sequence. The in-vitro study showed that total turbulent kinetic energy (TKE) was less affected by the signal-to-noise ratio (SNR), however, maximum principal turbulence shear stress (MPTSS) and total turbulence production (TP) had a noise-induced bias. Smaller degree of the bias was observed for TP compared to MPTSS. In-vivo study showed that the subject-variability on turbulence quantification was relatively low for the consistent scan protocol. The in vivo demonstration of the stenosis patient showed that the turbulence analysis could clearly distinguish the difference in all turbulence parameters as they were at least an order of magnitude larger than those from the normal subjects.
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Affiliation(s)
- Hojin Ha
- Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, South Korea
| | - Hyung Kyu Huh
- Daegu-Gyeongbuk Medical Innovation Foundation, Medical Device Development Center, Daegu, South Korea
| | - Kyung Jin Park
- Department of Electrical and Electronic Engineering, Yonsei Univeristy, Seoul, South Korea.,Department of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul, South Korea
| | - Petter Dyverfeldt
- Department of Health, Medicine and Caring Science, Linköping University, Linköping, Sweden.,Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden
| | - Tino Ebbers
- Department of Health, Medicine and Caring Science, Linköping University, Linköping, Sweden.,Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden
| | - Dae-Hee Kim
- Department of Cardiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul, South Korea
| | - Dong Hyun Yang
- Department of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul, South Korea
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14
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Marlevi D, Schollenberger J, Aristova M, Ferdian E, Ma Y, Young AA, Edelman ER, Schnell S, Figueroa CA, Nordsletten DA. Noninvasive quantification of cerebrovascular pressure changes using 4D Flow MRI. Magn Reson Med 2021; 86:3096-3110. [PMID: 34431550 DOI: 10.1002/mrm.28928] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Revised: 05/24/2021] [Accepted: 06/25/2021] [Indexed: 12/28/2022]
Abstract
PURPOSE Hemodynamic alterations are indicative of cerebrovascular disease. However, the narrow and tortuous cerebrovasculature complicates image-based assessment, especially when quantifying relative pressure. Here, we present a systematic evaluation of image-based cerebrovascular relative pressure mapping, investigating the accuracy of the routinely used reduced Bernoulli (RB), the extended unsteady Bernoulli (UB), and the full-field virtual work-energy relative pressure ( ν WERP) method. METHODS Patient-specific in silico models were used to generate synthetic cerebrovascular 4D Flow MRI, with RB, UB, and ν WERP performance quantified as a function of spatiotemporal sampling and image noise. Cerebrovascular relative pressures were also derived in 4D Flow MRI from healthy volunteers ( n = 8 ), acquired at two spatial resolutions (dx = 1.1 and 0.8 mm). RESULTS The in silico analysis indicate that accurate relative pressure estimations are inherently coupled to spatial sampling: at dx = 1.0 mm high errors are reported for all methods; at dx = 0.5 mm ν WERP recovers relative pressures at a mean error of 0.02 ± 0.25 mm Hg, while errors remain higher for RB and UB (mean error of -2.18 ± 1.91 and -2.18 ± 1.87 mm Hg, respectively). The dependence on spatial sampling is also indicated in vivo, albeit with higher correlative dependence between resolutions using ν WERP (k = 0.64, R2 = 0.81 for dx = 1.1 vs. 0.8 mm) than with RB or UB (k = 0.04, R2 = 0.03, and k = 0.07, R2 = 0.07, respectively). CONCLUSION Image-based full-field methods such as ν WERP enable cerebrovascular relative pressure mapping; however, accuracy is directly dependent on utilized spatial resolution.
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Affiliation(s)
- David Marlevi
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Jonas Schollenberger
- Department of Surgery and Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Maria Aristova
- Department of Radiology, Northwestern University, Chicago, IL, USA
| | - Edward Ferdian
- Department of Anatomy and Medical Imaging, University of Auckland, Auckland, New Zealand
| | - Yue Ma
- Department of Radiology, Northwestern University, Chicago, IL, USA
- Department of Radiology, Shengjing Hospital of China Medical University, Shenyang, China
| | - Alistair A Young
- Department of Anatomy and Medical Imaging, University of Auckland, Auckland, New Zealand
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, UK
| | - Elazer R Edelman
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Susanne Schnell
- Department of Radiology, Northwestern University, Chicago, IL, USA
- Department of Medical Physics, Institute of Physics, University of Greifswald, Greifswald, Germany
| | - C Alberto Figueroa
- Department of Surgery and Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - David A Nordsletten
- Department of Surgery and Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, UK
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15
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Hoeijmakers MJMM, Huberts W, Rutten MCM, van de Vosse FN. The impact of shape uncertainty on aortic-valve pressure-drop computations. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3518. [PMID: 34350705 PMCID: PMC9286381 DOI: 10.1002/cnm.3518] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Revised: 05/17/2021] [Accepted: 07/04/2021] [Indexed: 06/13/2023]
Abstract
Patient-specific image-based computational fluid dynamics (CFD) is widely adopted in the cardiovascular research community to study hemodynamics, and will become increasingly important for personalized medicine. However, segmentation of the flow domain is not exact and geometric uncertainty can be expected which propagates through the computational model, leading to uncertainty in model output. Seventy-four aortic-valves were segmented from computed tomography images at peak systole. Statistical shape modeling was used to obtain an approximate parameterization of the original segmentations. This parameterization was used to train a meta-model that related the first five shape mode coefficients and flowrate to the CFD-computed transvalvular pressure-drop. Consequently, shape uncertainty in the order of 0.5 and 1.0 mm was emulated by introducing uncertainty in the shape mode coefficients. A global variance-based sensitivity analysis was performed to quantify output uncertainty and to determine relative importance of the shape modes. The first shape mode captured the opening/closing behavior of the valve and uncertainty in this mode coefficient accounted for more than 90% of the output variance. However, sensitivity to shape uncertainty is patient-specific, and the relative importance of the fourth shape mode coefficient tended to increase with increases in valvular area. These results show that geometric uncertainty in the order of image voxel size may lead to substantial uncertainty in CFD-computed transvalvular pressure-drops. Moreover, this illustrates that it is essential to assess the impact of geometric uncertainty on model output, and that this should be thoroughly quantified for applications that wish to use image-based CFD models.
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Affiliation(s)
- M. J. M. M. Hoeijmakers
- Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
- AnsysUtrechtThe Netherlands
| | - W. Huberts
- Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
- Department of Biomedical Engineering, School for Cardiovsacular DiseasesMaastricht UniversityMaastrichtThe Netherlands
| | - M. C. M. Rutten
- Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
| | - F. N. van de Vosse
- Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
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16
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Nolte D, Urbina J, Sotelo J, Sok L, Montalba C, Valverde I, Osses A, Uribe S, Bertoglio C. Validation of 4D Flow based relative pressure maps in aortic flows. Med Image Anal 2021; 74:102195. [PMID: 34419837 DOI: 10.1016/j.media.2021.102195] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Revised: 06/11/2021] [Accepted: 07/22/2021] [Indexed: 12/18/2022]
Abstract
While the clinical gold standard for pressure difference measurements is invasive catheterization, 4D Flow MRI is a promising tool for enabling a non-invasive quantification, by linking highly spatially resolved velocity measurements with pressure differences via the incompressible Navier-Stokes equations. In this work we provide a validation and comparison with phantom and clinical patient data of pressure difference maps estimators. We compare the classical Pressure Poisson Estimator (PPE) and the new Stokes Estimator (STE) against catheter pressure measurements under a variety of stenosis severities and flow intensities. Specifically, we use several 4D Flow data sets of realistic aortic phantoms with different anatomic and hemodynamic severities and two patients with aortic coarctation. The phantom data sets are enriched by subsampling to lower resolutions, modification of the segmentation and addition of synthetic noise, in order to study the sensitivity of the pressure difference estimators to these factors. Overall, the STE method yields more accurate results than the PPE method compared to catheterization data. The superiority of the STE becomes more evident at increasing Reynolds numbers with a better capacity of capturing pressure gradients in strongly convective flow regimes. The results indicate an improved robustness of the STE method with respect to variation in lumen segmentation. However, with heuristic removal of the wall-voxels, the PPE can reach a comparable accuracy for lower Reynolds' numbers.
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Affiliation(s)
- David Nolte
- Bernoulli Institute, University of Groningen, Groningen, 9747AG, The Netherlands; Center for Mathematical Modeling, Universidad de Chile, Santiago, 8370456, Chile
| | - Jesús Urbina
- Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, 7820436, Chile; Department of Radiology, School of Medicine, Pontificia Universidad Católica de Chile, Santiago, 833002, Chile; Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, 7820436, Chile
| | - Julio Sotelo
- Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, 7820436, Chile; Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, 7820436, Chile; School of Biomedical Engineering, Universidad de Valparaíso, Valparaíso, Chile; Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Santiago, 7820436, Chile
| | - Leo Sok
- Bernoulli Institute, University of Groningen, Groningen, 9747AG, The Netherlands
| | - Cristian Montalba
- Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, 7820436, Chile; Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, 7820436, Chile
| | - Israel Valverde
- Hospital Universitario Virgen del Rocío, Sevilla, 41013, Spain
| | - Axel Osses
- Center for Mathematical Modeling, Universidad de Chile, Santiago, 8370456, Chile; Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, 7820436, Chile
| | - Sergio Uribe
- Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, 7820436, Chile; Department of Radiology, School of Medicine, Pontificia Universidad Católica de Chile, Santiago, 833002, Chile; Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, 7820436, Chile
| | - Cristóbal Bertoglio
- Bernoulli Institute, University of Groningen, Groningen, 9747AG, The Netherlands; Center for Mathematical Modeling, Universidad de Chile, Santiago, 8370456, Chile.
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17
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Comparison of Four-Dimensional Flow Magnetic Resonance Imaging and Particle Image Velocimetry to Quantify Velocity and Turbulence Parameters. FLUIDS 2021. [DOI: 10.3390/fluids6080277] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Although recent advances of four-dimensional (4D) flow magnetic resonance imaging (MRI) has introduced a new way to measure Reynolds stress tensor (RST) in turbulent flows, its measurement accuracy and possible bias have remained to be revealed. The purpose of this study was to compare the turbulent flow measurement of 4D flow MRI and particle image velocimetry (PIV) in terms of velocity and turbulence quantification. Two difference flow rates of 10 and 20 L/min through a 50% stenosis were measured with both PIV and 4D flow MRI. Not only velocity through the stenosis but also the turbulence parameters such as turbulence kinetic energy and turbulence production were quantitatively compared. Results shows that 4D flow MRI velocity measurement well agreed with the that of PIV, showing the linear regression slopes of two methods are 0.94 and 0.89, respectively. Although turbulence mapping of 4D flow MRI was qualitatively agreed with that of PIV, the quantitative comparison shows that the 4D flow MRI overestimates RST showing the linear regression slopes of 1.44 and 1.66, respectively. In this study, we demonstrate that the 4D flow MRI visualize and quantify not only flow velocity and also turbulence tensor. However, further optimization of 4D flow MRI for better accuracy might be remained.
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18
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Non-invasive estimation of relative pressure for intracardiac flows using virtual work-energy. Med Image Anal 2020; 68:101948. [PMID: 33383332 DOI: 10.1016/j.media.2020.101948] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Revised: 12/10/2020] [Accepted: 12/11/2020] [Indexed: 01/18/2023]
Abstract
Intracardiac blood flow is driven by differences in relative pressure, and assessing these is critical in understanding cardiac disease. Non-invasive image-based methods exist to assess relative pressure, however, the complex flow and dynamically moving fluid domain of the intracardiac space limits assessment. Recently, we proposed a method, νWERP, utilizing an auxiliary virtual field to probe relative pressure through complex, and previously inaccessible flow domains. Here we present an extension of νWERP for intracardiac flow assessments, solving the virtual field over sub-domains to effectively handle the dynamically shifting flow domain. The extended νWERP is validated in an in-silico benchmark problem, as well as in a patient-specific simulation model of the left heart, proving accurate over ranges of realistic image resolutions and noise levels, as well as superior to alternative approaches. Lastly, the extended νWERP is applied on clinically acquired 4D Flow MRI data, exhibiting realistic ventricular relative pressure patterns, as well as indicating signs of diastolic dysfunction in an exemplifying patient case. Summarized, the extended νWERP approach represents a directly applicable implementation for intracardiac flow assessments.
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Ha H, Park KJ, Dyverfeldt P, Ebbers T, Yang DH. In vitro experiments on ICOSA6 4D flow MRI measurement for the quantification of velocity and turbulence parameters. Magn Reson Imaging 2020; 72:49-60. [PMID: 32619720 DOI: 10.1016/j.mri.2020.06.020] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 05/15/2020] [Accepted: 06/25/2020] [Indexed: 12/22/2022]
Abstract
PURPOSE To perform comprehensive in vitro experiments using six-directional icosahedral flow encoding (ICOSA6) 4D flow magnetic resonance imaging (MRI) under various scan conditions to analyze the robustness of velocity and turbulence quantification. MATERIALS AND METHODS In vitro flow phantoms with steady flow rates of 10 and 20 L/min were scanned using both conventional 4D flow MRI and ICOSA6. Experiments focused on comparisons between ICOSA6 and conventional four point (4P) methods, and the effects of contrast agents, velocity encoding range (Venc), and scan direction on velocity and turbulence quantification. RESULTS The results demonstrated that 1) ICOSA6 improves the velocity-to-noise ratio (VNR) of velocity estimation by 33% (on average) and results in similar turbulent kinetic energy (TKE) estimation as the 4P method. 2) Measurements with a contrast agent resulted in more than a 2.5 fold increase in average VNR. However, the improvement of total TKE quantification was not obvious. 3) TKE estimation was less affected by Venc and the scan direction, whereas turbulence production (TP) estimation was largely affected by these measurement conditions. The effects of Venc and scan direction accounted for less than 11.63% of TKE estimation, but up to 33.89% of TP estimation. CONCLUSION The ICOSA6 scheme is compatible with conventional 4D flow MRI for velocity and TKE measurement. Contrast agents are effective at increasing VNR, but not signal-to-noise ratio for TKE quantification. The effects of Venc and scan direction influence total TP more than total TKE.
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Affiliation(s)
- Hojin Ha
- Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, South Korea.
| | - Kyung Jin Park
- Department of Electrical and Electronic Engineering, Yonsei Univeristy, Seoul, South Korea; Department of Radiology, University of Ulsan College of Medicine, Asan Medical Center, Seoul, South Korea
| | - Petter Dyverfeldt
- Department of Health, Medicine and Caring Science, Linköping University, Linköping, Sweden; Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden
| | - Tino Ebbers
- Department of Health, Medicine and Caring Science, Linköping University, Linköping, Sweden; Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden
| | - Dong Hyun Yang
- Department of Radiology, University of Ulsan College of Medicine, Asan Medical Center, Seoul, South Korea
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