Meso-Scale Particle Image Velocimetry Studies of Neurovascular Flows In Vitro

Summary

Here we present simplified methods for fabricating transparent neurovascular phantoms and characterizing the flow therein. We highlight several important parameters and demonstrate their relationship to field accuracy.

Abstract

Particle image velocimetry (PIV) is used in a wide variety of fields, due to the opportunity it provides for precisely visualizing and quantifying flows across a large spatiotemporal range. However, its implementation typically requires the use of expensive and specialized instrumentation, which limits its broader utility. Moreover, within the field of bioengineering, in vitro flow visualization studies are also often further limited by the high cost of commercially sourced tissue phantoms that recapitulate desired anatomical structures, particularly for those that span the mesoscale regime (i.e., submillimeter to millimeter length scales). Herein, we present a simplified experimental protocol developed to address these limitations, the key elements of which include 1) a relatively low-cost method for fabricating mesoscale tissue phantoms using 3-D printing and silicone casting, and 2) an open-source image analysis and processing framework that reduces the demand upon the instrumentation for measuring mesoscale flows (i.e., velocities up to tens of millimeters/second). Collectively, this lowers the barrier to entry for nonexperts, by leveraging resources already at the disposal of many bioengineering researchers. We demonstratethe applicability of this protocol within the context of neurovascular flow characterization; however, it is expected to be relevant to a broader range of mesoscale applications in bioengineering and beyond.

Introduction

PIV is widely used in experimental fluid mechanics for flow visualization and quantitative investigations of fluid motion that vary in length scale from atmospheric to microcirculatory flows^1,2,3. While the specifics of its implementation can vary as widely as its applications, one aspect common to nearly all PIV studies is the use of video imaging of tracer particles seeded within the working fluid, followed by a pair-wise analysis of consecutive image frames to extract desired flow characteristics. Typically, this is accomplished by first subdividing each image frame into smaller regions termed interrogation windows. As a consequence of the random positions of the dispersed particles, each interrogation window contains a unique distribution of pixel intensities. If the window size and data acquisition rate are chosen appropriately, cross-correlation of the intensity signal in each window can be used to estimate the average displacement within that region. Finally, given that the magnification and frame rate are known experimental parameters, an instantaneous velocity vector field can be readily computed.

A major advantage of PIV over single-point measurement techniques is its ability to map vector fields across a two- or three-dimensional domain. Hemodynamic applications, in particular, have benefited from this capability, since it allows a thorough investigation of local flows, which are known to play a significant role in vascular disease or remodeling (e.g., atherosclerosis, angiogenesis)^4,5,6. This has also been true for the evaluation of neurovascular flows, and the interactions thereof with endovascular devices (e.g., flow diverters, stents, intrasaccular coils), since the relevant length-scales in such applications can often span one or more orders of magnitude (e.g., from micrometer to millimeter), and device geometry and placement can significantly impact the local fluid mechanics⁷.

Most groups conducting PIV-based hemodynamic studies have relied on experimental set-ups that closely mimic some of the earliest investigations of stent influence on vascular flow^7,8. Typically, these include a) pulsed lasers and high-speed cameras, to capture high-velocity flows; b) synchronizers, to prevent aliasing between the pulse frequency of the laser and the camera acquisition frame rate; c) cylindrical optics, to form a light sheet and, thus, minimize the background fluorescence from tracer particles above and below the interrogation plane; d) in the case of commercial turn-key systems, proprietary software packages, to perform the cross-correlation analyses. However, while some applications require the performance and/or versatility collectively afforded by these components, many others do not. Moreover, the high cost of commercially sourced tissue phantoms that recapitulate desired vascular structures can also prove limiting for many in vitro studies, particularly for phantoms with features that bridge the mesoscale regime (> 500 USD/phantom). Herein, we report the development of a simplified protocol for implementing PIV for the in vitro visualization of neurovascular flows, which typically lie both spatially and temporally within the mesoscale regime (i.e., length scales ranging from submillimeter to millimeter, and velocities up to tens of millimeters/second). The protocol seeks to leverage resources already at the disposal of many bioengineering researchers, thus lowering the barrier to entry for nonexperts.

The first element of this protocol involves the use of an investment casting technique to enable the in-house fabrication of transparent, polydimethylsiloxane (PDMS)-based tissue phantoms from 3-D-printed sacrificial molds. By leveraging the increasing availability of 3-D printers in recent years, particularly those in shared/multi-user facilities (e.g., institutional facilities or public makerspaces), this methodology cuts costs significantly (e.g., < 100 USD/phantom in the case presented here), while enabling a rapid turnaround for the fabrication of a wide variety of designs and geometries. In the current protocol, a fused deposition modeling system is used with acrylonitrile butadiene styrene (ABS) as the building material, and the printed part serves as a sacrificial mold for the subsequent phantom casting. Our experience has shown that ABS is well-suited for such use since it is soluble in common solvents (e.g., acetone), and it has sufficient strength and rigidity to maintain mold integrity after the removal of the support material (e.g., to prevent the deformation or fracture of diminutive mold features). In the current protocol, mold integrity is further ensured using solid printed models, although this comes at the expense of increased dissolution time. The use of hollow models may also be possible in some cases, to enhance solvent access, and thus, reduce dissolution time. However, careful consideration should be given to the effect this may have on mold integrity. Finally, while the phantoms fabricated herein are based upon idealized representations of neurovascular structures generated using a common computer-aided design (CAD) software package, the protocol is expected to be amenable to the fabrication of more complex, patient-specific geometries as well (e.g., via the use of model files generated by the conversion of clinical imaging data to the .STL file format used by most 3-D printers). Further details regarding the phantom fabrication process are provided in section 2 of the protocol.

The second element of the protocol involves the use of an open-source plug-in for ImageJ to conduct the cross-correlation analyses⁹. This is coupled with the implementation of a simple statistical thresholding scheme (i.e., intensity capping)¹⁰ to improve the image signal prior to cross-correlation, as well as a postcorrelation vector validation scheme, the normalized median test (NMT), to eliminate spurious vectors through a comparison of each to its nearest neighbors¹¹. Collectively, this allows imaging to be accomplished using equipment commonly found in many bioengineering laboratories, thus eliminating the need for the acquisition of many of the costly components of typical PIV systems (e.g., pulsed laser, synchronizer, cylindrical optics, and proprietary software). Further details regarding the video collection, image processing, and data analysis are provided in sections 5 and 6 of the protocol.

Figure 1 illustrates the PIV set-up used in this protocol, which relies upon a fluorescence microscope equipped with a high-speed camera for imaging, as well as an external, continuous white-light source (i.e., metal halide lamp) for through-objective volumetric illumination. A variable-speed gear pump is used to impose the recirculating flow of a transparent mock blood solution through the neurovascular tissue phantoms. The solution is composed of a 60:40 mixture of deionized (DI) water and glycerol, which is a common substitute for blood in hemodynamic studies^12,13,14, due to a) its similar density and viscosity (i.e., 1,080 kg/m³ and 3.5 cP vs. 1,050 kg/m³ and 3 - 5 cP for blood)^15,16; b) its transparency in the visible range; c) its similar refractive index as PDMS (1.38 vs. 1.42 for PDMS)^17,18,19,20, which minimizes optical distortion; d) the ease with which non-Newtonian behavior can be introduced, if needed, via the addition of xanthane²¹. Finally, fluorescent polystyrene beads are used as tracer particles (10.3 µm in diameter; 480 nm/501 nm excitation/emission). While neutrally buoyant beads are desired, sourcing tracer particles with optimal fluid mechanical properties (e.g., density, size, composition) and emission wavelength can prove challenging. For example, the beads used herein are slightly less dense than the glycerol solution (1,050 kg/m³ vs. 1,080 kg/m³). However, the hydrodynamic effects, thereof, are negligible, given that the duration of a typical experiment is far shorter than the time scale associated with buoyancy effects (i.e., 5 min and 20 min, respectively). Further details regarding the mock blood solution formulation and in vitro circulatory system set-up are provided in sections 3 and 4 of the protocol.

Protocol

1. ABS-based Sacrificial Mold Fabrication

1. Design an inverse model of the desired tissue phantom using CAD software.
2. Print the model using a 3-D printer with ABS as the building material.

2. PDMS-based Vascular Phantom Fabrication

1. Mixing
   1. Mix the PDMS prepolymer base and curing agent in a 10:1 ratio (by weight); a 66 g mixture provides sufficient material for the fabrication of phantoms with volumes up to 50 cm³.
   2. Place the mixture in a vacuum desiccator for 60 min to degas and minimize the bubble entrapment. Use cyclic pressurization/depressurization to facilitate bubble rupture.
2. Casting
   1. Mount the printed ABS mold on a glass slide using molding putty to seal the interface.
   2. Carefully pour the PDMS mixture into the mold while trying to minimize bubble entrapment. Lingering bubbles can be manually ruptured using a needle.
   3. Cure the cast phantom at room temperature (25 °C) for at least 24 h.
      NOTE: At higher temperatures, this process can be accelerated²².
3. Demolding
   1. Dissolve the ABS by submerging the phantom in acetone and sonicating for at least 15 min, using powers up to 70 W.
      CAUTION: Acetone has a high vapor pressure at room temperature and a low flash point. Consequently, always work under a fume hood and away from potential ignition sources. Wear proper personal protective equipment (e.g., goggles or face shield, lab coat, acetone-resistant gloves).
   2. Thoroughly rinse the phantom with isopropyl alcohol and, then, DI water to remove solvent residues.
      NOTE: PDMS swells upon exposure to acetone; however, the swelling subsides once the phantom is rinsed and dried sufficiently²³.
4. Confirmation of phantom fidelity using optical microscopy
   1. Using an optical microscope with an attached camera and image capture software, capture an image of a critical feature within the phantom under a magnification that maximizes the feature within the field of view.
   2. Capture an image of an appropriate calibration reticle at the same magnification.
   3. Load both images into ImageJ by dragging them onto the Toolbar.
   4. Click on the calibration reticle image to make it active and, then, select the Line tool. Using the mouse, draw a line along a feature of a known distance and select Analyze > Set Scale from the ImageJ menu.
      NOTE: In the Set Scale window, the field labeled Distance in pixels should be prepopulated with the length of the drawn line in units of pixels.
   5. Enter the length of the feature in the field labeled Known Distance, and its unit in the field labeled Unit of Length. Check the box labeled Global to apply this calibration factor to all open images.
   6. Make the image of the phantom critical feature active and use the Line tool to draw a line along a feature of interest.From the ImageJ menu, select Analyze > Measure (or press Ctrl + M) to measure the length of the line.
   7. Compare the expected value against the value in the column marked Length in the Results window to confirm phantom fidelity.

3. Mock Blood Solution Formulation

1. Mix DI water and glycerol in a 60:40 ratio (by volume).
   NOTE: A 100 mL volume is sufficient for the in vitro circulatory system described herein.
2. Add 1 mL of 2.5% w/v fluorescent polystyrene bead solution (i.e., tracer particles) to the mock blood solution.
3. Homogenize the mixture on a magnetic stir plate at 400 rpm for 10 min.

4. In Vitro Circulatory System Set-up

1. Pump set-up
   1. Use a wire stripper tool to cut off the DC-end plug from the AC-to-DC adapter power source.
   2. Strip the coating off the power and ground wires and connect them to the input terminal of the pulse width modulation (PWM) voltage regulator.
   3. Connect the power and ground wires from the pump's DC motor to the output terminal of the PWM voltage regulator.
      NOTE: The PWM's seven-segment display outputs the duty cycle (0% - 100%) used to achieve a variable voltage to the DC motor.
2. Pump calibration
   1. Prepare 200 mL of mock blood solution (see section 3).
   2. Place tubing from the pump inlet to the beaker holding the mock blood solution.
   3. Place tubing from the pump outlet to an empty beaker.
   4. Select a desired duty cycle set point (0% - 100%). Press the On button and start a timer.
   5. Stop the timer once the pump has transferred the entire volume of mock blood solution. Use this time to calculate the volumetric flow rate.
   6. Repeat steps 4.2.1 - 4.2.5 for at least five different duty cycle set points to establish a least-squares regression curve.
      NOTE: A minimum of three replicate points per duty cycle set point is recommended. This relationship can be used to correlate the desired flow rate to the required PWM duty cycle.

5. Video Collection

1. Image calibration
   1. Determine the calibration ratio for the video imaging (see section 2).
2. Apparatus set-up
   1. Place the PDMS phantom on the stage of the fluorescence microscope.
   2. Connect the phantom to the gear pump and introduce the mock blood solution.
      NOTE: Optionally, prefill the model with ethanol to facilitate full wetting; then, flush and fill it with the mock blood solution. This may be particularly beneficial for models with smaller vessels and/or blind features.
   3. Set the pump motor controller for the desired flow rate based on the pump calibration curve.
   4. Run the pump for 1 - 5 min prior to the experiment to ensure steady-state conditions.
   5. Turn on the external lamp to illuminate the field of view. Select an appropriate filter based on the excitation wavelength of the fluorescent beads.
   6. Adjust the imaging focal plane to the vessel midplane.
      NOTE: This can be achieved by using a focal length that maximizes the imaged vessel cross-section (e.g., when using phantoms with circular vessel cross sections); and/or indexing off of a phantom feature designed to facilitate the identification of the vessel mid-plane.
3. Video recording
   1. Select the video recording parameters to optimize the signal-to-noise ratio (SNR). Key parameters include exposure time, frame rate, and gain.
      NOTE: In this protocol, we use a frame rate of 2,000 fps and a gain of 1.0. However, these parameters may vary based on the application (see the discussion section for further details).
   2. Collect the video and save it in AVI format.
4. Phantom clean-up
   1. If bead-sticking is observed after an experiment, sonicate the phantom in an aqueous detergent solution using powers up to 70 W.

6. Image Processing and Data Analysis

1. Image preprocessing
   1. Drag the saved AVI file onto the ImageJ window to import it. Select the box marked Convert to Grayscale.
   2. From the ImageJ menu, select Analyze > Generate Histogram (or press Ctrl + H) to generate a histogram of image pixel intensities. Take note of the mean and standard deviation for the unprocessed image.
      NOTE: At high frame rates, it is not unusual for the distribution to be skewed heavily toward zero (i.e., no signal).
   3. From the ImageJ menu, select Image > Adjust > Brightness and Contrast (or press Shift + Ctrl + H) to apply a brightness/contrast filter.
   4. On the Brightness and Contrast menu, press the Set button to define the image limits. Set the minimum value to be the mean value plus one standard deviation, and the maximum value to be the maximum intensity of the image (both based on statistics obtained in step 6.1.2).
      NOTE: This typically eliminates all but the top 10% of the pixel intensities. The number of standard deviations may be varied depending on the desired distribution of the pixel intensities. A custom macro script for performing the intensity capping operation is provided in the Supplemental Materials.
   5. From the ImageJ menu, select Process > Noise > Despeckle to reduce the number of saturated pixels.
      NOTE: This operation is necessitated by the increased potential for pixel saturation that arises during the optimization of the brightness and contrast, which can produce spurious vectors during subsequent cross-correlation.
   6. From the ImageJ menu, select Process > Filters > Gaussian Blur with a radius of 1.5 to reduce artifacts arising from the occasional removal of illuminated pixels in a 3 x 3 neighborhood by the prior despeckling operation.
   7. Click on the Polygon tool and, then, click on the image to outline the region of interest (ROI).
   8. From the ImageJ menu, select Edit > Clear Outside to remove sensor noise in locations where no signal is expected (e.g., areas beyond the vessel wall boundary), which can decrease the overall SNR.
2. PIV calculation
   NOTE: This portion of the protocol employs a third-party PIV plug-in for ImageJ, which relies upon Gaussian peak-fitting to enable an estimation of displacement with subpixel accuracy.
   1. From the ImageJ menu, select Plugins > Macros > Run… and navigate to the saved macro Supplemental Code 2.ijjm to cross-correlate successive image pairs.
      NOTE: The macro proceeds as follows. 1) A cross-correlation of the intensity field within consecutive images is first performed to determine the local displacement of advected tracer particles (i.e., the first image pair consists of the first and second images, the second image pair consists of the second and third images, etc.). 2) A two-step multipass evaluation is then performed with initial and final interrogation window sizes of 256 x 256 pixels and 128 x 128 pixels, respectively. Finally, 3) the macro performs a temporal average to further reduce the appearance of spurious vectors.
3. Normalized median test (NMT)
   1. From the ImageJ menu, select Plugins > Macros > Run… and navigate to the saved macro Supplemental Code 3.ijjm to validate the velocity fields via the normalized median test.
      NOTE: The macro proceeds as follows. 1) Each vector in an instantaneous vector field is first compared to its eight nearest neighbors to compute the median value. 2) The array of residual errors is then calculated as the difference between each neighboring vector and the calculated median. 3) The difference between the vector under investigation and the median neighboring vector value is then normalized by the median of the residuals. 4) This is then compared to a threshold value (typically, 0.2 pixels), which can be varied based on a priori knowledge of noise during the image acquisition. Finally, 5) a temporal average of all validated instantaneous vector fields is performed to produce a composite field, as this has been shown to increase the vector field quality²⁴.

Results

Figure 2 illustrates the PDMS tissue phantom fabrication process. The phantoms designed herein are intended for the study of flow in idealized wide-necked, saccular, intracranial aneurysms, as well as proximal branching perforator arteries. Important additional design features include 1) a common reservoir that all vessels drain into, to ensure unencumbered fluid egress from the phantom - otherwise, droplet formation may occur at the smaller vessel outlets; 2...

Discussion

The protocol described herein outlines a simplified method for performing PIV studies to visualize neurovascular flows at physiologically relevant dimensions and flow conditions in vitro. In doing so, it serves to complement protocols reported by others that have also focused on simplifying the quantification of vector fields, but within very different contexts that require the consideration of far larger length scales²⁵ or lower flow rates^26,

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Solidworks 2015	Dassault Systems	N/A	CAD Software
Dow Corning Sylgard 184 Kit	Ellsworth Adhesive	184 SIL ELAST KIT 3.9KG	PDMS Kit
Stratasys Dimension Elite	Stratasys	9180-00105	3D printer
P430 Model Material Cartridge	Stratasys	340-21202	ABS build material
P400 SR Soluble Support Material Cartridge	Stratasys	340-30200	Support material
CleanStation DT3	PM3 Technologies	00-00300R	Base bath
Lindberg Blue M LGO Box Furnace	Thermo Scientific	LB305745M	Oven
21G BD PrecisionGlide Needle	Betcon Dickenson	BD 305167	Branching perforator mold segment
Desiccator (Vacuum)	Polylab	55205	Desiccator
Branson 1800 Utrasonic Cleaning	Branson	CPX-952-116R	Sonicator
Acetone	Fisher Chemical	A9494	Acetone
Isopropol Alcohol	Fisher Chemical	A4514	Isopropol Alcohol
Glycerol	Fisher Chemical	GW33500	Glycerol
10um Polystyrene Yellow-Green Fluorescent Particles	Magsphere	PSF-010UM	Fluorescent beads
Phantom Miro	Vision Research	Miro M310	High speed camera
Micropump	Cole-Parmer	81101	Recirculating pump
Leica DM2000	Leica Microsystems	DM2000	Fluorescent Microscope
Leica 10X Objective	Leica Microsystems	506259	Objective for perforator
Leica 2.5X Objective	Leica Microsystems	11506083	Objective aneurysm sac
Leica Blue Filter Cube L5	Leica Microsystems	513840	Blue filter cube
Leica EL6000	Leica Microsystems	11504115	Light source
Alconox	Alconox Inc	1104-1	Detergent
ImageJ	NIH	N/A	Open source image analysis software https://imagej.nih.gov/ij/
Particle Image Velocimetry PIV Plugin	Qingson Tseng	N/A	https://sites.google.com/site/qingzongtseng/piv