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Pancóatl-Bortolotti P, Enríquez-Caldera RA, Costa AH, Tello-Bello M, Guerrero-Castellanos JF. Adaptive Doppler bio-signal detector and time-frequency representation based on non-Liènard oscillator. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024; 40:e3794. [PMID: 37991118 DOI: 10.1002/cnm.3794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Revised: 10/04/2023] [Accepted: 11/01/2023] [Indexed: 11/23/2023]
Abstract
The work presented here provides the guidelines and results for designing and implementing a highly sensitive modified Van der Pol - Duffing oscillator with a trigonometric damping function (VTD). This VTD can exhibit periodic and quasi-chaotic behavior necessary for application in weak signal detection. Here, we present two proposals: (1) A method based on a quasi-chaotic intermittent array (ANLIOA), whose all VTD parameters are calculated and fine-tuned toward a critical state between chaotic and periodic state through a Lyapunov exponent procedure, and (2) A method based on a single oscillator in an adaptive stopping oscillation system (ANLSOS), where VTD is established within an oscillatory regime. Both systems can detect non-stationary signals while reconstructing the time-frequency spectrogram in high resolution within severe noise conditions. The systems were adapted for the detection of a synthesized Doppler signal corresponding to the blood flow velocity profile from an artery. Comparative results using typical oscillators such as Duffing or Van der Pol demonstrate the superiority of the VTD oscillator in detection when used for both methods, whose mean absolute percentage error reached around 6% for a signal-to-noise ratio (SNR) of -10 dB. Furthermore, compared to other time-frequency methods, ANLIOA and ANLSOS promise high precision in detecting Doppler signals with low rates of frequency changes while minimizing energy emission and avoiding possible bio-thermal effects.
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Affiliation(s)
| | | | - Antonio H Costa
- Department of Electrical and Computer Engineering, University of Massachusetts Dartmouth, Dartmouth, Massachusetts, United States
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2
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Cheng L, Huang Y, Yao H, Luo J, Zhang L, Fu R, Lv J, Yang B, Yan L. Wall Shear Stress Reduction Activates Angiotensin II to Facilitate Aneurysmal Subarachnoid Hemorrhage in Intracranial Aneurysms Through MicroRNA-29/The Growth Factor-Beta Receptor Type II/Smad3 Axis. World Neurosurg 2023; 176:e314-e326. [PMID: 37230243 DOI: 10.1016/j.wneu.2023.05.056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Revised: 05/16/2023] [Accepted: 05/17/2023] [Indexed: 05/27/2023]
Abstract
OBJECTIVE We tried to broaden our knowledge of the possible role of wall shear stress (WSS) in the occurrence of intracranial aneurysms (IAs). METHODS Genes implicated in IAs and genes related to WSS were predicted through in silico analysis. Rat models of IAs were established, in which the expression patterns of angiotensin II (Ang II) were characterized, and WSS was assessed. Vascular endothelial cells isolated from rats bearing IAs were treated with microRNA-29 (miR-29) mimic/inhibitor, small interfering RNA-TGF-β receptor type II (TGFBR2)/overexpressed TGFBR2, Ang II, or angiotensin-converting enzyme (ACE) inhibitor. Then, the endothelial-to-mesenchymal transition (EndMT) was evaluated by flow cytometry. Finally, the volume of IAs and risk of subarachnoid hemorrhage were analyzed in vivo in response to miR-29 gain of function. RESULTS WSS was decreased in the IA bearing arteries, which showed a positive correlation with ACE and Ang II in the vascular tissues of IA rats. Reduced miR-29 and increased ACE, Ang II, and TGFBR2 were detected in the vascular tissues of IA rats. Ang II inhibited miR-29, which targeted TGFBR2. Downregulated TGFBR2 was accompanied by suppression of Smad3 phosphorylation. Through impairing miR-29-dependent inhibition of TGFBR2, Ang II enhanced EndMT. In vivo data confirmed that treatment of miR-29 agomir delayed the formation of IA and decreased the risk of subarachnoid hemorrhage. CONCLUSIONS The current study provided evidence that WSS reduction could activate Ang II, reduce miR-29 expression, and activate the TGFBR2/Smad3 axis, thus promoting EndMT and accelerating the progression of IAs.
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Affiliation(s)
- Longhai Cheng
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
| | - Yan Huang
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
| | - Hong Yao
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
| | - Jie Luo
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
| | - Li Zhang
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
| | - Rui Fu
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
| | - Junti Lv
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China.
| | - Bowen Yang
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
| | - Lidong Yan
- Department of Neurosurgery, Taihe Hospital, Hubei University of Medicine, Shiyan, P.R. China
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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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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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5
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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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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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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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Wang Y, Lee WN. Non-Invasive Estimation of Localized Dynamic Luminal Pressure Change by Ultrasound Elastography in Arteries With Normal and Abnormal Geometries. IEEE Trans Biomed Eng 2021; 68:1627-1637. [DOI: 10.1109/tbme.2020.3028186] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Galarce F, Lombardi D, Mula O. Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3416. [PMID: 33219632 DOI: 10.1002/cnm.3416] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2020] [Revised: 11/06/2020] [Accepted: 11/07/2020] [Indexed: 06/11/2023]
Abstract
The present contribution deals with the estimation of haemodynamics Quantities of Interest by exploiting Ultrasound Doppler measurements. A fast method is proposed, based on the Parameterized Background Data-Weak (PBDW) method. Several methodological contributions are described: a sub-manifold partitioning is introduced to improve the reduced-order approximation, two different ways to estimate the pressure drop are compared, and an error estimation is derived. A fully synthetic test-case on a realistic common carotid geometry is presented, showing that the proposed approach is promising in view of realistic applications.
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Affiliation(s)
- Felipe Galarce
- Centre de Recherche INRIA de Paris, Laboratoire Jacques-Louis Lions Faculté des Sciences de Sorbonne Université, INRIA, Paris, France
| | - Damiano Lombardi
- Centre de Recherche INRIA de Paris, Laboratoire Jacques-Louis Lions Faculté des Sciences de Sorbonne Université, INRIA, Paris, France
| | - Olga Mula
- Centre de Recherche INRIA de Paris, Laboratoire Jacques-Louis Lions Faculté des Sciences de Sorbonne Université, INRIA, Paris, France
- CEREMADE, Paris-Dauphine University, PSL Research University, CNRS, Paris, France
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10
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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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Marlevi D, Ha H, Dillon-Murphy D, Fernandes JF, Fovargue D, Colarieti-Tosti M, Larsson M, Lamata P, Figueroa CA, Ebbers T, Nordsletten DA. Non-invasive estimation of relative pressure in turbulent flow using virtual work-energy. Med Image Anal 2020; 60:101627. [PMID: 31865280 DOI: 10.1016/j.media.2019.101627] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 10/11/2019] [Accepted: 12/05/2019] [Indexed: 10/25/2022]
Abstract
Vascular pressure differences are established risk markers for a number of cardiovascular diseases. Relative pressures are, however, often driven by turbulence-induced flow fluctuations, where conventional non-invasive methods may yield inaccurate results. Recently, we proposed a novel method for non-turbulent flows, νWERP, utilizing the concept of virtual work-energy to accurately probe relative pressure through complex branching vasculature. Here, we present an extension of this approach for turbulent flows: νWERP-t. We present a theoretical method derivation based on flow covariance, quantifying the impact of flow fluctuations on relative pressure. νWERP-t is tested on a set of in-vitro stenotic flow phantoms with data acquired by 4D flow MRI with six-directional flow encoding, as well as on a patient-specific in-silico model of an acute aortic dissection. Over all tests νWERP-t shows improved accuracy over alternative energy-based approaches, with excellent recovery of estimated relative pressures. In particular, the use of a guaranteed divergence-free virtual field improves accuracy in cases where turbulent flows skew the apparent divergence of the acquired field. With the original νWERP allowing for assessment of relative pressure into previously inaccessible vasculatures, the extended νWERP-t further enlarges the method's clinical scope, underlining its potential as a novel tool for assessing relative pressure in-vivo.
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Affiliation(s)
- David Marlevi
- Department of Biomedical Engineering and Health Systems, KTH Royal Institute of Technology, Hälsovägen 11, 14152, Huddinge, Sweden; Department of Clinical Sciences, Karolinska Institutet, Danderyds sjukhus, Mörbygårdsvägen, Danderyd, 18288, Sweden.
| | - Hojin Ha
- Department of Medical and Health Sciences and Center for Medical Image Science and Visualization (CMIV), Linköping Unversity, Linköping, SE-58185, Sweden; Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, 24341, Republic of Korea.
| | - Desmond Dillon-Murphy
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, SE1 7EH, United Kingdom.
| | - Joao F Fernandes
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, SE1 7EH, United Kingdom.
| | - Daniel Fovargue
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, SE1 7EH, United Kingdom.
| | - Massimiliano Colarieti-Tosti
- Department of Biomedical Engineering and Health Systems, KTH Royal Institute of Technology, Hälsovägen 11, 14152, Huddinge, Sweden.
| | - Matilda Larsson
- Department of Biomedical Engineering and Health Systems, KTH Royal Institute of Technology, Hälsovägen 11, 14152, Huddinge, Sweden.
| | - Pablo Lamata
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, SE1 7EH, United Kingdom.
| | - C Alberto Figueroa
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, SE1 7EH, United Kingdom; Department of Surgery and Biomedical Engineering, University of Michigan, 2800 Plymouth Rd, 48109, Ann Arbor, MI, USA.
| | - Tino Ebbers
- Department of Medical and Health Sciences and Center for Medical Image Science and Visualization (CMIV), Linköping Unversity, Linköping, SE-58185, Sweden.
| | - David A Nordsletten
- School of Biomedical Engineering and Imaging Sciences, The Rayne Institute, King's College London, London, SE1 7EH, United Kingdom; Department of Surgery and Biomedical Engineering, University of Michigan, 2800 Plymouth Rd, 48109, Ann Arbor, MI, USA
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Evaluation of 4D flow MRI-based non-invasive pressure assessment in aortic coarctations. J Biomech 2019; 94:13-21. [PMID: 31326119 DOI: 10.1016/j.jbiomech.2019.07.004] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2018] [Revised: 06/12/2019] [Accepted: 07/04/2019] [Indexed: 12/20/2022]
Abstract
Severity of aortic coarctation (CoA) is currently assessed by estimating trans-coarctation pressure drops through cardiac catheterization or echocardiography. In principle, more detailed information could be obtained non-invasively based on space- and time-resolved magnetic resonance imaging (4D flow) data. Yet the limitations of this imaging technique require testing the accuracy of 4D flow-derived hemodynamic quantities against other methodologies. With the objective of assessing the feasibility and accuracy of this non-invasive method to support the clinical diagnosis of CoA, we developed an algorithm (4DF-FEPPE) to obtain relative pressure distributions from 4D flow data by solving the Poisson pressure equation. 4DF-FEPPE was tested against results from a patient-specific fluid-structure interaction (FSI) simulation, whose patient-specific boundary conditions were prescribed based on 4D flow data. Since numerical simulations provide noise-free pressure fields on fine spatial and temporal scales, our analysis allowed to assess the uncertainties related to 4D flow noise and limited resolution. 4DF-FEPPE and FSI results were compared on a series of cross-sections along the aorta. Bland-Altman analysis revealed very good agreement between the two methodologies in terms of instantaneous data at peak systole, end-diastole and time-averaged values: biases (means of differences) were +0.4 mmHg, -1.1 mmHg and +0.6 mmHg, respectively. Limits of agreement (2 SD) were ±0.978 mmHg, ±1.06 mmHg and ±1.97 mmHg, respectively. Peak-to-peak and maximum trans-coarctation pressure drops obtained with 4DF-FEPPE differed from FSI results by 0.75 mmHg and -1.34 mmHg respectively. The present study considers important validation aspects of non-invasive pressure difference estimation based on 4D flow MRI, showing the potential of this technology to be more broadly applied to the clinical practice.
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Nolte D, Bertoglio C. Reducing the impact of geometric errors in flow computations using velocity measurements. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3203. [PMID: 30932361 PMCID: PMC6619346 DOI: 10.1002/cnm.3203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/12/2018] [Revised: 02/26/2019] [Accepted: 03/12/2019] [Indexed: 06/09/2023]
Abstract
Numerical blood flow simulations are typically set up from anatomical medical images and calibrated using velocity measurements. However, the accuracy of the computational geometry itself is limited by the resolution of the anatomical image. We first show that applying standard no-slip boundary conditions on inaccurately extracted boundaries can cause large errors in the results, in particular the pressure gradient. In this work, we therefore propose to augment the flow model calibration by slip/transpiration boundary conditions, whose parameters are then estimated using velocity measurements. Numerical experiments show that this methodology can considerably improve the accuracy of the estimated pressure gradients and 3D velocity fields when the vessel geometry is uncertain.
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Affiliation(s)
- David Nolte
- Bernoulli InstituteUniversity of GroningenGroningenNetherlands
- Center of Mathematical ModelingUniversity of ChileSantiagoChile
| | - Cristóbal Bertoglio
- Bernoulli InstituteUniversity of GroningenGroningenNetherlands
- Center of Mathematical ModelingUniversity of ChileSantiagoChile
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Marlevi D, Ruijsink B, Balmus M, Dillon-Murphy D, Fovargue D, Pushparajah K, Bertoglio C, Colarieti-Tosti M, Larsson M, Lamata P, Figueroa CA, Razavi R, Nordsletten DA. Estimation of Cardiovascular Relative Pressure Using Virtual Work-Energy. Sci Rep 2019; 9:1375. [PMID: 30718699 PMCID: PMC6362021 DOI: 10.1038/s41598-018-37714-0] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Accepted: 12/12/2018] [Indexed: 12/21/2022] Open
Abstract
Many cardiovascular diseases lead to local increases in relative pressure, reflecting the higher costs of driving blood flow. The utility of this biomarker for stratifying the severity of disease has thus driven the development of methods to measure these relative pressures. While intravascular catheterisation remains the most direct measure, its invasiveness limits clinical application in many instances. Non-invasive Doppler ultrasound estimates have partially addressed this gap; however only provide relative pressure estimates for a range of constricted cardiovascular conditions. Here we introduce a non-invasive method that enables arbitrary interrogation of relative pressures throughout an imaged vascular structure, leveraging modern phase contrast magnetic resonance imaging, the virtual work-energy equations, and a virtual field to provide robust and accurate estimates. The versatility and accuracy of the method is verified in a set of complex patient-specific cardiovascular models, where relative pressures into previously inaccessible flow regions are assessed. The method is further validated within a cohort of congenital heart disease patients, providing a novel tool for probing relative pressures in-vivo.
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Affiliation(s)
- David Marlevi
- Department of Biomedical Engineering and Health Systems, KTH Royal Institute of Technology, Stockholm, Sweden.
- Department of Clinical Sciences, Karolinska Institutet, Stockholm, Sweden.
| | - Bram Ruijsink
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
- Department of Congenital Heart Disease, Evelina Children's Hospital, London, United Kingdom
| | - Maximilian Balmus
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
| | - Desmond Dillon-Murphy
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
| | - Daniel Fovargue
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
| | - Kuberan Pushparajah
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
- Department of Congenital Heart Disease, Evelina Children's Hospital, London, United Kingdom
| | - Cristóbal Bertoglio
- Bernoulli Institute, University of Groningen, Groningen, The Netherlands
- Center for Mathematical Modeling, Universidad de Chile, Santiago, Chile
| | - Massimiliano Colarieti-Tosti
- Department of Biomedical Engineering and Health Systems, KTH Royal Institute of Technology, Stockholm, Sweden
- Department of Clinical Science, Intervention and Technology (CLINTEC), Karolinska Institutet, Stockholm, Sweden
| | - Matilda Larsson
- Department of Biomedical Engineering and Health Systems, KTH Royal Institute of Technology, Stockholm, Sweden
| | - Pablo Lamata
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
| | - C Alberto Figueroa
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
- Departments of Surgery and Biomedical Engineering, University of Michigan, Ann Arbor, USA
| | - Reza Razavi
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom
- Department of Congenital Heart Disease, Evelina Children's Hospital, London, United Kingdom
| | - David A Nordsletten
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St Thomas' Hospital, London, United Kingdom.
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