Time-resolved PIV of the pulsatile flow from an ex vivo heart …ltces.dem.ist.utl.pt/lxlaser/lxlaser2016/finalworks2016/... · 2016-06-17 · In this work, a mechanical flow loop

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Time-resolved PIV of the pulsatile flow from an ex vivo heart perfusion model

Katie Cameron1, Darren H. Freed2, David S. Nobes3 1: Dept. of Biomedical Engineering, University of Alberta, Canada

2: Dept. of Surgery, Physiology & Biomedical Engineering, University of Alberta, Canada 3: Dept. of Mechanical Engineering, University of Alberta, Canada

* Correspondent author: [email protected]

Keywords: time-resolved PIV, cardiovascular, pulsatile, Newtonian, non-Newtonian

ABSTRACT

In North America, only 36-39% of available donor hearts are successfully transplanted. This is often attributed to the

narrow six hour time window currently available for transplantation and the fact that many donated organs are

rendered unusable due to cell damage incurred upon donation. A method called ex vivo heart perfusion (EVHP)

enables the use of damaged donor hearts by preserving the heart’s beating function outside the body from the time

of donation until transplantation. To date, research efforts have been directed towards understanding the metabolic

environment required to sustain cardiac performance in the EVHP system, but now there is interest in

understanding the effect of fluid dynamics on system performance. The region of most interest is the left flow loop

which mimics an in vivo flow region that is characterized by the presence of the highly compliant aorta and

significant unsteady effects. This work has undertaken the development of a mechanical flow loop analogous to the

left side of the EVHP system with the ultimate intent of studying the effect of tubing compliance of both Newtonian

and non-Newtonian fluids in the large Womersley number pulsatile flow regime. The focus of this investigation was

to use time-resolved particle imaging velocimetry (PIV) to compare the flow fields obtained from Newtonian and

non-Newtonian fluids using the well-understood symmetric pulsatile flow from a peristaltic pump. Deionized

water and a 0.2 wt.% aqueous solution of polyacrylamide were used as the Newtonian and non-Newtonian fluid,

respectively. Results were compared based non-dimensionalized velocity profiles obtained at five time steps during

one pump cycle. These profiles indicate that fluid viscosity has a significant effect on the generated flow fields in

high-frequency pulsatile flow regimes, particularly during the deceleration phase of the flow.

1. Introduction

Demand for heart transplants far exceeds supply (Hornby et al. 2006). In North America, only

36-39% of available donor hearts are successfully transplanted (Hornby et al. 2006; Tuttle-

Newhall et al. 2008) due in part to evidence of impaired cardiac function upon donation and to

the narrow six hour window currently available for transplantation (White et al. 2013) under the

conditions of hypothermic storage. Ex vivo heart perfusion (EVHP) has been proposed as a

method by which damaged donor hearts can be resuscitated and preserved, thereby expanding

the donor pool and the window available for transplantation (White et al. 2013; White et al.

2015a). EVHP involves connecting donor hearts to a mechanical system that facilitates the heart


function outside the body for extended periods of time. This method not only allows the

opportunity for recovery through control of metabolic conditions such as perfusate composition

but also facilitates the crucial task of monitoring myocardial function for assessing

transplantation viability (White et al. 2013; White et al. 2015a). Control of the metabolic

environment of the EVHP system is well-understood and continues to be optimized, but the

fluid mechanics of the system remain to be understood. Blood is a non-Newtonian power-law

fluid whose shear thinning behavior is dependent on red blood cell (RBC) concentration (Barrett

et al. 2012). Since the EVHP system is operated using perfusates with varying RBC

concentrations, understanding the impact of viscous effects on the flow fields is an important

step towards understanding system behavior.

In this work, a mechanical flow loop analogous to the left flow loop of the EVHP system was

developed. Time-resolved PIV was used to compare the flow fields downstream of a compliant

section resulting from a Newtonian and non-Newtonian pulsatile flow driven by a peristaltic

pump. The left flow loop of the EVHP system was chosen as a basis for the mechanical flow loop

because it reflects a dynamic in vivo region where the highly unsteady nature of the flow and

compliant behavior of the aorta significantly affect flow patterns (Ku 1997). In this experiment,

velocity profiles were obtained at characteristic times throughout one pumping cycle to

investigate the behavior of both Newtonian and non-Newtonian fluids in a high-Womersley

number pulsatile flow regime.

1.1 Background

Cardiovascular fluid mechanics is a well-developed field of study, both computationally and

experimentally (Taylor and Draney 2004). Cardiovascular flow exhibits many unique

characteristics; the investigation outlined in this paper focuses on pulsatile flow of Newtonian

and non-Newtonian fluids and will ultimately involve interaction with compliant vessels. The

non-Newtonian property of blood has often been disregarded in analysis of cardiovascular flow

regimes, particularly in large arteries where shear rates are above 100 s-1 (Ku 1997). However,

this remains a topic of debate, with many suggesting that non-Newtonian effects will produce

different velocity distributions than their Newtonian counterparts under pulsatile flow

conditions (Gijsen et al. 1999; Walker 2013; Karimi et al. 2014). Mathematical models describing

pulsatile flow through rigid pipes are well-developed (Pontrelli 1998) and the behavior of such

systems have been computationally characterized using the dimensionless Womersley number,

Wo = (d/2)(ω/υ)1/2 where d is the diameter of the tube, ω is the pulsing frequency and υ is the


dynamic viscosity of the fluid (Womersley 1955; Loudon and Tordesillas 1998). These models

have also been explored experimentally (Çarpinlioǧlu and Gündoǧdu 2001). Experiments using

rigid tubes are limited in their physiological accuracy because in reality blood vessels are elastic.

In recent years, a great deal of research has been undertaken to understand cardiovascular flow

velocity distributions through compliant phantoms using PIV or PTV (Yip et al. 2011;

Geoghegan et al. 2012; Gülan et al. 2012; Huetter et al. 2015), as well as the effect of certain

pathophysiology, such as stenosis (Geoghegan et al. 2010; Geoghegan et al. 2013), in compliant

pulsatile flow regimes through the use of SPIV and time-resolved PIV.

To the author’s knowledge, there remains limited understanding of the effect of tubing

compliance on the conditions experienced both downstream of the compliant section and

upstream on the pumping device, the heart. Additionally, it has been suggested in recent years

that the effect of non-Newtonian properties are only important in large arteries during the

diastole phase of the cardiac cycle (Karimi et al. 2014), but to the author’s knowledge this has yet

to be experimentally verified. The EVHP system provides a unique and relevant platform in

which to study Newtonian and non-Newtonian behavior in a pulsatile flow regime. The effect of

non-Newtonian properties is particularly relevant to the EVHP system since the optimal

composition of perfusate is an on-going discussion (White et al. 2015b). The use of a peristaltic

pump allows the isolated study of Newtonian and non-Newtonian responses under a simplified

pulsatile flow condition that in its own right could have relevance to other medical applications

such as heart-lung machines. Later work will involve the use of the VAD to study a more

complex physiological pulsatile flow with compliant response.

1.1 Current EVHP System

The current EVHP setup is comprised of a pacemaker-implanted pig heart, a reservoir, arterial

filter, two centrifugal pumps, an oxygenator and a series of tubes, as shown in Fig. 1. Pump 1

(P1) supplies flow to the left and right atrium of the heart and upon pacemaker stimulation heart

chambers contract. This ejects perfusate, a mixture of blood and support nutrients, into ⅜” and

½”tubing on the left and right side of the heart, respectively. Pump 2 (P2) simulates vascular

afterload by supplying a back pressure that allows the aortic and pulmonary valve to close

during diastole. Flow ejected from the left ventricle combines with flow supplied by P2, passes

through an oxygenator, then combines with flow from the right ventricle and finally, returns to

the reservoir. Pressure and flow monitoring at several locations provides direct feedback of the

conditions and performance of the heart.


Heart

LA Left Atrium

MV Mitral Valve

LV Left Ventricle

AV Aortic Valve

RA Right Atrium

TV Tricuspid Valve

RV Right Ventricle

PV Pulmonary Valve

EVHP System

FIC Flow Indicating

Controller

FT Flow Transmitter

PT Pressure Transmitter

Fig. 1 A schematic of the current EVHP flow loop

2. Methodology

2.1 Experimental Setup

The mechanical analog flow loop used for this experiment, shown in Fig. 2, has two regions of

interest: a compliant section and an imaging section. The compliant section is constructed from

thin-walled silicone tubing with ½” ID, a size which was chosen to ensure consistency with non-

dimensional scaling of the EVHP system while easily allowing for future scaling to accomodate

human aortic geometry. The length of the compliant section is 137 mm; this length is based off of

the length to diameter ratios averaged across all section of the in vivo aorta, as per the geometric

data summarized by Huetter et al. (2015). After the compliant section, flow moves through a ½”

ID thin-walled glass test section surrounded by an imaging chamber comprised of four, 1/16”

thick acrylic imaging windows.


The focus of this setup is to investigate the flow field immediately downstream of the compliant

section and compare velocity distribution results from a Newtonian and non-Newtonian fluid.

Deionized water and a 0.2 wt.% aqueous solution of polyacrylamide were used as the

Newtonian and non-Newtonian fluid, respectively. The flow was driven by a peristaltic pump

(L/S® 07523-80, Masterflex®) in order to obtain baseline data for a Newtonian and non-

Newtonian pulsatile flow without the effects of the compliant response expected under more

physiologically realistic conditions. A pulse frequency of 1.67 Hz (100 bpm) was used to reflect

the current operating conditions of the EVHP system which, given the geometry of the flow

loop, indicates a Womersley number of 20.5 for the Newtonian fluid. This value of Womersley is

on the higher end of what is expected for in vivo aortic flow (Bronzino 2000; Stalder et al. 2009).

Under these operating conditions, velocity distributions were obtained at the bottom of the

imaging section by means of time-resolved PIV. Later work with this experimental setup will

address a more physiologically realistic pulsatile flow, in which compliant response is expected,

using a commercial ventricular assist device (VAD) (Ventricular Assist Device, Thoratec®

Corporation). Pressure monitoring (Edwards® Truwave Disposable Pressure Transducers) is

available to capture accurate pressure waveforms for these future experiments.

(a) (b)

Fig. 2 Experimental setup (a) schematic of the flow loop, (b) labelled photo of the flow loop and optical setup


2.2 Optical Setup

The optical setup used to capture the velocity fields is shown in Fig. 2(b). Images were captured

using a CMOS camera (SP-5000M-PMCL-CX; JAI Inc.) with a resolution of 2560×2048 pixels at a

collection rate of 90 fps. A 50 mm SLR lens (NIKKOR 50mm, Nikon Corporation) with an

extension tube set at f# = 4 was used to image a 23.2×12.7 mm field of view at the bottom of the

test section with a resolution of 0.0116 mm/pixel and an average particle size of approximately

1.5 pixels. Images were collected in back-illumination/shadowgraph mode using a high current

green 4” × 4” side-fired LED back light (BX0404-520 nm; Advanced Illumination Inc.). The light

source was used in pulsed mode with a strobe controller (Pulsar 320 Strobe Controller;

Advanced Illumination Inc.) to generate 5 μsec flashes of light. Both the LED and camera were

synchronized and controlled by a function generator (TDS 2024B; Tektronix Inc.). Hollow

borosilicate glass microspheres (ASTM C169; Potters Industries Inc.) with mean diameter of

18µm and bulk density of 0.49 g.cm-3 were used as seeding particles.

2.3 Data Collection and PIV Processing

The peristaltic pump was set to 25 RPM to obtain a pulsation frequency of 100 bpm (1.67 Hz).

During imaging, the imaging chamber was filled with deionized water to improve refractive

index matching. The camera collected 300 images using in-house image capture code

(LabWindows CVI, National Instruments) and the images were saved as AVI files. Captured

images were processed using commercial PIV software (DaVis Imaging Software 8.1.4, LaVision

GmbH.). First, the images were inverted and a geometric mask was applied to constrain the

image to the desired field of view. Decreasing multi-pass time series cross-correlation was

applied to generate the vector map. The first two passes were 256×256 square windows with 50%

overlap and the third pass was a 24×24 4:1 ellipsoid window with 50% overlap. The ellipsoid

window was used in order to improve spatial resolution in the near wall region.


3. Results and Discussion

Fig. 3 depicts the changes in normalized centerline velocity over four pump cycles for (a) the

Newtonian and (b) the non-Newtonian case. The phase time (t) is normalized by the cycle

time (). Both cycles have been indexed to begin at the beginning of the acceleration phase of the

flow based on visual interpretation of the flow videos. For each fluid, behavior is shown to be

consistent across many cycles. There are however notable variances in behavior between the two

fluids.

(a)

(b)

Fig. 3 Plot of normalized centerline velocities over multiple pump cycles for (a) Newtonian fluid (water), (b) non-

Newtonian fluid (polyacrylamide)


To examine these differences in more detail, Fig. 4 shows the normalized centerline velocity plots

for both fluids over one pump cycle for (a) Newtonian fluid (water) and (b) non-Newtonian fluid

(polyacrylamide). The acceleration of the non-Newtonian fluid to its peak centerline velocity is

much smoother and is obtained earlier in the cycle than that of water, which dips prior to

obtaining its peak value. However, both reach a maximum in the range of 0.25 < t/ < 0.35. Most

notably, around t/ = 0.8, the centerline velocity of non-Newtonian fluid abruptly becomes

negative, while the centerline velocity of water always remains positive.

(a)

(b)

Fig. 4 Plot of normalized centerline velocity over one pump cycle for (a) Newtonian fluid (water), (b) non-

Newtonian fluid (polyacrylamide)


t/τ = 0.2

t/τ = 0.4

t/τ = 0.6

t/τ = 0.8

t/τ = 1.0

(a) (b) (c)

Fig. 5 Velocity data obtained at times during pump cycle: t/=0.2, 0.4, 0.6, 0.8, 1.0 (a) Non-dimensionalized velocity profiles for Newtonian (water) and non-Newtonian (polyacrylamide) fluids (b) vector map of water velocity fields

(c) vector map of 0.2 wt.% polyacrylamide velocity fields


Fig. 5 compares the non-dimensionalized velocity profiles of the two fluids obtained at five time

steps during one pumping cycle. The profiles in general show that for both fluids the velocity

distributions are symmetrical about the axis of the flow tube. The figure also depicts the vector

maps at each time step for both fluids. The first profile (t/ = 0.2) shows the flow behavior

during the acceleration phase of the flow. The subsequent two profiles (t/ = 0.4, 0.6) show the

behavior as the flow decelerates. The Newtonian fluid (water) results show the presence of

negative velocities near the walls, which is in excellent agreement with the theoretical findings of

Loudon & Tordesillas (1998) for flows with Womersley number greater than 10. The non-

Newtonian fluid (polyacrylamide) shows a comparatively flatter profile at t/ = 0.4, and at

t/ = 0.6 the velocities near the wall begin to move faster relative to the centerline velocity. At

t/ = 0.8, the centerline velocity becomes negative and the flow’s maximum velocity occurs near

the walls (y/D ≈ ±0.35). This result supports the numerical result obtained by Karimi et al. (2014)

suggesting that non-Newtonian effects are most apparent during the deceleration phase of a

pulsatile flow. At t/ = 1.0, the centerline velocity of the polyacrylamide is positive, but the

maximum flow velocity in the channel still occurs at y/D ≈ ±0.35.

4. Conclusion

This paper presents results obtained using time-resolved PIV on a mechanical flow loop

analogous to the left flow loop of the EVHP system under the pulsatile flow conditions of a

peristaltic pump operating at a pulse frequency of 1.67 Hz. Newtonian and non-Newtonian

behaviors, using water and 0.2 wt.% solution of polyacrylamide, respectively, were compared

based on non-dimensionalized centerline velocities, non-dimensionalized velocity profiles and

vector maps at five time steps during one pump cycle. These results serve to give a fundamental

understanding of flow fields in the system when it is subjected to a simplified, symmetric and

well-controlled pulsatile flow for both the Newtonian and non-Newtonian case. Future work,

which will be presented at the conference, will involve the pulsatile flow being generated by a

VAD which will generate a more complex pressure waveform and introduce compliant response

into the system. This will allow for comparison of Newtonian and non-Newtonian fluid response

in the flow loop under more physiologically realistic conditions.

5. Acknowledgements

We would like to thank Bona Yu and Joshua Mulder for their contributions to the figures used in

this paper. This work is being conducted with the support of the Natural Sciences and

Engineering Research Council (NSERC) of Canada, the Canadian Foundation of Innovation


(CFI), the Canadian National Transplant Research Program (CIHR/CNTRP) and the University

Hospital Foundation (UHF).

7. References

Barrett KE, Barman SM, Boitano S, Brooks HL (2012) Ganong’s Review of Medical Physiology,

24th edn. McGraw-Hill

Bronzino JD (2000) The Biomedical Engineering Handbook 1, 2nd Editio. Springer Science &

Business Media, New York

Çarpinlioǧlu MO, Gündoǧdu MY (2001) Presentation of a test system in terms of generated

pulsatile flow characteristics. Flow Meas Instrum. doi: 10.1016/S0955-5986(01)00019-X

Geoghegan PH, Buchmann NA, Jermy MC, et al (2010) SPIV and image correlation

measurements of surface displacement during pulsatile flow in models of compliant,

healthy and stenosed arteries. In: 15th International Symposium on Applications of Laser

Techniques to Fluid Mechanics. pp 5–8

Geoghegan PH, Buchmann NA, Soria J, Jermy MC (2013) Time-resolved PIV measurements of

the flow field in a stenosed, compliant arterial model. Exp Fluids 54:1528. doi:

10.1007/s00348-013-1528-0

Geoghegan PH, Buchmann NA, Spence CJT, et al (2012) Fabrication of rigid and flexible

refractive-index-matched flow phantoms for flow visualisation and optical flow

measurements. Exp Fluids 52:1331–1347. doi: 10.1007/s00348-011-1258-0

Gijsen FJH, Van De Vosse FN, Janssen JD (1999) The influence of the non-Newtonian properties

of blood on the flow in large arteries: steady flow in a carotid bifurcation model. J Biomech

32:601–608.

Gülan U, Lüthi B, Holzner M, et al (2012) Experimental study of aortic flow in the ascending

aorta via Particle Tracking Velocimetry. Exp Fluids 53:1469–1485. doi: 10.1007/s00348-012-

1371-8

Hornby K, Ross H, Keshavjee S, et al (2006) Non-utilization of hearts and lungs after consent for

donation: a Canadian multicentre study. Can J Anaesth 53:831–7. doi: 10.1007/BF03022801

Huetter L, Geoghegan PH, Docherty PD, et al (2015) Application of a meta-analysis of aortic

geometry to the generation of a compliant phantom for use in particle image velocimetry

experimentation. In: IFAC-PapersOnLine. Elsevier B.V., pp 407–412

Karimi S, Dabagh M, Vasava P, et al (2014) Effect of rheological models on the hemodynamics

within human aorta: CFD study on CT image-based geometry. J Nonnewton Fluid Mech

207:42–52. doi: 10.1016/j.jnnfm.2014.03.007

Ku DN (1997) Blood Flow in Arteries. Annu Rev Fluid Mech 29:399–434. doi:


10.1146/annurev.fluid.29.1.399

Loudon C, Tordesillas A (1998) The use of the dimensionless Womersley number to characterize

the unsteady nature of internal flow. J Theor Biol 191:63–78. doi: 10.1006/jtbi.1997.0564

Pontrelli G (1998) Pulsatile blood flow in a pipe. Comput Fluids 27:367–380. doi: 10.1016/S0045-

7930(97)00041-8

Stalder a, Frydrychowicz a, Russe M, et al (2009) Blood Flow in the Healthy Aorta: Turbulent or

not? Proc 17th Sci Meet Int Soc Magn Reson Med Honolulu:3851.

Taylor CA, Draney MT (2004) Experimental and Computational Methods in Cardiovascular

Fluid Mechanics. Ann Phys (N Y) 36:197–231. doi: 10.1146/annurev.fluid.36.050802.121944

Tuttle-Newhall JE, Munksgaard B, Sung RS, et al (2008) Organ Donation and Utilization in the

United States. Am J Transplant 8:922–934. doi: 10.1111/j.1600-6143.2008.02171.x

Walker AM (2013) The Characterization of Common Cardiovascular Flow Regimes Using

Newtonian and Non-Newtonian Fluids. , University of Calgary Department of Mechanical

and Manufacturing Engineering

White CW, Ali A, Hasanally D, et al (2013) A cardioprotective preservation strategy employing

ex vivo heart perfusion facilitates successful transplant of donor hearts after

cardiocirculatory death. J Heart Lung Transplant 32:734–43. doi: 10.1016/j.healun.2013.04.016

White CW, Ambrose E, Müller A, et al (2015a) Assessment of donor heart viability during ex

vivo heart perfusion. Can J Physiol Pharmacol 901:893–901.

White CW, Hasanally D, Mundt P, et al (2015b) A whole blood-based perfusate provides

superior preservation of myocardial function during ex vivo heart perfusion. J Heart Lung

Transplant 34:113–21. doi: 10.1016/j.healun.2014.09.021

Womersley JR (1955) Method for the calculation of velocity, rate of flow and viscous drag in

arteries when the pressure gradient is known. J Physiol. doi: 10.1113/jphysiol.1955.sp005276

Yip R, Mongrain R, Ranga A (2011) Development of anatomically correct mock-ups of the aorta

for PIV investigations. 1–10.

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Time-resolved PIV of the pulsatile flow from an ex vivo heart …ltces.dem.ist.utl.pt/lxlaser/lxlaser2016/finalworks2016/... · 2016-06-17 · In this work, a mechanical flow loop