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Park WY, Lee SY, Seo J. Hemodynamic Analysis in Aortic Dilatation after Arterial Switch Operation for Patients with Transposition of Great Arteries Using Computational Fluid Dynamics. J Cardiovasc Transl Res 2024:10.1007/s12265-024-10562-2. [PMID: 39320418 DOI: 10.1007/s12265-024-10562-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/29/2024] [Accepted: 09/12/2024] [Indexed: 09/26/2024]
Abstract
After an arterial switch operation for complete transposition of the great arteries, neo-aortic root dilatation occurs, with unclear hemodynamic effects. This study analyzes three groups (severe dilation, mild dilation, and normal) using computational fluid dynamics (CFD) on cardiac CT scans. Aortic arch angles in severe (median 72.3, range: 68.5-77.2) and mild dilation (76.6, 71.1-85.2) groups are significantly smaller than the normal group (97.3, 87.4-99.0). In the normal and mild dilatation groups, Wall Shear Stress (WSS) exhibits a consistent pattern: it is lowest at the aortic root, gradually increases until just before the bend in the aortic arch, peaks, and then subsequently decreases. However, severe dilation shows disrupted WSS patterns, notably lower in the distal ascending aorta, attributed to local recirculation. This unique WSS pattern observed in severely dilated patients, especially in the transverse aorta. CFD plays an essential role in comprehensively studying the pathophysiology underlying aortic dilation in this population.
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Affiliation(s)
- Woo Young Park
- Department of Pediatrics, Seoul National University Children's Hospital, Seoul National University College of Medicine, 101, Daehak-ro, Jongno-gu, Seoul, Republic of Korea
| | - Sang Yun Lee
- Department of Pediatrics, Seoul National University Children's Hospital, Seoul National University College of Medicine, 101, Daehak-ro, Jongno-gu, Seoul, Republic of Korea.
| | - Jongmin Seo
- Department of Mechanical Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do, Republic of Korea.
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Özcan C, Kocatürk Ö, Işlak C, Öztürk C. Integrated particle image velocimetry and fluid-structure interaction analysis for patient-specific abdominal aortic aneurysm studies. Biomed Eng Online 2023; 22:113. [PMID: 38044423 PMCID: PMC10693692 DOI: 10.1186/s12938-023-01179-8] [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: 10/03/2023] [Accepted: 11/23/2023] [Indexed: 12/05/2023] Open
Abstract
BACKGROUND Understanding the hemodynamics of an abdominal aortic aneurysm (AAA) is crucial for risk assessment and treatment planning. This study introduces a low-cost, patient-specific in vitro AAA model to investigate hemodynamics using particle image velocimetry (PIV) and flow-simulating circuit, validated through fluid-structure interaction (FSI) simulations. METHODS In this study, 3D printing was employed to manufacture a flexible patient-specific AAA phantom using a lost-core casting technique. A pulsatile flow circuit was constructed using off-the-shelf components. A particle image velocimetry (PIV) setup was built using an affordable laser source and global shutter camera, and finally, the flow field inside the AAA was analyzed using open-source software. Fluid-structure interaction (FSI) simulations were performed to enhance our understanding of the flow field, and the results were validated by PIV analysis. Both steady-state and transient flow conditions were investigated. RESULTS Our experimental setup replicated physiological conditions, analyzing arterial wall deformations and flow characteristics within the aneurysm. Under constant flow, peak wall deformations and flow velocities showed deviations within - 12% to + 27% and - 7% to + 5%, respectively, compared to FSI simulations. Pulsatile flow conditions further demonstrated a strong correlation (Pearson coefficient 0.85) in flow velocities and vectors throughout the cardiac cycle. Transient phenomena, particularly the formation and progression of vortex structures during systole, were consistently depicted between experimental and numerical models. CONCLUSIONS By bridging high-fidelity experimental observations with comprehensive computational analyses, this study underscores the potential of integrated methodologies in enhancing our understanding of AAA pathophysiology. The convergence of realistic AAA phantoms, precise PIV measurements at affordable cost point, and validated FSI models heralds a new paradigm in vascular research, with significant implications for personalized medicine and bioengineering innovations.
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Affiliation(s)
- Can Özcan
- Institute of Biomedical Engineering, Boğaziçi University, Kandilli Campus, Feza Gürsey Bld., Çengelköy, 34685, Istanbul, Turkey.
| | - Özgür Kocatürk
- Institute of Biomedical Engineering, Boğaziçi University, Kandilli Campus, Feza Gürsey Bld., Çengelköy, 34685, Istanbul, Turkey
| | - Civan Işlak
- Department of Radiology, Division of Neuroradiology, Cerrahpaşa Medical Faculty, Istanbul University Cerrahpaşa, Istanbul, Turkey
| | - Cengizhan Öztürk
- Institute of Biomedical Engineering, Boğaziçi University, Kandilli Campus, Feza Gürsey Bld., Çengelköy, 34685, Istanbul, Turkey
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Lyu Z, King K, Rezaeitaleshmahalleh M, Pienta D, Mu N, Zhao C, Zhou W, Jiang J. Deep-learning-based image segmentation for image-based computational hemodynamic analysis of abdominal aortic aneurysms: a comparison study. Biomed Phys Eng Express 2023; 9:067001. [PMID: 37625388 DOI: 10.1088/2057-1976/acf3ed] [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: 06/01/2023] [Accepted: 08/25/2023] [Indexed: 08/27/2023]
Abstract
Computational hemodynamics is increasingly being used to quantify hemodynamic characteristics in and around abdominal aortic aneurysms (AAA) in a patient-specific fashion. However, the time-consuming manual annotation hinders the clinical translation of computational hemodynamic analysis. Thus, we investigate the feasibility of using deep-learning-based image segmentation methods to reduce the time required for manual segmentation. Two of the latest deep-learning-based image segmentation methods, ARU-Net and CACU-Net, were used to test the feasibility of automated computer model creation for computational hemodynamic analysis. Morphological features and hemodynamic metrics of 30 computed tomography angiography (CTA) scans were compared between pre-dictions and manual models. The DICE score for both networks was 0.916, and the correlation value was above 0.95, indicating their ability to generate models comparable to human segmentation. The Bland-Altman analysis shows a good agreement between deep learning and manual segmentation results. Compared with manual (computational hemodynamics) model recreation, the time for automated computer model generation was significantly reduced (from ∼2 h to ∼10 min). Automated image segmentation can significantly reduce time expenses on the recreation of patient-specific AAA models. Moreover, our study showed that both CACU-Net and ARU-Net could accomplish AAA segmentation, and CACU-Net outperformed ARU-Net in terms of accuracy and time-saving.
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Affiliation(s)
- Zonghan Lyu
- Biomedical Engineering, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
| | - Kristin King
- Biomedical Engineering, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
| | - Mostafa Rezaeitaleshmahalleh
- Biomedical Engineering, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
| | - Drew Pienta
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Applied Computing, Michigan Technological University, Houghton, Michigan, MI, United States of America
| | - Nan Mu
- Biomedical Engineering, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
| | - Chen Zhao
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Applied Computing, Michigan Technological University, Houghton, Michigan, MI, United States of America
| | - Weihua Zhou
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Applied Computing, Michigan Technological University, Houghton, Michigan, MI, United States of America
| | - Jingfeng Jiang
- Biomedical Engineering, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Joint Center for Biocomputing and Digital Health, Health Research Institute and Institute of Computing and Cybernetics, Michigan Technological University, Houghton, Michigan, MI, United States of America
- Department of Radiology, Mayo Clinic, Rochester, Minnesota, MN, United States of America
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Umo A, Kung EO. A Protocol for Coupling Volumetrically Dynamic In-Vitro Experiments to Numerical Physiology Simulation for a Hybrid Cardiovascular Model. IEEE Trans Biomed Eng 2023; 70:1351-1358. [PMID: 36269903 PMCID: PMC11232494 DOI: 10.1109/tbme.2022.3216542] [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] [Indexed: 11/06/2022]
Abstract
OBJECTIVE The Physiology Simulation Coupled Experiment (PSCOPE) is a hybrid modeling framework that enables a physical fluid experiment to operate in the context of a closed-loop computational simulation of cardiovascular physiology. Previous PSCOPE methods coupled rigid experiments to a lumped parameter network (LPN) of physiology but are incompatible with volumetrically dynamic experiments where fluid volume varies periodically. We address this limitation by introducing a method capable of coupling multi-branch and volumetrically dynamic in-vitro experiments to an LPN. METHODS Our proposed method utilizes an iterative weighted-averaging algorithm to identify the unique solution waveforms for a given PSCOPE model. We confirm the accuracy of these PSCOPE solutions by integrating mathematical surrogates of in-vitro experiments directly into the LPN to derive reference solutions, which serve as the gold standard to validate the solutions obtained from using our proposed method to couple the same mathematical surrogates to the LPN. Finally, we illustrate a practical application of our PSCOPE method by coupling an in-vitro renal circulation experiment to the LPN. RESULTS Compared to the reference solution, the normalized root mean square error of the flow and pressure waveforms were 0.001%∼0.55%, demonstrating the accuracy of the coupling method. CONCLUSION We successfully coupled the in-vitro experiment to the LPN, demonstrating the real-world performance within the constraints of sensor and actuation limitations in the physical experiment. SIGNIFICANCE This study introduces a PSCOPE method that can be used to investigate medical devices and anatomies that exhibit periodic volume changes, expanding the utility of the hybrid framework.
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Lan IS, Liu J, Yang W, Zimmermann J, Ennis DB, Marsden AL. Validation of the Reduced Unified Continuum Formulation Against In Vitro 4D-Flow MRI. Ann Biomed Eng 2023; 51:377-393. [PMID: 35963921 PMCID: PMC11402517 DOI: 10.1007/s10439-022-03038-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Accepted: 07/25/2022] [Indexed: 01/25/2023]
Abstract
We previously introduced and verified the reduced unified continuum formulation for vascular fluid-structure interaction (FSI) against Womersley's deformable wall theory. Our present work seeks to investigate its performance in a patient-specific aortic setting in which assumptions of idealized geometries and velocity profiles are invalid. Specifically, we leveraged 2D magnetic resonance imaging (MRI) and 4D-flow MRI to extract high-resolution anatomical and hemodynamic information from an in vitro flow circuit embedding a compliant 3D-printed aortic phantom. To accurately reflect experimental conditions, we numerically implemented viscoelastic external tissue support, vascular tissue prestressing, and skew boundary conditions enabling in-plane vascular motion at each inlet and outlet. Validation of our formulation is achieved through close quantitative agreement in pressures, lumen area changes, pulse wave velocity, and early systolic velocities, as well as qualitative agreement in late systolic flow structures. Our validated suite of FSI techniques offers a computationally efficient approach for numerical simulation of vascular hemodynamics. This study is among the first to validate a cardiovascular FSI formulation against an in vitro flow circuit involving a compliant vascular phantom of complex patient-specific anatomy.
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Affiliation(s)
- Ingrid S Lan
- Department of Bioengineering, Stanford University, Clark Center E1.3 318 Campus Drive, Stanford, CA, 94305-5428, USA
| | - Ju Liu
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People's Republic of China
- Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People's Republic of China
| | - Weiguang Yang
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, 94305, USA
| | - Judith Zimmermann
- Department of Radiology, Stanford University, Stanford, CA, 94305, USA
- Department of Informatics, Technical University of Munich, 85748, Garching, Germany
| | - Daniel B Ennis
- Department of Radiology, Stanford University, Stanford, CA, 94305, USA
- Division of Radiology, Veterans Affairs Health Care System, Palo Alto, CA, 94304, USA
| | - Alison L Marsden
- Department of Bioengineering, Stanford University, Clark Center E1.3 318 Campus Drive, Stanford, CA, 94305-5428, USA.
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, 94305, USA.
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305, USA.
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He Y, Northrup H, Le H, Cheung AK, Berceli SA, Shiu YT. Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases. Front Bioeng Biotechnol 2022; 10:855791. [PMID: 35573253 PMCID: PMC9091352 DOI: 10.3389/fbioe.2022.855791] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2022] [Accepted: 04/08/2022] [Indexed: 01/17/2023] Open
Abstract
Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.
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Affiliation(s)
- Yong He
- Division of Vascular Surgery and Endovascular Therapy, University of Florida, Gainesville, FL, United States
| | - Hannah Northrup
- Department of Biomedical Engineering, University of Utah, Salt Lake City, UT, United States
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
| | - Ha Le
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
| | - Alfred K. Cheung
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
- Veterans Affairs Salt Lake City Healthcare System, Salt Lake City, UT, United States
| | - Scott A. Berceli
- Division of Vascular Surgery and Endovascular Therapy, University of Florida, Gainesville, FL, United States
- Vascular Surgery Section, Malcom Randall Veterans Affairs Medical Center, Gainesville, FL, United States
| | - Yan Tin Shiu
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
- Veterans Affairs Salt Lake City Healthcare System, Salt Lake City, UT, United States
- *Correspondence: Yan Tin Shiu,
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7
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Shi Y, Peng C, Liu J, Lan H, Li C, Qin W, Yuan T, Kan Y, Wang S, Fu W. A modified method of computed fluid dynamics simulation in abdominal aorta and visceral arteries. Comput Methods Biomech Biomed Engin 2021; 24:1718-1729. [PMID: 34569360 DOI: 10.1080/10255842.2021.1912742] [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: 10/20/2022]
Abstract
PURPOSE The flow velocity of visceral arteries was measured by 2D PCMRI to produce the patient-specific flow BC imposed on the outlets of visceral arteries in CFD simulation. This modified method aimed to improve the CFD accuracy in the abdominal aorta and visceral arteries. METHODS A volunteer underwent non-contrast-enhanced MRA to scan the abdominal aorta and visceral arteries, and 2D PCMRI to obtain the flow velocity of the aforementioned vessels. The three-dimensional geometric model was reconstructed using the MRI scan data of the abdominal aorta and visceral arteries. The flow waveforms measured by 2D PCMRI were processed and then imposed on the aortic inlet and the outlets of all visceral arteries as the flow BC. The RCR parameters of the three elements Windkessel model were modulated and imposed on the aortic outlet. CFD simulation was run in the open-source software: svSolver. The same volunteer underwent 4D flow MRI to compare the flow field with those extracted from CFD results. RESULTS Four specific time points in a cardiac cycle and three cross-sectional planes of aorta were selected to analyze the flow field, pressure and wall shear stress (WSS) from CFD. The flow waveforms and streamlines of CFD agreed with those of 4D flow MRI. The pressure waveforms, pressure distribution and WSS distribution from CFD conformed with the physiological condition of human body. CONCLUSION These results suggest this modified CFD method may yield reasonable flow field, pressure and WSS in the abdominal aorta and visceral arteries.
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Affiliation(s)
- Yun Shi
- Department of Vascular Surgery, Zhongshan Hospital, Fudan University, Shanghai, China
| | - Chen Peng
- Department of aeronautics and astronautics, Fudan University, Shanghai, China
| | - Junzhen Liu
- Department of Radiology, Zhongshan Hospital, Fudan University, Shanghai, China
| | - Hongzhi Lan
- Shenzhen Raysight Intelligent Medical Technology Corporation, Shenzhen, China
| | - Chong Li
- Department of MR Enhance Application, GE Healthcare, Shanghai, China
| | - Wang Qin
- Department of aeronautics and astronautics, Fudan University, Shanghai, China
| | - Tong Yuan
- Department of Vascular Surgery, Zhongshan Hospital, Fudan University, Shanghai, China
| | - Yuanqing Kan
- Department of Vascular Surgery, Zhongshan Hospital, Fudan University, Shanghai, China
| | - Shengzhang Wang
- Department of aeronautics and astronautics, Fudan University, Shanghai, China
| | - Weiguo Fu
- Department of Vascular Surgery, Zhongshan Hospital, Fudan University, Shanghai, China
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Thirugnanasambandam M, Canchi T, Piskin S, Karmonik C, Kung E, Menon PG, Avril S, Finol EA. Design, Development, and Temporal Evaluation of a Magnetic Resonance Imaging-Compatible In Vitro Circulation Model Using a Compliant Abdominal Aortic Aneurysm Phantom. J Biomech Eng 2021; 143:051004. [PMID: 33493273 PMCID: PMC8086180 DOI: 10.1115/1.4049894] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Revised: 01/05/2021] [Indexed: 11/08/2022]
Abstract
Biomechanical characterization of abdominal aortic aneurysms (AAAs) has become commonplace in rupture risk assessment studies. However, its translation to the clinic has been greatly limited due to the complexity associated with its tools and their implementation. The unattainability of patient-specific tissue properties leads to the use of generalized population-averaged material models in finite element analyses, which adds a degree of uncertainty to the wall mechanics quantification. In addition, computational fluid dynamics modeling of AAA typically lacks the patient-specific inflow and outflow boundary conditions that should be obtained by nonstandard of care clinical imaging. An alternative approach for analyzing AAA flow and sac volume changes is to conduct in vitro experiments in a controlled laboratory environment. In this study, we designed, built, and characterized quantitatively a benchtop flow loop using a deformable AAA silicone phantom representative of a patient-specific geometry. The impedance modules, which are essential components of the flow loop, were fine-tuned to ensure typical intraluminal pressure conditions within the AAA sac. The phantom was imaged with a magnetic resonance imaging (MRI) scanner to acquire time-resolved images of the moving wall and the velocity field inside the sac. Temporal AAA sac volume changes lead to a corresponding variation in compliance throughout the cardiac cycle. The primary outcome of this work was the design optimization of the impedance elements, the quantitative characterization of the resistive and capacitive attributes of a compliant AAA phantom, and the exemplary use of MRI for flow visualization and quantification of the deformed AAA geometry.
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Affiliation(s)
- Mirunalini Thirugnanasambandam
- University of Texas at San Antonio, UTSA/UTHSCSA Joint Graduate Program in Biomedical Engineering, San Antonio, TX 78249
| | - Tejas Canchi
- Department of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798
| | - Senol Piskin
- Department of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249; Department of Mechanical Engineering, Istinye University, Istanbul 34010, Turkey
| | | | - Ethan Kung
- Department of Mechanical Engineering, Clemson UniversityClemson, SC 29634
| | - Prahlad G. Menon
- Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15260
| | - Stephane Avril
- Ecole Nationale Supérieure des Mines, Center for Biomedical and Healthcare Engineering, St-Etienne 75006, France
| | - Ender A. Finol
- University of Texas at San Antonio, UTSA/UTHSCSA Joint Graduate Program in Biomedical Engineering, San Antonio, TX 78249; Department of Mechanical Engineering, University of Texas at San Antonio, Room EB 3.04.08 One UTSA Circle, San Antonio, TX 78249
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Taebi A, Vu CT, Roncali E. Multiscale Computational Fluid Dynamics Modeling for Personalized Liver Cancer Radioembolization Dosimetry. J Biomech Eng 2021; 143:011002. [PMID: 32601676 PMCID: PMC7580665 DOI: 10.1115/1.4047656] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 06/17/2020] [Indexed: 12/13/2022]
Abstract
Yttrium-90 (90Y) radioembolization is a minimally invasive procedure increasingly used for advanced liver cancer treatment. In this method, radioactive microspheres are injected into the hepatic arterial bloodstream to target, irradiate, and kill cancer cells. Accurate and precise treatment planning can lead to more efficient and safer treatment by delivering a higher radiation dose to the tumor while minimizing the exposure of the surrounding liver parenchyma. Treatment planning primarily relies on the estimated radiation dose delivered to tissue. However, current methods used to estimate the dose are based on simplified assumptions that make the dosimetry results unreliable. In this work, we present a computational model to predict the radiation dose from the 90Y activity in different liver segments to provide a more realistic and personalized dosimetry. Computational fluid dynamics (CFD) simulations were performed in a 3D hepatic arterial tree model segmented from cone-beam CT angiographic data obtained from a patient with hepatocellular carcinoma (HCC). The microsphere trajectories were predicted from the velocity field. 90Y dose distribution was then calculated from the volumetric distribution of the microspheres. Two injection locations were considered for the microsphere administration, a lobar and a selective injection. Results showed that 22% and 82% of the microspheres were delivered to the tumor, after each injection, respectively, and the combination of both injections ultimately delivered 49% of the total administered 90Y microspheres to the tumor. Results also illustrated the nonhomogeneous distribution of microspheres between liver segments, indicating the importance of developing patient-specific dosimetry methods for effective radioembolization treatment.
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Affiliation(s)
- Amirtahà Taebi
- Department of Biomedical Engineering, University of California Davis, One Shields Avenue, Davis, CA 95616
| | - Catherine T. Vu
- Department of Radiology, University of California Davis, 4860 Y Street, Suite 3100, Sacramento, CA 95817
| | - Emilie Roncali
- Department of Biomedical Engineering, University of California Davis, One Shields Avenue, Davis, CA 95616
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10
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Taebi A, Pillai RM, S. Roudsari B, Vu CT, Roncali E. Computational Modeling of the Liver Arterial Blood Flow for Microsphere Therapy: Effect of Boundary Conditions. Bioengineering (Basel) 2020; 7:E64. [PMID: 32610459 PMCID: PMC7552664 DOI: 10.3390/bioengineering7030064] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Revised: 06/24/2020] [Accepted: 06/25/2020] [Indexed: 12/11/2022] Open
Abstract
Transarterial embolization is a minimally invasive treatment for advanced liver cancer using microspheres loaded with a chemotherapeutic drug or radioactive yttrium-90 (90Y) that are injected into the hepatic arterial tree through a catheter. For personalized treatment, the microsphere distribution in the liver should be optimized through the injection volume and location. Computational fluid dynamics (CFD) simulations of the blood flow in the hepatic artery can help estimate this distribution if carefully parameterized. An important aspect is the choice of the boundary conditions imposed at the inlet and outlets of the computational domain. In this study, the effect of boundary conditions on the hepatic arterial tree hemodynamics was investigated. The outlet boundary conditions were modeled with three-element Windkessel circuits, representative of the downstream vasculature resistance. Results demonstrated that the downstream vasculature resistance affected the hepatic artery hemodynamics such as the velocity field, the pressure field and the blood flow streamline trajectories. Moreover, the number of microspheres received by the tumor significantly changed (more than 10% of the total injected microspheres) with downstream resistance variations. These findings suggest that patient-specific boundary conditions should be used in order to achieve a more accurate drug distribution estimation with CFD in transarterial embolization treatment planning.
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Affiliation(s)
- Amirtahà Taebi
- Department of Biomedical Engineering, University of California Davis, One Shields Ave., Davis, CA 95616, USA
| | - Rex M. Pillai
- Department of Radiology, University of California Davis, 4860 Y Street, Suite 3100, Sacramento, CA 95817, USA; (R.M.P.); (C.T.V.)
| | | | - Catherine T. Vu
- Department of Radiology, University of California Davis, 4860 Y Street, Suite 3100, Sacramento, CA 95817, USA; (R.M.P.); (C.T.V.)
| | - Emilie Roncali
- Department of Biomedical Engineering, University of California Davis, One Shields Ave., Davis, CA 95616, USA
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11
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Lipp SN, Niedert EE, Cebull HL, Diorio TC, Ma JL, Rothenberger SM, Stevens Boster KA, Goergen CJ. Computational Hemodynamic Modeling of Arterial Aneurysms: A Mini-Review. Front Physiol 2020; 11:454. [PMID: 32477163 PMCID: PMC7235429 DOI: 10.3389/fphys.2020.00454] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 04/09/2020] [Indexed: 01/02/2023] Open
Abstract
Arterial aneurysms are pathological dilations of blood vessels, which can be of clinical concern due to thrombosis, dissection, or rupture. Aneurysms can form throughout the arterial system, including intracranial, thoracic, abdominal, visceral, peripheral, or coronary arteries. Currently, aneurysm diameter and expansion rates are the most commonly used metrics to assess rupture risk. Surgical or endovascular interventions are clinical treatment options, but are invasive and associated with risk for the patient. For aneurysms in locations where thrombosis is the primary concern, diameter is also used to determine the level of therapeutic anticoagulation, a treatment that increases the possibility of internal bleeding. Since simple diameter is often insufficient to reliably determine rupture and thrombosis risk, computational hemodynamic simulations are being developed to help assess when an intervention is warranted. Created from subject-specific data, computational models have the potential to be used to predict growth, dissection, rupture, and thrombus-formation risk based on hemodynamic parameters, including wall shear stress, oscillatory shear index, residence time, and anomalous blood flow patterns. Generally, endothelial damage and flow stagnation within aneurysms can lead to coagulation, inflammation, and the release of proteases, which alter extracellular matrix composition, increasing risk of rupture. In this review, we highlight recent work that investigates aneurysm geometry, model parameter assumptions, and other specific considerations that influence computational aneurysm simulations. By highlighting modeling validation and verification approaches, we hope to inspire future computational efforts aimed at improving our understanding of aneurysm pathology and treatment risk stratification.
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Affiliation(s)
- Sarah N. Lipp
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Elizabeth E. Niedert
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Hannah L. Cebull
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Tyler C. Diorio
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Jessica L. Ma
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Sean M. Rothenberger
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Kimberly A. Stevens Boster
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
- School of Mechanical Engineering, Purdue University, West Lafayette, IN, United States
| | - Craig J. Goergen
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
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12
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Mirzaei E, Farahmand M, Kung E. An algorithm for coupling multibranch in vitro experiment to numerical physiology simulation for a hybrid cardiovascular model. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2020; 36:e3289. [PMID: 31816194 DOI: 10.1002/cnm.3289] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2018] [Accepted: 11/12/2019] [Indexed: 06/10/2023]
Abstract
The hybrid cardiovascular modeling approach integrates an in vitro experiment with a computational lumped-parameter simulation, enabling direct physical testing of medical devices in the context of closed-loop physiology. The interface between the in vitro and computational domains is essential for properly capturing the dynamic interactions of the two. To this end, we developed an iterative algorithm capable of coupling an in vitro experiment containing multiple branches to a lumped-parameter physiology simulation. This algorithm identifies the unique flow waveform solution for each branch of the experiment using an iterative Broyden's approach. For the purpose of algorithm testing, we first used mathematical surrogates to represent the in vitro experiments and demonstrated five scenarios where the in vitro surrogates are coupled to the computational physiology of a Fontan patient. This testing approach allows validation of the coupling result accuracy as the mathematical surrogates can be directly integrated into the computational simulation to obtain the "true solution" of the coupled system. Our algorithm successfully identified the solution flow waveforms in all test scenarios with results matching the true solutions with high accuracy. In all test cases, the number of iterations to achieve the desired convergence criteria was less than 130. To emulate realistic in vitro experiments in which noise contaminates the measurements, we perturbed the surrogate models by adding random noise. The convergence tolerance achievable with the coupling algorithm remained below the magnitudes of the added noise in all cases. Finally, we used this algorithm to couple a physical experiment to the computational physiology model to demonstrate its real-world applicability.
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Affiliation(s)
- Ehsan Mirzaei
- Department of Mechanical Engineering, Clemson University, Clemson, South Carolina, USA
| | - Masoud Farahmand
- Department of Mechanical Engineering, Clemson University, Clemson, South Carolina, USA
| | - Ethan Kung
- Department of Mechanical Engineering, Clemson University, Clemson, South Carolina, USA
- Department of Bioengineering, Clemson University, Clemson, South Carolina, USA
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13
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Computational Fluid Dynamics Modeling of Hemodynamic Parameters in the Human Diseased Aorta: A Systematic Review. Ann Vasc Surg 2020; 63:336-381. [DOI: 10.1016/j.avsg.2019.04.032] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2018] [Revised: 03/09/2019] [Accepted: 04/18/2019] [Indexed: 02/07/2023]
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14
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He Z, Mongrain R, Lessard S, Chayer B, Cloutier G, Soulez G. Anthropomorphic and biomechanical mockup for abdominal aortic aneurysm. Med Eng Phys 2020; 77:60-68. [PMID: 31954613 DOI: 10.1016/j.medengphy.2019.12.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Revised: 09/08/2019] [Accepted: 12/15/2019] [Indexed: 11/16/2022]
Abstract
Abdominal aortic aneurysm (AAA) is an asymptomatic condition due to the dilation of abdominal aorta along with progressive wall degeneration, where rupture of AAA is life-threatening. Failures of AAA endovascular repair (EVAR) reflect our inadequate knowledge about the complex interaction between the aortic wall and medical devices. In this regard, we are presenting a hydrogel-based anthropomorphic mockup (AMM) to better understand the biomechanical constraints during EVAR. By adjusting the cryogenic treatments, we tailored the hydrogel to mimic the mechanical behavior of human AAA wall, thrombus and abdominal fat. A specific molding sequence and a pressurizing system were designed to reproduce the geometrical and diseased characteristics of AAA. A mechanically, anatomically and pathologically realistic AMM for AAA was developed for the first time, EVAR experiments were then performed with and without the surrounding fat. Substantial displacements of the aortic centerlines and vessel expansion were observed in the case without surrounding fat, revealing an essential framework created by the surrounding fat to account for the interactions with medical devices. In conclusion, the importance to consider surrounding tissue for the global deformation of AAA during EVAR was highlighted. Furthermore, potential use of this AMM for medical training was also suggested.
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Affiliation(s)
- Zinan He
- McGill University, 845 Sherbrooke Street West, Montréal, Québec H3A 0G4, Canada; Centre de recherche du Centre hospitalier de l'Université de Montréal (CRCHUM), 900 Rue Saint-Denis, Montréal, Québec H2X 0A9, Canada
| | - Rosaire Mongrain
- McGill University, 845 Sherbrooke Street West, Montréal, Québec H3A 0G4, Canada
| | - Simon Lessard
- Centre de recherche du Centre hospitalier de l'Université de Montréal (CRCHUM), 900 Rue Saint-Denis, Montréal, Québec H2X 0A9, Canada
| | - Boris Chayer
- Centre de recherche du Centre hospitalier de l'Université de Montréal (CRCHUM), 900 Rue Saint-Denis, Montréal, Québec H2X 0A9, Canada
| | - Guy Cloutier
- Centre de recherche du Centre hospitalier de l'Université de Montréal (CRCHUM), 900 Rue Saint-Denis, Montréal, Québec H2X 0A9, Canada; Université de Montréal, 2900 Boulevard Edouard-Montpetit, Montréal, Québec H3T 1J4, Canada
| | - Gilles Soulez
- Centre de recherche du Centre hospitalier de l'Université de Montréal (CRCHUM), 900 Rue Saint-Denis, Montréal, Québec H2X 0A9, Canada; Université de Montréal, 2900 Boulevard Edouard-Montpetit, Montréal, Québec H3T 1J4, Canada.
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15
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Gellner B, Xin L, Ribeiro RVP, Bissoondath V, Lu P, Adamson MB, Yu F, Paradiso E, Zu J, Simmons CA, Badiwala MV. The Implementation of an Adjustable Afterload Module for Ex Situ Heart Perfusion. Cardiovasc Eng Technol 2019; 11:96-110. [PMID: 31797263 DOI: 10.1007/s13239-019-00447-w] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/16/2019] [Accepted: 11/24/2019] [Indexed: 12/23/2022]
Abstract
PURPOSE Windkessel impedance analysis has proven to be an effective technique for instituting artificial afterload on ex situ hearts. Traditional fixed parameter afterload modules, however, are unable to handle the changing contractile conditions associated with prolonged ex situ heart perfusion. In this paper, an adjustable afterload module is described comprising of three fully adjustable sub-components: a systemic resistor, a proximal resistor and a compliance chamber. METHODS Using a centrifugal pump, the systemic resistor and compliance chamber were subjected to testing across their operating ranges, whereby the predictability of resistance and compliance values was evaluated. The components were then assembled, and the full module tested on three separate porcine hearts perfused for 6 h with success defined by the ability to maintain physiological systolic and diastolic aortic pressures across flow rate variability. RESULTS For both the systemic resistor and compliance chamber, experimental measurements agreed with their theoretical equivalents, with coefficients of determination of 0.99 and 0.97 for the systemic resistor and compliance chamber, respectively. During ex situ perfusion, overall 95% confidence intervals demonstrate that physiological systolic (95-96.21 mmHg) and diastolic (26.8-28.8 mmHg) pressures were successfully maintained, despite large variability in aortic flow. Left ventricular contractile parameters, were found to be in line with those in previous studies, suggesting the afterload module has no detrimental impact on functional preservation. CONCLUSIONS We conclude that due to the demonstrable control of our afterload module, we can maintain physiological aortic pressures in a passive afterload working mode across prolonged perfusion periods, enabling effective perfusion regardless of contractile performance.
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Affiliation(s)
- Bryan Gellner
- Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada
- Translational Biology & Engineering Program, Ted Rogers Centre for Heart Research, Toronto, ON, Canada
| | - Liming Xin
- Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada
- Division of Cardiovascular Surgery, Toronto General Hospital, University Health Network, Toronto, ON, Canada
- State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, China
| | - Roberto Vanin Pinto Ribeiro
- Division of Cardiovascular Surgery, Toronto General Hospital, University Health Network, Toronto, ON, Canada
- Institute of Medical Science, University of Toronto, Toronto, ON, Canada
| | - Ved Bissoondath
- Division of Cardiovascular Surgery, Toronto General Hospital, University Health Network, Toronto, ON, Canada
| | - Pengzhou Lu
- Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada
- Division of Cardiovascular Surgery, Toronto General Hospital, University Health Network, Toronto, ON, Canada
| | - Mitchell B Adamson
- Division of Cardiovascular Surgery, Toronto General Hospital, University Health Network, Toronto, ON, Canada
- Institute of Medical Science, University of Toronto, Toronto, ON, Canada
| | - Frank Yu
- Division of Cardiovascular Surgery, Toronto General Hospital, University Health Network, Toronto, ON, Canada
| | - Emanuela Paradiso
- Department of Anesthesia and Pain Management, Toronto General Hospital, University Health Network, Toronto, ON, Canada
| | - Jean Zu
- Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada
| | - Craig A Simmons
- Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada.
- Translational Biology & Engineering Program, Ted Rogers Centre for Heart Research, Toronto, ON, Canada.
- Institute of Biomaterials & Biomedical Engineering, University of Toronto, Toronto, ON, Canada.
| | - Mitesh V Badiwala
- Division of Cardiovascular Surgery, Toronto General Hospital, University Health Network, Toronto, ON, Canada
- Department of Surgery, University of Toronto, Toronto, ON, Canada
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16
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Salman HE, Ramazanli B, Yavuz MM, Yalcin HC. Biomechanical Investigation of Disturbed Hemodynamics-Induced Tissue Degeneration in Abdominal Aortic Aneurysms Using Computational and Experimental Techniques. Front Bioeng Biotechnol 2019; 7:111. [PMID: 31214581 PMCID: PMC6555197 DOI: 10.3389/fbioe.2019.00111] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2019] [Accepted: 05/02/2019] [Indexed: 11/13/2022] Open
Abstract
Abdominal aortic aneurysm (AAA) is the dilatation of the aorta beyond 50% of the normal vessel diameter. It is reported that 4-8% of men and 0.5-1% of women above 50 years of age bear an AAA and it accounts for ~15,000 deaths per year in the United States alone. If left untreated, AAA might gradually expand until rupture; the most catastrophic complication of the aneurysmal disease that is accompanied by a striking overall mortality of 80%. The precise mechanisms leading to AAA rupture remains unclear. Therefore, characterization of disturbed hemodynamics within AAAs will help to understand the mechanobiological development of the condition which will contribute to novel therapies for the condition. Due to geometrical complexities, it is challenging to directly quantify disturbed flows for AAAs clinically. Two other approaches for this investigation are computational modeling and experimental flow measurement. In computational modeling, the problem is first defined mathematically, and the solution is approximated with numerical techniques to get characteristics of flow. In experimental flow measurement, once the setup providing physiological flow pattern in a phantom geometry is constructed, velocity measurement system such as particle image velocimetry (PIV) enables characterization of the flow. We witness increasing number of applications of these complimentary approaches for AAA investigations in recent years. In this paper, we outline the details of computational modeling procedures and experimental settings and summarize important findings from recent studies, which will help researchers for AAA investigations and rupture mechanics.
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Affiliation(s)
| | - Burcu Ramazanli
- Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey
| | - Mehmet Metin Yavuz
- Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey
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17
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Pewowaruk R, Roldán-Alzate A. 4D Flow MRI Estimation of Boundary Conditions for Patient Specific Cardiovascular Simulation. Ann Biomed Eng 2019; 47:1786-1798. [PMID: 31069584 DOI: 10.1007/s10439-019-02285-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Accepted: 05/02/2019] [Indexed: 12/11/2022]
Abstract
Accurate image based cardiovascular simulations require patient specific boundary conditions (BCs) for inlets, outlets and vessel wall mechanical properties. While inlet BCs are typically determined non-invasively, invasive pressure catheterization is often used to determine patient specific outlet BCs and vessel wall mechanical properties. A method using 4D Flow MRI to non-invasively determine both patient specific outlet BCs and vessel wall mechanical properties is presented and results for both in vitro validation with a latex tube and an in vivo pulmonary artery stenosis (PAS) stent intervention are presented. For in vitro validation, acceptable agreement is found between simulation using BCs from 4D Flow MRI and benchtop measurements. For the PAS virtual intervention, simulation correctly predicts flow distribution with 9% error compared to MRI. Using 4D Flow MRI to noninvasively determine patient specific BCs increases the ability to use image based simulations as pressure catheterization is not always performed.
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Affiliation(s)
- Ryan Pewowaruk
- Biomedical Engineering, University of Wisconsin - Madison, 1111 Highland Ave, Room 2476 WIMR 2, Madison, WI, 53705, USA
| | - Alejandro Roldán-Alzate
- Biomedical Engineering, University of Wisconsin - Madison, 1111 Highland Ave, Room 2476 WIMR 2, Madison, WI, 53705, USA. .,Mechanical Engineering, University of Wisconsin - Madison, 1111 Highland Ave, Room 2476 WIMR 2, Madison, WI, 53705, USA. .,Department of Radiology, University of Wisconsin - Madison, 1111 Highland Ave, Room 2476 WIMR 2, Madison, WI, 53705, USA.
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18
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Kung E, Farahmand M, Gupta A. A Hybrid Experimental-Computational Modeling Framework for Cardiovascular Device Testing. J Biomech Eng 2019; 141:051012. [PMID: 30698632 DOI: 10.1115/1.4042665] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2018] [Indexed: 11/08/2022]
Abstract
Significant advances in biomedical science often leverage powerful computational and experimental modeling platforms. We present a framework named physiology simulation coupled experiment ("PSCOPE") that can capitalize on the strengths of both types of platforms in a single hybrid model. PSCOPE uses an iterative method to couple an in vitro mock circuit to a lumped-parameter numerical simulation of physiology, obtaining closed-loop feedback between the two. We first compared the results of Fontan graft obstruction scenarios modeled using both PSCOPE and an established multiscale computational fluid dynamics method; the normalized root-mean-square error values of important physiologic parameters were between 0.1% and 2.1%, confirming the fidelity of the PSCOPE framework. Next, we demonstrate an example application of PSCOPE to model a scenario beyond the current capabilities of multiscale computational methods-the implantation of a Jarvik 2000 blood pump for cavopulmonary support in the single-ventricle circulation; we found that the commercial Jarvik 2000 controller can be modified to produce a suitable rotor speed for augmenting cardiac output by approximately 20% while maintaining blood pressures within safe ranges. The unified modeling framework enables a testing environment which simultaneously operates a medical device and performs computational simulations of the resulting physiology, providing a tool for physically testing medical devices with simulated physiologic feedback.
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Affiliation(s)
- Ethan Kung
- Department of Mechanical Engineering,Clemson University,Clemson, SC 29634
- Department of Bioengineering,Clemson University,Clemson, SC 29634e-mail:
| | - Masoud Farahmand
- Department of Mechanical Engineering,Clemson University,Clemson, SC 29634e-mail:
| | - Akash Gupta
- Department of Mechanical Engineering,Clemson University,Clemson, SC 29634e-mail:
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19
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Domagała Z, Stępak H, Drapikowski P, Kociemba A, Pyda M, Karmelita-Katulska K, Dzieciuchowicz Ł, Oszkinis G. Geometric verification of the validity of Finite Element Method analysis of Abdominal Aortic Aneurysms based on Magnetic Resonance Imaging. Biocybern Biomed Eng 2018. [DOI: 10.1016/j.bbe.2018.04.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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20
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Kemmerling EMC, Peattie RA. Abdominal Aortic Aneurysm Pathomechanics: Current Understanding and Future Directions. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2018; 1097:157-179. [DOI: 10.1007/978-3-319-96445-4_8] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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21
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Yang Y, Zou Y. [A correction method for calculating resistance of Westerhof 's resistor]. SHENG WU YI XUE GONG CHENG XUE ZA ZHI = JOURNAL OF BIOMEDICAL ENGINEERING = SHENGWU YIXUE GONGCHENGXUE ZAZHI 2017; 34:627-631. [PMID: 29745563 PMCID: PMC9935306 DOI: 10.7507/1001-5515.201703020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Received: 03/04/2017] [Indexed: 11/03/2022]
Abstract
The objective of the mock circulatory system (MCS) is to construct the characteristics of cardiovascular hemodynamics. Westerhof 's resistor that often regarded as the laminar flow resistance in the MCS, is commonly used to simulate the peripheral resistance of the cardiovascular system. However, the theoretical calculation value of fluid resistance of the Westerhof 's resistor shows distinguished difference with the actual needed value. If the theoretical resistance is regarded as the actual needed one and be used directly in the experiment, the experimental accuracy would not be acceptable. In order to improve the accuracy, an effective correction method for calculating the resistance of Westerhof 's resistor was proposed in this paper. Simulation software was also developed to compute accurately the capillary number, total length and resistance. The results demonstrate the proposed method is able to reduce the difficulty and complexity of the design of the resistor, which would obviously increase the manufactured precision of the Westerhof 's resistor. Simulation software would provide great support to the construction of various MCSs.
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Affiliation(s)
- Yunshu Yang
- Department of Biomedical Engineering, College of Materials Science & Engineering, Sichuan University, Chengdu 610065, P.R.China
| | - Yuanwen Zou
- Department of Biomedical Engineering, College of Materials Science & Engineering, Sichuan University, Chengdu 610065,
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22
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Hariharan P, D’Souza GA, Horner M, Morrison TM, Malinauskas RA, Myers MR. Use of the FDA nozzle model to illustrate validation techniques in computational fluid dynamics (CFD) simulations. PLoS One 2017; 12:e0178749. [PMID: 28594889 PMCID: PMC5464577 DOI: 10.1371/journal.pone.0178749] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Accepted: 05/18/2017] [Indexed: 12/14/2022] Open
Abstract
A "credible" computational fluid dynamics (CFD) model has the potential to provide a meaningful evaluation of safety in medical devices. One major challenge in establishing "model credibility" is to determine the required degree of similarity between the model and experimental results for the model to be considered sufficiently validated. This study proposes a "threshold-based" validation approach that provides a well-defined acceptance criteria, which is a function of how close the simulation and experimental results are to the safety threshold, for establishing the model validity. The validation criteria developed following the threshold approach is not only a function of Comparison Error, E (which is the difference between experiments and simulations) but also takes in to account the risk to patient safety because of E. The method is applicable for scenarios in which a safety threshold can be clearly defined (e.g., the viscous shear-stress threshold for hemolysis in blood contacting devices). The applicability of the new validation approach was tested on the FDA nozzle geometry. The context of use (COU) was to evaluate if the instantaneous viscous shear stress in the nozzle geometry at Reynolds numbers (Re) of 3500 and 6500 was below the commonly accepted threshold for hemolysis. The CFD results ("S") of velocity and viscous shear stress were compared with inter-laboratory experimental measurements ("D"). The uncertainties in the CFD and experimental results due to input parameter uncertainties were quantified following the ASME V&V 20 standard. The CFD models for both Re = 3500 and 6500 could not be sufficiently validated by performing a direct comparison between CFD and experimental results using the Student's t-test. However, following the threshold-based approach, a Student's t-test comparing |S-D| and |Threshold-S| showed that relative to the threshold, the CFD and experimental datasets for Re = 3500 were statistically similar and the model could be considered sufficiently validated for the COU. However, for Re = 6500, at certain locations where the shear stress is close the hemolysis threshold, the CFD model could not be considered sufficiently validated for the COU. Our analysis showed that the model could be sufficiently validated either by reducing the uncertainties in experiments, simulations, and the threshold or by increasing the sample size for the experiments and simulations. The threshold approach can be applied to all types of computational models and provides an objective way of determining model credibility and for evaluating medical devices.
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Affiliation(s)
- Prasanna Hariharan
- US Food and Drug Administration, Silver Spring, Maryland, United States of America
- * E-mail:
| | - Gavin A. D’Souza
- US Food and Drug Administration, Silver Spring, Maryland, United States of America
| | - Marc Horner
- ANSYS, Inc., Evanston, Illinois, United States of America
| | - Tina M. Morrison
- US Food and Drug Administration, Silver Spring, Maryland, United States of America
| | | | - Matthew R. Myers
- US Food and Drug Administration, Silver Spring, Maryland, United States of America
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23
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Sotelo J, Urbina J, Valverde I, Mura J, Tejos C, Irarrazaval P, Andia ME, Hurtado DE, Uribe S. Three-dimensional quantification of vorticity and helicity from 3D cine PC-MRI using finite-element interpolations. Magn Reson Med 2017; 79:541-553. [DOI: 10.1002/mrm.26687] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Revised: 03/01/2017] [Accepted: 03/05/2017] [Indexed: 11/07/2022]
Affiliation(s)
- Julio Sotelo
- Biomedical Imaging Center; Pontificia Universidad Católica de Chile; Santiago Chile
- Department of Electrical Engineering; Pontificia Universidad Católica de Chile; Santiago Chile
- Department of Structural and Geotechnical Engineering; Pontificia Universidad Católica de Chile; Santiago Chile
| | - Jesús Urbina
- Biomedical Imaging Center; Pontificia Universidad Católica de Chile; Santiago Chile
- Department of Radiology; School of Medicine, Pontificia Universidad Católica de Chile; Santiago Chile
| | - Israel Valverde
- Pediatric Cardiology Unit; Hospital Virgen del Rocio; Sevilla Spain
- Cardiovascular Pathology Unit; Institute of Biomedicine of Seville (IBIS), Hospital Virgen del Rocio; Sevilla Spain
| | - Joaquín Mura
- Biomedical Imaging Center; Pontificia Universidad Católica de Chile; Santiago Chile
| | - Cristián Tejos
- Biomedical Imaging Center; Pontificia Universidad Católica de Chile; Santiago Chile
- Department of Electrical Engineering; Pontificia Universidad Católica de Chile; Santiago Chile
- Institute for Biological and Medical Engineering; Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile; Santaigo Chile
| | - Pablo Irarrazaval
- Biomedical Imaging Center; Pontificia Universidad Católica de Chile; Santiago Chile
- Department of Electrical Engineering; Pontificia Universidad Católica de Chile; Santiago Chile
- Institute for Biological and Medical Engineering; Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile; Santaigo Chile
| | - Marcelo E. Andia
- Biomedical Imaging Center; Pontificia Universidad Católica de Chile; Santiago Chile
- Department of Radiology; School of Medicine, Pontificia Universidad Católica de Chile; Santiago Chile
- Institute for Biological and Medical Engineering; Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile; Santaigo Chile
| | - Daniel E. Hurtado
- Department of Structural and Geotechnical Engineering; Pontificia Universidad Católica de Chile; Santiago Chile
- Institute for Biological and Medical Engineering; Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile; Santaigo Chile
| | - Sergio Uribe
- Biomedical Imaging Center; Pontificia Universidad Católica de Chile; Santiago Chile
- Department of Radiology; School of Medicine, Pontificia Universidad Católica de Chile; Santiago Chile
- Institute for Biological and Medical Engineering; Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile; Santaigo Chile
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24
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Mechoor RR, Schmidt T, Kung E. A Real-Time Programmable Pulsatile Flow Pump for In Vitro Cardiovascular Experimentation. J Biomech Eng 2016; 138:2551746. [PMID: 27590025 DOI: 10.1115/1.4034561] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2016] [Indexed: 05/10/2024]
Abstract
Benchtop in vitro experiments are valuable tools for investigating the cardiovascular system and testing medical devices. Accurate reproduction of the physiologic flow waveforms at various anatomic locations is an important component of these experimental methods. This study discusses the design, construction, and testing of a low-cost and fully programmable pulsatile flow pump capable of continuously producing unlimited cycles of physiologic waveforms. It consists of a gear pump actuated by an AC servomotor and a feedback algorithm to achieve highly accurate reproduction of flow waveforms for flow rates up to 300 ml/s across a range of loading conditions. The iterative feedback algorithm uses the flow error values in one iteration to modify the motor control waveform for the next iteration to better match the desired flow. Within four to seven iterations of feedback, the pump replicated desired physiologic flow waveforms to within 2% normalized RMS error (for flow rates above 20 mL/s) under varying downstream impedances. This pump device is significantly more affordable (∼10% of the cost) than current commercial options. More importantly, the pump can be controlled via common scientific software and thus easily implemented into large automation frameworks.
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Affiliation(s)
- Rahul Raj Mechoor
- Department of Mechanical Engineering, Clemson University, 252 Fluor Daniel EIB, Clemson, SC 29631 e-mail:
| | - Tyler Schmidt
- Department of Mechanical Engineering, Clemson University, 252 Fluor Daniel EIB, Clemson, SC 29631 e-mail:
| | - Ethan Kung
- Mem. ASME Department of Mechanical Engineering, Clemson University, 231 Fluor Daniel EIB, Clemson, SC 29634-0921 e-mail:
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25
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Raptis A, Xenos M, Georgakarakos E, Kouvelos G, Giannoukas A, Labropoulos N, Matsagkas M. Comparison of physiological and post-endovascular aneurysm repair infrarenal blood flow. Comput Methods Biomech Biomed Engin 2016; 20:242-249. [DOI: 10.1080/10255842.2016.1215437] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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26
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A High Performance Pulsatile Pump for Aortic Flow Experiments in 3-Dimensional Models. Cardiovasc Eng Technol 2016; 7:148-58. [PMID: 26983961 DOI: 10.1007/s13239-016-0260-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/10/2015] [Accepted: 03/03/2016] [Indexed: 10/22/2022]
Abstract
Aortic pathologies such as coarctation, dissection, and aneurysm represent a particularly emergent class of cardiovascular diseases. Computational simulations of aortic flows are growing increasingly important as tools for gaining understanding of these pathologies, as well as for planning their surgical repair. In vitro experiments are required to validate the simulations against real world data, and the experiments require a pulsatile flow pump system that can provide physiologic flow conditions characteristic of the aorta. We designed a newly capable piston-based pulsatile flow pump system that can generate high volume flow rates (850 mL/s), replicate physiologic waveforms, and pump high viscosity fluids against large impedances. The system is also compatible with a broad range of fluid types, and is operable in magnetic resonance imaging environments. Performance of the system was validated using image processing-based analysis of piston motion as well as particle image velocimetry. The new system represents a more capable pumping solution for aortic flow experiments than other available designs, and can be manufactured at a relatively low cost.
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Abstract
PURPOSE OF REVIEW Recent methodological advances in computational simulations are enabling increasingly realistic simulations of hemodynamics and physiology, driving increased clinical utility. We review recent developments in the use of computational simulations in pediatric and congenital heart disease, describe the clinical impact in modeling in single-ventricle patients, and provide an overview of emerging areas. RECENT FINDINGS Multiscale modeling combining patient-specific hemodynamics with reduced order (i.e., mathematically and computationally simplified) circulatory models has become the de-facto standard for modeling local hemodynamics and 'global' circulatory physiology. We review recent advances that have enabled faster solutions, discuss new methods (e.g., fluid structure interaction and uncertainty quantification), which lend realism both computationally and clinically to results, highlight novel computationally derived surgical methods for single-ventricle patients, and discuss areas in which modeling has begun to exert its influence including Kawasaki disease, fetal circulation, tetralogy of Fallot (and pulmonary tree), and circulatory support. SUMMARY Computational modeling is emerging as a crucial tool for clinical decision-making and evaluation of novel surgical methods and interventions in pediatric cardiology and beyond. Continued development of modeling methods, with an eye towards clinical needs, will enable clinical adoption in a wide range of pediatric and congenital heart diseases.
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Suess T, Anderson J, Danielson L, Pohlson K, Remund T, Blears E, Gent S, Kelly P. Examination of near-wall hemodynamic parameters in the renal bridging stent of various stent graft configurations for repairing visceral branched aortic aneurysms. J Vasc Surg 2015. [PMID: 26209577 DOI: 10.1016/j.jvs.2015.04.421] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Abstract
OBJECTIVE This study examined the flow behavior of four stent graft configurations for endovascular repair of complex aneurysms of the descending aorta. METHODS Computational fluid dynamics models with transient boundary conditions and rigid wall simplifying assumptions were developed and used with four distinct geometries to compare various near-wall hemodynamic parameters. RESULTS Graphic plots for time-averaged wall shear stress, oscillating shear index, and relative residence time were presented and compared among the four stent graft configurations of interest. CONCLUSIONS Abrupt 90° and 180° changes in stent geometry (particularly in the side branches) cause a high momentum change and thus increased flow separation and mixing, which has significant implications in blood flow characteristics near the wall. By comparison, longer bridging stents provide more gradual changes in momentum, thus allowing blood flow to develop before reaching the target vessel.
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Affiliation(s)
- Taylor Suess
- Department of Mechanical Engineering, South Dakota State University, Brookings, SDak
| | | | | | | | | | | | - Stephen Gent
- Department of Mechanical Engineering, South Dakota State University, Brookings, SDak
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Comparison Between Bench-Top and Computational Modelling of Cerebral Thromboembolism in Ventricular Assist Device Circulation. Cardiovasc Eng Technol 2015; 6:242-55. [DOI: 10.1007/s13239-015-0230-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/04/2015] [Accepted: 06/08/2015] [Indexed: 12/13/2022]
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Chen CY, Antón R, Hung MY, Menon P, Finol EA, Pekkan K. Effects of intraluminal thrombus on patient-specific abdominal aortic aneurysm hemodynamics via stereoscopic particle image velocity and computational fluid dynamics modeling. J Biomech Eng 2014; 136:031001. [PMID: 24316984 DOI: 10.1115/1.4026160] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2012] [Accepted: 12/05/2013] [Indexed: 11/08/2022]
Abstract
The pathology of the human abdominal aortic aneurysm (AAA) and its relationship to the later complication of intraluminal thrombus (ILT) formation remains unclear. The hemodynamics in the diseased abdominal aorta are hypothesized to be a key contributor to the formation and growth of ILT. The objective of this investigation is to establish a reliable 3D flow visualization method with corresponding validation tests with high confidence in order to provide insight into the basic hemodynamic features for a better understanding of hemodynamics in AAA pathology and seek potential treatment for AAA diseases. A stereoscopic particle image velocity (PIV) experiment was conducted using transparent patient-specific experimental AAA models (with and without ILT) at three axial planes. Results show that before ILT formation, a 3D vortex was generated in the AAA phantom. This geometry-related vortex was not observed after the formation of ILT, indicating its possible role in the subsequent appearance of ILT in this patient. It may indicate that a longer residence time of recirculated blood flow in the aortic lumen due to this vortex caused sufficient shear-induced platelet activation to develop ILT and maintain uniform flow conditions. Additionally, two computational fluid dynamics (CFD) modeling codes (Fluent and an in-house cardiovascular CFD code) were compared with the two-dimensional, three-component velocity stereoscopic PIV data. Results showed that correlation coefficients of the out-of-plane velocity data between PIV and both CFD methods are greater than 0.85, demonstrating good quantitative agreement. The stereoscopic PIV study can be utilized as test case templates for ongoing efforts in cardiovascular CFD solver development. Likewise, it is envisaged that the patient-specific data may provide a benchmark for further studying hemodynamics of actual AAA, ILT, and their convolution effects under physiological conditions for clinical applications.
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Gallo D, Gülan U, Di Stefano A, Ponzini R, Lüthi B, Holzner M, Morbiducci U. Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics. J Biomech 2014; 47:3149-55. [DOI: 10.1016/j.jbiomech.2014.06.017] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2013] [Revised: 06/05/2014] [Accepted: 06/12/2014] [Indexed: 11/24/2022]
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Computational Models of Aortic Coarctation in Hypoplastic Left Heart Syndrome: Considerations on Validation of a Detailed 3D model. Int J Artif Organs 2014; 37:371-81. [DOI: 10.5301/ijao.5000332] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/16/2014] [Indexed: 11/20/2022]
Abstract
Background Reliability of computational models for cardiovascular investigations strongly depends on their validation against physical data. This study aims to experimentally validate a computational model of complex congenital heart disease (i.e., surgically palliated hypoplastic left heart syndrome with aortic coarctation) thus demonstrating that hemodynamic information can be reliably extrapolated from the model for clinically meaningful investigations. Materials and methods A patient-specific aortic arch model was tested in a mock circulatory system and the same flow conditions were re-created in silico, by setting an appropriate lumped parameter network (LPN) attached to the same three-dimensional (3D) aortic model (i.e., multi-scale approach). The model included a modified Blalock-Taussig shunt and coarctation of the aorta. Different flow regimes were tested as well as the impact of uncertainty in viscosity. Results Computational flow and pressure results were in good agreement with the experimental signals, both qualitatively, in terms of the shape of the waveforms, and quantitatively (mean aortic pressure 62.3 vs. 65.1 mmHg, 4.8% difference; mean aortic flow 28.0 vs. 28.4% inlet flow, 1.4% difference; coarctation pressure drop 30.0 vs. 33.5 mmHg, 10.4% difference), proving the reliability of the numerical approach. It was observed that substantial changes in fluid viscosity or using a turbulent model in the numerical simulations did not significantly affect flows and pressures of the investigated physiology. Results highlighted how the non-linear fluid dynamic phenomena occurring in vitro must be properly described to ensure satisfactory agreement. Conclusions This study presents methodological considerations for using experimental data to preliminarily set up a computational model, and then simulate a complex congenital physiology using a multi-scale approach.
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Kung E, Kahn AM, Burns JC, Marsden A. In Vitro Validation of Patient-Specific Hemodynamic Simulations in Coronary Aneurysms Caused by Kawasaki Disease. Cardiovasc Eng Technol 2014; 5:189-201. [PMID: 25050140 DOI: 10.1007/s13239-014-0184-8] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
To perform experimental validation of computational fluid dynamics (CFD) applied to patient specific coronary aneurysm anatomy of Kawasaki disease. We quantified hemodynamics in a patient-specific coronary artery aneurysm physical phantom under physiologic rest and exercise flow conditions. Using phase contrast MRI (PCMRI), we acquired 3-component flow velocity at two slice locations in the aneurysms. We then performed numerical simulations with the same geometry and inflow conditions, and performed qualitative and quantitative comparisons of velocities between experimental measurements and simulation results. We observed excellent qualitative agreement in flow pattern features. The quantitative spatially and temporally varying differences in velocity between PCMRI and CFD were proportional to the flow velocity. As a result, the percent discrepancy between simulation and experiment was relatively constant regardless of flow velocity variations. Through 1D and 2D quantitative comparisons, we found a 5-17% difference between measured and simulated velocities. Additional analysis assessed wall shear stress differences between deformable and rigid wall simulations. This study demonstrated that CFD produced good qualitative and quantitative predictions of velocities in a realistic coronary aneurysm anatomy under physiological flow conditions. The results provide insights on factors that may influence the level of agreement, and a set of in vitro experimental data that can be used by others to compare against CFD simulation results. The findings of this study increase confidence in the use of CFD for investigating hemodynamics in the specialized anatomy of coronary aneurysms. This provides a basis for future hemodynamics studies in patient-specific models of Kawasaki disease.
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Affiliation(s)
- Ethan Kung
- Mechanical and Aerospace Engineering Department, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
| | - Andrew M Kahn
- Departments of Medicine and Pediatrics, University of California San Diego School of Medicine, San Diego, CA, USA
| | - Jane C Burns
- Departments of Medicine and Pediatrics, University of California San Diego School of Medicine, San Diego, CA, USA ; Kawasaki Disease Research Center, Rady Children's Hospital, San Diego, CA, USA
| | - Alison Marsden
- Mechanical and Aerospace Engineering Department, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
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Nash RW, Carver HB, Bernabeu MO, Hetherington J, Groen D, Krüger T, Coveney PV. Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:023303. [PMID: 25353601 DOI: 10.1103/physreve.89.023303] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2012] [Indexed: 06/04/2023]
Abstract
Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.
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Affiliation(s)
- Rupert W Nash
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom
| | - Hywel B Carver
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and CoMPLEX, University College London, Physics Building, Gower Street, London, WC1E 6BT, United Kingdom
| | - Miguel O Bernabeu
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and CoMPLEX, University College London, Physics Building, Gower Street, London, WC1E 6BT, United Kingdom
| | - James Hetherington
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and Research Software Development Team, Research Computing and Facilitating Services, University College London, Podium Building - 1st Floor, Gower Street, London, WC1E 6BT, United Kingdom
| | - Derek Groen
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom
| | - Timm Krüger
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and Institute for Materials and Processes, School of Engineering, University of Edinburgh, King's Buildings, Mayfield Road, Edinburgh, EH9 3JL, United Kingdom
| | - Peter V Coveney
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom
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Biglino G, Giardini A, Hsia TY, Figliola R, Taylor AM, Schievano S. Modeling single ventricle physiology: review of engineering tools to study first stage palliation of hypoplastic left heart syndrome. Front Pediatr 2013; 1:31. [PMID: 24400277 PMCID: PMC3864195 DOI: 10.3389/fped.2013.00031] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/29/2013] [Accepted: 10/11/2013] [Indexed: 12/27/2022] Open
Abstract
First stage palliation of hypoplastic left heart syndrome, i.e., the Norwood operation, results in a complex physiological arrangement, involving different shunting options (modified Blalock-Taussig, RV-PA conduit, central shunt from the ascending aorta) and enlargement of the hypoplastic ascending aorta. Engineering techniques, both computational and experimental, can aid in the understanding of the Norwood physiology and their correct implementation can potentially lead to refinement of the decision-making process, by means of patient-specific simulations. This paper presents some of the available tools that can corroborate clinical evidence by providing detailed insight into the fluid dynamics of the Norwood circulation as well as alternative surgical scenarios (i.e., virtual surgery). Patient-specific anatomies can be manufactured by means of rapid prototyping and such models can be inserted in experimental set-ups (mock circulatory loops) that can provide a valuable source of validation data as well as hydrodynamic information. Such models can be tuned to respond to differing the patient physiologies. Experimental set-ups can also be compatible with visualization techniques, like particle image velocimetry and cardiovascular magnetic resonance, further adding to the knowledge of the local fluid dynamics. Multi-scale computational models include detailed three-dimensional (3D) anatomical information coupled to a lumped parameter network representing the remainder of the circulation. These models output both overall hemodynamic parameters while also enabling to investigate the local fluid dynamics of the aortic arch or the shunt. As an alternative, pure lumped parameter models can also be employed to model Stage 1 palliation, taking advantage of a much lower computational cost, albeit missing the 3D anatomical component. Finally, analytical techniques, such as wave intensity analysis, can be employed to study the Norwood physiology, providing a mechanistic perspective on the ventriculo-arterial coupling for this specific surgical scenario.
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Affiliation(s)
- Giovanni Biglino
- Centre for Cardiovascular Imaging, UCL Institute of Cardiovascular Science , London , UK ; Cardiorespiratory Unit, Great Ormond Street Hospital for Children, NHS Foundation Trust , London , UK
| | - Alessandro Giardini
- Cardiorespiratory Unit, Great Ormond Street Hospital for Children, NHS Foundation Trust , London , UK
| | - Tain-Yen Hsia
- Cardiorespiratory Unit, Great Ormond Street Hospital for Children, NHS Foundation Trust , London , UK
| | - Richard Figliola
- Departments of Bioengineering and Mechanical Engineering, Clemson University , Clemson, SC , USA
| | - Andrew M Taylor
- Centre for Cardiovascular Imaging, UCL Institute of Cardiovascular Science , London , UK ; Cardiorespiratory Unit, Great Ormond Street Hospital for Children, NHS Foundation Trust , London , UK
| | - Silvia Schievano
- Centre for Cardiovascular Imaging, UCL Institute of Cardiovascular Science , London , UK ; Cardiorespiratory Unit, Great Ormond Street Hospital for Children, NHS Foundation Trust , London , UK
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Marsden AL. Simulation based planning of surgical interventions in pediatric cardiology. PHYSICS OF FLUIDS (WOODBURY, N.Y. : 1994) 2013; 25:101303. [PMID: 24255590 PMCID: PMC3820639 DOI: 10.1063/1.4825031] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Accepted: 09/22/2013] [Indexed: 05/17/2023]
Abstract
Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.
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Affiliation(s)
- Alison L Marsden
- Mechanical and Aerospace Engineering Department, University of California San Diego, La Jolla, California 92093, USA
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Carr IA, Nemoto N, Schwartz RS, Shadden SC. Size-dependent predilections of cardiogenic embolic transport. Am J Physiol Heart Circ Physiol 2013; 305:H732-9. [PMID: 23792681 DOI: 10.1152/ajpheart.00320.2013] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
While it is intuitively clear that aortic anatomy and embolus size could be important determinants for cardiogenic embolic stroke risk and stroke location, few data exist confirming or characterizing this hypothesis. The objective of this study is to use medical imaging and computational modeling to better understand if aortic anatomy and embolus size influence predilections for cardiogenic embolic transport and right vs. left hemisphere propensity. Anatomically accurate models of the human aorta and branch arteries to the head were reconstructed from computed tomography (CT) angiography of 10 patients. Blood flow was modeled by the Navier-Stokes equations using a well-validated flow solver with physiologic inflow and boundary conditions. Embolic particulate was released from the aortic root and tracked through the common carotid and vertebral arteries for a range of particle sizes. Cardiogenic emboli reaching the carotid and vertebral arteries appeared to have a strong size-destination relationship that varied markedly from expectations based on blood distribution. Observed trends were robust to modeling parameters. A patient's aortic anatomy appeared to significantly influence the probability a cardiogenic particle becomes embolic to the head. Right hemisphere propensity appeared dominant for cardiogenic emboli, which has been confirmed clinically. The predilections discovered through this modeling could represent an important mechanism underlying cardiogenic embolic stroke etiology.
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Affiliation(s)
- Ian A Carr
- Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, Illionis
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Deplano V, Meyer C, Guivier-Curien C, Bertrand E. New insights into the understanding of flow dynamics in an in vitro model for abdominal aortic aneurysms. Med Eng Phys 2012; 35:800-9. [PMID: 22981221 DOI: 10.1016/j.medengphy.2012.08.010] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2012] [Revised: 06/05/2012] [Accepted: 08/17/2012] [Indexed: 10/27/2022]
Abstract
An in vitro dynamics set-up of the flow in a compliant abdominal aortic aneurysm (AAA) model with an anterior posterior asymmetry, aorto-iliac bifurcation, and physiological inlet flow rate and outlet pressure waveforms was developed. The aims were first to show that the structural mechanical behavior of the used material to mimic the AAA wall was similar to this of patients with AAA and then to study the influence of the aorto-iliac bifurcation presence and to study the influence of the imbalanced flow rate in the iliac branches on the AAA flow field. 3D visualizations, never performed in the literature, have clearly put into evidence the development of a vortex ring generated at the AAA proximal neck during the decelerating phase of flow rate, which detaches and progresses downstream during the cardiac cycle, impinges on the anterior wall in the distal AAA region, breaks up, and separates into two vortices of which one rolls on upstream along the anterior wall. 2D particle image velocimetry measurements, swirling strength and enstrophy calculations allowed quantification of the vorticity, vortex trajectory and energy for the different geometrical and hydrodynamical conditions. The main results show that the instant and the intensity of the vortex ring impingement depend on the presence of the aorto-iliac bifurcation, with higher intensity, by about 90%, for an AAA without bifurcation. The imbalance of the flow rates into the iliac branches induces different propagation velocities of the vortex ring and lowers the intensity of the vortex impact by about 60%. The potential influence of the AAA dynamics is discussed in terms of AAA remodeling and rupture.
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Biglino G, Capelli C, Binazzi A, Reggiani R, Cosentino D, Migliavacca F, Bonhoeffer P, Taylor AM, Schievano S. Virtual and real bench testing of a new percutaneous valve device: a case study. EUROINTERVENTION 2012; 8:120-8. [PMID: 22580256 DOI: 10.4244/eijv8i1a19] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
AIMS To validate patient-specific computational testing of a second-generation device for percutaneous pulmonary valve implantation (PPVI), against realistic in vitro data. METHODS AND RESULTS Tests were initially carried out in a simple loading mode, performing a compliance test on a rapid prototyped cylinder. This model was reproduced computationally and validated against the experimental data. A second-generation PPVI stent-graft, with no valve mounted, was then deployed in a simplified cylindrical geometry, measuring its displacement when subjected to a pressure pulse. Experimental and computational measurements were in good agreement. Finally, having selected a patient regarded as unsuitable for first-generation PPVI, but potentially suitable for a second-generation device, the stent-graft was studied in the rapidly prototyped patient-specific right ventricular outflow tract (RVOT). Stent positioning and radial displacements with pulsatile flow were observed in a mock circuit using fluoroscopy imaging. Stent deformation and anchoring were measured both in vitro and computationally. Both tests indicated that the stent was well anchored in the RVOT, especially in the distal position, and its central region was rounded, ensuring, were a valve present, optimal valve function. CONCLUSION We suggest that an experimentally validated computational model can be used for preclinical device characterisation and patient selection.
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Affiliation(s)
- Giovanni Biglino
- Centre for Cardiovascular Imaging, UCL Institute of Cardiovascular Science and Great Ormond Street Hospital for Children, London, United Kingdom
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Arzani A, Shadden SC. Characterization of the transport topology in patient-specific abdominal aortic aneurysm models. PHYSICS OF FLUIDS (WOODBURY, N.Y. : 1994) 2012; 24:81901. [PMID: 22952409 PMCID: PMC3427345 DOI: 10.1063/1.4744984] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2012] [Accepted: 07/19/2012] [Indexed: 05/24/2023]
Abstract
Abdominal aortic aneurysm (AAA) is characterized by disturbed blood flow patterns that are hypothesized to contribute to disease progression. The transport topology in six patient-specific abdominal aortic aneurysms was studied. Velocity data were obtained by image-based computational fluid dynamics modeling, with magnetic resonance imaging providing the necessary simulation parameters. Finite-time Lyapunov exponent (FTLE) fields were computed from the velocity data, and used to identify Lagrangian coherent structures (LCS). The combination of FTLE fields and LCS was used to characterize topological flow features such as separation zones, vortex transport, mixing regions, and flow impingement. These measures offer a novel perspective into AAA flow. It was observed that all aneurysms exhibited coherent vortex formation at the proximal segment of the aneurysm. The evolution of the systolic vortex strongly influences the flow topology in the aneurysm. It was difficult to predict the vortex dynamics from the aneurysm morphology, motivating the application of image-based flow modeling.
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Affiliation(s)
- Amirhossein Arzani
- Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, 10 W 32nd St., Chicago, Illinois 60616, USA
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Torii R, Xu XY, El-Hamamsy I, Mohiaddin R, Yacoub MH. Computational biomechanics of the aortic root. ACTA ACUST UNITED AC 2011. [DOI: 10.5339/ahcsps.2011.16] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Ryo Torii
- 1Qatar Cardiovascular Research Center, Doha,
Qatar
- 2Harefield Heart Science Centre, Imperial College London, Harefield,
UK
- 5Department of Chemical Engineering,
Imperial College London, London, UK
| | - Xiao Yun Xu
- 5Department of Chemical Engineering,
Imperial College London, London, UK
| | - Ismail El-Hamamsy
- 4Department of Cardiac Surgery, Montreal
Heart Institute, Montreal, Canada
| | - Raad Mohiaddin
- 3Cardiovascular Magnetic Resonance Unit, Royal Brompton Hospital and
Imperial College London, London, UK
| | - Magdi H. Yacoub
- 1Qatar Cardiovascular Research Center, Doha,
Qatar
- 2Harefield Heart Science Centre, Imperial College London, Harefield,
UK
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Sengupta D, Kahn AM, Burns JC, Sankaran S, Shadden SC, Marsden AL. Image-based modeling of hemodynamics in coronary artery aneurysms caused by Kawasaki disease. Biomech Model Mechanobiol 2011; 11:915-32. [PMID: 22120599 DOI: 10.1007/s10237-011-0361-8] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2011] [Accepted: 11/07/2011] [Indexed: 11/25/2022]
Abstract
Kawasaki Disease (KD) is the leading cause of acquired pediatric heart disease. A subset of KD patients develops aneurysms in the coronary arteries, leading to increased risk of thrombosis and myocardial infarction. Currently, there are limited clinical data to guide the management of these patients, and the hemodynamic effects of these aneurysms are unknown. We applied patient-specific modeling to systematically quantify hemodynamics and wall shear stress in coronary arteries with aneurysms caused by KD. We modeled the hemodynamics in the aneurysms using anatomic data obtained by multi-detector computed tomography (CT) in a 10-year-old male subject who suffered KD at age 3 years. The altered hemodynamics were compared to that of a reconstructed normal coronary anatomy using our subject as the model. Computer simulations using a robust finite element framework were used to quantify time-varying shear stresses and particle trajectories in the coronary arteries. We accounted for the cardiac contractility and the microcirculation using physiologic downstream boundary conditions. The presence of aneurysms in the proximal coronary artery leads to flow recirculation, reduced wall shear stress within the aneurysm, and high wall shear stress gradients at the neck of the aneurysm. The wall shear stress in the KD subject (2.95-3.81 dynes/sq cm) was an order of magnitude lower than the normal control model (17.10-27.15 dynes/sq cm). Particle residence times were significantly higher, taking 5 cardiac cycles to fully clear from the aneurysmal regions in the KD subject compared to only 1.3 cardiac cycles from the corresponding regions of the normal model. In this novel quantitative study of hemodynamics in coronary aneurysms caused by KD, we documented markedly abnormal flow patterns that are associated with increased risk of thrombosis. This methodology has the potential to provide further insights into the effects of aneurysms in KD and to help risk stratify patients for appropriate medical and surgical interventions.
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Affiliation(s)
- Dibyendu Sengupta
- Department of Mechanical and Aerospace Engineering, University of California San Diego-UCSD, San Diego, CA, USA
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Delp SL, Ku JP, Pande VS, Sherman MA, Altman RB. Simbios: an NIH national center for physics-based simulation of biological structures. J Am Med Inform Assoc 2011; 19:186-9. [PMID: 22081222 DOI: 10.1136/amiajnl-2011-000488] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Physics-based simulation provides a powerful framework for understanding biological form and function. Simulations can be used by biologists to study macromolecular assemblies and by clinicians to design treatments for diseases. Simulations help biomedical researchers understand the physical constraints on biological systems as they engineer novel drugs, synthetic tissues, medical devices, and surgical interventions. Although individual biomedical investigators make outstanding contributions to physics-based simulation, the field has been fragmented. Applications are typically limited to a single physical scale, and individual investigators usually must create their own software. These conditions created a major barrier to advancing simulation capabilities. In 2004, we established a National Center for Physics-Based Simulation of Biological Structures (Simbios) to help integrate the field and accelerate biomedical research. In 6 years, Simbios has become a vibrant national center, with collaborators in 16 states and eight countries. Simbios focuses on problems at both the molecular scale and the organismal level, with a long-term goal of uniting these in accurate multiscale simulations.
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Affiliation(s)
- Scott L Delp
- Department of Bioengineering, Stanford University, Stanford, California 94305-5444, USA
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In vivo validation of numerical prediction for turbulence intensity in an aortic coarctation. Ann Biomed Eng 2011; 40:860-70. [PMID: 22016327 DOI: 10.1007/s10439-011-0447-6] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2011] [Accepted: 10/13/2011] [Indexed: 10/16/2022]
Abstract
This paper compares numerical predictions of turbulence intensity with in vivo measurement. Magnetic resonance imaging (MRI) was carried out on a 60-year-old female with a restenosed aortic coarctation. Time-resolved three-directional phase-contrast (PC) MRI data was acquired to enable turbulence intensity estimation. A contrast-enhanced MR angiography (MRA) and a time-resolved 2D PCMRI measurement were also performed to acquire data needed to perform subsequent image-based computational fluid dynamics (CFD) modeling. A 3D model of the aortic coarctation and surrounding vasculature was constructed from the MRA data, and physiologic boundary conditions were modeled to match 2D PCMRI and pressure pulse measurements. Blood flow velocity data was subsequently obtained by numerical simulation. Turbulent kinetic energy (TKE) was computed from the resulting CFD data. Results indicate relative agreement (error ≈10%) between the in vivo measurements and the CFD predictions of TKE. The discrepancies in modeled vs. measured TKE values were within expectations due to modeling and measurement errors.
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Huan Huang, Ming Yang, Wangfu Zang, Shunjie Wu, Yafei Pang. In Vitro Identification of Four-Element Windkessel Models Based on Iterated Unscented Kalman Filter. IEEE Trans Biomed Eng 2011; 58:2672-80. [DOI: 10.1109/tbme.2011.2161477] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Kung EO, Les AS, Figueroa CA, Medina F, Arcaute K, Wicker RB, McConnell MV, Taylor CA. In vitro validation of finite element analysis of blood flow in deformable models. Ann Biomed Eng 2011; 39:1947-60. [PMID: 21404126 DOI: 10.1007/s10439-011-0284-7] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2010] [Accepted: 02/21/2011] [Indexed: 11/26/2022]
Abstract
The purpose of this article is to validate numerical simulations of flow and pressure incorporating deformable walls using in vitro flow phantoms under physiological flow and pressure conditions. We constructed two deformable flow phantoms mimicking a normal and a restricted thoracic aorta, and used a Windkessel model at the outlet boundary. We acquired flow and pressure data in the phantom while it operated under physiological conditions. Next, in silico numerical simulations were performed, and velocities, flows, and pressures in the in silico simulations were compared to those measured in the in vitro phantoms. The experimental measurements and simulated results of pressure and flow waveform shapes and magnitudes compared favorably at all of the different measurement locations in the two deformable phantoms. The average difference between measured and simulated flow and pressure was approximately 3.5 cc/s (13% of mean) and 1.5 mmHg (1.8% of mean), respectively. Velocity patterns also showed good qualitative agreement between experiment and simulation especially in regions with less complex flow patterns. We demonstrated the capabilities of numerical simulations incorporating deformable walls to capture both the vessel wall motion and wave propagation by accurately predicting the changes in the flow and pressure waveforms at various locations down the length of the deformable flow phantoms.
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Affiliation(s)
- Ethan O Kung
- Department of Bioengineering, James H. Clark Center, Stanford University, Stanford, CA 94305, USA
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