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Williamson PN, Docherty PD, Jermy M, Steven BM. Literature Survey for In-Vivo Reynolds and Womersley Numbers of Various Arteries and Implications for Compliant In-Vitro Modelling. Cardiovasc Eng Technol 2024; 15:418-430. [PMID: 38499933 PMCID: PMC11319390 DOI: 10.1007/s13239-024-00723-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 02/19/2024] [Indexed: 03/20/2024]
Abstract
PURPOSE In-vitro modelling can be used to investigate haemodynamics of arterial geometry and stent implants. However, in-vitro model fidelity relies on precise matching of in-vivo conditions. In pulsatile flow, velocity distribution and wall shear stress depend on compliance, and the Reynolds and Womersley numbers. However, matching such values may lead to unachievable tolerances in phantom fabrication. METHODS Published Reynolds and Womersley numbers for 14 major arteries in the human body were determined via a literature search. Preference was given to in-vivo publications but in-vitro and in-silico values were presented when in-vivo values were not found. Subsequently ascending aorta and carotid artery case studies were presented to highlight the limitations dynamic matching would apply to phantom fabrication. RESULTS Seven studies reported the in-vivo Reynolds and Womersley numbers for the aorta and two for the carotid artery. However, only one study each reported in-vivo numbers for the remaining ten arteries. No in-vivo data could be found for the femoral, superior mesenteric and renal arteries. Thus, information derived in-vitro and in-silico were provided instead. The ascending aorta and carotid artery models required scaling to 1.5× and 3× life-scale, respectively, to achieve dimensional tolerance restrictions. Modelling the ascending aorta with the comparatively high viscosity water/glycerine solution will lead to high pump power demands. However, all the working fluids considered could be dynamically matched with low pump demand for the carotid model. CONCLUSION This paper compiles available human haemodynamic information, and highlights the paucity of information for some arteries. It also provides a method for optimal in-vitro experimental configuration.
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Affiliation(s)
- P N Williamson
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand
| | - P D Docherty
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand.
- Institute of Technical Medicine, Furtwangen University, Campus Villingen-Schwenningen, Jakob-Kienzle Strasse 17, 78054, Villingen-Schwenningen, Germany.
| | - M Jermy
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand
| | - B M Steven
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand
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Williamson PN, Docherty PD, Yazdi SG, Khanafer A, Kabaliuk N, Jermy M, Geoghegan PH. Review of the Development of Hemodynamic Modeling Techniques to Capture Flow Behavior in Arteries Affected by Aneurysm, Atherosclerosis, and Stenting. J Biomech Eng 2022; 144:1128816. [PMID: 34802061 DOI: 10.1115/1.4053082] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Indexed: 02/05/2023]
Abstract
Cardiovascular diseases (CVDs) are the leading cause of death in the developed world. CVD can include atherosclerosis, aneurysm, dissection, or occlusion of the main arteries. Many CVDs are caused by unhealthy hemodynamics. Some CVDs can be treated with the implantation of stents and stent grafts. Investigations have been carried out to understand the effects of stents and stent grafts have on arteries and the hemodynamic changes post-treatment. Numerous studies on stent hemodynamics have been carried out using computational fluid dynamics (CFD) which has yielded significant insight into the effect of stent mesh design on near-wall blood flow and improving hemodynamics. Particle image velocimetry (PIV) has also been used to capture behavior of fluids that mimic physiological hemodynamics. However, PIV studies have largely been restricted to unstented models or intra-aneurysmal flow rather than peri or distal stent flow behaviors. PIV has been used both as a standalone measurement method and as a comparison to validate the CFD studies. This article reviews the successes and limitations of CFD and PIV-based modeling methods used to investigate the hemodynamic effects of stents. The review includes an overview of physiology and relevant mechanics of arteries as well as consideration of boundary conditions and the working fluids used to simulate blood for each modeling method along with the benefits and limitations introduced.
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Affiliation(s)
- Petra N Williamson
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
| | - Paul D Docherty
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
| | - Sina G Yazdi
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
| | - Adib Khanafer
- Vascular, Endovascular, and Renal Transplant Unit, Christchurch Hospital, Canterbury District Health Board, Riccarton Avenue, Christchurch 8053, New Zealand; Christchurch School of Medicine, University of Otago, Dunedin 9016, New Zealand
| | - Natalia Kabaliuk
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
| | - Mark Jermy
- Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
| | - Patrick H Geoghegan
- School of Life and Health Sciences, Aston University, Birmingham B4 7ET, UK; Department of Mechanical and Industrial Engineering, University of South Africa, Johannesburg 2006, South Africa
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Li RX, Apostolakis IZ, Kemper P, McGarry MDJ, Ip A, Connolly ES, McKinsey JF, Konofagou EE. Pulse Wave Imaging in Carotid Artery Stenosis Human Patients in Vivo. ULTRASOUND IN MEDICINE & BIOLOGY 2019; 45:353-366. [PMID: 30442386 PMCID: PMC6375685 DOI: 10.1016/j.ultrasmedbio.2018.07.013] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2017] [Revised: 06/29/2018] [Accepted: 07/16/2018] [Indexed: 05/03/2023]
Abstract
Carotid stenosis involves narrowing of the lumen in the carotid artery potentially leading to a stroke, which is the third leading cause of death in the United States. Several recent investigations have found that plaque structure and composition may represent a more direct biomarker of plaque rupture risk compared with the degree of stenosis. In this study, pulse wave imaging was applied in 111 (n = 11, N = 13 plaques) patients diagnosed with moderate (>50%) to severe (>80%) carotid artery stenosis to investigate the feasibility of characterizing plaque properties based on the pulse wave-induced arterial wall dynamics captured by pulse wave imaging. Five (n = 5 patients, N = 20 measurements) healthy volunteers were also imaged as a control group. Both conventional and high-frame-rate plane wave radiofrequency imaging sequences were used to generate piecewise maps of the pulse wave velocity (PWV) at a single depth along stenotic carotid segments, as well as intra-plaque PWV mapping at multiple depths. Intra-plaque cumulative displacement and strain maps were also calculated for each plaque region. The Bramwell-Hill equation was used to estimate the compliance of the plaque regions based on the PWV and diameter. Qualitatively, wave convergence, elevated PWV and decreased cumulative displacement around and/or within regions of atherosclerotic plaque were observed and may serve as biomarkers for plaque characterization. Intra-plaque mapping revealed the potential to capture wave reflections between calcified inclusions and differentiate stable (i.e., calcified) from vulnerable (i.e., lipid) plaque components based on the intra-plaque PWV and cumulative strain. Quantitatively, one-way analysis of variance indicated that the pulse wave-induced cumulative strain was significantly lower (p < 0.01) in the moderately and severely calcified plaques compared with the normal controls. As expected, compliance was also significantly lower in the severely calcified plaques regions compared with the normal controls (p < 0.01). The results from this pilot study indicated the potential of pulse wave imaging coupled with strain imaging to differentiate plaques of varying stiffness, location and composition. Such findings may serve as valuable information to compensate for the limitations of currently used methods for the assessment of stroke risk.
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Affiliation(s)
- Ronny X Li
- Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, New York, USA
| | - Iason Z Apostolakis
- Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, New York, USA
| | - Paul Kemper
- Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, New York, USA
| | - Matthew D J McGarry
- Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, New York, USA
| | - Ada Ip
- Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, New York, USA
| | - Edward S Connolly
- Department of Neurologic Surgery, New York-Presbyterian Hospital/Columbia University Medical Center, New York, New York, USA
| | - James F McKinsey
- Division of Vascular Surgery and Endovascular Interventions, New York-Presbyterian Hospital/Columbia University Medical Center, New York, New York, USA
| | - Elisa E Konofagou
- Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, New York, USA; Department of Radiology, Columbia University Medical Center, New York, New York, USA.
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Bahramian F, Mohammadi H. A novel periodic boundary condition for computational hemodynamics studies. Proc Inst Mech Eng H 2014; 228:643-51. [PMID: 25015666 DOI: 10.1177/0954411914542170] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In computational fluid dynamics models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. For major cardiovascular models, the realistic boundary conditions are not available. In order to address this issue, the whole computational domain needs to be modeled, which is practically impossible. For simulating fully developed turbulent flows using the large eddy simulation and dynamic numerical solution methods, which are very popular in hemodynamics studies, periodic boundary conditions are suitable. This is mainly because the computational domain can be reduced considerably. In this study, a novel periodic boundary condition is proposed, which is based on mass flow condition. The proposed boundary condition is applied on a square duct for the sake of validation. The mass-based condition was shown to obtain the solution in 15% less time. As such, the mass-based condition has two decisive advantages: first, the solution for a given Reynolds number can be obtained in a single simulation because of the direct specification of the mass flow, and second, simulations can be made more quickly.
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Affiliation(s)
- Fereshteh Bahramian
- Division of Mechanical Engineering, School of Engineering, Faculty of Applied Science, The University of British Columbia, Kelowna, BC, Canada
| | - Hadi Mohammadi
- Division of Mechanical Engineering, School of Engineering, Faculty of Applied Science, The University of British Columbia, Kelowna, BC, Canada Biomedical Engineering Graduate Program, Faculty of Applied Science, The University of British Columbia, Vancouver, BC, Canada
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Park ST, Yoon K, Ko YB, Suh DC. Computational Fluid Dynamics of Intracranial and Extracranal Arteries using 3-Dimensional Angiography: Technical Considerations with Physician's Point of View. Neurointervention 2013; 8:92-100. [PMID: 24024073 PMCID: PMC3766807 DOI: 10.5469/neuroint.2013.8.2.92] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2013] [Accepted: 06/23/2013] [Indexed: 11/24/2022] Open
Abstract
We investigate the potentials and limitations of computational fluid dynamics (CFD) analysis of patient specific models from 3D angiographies. There are many technical problems in acquisition of proper vascular models, in pre-processing for making 2D surface and 3D volume meshes and also in post-processing steps for display the CFD analysis. We hope that our study could serves as a technical reference to validating other tools and CFD results.
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Affiliation(s)
- Sung-Tae Park
- Department of Radiology, Soonchunhyang University Hospital, Seoul, Korea
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