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Sautory T, Shadden SC. Unsupervised Denoising and Super-Resolution of Vascular Flow Data by Physics-Informed Machine Learning. J Biomech Eng 2024; 146:091006. [PMID: 38529728 DOI: 10.1115/1.4065165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Accepted: 03/18/2024] [Indexed: 03/27/2024]
Abstract
We present an unsupervised deep learning method to perform flow denoising and super-resolution without high-resolution labels. We demonstrate the ability of a single model to reconstruct three-dimensional stenosis and aneurysm flows, with varying geometries, orientations, and boundary conditions. Ground truth data was generated using computational fluid dynamics, and then corrupted with multiplicative Gaussian noise. Auto-encoders were used to compress the representations of the flow domain geometry and the (possibly noisy and low-resolution) flow field. These representations were used to condition a physics-informed neural network. A physics-based loss was implemented to train the model to recover lost information from the noisy input by transforming the flow to a solution of the Navier-Stokes equations. Our experiments achieved mean squared errors in the true flow reconstruction of O(1.0 × 10-4), and root mean squared residuals of O(1.0 × 10-2) for the momentum and continuity equations. Our method yielded correlation coefficients of 0.971 for the hidden pressure field and 0.82 for the derived wall shear stress field. By performing point-wise predictions of the flow, the model was able to robustly denoise and super-resolve the field to 20× the input resolution.
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Affiliation(s)
- Théophile Sautory
- Department of Mechanical Engineering, University of California, Berkeley, CA 94501
- University of California, Berkeley
| | - Shawn C Shadden
- Department of Mechanical Engineering, University of California, Berkeley, CA 94501
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2
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Truskey GA. The Potential of Deep Learning to Advance Clinical Applications of Computational Biomechanics. Bioengineering (Basel) 2023; 10:1066. [PMID: 37760168 PMCID: PMC10525821 DOI: 10.3390/bioengineering10091066] [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: 08/07/2023] [Revised: 09/06/2023] [Accepted: 09/07/2023] [Indexed: 09/29/2023] Open
Abstract
When combined with patient information provided by advanced imaging techniques, computational biomechanics can provide detailed patient-specific information about stresses and strains acting on tissues that can be useful in diagnosing and assessing treatments for diseases and injuries. This approach is most advanced in cardiovascular applications but can be applied to other tissues. The challenges for advancing computational biomechanics for real-time patient diagnostics and treatment include errors and missing information in the patient data, the large computational requirements for the numerical solutions to multiscale biomechanical equations, and the uncertainty over boundary conditions and constitutive relations. This review summarizes current efforts to use deep learning to address these challenges and integrate large data sets and computational methods to enable real-time clinical information. Examples are drawn from cardiovascular fluid mechanics, soft-tissue mechanics, and bone biomechanics. The application of deep-learning convolutional neural networks can reduce the time taken to complete image segmentation, and meshing and solution of finite element models, as well as improving the accuracy of inlet and outlet conditions. Such advances are likely to facilitate the adoption of these models to aid in the assessment of the severity of cardiovascular disease and the development of new surgical treatments.
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Affiliation(s)
- George A Truskey
- Department of Biomedical Engineering, Duke University, Durham, NC 27701, USA
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3
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Chatpattanasiri C, Franzetti G, Bonfanti M, Diaz-Zuccarini V, Balabani S. Towards Reduced Order Models via Robust Proper Orthogonal Decomposition to capture personalised aortic haemodynamics. J Biomech 2023; 158:111759. [PMID: 37657234 PMCID: PMC7615718 DOI: 10.1016/j.jbiomech.2023.111759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Revised: 07/19/2023] [Accepted: 08/07/2023] [Indexed: 09/03/2023]
Abstract
Data driven, reduced order modelling has shown promise in tackling the challenges associated with computational and experimental haemodynamic models. In this work, we focus on the use of Reduced Order Models (ROMs) to reconstruct velocity fields in a patient-specific dissected aorta, with the objective being to compare the ROMs obtained from Robust Proper Orthogonal Decomposition (RPOD) to those obtained from the traditional Proper Orthogonal Decomposition (POD). POD and RPOD are applied to in vitro, haemodynamic data acquired by Particle Image Velocimetry and compare the decomposed flows to those derived from Computational Fluid Dynamics (CFD) data for the same geometry and flow conditions. In this work, PIV and CFD results act as surrogates for clinical haemodynamic data e.g. MR, helping to demonstrate the potential use of ROMS in real clinical scenarios. The flow is reconstructed using different numbers of POD modes and the flow features obtained throughout the cardiac cycle are compared to the original Full Order Models (FOMs). Robust Principal Component Analysis (RPCA), the first step of RPOD, has been found to enhance the quality of PIV data, allowing POD to capture most of the kinetic energy of the flow in just two modes similar to the numerical data that are free from measurement noise. The reconstruction errors differ along the cardiac cycle with diastolic flows requiring more modes for accurate reconstruction. In general, modes 1-10 are found sufficient to represent the flow field. The results demonstrate that the coherent structures that characterise this aortic dissection flow are described by the first few POD modes suggesting that it is possible to represent the macroscale behaviour of aortic flow in a low-dimensional space; thus significantly simplifying the problem, and allowing for more computationally efficient flow simulations or machine learning based flow predictions that can pave the way for translation of such models to the clinic.
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Affiliation(s)
| | - Gaia Franzetti
- Department of Mechanical Engineering, University College London, London, UK
| | - Mirko Bonfanti
- Department of Mechanical Engineering, University College London, London, UK
| | - Vanessa Diaz-Zuccarini
- Department of Mechanical Engineering, University College London, London, UK; Wellcome/EPSRC Centre for Interventional and Surgical Sciences (WEISS), Department of Medical Physics and Biomedical Engineering, University College London, London, UK
| | - Stavroula Balabani
- Department of Mechanical Engineering, University College London, London, UK.
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4
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Cherry M, Khatir Z, Khan A, Bissell M. The impact of 4D-Flow MRI spatial resolution on patient-specific CFD simulations of the thoracic aorta. Sci Rep 2022; 12:15128. [PMID: 36068322 PMCID: PMC9448751 DOI: 10.1038/s41598-022-19347-6] [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: 06/22/2022] [Accepted: 08/29/2022] [Indexed: 11/29/2022] Open
Abstract
Magnetic Resonance Imaging (MRI) is considered the gold standard of medical imaging technologies as it allows for accurate imaging of blood vessels. 4-Dimensional Flow Magnetic Resonance Imaging (4D-Flow MRI) is built on conventional MRI, and provides flow data in the three vector directions and a time resolved magnitude data set. As such it can be used to retrospectively calculate haemodynamic parameters of interest, such as Wall Shear Stress (WSS). However, multiple studies have indicated that a significant limitation of the imaging technique is the spatiotemporal resolution that is currently available. Recent advances have proposed and successfully integrated 4D-Flow MRI imaging techniques with Computational Fluid Dynamics (CFD) to produce patient-specific simulations that have the potential to aid in treatments,surgical decision making, and risk stratification. However, the consequences of using insufficient 4D-Flow MRI spatial resolutions on any patient-specific CFD simulations is currently unclear, despite being a recognised limitation. The research presented in this study aims to quantify the inaccuracies in patient-specific 4D-Flow MRI based CFD simulations that can be attributed to insufficient spatial resolutions when acquiring 4D-Flow MRI data. For this research, a patient has undergone four 4D-Flow MRI scans acquired at various isotropic spatial resolutions and patient-specific CFD simulations have subsequently been run using geometry and velocity data produced from each scan. It was found that compared to CFD simulations based on a \documentclass[12pt]{minimal}
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\begin{document}$$1.5\,{\text {mm}} \times 1.5\,{\text {mm}} \times 1.5\,{\text {mm}}$$\end{document}1.5mm×1.5mm×1.5mm, using a spatial resolution of \documentclass[12pt]{minimal}
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\begin{document}$$4\,{\text {mm}} \times 4\,{\text {mm}} \times 4\,{\text {mm}}$$\end{document}4mm×4mm×4mm substantially underestimated the maximum velocity magnitude at peak systole by \documentclass[12pt]{minimal}
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\begin{document}$$110.55\%$$\end{document}110.55%. The impacts of 4D-Flow MRI spatial resolution on WSS calculated from CFD simulations have been investigated and it has been shown that WSS is underestimated in CFD simulations that are based on a coarse 4D-Flow MRI spatial resolution. The authors have concluded that a minimum 4D-Flow MRI spatial resolution of \documentclass[12pt]{minimal}
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\begin{document}$$1.5\,{\text {mm}} \times 1.5\,{\text {mm}} \times 1.5\,{\text {mm}}$$\end{document}1.5mm×1.5mm×1.5mm must be used when acquiring 4D-Flow MRI data to perform patient-specific CFD simulations. A coarser spatial resolution will produce substantial differences within the flow field and geometry.
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Affiliation(s)
- Molly Cherry
- CDT in Fluid Dynamics, School of Computing, University of Leeds, Leeds, LS2 9JT, UK.
| | - Zinedine Khatir
- School of Engineering and the Built Environment, Birmingham City University, Birmingham, B4 7XG, UK.,School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UK
| | - Amirul Khan
- School of Civil Engineering, University of Leeds, Leeds, LS2 9JT, UK
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5
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Shit S, Zimmermann J, Ezhov I, Paetzold JC, Sanches AF, Pirkl C, Menze BH. SRflow: Deep learning based super-resolution of 4D-flow MRI data. Front Artif Intell 2022; 5:928181. [PMID: 36034591 PMCID: PMC9411720 DOI: 10.3389/frai.2022.928181] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 07/11/2022] [Indexed: 11/13/2022] Open
Abstract
Exploiting 4D-flow magnetic resonance imaging (MRI) data to quantify hemodynamics requires an adequate spatio-temporal vector field resolution at a low noise level. To address this challenge, we provide a learned solution to super-resolve in vivo 4D-flow MRI data at a post-processing level. We propose a deep convolutional neural network (CNN) that learns the inter-scale relationship of the velocity vector map and leverages an efficient residual learning scheme to make it computationally feasible. A novel, direction-sensitive, and robust loss function is crucial to learning vector-field data. We present a detailed comparative study between the proposed super-resolution and the conventional cubic B-spline based vector-field super-resolution. Our method improves the peak-velocity to noise ratio of the flow field by 10 and 30% for in vivo cardiovascular and cerebrovascular data, respectively, for 4 × super-resolution over the state-of-the-art cubic B-spline. Significantly, our method offers 10x faster inference over the cubic B-spline. The proposed approach for super-resolution of 4D-flow data would potentially improve the subsequent calculation of hemodynamic quantities.
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Affiliation(s)
- Suprosanna Shit
- Department of Informatics, Technical University of Munich, Munich, Germany
- Department of Quantitative Biomedicine, University of Zurich, Zurich, Switzerland
- *Correspondence: Suprosanna Shit
| | - Judith Zimmermann
- Department of Informatics, Technical University of Munich, Munich, Germany
| | - Ivan Ezhov
- Department of Informatics, Technical University of Munich, Munich, Germany
| | | | - Augusto F. Sanches
- Institute of Neuroradiology, University Hospital LMU Munich, Munich, Germany
| | - Carolin Pirkl
- Department of Informatics, Technical University of Munich, Munich, Germany
| | - Bjoern H. Menze
- Department of Quantitative Biomedicine, University of Zurich, Zurich, Switzerland
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6
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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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7
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Groun N, Villalba-Orero M, Lara-Pezzi E, Valero E, Garicano-Mena J, Le Clainche S. Higher order dynamic mode decomposition: From fluid dynamics to heart disease analysis. Comput Biol Med 2022; 144:105384. [DOI: 10.1016/j.compbiomed.2022.105384] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 02/26/2022] [Accepted: 03/02/2022] [Indexed: 11/15/2022]
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8
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Cook J, Umar M, Khalili F, Taebi A. Body Acoustics for the Non-Invasive Diagnosis of Medical Conditions. Bioengineering (Basel) 2022; 9:bioengineering9040149. [PMID: 35447708 PMCID: PMC9032059 DOI: 10.3390/bioengineering9040149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Revised: 03/27/2022] [Accepted: 03/30/2022] [Indexed: 11/16/2022] Open
Abstract
In the past few decades, many non-invasive monitoring methods have been developed based on body acoustics to investigate a wide range of medical conditions, including cardiovascular diseases, respiratory problems, nervous system disorders, and gastrointestinal tract diseases. Recent advances in sensing technologies and computational resources have given a further boost to the interest in the development of acoustic-based diagnostic solutions. In these methods, the acoustic signals are usually recorded by acoustic sensors, such as microphones and accelerometers, and are analyzed using various signal processing, machine learning, and computational methods. This paper reviews the advances in these areas to shed light on the state-of-the-art, evaluate the major challenges, and discuss future directions. This review suggests that rigorous data analysis and physiological understandings can eventually convert these acoustic-based research investigations into novel health monitoring and point-of-care solutions.
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Affiliation(s)
- Jadyn Cook
- Department of Agricultural and Biological Engineering, Mississippi State University, 130 Creelman Street, Starkville, MS 39762, USA;
| | - Muneebah Umar
- Department of Biological Sciences, Mississippi State University, 295 Lee Blvd, Starkville, MS 39762, USA;
| | - Fardin Khalili
- Department of Mechanical Engineering, Embry-Riddle Aeronautical University, 1 Aerospace Blvd, Daytona Beach, FL 32114, USA;
| | - Amirtahà Taebi
- Department of Agricultural and Biological Engineering, Mississippi State University, 130 Creelman Street, Starkville, MS 39762, USA;
- Correspondence: ; Tel.: +1-(662)-325-5987
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9
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Zhang J, Brindise MC, Rothenberger SM, Markl M, Rayz VL, Vlachos PP. A multi-modality approach for enhancing 4D flow magnetic resonance imaging via sparse representation. J R Soc Interface 2022; 19:20210751. [PMID: 35042385 PMCID: PMC8767185 DOI: 10.1098/rsif.2021.0751] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
This work evaluates and applies a multi-modality approach to enhance blood flow measurements and haemodynamic analysis with phase-contrast magnetic resonance imaging (4D flow MRI) in cerebral aneurysms (CAs). Using a library of high-resolution velocity fields from patient-specific computational fluid dynamic simulations and in vitro particle tracking velocimetry measurements, the flow field of 4D flow MRI data is reconstructed as the sparse representation of the library. The method was evaluated with synthetic 4D flow MRI data in two CAs. The reconstruction enhanced the spatial resolution and velocity accuracy of the synthetic MRI data, leading to reliable pressure and wall shear stress (WSS) evaluation. The method was applied on in vivo 4D flow MRI data acquired in the same CAs. The reconstruction increased the velocity and WSS by 6-13% and 39-61%, respectively, suggesting that the accuracy of these quantities was improved since the raw MRI data underestimated the velocity and WSS by 10-20% and 40-50%, respectively. The computed pressure fields from the reconstructed data were consistent with the observed flow structures. The results suggest that using the sparse representation flow reconstruction with in vivo 4D flow MRI enhances blood flow measurement and haemodynamic analysis.
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Affiliation(s)
- Jiacheng Zhang
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA
| | - Melissa C. Brindise
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA
| | - Sean M. Rothenberger
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907 USA
| | - Michael Markl
- Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA,McCormick School of Engineering, Northwestern University, Evanston, IL 60208, USA
| | - Vitaliy L. Rayz
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA,Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907 USA
| | - Pavlos P. Vlachos
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA,Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907 USA
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10
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Li J, Li J, Hu Q. Analysis on Characteristics of Magnetic Resonance Imaging Image under Low-Rank Matrix Denoising Algorithm in the Diagnosis of Cerebral Aneurysm. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2021; 2021:9751009. [PMID: 34917169 PMCID: PMC8670014 DOI: 10.1155/2021/9751009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Revised: 10/12/2021] [Accepted: 10/20/2021] [Indexed: 11/24/2022]
Abstract
This study was to explore the effect of a low-rank matrix denoising (LRMD) algorithm based on the Gaussian mixture model (GMM) on magnetic resonance imaging (MRI) images of patients with cerebral aneurysm and to evaluate the practical value of the LRMD algorithm in the clinical diagnosis of cerebral aneurysm. In this study, the intracranial MRI data of 40 patients with cerebral aneurysm were selected to study the denoising effect of the low-rank matrix denoising algorithm based on the Gaussian mixture model on MRI images of cerebral aneurysm under the influence of Rice noise, to evaluate the PSNR value, SSIM value, and clarity of MRI images before and after denoising. The diagnostic accuracy of MRI images of cerebral aneurysms before and after denoising was compared. The results showed that after the low-rank matrix denoising algorithm based on the Gaussian mixture model, the PSNR, SSIM, and sharpness values of intracranial MRI images of 10 patients were significantly improved (P < 0.05), and the diagnostic accuracy of MRI images of cerebral aneurysm increased from 76.2 ± 5.6% to 93.1 ± 7.9%, which could diagnose cerebral aneurysm more accurately and quickly. In conclusion, the MRI images processed based on the low-rank matrix denoising algorithm under the Gaussian mixture model can effectively remove the interference of noise, improve the quality of MRI images, optimize the accuracy of MRI image diagnosis of patients with cerebral aneurysm, and shorten the average diagnosis time, which is worth promoting in the clinical diagnosis of patients with cerebral aneurysm.
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Affiliation(s)
- Jun Li
- Department of Radiology, The Jingmen No.1 People's Hospital, Jingmen, 448000 Hubei, China
| | - Jin Li
- Department of Radiology, The Jingmen No.1 People's Hospital, Jingmen, 448000 Hubei, China
| | - Qin Hu
- Department of Radiology, The Jingmen No.1 People's Hospital, Jingmen, 448000 Hubei, China
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11
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De Marinis D, Obrist D. Data Assimilation by Stochastic Ensemble Kalman Filtering to Enhance Turbulent Cardiovascular Flow Data From Under-Resolved Observations. Front Cardiovasc Med 2021; 8:742110. [PMID: 34796213 PMCID: PMC8594566 DOI: 10.3389/fcvm.2021.742110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 10/06/2021] [Indexed: 11/13/2022] Open
Abstract
We propose a data assimilation methodology that can be used to enhance the spatial and temporal resolution of voxel-based data as it may be obtained from biomedical imaging modalities. It can be used to improve the assessment of turbulent blood flow in large vessels by combining observed data with a computational fluid dynamics solver. The methodology is based on a Stochastic Ensemble Kalman Filter (SEnKF) approach and geared toward pulsatile and turbulent flow configurations. We describe the observed flow fields by a mean value and its covariance. These flow fields are combined with forecasts obtained from a direct numerical simulation of the flow field. The method is validated against canonical pulsatile and turbulent flows. Finally, it is applied to a clinically relevant configuration, namely the flow downstream of a bioprosthetic valve in an aorta phantom. It is demonstrated how the 4D flow field obtained from experimental observations can be enhanced by the data assimilation algorithm. Results show that the presented method is promising for future use with in vivo data from 4D Flow Magnetic Resonance Imaging (4D Flow MRI). 4D Flow MRI returns spatially and temporally averaged flow fields that are limited by the spatial and the temporal resolution of the tool. These averaged flow fields and the associated uncertainty might be used as observation data in the context of the proposed methodology.
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Affiliation(s)
- Dario De Marinis
- ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland
- Dipartimento di Meccanica, Matematica e Management and Centro di Eccellenza in Meccanica Computazionale, Politecnico di Bari, Bari, Italy
| | - Dominik Obrist
- ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland
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12
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Integrating multi-fidelity blood flow data with reduced-order data assimilation. Comput Biol Med 2021; 135:104566. [PMID: 34157468 DOI: 10.1016/j.compbiomed.2021.104566] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2021] [Revised: 05/30/2021] [Accepted: 06/08/2021] [Indexed: 11/20/2022]
Abstract
High-fidelity patient-specific modeling of cardiovascular flows and hemodynamics is challenging. Direct blood flow measurement inside the body with in-vivo measurement modalities such as 4D flow magnetic resonance imaging (4D flow MRI) suffer from low resolution and acquisition noise. In-vitro experimental modeling and patient-specific computational fluid dynamics (CFD) models are subject to uncertainty in patient-specific boundary conditions and model parameters. Furthermore, collecting blood flow data in the near-wall region (e.g., wall shear stress) with experimental measurement modalities poses additional challenges. In this study, a computationally efficient data assimilation method called reduced-order modeling Kalman filter (ROM-KF) was proposed, which combined a sequential Kalman filter with reduced-order modeling using a linear model provided by dynamic mode decomposition (DMD). The goal of ROM-KF was to overcome low resolution and noise in experimental and uncertainty in CFD modeling of cardiovascular flows. The accuracy of the method was assessed with 1D Womersley flow, 2D idealized aneurysm, and 3D patient-specific cerebral aneurysm models. Synthetic experimental data were used to enable direct quantification of errors using benchmark datasets. The accuracy of ROM-KF in reconstructing near-wall hemodynamics was assessed by applying the method to problems where near-wall blood flow data were missing in the experimental dataset. The ROM-KF method provided blood flow data that were more accurate than the computational and synthetic experimental datasets and improved near-wall hemodynamics quantification.
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13
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Spectral Decomposition of the Flow and Characterization of the Sound Signals through Stenoses with Different Levels of Severity. Bioengineering (Basel) 2021; 8:bioengineering8030041. [PMID: 33808744 PMCID: PMC8003520 DOI: 10.3390/bioengineering8030041] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2020] [Revised: 03/15/2021] [Accepted: 03/15/2021] [Indexed: 11/17/2022] Open
Abstract
Treatments of atherosclerosis depend on the severity of the disease at the diagnosis time. Non-invasive diagnosis techniques, capable of detecting stenosis at early stages, are essential to reduce associated costs and mortality rates. We used computational fluid dynamics and acoustics analysis to extensively investigate the sound sources arising from high-turbulent fluctuating flow through stenosis. The frequency spectral analysis and proper orthogonal decomposition unveiled the frequency contents of the fluctuations for different severities and decomposed the flow into several frequency bandwidths. Results showed that high-intensity turbulent pressure fluctuations appeared inside the stenosis for severities above 70%, concentrated at plaque surface, and immediately in the post-stenotic region. Analysis of these fluctuations with the progression of the stenosis indicated that (a) there was a distinct break frequency for each severity level, ranging from 40 to 230 Hz, (b) acoustic spatial-frequency maps demonstrated the variation of the frequency content with respect to the distance from the stenosis, and (c) high-energy, high-frequency fluctuations existed inside the stenosis only for severe cases. This information can be essential for predicting the severity level of progressive stenosis, comprehending the nature of the sound sources, and determining the location of the stenosis with respect to the point of measurements.
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14
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Arzani A, Dawson STM. Data-driven cardiovascular flow modelling: examples and opportunities. J R Soc Interface 2021; 18:20200802. [PMID: 33561376 PMCID: PMC8086862 DOI: 10.1098/rsif.2020.0802] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Accepted: 01/18/2021] [Indexed: 12/14/2022] Open
Abstract
High-fidelity blood flow modelling is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from such investigations remains limited by the presence of uncertainty in parameters, low resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Data-driven modelling techniques have the potential to overcome these challenges and transform cardiovascular flow modelling. Here, we review several data-driven modelling techniques, highlight the common ideas and principles that emerge across numerous such techniques, and provide illustrative examples of how they could be used in the context of cardiovascular fluid mechanics. In particular, we discuss principal component analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data assimilation, low-rank data recovery, and several additional methods for reduced-order modelling of cardiovascular flows, including the dynamic mode decomposition and the sparse identification of nonlinear dynamics. All techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modelling techniques have the potential to transform computational and experimental cardiovascular research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modelling.
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Affiliation(s)
- Amirhossein Arzani
- Department of Mechanical Engineering, Northern Arizona University, Flagstaff, AZ, USA
| | - Scott T. M. Dawson
- Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL, USA
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Perez-Raya I, Fathi MF, Baghaie A, Sacho R, D'Souza RM. Modeling and Reducing the Effect of Geometric Uncertainties in Intracranial Aneurysms with Polynomial Chaos Expansion, Data Decomposition, and 4D-Flow MRI. Cardiovasc Eng Technol 2021; 12:127-143. [PMID: 33415699 DOI: 10.1007/s13239-020-00511-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Accepted: 12/16/2020] [Indexed: 11/27/2022]
Abstract
PURPOSE Variations in the vessel radius of segmented surfaces of intracranial aneurysms significantly influence the fluid velocities given by computer simulations. It is important to generate models that capture the effect of these variations in order to have a better interpretation of the numerically predicted hemodynamics. Also, it is highly relevant to develop methods that combine experimental observations with uncertainty modeling to get a closer approximation to the blood flow behavior. METHODS This work applies polynomial chaos expansion to model the effect of geometric uncertainties on the simulated fluid velocities of intracranial aneurysms. The radius of the vessel is defined as the uncertainty variable. Proper orthogonal decomposition is applied to characterize the solution space of fluid velocities. Next, a process of projecting the 4D-Flow MRI velocities on the basis vectors followed by coefficient mapping using generalized dynamic mode decomposition enables the merging of 4D-Flow MRI with the uncertainty propagated fluid velocities. RESULTS Polynomial chaos expansion propagates the fluid velocities with an error of 2% in velocity magnitude relative to computer simulations. Also, the bifurcation region (or impingement location) shows a standard deviation of 0.17 m/s (since an available reported variance in the vessel radius is adopted to model the uncertainty, the expected standard deviation may be different). Numerical phantom experiments indicate that the proposed approach reconstructs the fluid velocities with 0.3% relative error in presence of geometric uncertainties. CONCLUSION Polynomial chaos expansion is an effective approach to propagate the effect of the uncertainty variable in the blood flow velocities of intracranial aneurysms. Merging 4D-Flow MRI and uncertainty propagated fluid velocities leads to more realistic flow trends relative to ignoring the uncertainty in the vessel radius.
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Affiliation(s)
- Isaac Perez-Raya
- Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA.
| | - Mojtaba F Fathi
- Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA
| | - Ahmadreza Baghaie
- Department of Electrical and Computer Engineering, New York Institute of Technology, Old Westbury, NY, 11568, USA
| | - Raphael Sacho
- Department of Neurosurgery, Medical College of Wisconsin, Milwaukee, WI, 53226, USA
| | - Roshan M D'Souza
- Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA
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Abderezaei J, Martinez J, Terem I, Fabris G, Pionteck A, Yang Y, Holdsworth SJ, Nael K, Kurt M. Amplified Flow Imaging (aFlow): A Novel MRI-Based Tool to Unravel the Coupled Dynamics Between the Human Brain and Cerebrovasculature. IEEE TRANSACTIONS ON MEDICAL IMAGING 2020; 39:4113-4123. [PMID: 32746150 DOI: 10.1109/tmi.2020.3012932] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
With each heartbeat, periodic variations in arterial blood pressure are transmitted along the vasculature, resulting in localized deformations of the arterial wall and its surrounding tissue. Quantification of such motions may help understand various cerebrovascular conditions, yet it has proven technically challenging thus far. We introduce a new image processing algorithm called amplified Flow (aFlow) which allows to study the coupled brain-blood flow motion by combining the amplification of cine and 4D flow MRI. By incorporating a modal analysis technique known as dynamic mode decomposition into the algorithm, aFlow is able to capture the characteristics of transient events present in the brain and arterial wall deformation. Validating aFlow, we tested it on phantom simulations mimicking arterial walls motion and observed that aFlow displays almost twice higher SNR than its predecessor amplified MRI (aMRI). We then applied aFlow to 4D flow and cine MRI datasets of 5 healthy subjects, finding high correlations between blood flow velocity and tissue deformation in selected brain regions, with correlation values r = 0.61 , 0.59, 0.52 for the pons, frontal and occipital lobe ( ). Finally, we explored the potential diagnostic applicability of aFlow by studying intracranial aneurysm dynamics, which seems to be indicative of rupture risk. In two patients, aFlow successfully visualized the imperceptible aneurysm wall motion, additionally quantifying the increase in the high frequency wall displacement after a one-year follow-up period (20%, 76%). These preliminary data suggest that aFlow may provide a novel imaging biomarker for the assessment of aneurysms evolution, with important potential diagnostic implications.
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Abstract
Geological flows-from mudslides to volcanic eruptions-are often opaque and consist of multiple interacting phases. Scaled laboratory geological experiments using analog materials have often been limited to optical imaging of flow exteriors or ex situ measurements. Geological flows often include internal phase transitions and chemical reactions that are difficult to image externally. Thus, many physical mechanisms underlying geological flows remain unknown, hindering model development. We propose using magnetic resonance imaging (MRI) to enhance geosciences via non-invasive, in situ measurements of 3D flows. MRI is currently used to characterize the interior dynamics of multiphase flows, distinguishing between different chemical species as well as gas, liquid, and solid phases, while quantitatively measuring concentration, velocity, and diffusion fields. This perspective describes the potential of MRI techniques to image dynamics within scaled geological flow experiments and the potential of technique development for geological samples to be transferred to other disciplines utilizing MRI.
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Gaidzik F, Pathiraja S, Saalfeld S, Stucht D, Speck O, Thévenin D, Janiga G. Hemodynamic Data Assimilation in a Subject-specific Circle of Willis Geometry. Clin Neuroradiol 2020; 31:643-651. [PMID: 32974727 PMCID: PMC8463518 DOI: 10.1007/s00062-020-00959-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 08/27/2020] [Indexed: 01/13/2023]
Abstract
PURPOSE The anatomy of the circle of Willis (CoW), the brain's main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations. METHODS To the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF). RESULTS Quantitative evaluation shows a considerable reduction (up to 90%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone. CONCLUSION This study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.
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Affiliation(s)
- Franziska Gaidzik
- Lab. of Fluid Dynamics and Technical Flows, Otto von Guericke University Magdeburg, Magdeburg, Germany
| | - Sahani Pathiraja
- Institute for Mathematics, University of Potsdam, Potsdam, Germany
| | - Sylvia Saalfeld
- Department of Simulation and Graphics, Otto von Guericke University Magdeburg, Magdeburg, Germany
| | - Daniel Stucht
- Institute for Physics, Otto von Guericke University Magdeburg, Magdeburg, Germany.,Institute of Biometry and Medical Informatics, Otto von Guericke University Magdeburg, Magdeburg, Germany
| | - Oliver Speck
- Institute for Physics, Otto von Guericke University Magdeburg, Magdeburg, Germany.,Leibniz Institute for Neurobiology, Magdeburg, Germany
| | - Dominique Thévenin
- Lab. of Fluid Dynamics and Technical Flows, Otto von Guericke University Magdeburg, Magdeburg, Germany
| | - Gábor Janiga
- Lab. of Fluid Dynamics and Technical Flows, Otto von Guericke University Magdeburg, Magdeburg, Germany.
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Dynamic Denoising and Gappy Data Reconstruction Based on Dynamic Mode Decomposition and Discrete Cosine Transform. APPLIED SCIENCES-BASEL 2018. [DOI: 10.3390/app8091515] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Dynamic Mode Decomposition (DMD) is a data-driven method to analyze the dynamics, first applied to fluid dynamics. It extracts modes and their corresponding eigenvalues, where the modes are spatial fields that identify coherent structures in the flow and the eigenvalues describe the temporal growth/decay rates and oscillation frequencies for each mode. The recently introduced compressed sensing DMD (csDMD) reduces computation times and also has the ability to deal with sub-sampled datasets. In this paper, we present a similar technique based on discrete cosine transform to reconstruct the fully-sampled dataset (as opposed to DMD modes as in csDMD) from sub-sampled noisy and gappy data using l 1 minimization. The proposed method was benchmarked against csDMD in terms of denoising and gap-filling using three datasets. The first was the 2-D time-resolved plot of a double gyre oscillator which has about nine oscillatory modes. The second dataset was derived from a Duffing oscillator. This dataset has several modes associated with complex eigenvalues which makes them oscillatory. The third dataset was taken from the 2-D simulation of a wake behind a cylinder at Re = 100 and was used for investigating the effect of changing various parameters on reconstruction error. The Duffing and 2-D wake datasets were tested in presence of noise and rectangular gaps. While the performance for the double-gyre dataset is comparable to csDMD, the proposed method performs substantially better (lower reconstruction error) for the dataset derived from the Duffing equation and also, the 2-D wake dataset according to the defined reconstruction error metrics.
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