Name: Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section (Video) | JoVE Journal
Uploaded: 2016-07-19T13:00:00.000+00:00
Duration: 11 min
Description: Learn Particle Image Velocimetry and Coherent Structure Detection to analyze secondary flow patterns in curved arteries with Type IV stent fractures. This method reveals how stent failures alter cardiovascular hemodynamics and disease progression.

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The authors acknowledge support from NSF grant CBET-0909678 and funding from the GW Center for Biomimetics and Bioinspired Engineering (COBRE). We thank the students, Mr. Christopher Popma, Ms. Leanne Penna, Ms. Shannon Callahan, Mr. Shadman Hussain, Mr. Mohammed R. Najjari, and Ms. Jessica Hinke for help in the laboratory and Mr. Mathieu Barraja for assisting in CAD drawings.

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No conflicts of interest declared.

The protocol presented in this paper describes the acquisition of high fidelity experimental data using particle image velocimetry technique (PIV) and coherent structure detection methods, viz., continuous wavelet transforms, <img alt="Q and λ&lt;sub&gt;ci&lt;/sub&gt; criteria equation; relevant for physics analysis, optimization methods." src="/files/ftp_upload/51288/51288eq1.jpg" data-altupdatedat="1787630408000" data-alt="Equation 1">, suited for identification of vortex and shear-dominated flows. Analysis of experime...

Secondary flow structures are vortical flow patterns that occur in internal flow geometries with curvatures such as curved pipes and channels. These vortical structures arise due to the combined action of centrifugal forces, adverse pressure gradients and inflow characteristics. In general, secondary flow structures appear in planar cross-sections of curved pipes as symmetric Dean-type vortices under steady inflow and, symmetric Dean- and Lyne-type vortices under oscillatory inflow conditions 1 - 3. Secondary flow morphologies are greatly affected by pulsatility and multiple harmonics of pulsatile, physiological inflow conditions. These structures acquire markedly different size-strength-shape characteristics compared to non-physiological (steady and oscillatory) flows 1 - 6. Atherosclerotic lesion development in arteries is affected by the existence of high frequency shear oscillations in regions experiencing low mean shear 27, 28. Secondary flow structures may influence the progress of diseases such as atherosclerosis and possibly, mediate the endothelial response due to pulsatile blood flow by altering wall shear stresses and exposure times of blood-borne particles.
A common treatment to atherosclerosis, a complication resulting in narrowing of arteries by obstructive lesions, is the implantation of stents. Stent fractures are structural failures of implanted stents that lead to further medical complications such as in-stent restenosis (ISR), stent thrombosis and aneurysm formation 9 - 13. Stent fractures have been categorized into various failure "Types I-to-IV", wherein "Type IV" characterizes the highest clinical severity and is defined as the complete transverse fracture of stent struts along with linear displacements of the stent fragments 14. The protocol presented in this study describes an experimental method of visualization of secondary flow structures downstream of an idealized "Type IV" stent fracture in a curved artery model.
The suggested protocol has the following four essential features:
Design and fabrication of laboratory-scale stent models: Geometric description of stents can be associated with a set of self-expandable spirals (springs or helices) intertwined using Nitinol (an alloy of nickel and titanium) wires 29. The length of the stent and its strut diameter depend on the length scale of arterial lesions encountered during clinical implantation 5. Parametric variation of strut diameter and the rising of the winding (or pitch) leads to stents of various geometric configurations. A summary of stent design parameters chosen for 3D printing are presented in Table 1.
Preparation of a blood analog working fluid matched with kinematic viscosity of blood and refractive index of the test section: Optical access to the curved artery test section is required in order to make non-invasive velocity measurements. Accordingly, a Newtonian blood-mimicking working fluid with the refractive index of the vascular model and ideally, a dynamic viscosity, matching human blood is used to obtain accurate blood flow measurements 16 - 18, 30. The working fluid used in this study was reported by Deutsch et al. (2006), that comprised of 79% saturated aqueous sodium iodide (NaI), 20% pure glycerol, and 1% water (by volume)16.
Experimental arrangement for the detection of coherent secondary flow structures using a two-component, two-dimensional particle image velocimetry (2C-2D PIV): Experiments were designed to acquire phase-averaged secondary flow velocity data at various planar cross-sectional locations downstream of a combination of straight and curved stent sections embodying an idealized "Type IV" stent fracture 5, 6, 9, 14. The protocol-steps pertaining to the acquisition of secondary flow velocity fields using particle image velocimetry (PIV) technique involves a PIV system that comprises of a laser (light sheet) source, optics to focus and illuminate the regions of flow, a special cross-correlation charge coupled device (CCD-sensor or camera) and tracer particles to be illuminated by the light sheet within a short time interval (Δt; see Table 4) 31, 32.
The steps in the protocol assume the following: First, a calibrated, experimental set-up of a two-component, two-dimensional (2C-2D) PIV system that evaluates images by double-frame, single-exposure recordings. Second, the 2C-2D PIV system calculates the mean displacements of tracer particles by performing cross-correlation between two image frames acquired during each recording. A brief summary of PIV specifications and image acquisition software is presented in the materials and equipment table. Third, all safety precautions needed to operate the laser are followed by trained laboratory personnel according to the guidelines provided by the host institution. The authors suggest Refs. 31 and 32 for a holistic understanding of the implementation, functionality and application of PIV technique in aero-, hydro- and microfluid dynamics, correlation peak detection and displacement estimation, material and density of tracer particles and, measurement noise and accuracy. Also note that the laser and camera can be controlled by the PIV data acquisition computer (Figure 3A) and data processing software.
Data acquisition and post-processing for coherent structure detection: Phase-averaged secondary flow velocity measurements using a 2C-2D PIV were generated using the protocol description that follows. Post-processing of the data involved coherent secondary flow structure detection using the following three methods: continuous wavelet transforms, <img alt="Q and λ&lt;sub&gt;ci&lt;/sub&gt; criteria equation; relevant for physics analysis, optimization methods." src="/files/ftp_upload/51288/51288eq1.jpg" data-altupdatedat="1787630408000" data-alt="Equation 1"> 5, 6, 19 - 24, 26.
The authors note that the velocity gradient tensor is essentially, a 3 x 3 matrix, 
<img alt="Partial derivatives matrix, fluid dynamics, Jacobian, vector calculus method, educational diagram." src="/files/ftp_upload/51288/51288eq2.jpg" data-altupdatedat="1787630408000" data-alt="Equation 2">.
The protocol presents a method of acquiring two-dimensional experimental measurements (from 2C-2D PIV technique). Therefore, full experimental access to the velocity gradient tensor will not be attainable using this method. The velocity gradient tensor for each pixel <img alt="Static equilibrium ΣFx=0 diagram; dynamic setup analysis; force balance physics study." src="/files/ftp_upload/51288/51288eq3.jpg" data-altupdatedat="1787630408000" data-alt="Equation 3"> of the PIV image <img alt="Static equilibrium diagram; ΣFx=0; educational physics analysis; mechanical stability study." src="/files/ftp_upload/51288/51288eq4.jpg" data-altupdatedat="1787630408000" data-alt="Equation 4"> should be a 2 x 2 matrix, <img alt="Static equilibrium, 2D gradient matrix, mathematical equation, partial derivatives diagram." src="/files/ftp_upload/51288/51288eq5.jpg" data-altupdatedat="1787630408000" data-alt="Equation 5">. The z-component vorticity <img alt="Vorticity equation ω_mn^z diagram, fluid dynamics analysis, showing partial derivatives of velocity." src="/files/ftp_upload/51288/51288eq6.jpg" data-altupdatedat="1787630408000" data-alt="Equation 6"> for each pixel <img alt="Static equilibrium; ΣFx=0; engineering diagram." src="/files/ftp_upload/51288/51288eq7.jpg" data-altupdatedat="1787630408000" data-alt="Equation 7"> is computed using the anti-symmetric part of the velocity gradient tensor <img alt="Dynamic variable (Ω̅mn) in physics equations for educational research analysis." src="/files/ftp_upload/51288/51288eq8.jpg" data-altupdatedat="1787630408000" data-alt="Equation 8">. The result will be a 2D array of vorticity <img alt="Static equilibrium formula (ω), mathematical symbol for rotational motion analysis." src="/files/ftp_upload/51288/51288eq9.jpg" data-altupdatedat="1787630408000" data-alt="Equation 9"> that can be visualized in a contour plot. The authors strongly suggest Ref. 25 for an eloquent discussion experimental access to the velocity gradient tensor toward enhancing the knowledge of vorticity dissipation, strain rates and coherent structure detection. Furthermore, the authors do not attempt to explore the inter-relationships between the aforementioned coherent structure detection methods and suggest Ref. 23, 24 for a comprehensive discussion on that subject.
The focus of the steps in the protocol is the quantitative identification of secondary flow (vortical) structures (also known as coherent structures). Three methods of coherent structure detection viz., <img alt="Q, λᵢ - criteria; equation symbol; academic research notation." src="/files/ftp_upload/51288/51288eq10.jpg" data-altupdatedat="1787630408000" data-alt="Equation 10"> and wavelet transformed vorticity <img alt="Mathematical symbol Omega with hat, used in physics equations, symbol concept." src="/files/ftp_upload/51288/51288eq11.jpg" data-altupdatedat="1787630408000" data-alt="Equation 11"> are applied to velocity field data toward detection of multi-scale, multi-strength occurrences of secondary flow structures downstream of the idealized "Type IV" stent fracture.
The <img alt="Static equilibrium equations ΣFx=0, ΣFy=0; mathematical analysis; educational diagram." src="/files/ftp_upload/51288/51288eq12.jpg" data-altupdatedat="1787630408000" data-alt="Equation 12">, defines a vortex as a spatial region where the Euclidean norm of the vorticity tensor dominates that of the rate of strain 19, 23, 24.The velocity gradient matrix is decomposed into symmetric (strain rate) and anti-symmetric (rotation) parts. Eigenvalues of strain rate matrix are computed; <img alt="Eigenvalues equation \(eig(S_{mn})=(s_1,s_2)\), mathematical formula, matrix analysis." src="/files/ftp_upload/51288/51288eq13.jpg" data-altupdatedat="1787630408000" data-alt="Equation 13">. Norm of the strain rate is then calculated; <img alt="Eigenvalue formula, static equilibrium, equation depicting vector norm calculation method." src="/files/ftp_upload/51288/51288eq14.jpg" data-altupdatedat="1787630408000" data-alt="Equation 14">. Vorticity is computed from the anti- symmetric part. Enstrophy or square of z-component vorticity, <img alt="Mathematical expression showing squared norm of Ω with subscript mn in equation format." src="/files/ftp_upload/51288/51288eq15.jpg" data-altupdatedat="1787630408000" data-alt="Equation 15">) is then computed. The <img alt="Q-criterion equation, fluid dynamics, stability analysis, critical point determination, educational use." src="/files/ftp_upload/51288/51288eq16.jpg" data-altupdatedat="1787630408000" data-alt="Equation 16"> is finally computed; <img alt="Formula for Qmn in spectral analysis equation." src="/files/ftp_upload/51288/51288eq17.jpg" data-altupdatedat="1787630408000" data-alt="Equation 17">. A contour plot of the entire set of <img alt="Thermodynamic coefficient Qmn equations; static equilibrium analysis; educational diagram." src="/files/ftp_upload/51288/51288eq18.jpg" data-altupdatedat="1787630408000" data-alt="Equation 18"> with iso-regions of <img alt="Chemical stability analysis, equation Qmn&gt;0, thermodynamics formula, educational use." src="/files/ftp_upload/51288/51288eq19.jpg" data-altupdatedat="1787630408000" data-alt="Equation 19">, will indicate secondary flow structures 19. 
The <img alt="Static equilibrium formula ΣFx=0, diagram of force vector analysis." src="/files/ftp_upload/51288/51288eq20.jpg" data-altupdatedat="1787630408000" data-alt="Equation 20">, also known as 'swirling strength' is a vortex identification method performed by critical-point analysis of the local velocity gradient tensor and its corresponding eigenvalues 20 - 24. Eigenvalues of the velocity gradient tensor at each pixel <img alt="Static equilibrium, ΣFx=0, formula, mathematical analysis, relevant to physics study." src="/files/ftp_upload/51288/51288eq21.jpg" data-altupdatedat="1787630408000" data-alt="Equation 21"> are computed. The eigenvalues should be of the form, <img alt="Eigenvalue equation λ=r±iλ_ci, formula diagram, linear algebra concepts." src="/files/ftp_upload/51288/51288eq22.jpg" data-altupdatedat="1787630408000" data-alt="Equation 22">. A contour plot of <img alt="Static equilibrium equation ΣFx=0; diagram on forces and balance; educational physics concept." src="/files/ftp_upload/51288/51288eq23.jpg" data-altupdatedat="1787630408000" data-alt="Equation 23"> with iso-regions of <img alt="Equation with lambda notation, λ_ci &gt; 0, representing positive condition concept." src="/files/ftp_upload/51288/51288eq24.jpg" data-altupdatedat="1787630408000" data-alt="Equation 24"> will indicate secondary flow structures 20 - 22.
Wavelet transform method utilizes an analyzing function (or wavelet) that has smoothness in physical and spectral spaces, is admissible (or has zero mean) and has a finite <img alt="L² norm equation; formula; mathematics; vector magnitude; Euclidean distance; educational diagram." src="/files/ftp_upload/51288/51288eq25.jpg" data-altupdatedat="1787630408000" data-alt="Equation 25">5, 6, 26. By convolving a dilated or contracted wavelet with a 2D vorticity field, wavelet transformed vorticity <img alt="Ohm symbol inside parentheses, representing electrical resistance." src="/files/ftp_upload/51288/51288eq26.jpg" data-altupdatedat="1787630408000" data-alt="Equation 26"> field is generated comprising of coherent structures with a wide range of scales and strengths 5, 6, 26. Shannon entropy of the 2D wavelet-transformed vorticity field is computed to estimate the optimal wavelet scale at which all the coherent structures are adequately resolved. This entropy estimation involves a set of probabilities <img alt="Static equilibrium; ΣFx=0, ΣFy=0, torque=0; free body diagram; forces and moments analysis." src="/files/ftp_upload/51288/51288eq27.jpg" data-altupdatedat="1787630408000" data-alt="Equation 27"> for each pixel <img alt="Static equilibrium, ΣFx=0, formula, mathematical analysis, relevant to physics study." src="/files/ftp_upload/51288/51288eq21.jpg" data-altupdatedat="1787630408000" data-alt="Equation 21"> such that  <img alt="Equation for probability distribution in quantum mechanics; formula p&lt;sub&gt;mn&lt;/sub&gt;=|ω&lt;sub&gt;mn&lt;/sub&gt;|&lt;sup&gt;2&lt;/sup&gt;/||ω||&lt;sup&gt;2&lt;/sup&gt;." src="/files/ftp_upload/51288/51288eq28.jpg" data-altupdatedat="1787630408000" data-alt="Equation 28">, the normalized square modulus of the vorticity associated with the pixel at location m, n 5, 6. The procedural steps are presented graphically in Figure 6. The restrictions placed on the choice of the wavelet are presented in detail in Ref. 26. This protocol step describes the procedure for coherent structure detection using a 2D Ricker wavelet. The justification for the use of this wavelet for vortical pattern matching is presented in Ref. 5, 6 and the pertinent references cited therein.

<table><tbody><tr><td>Acrylic tubes and sheet</td><td>McMaster-Carr Supply Company</td><td></td><td>Inlet and outlet pipes and material of the curved artery test section</td></tr><tr><td>Object24 Desktop 3D printer</td><td>Stratasys</td><td></td><td>Desktop rapid prototyping machine. http://www.stratasys.com</td></tr><tr><td>VeroWhitePlus Opaque material</td><td>Stratasys</td><td></td><td>Building material for Object24 Desktop 3D printer</td></tr><tr><td>Fullcure 705</td><td>Stratasys</td><td></td><td>Non-toxic gel-like photopolymer Support material for Object24 Desktop 3D printer</td></tr><tr><td>Ubbelohde viscometer</td><td>Cole Parmer</td><td>YO-98934-12</td><td>Toward measurement of kinematic viscosity of the blood-analog fluid</td></tr><tr><td>VELP scientifica - ESP stirrer&amp;nbsp;</td><td>VELP Scientifica</td><td>F206A0179</td><td>Magnetic stirrer</td></tr><tr><td>Ohaus Scout Pro SP 601&amp;nbsp;</td><td>The Lab Depot</td><td>SP4001</td><td>Weigh scale</td></tr><tr><td>Refractometer</td><td>Atago</td><td>PAL-RI</td><td>Toward measurement of refractive index of blood-analog fluid</td></tr><tr><td>Beakers, pipettes, syringes and spatula</td><td>Sigma-Aldrich&amp;nbsp;</td><td>CLS710110,&amp;nbsp; CLS10031L, CLS71015, CLS71011 Z193216</td><td>Toward handling materials required for blood-analog solution preparation</td></tr><tr><td>Sodium Iodide</td><td>Sigma-Aldrich</td><td>383112-2.5KG&amp;nbsp;</td><td>Crystalline</td></tr><tr><td>Glycerol</td><td>Sigma-Aldrich</td><td>G5516-1L</td><td>Liquid</td></tr><tr><td>Deionized Water</td><td>-</td><td>-</td><td>Liquid</td></tr><tr><td>Sodium thiosulfate anhydrous</td><td>Sigma-Aldrich</td><td>72049-250G</td><td>Powder</td></tr><tr><td>PIV Recording medium</td><td>LaVision</td><td>Imager Intense 10Hz</td><td>PIV Image acquisition CCD camera</td></tr><tr><td>PIV Illumination source</td><td>New Wave Research</td><td>Solo III-15</td><td>PIV Laser source, Nd:YAG laser, 532 nm, dual pulse 70 mJ/pulse</td></tr><tr><td>PIV Imaging software</td><td>LaVision</td><td>DaVis 7.2</td><td>PIV data acquisition and instrument control</td></tr><tr><td>PIV Seeding material</td><td>Thermo-scientific&amp;nbsp;&amp;nbsp;</td><td>Flouro-Max</td><td>Red fluorescent polymer microspheres (&amp;asymp; 7 &amp;micro;m); Dry dyed polystyrene (DVB) fluorescent microspheres emit bright and distinct colors when illuminated by the light of shorter&amp;nbsp; wavelengths than the emission wavelength.&amp;nbsp;</td></tr></tbody></table>

experimental investigation of secondary flow structures downstream of a model type iv stent failure in a 180&#176; curved artery test section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section

The arterial network in the human vasculature comprises of ubiquitously present blood vessels with complex geometries (branches, curvatures and tortuosity). Secondary flow structures are vortical flow patterns that occur in curved arteries due to the combined action of centrifugal forces, adverse pressure gradients and inflow characteristics. Such flow morphologies are greatly affected by pulsatility and multiple harmonics of physiological inflow conditions and vary greatly in size-strength-shape characteristics compared to non-physiological (steady and oscillatory) flows 1 - 7.
Secondary flow structures may ultimately influence the wall shear stress and exposure time of blood-borne particles toward progression of atherosclerosis, restenosis, sensitization of platelets and thrombosis 4 - 6, 8 - 13. Therefore, the ability to detect and characterize these structures under laboratory-controlled conditions is precursor to further clinical investigations.
A common surgical treatment to atherosclerosis is stent implantation, to open up stenosed arteries for unobstructed blood flow. But the concomitant flow perturbations due to stent installations result in multi-scale secondary flow morphologies 4 - 6. Progressively higher order complexities such as asymmetry and loss in coherence can be induced by ensuing stent failures vis-&#224;-vis those under unperturbed flows 5. These stent failures have been classified as &#34;Types I-to-IV&#34; based on failure considerations and clinical severity 14.
This study presents a protocol for the experimental investigation of the complex secondary flow structures due to complete transverse stent fracture and linear displacement of fractured parts (&#34;Type IV&#34;) in a curved artery model. The experimental method involves the implementation of particle image velocimetry (2C-2D PIV) techniques with an archetypal carotid artery inflow waveform, a refractive index matched blood-analog working fluid for phase-averaged measurements 15 - 18. Quantitative identification of secondary flow structures was achieved using concepts of flow physics, critical point theory and a novel wavelet transform algorithm applied to experimental PIV data 5, 6, 19 - 26.

Results presented in Figure 7A-D were generated after post processing secondary flow velocity data (see Figures 5, 6) acquired from 2C-2D PIV system shown in Figure 3A. The inflow condition supplied to the curved artery test section with an idealized "Type IV" stent fracture was the carotid artery waveform shown in Figure 4B. Our previous studies have demonstrated the sensitivity of secondary flow structures to decelerati...

Stent implants in stenosed arterial curvatures are prone to "Type IV" failures involving the complete transverse fracture of stents and linear displacement of the fractured parts. We present a protocol for detection of secondary flow (vortical) structures in a curved artery model, downstream of clinically relevant "Type IV" stent failures.

The arterial network in the human vasculature comprises of ubiquitously present blood vessels with complex geometries (branches, curvatures and ...

This video shows how to use Particle Image Velocimetry, and Coherent Structure Detection, to detect secondary flow or wortical structures in a curved artery model, to better understand the clinical relevance of Type IV stent failures. This method can help answer key questions in cardiovascular hemodynamics. Such as, how stents, which can deteriorate over time and ultimately fracture, can influence blood flow patterns and affect disease progression in vascular remodeling.The main advantage of this technique is that it facilitates investigation of in-vivo and in-vitro measurements in complex physiological arterial flows involving stent and stent fractures. Demonstrating procedure will be Mohammad Najjari, a graduate student, and Jessica Hinke, an undergraduate student. Prepare a blood-analog solution comprised of 79%saturated sodium iodide solution, 20%glycerol, and 1%deionized water.Start with saturated sodium iodide solution, then, add the glycerol in small increments using a syringe until the entire volume of glycerol has been added. Between additions, wait for the solution to become visibly homogenized, and take note of the volume of each glycerol addition. Next, add the required

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Learn Particle Image Velocimetry and Coherent Structure Detection to analyze secondary flow patterns in curved arteries with Type IV stent fractures. This method reveals how stent failures alter cardiovascular hemodynamics and disease progression.

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section (Video) | JoVE Journal

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

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