Characterization of Transition to Turbulence for Blood In

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CHARACTERIZATION OF TRANSITION TO TURBULENCE FOR BLOOD IN

AN ECCENTRIC STENOSIS UNDER STEADY FLOW CONDITIONS

Thesis

Presented to

The Graduate Faculty of The University of Akron

In Partial Fulfillment

of the Requirements for the Degree

Master of Engineering

David Casey

December, 2014

CHARACTERIZATION OF TRANSITION TO TURBULENCE FOR BLOOD IN

AN ECCENTRIC STENOSIS UNDER STEADY FLOW CONDITIONS

David Casey

Thesis

Approved: Accepted:

______Advisor Department Chair Dr. Francis Loth Dr. Sergio D. Felicelli

______Committee Member Dean of the College Dr. Yang H. Yun Dr. George K. Haritos

______Committee Member Interim Dean of the Graduate School Dr. Abhilash Chandy Dr. Rex Ramsier

______Date

ABSTRACT

Blood is a complex fluid that consists of approximately 45% solid particulates by volume. These solid particulates, erythrocytes, cause the fluid to exhibit a non-Newtonian, shear thinning rheology under low shear rates (<200s-1) and Newtonian rheology otherwise. Many researchers employ Newtonian blood analogs to study the relationship between hemodynamics and morphogenesis when the predominant shear rates in the vessel are high. Non-biological, shear thinning fluids have been observed to transition from laminar to turbulent flow differently than Newtonian fluids. A discrepancy between the critical Reynolds number of blood and a Newtonian analog could result in erroneous predictions of hemodynamic forces. The goal of the present study was to compare velocity profiles near transition to turbulence of whole blood and a Newtonian blood analog downstream of a stenosis under steady flow conditions. Doppler ultrasound was used to measure velocity profiles of whole porcine blood and a

Newtonian fluid in an in vitro experiment at 13 different Reynolds numbers ranging from 150 to 1200. Three samples of each fluid were examined and fluid rheology was measured before and after each experiment. Results show parabolic like velocity profiles for both whole blood and the Newtonian fluid at

Reynolds numbers less than 250 (based on the viscosity at 400s-1). The

Newtonian fluid had blunt velocity profiles with large velocity fluctuations (root

iii

mean square as high as 25%) starting at Reynolds numbers ~250 which indicated transition to turbulence. In contrast, whole blood did not transition to turbulence until a Reynolds number of ~300-600. All three blood samples were delayed compared to that of the Newtonian fluid, although there were variabilities between the critical Reynolds numbers. For Reynolds numbers larger than 700, the delay in transition resulted in differences in velocity profiles between the two fluids as high as 35%. A Newtonian assumption for blood at flow conditions near transition can lead to large errors in velocity prediction for steady flow in a post- stenotic flow field. Since this study was limited to a single velocity profile, further studies are required to fully understand the post-stenotic flow field. Further research is necessary to understand the importance of pulsatile flow and compliance.

ACKNOWLEDGEMENTS

I would like to start by acknowledging Nickolas Shaffer. Without the patience and teaching of Nick, I would not have lasted a single semester in undergraduate Engineering. Nick literally saved me from a life of Accountancy. I would also like to acknowledge Dale Eartly who graciously gave much of his time to help us design the experimental setup.

I would like to thank my thesis committee members, Dr. Abhilash Chandy and Dr. Yang Yun, whose guidance and critiques have greatly improved the quality of thesis. This work builds upon the work of Dipankar Biswas, and I am deeply grateful that he allowed me to join him on his research project. His years of hard work and analysis made this study possible. I would like to thank my advisor, Dr. Francis Loth, who is the single handedly the most influential teacher I have ever had. He has taught me as much about life as he has about fluid mechanics.

Finally, I would like acknowledge my loving wife Allison, whose encouragement and understanding kept me going even during the tough times. I love you more than I can express in words.

-Dave

TABLE OF CONTENTS

Page

LIST OF TABLES ...... viii

LIST OF FIGURES ...... ix

CHAPTER

I. INTRODUCTION ...... 1

Introduction and Background ...... 1

Literature Review ...... 2

Blood rheology ...... 2

In Vivo Turbulence Studies ...... 3

Effects of Turbulence on the Cardiovascular System ...... 5

In Vitro Transition to Turbulence Experiments ...... 6

Numerical Simulations ...... 14

Aim of Current Work ...... 16

II. EXPERIMENTAL SETUP ...... 17

Eccentric Stenosis Geometry ...... 17

Experimental Flow Circuit...... 19

Composition of Test Fluids ...... 24

Instrument Calibration ...... 25

Blood Rheology ...... 25

Red Blood Cell Evaluation...... 26

Doppler Ultrasound Signal Processing ...... 27

III. RESULTS ...... 29

IV. DISCUSSION ...... 39

Limitations ...... 46

V. CONCLUSION ...... 51

REFERENCES ...... 52

APPENDICES ...... 56

APPENDIX A. SUPPLIMENTARY FIGURES ...... 57

APPENDIX B. RHEOLGY PROCEDURES ...... 60

APPENDIX C. RHEOLOGY VALIDATION ...... 87

APPENDIX D. CURRICULUM VITAE ...... 106

vii

LIST OF TABLES

Figure Page

1 Critical Re using different TT detection methods...... 43

2 Viscosity standards reported viscosities [cP] ...... 103

viii

LIST OF FIGURES

Figure Page

1 Straight Pipe Velocity Time Traces ...... 9

2 Straight Pipe Normalized Average Velocity Profiles...... 10

3 Straight Pipe RMS as a Function of Re and Radial Position ...... 11

4 Straight Pipe Mean Percent Difference between BL and WG ...... 12

5 Eccentric Stenosis Model Rendering ...... 18

6 Eccentric Stenosis Experimental Geometry ...... 19

7 Photo of Experimental Flow Circuit ...... 22

8 Centrifugal Blood Pump ...... 23

9 Heat Exchanger Coil ...... 24

10 Average Rheology ...... 30

11 Representative Blood Micrographs ...... 31

12 Velocity Time Trace for BL and WG Sample 1...... 32

13 Velocity Time Trace for BL and WG Sample 2...... 33

14 Velocity Time Trace for BL and WG Sample 3...... 34

15 Velocity Profiles for BL and WG Sample 1...... 35

16 Velocity Profiles for BL and WG Sample 2...... 36

17 Velocity Profiles for BL and WG sample 3 ...... 36

18 Mean velocity profiles ...... 37

19 RMS Velocity as a Function of Re and Radial Position...... 38

20 Percent Standard Error of Normalized Mean Velocity...... 42

21 Mean Velocity Percent Difference between BL and WG...... 45

22 Newtonian Rheology ...... 57

23 Whole Blood Rheology ...... 58

24 Dead RBCs found in Blood Sample 2 ...... 59

25 Compressed Air Line Ball Valve...... 61

26 Air Filter and Pressure Regulator...... 62

27 Remove Black Bearing Lock Cap...... 63

28 Peltier Plate Chiller and Power Switch...... 63

29 Solvent Trap Centering Ring...... 64

30 AR 2000 EX Mainframe...... 65

31 Rheology Advantage Shortcut Icon...... 65

32 Rheology Advantage Main Screen ...... 66

33 System Inertia Calibration Dialog Box ...... 67

34 System Inertia Values ...... 68

35 Parallel Plate...... 69

36 Plate Description Dialog Box ...... 70

37 Plate Dimensions Dialog Box ...... 70

38 Rotational Mapping Icon ...... 71

39 Rotational Mapping Dialog Box...... 72

40 Instrument Options Dialog Box...... 73

41 Temperature Parameter Row...... 73

42 Zero Gap Icon...... 74

43 Zero Gap Dialog Box...... 74

44 Pipette Filling Solvent Well...... 75

45 Geometry Settings Dialog Box...... 76

46 Thermistor Centered between Parallel Plates...... 77

47 Representative Temperature Calibration Plot ...... 78

48 Test Protocol Main Screen...... 79

49 Experimental Steps Setup...... 80

50 Post Experimental Step Settings...... 81

51 Go to Geometry Gap Icon ...... 82

52 Load Test Fluid between Parallel Plates using the Pipette...... 82

53 Solvent Trap enclosing Parallel Plate...... 83

54 Run Experiment Icon ...... 83

55 Experiment Run Information Dialog Box ...... 84

56 Results Directory Dialog Box ...... 85

57 Update Experimental Notes Field ...... 86

58 Temperature Drift...... 95

59 Temperature Drift Error...... 96

60 Peltier Plate Temperature Variation over Time ...... 97

61 Viscosity Drift over First Hour ...... 99

62 Viscosity Drift Error over First Hour ...... 100

63 Viscosity Drift over Last Hour and a Half ...... 101

64 Viscosity Drift Error over Last Hour and a Half ...... 102

65 Expected percent Error for Blood Rheology ...... 104

CHAPTER I

I. INTRODUCTION

Introduction and Background

Hemodynamics has been shown to impact the localization of vascular diseases [1-5]. Non-invasive measurements of blood velocity and wall shear stress are difficult due to the small size of blood vessels and invasive studies inherently carry risk. As a result, many researchers have conducted in vitro and numerical studies to quantify the blood vessel hemodynamics. As computational power has increased, image-based computational fluid dynamics has emerged as the tool of choice for the study of hemodynamics and its role in the development, progression and diagnosis of cardiovascular diseases [6]. It is well established that the rheology of whole blood is non-Newtonian, shear thinning for low shear rates (<200s-1) and is Newtonian at larger shear rates (>200s-1) [7, 8].

Shear thinning blood analogs can approximate blood rheology; however, matching the exact shear-thinning nature is difficult [9]. As an alternative, many researchers have conducted studies that employ a Newtonian fluid as a

blood analog, citing the fact that the predominant shear rates in their flow fields are large [10-16]. This assumption may or may not yield accurate results depending on the flow conditions and geometry [8, 17-19], but it is impossible to assess this accuracy, considering the fact that a comparative study has yet to be conducted for a physiologically significant vessel geometry and flow conditions.

Potentially the largest source of error could be near the critical Reynolds Number

(CRN) for Newtonian fluid, since Newtonian fluids have been shown to transition to turbulence (TT) earlier than that of non-Newtonian, shear thinning fluids. The goal of this study is to evaluate the accuracy of this assumption downstream of a stenosed vessel under steady flow conditions.

Literature Review

Over the past 97 years, researchers have studied whole blood rheology and hemodynamics separately, but very few studies have examined both. This section examines previous studies which focused on blood rheology, transition to turbulence and its effects on the cardiovascular system in order to lay a foundation for the current study.

Blood rheology

Whole blood is a complex biological fluid, which contains solid particulates, erythrocytes, and is well understood to have a non-Newtonian shear thinning rheology [7, 8, 20-25]. The non-Newtonian nature of blood is a result of erythrocytes stacking together, along their short axis, to form a long chain of cells

called the rouleaux formation. Chien et al. demonstrated that erythrocytes, red blood cells (RBCs), did not form rouleaux in the absence of fibrinogen and that blood rheology became approximately Newtonian[22]. The authors also showed that as rouleaux formed longer and longer chains of RBCs, the whole blood viscosity increased non-linearly [22]. Conversely, as shearing forces act on the rouleaux formation, these cellular chains break apart causing the whole blood viscosity to non-linearly decreases up to ~200s-1. The viscosity of whole blood is also a function on hematocrit (HCT), where a 1% increase in hematocrit can increase the blood apparent viscosity by 4% [26, 27]. Researchers have employed different types of rheological instruments to quantify the viscosity of whole blood which may be the reason behind the widely varying results [21, 28-

30].

In Vivo Turbulence Studies

Blood flow in the human body is typically laminar; however, transition to turbulence (TT) has been observed in various locations in the human body. High frequency fluctuations have been observed in arteriovenous (AV) grafts [15] and in a stenosed carotid bifurcation [13]. Thorne et al. showed that introduction of a stent significantly increased the turbulent intensity in the internal and external carotid arteries [31]. Kurtz attributed the vascular sounds (bruits and hums) in the head and neck of patients to turbulence in blood flow [32].

Hess is considered to be the first researcher to study turbulence in the cardiovascular system, as he studied the hemodynamics of the canine aorta in

1917 [33]. He employed two methods for detecting turbulence, auscultation and flow visualization. Hess concluded that the blood flow inside the canine aorta was laminar since no bruits or hums were detected during auscultation and the fact that the dye followed a laminar stream line down the aorta after injection.

A similar experiment was conducted by McDonald in 1952, who studied lapine (rabbit) cardiovascular hemodynamics [34]. Using flow visualization and a high speed camera, McDonald observed that the first 12 milliseconds of systole were characteristic of laminar flow, followed by a sudden transition to turbulence which persisted until the end of systole. The exact time point at which the flow field relaminarized could not be determined. McDonald concluded that since the dye was evenly distributed across the aorta, both the axial cell core and cell free layer experienced similar levels of turbulence.

Nerem & Seed studied canine cardiovascular hemodynamics utilizing hot film anemometry [35]. The hot-film needle probe placed at the center of the descending aorta was able to detect turbulence, since it could capture high frequency velocity fluctuations. The authors observed both laminar and transitional blood flow over a wide range of Reynolds number (Re), when Re was defined as 4 times the product of density and average flow rate and divided by pi, artery diameter and viscosity. An example of this can be seen for dog #35, where blood flow at Re = 1960 (heart rate of 46 beats per minute) was observed to be transitional, as opposed to Re = 2270 (heart rate of 215 beats per minute) where it was observed to be laminar flow. Nerem & Seed concluded that the

critical Re (CRN) was not simply a constant, but rather a function of Womersly number, such that CRN= 250 α.

Effects of Turbulence on the Cardiovascular System

Many researchers have studied the effects that turbulence has on endothelial cells (ECs) lining the inner surface of the atrial wall. Both Davies et al. [36] and McCormick et al. [37] constructed in vitro experiments to control the flow conditions to which ECs were exposed. Davies et al. examined bovine aortic ECs and McCormick et al. used human umbilical vein ECs. The authors of both studies observed EC elongation and alignment to the direction of bulk flow when exposed to laminar shear stresses. When the endothelial cells were exposed to turbulent shear stresses, the authors of both studies observed morphological and orientational changes in the ECs. Davies et al. noted that

ECs exposed to turbulent shear stress of 14 dynes/cm2 increased the DNA synthesis by 44% and, therefore, cell turnover rate. Once cells begin mitosis under these conditions, the new cell typically did not attach to the substratum. In cases where turbulence persisted for longer than 24 hours, gaps in the EC monolayer would appear, indicating cell retraction and loss. McCormick et al. observed that the magnitude of EC elongation was directly proportional to the magnitude of the shear stress applied to the ECs; whereas, ECs began to take on a more round shape when exposed to transitional turbulent shear stresses.

At the highest Re, the cells again became more elongated compared to that of the laminar flow cases. Cells exposed to turbulent flow conditions were randomly oriented and equally distributed between angles 0° and 180°.

Fry studied the effects of shear stress on endothelial cells in the canine thoracic aorta by implanting an artificial stenosis which constricted lumen diameter and increased the blood velocity [4]. Fry hypothesized that damaged endothelial cells would allow plasma proteins to easily pass through the lipid bi- layer and into their cytoplasm. He used Evens blue dye to tag albumin (one of many plasma proteins) and identified regions of damaged endothelial cells. Fry observed endothelial cell damage in regions of high laminar shear stress and regions of low shear stress but high turbulent energy. While the importance of

TT in arterial disease is not fully understood, it is clear that in order to obtain accurate hemodynamic forces under transitional flow conditions, in vitro experiments and computational simulations must accurately predict TT for a given flow problem.

In Vitro Transition to Turbulence Experiments

The first in vitro hemodynamic study utilizing whole blood in a straight rigid pipe under steady flow conditions was conducted by Coulter & Pappenheimer in

1949 [38]. Coulter & Pappenheimer based Re on a viscosity inside the pipe, which was found by assuming parabolic flow, measuring the pressure drop, flow rate and density. They repeated this process for higher flow rates until the apparent viscosity no longer decreased, and used this value to calculate Re.

Specific to their experimental system, they observed the CRN to be 2160 ± 80 and 1900 ± 227 for water and whole bovine blood, respectively. Assuming a normal distribution, a one sample student t-test demonstrate whether these two

CRN ranges are statically significantly different from one another. A one sample student t-test was chosen since 3 data points were provided for blood and only a single data point was provided for water. Since the authors listed a range of

CRN for each experiment rather than a single value, a representative CRN must be chosen in order to perform statistics. For this reason, the average of each

CRN range was chosen. Using this statistical method, the true population mean

CRN for whole bovine blood, detected by means of the friction coefficient, was significantly lower than the CRN of water (2 tailed p-value = 0.016). They observed that the electrical resistance for transitional flow was comparable to that of laminar flow and, therefore, concluded that the axial erythrocyte core remained laminar while the cell free layer was transitional.

Ferrari et al. conducted a study to determine at which Re Doppler guide wire could accurately predict the flow rate of whole human blood under weakly pulsatile conditions in a straight rigid glass pipe [39]. This was accomplished by taking half of the measured centerline velocity and multiplying it by the cross- sectional area of the pipe. The Doppler guide wire accurately predicted the flow rate for Re < 500, but under estimated the flow rate for Re > 500. They concluded that the CRN ~ 500, based on measured centerline velocities being less than that predicted by the Poiseuille equation. This indicates that the velocity profile was becoming blunt and therefore transitioning to turbulence.

In order to assess the impact of a Newtonian blood assumption, Biswas et al. performed an experiment similar to that of Coulter & Pappenheimer in which both experiments examined whole blood and a Newtonian analog (water-

glycerin) in a straight rigid pipe under steady flow conditions [40]. The method to detecte turbulence was similar to that of Ferrari, except a Doppler ultrasound probe mounted at the end of a rigid pipe was used instead of a Doppler guide wire. For both blood and the Newtonian analog, mean and fluctuating velocity profiles were measured at 21 different radial positions. Three detection techniques were utilized to determine the critical Reynolds number for each test fluid. First, velocity time traces can detect vortices in the flow field which appear as velocity fluctuations and are indicative of non-laminar flow. An example of two velocity time traces at the center of the straight pipe can be seen below in Figure

1 [40]. The fluctuating component of the velocity has been scaled by the mean velocity in order to compare between different Reynolds numbers and different fluids. The Reynolds number is labeled on the right hand side of the velocity time trace for each respective measurement. For the Newtonian fluid, there are no large scale velocity fluctuations below Re = 1900, indicating that the flow field is laminar. Between 2000 ≤ Re ≤ 2500, large scale velocity fluctuations can be seen which demonstrate that the fluid has transitioned to turbulence. For the whole blood measurements, no large scale velocity fluctuations below Re =

2400, indicating that the flow field is laminar. Between 2500 ≤ Re ≤ 3000, large scale velocity fluctuations can be seen which demonstrate that the fluid has transitioned to turbulence.

Figure 1: Straight Pipe Velocity Time Traces

Second, TT can be detected by comparing the shape of velocity profiles for each test fluid (Figure 2) [40]. Each data point is the average velocity over the three second measurement period, scaled by the mean velocity (flow rate divided by cross-sectional area) for each respective Re. The Re for each measurement is located adjacent to each profile. Note that for each profile, the

root mean square (RMS) velocity has been plotted as error bars for each radial location. It is well established that the velocity profiles for a straight rigid pipe under steady flow conditions will shift from parabolic at laminar flow rates to blunt velocity profiles at transitional and turbulent flow rates. For the Newtonian fluid, parabolic velocity profiles with low RMS velocity can be below Re = 2000 and blunt velocity profiles with high RMS velocities above Re = 2400.

Figure 2: Straight Pipe Normalized Average Velocity Profiles.

In a similar fashion as the first method, the third detection technique to detect TT is RMS velocity, since the RMS velocity is another quantitative measure of velocity fluctuations. Large RMS values indicate large velocity fluctuations and, therefore, non-laminar flow. For the Newtonian blood analog,

low RMS values can be seen below Re = 2000 and large RMS values are centered around Re = 2200. RMS velocity plotted as a function of both Re and radial position can be seen below in Figure 3. Note that radial positions near the wall for both test fluids have been omitted, as they can yield erroneous results due to spectral broadening. Utilizing all three of these methods, we concluded that the CRN for blood and water glycerin (WG) are ~2700 and ~ 2100-2300, respectively.

Figure 3: Straight Pipe RMS as a Function of Re and Radial Position

In all experiments, the Newtonian fluid had a lower CRN than that of blood, on average transitioning to turbulence ~15% earlier. This resulted in velocity differences between blood and WG to be as large as 23% (Figure 4) at the centerline of the rigid pipe between 2200 < Re < 3000. Due to the large

velocity errors, we concluded that an assumption of Newtonian blood rheology may not be appropriate in a straight pipe under steady flow conditions for Re near TT.

Figure 4: Straight Pipe Mean Percent Difference between BL and WG

The straight pipe geometry used in these studies was chosen since the flow field is well understood for both the laminar and transitional regime and for our purposes serve as a baseline for which more complicated anatomical geometries can be compared. Although both Biswas et al. and Coultier &

Pappenheimer’s studies employed a similar geometry under similar flow conditions, the CRN for whole blood reported in each conflict with one another.

The results presented by Coulter & Pappenheimer appear to be robust since the authors verified their experimental methods by testing water and showing that their CRN agreed with Reynolds’ findings. Although their CRN for whole blood differs from Biswas et al.’s findings by ~15%, this may be attributed to the difference in concentration of anticoagulants, the addition of cyanide, the difference between animal species or rheological measurement techniques. As

previously discussed, blood typically exhibits a shear thinning nature, but the rheology of Coulter and Pappenheimer’s blood samples were essentially

Newtonian. It is intuitive that if blood exhibited a Newtonian like rheology, then the CRN should be similar to that of a Newtonian analog. This may explain the difference between CRN of the two experiments, but further research is required to confirm.

Our findings conflict with hypothesis proposed by Coulter & Pappenheimer that turbulence is limited to the cell free layer in the vessel and the erythrocyte core remains laminar. The results in this study demonstrate that large scale velocity fluctuations are not limited to the cell free layer of the pipe, but rather seem to permeate the entire diameter with a maximum at the center (Figure 3).

At the CRN for both blood and WG, we observed that the velocity profiles began to shift from parabolic to blunt, which would not be the case if the erythrocyte axial core was experiencing laminar flow conditions.

Ahmed & Giddens studied the flow field downstream of three different stenosis models. Using laser Doppler anemometry and WG (63% glycerin by weight) as the test fluid, they observed laminar flow for a 25% reduced stenosis for Re ≤ 1000. The authors also observed vortex shedding without transition to turbulence for the 50% reduction stenosis at Re = 2000 and turbulent flow three diameters downstream of the stenosis for Re = 1000 and 2000. It has yet to be determined how well a Newtonian analog approximates the rheology of whole blood in the post-stenotic flow field. It is difficult to predict the effect of this

assumption, in light of the conflicting results between Biswas et al. and Coulter &

Pappenheimer’s straight pipe studies.

Numerical Simulations

Currently there is some controversy in the computational field as to the impact of non-Newtonian rheology of whole blood on computational fluid dynamic

(CFD) simulations. Lee and Steinman examined the importance of blood’s shear thinning nature by simulating blood flow through a patient specific carotid bifurcation using both a constant Newtonian viscosity and a shear thinning viscosity described by the Carreau model [18]. They found negligible differences between the two simulations’ predicted time averaged wall shear stress (WSS) patterns and velocity profiles. Lee and Steinman noted that their results conflict with those of Gijsen et al. [17] who also investigated the effects of blood’s shear thinning rheology by conducting both CFD simulations and in vitro experiments.

Gijsen et al. choose potassium thiocyanate (71% by weight) with 250 parts per million Xanthan gum (XSCN-X) dissolved in water as their blood analog. The experimental data from the non-Newtonian properties of XSCN-X were incorporated into the Carreau-Yasuda model to create a numerical blood analog.

Velocity profiles measured using laser Doppler anemometry showed excellent agreement with the numerical velocity profiles for both the Newtonian and non-

Newtonian experiments. Significant differences were found when the Newtonian results were compared to the non-Newtonian results. At every measurement location, the Newtonian fluid was shown to have a more skewed velocity profile

than that of the shear thinning fluid. This resulted in the Newtonian experiments having a greater peak velocity than that of the non-Newtonian cases, as much as

~30%, approximately one diameter downstream of the carotid bifurcation in the internal carotid artery. Lee and Steinman attributed the differences between their results and Gijsen’s results to Gijsen et al.’s use of an idealized geometry,

Gijsen’s flow wave form with extended diastolic phase and their choice of XSCN-

X as a non-Newtonian blood analog.

The common carotid artery was relatively straight for both studies and thus, a comparison of the inlet velocity profiles is warranted. Both studies showed negligible differences between their respective Newtonian and non-

Newtonian blood analogs in the common carotid artery under steady and pulsatile conditions. The results of both studies are in agreement with the results of Biswas et al. for Re < 2200.

Varghese et al. numerically studied the flow field downstream of idealized stenosis using direct numerical simulation and spectral element method [41].

The authors chose the parameters of the stenosis and flow conditions similar to those of Ahmed & Giddens [42] in order to verify their numerical findings experimentally. Both studies adopted the same nondimensionalization scheme to describe the region downstream of the stenosis, by scaling the actual distance from the region of interest to the stenosis by the inner diameter (D) of the vessel.

Varghese et al. showed that their flow field predicted by CFD matched the experimental results up to 2.5D downstream of the axisymmetric stenosis. The authors noted that discrepancies up to 20% were shown at 4 and 6D

downstream near the wall, but this might have been an effect of spectral broadening. For the 75% area reduction and 5% eccentric stenosis, Varghese et al. found laminar flow downstream of the stenosis at Re = 500 and transitional vortical structures at Re = 1000. The flow field between 0 and 6D remained laminar even at Re = 1000. Between 6 and 8D, streamwise vortical structures formed and rapidly broke down into transitional vortical structures between ~9 and 12D. Again, it has yet to be determined how well a Newtonian analog approximates the rheology of whole blood in the post-stenosis flow field, and it is difficult to predict considering the conflicting results between Lee and Steinman and Gijsen et al. in a physiological geometry.

Aim of Current Work

The goal of this study was to compare TT based on fluctuating and mean velocity for whole porcine blood and a Newtonian analog in a postsenotic flow field under steady flow conditions. Due to the opacity of whole blood, Doppler ultrasound (DUS) was employed to measure the velocity profiles for each fluid instead of laser Doppler or particle image velocimetry. The study herein utilized the system designed in the straight rigid pipe experiment to examine steady flow downstream of an eccentric stenosis at Re near TT for both whole porcine blood and a Newtonian analog to access the accuracy of a Newtonian blood rheology assumption.

CHAPTER II

II. EXPERIMENTAL SETUP

Eccentric Stenosis Geometry

In this study, the velocity profiles downstream of an eccentric stenosis was studied for both water-glycerin and whole blood based on the encouragement and initial analysis of Dipankar Biswas. The flow model lumen geometry was selected to closely resemble those of both Varghese [41] and Ahmed & Giddens

[42]. At the throat, the vessel cross-sectional area is reduced 84% and the eccentricity by 5% of the pipe inner diameter. Note: this differs from that of

Varghese whose stenosis reduced the lumen area 75%. The stenosis eccentricity is the same in both studies. The model was created using Solid

Works (Waltham, Massachusetts, USA) and machined by Dale Ertley on a 3 axis

CNC (computer numerical control) mill.

The fluid space of the eccentric stenosis was created by extruding a circle of radius R(z) centered at C(z) along the curve C(z) along the axial coordinate z

bounded by z described by Eqn. 1 and 2 below. The

eccentric stenosis model created from Eqn. 1 and 2 can be seen in Figure 5 and the experimental geometry used in this study can be seen below in Figure 6.

Eqn. 1

Eqn. 2

Where

ID = Inner diameter of the entry length pipe (6.35 mm)

= 0.25

= Length of the stenosis model, equal to twice the ID (12.7 mm)

= Z-coordinate of the center of the stenosis model

Figure 5: Eccentric Stenosis Model Rendering

Figure 6: Eccentric Stenosis Experimental Geometry

Experimental Flow Circuit

This study used a flow circuit originally designed by Dipankar Biswas to conduct experiments for his Ph.D. dissertation (Figure 7). During testing of the system, design improvements were identified and implemented by both Mr.

Biswas and Mr. Casey. These included placing the experiment in an insulated temperature controlled chamber and constructing an adjustable aluminum support structure. The test fluid was driven by a centrifugal blood pump (Sarns

Disposable Centrifugal Pump 7850, Terumo Corporation, Ann Arbor, Michigan).

Constant flow rate was achieved (within 1.5%) by controlling the voltage of the blood pump (Figure 8) with a computer controlled power supply (1685B ,BK

Precision, Yorba Linda, California ) while the flow rate was monitored by an inline flow meter (TS410, Transonic Systems Inc., Ithaca, New York). The blood pump was connected to the eccentric stenosis model through a straight rigid Butyrate pipe. In order to ensure that the velocity profile entering the stenosis was fully developed, the following Eqn. 3 was used to determine the required entry length for the Butyrate tube.

Eqn. 3

Where

= entrance length [mm]

= Reynolds number

= inner diameter of the entry length tube [mm]

A Reynolds number of 2000 was chosen for the entry length calculation.

This is the maximum flow rate at which a Newtonian fluid can be driven in the entry length pipe and still remain laminar. Hence this is the upper bound of flow rates that could have been included in this study. The inner diameter of the pipe is 0.635 cm, which yields and entry length of 0.05 x 2000 x 0.635 cm = 63.5 cm.

The tube had a length of 78.7 cm, which is greater than the required 63.5 cm, thus, ensuring that the velocity profile entering the stenosis was fully developed.

The eccentric stenosis model was positioned such that the eccentricity was parallel to the floor, and directed toward the DUS probe. Velocity profiles

were measured 11 diameters (70mm) downstream of the eccentric stenosis model by a 20 MHz pulsed Doppler ultrasound probe (Mouse Doppler tube mounted, Indus Instruments, Webster, TX). The Doppler signal was processed by an ultrasound mainframe (Crystal Biotech, Northborough, MA). The 500 micron x 300 micron insonified volume was positioned 4 mm in front of the ultrasound probe, which required the ultrasound probe to enter the flow field for

11 of the 21 measurements. The probe was positioned at an angle of 60° with respect to the entry length pipe. The position of the insonified volume was controlled to within 2 microns by a combination of a computer controlled linear stage (SGSP 26-150, Sigma Koki, Tokyo, Japan), a rotary stage (M 481A,

Newport Corporation, Irvine, CA) and a miniature linear three axis stage (M-MT-

XYZ, Newport Corporation, Irvine, CA).

The flow circuit was housed inside a temperature controlled enclosure which helped maintain the fluid temperature at 37 ± 0.5°C. The air temperature was maintained at 37°C by four independently controlled incubator heaters

(INCUKIT, Fruitland, ID). The fluid temperature was monitored by a thermistor

(OL-703, OMEGA Engineering, INC., Stamford, CT) located downstream of the ultrasound probe. The fluid temperature was modulated by two heat exchangers submerged inside the fluid reservoir. Both heat exchangers consisted of 0.25ʺ x

0.375ʺ vinyl tubing coiled into sixteen, 1.5ʺ diameter rings (Figure 9). The test fluid temperature was controlled by adjusting the flow rates the cold and hot water within their respective coil. Each heat exchanger’s flow rate was controlled

by a computer controlled power supply (1685B, BK Precision, Yorba Linda,

California).

Figure 7: Photo of Experimental Flow Circuit

Figure 8: Centrifugal Blood Pump

Figure 9: Heat Exchanger Coil

Composition of Test Fluids

Two different test fluids were examined. First, three samples of whole porcine blood with 10% sodium citrate (BL) were purchased from Animal

Technologies (Tyler, Texas). Each aliquot of blood was collected from a unique animal, and all aliquots were collected at the same time. Second, three samples of water glycerin were used as a Newtonian blood analog. The first sample of water glycerin had a ratio that consisted of 55:45 by volume and the other two samples had a ratio of 50:50 by volume. Tap water was mixed with glycerin

(Ringwood, IL) to make the WG mixture. 0.1 gram of TiO2 (Spectrum Chemical,

New Brunswick, NJ) was added to the WG mixtures to reflect DUS.

Instrument Calibration

Calibration of the flowmeter was performed using a graduated cylinder and stopwatch. The voltage of the power supply driving the centrifugal blood pump was set to 10V and fluid was collected in the graduated cylinder in parallel to the flowmeter’s ultrasonic measurement. Measurement of fluid density was made using a 250cc graduated cylinder and high-resolution scale (PB1502,

Mettler Toledo, Columbus, OH). The rheometer accuracy was checked by following the procedures laid out in Appendix B and measuring the viscosity of four Newtonian viscosity calibration fluids.

Blood Rheology

The shear thinning nature of each fluid was characterized by an AR 2000

EX rheometer. A 60mm parallel plate was used to measure the viscosity of each experimental fluid for shear rates between 1 and 500s-1. The acrylic parallel plate was positioned 500 microns above the peltier plate. This gap size was chosen based on a hematocrit of 35% from Barnes [43]. Based on Barnes analysis and the parameters listed above, the presence of the red blood cells

(RBCs) would contribute approximately -2% errors in the apparent viscosity measurement. For each measurement, the rheometer held a constant shear rate for 20 seconds allowing the fluid to reach equilibrium, followed by a 5 second measurement. The temperature of the peltier plate was held at a constant 37 ±

0.1°C. Rheological measurements were taken before and after each experiment.

Red Blood Cell Evaluation

In order to verify that the testing procedure was physiologically appropriate, blood was monitored via microscopy before and after each experiment, as well as periodically throughout the experiment. A blood sample was diluted 1:10,000 in phosphate buffered saline containing a 1:10 dilution of trypan blue (Dow Corning, Midland, Michigan) to stain cells with compromised cell membranes. Ten microliters of the resulting solution was then loaded into a

Hausser Scientific hemocytometer (Horsham, Pennsylvania). The erythrocytes were visually examined to ensure that their morphology was normal with that observed in vivo and to determine that cell fragments and trypan blue-stained cells are absent from the solution. Additionally, the blood was examined to determine if clots were present. Images were acquired using an Axiovert 200 inverted microscope (Zeis,Germany) and the accompanying AxioVision software.

Upon erythrocyte lysis, hemoglobin is released into the plasma; thus, hemoglobin can be used as an indirect measure of erythrocyte membrane integrity. In order to demonstrate that the flow apparatus does not cause damage to erythrocytes, the free hemoglobin concentration was measured via visible light spectroscopy using a SpectraMax microplate reader (Molecular

Devices, Sunnyvale, CA). An absorbance spectrum between 400 and 450nm on the blood samples revealed a globally strong, locally weak peak at 418nm with a strong linear concentration-dependent response. Thus, the 418nm wavelength was used for analyzing all samples. A paired two-tailed Student’s t-test was

used to determine if significant lyses occurred with a p-value of 0.05 considered to be significant.

Doppler Ultrasound Signal Processing

Software was developed to process the Doppler signal for mean and unsteady velocity using a fast Fourier transform (FFT), (Matlab, Mathworks,

Natick, MA). Mean velocity was obtained by averaging many power spectra taken over the three-second period [44]. A power spectrum was obtained for a bin of size 1024 points (corresponding to 4.095ms) and repeated to obtain 767 spectra over the three-second period. An average power spectrum was obtained by averaging the coefficients for each frequency separately. Frequencies with the largest powers (>85% of the maximum power) were averaged to estimate the dominant Doppler frequency. A digital high-pass filter removed frequencies below

1.2 Hz. The mean velocity was then computed using the well-known Doppler relationship seen below as Eqn. 4 [45-49].

Eqn. 4

Where

[ ]

The unsteady velocity was computed by segmenting the Doppler signal into bins of 2048 data points (8.19 ms). An overlap of 50% of each bin was used to provide a velocity value every 4.095 ms [48]. The dominant frequency was detected for each bin by applying a first moment to the FFT for frequencies with power > 15% of the maximum to reduce the effects of noise. A digital high-pass filter removed frequencies below 0.6Hz. The root mean squared (RMS) values were computed based on this velocity time trace.

CHAPTER III

III. RESULTS

Measurements of WG rheology showed it to have a Newtonian behavior for all shear rates while blood demonstrated shear thinning, non-Newtonian rheology. For blood, the average viscosity at high shear rate (400 s-1) was 3.73 ±

0.13 cP, and at lower shear rate (20 s-1), the average viscosity was 5.05 ± 0.35 cP. The shear thinning nature observed in all three blood samples was not monotonic and is not typical of whole blood. The average rheological measurements for each test fluid can be seen below in Figure 10.

Rheology 22 Newtonian 20 Blood

10 Viscosity [cP]

2 0 1 2 10 10 10 Shear Rate [1/s]

Figure 10: Average Rheology

Microscopy demonstrated the absence of both clotting and cell lysis as a result of the flow circuit. For blood sample 1, the RBCs had a normal biconcave morphology. There were no visible cell fragments. For the second blood sample, ~10% of the RBCs appeared to be dead both before and after the experiment. These cells were dark in color, and many lost their biconcave morphology. Representative blood micrographs from blood sample 1 can be seen in Figure 11.

Before Experiment After Experiment

Figure 11: Representative Blood Micrographs

Centerline fluctuating velocity as a function of both time and Re are shown in Figures 12, 13 and 14 for both WG and Blood. Fluctuating velocity was calculated by subtracting the mean velocity from the velocity time trace and non- dimensionalizing the quantity by the mean velocity (flow rate divided by cross- sectional area). A sharp increase in velocity fluctuations for WG can only be seen for sample 1 at Re ~250. For the other two samples, the largest velocity fluctuations occur at Re ~150-400. This is addressed in the limitations section and may be a result of poor signal quality. A sharp increase in velocity fluctuations for the blood samples can be seen at Re ~500, 350 and 400 for

Blood samples 1, 2 and 3, respectively.

Figure 12: Velocity Time Trace for BL and WG Sample 1.

Figure 13: Velocity Time Trace for BL and WG Sample 2.

Figure 14: Velocity Time Trace for BL and WG Sample 3.

Velocity profiles for each of the six experiments are shown in Figures 15,

16 and 17. Velocity profiles were created by averaging the velocity time traces

(three second velocity measurement) for each respective radial location. Each velocity profile was nondimentionalized by the average flow rate between the twenty-one separate radial positions for each of the respective Re. For each of

the three WG experiments, the profile became blunt (Re ~250) at a lower Re than that of the blood experiments (Re ~500-600, 300-350 and 450-500 for samples 1, 2 and 3, respectively). These results are consistent with the average velocity profiles (over three samples) for blood and WG (Figure 18), where WG velocity profiles shifted from parabolic to blunt at Re ~250 and blood at Re ~450.

The mean test fluid velocity profile is shown below in Figure 18. The Newtonain velocity profiles were not symmetric like the blood profiles, but rather were skewed in the same direction as the eccentricity in the stenosis geometry. In the spirit of full disclosure, the profiles for Blood sample 1 at Re = 400 and Blood sample 3 at Re = 100 were not removed, even though the data appears to be nonsensical.

Figure 15: Velocity Profiles for BL and WG Sample 1.

Figure 16: Velocity Profiles for BL and WG Sample 2.

Figure 17: Velocity Profiles for BL and WG sample 3

Figure 18: Mean velocity profiles

Velocity RMS as a function of Re and radial position are shown in Figure

19. A sharp increase in velocity RMS occurred at Re ~200 for WG sample 1.

For the other two WG samples, large RMS values occur at the range Re ~150-

500. Again, this is addressed further in the limitations section. A sharp increase in velocity RMS occurs at Re ~ 400, 350 and 400 for Blood samples 1, 2 and 3, respectively.

Figure 19: RMS Velocity as a Function of Re and Radial Position.

CHAPTER IV

IV. DISCUSSION

The relationship between hemodynamics forces and arterial pathogenesis has been studied through in vivo, in vitro and in silico studies. With the exception of studies previously mentioned, hemodynamic studies outside of a living body do not use whole blood and none have studied an anatomically relevant geometry. The majority of these studies have assumed that blood’s rheology is

Newtonian, citing predominant shear rates above 200s-1 where blood’s rheology is independent of shear rate. To investigate the impact of this assumption in the post-stenosic flow field of an eccentric stenosis (5% eccentric on the diameter and 84% reduction in lumen area), velocity profiles at thirteen Re have been measured across the diameter of a straight rigid pipe 11D downstream of the stenosis for both whole blood and a Newtonian analog under steady flow conditions. Considerable differences in mean and unsteady velocity were observed between the two test fluids at Re near TT. In contrast to these findings, striking similarities were found at large Re.

Two classical techniques were used to determine the critical Reynolds number for each test fluid: fluctuating velocity time trace and profile shape change. The unsteady velocity time traces can be seen in Figures 12, 13 and14.

For all radial positions, the sudden appearance of large instantaneous velocity

fluctuations at a given Re indicates vortical structures have formed and are propagating downstream beyond 11D. These vortical structures, which are indicative of transitional flow, break down the laminar stream lines. RMS velocity is a quantitative measure of the intensity of fluctuations over a period of time. A sharp increase in RMS velocity between two consecutive Re, at the same radial position, indicates an increase in velocity fluctuation, therefore TT (Figure 19).

For the Newtonian blood analog sample 1, this occurred at Re ~ 250 as opposed to blood which occurred at Re ~ 375-475, 300 and 400 for blood samples 1, 2 and 3, respectively. It is important to note that for blood sample 1 at Re = 350, large velocity fluctuations were only observed for a portion of the velocity flow

(near r =1 and -1 mm) and no fluctuations at the center (r = 0 mm). This indicates that the entire velocity profile did not transition to turbulence at the same Re.

Vorticies that form in the flow field redistribute the momentum by mixing the individual particles from separate laminar stream lines. Under turbulent flow conditions, the number of vorticies present in the flow field is so great that the entire flow field’s momentum is almost evenly distributed. This results in a blunt velocity profile, thus a velocity profile changing from parabolic to blunt is an indication that the fluid has transitioned from laminar flow (Figure 15-18).

Standard error of mean velocity (SEMV) is a quantitative method to determine the consistency of both the experiments and the velocity profile shape changes. SEMV was calculated for each test fluid between the three respective samples and can be seen below in Figure 24. The SEMV for blood in the laminar

regime (Re<350) is approximately 5%, with a notable exception at Re = 150.

The large SEMV for this Re is due to the deference in velocity profile shape for blood sample 3. Large SEMV typically over 10% can be seen for the beginning of the transitional regime (350

(Re>300). This indicates that poor velocity time traces for Newtonian samples 2 and 3 did not affect the overall mean velocity profile since the SEMV values are low. This also shows that the experimental setup (especially the strictness of the entry length pipe) did not change over the course of the six experiments since

Newtonian sample 1 was tested first, then the three blood samples followed by

Newtonian samples 2 and 3.

Figure 20: Percent Standard Error of Normalized Mean Velocity.

A summary of critical Re based on TT detection technique and test fluid type is given below in Table 1. All detection techniques show that the Newtonian analog transitioned to turbulence earlier than blood. Hematocrit, density and viscosity are also indicated for each respective experiment.

Table 1: Critical Re using different TT detection methods. Measurements of

density and viscosity are listed as before / after experiment.

Fluid HCT Density Viscosity CRN CRN CRN Sample [%] [g/cc] [cP] (Centerline) (Profile) (RMS) Newtonian - 1.10 / 1.10 3.52 / 3.64 ~250 ~200 - 250 ~200 1 Newtonian - 1.11 / 1.11 4.52 / 4.61 N/A ~200 - 250 N/A 2 Newtonian - 1.11 / 1.10 4.76 / 4.55 N/A ~200 - 250 N/A 3 Blood 53 1.04 / 1.04 4.48 / 4.26 ~500 ~ 500 - 600 ~375 - 475 1 Blood 43 1.03 / 1.03 4.12 / 3.29 ~350 ~ 300 ~300 2 Blood N/A 1.03 / 1.03 3.41 / 3.09 ~400 ~ 400 ~400 3

The results from Table 1 demonstrate that the Newtonian blood analog transitions to turbulence earlier than blood. Assuming a normal distribution, a one sample student t-test can test whether the true population of mean CRN of whole porcine blood is significantly larger than that of the Newtonian blood analog for both the Centerline and RMS methods. Again assuming a normal distribution, a two sample student t-test with unequal variances can test whether the true population mean CRN of whole porcine blood is significantly larger than that of the Newtonian blood analog for the profile method. The two sample student t-test cannot accommodate a range of CRN for a given observation; therefore, the average of each range was taken as a representative CRN. For all

Newtonian samples, the representative CRN detected by a change in velocity profile was 225. For blood sample 1, the representative CRN detected by a change in velocity profile was 550. The representative CRN detected by an increase in RMS velocity for blood sample 1 was 425.

Using the statistical methods described above, the true population mean

CRN of whole porcine blood detected by the centerline velocity time trace was significantly larger than the true population mean CRN of the Newtonian blood analog (p-value = 0.032). The true population mean CRN of whole porcine blood detected by the change in velocity profile was significantly larger than the true population mean CRN of the Newtonian blood analog (p-value = 0.059). The true population mean CRN of whole porcine blood detected by the change in

RMS velocity was significantly larger than the true population mean CRN of the

Newtonian blood analog (p-value = 0.022).

The absolute value of the percent velocity difference has been plotted in

Figure 25. Since the goal of this study is to access the impact of assuming whole blood to have a Newtonian rheology, these percent differences are taken with respect to the whole blood velocity. Hash marks in the figure denote a difference that is < 5% between the two test fluids. The sign of the difference is indicated by either an open or closed circle, where a positive difference is indicated by a closed circle and a negative difference is indicated by an open circle. The first two Re show a pattern of open and closed markers consistent with the

Newtonain velocity profiles being asymmetric and skewed in the direction of the stenosis eccentricity. This is consistent with the results in Figure 20. Differences as large as 30% can be seen in the range 250 ≤ Re ≤ 500. An example statistical analysis is provided for Re = 350 at the center of the pipe. Assuming a normal distribution, a two sample student t-test with unequal variances yielded a p-value of 0.018, indicating that the true population mean velocity for blood is

statistically significantly larger than the true population mean velocity of the

Newtonian blood analog for this given location. This range corresponds to the discrepancy in TT between the two test fluids. This discrepancy is negligible for

Re > 600, where both fluids have transitioned to turbulence. The difference between the mean velocity profiles for blood and WG is shown in Figure 23. This is the difference between the average values over three samples for each test fluid.

Figure 21: Mean Velocity Percent Difference between BL and WG.

Direct comparison between these results and the results presented by both Vargheese et al. and Ahmed & Giddens was not possible due to the differences in geometries, and the fact that DUS can not capture the actual velocity (see the Limitations section). Both research groups were able to visualize a larger region of the flow field downstream of the stenosis than that was possible in this study. Above the CRN, both studies observed laminar flow exiting the stenosis and then a rapid TT, although there is a discrepancy between the locations where this phenomena occurs. The results of this study suggest

that the CRN for whole blood is delayed compared to that of a Newtonian analog, but it is unknown whether or not blood transitioned from laminar flow downstream of the DUS measurement location (>11D). A second study is required in order to determine if the location of TT is also delayed in blood compared to that of WG.

Regardless, our results demonstrate that a Newtonian rheology assumption for whole blood down steam of a stenosis may not be appropriate for Re < 600.

These results would lead one to expect large discrepancies between the

Newtonian analog velocity profiles published by both Vargheese and Ahmed &

Giddens compared to that of whole blood. Due to the limitations of DUS, was is not possible to quantify these differences.

Limitations

The greatest limitation of this study was the fact that only one location downstream of the stenosis was observed. The addition of a second measurement location is not a trivial process, since a significant portion of the experimental setup would need to be torn down. This process typically took between one and two hours. This added time would easily exceed the maximum time any blood sample has stayed in the system without clotting.

Precise measurement of true velocity profiles was not required for this study since the results are based on comparison between the test fluids. Thus, a small systematic error in the DUS measurement was acceptable, provided it was consistent between all tests. Potential causes for this discrepancy are numerous and described below.

First, ultrasound requires reflectors to be suspended in the test fluid. For

WG, TiO2 particles (mean diameter 650nm) were used as reflectors. Whole blood did not require TiO2 since the RBCs act as excellent reflectors (mean diameter 6-8 μm). TiO2 particles produced a lower signal to noise ration than

RBCs, which resulted in a consistently larger RMS for the blood analog fluids in the laminar regime (Figure 15 and 16). The low signal to noise ratio is most likely due to use of lower sample volume concentration of TiO2 particles (87K) compared with RBCs (2.6 million) as well as less total reflective surface area of

TiO2 compare with RBCs. The concentration of TiO2 in the second and third WG samples was not sufficient to capture instantaneous velocities. Second, wall reflection noise restricted measurements 374μm from the far wall. Third, cylindrical DUS probe volume is relatively large (500 μm in diameter, 300 μm in length) and thus, velocity magnitudes are not precise (value obtained is a volumetric average). RMS velocity can be erroneously large due to velocity gradients. Fourth, the DUS process requires a finite time period (8.19 ms) to obtain frequency spectrum using FFT which restricts the size of the fluctuations that the probe can detect and effectively acts as a low pass filter. Thus, while

RMS velocities measured are representative of the velocity fluctuations in the flow, they do not capture all the frequencies with equal weighting. There can be errors in this method since unsteady laminar fluctuations can appear as RMS.

Thus, von Karman vortex shedding downstream of the stenosis could erroneously appear to be TT. This is not a major concern for this thesis since we are looking for the Re number where this begins. Finally, the DUS probe was

inside the pipe, downstream of the measurement region and the probe volume was four millimeters from the probe tip. The probe tip entered the flow field for velocity measurements near the far wall (r = 3.175 mm).

Rheological properties of whole blood are difficult to measure and the results for whole blood in this study varied between samples (Appendix A).

There was also variability within a given sample during the two-hour experiment

(Table 1). While significant efforts were made to insure blood rheology remained consistent throughout the experiment, the inherent difficulty of viscosity measurements at the relevant shear rates must be acknowledged. There was a large discrepancy between the viscosity measurements taken at 400s-1 before and after the experiment for blood sample 2. Before the experiment, the viscosity was measured as 4.12 cP and 3.50 cP. The second measurement was taken 20 min. after the experiment had already started. In the interest of minimizing the time blood circulated within the flow circuit, the first viscosity measurement was used to calculate Re. Two measurements were taken after the experiment had concluded and the values were 3.29 cP and 3.44 cP respectively, which imply that the first measurement of 4.12 cP was not correct.

This can be checked by assuming a normal distribution and conducting a one sample student t-test. There is a 99.3% probability that the one sample student t-test accurately predicted that the true viscosity population mean is not equal to

4.12 cP (p-value = 0.0076). Assuming that the true viscosity before the experiment was 3.50 cP, all of the reported Re in this particular blood experiment would increase by 18%. Even if the viscosity was chosen incorrectly, this fact

does not change the conclusions of this study, but rather would demonstrate a greater difference in TT between whole blood and a Newtonian analog. The shear thinning properties of the blood supplied by Animal Technologies in this experiment was not consistent with blood supplied in preliminary experiments. In the previous straight pipe study, the non-Newtonian, shear thinning blood rheology was in good agreement with published literature, but the whole blood used in this study did not exhibit a strictly monotonically shear-thinning nature

(Figure 23).

Measurements of pressure fluctuations were attempted in this system and found to be difficult because the magnitude is below that of many pressure sensors (~0.5 mmHg). Pressure fluctuations are expected to be of the order 10-1

mmHg based on an estimate of the fluctuating momentum

Approximately 10% of the RBCs were observed to be dead for both before and after experiment samples. Although the blood was purchased by the same company, presumably under similar conditions, RBC death before an experiment had never been observed before the eccentric stenosis. It is unclear exactly how the presence of the dead RBCs affected the results, but in all likelihood, this could be the reason why the whole blood rheology did not exhibit a strong shear thinning nature as it did in previous experiments, since dead RBCs do not form rouleaux.

The viscous dissipation alone was not sufficient to keep the blood temperature near 37 °C, so a heating coil was installed in the resoviour. In order

to heat the blood quickly, 52 °C water was passed through the heating coil. This raised the temperature of the outer surface of the coil to a level sufficient to denature the plasma proteins.

While the results herein are specifically for steady flow conditions, they are relevant since a quasi-steady assumption is sometimes reasonable for the diastolic phase. In addition, it is important to establish an understanding of the steady flow case before moving on to pulsatile flow which will have more variables such heart rate, peak Re, mean Re, and waveform shape.

CHAPTER V

V. CONCLUSION

The results presented here indicate that one should be cautious when choosing a blood analog for hemodynamic studies. A Newtonian blood analog may not be appropriate for post-steonotic flow fields, even though the shear rates are high. The velocity time trace results show that the minimum CRN for whole blood (CRN ~350-500) is considerably larger (>30-60%) than that observed for a

Newtonian fluid (~250) downstream of an eccentric stenosis under steady flow conditions. These results were confirmed by similar changes observed in the

RMS velocity, maximum velocity and mean velocity profile shape change.

Repeated measurements showed that the Newtonian analog transitioned to turbulence earlier than whole blood in each experiment. This study was limited to a single velocity profile and further studies should be conducted to examine the entire post-stenotic flow field. Further research is necessary to understand the importance of pulsatile flow and compliance.

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APPENDICES

APPENDIX A

APPENDIX A. SUPPLIMENTARY FIGURES

Rheology 7.5 Newtonian Sample 1 7 Newtonian Sample 2 Newtonian Sample 3 6.5

5.5

5 Viscosity [cP] 4.5

3.5

3 0 1 2 10 10 10 Shear Rate [1/s]

Figure 22: Newtonian Rheology

Rheology 35 Blood Sample 1 Blood Sample 2 30 Blood Sample 3

15 Viscosity [cP]

0 0 1 2 10 10 10 Shear Rate [1/s]

Figure 23: Whole Blood Rheology

Figure 24: Dead RBCs found in Blood Sample 2

APPENDIX B

APPENDIX B. RHEOLGY PROCEDURES

The following document contains detailed procedures on the operation of the AR 2000EX parallel plate rheometer (TA Instruments, New Castle, DE). The procedures listed below allow one to operate the rheometer safely and consistently. These steps ensure that each individual is following the same protocol, thus minimizing interoperator error. This following document was assembled with the help and hard work of Kenneth Smith.

System Startup

STEP 1 - Open the compressed air line by turning the yellow ball valve located on the far left wall.

Figure 25: Compressed Air Line Ball Valve.

STEP 2 – Check the pressure regulator located behind the Rheometer. To avoid damaging the bearing, do not remove locking cap if pressure is less than 30 PSI.

Figure 26: Air Filter and Pressure Regulator.

STEP 3 – Remove the black locking cap. This can be accomplished by gripping the cap securely with one hand and twisting the chrome knob counter clockwise.

Figure 27: Remove Black Bearing Lock Cap.

STEP 4 – Turn the Chiller on by flipping the toggle switch located on the back of the machine.

Figure 28: Peltier Plate Chiller and Power Switch.

STEP 5 – Place the solvent trap centering ring on the peltier plate.

Figure 29: Solvent Trap Centering Ring.

STEP 6 – Turn the Rheometer’s mainframe by flipping the black switch located on the back of the tower.

Figure 30: AR 2000 EX Mainframe.

STEP 7 – Launch the Rheology Advantage software bydouble click on the

Rheology Advantage icon shown.

Figure 31: Rheology Advantage Shortcut Icon. 65

Figure 32: Rheology Advantage Main Screen

System Calibration

STEP 8 – From the main tool bar, select Options, Instrument. Under the Inertia

Tab, click the Calibrate button then Next to calibrate the Instrument Inertia. The calibration process takes about 30 seconds to complete. When the system inertia has been calibrated, click Finish then Close. The system inertia only needs to be calibrated once a month.

Figure 33: System Inertia Calibration Dialog Box

Figure 34: System Inertia Values

Note – If the New Value is more than 10% different from the Previous Value do not run experiment since this indicates an internal component may have failed.

Call the Rheology Hotline at 302-427-4167.

STEP 9 – Attach the geometry (parallel or cone plate) by holding the plate steady and rotate the threads clockwise.

Figure 35: Parallel Plate.

STEP 10 – Click on the Plate Tab. In this instance, the tab is labeled 60mm

Acrylic Plate since this was the geometry used in the last experiment. Under the

Description Tab, set the Name to either 60mm Acrylic Plate or 60mm Aluminum

Plate depending on which of the two plates which are mounted to the

Rheometer. Change the Material to also reflect the mounted plate. Select the

Solvent trap check box if Solvent Trap will be used.

Figure 36: Plate Description Dialog Box

Click on the Dimensions Tab. Set the Dimensions to 6.0 cm and the Gap to the desired height. The Gap refers to the distance (in microns) between the two parallel plates. Note: The Gap size should be 10x the size of the largest particle suspended in the fluid.

Figure 37: Plate Dimensions Dialog Box

STEP 11 – Click on the Instrument Rotational Mapping Icon located on the left hand tool bar.

Figure 38: Rotational Mapping Icon

Select one of the following options for Bearing Mapping Type from the drop down menu: Fast [ ], Standard [ ], or Precision [ ]. Also select the

number of iterations the mapping should perform. Click Perform Mapping. Note:

Do not bump the work station while the system is performing mapping- this will skew experimental measurements.

Figure 39: Rotational Mapping Dialog Box.

STEP 12 – To Calibrate the Bearing Friction click Options, Instruments. Under the Miscellaneous Tab click Calibrate next to Bearing Friction, and then click

Next. After Calibration is complete, click Apply then Ok.

Figure 40: Instrument Options Dialog Box.

STEP 13 – Set the temperature at which the experiment will be run by double clicking anywhere within the Temperature parameter row on the main screen.

Set the new desired temperature value, and then click Send.

Figure 41: Temperature Parameter Row.

STEP 14 –Click on the Zero Gap Icon located on the left hand side tool bar.

Using the Down Arrow, position the parallel plates approximately 1cm apart, then click Continue.

Figure 42: Zero Gap Icon.

Figure 43: Zero Gap Dialog Box.

STEP 15 – Using a pipette, fill the solvent well (located on the top of the attached geometry) 50% with Cannon S3. This will require approximately 300µL of fluid.

Figure 44: Pipette Filling Solvent Well.

STEP 16 – Click on the Geometry Button located in the main tool bar and select the Settings Tab. Set the Back Off Distance to 45,000 microns. The Back off

Distance is the distance between the two parallel plates used when preparing the experiment. From this dialog box calibrate the Geometry Inertia. To do this click the Calibrate button, then Next. Note: This calibration is only required once a month or if the parallel plate is exchanged for different geometry.

Figure 45: Geometry Settings Dialog Box.

STEP 17 – The rheometer’s accuracy should be checked using the same cannon viscosity standard. If the error is less than 3%, then skip STEPS 18 and 19.

STEP 18 – To calibrate the temperature of the peltier plate, select Options then

Instrument from the main tool bar. Under the Miscellaneous Tab, set the Span and Offset values to 1 and zero respectively. Click on the set gap button located on the left hand tool bar, set the gap to 5000 microns. Center the last inch of the

QTI USB Thermistor on the peltier plate being conscious not to touch the attached geometry. Using capillary action, fill the empty space between the geometry and the peltier plate with tap water. Replace water lost to evaporation regularly.

Figure 46: Thermistor Centered between Parallel Plates.

Set the required temperature of the peltier plate to 35C by double clicking anywhere on the temperature line on the main screen, typing 35 into the dialog box and click send. Start usbTemperatureCode.M. This code will run until the temperature has converged to within 0.1C. Repeat this process for 37C and

40C.

The actual temperature is defined as the measured temperature of the thermistor. Using Excel, plot the required temperature vs. actual temperature.

Apply a linear curve fit to the data. The Span and Offset are defined by

and , where variables m and b are found using the linear curve fit

is . From the main tool bar, select Options then Instrument. Under the Miscellaneous Tab and update the Span and Offset values.

An example of this can be seen below. and .

42.5

C) 40.5 °

( y = 0.8806x + 3.4888 38.5 R² = 0.9997

36.5

34.5

Actual Temperature Actual Temperature 32.5 34 35 36 37 38 39 40 41 42 43 44 Required Temperature (°C)

Figure 47: Representative Temperature Calibration Plot

The actual temperature should be rechecked for the temperature limits (35 and

40C) to verify the calibration. If the calibration does not match, repeat the above process with a smaller range of temperatures.

STEP 19 – The rheometer’s accuracy should be checked again using the same cannon viscosity standard.

Initialize Experiment Procedures

STEP 20 – Click on the Testing Protocol Button located at the top of the main screen, then select the Experimental Initial Condition Step. Changing the Initial

Temperature dialog box will automatically change the Temperature for all experimental steps except Post-Experiment Step. Ensure that the Set temperature , Wait for correct temperature and Perform equilibrium check boxes are selected. The equilibrium duration should be set to 2 minutes. These settings are automatically saved, and will display the previous tests settings.

Figure 48: Test Protocol Main Screen.

STEP 21 – Click on each of the Experiment steps and check that the Test Type is set to Stepped Flow, Ramp is Shear rate (1/sec), Mode is Linear, the Wait check box next to Temperate is selected, Constant Time is set to 25 seconds and Average last x seconds is set to 5 seconds. Do not change the range of shear rate samples or the number of sample points.

Figure 49: Experimental Steps Setup.

STEP 22 – Set the Post-Experiment Temperature to same value as used in the previous steps.

Figure 50: Post Experimental Step Settings.

Start Experiment

STEP 23 – Click on the Go to Geometry Gap button located on the left hand side tool bar. Load the test fluid using a pipette and capillary action. Note: 1500 µL

(750 µL x2) of the test fluid is required for a 60mm parallel plate with a 500µm gap. If using a different geometry or different gap size reference Calibration

STEP 9 for the approximate required fluid volume.

Figure 51: Go to Geometry Gap Icon

Figure 52: Load Test Fluid between Parallel Plates using the Pipette.

STEP 24 – To control and delay the evaporation of your solution during the experiment, put the solvent trap cover on the plate.

Figure 53: Solvent Trap enclosing Parallel Plate.

STEP 25 – Click the Run Experiment Button located in the main tool bar at the top of the screen.

Figure 54: Run Experiment Icon

STEP 26 – The Experiment run information dialog box will appear on the screen.

Change the sample name to reflect the current fluid being tested, today’s date and the current number of times this particular sample had been tested today.

Format the file name by SAMPLEFLUID_DAY-MONTH-YEAR_RUN #. Copy the sample name and paste it in the line designated file name. Click on the Browse directory button.

Figure 55: Experiment Run Information Dialog Box

STEP 27 – Select the appropriate directory for the current sample fluid by simply clicking on the folder icon. Select OK when complete.

Figure 56: Results Directory Dialog Box

STEP 28 –Enter your name on the Operator line. Note that the sample density can be updated, but it will not have any bearing on the accuracy of the measurement. Fill out a few notes in the Experimental Notes section. It is good practice to include the sample fluid, why the test is being run, the geometry type, test type and range of shear rates.

Figure 57: Update Experimental Notes Field

APPENDIX C

APPENDIX C. RHEOLOGY VALIDATION

Motivation The goal of this work is to verify the accuracy of AR 2000Ex rheometer.

Accurate rheological measurements are required in order to find the critical

Reynolds’s number of transition to turbulence for non-Newtonian fluids. For this reason, the machine must stay calibrated, not just at a single point in time, but over an extended period of time. We seek to limit the maximum error to within

3% over the course of two and half hours, the maximum time a transition to turbulence study can last before clots begin to form.

Experimental Methods

Start Up

1. Open the yellow ball valve on the far left wall. To avoid damaging the air bearing, do not operate the rheometer if the pressure regulator is reading less than 25 PSI. If the pressure is less than this value, shut rheometer down to avoid damaging the air bearing.

2. Remove the black locking cap by twisting the chrome knob counter clockwise.

3. Turn on chiller by toggling the rocker switch located on the bottom of the rear panel. Periodically check the pump by removing the clear plastic cap and placing a finger over the brown pipe. Pressure build up behind finger indicates that the pump is working, and that the peltier plate is receiving sufficient water.

4. Turn on the rheometer’s mainframe by toggling the rocker switch located on the back panel next to the power chord. Allow 15 seconds for boot up.

5. Launch the Rheology Advantage software. Click on the AR 2000EX tab to check that the rheometer is communicating with the mainframe. If the software is booted up before the mainframe is turned on, it is possible that COM port will not be available. Simply restart the software.

6. Click on the Geometry Tab located next to the AR-2000EX tab and select

Description. Select the box marked Solvent Trap if the test fluid is prone to evaporation. Under the Description and Dimensions tabs, check to see if the current geometry described in the dialog boxes matches the attached geometry.

If this is not the case, select Geometry from the main tool bar and select the appropriate geometry from the list.

Calibration

The calibration procedures are laid out in the following section.

Calibration is required before every experiment. An additional calibration may be required if there is any doubt on the rheological measurement.

Loading Sample Fluid

7. Click the Go to Geometry Gap icon located on the left hand tool bar. Load

1500µL of sample fluid, between the attached geometry and the peltier plate via capillary action. As a rule of thumb, place the pipette a few millimeters from the geometry, at a 45 degree angle. Load slowly to ensure no air is trapped in the gap. Excess fluid will escape from between the geometry and the peltier plate.

Remove excess fluid with paper towels. Ideally the meniscus should be slightly convex, but this is not possible low surface tension fluids. In this instance, minimize the amount of excess fluid that is touching the peltier plate.

Test Methods

8. Click on the Procedure Tab located next to the Geometry Tab. Select the appropriate experimental steps that correspond to stepped flow for shear rates ranging between 1 and 500 1/s. These steps have been set to hold a shear rate constant for 20 seconds, minimizing the errors introduced by inertia. The rheometer will then record 5 seconds of data and report the average. Allow the peltier plate a minimum of two minutes to bring the sample fluid the required temperature.

9. Attach the solvent trap if measuring a fluid prone to evaporation.

10. Start the experiment by selecting the green play button, located under the main tool bar. An experiment can be aborted at any time by clicking the black stop button to the right of the launch button.

Removing sample fluid

11. Sample fluid should be wicked away using an absorbent paper towel.

Both the attached geometry and the peltier plate should first be gently wiped down with a dry paper towel, wiped down with a slightly damp paper towel, then with a small amount of isopropyl alcohol. Do not reload sample until the alcohol has had sufficient time to evaporate. Recheck the bearing friction and geometry inertia to insure that the machine was not thrown out of calibration.

Calibration

System Inertia

From the main tool bar, select Options then Instrument. Under the Inertia

Tab, click the Calibrate button then Next to calibrate the Instrument Inertia. The system inertia calibration takes 30 seconds to complete. When the system inertia has been calibrated, click Finish then Close. TA Instruments recommends that this only be checked once a month, but it should be checked before every experiment. Note – If the New Value is more than 10% different from the previous value do not run experiment. This indicates an internal component may have failed. Call the Rheology Hotline at 302-427-4167.

Rotational Mapping

Attach Geometry. Select the Geometry tab from the main tool bar and select the attached plate. Click on the Instrument Rotational Mapping Icon located on the left hand tool bar. TA instruments recommends Standard Bearing mapping type for 1 iteration, but for experiments, select Precision Bearing mapping type for 2 iterations. Click on the Perform Mapping button located at the bottom of the dialog box. Note: Do not bump the work station while the system is performing mapping- this will skew experimental measurements.

Bearing Friction

To Calibrate the Bearing Friction click Options, Instruments. Under the

Miscellaneous Tab click Calibrate next to Bearing Friction, and then click Next.

After Calibration is complete, click Apply then Ok.

Zero Gap

Click on the Zero Gap Icon located on the left hand side tool bar. Using the Down Arrow, positioning the parallel plates approximately 1cm apart, then click Continue. Click Yes when prompted to raise the plate to the back off distance.

Geometry Inertia

Click on the View Geometry button, select the Settings Tab. Click on the Calibrate button next to the Geometry Inertia line. Click Next and Finish. TA

Instruments recommends that this only be checked once a month, but it should be checked before every experiment.

TA Instruments recommends that this be checked every time a new geometry is attached.

Verifying Calibration

The above steps are required for every experiment. Due to the significant time required to calibrate the temperature, the rheometer’s accuracy is checked by measuring the viscosity of a cannon viscosity standard. If the error is less than 3%, skip the following Temperature calibration step.

Temperature

From the main tool bar, select Options then Instrument. Under the

Miscellaneous Tab, set the Span and Offset values to 1 and zero respectively.

Click on the set gap button located on the left hand tool bar, set the gap to 5000 microns. Center the last inch of the QTI USB Thermistor on the peltier plate being conscious not to touch the attached geometry. Using capillary action, fill the empty space between the geometry and the peltier plate with tap water.

Replace water lost to evaporation regularly. Set the required temperature of the peltier plate to 35C by double clicking anywhere on the temperature line on the main screen, typing 35 into the dialog box and click send. Start the usbTemperatureCode.M. This will record the temperature every second for 10 seconds and compute the average. It will record an additional 10 seconds of

data and compute a second average. If the difference between these 2 averages is equal to or less than 0.1C, the code will stop and will print the average. If the difference between the two averages is greater than 0.1C, the code will repeat the above steps until the average temperatures have converged. Repeat this process for 37C and 40C.

The actual temperature is defined as the measured temperature of the thermistor. Using Excel, plot the required temperature vs. actual temperature.

Apply a linear curve fit to the data. The Span and Offset are defined by

and , where variables m and b are found using the linear curve fit

is . From the main tool bar, select Options then Instrument. Under the Miscellaneous Tab and update the Span and Offset values. The actual temperature should be rechecked for the temperature limits (35 and 40C) to verify the calibration. If the calibration does not match, repeat the above process with a smaller range of temperatures.

The rheometer’s accuracy should again be checked using the same cannon viscosity standard.

Validation

As stated previously, we seek to verify the accuracy of the rheometer. To accomplish this, the calibration must be checked, not just for one time, but over an extended period of time; therefore we have conducted a few calibration tests.

These calibration tests utilized the protocol that was laid out in the previous sections.

Calibration Test #1 – Temperature Calibration Drift

This test was conducted to determine the accuracy of viscosity measurements without recalibrating the temperature of the peltier plate. On 05-

12-2014, the rheometer was calibrated (both for torque and temperature). The accuracy of the machine was checked using the Cannon viscosity standard

(CVS) N7.5 at 40°C. Of the possible standards to choose from, Cannon N26 allows us to check viscosities that are larger than blood at 1/s and Cannon S3a allows us to test viscosities lower than that of blood at 500 1/s. Cannon N7.5 was chosen simply because 5.906 cP it is not an extreme value and was measured at 40°C since this is yields the lowest viscosity within our temperature range. This same process was repeated on 05-15-2014, except the temperature was not calibrated. This data is shown below in Figure 58.

Figure 1 - Temperature Calibration Drift 6.3 CVS N7.5 - 5/12/2014 6.25 CVS N7.5 - 5/15/2014 Reported Viscosity Standard 6.2

6.15

6.1

6.05 Viscosity [cP] 6

5.95

5.9

5.85 0 1 2 3 10 10 10 10 Shear Rate [1/s]

Figure 58: Temperature Drift.

The Animal 6 rheology measurements showed that blood has a viscosity of 6 cP between 20 and 30 1/s. The rheometer had a max error of 2.95% between 20 and 30 1/s, which is just inside our target error window of 3%. The absolute value of percent error was calculated for each shear rate and was plotted below in Figure 59.

Figure 2 - Temperature Calibration Drift Error 6 CVS N7.5 - 5/12/2014 CVS N7.5 - 5/15/2014 5

3 Error [%]Error

0 0 1 2 3 10 10 10 10 Shear Rate [1/s]

Figure 59: Temperature Drift Error.

This indicates that the three day old temperature calibration was still valid, since 0.1% error is within our desired window of 3%. It is important to note that errors in Measurement 1 below 20 1/s are above the 3% threshold. This does not raise concern since we do not expect blood to exhibit an apparent viscosity of

6 cp at these shear rates. This specific concern is addressed in the final calibration test.

Calibration Test #2 – Temperature Control and Variation

The largest source of error recently has been the temperature of the peltier plate. To investigate the consistency of the peltier plate, the QTI

thermistor continuously measured temperature over the course of two and a half hours. A temperature of 10°C was chosen to minimize water loss due to evaporation. This data can be seen below in Figure 60.

Figure 3 - Temperature Variation over Time 9.9

9.8 Added 23°C Water

9.7

9.6 Temperature [C] Temperature 9.5

9.4

9.3 0 1000 2000 3000 4000 5000 6000 7000 8000 Time [s]

Figure 60: Peltier Plate Temperature Variation over Time

Over this period of time, the peltier plate held a constant temperature of 9.4 ±

0.05°C. This indicates that the peltier plate is capable of maintain a constant temperature for over two and a half hours, the maximum length of a blood experiment.

Note: the procedure for this experiment was identical to the calibration procedures explained in the above section with the exception that the geometry was pulled back to the back off distance. The upper portion of the thermistor and water were exposed to 23C ambient air. This does not invalidate the results, but rather is a worst case situation compared to an actual experiment. We do not need to conduct this experiment again since a tolerance of ± 0.05°C is sufficient for our measurements.

Calibration Test #3– Viscosity Drift

We have demonstrated that the peltier plate can maintain a constant temperature for an extended period of time, but this does ensure we will necessarily have accurate rheological measurements, since this is not the sole source of errors. To address this, we measured the viscosity of the Cannon viscosity standard N7.5 over the course of two and half hours, the maximum length of time a blood test would last. This data is shown below in Figure 61.

Figure 4 - Viscosity Drift over 1st Hour 6.4 0-30 min 30-60 min 6.3 Exact Visocisty

6.2

6.1

6 Viscosity [cP]

5.9

5.8

5.7 0 50 100 150 200 250 300 350 400 450 500 Shear Rate [1/s]

Figure 61: Viscosity Drift over First Hour

The absolute values of the errors were calculated for each shear rate viscosity pairs and are shown below in Figure 62 and 63. Note that errors above

20 1/s are all within the target window of 3%.

Figure 5 - Viscosity Drift over 1st Hour 6 0-30 min 30-60 min 5

3 Error [%]Error

0 0 50 100 150 200 250 300 350 400 450 500 Shear Rate [1/s]

Figure 62: Viscosity Drift Error over First Hour

100

Figure 6 - Viscosity Drift over Last Hour and a Half 6.08

6.06

6.04

6.02

5.98

Continous Measurement Viscosity [cP] Exact Viscosity 5.96

5.94

5.92

5.9 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time [s]

Figure 63: Viscosity Drift over Last Hour and a Half

On average over the hour and a half, the rheometer measured a viscosity that was 2.2% above the reported value by the Cannon viscosity standard of

5.906 cP. The measurements drifted a maximum of ± 0.7% over this time. The absolute error was calculated for each data point, and can be shown below in

Figure 64.

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Figure 7 - Viscosity Drift Error over Last Hour and a Half 2.8 Continous Measurement

2.6

2.4

2.2

Error [%]Error 2

1.8

1.6

1.4 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time [s]

Figure 64: Viscosity Drift Error over Last Hour and a Half

These three measurements demonstrate that the pre-experiment calibration can hold for a minimum of two and a half hours, since the maximum error did not exceed 3%. We should not expect to need to calibrate the AR

2000EX in the middle of transition to turbulence study, but it can be done if the need should arise.

Calibration Test #4 – Expected Errors for Blood Rheology

To fully characterize how well the AR 2000EX measures viscosity over the shear rates and viscosity we expect blood to experience, we measured 4 viscosity standards at a variety of temperatures to produce 12 different known

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viscosities. The exact viscosities are listed below in Table 2 by temperature and viscosity standard.

Table 2: Viscosity standards reported viscosities [cP]

Temperature [C] Viscosity Standard 20 25 37.8 40 Cannon N26 49.37 38.97 22.74 20.88 Cannon N7.5 11.39 9.505 6.303 5.906 Brookfield Fluid 5 - 4.7 - - Cannon S3a 4.045 3.533 2.605 -

The absolute value of error was calculated for each viscosity - shear rate pair.

The results are shown in the contour plot below in Figure 65. The highest error is greater than 7%, but these large errors occur at shear rate – viscosity pairs that we do not expect blood to experience. The average blood rheological measurements from all three blood experiments are plotted on top of the errors.

Using Animal 6 data, we can approximate the error blood would experience at each shear rate.

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This test has shown that we can expect blood rheology measurements to have less than 3% error for shear rates of 2-80 1/s and less than 3.5 % for shear rates 200-500. Although the high shear rate errors fall outside the target error window, an error of 3.5% should not stop us from moving forward with transition to turbulence studies.

Figure 8 - Expected Error for Blood Experiments

Percent Error 7 Blood Experiment 1 Average Rheology Blood Experiment 2 Average Rheology 6 Blood Experiment 3 Average Rheology

1 10

3 Viscosity [cP] Standard 2

0 1 2 10 10 10 Shear Rate [1/s]

Figure 65: Expected percent Error for Blood Rheology

In conclusion, we have shown that the calibration protocol for the AR

2000EX rheometer can minimize errors in rheological measurements. These

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experiments have shown that this protocol can limit the error at the beginning of the experiment to within 3.5%. We have identified that the rheometer can introduces an unsteady error ± 0.7% and human error introduced through loading the sample fluid is approximately 3%.

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APPENDIX D

APPENDIX D. CURRICULUM VITAE

NAME David M. Casey

EDUCATION Master of Science, Mechanical Engineering The University of Akron, December 2014

Bachelor of Science, Biomedical Engineering Double Major in Applied Mathematics The University of Akron, August 2012

WOEK The University of Akron, Mechanical Engineering Department EXPERIENCE Teaching Assistant, August 2012 – December 2014

DePuy Orthopaedics, Hips New Product Development Co-Op, January 2010 – August 2011

Kinetek Controls, Perry, Oh, Electrical Engineering Technician, May 2006 – August 2008

RESEARCH Biofluids Lab, Akron, Oh, May 2013 – December 2014

MASTERS D. M. Casey, B. S., “Characterization of Transition to THESIS Turbulence for Blood in an Eccentric Stenosis under Steady Flow Conditions,” Department of Mechanical Engineering, The University of Akron, Akron, Oh, December 2014.

PEER Dipankar Biswas, David Casey, Douglas C. Crowder, David A. REVIEWED Steinman, Yang H. Yun, Francis Loth (2014) Characterization JOURNAL of Transition to Turbulence for Blood in a Straight Pipe under Steady Flow Conditions Journal of Biomechanical Engineering December, 2014.

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POSTERS Casey D, Martin B, Bateman G, Pahlavian S, Shaffer N, Smith K and Loth F (2014). Numerical Simulation of Superior Sagittal Sinus Hemodynamics. World Congress of Biomechanics, Boston MA.

Casey D, Biswas D, Smith K, Crowder D, Yun Y, Loth F (2014). Importance of Temperature on the Rheological Properties of Blood. 2014 Midwest ASB Regional Meeting, Akron OH.

TEACHING Kinematics of Machines, System Dynamics & Response, Thermal Science and Mechanical Engineering lab.

PATENT J. Grostefon, D. Casey, Co-author of an orthopedic implant patent, DePuy Orthopaedics, Fall 2011. Patent pending.

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