TRANSITION TO TURBULENCE IN NON-NEWTONIAN FLUIDS: AN IN-VITRO STUDY USING PULSED DOPPLER ULTRASOUND FOR BIOLOGICAL FLOWS

Dissertation Presented to The Graduate Faculty of The University of Akron

In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

Dipankar Biswas December, 2014 TRANSITION TO TURBULENCE IN NON-NEWTONIAN FLUIDS: AN IN-VITRO STUDY USING PULSED DOPPLER ULTRASOUND FOR BIOLOGICAL FLOWS

Dipankar Biswas

Dissertation

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 Vice Provost Dr. Abhilash Chandy Dr. Rex D. Ramsier

______Committee Member Date: Dr. Alex Povitsky

______Committee Member Dr. Peter H. Niewiarowski

ii ABSTRACT

Blood is a complex fluid and has been established to behave as a shear thinning non-Newtonian fluid when exposed to low shear rates (<200s-1). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high shear rates. Shear thinning fluids have been shown to exhibit differences in transition to turbulence compared to that of

Newtonian fluids. Incorrect assumption of the transition point in a simulation could result in erroneous prediction of hemodynamic forces. The goal of the present study was to compare velocity profiles near transition to turbulence of whole blood and standard blood analogs in a straight rigid pipe and an S-shaped pipe under a range of steady flow conditions. Reynolds number for blood was defined based on the viscosity at a shear rate of 400s-1. The rheometer was calibrated at shear rates of interest using Newtonian viscosity standards. Doppler ultrasound was used to measure velocity profiles of whole porcine blood and a Newtonian fluid in an in vitro experiment at 18 different Reynolds numbers ranging from 750 to 3500

(straight pipe) and 21 different Reynolds numbers ranging from 500 to 2800 (S- shaped pipe). Three samples of each fluid were examined and fluid rheology was measured before and after each experiment. Straight pipe results show parabolic

iii velocity profiles for both whole blood and the Newtonian fluid at Reynolds numbers less than 2100 (based on high shear rate viscosity). The Newtonian fluid had blunt velocity profiles with large velocity fluctuations (root mean square as high as 18%) starting at Reynolds numbers ~2100-2300 which indicated transition to turbulence.

In contrast, whole blood did not transition to turbulence until a Reynolds number of ~2500-2700. This delay was consistent for all three samples. For Reynolds numbers larger than 2100, the delay in transition resulted in differences in velocity profiles between the two fluids as high as 20%. A Newtonian assumption for blood at flow conditions near transition can lead to large errors in velocity prediction for steady flow in a straight pipe. For the S-shaped pipe geometry, the RMS velocity results show that the minimum Re where transition initiated for whole blood

(~1000-1200) is slightly larger (>10%) than that observed for a Newtonian fluid

(~900-1000) under steady flow conditions. Repeated measurements show these results to be consistent for three different samples. These results show large differences in the magnitude of mean and fluctuation velocity between whole blood and a Newtonian fluid for Re>1000. Further research is necessary to understand this relation in more complex geometries and under pulsatile flow conditions.

iv

DEDICATION

This dissertation is dedicated to my dad: Dilip Kumar Biswas

And to my mom: Malati Biswas

You have made this possible with your everlasting love, support, sacrifice and

encouragement.

v ACKNOWLEDGEMENTS

This work would not have been completed without the support, assistance, guidance and advice of a lot of people; all of who have in someway shaped my thoughts towards research, science and life in general. First, I must thank my advisor and mentor Dr. Francis Loth who has supported, guided and motivated me at every stage of my research career and gave me the opportunity to get started with research in the field of biofluids.

I would like to also acknowledge Drs. David Smith and Sang-Wook Lee for their research findings that motivated this research, David M. Casey, Narender Ambati and Ian Key for their contribution in building the experimental setup, Kenneth W.

Smith Jr. avd Kevin Razavet for their help in running the experiments, Drs. Stanley

Rittgers and Stephen Jones for their invaluable suggestions on the experimental procedure and processing, Richard Nemer for his support in acquiring some instrumentation, Dale Ertley for his help in the design and construction of the experiment system and, Walid Qaqish and Douglas C. Crowder for their help with blood analysis. Finally, I thank Dr. Paul Fischer for his invaluable discussion over many years, which helped craft the overall design of this experiment.

vi TABLE OF CONTENTS

Page

LIST OF TABLES ...... x

LIST OF FIGURES ...... xi

CHAPTER

I. INTRODUCTION AND BACKGROUND ...... 1

II. LITERATURE REVIEW ...... 7

2.1 Hemodynamics and morphogenesis ...... 7

2.2 Ultrasound and velocity measurement ...... 9

2.3 Recr in non-Newtonian fluids ...... 9

2.4 Recr and velocity profile in blood ...... 10

2.5 Recr in S-shaped pipe ...... 13

2.6 Rheology of blood ...... 14

2.7 Temperature dependence of viscosity of Newtonian fluids ...... 16

III. PROPOSED STUDIES ...... 17

IV. METHODS ...... 20

4.1 Design of In Vitro Hemodynamics System (Straight Pipe) ...... 20

4.2 Design of In Vitro Hemodynamics System (S-Shaped Pipe) ...... 25

4.3 Viscosity Measurement ...... 26

4.4 Data acquisition and processing...... 29

4.5 Importance of Quadrature Signal ...... 37

vii 4.6 Voltage and Temperature Gradient Calibration ...... 38

4.7 Ultrasound Probe Range and Rotational Orientation ...... 40

4.8 Temperature Control ...... 42

4.9 Red Blood Cell Evaluation ...... 44

4.10 Statistics ...... 44

V. RESULTS (STRAIGHT PIPE) ...... 46

5.1 Results Overview ...... 46

5.2 Microscopy ...... 46

5.3 Rheology ...... 48

5.4 Transition to Turbulence ...... 49

VI. RESULTS (S-SHAPED PIPE) ...... 70

6.1 Results Overview ...... 70

6.2 Rheology ...... 71

6.3 Transition to Turbulence ...... 72

VII. DISCUSSION ...... 85

7.1 Overview ...... 85

7.2 Straight Pipe ...... 85

7.3 S-Shaped Pipe ...... 90

7.4 Overall Discussion ...... 93

VIII. LIMITATIONS ...... 95

8.1 Straight Pipe ...... 96

8.2 S-Shaped Pipe ...... 98

IX. CONCLUSION ...... 100

REFERENCES ...... 102

viii APPENDICES ...... 111

APPENDIX A. DATA ACQUISITION AND PROCESSING MATLAB CODE ...... 112

APPENDIX B. PolyImPro ...... 117

APPENDIX C. MGPtracker ...... 144

APPENDIX D. TRANSITION TO TURBULENCE IN ACCELERATING AND DECELERATING UNSTEADY FLOW ...... 155

APPENDIX E. CURRICULUM VITAE ...... 158

ix LIST OF TABLES

Table Page

1 Critical Reynolds number for transition to turbulence in three different fluids [39]...... 10

2 Critical Reynolds number for transition to turbulence for water flowing through different geometries [10]...... 14

3 Average viscosity for four test fluids. Blood and WG averaged before and after experiments and also between samples. WGXH and WGXL are the averages of before and after experiment only...... 49

4 Parameters and critical Re of TT for each test fluid. Density and viscosity are before/after experiment (note: viscosity is 400 s-1 for blood and 1100 s-1 for WGX)...... 62

5 Average viscosity of blood and WG averaged before and after experiment and also between samples...... 72

6 Parameters and critical Re of TT for each test fluid. Density and viscosity are before/after experiment (note: viscosity is 400 s-1 for blood)...... 81

7 NASCET scores, and volumes of plaque (total and calcium) of asymptomatic and symptomatic patients (eight each)...... 123

x LIST OF FIGURES

Figure Page

1 Comparison of centerline velocities for a range of Reynolds numbers obtained by Ferrari et al. against Poiseuille values for five different size straight pipes. ‘Peak-th’ is data for peak velocity calculated using Poiseuille equation (number indicates pipe diameter in mm), and ‘APV’ is the measured peak velocity [35]...... 12

2 Viscosity with respect to shear rate from various literatures. At a shear rate value of 10 s-1 the viscosity value is measured as 10.6 cP and at 100 s-1 as 4.6 cP and asymptotically comes down to around 3.5 cP as shear rate increases. But viscosity was observed to go up with shear rate beyond 631 s-1...... 15

3 The three geometries proposed to be examined in this study, (a) straight pipe, and (b) S-shaped pipe. Dotted line represents approximate path of Doppler ultrasound velocity measurement...... 18

4 Schematic of the straight pipe flow system...... 21

5 Mold (left) for sylgard model (right) that serves as an ultrasound probe access port of the blood flow pipe...... 21

6 Aluminum guardrail that acts as a support as well as coarse positioning of stage and flow section...... 22

7 Motorized linear stage (left), and custom probe holder (right)...... 22

8 Positioned probe (left), and incubator (right)...... 22

9 Condenser coil...... 23

10 Plexiglass tray to prevent spillage...... 23

11 Turbulator, constructed using monofilament string glued to a butyrate pipe...... 24

12 MBruler to measure angle of probe with respect to flow...... 25

xi 13 S-shaped pipe geometry...... 25

14 Minimum viscosities with respect to shear rates for Brookfields LVDV III UCP, LVT and TA Instruments AR2000EX viscometers and viscosities of blood as measured at TA Instruments laboratory...... 27

15 Snapshot of website used to calculate percentage of glycerin required to obtain a set viscosity at a set temperature...... 29

16 Data acquisition and processing flowchart...... 31

17 Schematic diagram of a pulsed Doppler instrument. The solid lines indicate the in-phase signal path and the dashed lines indicate the out-of-phase signal needed for the quadrature output...... 33

18 Doppler shifted frequency signal (left) and zoomed view (right). Note that this is an example and the data rate is different than what was used...... 34

19 Aliasing causing false frequency...... 35

20 Description of the difficulties of US with large probe volume to capture velocity fluctuations form different size vortices...... 36

21 Difference in centerline velocities with and without using the quadrature signals. If only the real part of the signal (single channel) is used the measured frequency aliases about the Nyquist frequency (PRF/2)...... 38

22 Calibrate voltage applied to pump power supply versus Reynolds number (flowrate). The flowrate varies linearly with voltage. The diamond represents the voltage applied at a particular run during the experiment to obtain flowrate corresponding to a set Reynolds number (Re = 750 in this case)...... 39

23 Map temperature gradient versus Reynolds number. It determines if a particular Reynolds number is heating (positive gradient) or cooling (negative gradient) and at what rate...... 40

24 Velocity profiles (9 points) measured at different range settings (focal lengths) between 2 and 10 mm...... 41

xii 25 Velocity profiles (21 points) measured at different range settings (focal lengths) between 4 and 6 mm...... 41

26 Rotational asymmetry of the Doppler ultrasound probe. One probe had a maximum difference of ~2% while the other one presented a maximum difference of ~51%. Probe 2 was used to measure velocities in blood and WG while probe 1 was used to measure velocities in WGX...... 42

27 Temperatures during data acquisition. The bands represent post- processing in between two Re measurements. The post- processing time increases with time (clogging up of the RAM might be a probable reason)...... 43

28 Representative micrographs of blood before (left) and after experiment (right). Images show that erythrocytes retain their physiological toroid morphology shape before and after the velocity experiment. Cell fragments are not visible indicating that cells were not mechanically or osmotically lysed during the experiment. No large change in the number of cells was observed also indicating that cells were not lysed. Additionally, large three- dimensional amorphous clusters of cells linked by dense fibrous masses were not observed, indicating that the blood did not clot during the velocity experiments...... 47

29 Viscosity of blood, water-glycerin (WG) and water-glycerin- xanthan gum (WGX) versus shear rate averaged for three samples (before, during and after experiment). AR200ex, the air bearing parallel plate rheometer shown in inset...... 48

30 Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 1. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at the expected Reynolds number for a Newtonian fluid (Re ~ 2100-2300) and a larger Reynolds number for blood (Re ~ 2500-2700). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG...... 51

31 Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 2. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity

xiii fluctuations under steady flow conditions show transition to turbulence at the expected Reynolds number for a Newtonian fluid (Re ~ 2100-2300) and a larger Reynolds number for blood (Re ~ 2500-2700). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG...... 52

32 Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 3. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at the expected Reynolds number for a Newtonian fluid (Re ~ 2100-2300) and a larger Reynolds number for blood (Re ~ 2500-2700). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG...... 53

33 Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number. In addition, these values represent the average values of mean and RMS velocity for three separate experiments. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number. Results show transition to turbulence at a lower Reynolds for Newtonian fluid (Re ~ 2100-2300) than that for blood (Re ~ 2500-2700) based on both the change in velocity profile (parabolic to blunt) and increase in velocity fluctuations near TT...... 54

34 Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 1. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number...... 55

35 Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 2. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number...... 56

xiv

36 Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 3. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number...... 57

37 Normalized mean and RMS velocity profiles measured by Doppler ultrasound for two difference shear thinning fluids (WGXH and WGXL) over three seconds. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number. Results show a delay in TT for WGX2 (Re ≈ 2800-3000) and an even greater delay for WGX1 (Re ≈ 3400-3600) compared to a Newtonian fluid. Rheology of each fluids is shown in Figure 29. Reynolds number is based on viscosity at a shear rate of 1100 s-1 for both fluids...... 58

38 RMS velocity distribution is shown as a function of both Re and radial position. An increase (>2x) at Re ≈ 2100, 2100 and 2000 for the three Newtonian samples 1, 2 and 3, respectively indicate TT. For Blood the same trend was observed at Re ≈ 2600, 2500 and 2500 respectively. For WGXH and WGXL the increases were observed at Re ≈ 3400 and 2800, respectively. Note radial locations near the wall have been excluded due to the artificial spectral broadening due to high shear rates...... 59

39 Measured centerline velocity (mean and RMS) over three seconds. Theoretical velocity is also shown based on a Poiseuille flow and measured volume flow rate. Plot shows comparison between all four fluids examined: Newtonian (A), blood (B), WGX1 (C) and WGX2 (D) for one experiment. Based on deviation of the mean velocity form theory and larger RMS values, TT is shown to be delayed for all three shear thinning fluids (B, C, and D) and indicate a Newtonian assumption to be reasonable only for Reynolds number below 2000 for steady flow in a straight rigid pipe...... 60

40 Normalized mean centerline velocity under steady flow conditions over three seconds. Mean velocity is normalized by aveage velocity over the cross-section at Re=1000 for each case. Plot shows comparison between all four fluids examined: blood and Newtonian (three samples each), and WGX1 and WGX2 (one sample each) to see the overall impact of shear thinning rheology on centerline velocity...... 61

xv 41 Mean Power of the centerline velocity trace vs. Reynolds number for three samples each of blood and WG shows slight difference in the Reynolds numbers where peak power occurs. Also shown are the mean powers for WGXH and WGXL...... 63

42 Mean Power of the centerline velocity trace vs. Reynolds number shows considerable difference in the Reynolds numbers where peak power occurs. The mean power for blood and WG are the average values for three samples...... 63

43 Repeatability for the six experiments (blood and Newtonian fluid experiments were repeated three times each) was assessed for the normalized velocity profiles both mean and RMS. Figure shows standard error (SEM) of the mean velocity of blood (A) and Newtonian fluid (B) with error-bars representing SEM of the RMS. Note multiple Reynolds numbers are shown separated on the x- axis using a shift of 10% for each Reynolds number. Mean velocity results show the experiments to be remarkably consistent for blood (<1%) and WG (<3%) near the centerline for Re <= 2200. Mean velocity variations were observed in blood at larger Reynolds numbers (Re>2700, ~10%). SEM of RMS in blood and Newtonian fluid at larger Reynolds numbers (Re>2600) did show greater variation although this was less than 5% of the mean normalized velocity. Values near the wall (< 1mm) were not included for clarity since SEs in the near wall region were large. Values below 2% is shown with open circles...... 64

44 Difference between normalized profiles of blood and Newtonian fluid for mean velocity at different Reynolds numbers. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 20 for each Reynolds number for the velocity. Results of mean velocity show small differences (<5% near the centerline for 1250 < Re <= 2200) between the blood and Newtonian fluid profiles in the laminar regime (Re<2200) and large differences for Re>2200. Note values near the wall (< 1mm) were not included for clarity since differences in the near wall region were large. Difference below 5% is shown with open circles...... 65

45 Velocity profile (top-left) and mean power spectrum at centerline (top-right) for laminar flow (Re = 1242) in blood. Velocity profile (bottom-left) and mean power spectrum at centerline (bottom- right) for turbulent flow (Re = 2896)...... 66

xvi

46 Velocity profile (top-left) and mean power spectrum at centerline (top-right) for laminar flow (Re = 1247) in WG. Velocity profile (bottom-left) and mean power spectrum at centerline (bottom- right) for turbulent flow (Re = 2605)...... 67

47 Velocity profile (top-left) and mean power spectrum at centerline (top-right) for laminar flow (Re = 1489) in WGXL. Velocity profile (bottom-left) and mean power spectrum at centerline (bottom- right) for turbulent flow (Re = 3268)...... 67

48 Velocity trace (a) and Power spectrum of the velocity distribution (b) for laminar flow, Re = 1242 (Green Box) and Velocity trace (c) and Power spectrum of the velocity distribution (d) for turbulent flow, Re = 2896 (Red box) in blood...... 68

49 Change in mean power and velocity fluctuation (non- dimensionalized by the mean velocity computed from measured centerline velocity) with Reynolds number for blood. The instantaneous velocity and mean power follow the same trend and increase by an order of magnitude around Re ≈ 2200...... 69

50 Rheology of blood and WG for S-shape pipe experiments...... 71

51 Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 1 in an S-shaped pipe. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at a lower than expected Reynolds number for a Newtonian fluid (Re ~ 1000) and a slightly larger Reynolds number for blood (Re ~ 1200). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG...... 73

52 Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 2 in an S-shaped pipe. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at a lower than expected Reynolds number for a Newtonian fluid (Re ~ 1000) and a slightly larger Reynolds number for blood (Re ~ 1100). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG...... 74

xvii 53 Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 3 in an S-shaped pipe. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at a lower than expected Reynolds number for a Newtonian fluid (Re ~ 1000) and a slightly larger Reynolds number for blood (Re ~ 1100). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG...... 75

54 Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number. In addition, these values represent the average values of mean and RMS velocity for three separate experiments. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number. Results show transition to turbulence at a slightly lower Reynolds for Newtonian fluid (Re ~ 900-1000) than that for blood (Re ~ 1000-1100) based on both the change in velocity profile (parabolic to blunt) and increase in velocity fluctuations near TT...... 76

55 Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 1. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number...... 77

56 Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 2. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number...... 78

57 Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds

xviii number for sample 3. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number...... 79

58 RMS velocity distribution is shown as a function of both Re and radial position. An increase (>4x) at Re ≈ 1000 for all three Newtonian samples indicate TT. For Blood the same trend was observed at Re ≈ 1200, 1100 and 1100 for samples 1, 2 and 3, respectively...... 80

59 Mean Power of the centerline velocity trace vs. Reynolds number for three samples each of blood and WG shows slight difference in the Reynolds numbers where peak power occurs...... 82

60 Repeatability for the six experiments (blood and Newtonian fluid experiments were repeated three times each) was assessed for the normalized velocity profiles both mean and RMS in the S- shaped pipe geometry. Figure shows standard error (SEM) of the mean velocity of blood (A) and Newtonian fluid (B) with error-bars representing SEM of the RMS. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 10% for each Reynolds number. Mean velocity results show the experiments to be remarkably consistent for blood (<2%) and WG (<1%) near the centerline for Re <= 900. Mean velocity variations were observed in blood at larger Reynolds numbers (Re>1100, ~10%) for half of the profile proximal to the probe entry wall. SEM of RMS in blood and Newtonian fluid at larger Reynolds numbers (Re>1300) were smaller compared to those in the transition region. Values near the wall (< 1mm) were not included for clarity since SEs in the near wall region were large. Values below 2% is shown with open circles...... 83

61 Difference between normalized profiles of blood and Newtonian fluid for mean velocity at different Reynolds numbers in an S- shaped pipe geometry. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 20 for each Reynolds number for the velocity. Results of mean velocity show small differences (<5% near the centerline for 500 < Re <= 1100 and Re > 1300) between the blood and Newtonian fluid profiles and large differences in the tranditional region for 1100

xix

62 Screenshot of cttech with polygons encompassing ROIs in one typical medical CT image of a diseased carotid artery...... 121

63 Binary images output from software cttech for healthy internal carotid (a), maximum stenosed internal carotid (b) and healthy common carotid artery (c)...... 121

64 3D reconstructed diseased carotid artery bifurcation, front and back view with plaque components (external carotid artery is not shown)...... 122

65 Comparison of mean TV (a) and mean percent CV (b) between symptomatic and asymptomatic groups...... 122

66 Step 1 – Load images and adjust contrast to make the ROI prominent...... 127

67 Step 2 – Identify the ROI with a polygon and smooth it...... 128

68 Step 3 – Convert to black and white and save as DICOM...... 128

69 Preview of the 3-dimensional structure ...... 129

70 Segmentation of the DICOM images to build a steriolithographic model...... 130

71 3D reconstructed upper airway (pre-surgery)...... 131

72 3D reconstructed upper airway (post-surgery)...... 131

73 Tetrahedral mesh at inlet bounded by prism boundary layer cells...... 132

74 Unsteady flow waveform used as inlet boundary condition ...... 133

75 Unsteady pressure drop in pre and post surgery upper airway for one breathing cycle ...... 134

76 Pressure distribution in pre-surgery upper airway...... 135

77 Pressure distribution in post-surgery upper airway...... 136

78 Velocity distribution in pre-surgery upper airway...... 137

79 Velocity distribution in post-surgery upper airway ...... 138

80 Strain rate distribution in pre-surgery upper airway walls...... 139 xx 81 Strain rate distribution in post-surgery upper airway walls...... 140

82 Comparison of total wall volume of the diseased internal carotid artery to the %NASCET scores...... 141

83 Comparison of calcium volume of the diseased internal carotid artery to the %NASCET scores...... 141

84 Comparison of %calcium volume (calcium volume/total wall volume) of the diseased internal carotid artery to the %NASCET scores...... 142

85 The front of cell movement is indicated as the read line (polygon) for the Drug case at the first time point (t=1). Front-polygon geometry is non-circular with some vertices far from center and some near depending on the angle...... 147

86 The front of cell movement is indicated as the read line (polygon) for the Drug case at the time point where the cells have reached the injury site in the center (t=18)...... 148

87 The front of cell movement is indicated as the read line (polygon) for the Control case at the first time point (t=1). Front-polygon geometry is non-circular but less so compared with the Drug case...... 149

88 The front of cell movement is indicated as the read line (polygon) for the Control case at the time point where the cells have reached the injury site in the center (t=11)...... 150

89 Comparison between the Drug and Control cases for average distance between the front-polygon and the outer edge of the injury site at the center as a function of time. Note that the average distance for the control case reaches the edge of center injury site faster than the drug case...... 151

90 Comparison between the Drug and Control cases for area between the front-polygon and the outer edge of the injury site at the center as a function of time. Note that the area for the control case is much smaller than the drug case. This could be affected by the fact that control case injury area is larger than that of the drug case. Also, differences in gray scale could impact this relationship...... 151

xxi 91 Comparison between the Drug and Control cases for average radial velocity of the front-polygon towards the outer edge of the injury site at the center as a function of time. These values are affected greatly by noise or cell angular movement...... 152

92 Comparison between the Drug and Control cases for shape index of the front-polygon as a function of time. These plots show the drug case is much less circular than the control case...... 152

93 Control case for each individual angular distance between the front-polygon and the outer edge of the injury site at the center as a function of angle at each time point...... 153

94 Drug case for each individual angular distance between the front- polygon and the outer edge of the injury site at the center as a function of angle at each time point...... 153

95 Control case for each individual radial velocity between the front- polygon and the outer edge of the injury site at the center as a function of angle at each time point...... 154

96 Drug case for each individual radial velocity between the front- polygon and the outer edge of the injury site at the center as a function of angle at each time point...... 154

97 Measured centerline velocity and theoretical centerline velocity (dotted line) by accelerating and decelerating flow between Re = 0 and Re = 4500 in 180 s...... 156

98 Measured centerline velocity and theoretical centerline velocity (dotted line) by accelerating and decelerating flow between Re = 0 and Re = 4500 in 5 s...... 157

xxii CHAPTER I CHAPTER

I. INTRODUCTION AND BACKGROUND

Hemodynamics has been shown to play a key role in the pathogenesis and morphogenesis of arterial disease [1-5]. Correct evaluation of the wall shear stress is necessary to predict the pathophysiology of the diseased vessel. Non-invasive measurement of velocity and shear stress is difficult due to the small size of the blood vessels. For this reason, researchers sometimes use computational fluid dynamic simulation of image based models to evaluate the development, progression and diagnosis of cardiovascular disease [6]. It is well established that blood behaves like a non-Newtonian fluid at low shear rates (<200 s-1) and like a

Newtonian fluid for high shear rates [7, 8]. Shear thinning blood analogs can approximate blood rheology; however, the precise variation of viscosity with shear rate in whole blood is difficult to match [9]. Most in vitro and in silico experiments assume blood to be Newtonian fluid under the presumption that the prevalent shear rates in their model are high (>200 s-1) [10-16]. This assumption may yield accurate results depending on the flow conditions and geometry [17, 18]. There are cases where the non-Newtonian nature of blood altered the flow pattern and the hemodynamic forces considerably [8, 19]. The goal of the current study was to evaluate the validity of this assumption under steady flow conditions in a straight

1 rigid pipe and an S-shaped geometry. Blood flow in the human body is typically laminar; however, transitional flow has also been observed in various locations, notably diseased locations. High frequency fluctuations are often observed in arteriovenous grafts [20-22], ascending aorta [23], flow past stenosis [24] and mechanical heart valves [25]. Loth et al. demonstrated through in vivo, in vitro and in silico studies of arteriovenous (AV) grafts that there are significantly high vein wall vibration (VWV) for flows with Reynolds numbers (Re) less than 2000, (in vivo greater than in silico) [26]. According to their hypothesis, the VWV is caused by the onset of turbulence. Lee et al. observed the same phenomena while studying the carotid bifurcation [13]. Thorne showed that introduction of a stent significantly increased turbulent intensity in the internal and external carotid artery [27]. Valen-

Sendstad implicated turbulent blood flow in carotid siphon and emphasized its importance in aneurysm initiation and even rupture [28]. Stein et al. showed that patients with aortic valvular disease and patients with a prosthetic aortic valve showed turbulent flow during nearly the entire period of ejection [23]. Researchers showed turbulent characteristics downstream of mechanical heart valves [25, 29].

Vascular sounds (bruits and hums) in the head and neck of patients have been attributed to turbulence in blood flow [30].

Researchers have shown that transitional flow affects the morphology of endothelial cells, the cells that form the inner lining of the blood vessels. Davies et al. exposed endothelial cells (EC) to turbulent flow using a cone and plate in an in vitro system. They found that the unsteady flow characteristics may be important in hemodynamically induced EC turnover [31]. McCormick et al. showed that the

2 endothelial cells were aligned with the flow direction under laminar flow as compared to transitional flow where the cells were stretched and less aligned to the flow direction [32]. Jones discussed how turbulent flows can cause cellular damage due to viscous shearing [33]. Fry et al. showed that elevated shear stress

“peels off” the endothelial cell layer that he observed in a stenosis model [4]. He also observed endothelial cell damage downstream of the stenosis where local turbulent flow instabilities in the flow were observed. Thus, it is important to correctly predict the onset of transition to turbulence (TT) in a particular geometry under a particular flow condition, when blood is used as the test fluid.

Blood is a non-Newtonian fluid, shear thinning in nature. Blood has been well documented for laminar flow; however, details about how blood differs from

Newtonian under transitional flow conditions is not well established. The critical

Reynolds number of transition to turbulence (Recr) for blood is not well known.

Nerem performed a canine study to characterize TT in the aorta with a hot film anemometer [34]. They found the critical Re for transition to be related to both the peak Re and heart rate. In the canine aorta, they found TT at peak Re between

2050 and 3230. Ferrari et al. conducted an ultrasound study to determine the range of Re values for which the flow rate was accurately predicted under the assumption of a Poiseuille flow profile. This assumption is for laminar flow only and does not apply during TT. For Poiseuille flow velocity profiles, if is well know that the centerline velocity is twice that of the mean (flow rate divided by cross-sectional area). Re is based on the product of mean velocity, pipe diameter and the inverse of kinematic viscosity. These experiments were conducted in a straight rigid glass

3 pipe with whole blood [35]. Based on changes in the centerline velocity magnitude, they determined the TT to be at Re~500. Nerem and Ferrari et al. provide evidence for the Recr of TT in whole blood even though this was not the goal of their research. Neither study employed a Newtonian fluid which would have helped to understand if a Newtonian assumption for blood is reasonable.

Coulter and Pappenheimer conducted whole blood studies in a straight pipe under steady flow conditions and compared their results to that of water [36]. In contrast to Ferrari et al., they found Recr of TT to be similar to that of a Newtonian fluid

(Re~2000). According to Steinman et al., the onset of turbulence in blood could be attributed to the presence of red blood cells, their chaotic motion and their changing in shape under various flow conditions [37].

Researchers have studied numerous shear thinning, non-Newtonian fluids to evaluate their respective Recr. They have shown that shear thinning, non-

Newtonian fluids transition at a different Reynolds number than a Newtonian fluid

[38-40]. Esmael et al. showed for carbopol solution TT occurs between Re 1800 and 3000 [40]. Peixinho et al. showed for another non-Newtonian shear thinning fluid (Sodium-Carboxy-Methyl-Cellulose and Carbopol) the velocity fluctuation peaks were recorded at Re = 2900 and 3700, respectively [39] which for Newtonian fluid was Re = 2500 [41].

Stehbens et al. investigated TT in different flow geometries (T-junction, S-shaped pipe etc.) using dye injection and visual observation [10]. His results indicate that the Recr was between 476 and 567 for the S-shaped geometry. They confirmed these results by visually observing dye in a straight pipe, and found Recr = 2000,

4 in accordance with others studies. Stehbens et al. extended the previous work using the same technique by testing 21 other S-shaped geometries, varying the lengths, radii of curvature and size [11]. None of his Recr were above 1200 confirming previous researchers. All these studies employed water as the test fluid, and it is not known how blood would have behaved in these geometries.

Chien et al. showed that the presence of red blood cells (RBC) alone do not cause blood to act as non-Newtonian fluid [44]. The presence of fibrinogen together with

RBCs is responsible for rouleaux formation at lower shear rates (<200 s-1).

However, rouleaux breaks down at higher shear rates such that blood acts like a

Newtonian fluid. Other researchers have shown that aging alters RBC rigidity and its ability to form rouleaux resulting in less dependence on shear rate [48, 49].

Research has shown that the viscosity of blood changes with the addition of anticoagulants [50]. Viscosity also changes with hematocrit. A one percent of RBC volume to total blood volume (hematocrit) can increase the viscosity of blood by as much as 4% [50, 51]. Many factors affect the viscosity of blood such as plasma viscosity [51], level of RBC aggregation and deformability [52], fibrinogen [44], flow geometry and size [53], rate of shear, hematocrit, male or female, smoker or non- smoker, temperature, lipid loading, hypocaloric diet, cholesterol level, and physical fitness index [54]. Researchers have employed different techniques and instruments to quantify the blood rheology and have obtained different results [43,

55-57].

The goal of this study was to compare TT based on fluctuating and mean velocity for whole porcine blood and a Newtonian analog. An experimental flow system

5 was designed and built to measure the velocity under steady flow conditions. This system allowed for the specific investigation of the minimum or critical Re at which

TT occurs. 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 examined steady blood flow in a straight pipe since this flow field is well established for both laminar and transitional flow for a Newtonian fluid. The goal was further extended to compare the Recr of blood and a Newtonian fluid for another geometry, downstream of an S-shaped pipe. This was done to observe the effect of geometry on the TT of blood as compared to a blood analog.

6

CHAPTER II

II. LITERATURE REVIEW

2.1 Hemodynamics and morphogenesis

Effect of hemodynamics on the morphogenesis and pathogenesis of arterial diseases have been studied for many decades. Ku et al. established a correlation between shear stress and plaque formation [1]. They studied the shear stress distribution on a plexiglass model (constructed 125X from biplanar angiograms of the carotid of 57 human subjects) using laser Doppler anemometry. They used pulsatile flow conditions and implemented a Newtonian fluid in their study. The authors then correlated the results with measurements and observation of plaques in human subjects, post-mortem. Results indicated strong correlation of plaque formation and low mean wall shear stress (p<0.001).

Studies on the effects of turbulence on endothelial cells have been conducted by many researchers to examine if a relation between arterial diseases and turbulence exists. Davies et al. conducted an in vitro study using bovine aortic EC, exposing them to shear stress in a cone and plate setup [31]. They found that ECs exposed to turbulent shear stress of 14 dynes/cm2 increased the DNA synthesis by 44% and cell turnover rate compared to ECs exposed to laminar shear stress of the same magnitude. In cases where turbulence persisted for longer than 24

7 hours, gaps in the EC monolayer indicated cell retraction and/or cell loss that did not appear for laminar flow for the same time duration. This work indicate EC response to shear stress is different from laminar to turbulent conditions at the same shear stress magnitude.

McCormick et al. used human umbilical vein EC to cover the inner wall of a straight pipe to observe the effect of different flowrates in an in vitro setup [32]. The authors 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 observed morphological changes in the ECs. They observed that the magnitude of EC elongation was directly proportional to the magnitude of the shear stress applied to the EC, whereas ECs began to take on a more round shape when exposed to shear stresses in the transitional regime. At the highest Re (3000, transitional), the cells again became elongated comparable to that of the laminar flow cases. Cells exposed to turbulent flow conditions were randomly oriented and equally distributed between angles 0° to 180°. Like the study by Davis et al., these results demonstrate altered EC response for laminar verses transitional flow at the same shear rate.

In another study, 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 more easily pass through the lipid bi-layer and into their cytoplasm. He used Evens blue dye to tag albumin and identified regions of damaged endothelial cells. He observed endothelial cell

8 damage in regions of high laminar shear stress and regions of low shear stress with high turbulent energy.

2.2 Ultrasound and velocity measurement

There are several studies that used an ultrasound or LDA system to investigate transition to turbulence [8, 10, 38-41, 58]. Wu et al. examined the importance of whole blood versus RBC suspension to understand how Doppler signal power would vary [59]. While this is not directly related to the present study, two of their methods employed were of interest and could be added in future studies, which are (i) correction of measured power spectra by subtracting a baseline noise spectra measured in stationary blood and (ii) discarding WBC and platelets to minimize coagulation.

2.3 Recr in non-Newtonian fluids

Peixinho investigated three fluids: shear thinning, yields stress, and Newtonian to discover how TT varied for each fluid under the same flow conditions [39]. The author measured the shear rate near the wall and used the corresponding viscosity to define Re. He compared friction factor, centerline velocity, and centerline velocity fluctuation computed from measured pressure and velocity and found that

TT is delayed in the shear thinning and the yield stress fluid as compared to the

Newtonian fluid.

9 Table 1: Critical Reynolds number for transition to turbulence in three different fluids [39]. Critical Reynolds number indicated by parameter Fluids Friction Centerline Centerline velocity factor velocity fluctuation Newtonian 2100 2050 1800 Shear thinning 2500 2300 2100 Yield stress 2700 2550 3300

Rudman et al. [58] compared the TT for two different shear thinning fluids

(Carboxy-Methyl-Cellulose and Ultrez 10) with similar apparent viscosities in a pipe using laser Doppler velocimeter with a sharp bend upstream of the measurement location. His research showed that TT in CMC was delayed (Re = 3500) as compared to the TT in Ultrez 10 solution (Re = 2800). He defined the Reynolds

휏푤 number in terms of the apparent viscosity at the shear rate at the wall (휇푎 = ⁄ ), 훾̇푤 where 휏푤 = Shear stress and 훾̇푤 = Shear rate at the wall. Natrajan et al. [60] found in micro-scale capillaries (ID = 536 μm) transition to turbulence of deionized water takes place at Re = 1900 indicated by pressure drop and instantaneous velocity measurements using particle image velocimetry.

2.4 Recr and velocity profile in blood

Nerem and Seed performed a canine study to characterize TT in the aorta with a hot film anemometer [34]. They recorded the instantaneous velocity waveforms in the thoracic aorta. These experiments were conducted before and after drugs were admistered to alter flowrate and heart rate. They found the Recr for transition to be related to both the peak Re and heart rate. In the canine aorta, they found

TT at peak Re between 2050 and 3230.

10 Ferrari et al. measured centerline velocity against Reynolds number in five different pipe sizes (1.5 mm through 5.5 mm in I.0 mm steps)(Figure 1) [35]. A number of factors associated with the method of acquiring data seem to be responsible for the fluctuations that Ferrari et al. observed in his data set. One reason might be the presence of the DUS probe upstream of the insonified sample volume, which caused the disturbance. At low velocities, the disturbance may have died down in the 5 mm gap between the probe and sample volume. Any small change in the probe angle, the position of the probe, or its movement during data acquisition might result in lower velocities since the probe volume would not be located in the center. The fact that the measured velocities nearly follow a Poiseuille value

(straight line) indicates the flow might not be transitional at these Reynolds numbers.

11 500

450

400 1.5 Peak-th 350 1.5 APV

300 2.5 Peak-th 2.5 APV 250 3.5 Peak-th 200 3.5 APV Velocity Velocity (cm/sec) 4.5 Peak-th 150 4.5 APV 100 5.5 Peak-th

50 5.5 APV

0 0 500 1000 1500 2000 Reynolds number

Figure 1: Comparison of centerline velocities for a range of Reynolds numbers obtained by Ferrari et al. against Poiseuille values for five different size straight pipes. ‘Peak-th’ is data for peak velocity calculated using Poiseuille equation (number indicates pipe diameter in mm), and ‘APV’ is the measured peak velocity [35].

One drawback in both the above studies is that the blood results were not compared to a Newtonian fluid in the same setup. Coulter and Pappenheimer conducted whole blood studies in a straight pipe under steady flow conditions and compared their results to that of water [36]. In contrast to Ferrari et al., they found

Recr of TT for blood to be similar to that of a Newtonian fluid (Re ≈ 2080 ± 80 and

Re = 1940 ± 160 for water and whole bovine blood respectively). Coulter and

Pappenheimer used the relation between friction coefficient and Re to detect turbulence. The experiments were carried out at 29±1°C for bovine blood (~30% hematocrit).

12 Yeleswarapu et al. showed for low Re (16, 20 and 25) flows of whole blood in a straight pipe the velocity profiles are considerably more blunt than that predicted for Newtonian models [8]. The centerline velocities were overestimated by the

Newtonian model by as much as 44%, but matched well with that predicted by the generalized Oldroyd-B model proposed by the author. Blunting of the profiles can be attributed to the lower shear rate near the center of the pipe (at Re = 20 the wall shear rate at the wall is 25 s-1 calculated from mean velocity of 2 cm/s and diameter of 0.635 cm). That means the entire flow-field experiences shear rate less than 25 s-1 where the viscosity is higher than that at higher shear rates (>100 s-1). With increasing Re, the low shear rate region will shrink and will be restricted to a small region near the centerline and velocity profiles will eventually become parabolic.

2.5 Recr in S-shaped pipe

Stehbens looked at TT of water in five different shaped pipe models representative of arterial bifurcation and carotid siphon and showed in each case the critical Re is lower than that in a straight pipe [10]. Table 2 shows the critical Re of the different shapes. It is clear that the pipe with significant curvature greatly alters the TT.

However, it is important to note that fluctuations in the flow are not always representative of turbulence, e.g. for a flow behind a cylinder the flow fluctuates, but the fluctuations are repeatable and not characteristic of random turbulent fluctuations. Curved pipe are representative of the carotid siphon, circle of Willis, and aortic arch.

13 Table 2: Critical Reynolds number for transition to turbulence for water flowing through different geometries [10]. Corresponding Type of model Critical Reynolds figure number 3A S-shaped curve (Forward flow) 567 3B S-shaped curve (Reverse flow) 521 3C T-piece (Forward flow) 347 3D T-piece (Reverse flow) 204 3E, 3F Y-piece, 90° angle (Reverse flow) 929 ---- Y-piece, 30° angle (Reverse flow) 1110 ---- Y-piece, 165° angle (Forward flow) 1473 ---- Y-piece, 165° angle (Reverse flow) 306

Stehbens et al. extended the above study by testing 21 different S-shapes and investigated the Recr of TT [11]. They used the dye injection technique to observe when the stream of dye deviated from a streamline. They used water as the test fluid and found the Recr of TT to vary between 418 and 1156 for the different shapes. Interesting to note that the Recr of TT were all much less than the well accepted value of 2100 in a straight pipe.

2.6 Rheology of blood

Viscosity is defined as the ratio of the applied shear stress to the strain rate [57].

This stress-strain rate relation is linear for Newtonian and non-linear for non-

Newtonian fluids. Non-Newtonian fluids, such as blood, have viscosities that decrease with shear rate, called a shear thinning fluid. Accepted values of viscosity for blood at high shear rates are approximately 3-6 cP. In a pilot study of evaluating rheometers for the present study, a blood sample was examined in the TA

Instruments research facility, and the results were compared to that reported in the

14 literatures. The measured rheology was similar to those reported in the literature

(Figure 2).

51 46 Measured 41 Brooks et al. Thurston et al. 36 Long et. al. 31 Chien et al. 26 Yeleswarapu et al.

21 Kim et al.

Viscosity (cP) Viscosity 16

11

6

1 1 10 100 1000 Shear Rate (s-1) Figure 2: Viscosity with respect to shear rate from various literatures. At a shear rate value of 10 s-1 the viscosity value is measured as 10.6 cP and at 100 s-1 as 4.6 cP and asymptotically comes down to around 3.5 cP as shear rate increases. But viscosity was observed to go up with shear rate beyond 631 s-1.

Yamamoto et al. [45] compared the viscosity of human blood with and without anticoagulants in a novel compact-sized falling needle rheometer and showed that the addition of anticoagulant (EDTA-2Na) can decrease the nominal viscosity of blood by as much as 17% at 37°C. Rosenblum [50] measured the viscosity of rabbit and monkey blood with different anticoagulants using capillary viscometer.

Addition of sodium citrate and heparin in mouse blood increased the viscosity by up to 9% than when only heparin was used and decreased the hematocrit by up to 7%. Addition of sodium oxalate increased the viscosity by up to 43% than

15 heparin alone in rabbit blood and up to 19% in monkey blood. He also showed that addition of EDTA decreased the viscosity by up to 10% for monkey blood.

Schmid-Schonbein [48] investigated the effect of deformability of RBC of human blood on its viscosity. This study showed that partial and total rigidification of RBC decreases the non-Newtonian shear thinning nature of blood considerably for hematocrit near 40%.

Rand et al. reported the viscosity of normal human blood under normothermic and hypothermic conditions [61]. For shear rates of 42, 100 and 212 s-1, the authors reported the viscosity to vary linearly with temperature above 27°C. The change in viscosity of blood (at these shear rates) at 37°C was ~1.8% for each 1°C

-1 increase in temperature. Nominal values of viscosity at 212 s was ~4cP at 37°C.

Brookshier et al. presented a recipe for transparent blood analog fluid using aqueous xanthan gum and glycerin that matches the viscosity and viscoelasticity of blood with different hematocrit contents [9]. He compared the wall shear rate and flow waveforms of the blood analog solution with whole porcine blood and showed that they are similar for straight and curved tube flows.

2.7 Temperature dependence of viscosity of Newtonian fluids

Cheng proposed empirical formula to calculate viscosity of a water glycerin mixture

[63]. Based on his formula, viscosities of a water-glycerin mixture were seen to rise

3% for 1°C drop in temperature at 37°C.

16

CHAPTER III

III. PROPOSED STUDIES

The purpose of this study is to investigate the Recr, defined earlier as the critical

Reynolds number of transition to turbulence, in whole blood and compare that to a Newtonian fluid with the same viscosity under steady flow conditions and two different flow geometries. The hypothesis for underlying this research is that the non-Newtonian nature of blood alters the Recr of TT under steady flow conditions depending on the vessel geometry. The present work will examine the geometric effect using two different, relatively simple, geometries. The first geometry is flow in straight pipe, which has the advantage that the flow field is well known for laminar and turbulent flow. The second geometry to be examined is an S-shaped pipe (idealized carotid siphon). In addition to a Newtonian fluid and whole porcine blood, the flow studies will be repeated with a blood analog fluid (shear thinning) to compare blood with the blood analog in the straight pipe as well.

An experimental flow system was built to be compatible with blood to reduce the formation of thrombus. A blood pump (clinical grade) was selected to produce flowrates high enough into the turbulence regime and yet be gentle on blood. The experimental flow system is flexible to accommodate different flow geometries.

There are many different experiments that could be used to fully examine the

17 importance of non-Newtonian rheology on the TT (e.g. geometry, parameters, flow conditions, temperature etc.) but only steady flow in a straight pipe and an S- shaped pipe has been examined in this study.

The two geometries examined are, a straight pipe and a S-shaped pipe which are shown in Figure 3. Flow in a straight pipe is the simplest of the geometries having an exact analytical solution for laminar flow. This will enable us to validate the system before moving on to more complex geometries.

1st Apex

2nd Apex Figure 3: The three geometries proposed to be examined in this study, (a) straight pipe, and (b) S-shaped pipe. Dotted line represents approximate path of Doppler ultrasound velocity measurement.

18 One major difference between the two geometries is the origin of instabilities that lead to transition to turbulence. In a straight pipe, the instabilities are generated at the wall, unlike the S-shaped geometry where the instabilities originate at the free shear layer as well as the wall [64, 65]. Research has shown that transition to turbulence is delayed for a shear-thinning non-Newtonian fluid flow in a straight pipe compared to a Newtonian fluid [39], but this has not yet been demonstrated for whole blood. This is the novel aspect of the proposed Ph.D. thesis research.

These two geometries are important to assess the alterations in TT for blood since they represent the two major origins of the instabilities . While blood flow in a straight pipe does not represent an important geometry in vascular disease, it is important to start with a well-established geometry to provide a baseline to which more complex geometries can be compared. Accurate values of the blood TT downstream of an S-shaped pipe may be important since it is representative of an internal carotid artery (carotid siphon). It has been observed that cerebral aneurysms form downstream of the carotid siphon, which may be attributed to flow instabilities [66] and blood wall shear stress and pressure fluctuations are thought to play a role in aneurysm initiation and rupture [28]. Thus, simulations that aim to predict these fluctuations need to know the true nature of TT in whole blood.

19 CHAPTER IV

IV. METHODS

4.1 Design of In Vitro Hemodynamics System (Straight Pipe)

A simple schematic of the experiment system is shown in Figure 4. A sylguard-184 model was created. It has one Doppler ultrasound (DUS) port (at an angle of 60° to flow direction) with provision for a Tuohy Borst adapter at the end to prevent leakage. The flow tube access section diameter was 0.3438" and constructed using a tool steel, tight-tolerance rod (diameter tolerance = ±0.0005"), for a 3/8” X

¼” (OD X ID) clear cellulose (butyrate) tube to fit snugly (Figure 5). A guardrail structure (Figure 6) was constructed from aluminum to give structural stability to the model as well as to enable positioning of the probe with considerable ease. A rotary stage (M 481A, Newport Corporation, Irvine, CA) and a miniature three axis stage (M-MT-XYZ, Newport Corporation, Irvine, CA) was installed for precision positioning of the probe mounted on a computer controlled stage (SGSP 26-150,

Sigma Koki, Tokyo, Japan) with a custom probe holder (Figure 7). Titanium

Dioxide (TiO2) particles (0.1 g/litre, mean diameter = 0.65 µm, Spectrum

Chemicals, T1081, Gardena, CA) were used as ultrasound reflectors for the blood analog fluids.

20 Figure 4: Schematic of the straight pipe flow system.

Figure 5: Mold (left) for sylgard model (right) that serves as an ultrasound probe access port of the blood flow pipe.

21 Figure 6: Aluminum guardrail that acts as a support as well as coarse positioning of stage and flow section.

Figure 7: Motorized linear stage (left), and custom probe holder (right).

Figure 8: Positioned probe (left), and incubator (right).

A wooden test chamber, insulated with 2” thick foam (Figure 8) was constructed to keep the entire experimental setup at a steady 37°C. Proportional type incubator heaters with inbuilt thermostats (Incubator Warehouse, Fruitland, ID, http://incubatorwarehouse.com/) along with a glass custom cooling coil, coated

22 with SigmaCoat (Sigma-Aldrich, St. Louis, MO) (Figure 9) were used to maintain the temperature at 37°C. The entire experiment system was seated on a Plexiglas tray (Figure 10) to contain the fluid in case of a leak.

Figure 9: Condenser coil.

Figure 10: Plexiglass tray to prevent spillage.

The experimental test section was made up of a 6.35 mm ID straight clear cellulose

(butyrate) pipe connected downstream to a plastic reservoir and upstream to a centrifugal blood pump (SarnsTM, Terumo Cardiovascular Group, Ann Arbor, MI).

The straight section upstream of the DUS probe, the entrance length (800mm), was chosen to meet the criterion for fully developed laminar flow at Re = 2100. A turbulator (Figure 11) was used downstream of the pump to obtain consistent flow conditions into the entrance length pipe. An transonic flow meter (TS410,

Transonic Systems Inc., Ithaca, NY) fitted with an inline flow probe (ME 6 PXN,

Transonic Systems Inc., Ithaca, NY) was used to measure flowrate and calibrated using a bucket and stop watch.

23 Flow rate was monitored by an ultrasonic transit time flowmeter. These types of flow meters measure the difference of the transit time of ultrasonic pulses propagating in and against the direction of flow. The time difference, which is a measure of the average velocity along the ultrasonic beam direction is used to calculate flowrate using the speed of sound in the test fluid. The flow probe used in this study consisted of four transducer sensors that resulted in good flowrate measurements at low as well as high flowrates with little effect from turbulence.

Figure 11: Turbulator, constructed using monofilament string glued to a butyrate pipe.

The pump was controlled using a computer controlled variable DC power supply

(1685B, B&K Precision Corporation, Yorba Linda, CA). A thermistor meter/controller (DP25-TH-A, OMEGA Engineering, INC., Stamford, CT) and a linear immersion thermistor sensor (OL-703, OMEGA Engineering, INC.,

Stamford, CT) were used to measure the temperature of blood. The meter/controller was configured to read 15-45°C and output a corresponding analog voltage of 0-10V.

A 20 MHz pulsed Doppler ultrasound probe (Mouse Doppler tube mounted, Indus

Instruments, Webster, TX) was used along with ultrasound unit (Crystal Biotech,

24 Northborough, MA) to measure velocity. The probe consisted of a 20 Mhz ultrasound crystal mounted at the tip of a 7 Fr (2.33 mm) OD steel pipe. The probe was introduced into the flowfield through a tuohy borst adapter (Qosina,

Edgewood, NY) at 60° angle, held in place by a sylgard block. MBruler software

(© Markus Bader - MB-Softwaresolutions, http://www.markus-bader.de/MB-Ruler) was used to measure the true angle of the probe (Figure 12). The probes were tested for symmetry by rotating with respect to the longitudinal axis and measuring velocity profiles.

Figure 12: MBruler to measure angle of probe with respect to flow.

4.2 Design of In Vitro Hemodynamics System (S-Shaped Pipe)

B

C A

Figure 13: S-shaped pipe geometry.

25 The experimental setup for the S-shaped pipe geometry was similar to the straight pipe apart from a few features particular to this geometry. Frist, there was no turbulator installed at the outlet of the pump. The S-shaped pipe was made using a vinyl tubing that was morphed in a channel made from wood. The entrance pipe

(A, Figure 13) used was made from clear cellulose (Butyrate) and was 0.53 m (~

83D) in length. The S-shape (B, Figure 13) had a length of 0.175 m along the curve and 0.12 m in the flow direction. The S-shape had a radius of curvature of ~ 5D.

The tubes were kinked near the apex of the S-bends. The straight portion of the flow domain after the S-shape up to the point of measurement (C, Figure 13) was

0.135 m. An US probe measured the velocity at an angle of 60° with the axial flow direction, 21D downstream of the S-shape.

4.3 Viscosity Measurement

Viscosity is an integral part of Reynolds number definition, hence, one must have accurate measurement of fluid rheology (viscosity with respect to shear rate).

Three fluids: a Newtonian, shear-thinning, and whole porcine blood were used in this study. Measurement of viscosity for Newtonian fluids is not difficult and many devices can be used for this purpose. However, measurement of a shear thinning fluids’ rheology can be difficult. Blood has solid particles, red blood cells, which makes it even more difficult to evaluate.

The non-Newtonian characteristic of blood restricts the number of instruments that can measure the viscosity of blood accurately. Some instruments only work in a specific range of shear rates, constrained due to a number of factors e.g. bearing

26 friction, temperature instability, inertia, gap size, evaporation etc. Viscometers can be classified into three types; rated discharge (capillary type), timed fall (falling body) and drag-torque (rotational type). In the present study a rotational type rheometer was used.

16.00

14.00

12.00 LVDV III UCP with CPE-41 10.00 LVT with UL adapter

8.00 TA_Ins_blood_analysis

6.00 viscosity (cP) viscosity

4.00

2.00

0.00 0 50 100 150 200 250 300 350 400 450 Shear Rate (s-1)

Figure 14: Minimum viscosities with respect to shear rates for Brookfields LVDV III UCP, LVT and TA Instruments AR2000EX viscometers and viscosities of blood as measured at TA Instruments laboratory.

Figure 14 shows that viscosity of blood can be measured from 73.44 down to 7.34 s-1 using a Brookfield LVT dial reading viscometer. Though the range is big, only four data points can be measured (shear rates 73.44, 36.72, 14.69 and 7.344 s-1) corresponding to speeds 60, 30, 12 and 6 RPMs. The LVDV III UCP with a 24 mm radius cone spindle can measure viscosity of blood above shear rates of 40 s-1.

Together these two viscometers can measure the viscosity of blood for shear rates

27 above 7.34 s-1. Hence, there was a need to search for a rheometer that can measure viscosity of blood for the entire range.

Viscosity of blood samples were measured at TA Instruments laboratory using

Discovery hybrid HR3. Viscosity was measured for shear rates ranging from 1 to

1000 s-1 sweeping up and down for two samples. The sample citrated blood consisted of 39% hematocrit. Plot of viscosity vs. shear rate clearly indicates the non-Newtonian nature of blood. The results matched with that reported in the literature (refer Chapter II). Based on the results a similar rheometer, AR2000ex, was bought from TA Instruments and viscosities were measured for shear rates ranging from 5 to 500 s-1. The temperature of the sample is controlled using a peltier plate and chiller combination. The whole process is computer controlled that enables one to measure viscosity at a wide range of shear rates and temperatures in a short span of time. A 60 mm acrylic parallel plate was used for the study. The gap size between the parallel plates used for this measurement was 1 mm. The rheometer was calibrated prior to each experiment and was shown to be within 1% of a viscosity standard (400 s-1) and repeatability errors were also ±1%.

In order to prepare the water glycerin mixtures, an online viscosity calculator was used (Figure 15). This calculator computed the precise amounts of water and glycerin to be used to attain the required viscosity at a predefined temperature.

28 Figure 15: Snapshot of website used to calculate percentage of glycerin required to obtain a set viscosity at a set temperature.

4.4 Data acquisition and processing

This section describes the process of data acquisition from the flow system (Figure

16). Calibration of the flowmeter was performed using a bucket and a stopwatch followed by density and rheology measurements. The measured parameters were updated in the code and calibration of flowrate with voltage applied to the pump was performed. This was accomplished by applying a set of predefined voltages to the pump and acquiring the flowrate. The next step was to map temperature gradient versus Re or, in other words, rate of dissipative heating with flowrate was

29 mapped. After computing the locations of measurement across the pipe, depending on the number of points used to construct the profile (21 in this case), the probe was moved to the first location. At this point temperature was checked whether it was within acceptable limits. If yes, flowrate and Doppler shifted frequency were measured and only stored if the absolute value of flowrate satisfied the <1.5% criterion. Otherwise the data was discarded, pump was corrected accordingly and measurements were taken again. If the flowrate criterion was met, the temperature was checked again and only if all three (temperature before, temperature after and flowrate) criteria were met, was the data stored. This process was applied to each point on the profile before the flowrate was set for the next Re measurements. After acquiring data for each profile they were processed and saved in a computer hard drive. After all the profile measurements were done, flowrate calibration, and measurements of density and viscosity were repeated for consistency.

30 START Calibrate flowmeter Measure ρ, μ Initialize parameters

Map Temp. gradient with Re # Calibrate flowrate with Voltage

Done acquiring Stop pump YES Write pdf data for all Re #?

END NO

Acquire and Specify locations for Move US probe Process velocity measurement

Check Temp. Plot

Velocity profile 36.5°C< T <37.5°C? Mean Velocity Heat/ Cool using YES NO pump /condenser coil * Compute velocity trace (3 sec) Acquire US, Increase/decrease T, Q (3 sec) pump speed Identify dominant NO frequency (peak) 푄 −푄 푚푒푎푠푢푟푒푑 푠푒푡 ≤ 1.5% 푄푠푒푡 Compute power spectra (FFT) on YES data bins 36.5°C< T Check Temp. NO <37.5°C? NO Read data YES Process Finished profile YES Save to file

Figure 16: Data acquisition and processing flowchart.

31 This section describes the processing methodology of the Doppler velocity signal obtained from a 20 MHz ultrasound probe placed within a flow system. The ultrasound unit (Crystal Biotech, Northborough, MA) drives a 20 MHz probe which is a piezoelectric crystal attached to the end of cylindrical shaped rod. The Doppler ultrasound signal processing method employed is similar to that described by

Thorne et al. [67] and Jones [68]. This processing within the ultrasound unit is described here in brief. A voltage is applied to a piezoelectric crystal (changes size with voltage applied) at a specified frequency (20 MHz) for a brief period of time, which causes ultrasound waves to be generated (in the form of a cosine wave). When the ultrasound signal hits a moving particle (reflector), it gets reflected at a slightly different frequency (higher if the particle is moving towards the probe and lower if away from it). This is known as the Doppler Effect. The crystal then receives the reflected signal for a brief period of time. This transmitting/receiving cycle is called the pulse repetition frequency (PRF) (62.5 kHz). The received signal is then passed through two multiplexers simultaneously, one of them is multiplied by the transmitted signal and the other is multiplied by the phase shifted transmitted signal. The two resultant signals are then passed through two low pass filters where the transmitted high frequencies are filtered out and only signals that are outputted are the signals carrying the Doppler shifted frequency and the phase shifted Doppler shifted frequency. Since the two signals are in quadrature to each other they are known as the quadrature signals. This signal is amplified and output as the audio signal (Figure 17).

32 Figure 17: Schematic diagram of a pulsed Doppler instrument. The solid lines indicate the in-phase signal path and the dashed lines indicate the out-of-phase signal needed for the quadrature output.

푆1(푡) = cos(휔0푡) ∙ cos[(휔0 + 휔푑)푡 + ∅] (Eq. 1)

푆2(푡) = sin(휔0푡)∙ cos[(휔0 + 휔푑)푡 + ∅] (Eq. 2) From trigonometric identities:

1 cos(퐴) ∙ cos(퐵) = [cos(퐴 − 퐵) + cos(퐴 + 퐵)] (Eq. 3) 2 1 sin(퐴) ∙ cos(퐵) = [sin(퐴 + 퐵) + sin(퐴 − 퐵)] (Eq. 4) 2 The two signals take the form;

1 푆 (푡) = [cos(휔 푡 + ∅) + cos([2휔 + 휔 ] ∙ 푡 + ∅)] (Eq. 5) 1 2 푑 0 푑 1 푆 (푡) = [sin([2휔 + 휔 ] ∙ 푡 + ∅) − sin(휔 푡 + ∅)] (Eq. 6) 2 2 0 푑 푑

Low pass filtering removes the high frequency component [2휔0 + 휔푑] and the resulting quadrature signals are;

1 퐼(푡) = cos(휔 ∙ 푡 + ∅) (Eq. 7) 2 푑 1 푄(푡) = − sin(휔 ∙ 푡 + ∅) (Eq. 8) 2 푑 Where, 퐼(푡) is in-phase and 푄(푡) is out-of-phase. The complex signal was obtained using formula:

퐶(푡) = 퐼(푡) − 𝑖 ∙ 푄(푡) (Eq. 9)

33

The Doppler shifted frequency signal (Figure 18) is given as audio output from the ultrasound unit. The maximum frequency that can be measured without aliasing

(Figure 19) is 31.25 kHz if only the real part of the signal is used [166 cm/s with a

20 MHz probe at 45° [69] because of Nyquist criteria, as the pulse repetition frequency is 62.5 kHz. If the quadrature signal is used, then the maximum frequency that can be measured equals the PRF (62.5 kHz). To obtain this, first the two quadrature signals had to be combined [CS(t) = I(t) – i*Q(t)], then complex

FFT had to be done on the combined signal. The first half of the FFT yielded frequencies up to the Nyquist frequency and the second half of the FFT yielded frequencies beyond Nyquist frequency but below the PRF. This analog signal was acquired using a data acquisition system (NI USB-6229, National Instruments,

Austin, TX), which then digitized the analog Doppler shifted frequency signal and recorded it on a computer at 250 kS/s for three seconds making the total number of data points = 750,000. Unsteady volume flow rate was recorded simultaneously at 250 kS/s using a transonic volume flowmeter.

Figure 18: Doppler shifted frequency signal (left) and zoomed view (right). Note that this is an example and the data rate is different than what was used.

34

Figure 19: Aliasing causing false frequency.

Within a straight pipe flow system (Figure 4), the time averaged velocity over three seconds was measured at 21 locations along a line at an angle of 60° across the diameter to obtain the velocity profile. To obtain the time average velocity, the power spectra for each bin of 1024 points was averaged over three seconds to obtain average power spectrum for each location. The mean of the frequencies having >85% power was calculated from the power spectrum and that frequency was used as the dominant Doppler shifted frequency to compute the time averaged velocity (Eq. 10) for that location in order to create a velocity profile. Velocity from

Doppler shifted frequency were obtained using the classic Doppler ultrasound relationship [67, 70-73].

푓푑∙푐 푣 = (Eq. 10) 2∙푓표∙cos 휃 Where, 푚 푣 = 푣푒푙표푐𝑖푡푦 [ ] 푠푒푐 푚 푐 = 푠푝푒푒푑 표푓 푠표푢푛푑 [ ] 푠

푓표 = 푇푟푎푛푠푚𝑖푡푡푒푑 푓푟푒푞푢푒푛푐푦 [퐻푧]

푓푑 = 퐷표푝푝푙푒푟 푓푟푒푞푢푒푛푐푦 [퐻푧] 휃 = 푃푟표푏푒 푎푛푔푙푒 푤𝑖푡ℎ 푟푒푠푝푒푐푡 푡표 푓푙표푤

35 The data for the center location was then segmented into bins containing 2048 data points each (8.19 ms). To increase the number of velocity time points after processing, 50% overlap of each bin was used (i.e. each bin consists of the trailing half of the previous bin combined with the leading half of the trailing bin) [67]. An

FFT was applied to each bin to obtain a power spectrum that represented the velocity of all the particles in the sample volume. The frequency for peak power was then detected for each bin representing the velocity over a period of 8.19 ms.

Due to the 50% overlap, velocity data was obtained every 4.095 ms.

(a)

(b) (c)

Figure 20: Description of the difficulties of US with large probe volume to capture velocity fluctuations form different size vortices.

The processing of US data caused the true instantaneous velocity values to be lost since a finite time period (8.19 ms) was needed to extract the Doppler frequency

(Figure 20a). Thus, vortices smaller than the probe volume were not detected (see

Figure 20b). In addition, vortices smaller than a distance equal to the mean velocity multiplied by 8.19 ms also went undetected as the sampling time window

36 limited the vortex size that could be detected. For example, a mean velocity of 1 m/s multiplied by 8.19 ms gave a time window length of 8.19 mm. Thus, fluctuations caused by a vortex 8 mm in length (or smaller) would also go largely undetected (see Figure 20c). Decreasing the bin size or increasing the data acquisition rate could help to detect smaller vortices.

Velocities computed from each bin when put together formed a velocity trace (see

Results Chapter V). These velocity trace data were then used to obtain the power spectrum. This power spectrum provided information about spectral broadening due to spatial gradients in velocity as well as velocity fluctuations in time related to transitional flow.

4.5 Importance of Quadrature Signal

Figure 21 illustrates the error associated with not using the quadrature signals as it might lead to a completely different result. Velocities corresponding to Doppler shifted frequencies larger than half of the PRF were represented by a frequency less than PRF/2. In all the measurements in this study complex FFT was performed on the combined quadrature signals obtained from both channels.

37 Figure 21: Difference in centerline velocities with and without using the quadrature signals. If only the real part of the signal (single channel) is used the measured frequency aliases about the Nyquist frequency (PRF/2).

4.6 Voltage and Temperature Gradient Calibration

Five set voltages (0.5, 0.75, 1.0, 1.25, 1.5, and 1.75 V) were supplied to the pump power supply analog input and corresponding flowrates were recorded (Figure 22).

The resultant calibration enabled us to set any flowrate by changing the analog input voltage.

38

Figure 22: Calibrate voltage applied to pump power supply versus Reynolds number (flowrate). The flowrate varies linearly with voltage. The diamond represents the voltage applied at a particular run during the experiment to obtain flowrate corresponding to a set Reynolds number (Re = 750 in this case).

To access the rate of heating and cooling for different Re a calibration code was run before the experiment. The idea was to obtain the temperature gradients for different Re so that the rate could be controlled and utilized during post-processing.

Figure 23 shows that the equilibrium Re ≈ 2043 i.e. any Re greater than the equilibrium will result in heating and lower than the equilibrium will result in cooling.

After data acquisition for one Re was done the code computed if it needed to heat up or cool down based on the next Re it was going to run and what the current temperature was. If the next Re was cooling the gradient of heating was computed from the temperature rise required and the previous post-processing time (for first post-processing the code assumed 180 s). Then using the above curve the required Re was computed and the pump was adjusted. In the later studies this

39 process was improved to incorporate automated heating and cooling (subsection

4.7).

Figure 23: Map temperature gradient versus Reynolds number. It determines if a particular Reynolds number is heating (positive gradient) or cooling (negative gradient) and at what rate.

4.7 Ultrasound Probe Range and Rotational Orientation

Measurements have been taken for ranges (focal length) from 2 to 10 mm in steps of 1 mm (Figure 24). The most consistent results are obtained when the ranges are between 4 and 6 mm. So tests were run again for ranges 4 to 6 mm in steps of 0.5 mm and an increased number of points on the profile (21 as opposed to 9 points) (Figure 25). A range of 4 mm was chosen as advised by Hartley [72] as the resulting sample volume will be the smallest (< 0.02 μL, 0.3 mm diameter, 0.3 mm long) [74].

40 Figure 24: Velocity profiles (9 points) measured at different range settings (focal lengths) between 2 and 10 mm.

Figure 25: Velocity profiles (21 points) measured at different range settings (focal lengths) between 4 and 6 mm.

41 Probe 1 Probe 2 250 250 217.6 209.5 190.1 200 189.1 200 158.6 156.6 145.4 144.4 136.2 135.2 135.1 134.8 134.2 133.8 133.7 150 150 133.2

100 100

50 50 Centerline Velocity [cm/s] Velocity Centerline [cm/s] Velocity Centerline 0 0 0 0 45 90 45 90 135 180 225 270 315 135 180 225 270 315 Probe Rotation Angle [Degree] Probe Rotation Angle [Degree]

Figure 26: Rotational asymmetry of the Doppler ultrasound probe. One probe had a maximum difference of ~2% while the other one presented a maximum difference of ~51%. Probe 2 was used to measure velocities in blood and WG while probe 1 was used to measure velocities in WGX.

The two pulsed Doppler ultrasound probes used in the present study behaved differently from one another. One of the probes (Probe 2) exhibited excellent consistency in measurement when rotated with respect to its axis, but the other

(Probe 1) did not, indicating that the piezo-electric crystal was not perpendicular to the axis of the containing tube. A maximum difference of ≈51% was observed between the measured velocities at different rotational orientations (Figure 26).

4.8 Temperature Control

Temperature was recorded during data acquisition (Figure 27). Temperature just before acquisition is shown as yellow circles and temperature just after data acquisition (successful) is shown in green. Black circles indicate heating and blue circles represent cooling during post-processing. The bands represent post-

42 processing in between data acquisition for two different Re. The post-processing time was observed to increase with time. This problem might have been caused by the RAM getting clogged. All data points were acquired between 36.75 and

37.35 °C. The cooling coil had to be used for the higher Re, because of heat generation due to viscous dissipation.

Figure 27: Temperatures during data acquisition. The bands represent post- processing in between two Re measurements. The post-processing time increases with time (clogging up of the RAM might be a probable reason).

For the later studies the process and algorithm of temperature control has been updated. Unlike previous experiments the temperature was recorded simultaneously with the US and the flowrate. If both the temperature and the flowrate were within the limits (same as before), the data were saved. The temperature was controlled using two fluids, one hot (50°C) and one cold (20°C) flowing through coils submerged in the test fluid in the reservoir. The flow of water was controlled using computer controlled pumps (DC40C-2445, ZKSJ, China).

The algorithm consisted of two major logics, heating/cooling depending on the

43

temperature differential between required and recorded, and preemptive heating/cooling depending on the gradient so as to avoid overshooting.

4.9 Red Blood Cell Evaluation

In order to verify if blood was normal, red blood cells were 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 to stain cells with compromised cell membranes. Ten microliters of the resulting solution was then loaded into a hemocytometer. The erythrocytes were visually examined to ensure their visibility and if their morphology was normal. Images were acquired using an Axiovert 200 inverted microscope and the accompanying AxioVision software (Zeiss, Jena, Germany).

To quantify if significant number of cells were lysed, 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 450 nm on the blood samples revealed a globally strong, locally weak peak at 418 nm with a strongly linear concentration-dependent response.

Thus, the 418nm wavelength was used for analyzing all samples.

4.10 Statistics

An unpaired 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. A paired two-tailed

44

Student’s t-test was used to determine changes in fluid properties (density and viscosity) before and after experiments and also to determine difference in Recr between the test fluids. RMS, standard deviation (SD), and standard error of mean

(SEM) are defined as follows:

∑푁 (푈 − 푈̅) 푅푀푆 = √ 1 푖 (퐸푞. 11) 푁

∑푁 (푈 − 푈̅) 푆퐷 = √ 1 푖 (퐸푞. 12) 푁 − 1 푆퐷 푆퐸푀 = (퐸푞. 13) √푁 − 1

Where,

th 푈푖 = velocity of i sample

푈̅ = mean velocity

푁 = number of samples

45 CHAPTER V

V. RESULTS (STRAIGHT PIPE)

5.1 Results Overview

The purpose of the experiment was to investigate the TT of blood and compare it to that of a Newtonian fluid (water-glycerin, WG) and a shear-thinning non-

Newtonian fluid (water-glycerin-xanthan-gum, WGX) in a straight pipe under steady flow condition. The results of the straight pipe study are shown in this

Chapter.

5.2 Microscopy

Microscopy demonstrated the absence of both clotting and cell lysis (Figure 28).

Erythrocytes maintained their biconcave morphology throughout the experiment.

The number of erythrocytes with compromised membranes, as revealed by trypan blue staining, was comparable for samples taken before and after experiments

(Figure 28 left and right, respectively). To quantify the lyses of red blood cells, the concentrations of hemoglobin before and after the experiment were analyzed. The concentrations of free hemoglobin in the before and after samples were not statistically significant (p = 0.10), validating our qualitative observations. These results indicate that structural integrity of the red blood cells was normal throughout the experiment.

46 Figure 28: Representative micrographs of blood before (left) and after experiment (right). Images show that erythrocytes retain their physiological toroid morphology shape before and after the velocity experiment. Cell fragments are not visible indicating that cells were not mechanically or osmotically lysed during the experiment. No large change in the number of cells was observed also indicating that cells were not lysed. Additionally, large three-dimensional amorphous clusters of cells linked by dense fibrous masses were not observed, indicating that the blood did not clot during the velocity experiments.

47

5.3 Rheology

Figure 29: Viscosity of blood, water-glycerin (WG) and water-glycerin-xanthan gum (WGX) versus shear rate averaged for three samples (before, during and after experiment). AR200ex, the air bearing parallel plate rheometer shown in inset.

Rheology of blood, WG and WGX were measured (Figure 29 and Table 3). The

Newtonian fluid (WG) depicted a constant viscosity with shear rate (3.3 ± 0.15 cP), as expected. Blood showed a shear thinning nature with viscosities 6.3 ± 0.47, and

3.3 ± 0.14 cP at 20 and 400 s-1, respectively. For WGX, the viscosities were similar to blood for the above two shear rates but were slightly higher in between

(maximum difference was 12.5%). The viscosities shown in Figure 29 and Table 3 were the average viscosities over three samples (before, during and after experiment). The smaller standard deviations indicate that the viscosities remained unchanged during the experiments. The viscosities at 400 s-1 were used to compute Re for blood and WG and viscosities at 1100 s-1 were used for the non-

Newtonian blood analogs.

48

Table 3: Average viscosity for four test fluids. Blood and WG averaged before and after experiments and also between samples. WGXH and WGXL are the averages of before and after experiment only.

% Standard Viscosity Shear Deviation Rate WG Blood WGXH WGXL WG Blood

[s-1] [cP] [cP] [cP] [cP] [%] [%] 1 - 33.45 44.11 7.00 - 27.88 2 - 18.14 39.17 6.30 - 14.95 4 - 12.52 32.70 5.95 - 9.57 6 - 10.22 28.56 5.73 - 7.36 8 - 8.94 25.97 5.62 - 7.54 10 - 8.13 23.90 5.49 - 7.42 12 - 7.55 22.38 5.33 - 7.78 15 3.34 6.95 20.51 5.21 6.32 7.76 20 3.29 6.29 18.26 4.98 5.22 7.62 30 3.31 5.51 15.33 4.67 5.88 7.16 40 3.30 5.04 13.46 4.45 5.49 6.98 60 3.30 4.48 11.14 4.14 5.43 6.63 80 3.31 4.13 9.71 3.92 5.90 6.38 100 3.29 3.90 8.71 3.75 5.13 6.24 200 3.28 3.40 6.23 3.29 4.94 5.45 300 3.26 3.30 5.14 3.05 4.72 4.91 400 3.25 3.30 4.50 2.90 4.70 4.48 500 3.25 3.35 4.07 2.79 4.70 4.05 700 - - 3.51 2.65 - - 900 - - 3.17 2.56 - - 1100 - - 2.94 2.50 - - 1300 - - 2.77 2.45 - - 1500 - - 2.64 2.43 - -

5.4 Transition to Turbulence

Straight pipe centerline velocity as a function of time for a range of Reynolds numbers between 750 and 3500 are shown in Figure 30 for blood (Sample 1) and

WG (Sample 1). The WG experimental measurements show velocity fluctuations

49 to increase greatly (fluctuations persist during time trace) at the expected Recr of

~2100 for a Newtonian fluid. Note that a large isolated flucutation was present on some traces which did not persist throughout the three second period. It is difficult to characterize these traces. In the present study, it was assumed these traces did not indicate the initiation of TT. While Recr depends on this assumption, consistant classification of Recr allows for comparison between cases. The blood experimental measurements, show a similar trend for velocity fluctuations; however, the Recr occurred at a larger value ~2600. The same is shown in Figure

31 for Sample 2 of blood and WG. Recr was observed at Re ≈ 2100 for WG and at Re ≈ 2500 for blood. For Sample 3 (Figure 32), Recr was observed at Re ≈ 2200 for WG and at Re ≈ 2700 for blood. The mean Recr of TT for the Newtonian fluid was ~2133 (SEM = 40) and for blood was ~2600 (SEM = 70). The blood experiment could only be conducted up to Re = 3100 for Sample 3, because clots were observed after that. Only data up to Re = 3000 has been reported since WG did not have corresponding data.

50 Figure 30: Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 1. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at the expected Reynolds number for a Newtonian fluid (Re ~ 2100- 2300) and a larger Reynolds number for blood (Re ~ 2500-2700). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG.

51 Figure 31: Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 2. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at the expected Reynolds number for a Newtonian fluid (Re ~ 2100- 2300) and a larger Reynolds number for blood (Re ~ 2500-2700). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG.

52 Figure 32: Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 3. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at the expected Reynolds number for a Newtonian fluid (Re ~ 2100- 2300) and a larger Reynolds number for blood (Re ~ 2500-2700). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG.

Mean and RMS velocity profiles are shown in Figure 33 for Blood and WG each as an average of three experiments employing three different fluid samples. These results show velocity profiles to change from parabolic to blunt which again demonstrates a larger critical Reynolds for blood compared to that of a Newtonian fluid. A range of Re were selected to be near the TT regiem based on large increases in RMS and a deviation from the laminar parabolic velocity profile. While

53 Recr depends on this assumption, consistant classification of Recr allows for comparison between cases. The mean Recr of TT for the Newtonian fluid was

~2216 (SEM = 20) and for blood was ~2733 (SEM = 54).

Figure 33: Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number. In addition, these values represent the average values of mean and RMS velocity for three separate experiments. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number. Results show transition to turbulence at a lower Reynolds for Newtonian fluid (Re ~ 2100-2300) than that for blood (Re ~ 2500-2700) based on both the change in velocity profile (parabolic to blunt) and increase in velocity fluctuations near TT.

Mean and RMS velocity profiles for individual samples are shown in Figure 34,

Figure 35 and Figure 36 for Blood and WG. From the velocity profiles, the corresponding Recr for WG for samples 1, 2 and 3 were observed as 2100 - 2300,

2100 - 2300 and 2200 - 2300, respectively. The same for blood was observed at

Re ≈ 2500 - 2800, 2700 - 2900 and 2700 - 2800, respectively.

54 Figure 34: Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 1. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number.

55 Figure 35: Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 2. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number.

56 Figure 36: Velocity profiles measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 3. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number.

Velocity and RMS profiles of two shear thinning fluids, WGXH and WGXL, demonstrated larger critical Reynolds numbers (Figure 37). The more viscous case (WGXH) showed TT near Re ~ 3400-3600 while the less viscous case

(WGXL) showed TT near Re ~ 2800-3000.

57 Figure 37: Normalized mean and RMS velocity profiles measured by Doppler ultrasound for two difference shear thinning fluids (WGXH and WGXL) over three seconds. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number. Results show a delay in TT for WGX2 (Re ≈ 2800-3000) and an even greater delay for WGX1 (Re ≈ 3400-3600) compared to a Newtonian fluid. Rheology of each fluids is shown in Figure 29. Reynolds number is based on viscosity at a shear rate of 1100 s-1 for both fluids.

RMS varying with Re and along the profile is shown in Figure 38 for all samples of blood, WG and the shear-thinning blood analogs. Results shows a two-fold increase at Re ≈ 2000 or 2100 and Re ≈ 2500 to 2600, for the WG and blood samples, respectively. Similar to the velocity time traces, Recr was classified for each RMS plot as the Re at which the RMS increase persisted over multiple radial locations and not limited to an isolated increases in RMS at one location. Again, the Recr will depend on this assumption, but as with the velocity time traces, consistant classification of Recr allows for comparison between cases. The mean

Recr of TT for the Newtonian fluid was ~2066 (SEM = 40) and for blood was ~2600

58 (SEM = 70). For WGXH and WGXL, the two-fold RMS increase were observed at

Re ≈ 3400 and 2800, respectively.

Figure 38: RMS velocity distribution is shown as a function of both Re and radial position. An increase (>2x) at Re ≈ 2100, 2100 and 2000 for the three Newtonian samples 1, 2 and 3, respectively indicate TT. For Blood the same trend was observed at Re ≈ 2600, 2500 and 2500 respectively. For WGXH and WGXL the increases were observed at Re ≈ 3400 and 2800, respectively. Note radial locations near the wall have been excluded due to the artificial spectral broadening due to high shear rates.

Centerline velocity for the four different test fluids show where the profiles become blunt. Only Sample 2 for blood and WG are shown in Figure 39 along with WGXH and WGXL. The theoretical centerline was calculated using Poiseuille laminar flow equations (twice the average velocity) and was plotted in the same figure. Recr was determined by observing where the measured centerline velocity “peeled off” from the theoretical centerline velocity. In addition RMS is also shown as error-bars.

Recr were observed approximately at 2700, 2100, 3400 and 3000 for blood, WG,

WGXH and WGXL, respectively. Note that this is a subjective estimate since the criteria for classification is not precise.

59 Figure 39: Measured centerline velocity (mean and RMS) over three seconds. Theoretical velocity is also shown based on a Poiseuille flow and measured volume flow rate. Plot shows comparison between all four fluids examined: Newtonian (A), blood (B), WGX1 (C) and WGX2 (D) for one experiment. Based on deviation of the mean velocity form theory and larger RMS values, TT is shown to be delayed for all three shear thinning fluids (B, C, and D) and indicate a Newtonian assumption to be reasonable only for Reynolds number below 2000 for steady flow in a straight rigid pipe.

Centerline velocity, normalized by the average velocity at Re = 1000 for all samples of blood, WG, WGXH and WGXL is shown in Figure 40. Results show clear demarcation of Recr between the test fluids. Recr for blood was observed at Re ≈

2600 and 2700, for WG at Re ≈ 2100 and 2200, and 3400 and 3000 for WGXH and WGXL, respectively. The mean Recr of TT for the Newtonian fluid was ~2133

(SEM = 40) and for blood was ~2666 (SEM = 40). These results also showed the repeatability of the experiments for each fluid.

60 Figure 40: Normalized mean centerline velocity under steady flow conditions over three seconds. Mean velocity is normalized by aveage velocity over the cross- section at Re=1000 for each case. Plot shows comparison between all four fluids examined: blood and Newtonian (three samples each), and WGX1 and WGX2 (one sample each) to see the overall impact of shear thinning rheology on centerline velocity.

The Recr for all samples of each fluid tested for transition to turbulence (all three detection methods, RMS, centerline and profile) is listed in Table 4. The density and viscosity, before and after each experiment are also listed along with the percent hematocrit. Hematocrit for Sample 3 of blood was not available due to clotting. The average Recr for blood were observed as 2600 ± 100, 2650 ± 50 and

2700 ± 200 using detection methods, RMS, Centerline and Profile, respectively.

For WG the average Recr were observed as 2050 ± 50, 2100 ± 50 and 2200 ± 100 using detection methods, RMS, Centerline and Profile, respectively. One sample each for WGXH and WGXL were tested and listed in Table 4. Assuming normal distribution of the experiment results the differences between the Recr of blood and the Newtonian fluid were found to be statistically significant (p = 0.003, 0.0003 and

61 0.003, for the three methods, RMS, centerline and profile, respectively as shown in Table 4). The changes in viscosity before and after experiments are insignificant, p = 0.91 and 0.48 for Newtonian and blood, respectively. Similar results were obtained for density before and after the experiments (p = 0.45 and 0.18 for

Newtonian and blood, respectively) confirming insignificant differences.

Table 4: Parameters and critical Re of TT for each test fluid. Density and viscosity are before/after experiment (note: viscosity is 400 s-1 for blood and 1100 s-1 for WGX). Hct ρ µ Fluid No. Recr Recr Re (Profile) [%] [g/cc] [cP] (RMS) (Centerline) cr Newtonian 1.09 3.50/ 1 - 2100 2100 2100-2300 /1.10 3.46 Newtonian 1.09 3.04/ 2 - 2100 2100 2100-2300 /1.11 3.02 Newtonian 1.12 3.28/ 3 - 2000 2200 2200-2300 /1.12 3.27 Blood 1.05 3.31/ 1 36.6 2600 2600 2500-2800 /1.06 3.35 Blood 1.05 3.35/ 2 35.9 2700 2700 2700-2900 /1.06 3.40 Blood 1.05 2.98/ 3 NA 2500 2700 2700-2800 /1.05 3.21 WGXH 0.99 3.07/ 1 - 3400 3400 3200-3800 /0.97 3.01 WGXL 1.05/1. 2.47/ 1 - 2800 3000 3000-3100 05 2.46

Figure 41 shows the mean spectral power of the velocity fluctuations at centerline of the pipe, averaged for all frequencies from 1 – 125 Hz for all samples of all fluids tested. Figure 42 shows the mean spectral power of the mean of three samples of blood and WG. Results show visible separation between peaks of the mean power.

A sudden jump in mean power for blood was observed at Re ≈ 2500, at Re ≈ 2000 for WG and Re ≈ 3400 and Re ≈ 2800 for WGXH and WGXL, respectively.

62 Figure 41: Mean Power of the centerline velocity trace vs. Reynolds number for three samples each of blood and WG shows slight difference in the Reynolds numbers where peak power occurs. Also shown are the mean powers for WGXH and WGXL.

Figure 42: Mean Power of the centerline velocity trace vs. Reynolds number shows considerable difference in the Reynolds numbers where peak power occurs. The mean power for blood and WG are the average values for three samples.

63 Figure 43: Repeatability for the six experiments (blood and Newtonian fluid experiments were repeated three times each) was assessed for the normalized velocity profiles both mean and RMS. Figure shows standard error (SEM) of the mean velocity of blood (A) and Newtonian fluid (B) with error-bars representing SEM of the RMS. Note multiple Reynolds numbers are shown separated on the x- axis using a shift of 10% for each Reynolds number. Mean velocity results show the experiments to be remarkably consistent for blood (<1%) and WG (<3%) near the centerline for Re <= 2200. Mean velocity variations were observed in blood at larger Reynolds numbers (Re>2700, ~10%). SEM of RMS in blood and Newtonian fluid at larger Reynolds numbers (Re>2600) did show greater variation although this was less than 5% of the mean normalized velocity. Values near the wall (< 1mm) were not included for clarity since SEs in the near wall region were large. Values below 2% is shown with open circles.

Standard error of mean (SEM) velocity measurements for different samples of each fluid show the experiments to be consistent (<3% difference between samples) (Figure 43) for both blood and Newtonian fluid. Quantitative comparison between the mean velocity for blood and WG is shown in Figure 44. For laminar flow (Re <= 2200), only small differences (< 10%) were observed between blood and WG mean velocity profiles for radial locations near the pipe center (r < 1mm or 30% of radius). However, differences as high as 40% were observed at the

64 larger Reynolds numbers in the region where TT was different for the two fluids

(2300 < Re < 2800). Velocity profiles were again similar at Re=3000. Values near the wall (close that 1mm from wall) were excluded since those values had noise.

Figure 44: Difference between normalized profiles of blood and Newtonian fluid for mean velocity at different Reynolds numbers. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 20 for each Reynolds number for the velocity. Results of mean velocity show small differences (<5% near the centerline for 1250 < Re <= 2200) between the blood and Newtonian fluid profiles in the laminar regime (Re<2200) and large differences for Re>2200. Note values near the wall (< 1mm) were not included for clarity since differences in the near wall region were large. Difference below 5% is shown with open circles.

Figure 45, Figure 46 and Figure 47 show the velocity profiles and the corresponding centerline power spectrums. As the velocity profile becomes blunt

(not laminar any more) the power spectrum broadens showing the existence of a large number of velocities indicating increased velocity fluctuations. The broadness of the power spectra increases from 43 – 79 %, 45 – 76 % and 43 – 78

% for blood, WG and WGXL, respectively. The red line in the figure is a parabola constructed using the maximum measured velocity in the profile to guide the eye.

The magenta lines were constructed using the velocity computed from the measured flowrate. A considerable difference was observed between the measured velocity peaks and the peak of the velocities computed from the measured flowrates. This difference was due to the ultrasound measurement

65 processing technique. Frequencies corresponding to the peaks of the bell shaped power spectra were used to calculate the dominant frequency, while velocities in the probe volume had a rather large distribution. For example in Figure 45 (top- right) the frequency chosen was 14.68 kHz but the power distribution ranged from

~12 to ~17 kHz. In WGX larger differences were noticed. That might have been because for WGX probe-1 was used that was not symmetric about the axis (Figure

26).

Figure 45: Velocity profile (top-left) and mean power spectrum at centerline (top- right) for laminar flow (Re = 1242) in blood. Velocity profile (bottom-left) and mean power spectrum at centerline (bottom-right) for turbulent flow (Re = 2896).

66 Figure 46: Velocity profile (top-left) and mean power spectrum at centerline (top- right) for laminar flow (Re = 1247) in WG. Velocity profile (bottom-left) and mean power spectrum at centerline (bottom-right) for turbulent flow (Re = 2605).

Figure 47: Velocity profile (top-left) and mean power spectrum at centerline (top- right) for laminar flow (Re = 1489) in WGXL. Velocity profile (bottom-left) and mean power spectrum at centerline (bottom-right) for turbulent flow (Re = 3268).

As the flowrate was increased, mean velocity and hence, Reynolds number (based on nominal viscosity) increased. Figure 48 show that the time averaged centerline velocity increased from 113.2 to 187.2 cm/s with a corresponding increase in Re from 1242 to 2896. Transition to turbulence was expected where the centerline

67 velocity no longer increased linearly as twice the mean velocity (as obtained from flow rate) as shown in Figure 39 and Figure 40.

(a) (b) (c) (d)

Figure 48: Velocity trace (a) and Power spectrum of the velocity distribution (b) for laminar flow, Re = 1242 (Green Box) and Velocity trace (c) and Power spectrum of the velocity distribution (d) for turbulent flow, Re = 2896 (Red box) in blood.

The standard deviation of the unsteady velocity measurement normalized by the time averaged centerline velocity showed changes (one order of magnitude) with

Reynolds number. This was likely due to the presence of chaotic movements in the flow and hence an indicator of transition to turbulence (Figure 49). In addition, the mean power of the velocity power spectrum in time increased significantly with

Reynolds number (two orders of magnitude). Mean power is typically related to the number of reflecting particles in the flow. In this case, the number reflecting particle per unit volume remained the same; however, increased velocity increased the number of particles passing through the probe volume for a given time period.

Rapid fluctuations in the flow would further increase the number of reflecting particles. Thus, mean power of the velocity time power spectrum may be an

68 indicator of the transition to turbulence as well. This parameter was shown to closely follow the standard deviation trend (Figure 49).

700 0.16

600 0.14

Mean Power 0.12 500 SD/Mean velocity /kHz)

2 0.1 400 0.08 300 0.06

200 (Dimensionless)

Mean Power (V Power Mean 0.04

100 0.02 Standard Deviation/Mean Velocity Velocity Deviation/Mean Standard 0 0 0 500 1000 1500 2000 2500 3000 3500 Reynolds number

Figure 49: Change in mean power and velocity fluctuation (non-dimensionalized by the mean velocity computed from measured centerline velocity) with Reynolds number for blood. The instantaneous velocity and mean power follow the same trend and increase by an order of magnitude around Re ≈ 2200.

69 CHAPTER VI

VI. RESULTS (S-SHAPED PIPE)

6.1 Results Overview

The purpose of the experiment was to investigate the TT of blood and compare it to that of a Newtonian fluid (water-glycerin, WG) in an S-shaped pipe under steady flow condition. The results of the S-shaped pipe study are shown in this Chapter.

70

6.2 Rheology

Figure 50: Rheology of blood and WG for S-shape pipe experiments.

As observed in Figure 50 and Table 5 WG showed a constant viscosity of 3.34 ±

0.05 cP; however, deviations were observed for low shear rates (<4 s-1). Blood showed a shear thinning nature with viscosities 4.34 ± 0.46, and 3.02 ± 0.14 cP at

20 and 400 s-1, respectively. However, the non-Newtonian behavior of the blood used in this case was to a lesser extent than that observed for the blood used in the straight pipe cases. The blood was not observed to have a “knee” (shear rate above which blood behaves as a Newtonian fluid) up to a shear rate of 400 s-1.

The 95% confidence interval calculated for the low shear rate viscosities (3.41 -

5.91 cP) does not overlap the ones calculated for the rest of the viscosity values

(3.31 – 3.37 cP). For this reason the viscosities measured at 1 and 2 s-1 have been discarded.

71

Table 5: Average viscosity of blood and WG averaged before and after experiment and also between samples.

Shear Viscosity % Standard Deviation Rate WG Blood WG Blood [s-1] [cP] [cP] [%] [%] 1 - 12.70 - 27.14 2 - 8.61 - 17.38 4 3.53 7.14 2.18 22.56 6 3.39 6.05 2.45 26.87 8 3.39 5.32 0.77 17.98 10 3.30 4.99 2.47 20.48 12 3.34 4.73 0.75 17.66 15 3.34 4.48 0.39 13.90 20 3.33 4.34 0.48 10.67 30 3.33 4.17 0.79 6.87 40 3.32 4.08 0.70 4.95 60 3.32 3.92 0.78 3.92 80 3.32 3.79 0.82 3.50 100 3.31 3.70 0.70 4.44 200 3.31 3.30 0.98 4.65 300 3.30 3.10 1.40 4.54 400 3.31 3.02 1.99 4.64 500 3.32 2.99 3.04 5.63

6.3 Transition to Turbulence

S-shaped pipe centerline velocity as a function of time for a range of Reynolds numbers between 500 and 2800 are shown in Figure 51 for Blood (Sample 1) and

WG (Sample 1). The WG experimental measurements show velocity fluctuations to increase greatly at a lower Recr ≈ 1000 than the expected value (Recr ≈ 2100) in a straight pipe for a Newtonian fluid. The blood experimental measurements show a similar trend for velocity fluctuations; however, the Recr occurred at a slightly larger value ~1200. The same is shown in Figure 52 for Sample 2 of blood and

WG. Recr was observed at Re ≈ 1000 for WG and at Re ≈ 1100 for blood. In case

72 of Sample 3 (Figure 53), Recr was observed at Re ≈ 1000 and Re ≈ 1100 for WG and blood, respectively. The mean Recr of TT for the Newtonian fluid was ~1000

(SEM = 0) and for blood was ~1133 (SEM = 40). Considerable amount of

“turbulent like” fluctuations were observed for WG at low Re (500). This can be attributed to a lower number of reflective particles (TiO2) at low velocities.

Figure 51: Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 1 in an S-shaped pipe. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at a lower than expected Reynolds number for a Newtonian fluid (Re ~ 1000) and a slightly larger Reynolds number for blood (Re ~ 1200). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG.

73 Figure 52: Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 2 in an S-shaped pipe. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at a lower than expected Reynolds number for a Newtonian fluid (Re ~ 1000) and a slightly larger Reynolds number for blood (Re ~ 1100). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG.

74 Figure 53: Velocity traces measured by Doppler ultrasound at pipe centerline for blood (A) and Newtonian fluid (B) for sample 3 in an S-shaped pipe. Note multiple Reynolds numbers are shown separated on the y-axis using a consistent shift of 1 for each Reynolds number. Velocity fluctuations under steady flow conditions show transition to turbulence at a lower than expected Reynolds number for a Newtonian fluid (Re ~ 1000) and a slightly larger Reynolds number for blood (Re ~ 1100). Reynolds number is based on viscosity at a shear rate of 400 s-1 for both blood and WG.

Mean and RMS velocity profiles in the S-shaped pipe are shown in Figure 54 for

Blood and WG each as an average of three experiments employing three different fluid samples. These results show velocity profiles to change from parabolic to blunt which again demonstrates a larger Recr for blood compared to that of a

Newtonian fluid. Recr was observed at Re ≈ 1000-1100 and Re ≈ 900-1000 for

75 blood and WG, respectively. A range of Re were selected to be near the TT regiem based on large increases in RMS and a development of a blunt velocity profile.

While Recr depends on this assumption, consistant classification of Recr allows for comparison between cases. The mean Recr of TT for the Newtonian fluid was ~950

(SEM = 0) and for blood was ~1050 (SEM = 0).

Figure 54: Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number. In addition, these values represent the average values of mean and RMS velocity for three separate experiments. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number. Results show transition to turbulence at a slightly lower Reynolds for Newtonian fluid (Re ~ 900-1000) than that for blood (Re ~ 1000-1100) based on both the change in velocity profile (parabolic to blunt) and increase in velocity fluctuations near TT.

Mean and RMS velocity profiles for individual samples are shown in Figure 55,

Figure 56 and Figure 57 for Blood and WG. From the velocity profiles, the

76 corresponding Recr for WG were observed as 900 – 1000 for all three samples.

The same for blood was observed at Re ≈ 1000 – 1100 for all three samples.

Figure 55: Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 1. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number.

77 Figure 56: Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 2. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number.

78 Figure 57: Velocity profiles in an S-shaped pipe, measured by Doppler ultrasound for blood (A) and Newtonian fluid (B) shown as the mean and RMS (shown as error-bars) velocity over three seconds normalized by the average velocity in the pipe for each Reynolds number for sample 3. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 0.5 for each Reynolds number.

RMS varying with Re and radial position for an S-shaped pipe is shown in Figure

58 for all samples of blood and WG. Results show more than a two-fold increase at Re ≈ 1000 and Re ≈ 1100 for the WG and blood samples, respectively. Recr was classified for each RMS plot as the Re at which the RMS increase persisted over multiple radial locations and not limited to an isolated increases in RMS at one location or near a wall. The Recr will depend on this assumption, but as previously stated, consistant classification of Recr allows for comparison between cases. The mean Recr of TT for the Newtonian fluid was ~1000 (SEM = 0) and for blood was

~1100 (SEM = 0). Radial locations near the walls have been excluded due to the artificial spectral broadening due to high shear rates.

79 Figure 58: RMS velocity distribution is shown as a function of both Re and radial position. An increase (>4x) at Re ≈ 1000 for all three Newtonian samples indicate TT. For Blood the same trend was observed at Re ≈ 1200, 1100 and 1100 for samples 1, 2 and 3, respectively.

The Recr for all samples of each fluid tested for transition to turbulence (all three detection methods, RMS, Centerline and Profile) is listed in Table 6. The density and viscosity, before and after each experiment are also listed along with the percent hematocrit. The average Recr for blood were observed as 1100, 1150 ± 50 and 1050 ± 50 using detection methods, RMS, Centerline velocity fluctuations and

Profile, respectively. For WG the average Recr were observed as 1000, 1000 and

950 ± 50 using detection methods, RMS, Centerline and Profile, respectively.

Assuming normal distribution of the experiment results the difference between the

Recr is statistically insignificant (p = 0.058) as calculated from the centerline results in Table 6. The changes in viscosity before and after experiments are also insignificant, p = 0.79 and 0.85 for Newtonian and blood, respectively. Similar

80 results were obtained for density before and after the experiments (p = 0.55 and

0.42 for Newtonian and blood, respectively) confirming insignificant differences.

Table 6: Parameters and critical Re of TT for each test fluid. Density and viscosity are before/after experiment (note: viscosity is 400 s-1 for blood).

Re Hct ρ cr Fluid No. µ [cP] Recr (Centerline Re (Profile) [%] [g/cc] (RMS) Velocity cr Fluctuations)

Newtonian 1.08/ 3.29/ 1 - 1000 1000 900-1000 1.12 3.24 Newtonian 1.10/ 3.35/ 2 - 1000 1000 900-1000 1.09 3.38 Newtonian 1.12/ 3.30/ 3 - 1000 1000 900-1000 1.12 3.28 Blood 1.02/ 2.87/ 1 34.6 1100 1200 1000-1100 1.02 2.92 Blood 1.03/ 3.00/ 2 35.3 1100 1100 1000-1100 1.02 3.08 Blood 1.02/ 3.19/ 3 35.8 1100 1100 1000-1100 1.02 3.13

Figure 59 shows the mean power of the velocity fluctuations at centerline of the pipe, averaged for all frequencies from 1 – 125 Hz. Results show a sudden jump in mean power, indicative of turbulence. Peak RMS for blood were observed at Re

≈ 1200, 1100 and 1100 for samples 1, 2 and 3, respectively, while for WG the same were observed at Re ≈ 1000 for all three samples.

81 Figure 59: Mean Power of the centerline velocity trace vs. Reynolds number for three samples each of blood and WG shows slight difference in the Reynolds numbers where peak power occurs.

This study utilized three different fluid samples for blood and WG, which provided an assessment of the variability and repeatability of these results. This can be seen in a plot showing standard error of the normalized mean velocity in Figure 60

(<3% for Re< 2700 for blood, <5% for all Re for WG). Normalized mean velocity was used since velocity for each Re was slightly different due to changes in viscosity or density. The computer controlled pump was regulated to maintain the flow rate such that the Re was within 1.5% of the set value. The variability and repeatability can also be assessed from the mean power of the centerline velocity at a range of Re values for each case (Figure 59) as well as in the contour plots of

RMS velocity (Figure 58).

82 Figure 60: Repeatability for the six experiments (blood and Newtonian fluid experiments were repeated three times each) was assessed for the normalized velocity profiles both mean and RMS in the S-shaped pipe geometry. Figure shows standard error (SEM) of the mean velocity of blood (A) and Newtonian fluid (B) with error-bars representing SEM of the RMS. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 10% for each Reynolds number. Mean velocity results show the experiments to be remarkably consistent for blood (<2%) and WG (<1%) near the centerline for Re <= 900. Mean velocity variations were observed in blood at larger Reynolds numbers (Re>1100, ~10%) for half of the profile proximal to the probe entry wall. SEM of RMS in blood and Newtonian fluid at larger Reynolds numbers (Re>1300) were smaller compared to those in the transition region. Values near the wall (< 1mm) were not included for clarity since SEs in the near wall region were large. Values below 2% is shown with open circles.

83 Figure 61: Difference between normalized profiles of blood and Newtonian fluid for mean velocity at different Reynolds numbers in an S-shaped pipe geometry. Note multiple Reynolds numbers are shown separated on the x-axis using a shift of 20 for each Reynolds number for the velocity. Results of mean velocity show small differences (<5% near the centerline for 500 < Re <= 1100 and Re > 1300) between the blood and Newtonian fluid profiles and large differences in the tranditional region for 1100

Quantitative comparison between the mean velocity for blood and WG is shown in

Figure 61. For laminar flow (Re <= 1100), only small differences (< 10%) were observed between blood and WG mean velocity profiles for radial locations near the pipe center (r < 1mm or 30% of radius). However, differences as high as 20% were observed at the larger Reynolds numbers in the region where TT was different for the two fluids (1100 < Re < 1300). Velocity profiles were again similar at Re>1300. Values near the wall (close that 1mm from wall) were excluded since those values had significant noise.

84 CHAPTER VII

VII. DISCUSSION

7.1 Overview

In vitro and in silico studies have been conducted to study the relationship between hemodynamic forces and the pathogenesis of arterial diseases [2, 28, 75]. These studies often examine hemodynamics in geometries with large shear rates (>200 s-1) where blood is assumed to behave much as a Newtonian fluid. To investigate the impact of this assumption, velocity profiles at various Re have been measured across the diameter of a straight rigid pipe and downstream of a S-shaped pipe for whole blood and a Newtonian analog under steady flow conditions. Substantial differences in mean and unsteady velocity were observed between the two test fluids at Re near TT in the straight pipe case.

7.2 Straight Pipe

The viscosity results for our experiments (Figure 29 and Table 3) show blood rheology to be shear thinning as reported in other studies in the literature [7, 8, 42,

44, 46, 47]. Blood rheology did not change appreciably (<10% for shear rates > 2 s-1) between measurements taken before and after each experiments nor did we observe changes in RBC morphology (Figure 28). The concentrations of

85 hemoglobin in the before and after samples were also not statistically significant indicating minimum cell lysis. Re for blood for all experiments was based on the measured viscosity at high shear rate (400 s-1) where viscosity no longer changes with shear rate. This viscosity was chosen to be consistent (with respect to definition of Re) with the previous researchers [10-16], who simulated blood as a

Newtonian fluid. Note that in a pipe, shear rate varies from zero at the centerline to a maximum value at the wall (linearly in the laminar regime).

Three velocity markers were utilized to determine the Re where TT first occurs for each test fluid. First, centerline velocity fluctuations demonstrate the Re at which large scale fluctuations first appear in the flow (Figure 30, Figure 31 and Figure

32) [38]. These fluctuations can be seen as a sudden increase in RMS velocity

(normalized by mean velocity) as Re is increased (Figure 30,Figure 31 and Figure

32). Second, this method can be applied to velocity traces at each radial measurement location across the pipe to insure that the entire flow field is following the centerline trend (Figure 33, Figure 34, Figure 35, Figure 36, Figure 37 and

Figure 38). Note that near wall velocity has been excluded in Figure 38 since the spectral broadening in the near wall high shear-rate regions would erroneously show high RMS even for low Re. Third, specific to straight pipes with steady flow, one can examine the change in velocity profile from parabolic at laminar conditions to blunt as flow transitions to turbulence. This change is most dramatic at the centerline and can be observed as a deviation from the theoretical centerline velocity (Figure 39 and Figure 40) [35]. The average velocity at Re = 1000 was used to normalize the centerline velocities in Figure 40. Note that any laminar Re

86 would be acceptable for this normalization. Velocity profiles at different Re on one plot demonstrate the shape change [38] (Figure 33, Figure 34, Figure 35, Figure

36 and Figure 37). While this method does show a change in the profile shape with Re, it is difficult to select one specific Re for TT since the change in shape is often gradual and not a sudden jump. In addition, there is noise in the data that can appear as the start of a change. Thus, we also used velocity profiles and RMS to dtermine the TT. The velocity profiles begin to shift from a parabolic to a blunt shape near Re ~ 2100-2300, ~2700, ~3000-3100, and 3200-3700 for WG, BL,

WGXL, and WGXH, respectively (Table 4). In addition, this study utilized three different fluid samples for blood and WG, which provided an assessment of the variability and repeatability of these results. This can be seen in a plot showing standard error of the normalized mean velocity in Figure 43 (<3% for Re< 2700 for blood, <5% for all Re for WG). Normalized mean velocity was used since velocity for each Re was slightly different due to changes in viscosity or density. The computer controlled pump was regulated to maintain the flow rate such that the Re was within 1.5% of the set value. The variability and repeatability can also be assessed form the centerline velocity at a range of Re values for each case (Figure

40) as well as in the contour plots of RMS velocity (Figure 38).

The TT results of our study differ greatly from Ferrari et al. [35] who also examined whole blood TT in a straight pipe. The whole blood Recr in our study was found to be ~2500-2700 while Ferrari et al. found it to be ~500. The results of Ferrari et al. are also in contrast to previously reported Recr for non-Newtonian fluids [39, 76,

77]. In general, the results presented by Ferrari et al. do not clearly indicate that

87 the flow transitioned from laminar for a variety of reasons. Frist, the DUS measurement location was downstream of the probe such that the probe wake could alter the measured velocity whereas the probe was directed upstream in the present study. Ferrari et al. also used a peristaltic pump, which results in steady flow plus a small pulsatile component of unknown magnitude, which may have altered the results, since pulsatility might alter the Recr (as shown by Nerem and

Seed [34] and an unsteady flow study, Appendix D). One interesting observation of the unsteady flow study was Recr of blood was delayed compared to that for the steady flow case for fast and slow acceleration as well as slow deceleration. Only fast deceleration showed a lower Recr. In summary, pulsatility alters transition. One reason for the difference in Recr between the accelerating and decelerating phase might be the time rate of change of viscosity that has not been evaluated in this study. Also, how the viscosity of blood behaves under oscillatory shear stress has not been documented in this thesis. The deviation of centerline velocity from the theoretical velocity was not abrupt but rather changed gradually up to Re≈1500.

Ferrari et al. used a catheter mounted DUS probe introduced in the pipe using a thin flexible wire that might shift from the centerline due to change in flowrate. This will cause the measured velocity to be lower since the centerline has the highest velocity. The orientation of the piezoelectric crystal (at the probe tip) with respect to the flow is important to evaluate the velocities accurately as this angle is a part of the velocity equation (Equation 1).

The present study results are similar to that reported by Nerem and Seed [34] who found fluctuations present at Re between 2050 and 3230. Note, the Recr value for

88 blood in our stady flow study is in the middle of the range reported by Nerem and

Seed. Their study was in vivo and under pulsatile conditions. Interesting to note that with increasing pulsatility, their Recr increased. This relationship was weak as it varied with the square root of the pulsatility (Recr = 250α, where = √푟휔⁄휗 ).

It is difficult to compare the present results to the previously mentioned carotid bifurcation studies with a non-Newtonian test fluid [17] [18] because the present flow geometry was a simple straight pipe under steady flow conditions. However, the inlet of the carotid bifurcation was relatively straight for both studies and thus, a comparison of the inlet velocity profiles is warranted. Both studies showed negligible differences between the non-Newtonian and Newtonian velocity profiles at the common carotid artery for systole, diastole, and under steady flow conditions in the laminar regime. These velocity results match with our steady flow findings for Re<2200 for both blood and Newtonian analog fluids in a straight pipe.

The difference between blood and WG mean velocity profiles are shown in Figure

44. For laminar flow (Re <= 2200), only small differences (< 5%) were observed for radial locations near the pipe center (< 1mm or 30% of radius). However, these velocity differences were as high as 23% for 2300 < Re < 2800 which corresponds to the Re where TT was different for the two fluids. Velocity profiles were found to be similar at Re ≥ 3000. Values near the wall (closer than 1mm from wall) were excluded due to relatively higher noise.

For the six straight tube experiments using blood and a Newtonian analog fluid

(three each), the Newtonian fluid always had a lower Recr of TT than that of blood,

89

on average ~15% less. The difference is small, but we have confidence in the

Reynolds numbers obtained for these experiments. This is because viscosity and density had insignificant changes before and after the experiment (<1%). In addition, the rheometer was calibrated prior to each experiment and was shown to be within 1% of a viscosity standard (400 s-1) and repeatability errors were also

±1%. Consistency is the important value since the two fluids compared had viscosity measurement in the same rheometry. One concern was if the viscosity of blood used to calculate Re was truly the asymptotic viscosity (independent of shear rate). If the blood viscosity did not come down to its asymptotic value at a shear rate of 400 s-1 (which was used to calculate Re), the value selected would be too large. Such an error would have resulted in Re values that would be artificially lower not higher (all three cases were high Recr). Flow meter calibration was checked before and after experiments and was <2% change. Thus, the conclusion that blood transitions at a higher Re than a Newtonian fluid in a straight pipe under steady flow conditions is a conservative conclusion.

7.3 S-Shaped Pipe

The viscosity results for our experiments Figure 50 and Table 5 show blood rheology to be shear thinning as reported in other studies in the literature [7, 8, 42,

44, 46, 47]. Blood rheology did not change appreciably (<2% for shear rates > 1 s-1) between measurements taken before and after each experiment nor did we observe changes in RBC morphology. Re for blood for all experiments was based on the measured viscosity at high shear rate (400s-1) where viscosity no longer changes with shear rate.

90

Two velocity markers were utilized to determine the Re where TT first occurs for each test fluid. First, centerline velocity fluctuations demonstrate the Re at which large scale fluctuations first appear in the flow (Figure 51, Figure 52 and Figure

53) [38]. These fluctuations can be seen as a sudden increase in RMS velocity

(normalized by mean velocity) as Re is increased (Figure 51,Figure 52 and Figure

53). Second, this method can be applied to velocity traces at each radial measurement location across the pipe to insure that the entire flow field is following the centerline trend (Figure 54, Figure 55, Figure 56, Figure 57 and Figure 58).

Note that near wall velocity has been excluded in Figure 58 since the spectral broadening in the near wall, high shear-rate regions would erroneously show high

RMS even for low Re.

Even though a 10% difference was observed between the Recr of blood and WG, it is difficult to conclude that there is a difference since it might be due to the cumulative errors of various parts and processes of the experimental system. The centerline velocity time-trace for low Re were noisy for both blood and WG. This may be due to the fact that the velocities corresponding to those Re were low and away from the “sweet spot” of the Doppler ultrasound velocimeter used in this study. The TiO2 particles had considerebly smaller signal to noise ratio, but with appropriate noise filtering the quality of signal was adequate for velocity measurement. We have confidence in the results since TiO2 was used for

Newtonian as well as non-Newtonian blood analogs that clearly demonstrated difference in Recr.

91 The S-shape employed in the current study was from Stehbens et al. in which they tested 21 different S-shapes for transition to turbulence [11]. The authors showed that the Recr decreased with decreasing radius of curvature of the S-shaped pipe.

The present study employed the 17th S-shape.

The profiles for both blood and WG did not change abruptly from parabolic to blunt

(like they did in the straight pipe study). Instead, they were skewed before taking the classic blunt turbulent profile shape. The profiles were seen to be skewed towards the near wall (more for blood than in WG). This observation matches with the results reported by Stehbens et al. where they showed that the disturbances downstream of the bend were skewed towards the far wall.

Stehbens et al. observed the Recr to change if there was any sudden bump to the experiment system. This problem is unlikely in our setup since the consistency in the results for the repeated experiments demonstrate the absence of any such phenomena. The authors showed increasing severity of flow disturbance with increasing Re [11]. Secondary flow was observed in the S bend in each case. At

Re = 625 the disturbance was located primarily on one side of the distal tube and at Re = 770 the disturbance appeared in the distal limb but was initiated immediately beyond the second apex of the S-bend. At Re = 1730, the disturbance commenced in between the first and second apex and was more pronounced with complete mixing distally whereas in the first two cases, the flow was laminar is this distal region.

92 The fact that a 15-20% difference was observed in the Recr of TT between blood and Newtonian fluid in a straight pipe and smaller difference (<10%) was observed in a S-shaped pipe can be attributed to the difference in shear stress distributions in the two geometries. In the S-shaped pipe, higher shear might have been more predominant than in the straight pipe which caused the blood act as a Newtonian fluid. In the straight pipe, lower shear rates (< 200 s-1) were more likely to be present, which caused the Recr to be larger, as the Re was defined using the viscosity of blood at higher shear rate.

7.4 Overall Discussion

The results of this thesis demonstrate that the non-Newtonian nature of blood can have an impact on TT depending on the geometry. This result is not exhaustive since blood flow in arteries is pulsatile in nature while these results are for steady flow. Nonetheless, it provides the groundwork that necessary before embarking on more complex geometries and flow conditions. Note that the complexities of working with whole blood makes such experiments difficult. Future numerical studies could examine Newtonian and non-Newtonian fluids to determine if TT can be predicted for whole blood using an assumed rheology. This would be interesting to determine the importance of rheology without inclusion of viscoelasticity. In addition, the computational model would presumably ignore

RBC particulate interaction. Results comparing blood and WGX which is also non-

Newtonian but without particulate concentration similar to that of blood (40%) demonstrated that the delay in Recr of TT could potentially be predicted with a

93 rheology model that did not account for RBCs, but, this should be examined in detail with mutiple geometries and pulsatile flow.

Is should recognized that adding geometric complexity and pulsatility might cause the alteration in Recr of TT to be undetectable using the present system. New measurement technologies, such as laser Doppler velcimetry, may be required to adequately capture any subtle differences that may be present. Private discussions with Dr. Darius Modarress, a laser exptert, have indicated this may be possible using a laser frequency that passes through whole blood.

Finally, the goal of this thesis was simply to identify the Recr of TT for simple geometries using modern experimental techniques. There could be many additional studies performed on the data obtained. For example, one could use parametric analysis or multi-variable correlations to develop models that predict

Recr of TT based on the multiple velocity detection methods (centerline, RMS, profile). However, this is beyond the scope of this study since contruction, testing, and validation of the whole blood flow system was a major engineering challenge.

In addition, such analysis would not alter the fundamental finding of this work which is that the non-Newtonian nature of blood can have an impact on TT depending on the geometry.

94 CHAPTER VII

VIII. LIMITATIONS

Blood flow experiments are difficult due to various reasons. Blood being a biological fluid may contain pathogens. Formation of thrombus is another grave problem, difficult to deal with. Controlling temperature of the blood within the physiologically possible limits is another challenge but should be attempted to keep the proteins from disintegrating. The Food and Drug Administration limits the storage of blood for 42 days. However, clots were observed in the whole blood stored for more than four days in the lab (stored at 4°C) possible due to contamination during blood collection. In most cases the blood could not be circulated for more than three hours. Blood being a shear-thinning non-Newtonian fluid the rheological properties must be measured accurately. The limited amount of time does not allow manual control, therefore, the system was fully automated.

Opacity is another factor that restricts certain measurement techniques to not work for blood (e.g. LDA, PIV etc.). The quality of the results is dependent upon flow control, accuracy of velocity measurement and the probe positioning. It is because of these difficulties that researchers almost always look for a blood analog fluid when conducting experiments even though a blood analog fluid might not yield accurate results.

95 8.1 Straight Pipe

While the measured velocity profiles are parabolic in shape for laminar Re, some asymmetry is visible. This may indicate systematic errors in the velocity measurement since the pipe was designed to be straight. 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 test fluids and profiles were reasonably close to the theoretical parabolic. This error was shown to be small for the laminar flow (Re<2100) with mean velocity differences less 5% for the majority of the profile (Figure 44). Potential causes for this discrepancy are numerous and described below.

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

WGXH and WGXL, TiO2 particles (mean diameter 650 nm) were used as reflectors. Blood did not require TiO2 since the RBCs act as excellent reflectors

(mean diameter 6-8 μm). TiO2 particles produced a noisier signal than RBCs

(roughly twice the fluctuations in laminar flow), which resulted in a consistently larger RMS velocity for the blood analog fluids. This was observed in the laminar regime for WG and blood (Figure 33). This is 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. This made comparison of RMS values between test fluids impossible and thus, only comparisons between mean velocities were possible (Figure 44). Second, the wall reflection noise restricted measurements to only 374 μm from the far wall. Third,

96 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 captured all the fluctuation frequencies with equal weighting. Fifth, the DUS probe was inside the pipe, downstream of the measurement region, and the probe volume was four millimeters from the probe tip. While we expect the probe to have a minimal impact on the velocity where measurements were made, some effect may alter the velocity field particularly when the probe positioned deeper in the flow.

Rheological properties of blood are difficult to measure and the results for whole blood in this study vary between samples (Figure 29). There was also variability within a given sample during the two-hour experiment (Table 3). Sample three had the greatest change from start (2.98 cP) to end (3.21 cP), which represents a

7% increase in base viscosity. Two additional measurements were made during the experiment on Sample 3 where viscosity was found to be 3.00 and 3.06 cP for

400 s-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. Based on the

97 consistency of the velocity results, the blood rheology was consistent for all three samples (Figure 40 and Figure 43).

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

2 ′ on an estimate of the fluctuating momentum (푝′ ~ 휌푢′ , 푢푚푎푥 ≈ 40 푐푚/푠).

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 as heart rate, peak Re, mean Re, and waveform shape.

8.2 S-Shaped Pipe

All the limitations described in the previous section concerning the straight pipe are also applicable to the S-shaped pipe geometry. In addition one limitation of the

S-shaped geometry was that the apex of the bends, where the pipe was kinked, might have caused changes in the flowfield. This flow disturbance might persist downstream resulting in skewed velocity profiles. Unlike the straight pipe this geometry presents the initiation of turbulence at different locations depending on the flowrate. This might be of concern since the measurement location was fixed.

If the flow relaminarized downstream of the probe measurement location, it was not detected. Also the measurement was taken along one radial direction parallel to the plane of the S-shape. We might have missed interesting flow phenomena

98 (secondary flows), if any, perpendicular to the plane of the S-shape. For both straight pipe and S-shaped pipe cases, the statistics were performed assuming the distribution of the experimental results to be normal; however, this may not be the case due to the complexity of the experimental process.

99 CHAPTER IX

IX. CONCLUSION

One should exercise caution when simulating transitional flows under an assumption that whole blood acts as a Newtonian fluid even when shear rates are high. One must be careful not to extrapolate these results to more physiological geometries and flow conditions.

For the straight pipe the RMS velocity results obtained show that the minimum Re where transition is initiated for whole blood (~2500-2700) is considerably larger

(>20%) than that observed for a Newtonian fluid (~2000-2100) in a straight rigid pipe under steady flow conditions. A greater delay in transition was observed for blood analog shear thinning fluids on the same experimental system. These results were confirmed by similar changes observed in the centerline velocity time trace and mean velocity profile shape change. Repeated measurements show these results to be consistent for three different samples. These results show large differences in the magnitude of mean and fluctuation velocity between whole blood and a Newtonian fluid for Re>2100.

Results show that for a straight pipe, blood can be assumed as a Newtonian fluid only in the lamiar flow regime Re<2100. In the transitional regime (Re>2100) this assumption will result in erroneous hemodynamic forces.

100 For the S-shaped pipe geometry the RMS velocity results obtained show that the minimum Re where transition is initiated for whole blood (~1000-1200) is slightly larger (>10%) than that observed for a Newtonian fluid (~900-1000) under steady flow conditions. These results were confirmed by similar changes observed in the centerline velocity time trace and mean power of the time trace. Repeated measurements show these results to be consistent for three different samples.

These results show large differences in the magnitude of mean and fluctuation velocity between whole blood and a Newtonian fluid for Re>1000.

This difference in results show the importance of geometry in studying transition to turbulence. In addition to CFD, this study also finds its importance in better design of medical devices like the ventricular assist device, dialysis machine etc. where steady flow is predominant. Further research is necessary to understand the importance of blood rheology for complex geometries, pulsatile flow, and compliance.

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110

APPENDICES

111 APPENDIX A

APPENDIX A. DATA ACQUISITION AND PROCESSING MATLAB CODE

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % main_data_acquisition_initialize_wt_Temp.m % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This file initializes the DAQ for I/O for continuous ramp DAQ % % Author - Dipankar Biswas % % Biofluids Lab, University of Akron. % % Department of Mechanical Engineering % % Director - Dr. Francis Loth % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Use the daq.getDevices command to display % a list of devices available to your machine and MATLAB d = daq.getDevices;

% The daq.createSession command creates a session. The session contains % information describing the hardware, scan rate, duration, % and other properties associated with the acquisition. Create a % session, and assign it to a variable ss = daq.createSession('ni'); ss.Rate = Fs; ss.DurationInSeconds = timetoacquire; %The addAnalogInputChannel command attaches an analog input channel to % the session. You can add more than one channel to a session ss.addAnalogInputChannel('Dev1',21,'Voltage'); %Q ss.addAnalogInputChannel('Dev1',22,'Voltage'); %US-A ss.addAnalogInputChannel('Dev1',23,'Voltage'); %US-B ss.addAnalogInputChannel('Dev1',20,'Voltage'); %Temp

%Voltage to AnalogOutputChannel ss.addAnalogOutputChannel('Dev1',0,'Voltage'); % Blood Voltage ss.addAnalogOutputChannel('Dev1',1,'Voltage'); % Current (Common for ALL 3) ss.addAnalogOutputChannel('Dev1',2,'Voltage'); % Heating Voltage ss.addAnalogOutputChannel('Dev1',3,'Voltage'); % Cooling Voltage End%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

112 x = data(:,2)-sqrt(-1)*data(:,3); % Combine Acquired Quadrature Signals End%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Power_Spectral_Analysis_Dual_Channel.m % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This file computes power spectrum for quadrature signals % % Author - Dipankar Biswas % % Biofluids Lab, University of Akron. % % Department of Mechanical Engineering % % Director - Dr. Francis Loth % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% segsplit = 1; kcalcck = k; f1 = Fs_Appropriate/2/1000*linspace(0,1,nps/2); f2 = Fs_Appropriate/2/1000*linspace(1,2,nps/2+1); fp(1:nps/2) = f1(1:nps/2); fp(nps/2:nps) = f2(1:nps/2+1); nps_cutoff = find((fp>60.00),1,'first');%-1; f=fp(1:nps_cutoff); if(negativeflag == 1) nyquist_cutoff = find((fp>31.25),1,'first'); f(nyquist_cutoff:nps_cutoff) = (0-(f(nyquist_cutoff:nps_cutoff)-31.25)); end if(overlap==0) nsegs = St_Appropriate/nps; for ips=1:nsegs ips; ips_start = (ips-1)*nps+1; ips_end = ips*nps; fftseg = fft(x(ips_start:ips_end)); fftsegc=fftseg.*conj(fftseg)/nps;

% Do not include the first points in the fftsegs variable as the first % point represents zero velocity which we DONT need to include % in addition to reduce noise values less than 3cm/sec are set to % zero(first 4 points). This was fount to be important for near wall % velocity measurements fftsegc(1:5) = 0; fftsegs(ips,1:nps_cutoff)= fftsegc(1:1:nps_cutoff)/max(fftsegc(2:1:nps_cutoff)); % fftsegs has 305 X nps_cutoff points. 305 = 625000/2048 (nsegs = St/nps)

113

% Goal is to acquire power spectrum over short period of time many times % over 5 sec period. These many spectra are then averaaged to produce a mean % spectra for the 5 sec period. Dr Steven Jones gave us this idea. end else nsegs = floor( ((St_Appropriate/nps)-2)/overlap ); % must multiply by two to get total number of segments for ips=2:nsegs delta = floor(nps*overlap); shift = delta; ips_start = ((ips-1)*delta+1)-shift; ips_end = (ips*delta); xseg(ips,:)=x(ips_start:ips_end); xsegreal(ips,:)=real(x(ips_start:ips_end)); fftseg = fft( xseg(ips,:) - mean(xseg(ips,:)) ); fftsegc=fftseg.*conj(fftseg)/nps; fftsegs(ips,1:nps_cutoff)= fftsegc(1:nps_cutoff)/max(fftsegc(2:nps_cutoff)); end end End%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Peak_tracker.m % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This file finds the peak of the power spectrum % % Author - Dipankar Biswas % % Biofluids Lab, University of Akron. % % Department of Mechanical Engineering % % Director - Dr. Francis Loth % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Find all indices having normalized frequency > 0.8 for Profile % and > 0.15 for Centerline and average them to find dominant frequency if (all_set_flag==1) PSx_Cutoff = Power_Spectrum_Cutoff_to_average; if(PF == 0 && CF == 1) PSx_Cutoff = 0.15; elseif(PF == 1 && CF == 0) PSx_Cutoff = 0.8; end else PSx_Cutoff = 0.9; % Default = 0.9 end

114 if(PF == 0 && CF == 1) PSx(find(PSxPSx_Cutoff); fmoment2 = mean(f(ind)); end End%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Vtimetrace.m % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This file finds the dominant frequency from power spectrum (1st moment) % % Author - Dipankar Biswas % % Biofluids Lab, University of Akron. % % Department of Mechanical Engineering % % Director - Dr. Francis Loth % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% maxfreq = 0; powerck = 0.025; %Considering power at 2.5% of max power fPtotal=0; Ptotal=0; for ifreq=2:nps_cutoff %nps/2 delf=f(ifreq)-f(ifreq-1); fmean = ( f(ifreq)+f(ifreq-1) )/2.; if PSx(ifreq) > 0.01 Ptotal = Ptotal + delf* ( PSx(ifreq)+PSx(ifreq-1) )/2.; fPtotal = fPtotal + fmean*delf* ( PSx(ifreq)+PSx(ifreq-1) )/2.; end end fmoment= fPtotal/Ptotal;

% rerun for better fmoment by using low pass filter to cut % frequencies 2 time higher than fmoment from first pass fPtotal=0; Ptotal=0; for ifreq=2:nps_cutoff delf=f(ifreq)-f(ifreq-1); fmean = ( f(ifreq)+f(ifreq-1) )/2.; if fmean > 2*fmoment fmean = 0; end

115 if PSx(ifreq) > 0.01 Ptotal = Ptotal + delf* ( PSx(ifreq)+PSx(ifreq-1) )/2.; fPtotal = fPtotal + fmean*delf* ( PSx(ifreq)+PSx(ifreq-1) )/2.; end end fmoment2= fPtotal/Ptotal; Vmoment_time=fmoment2*vthdop; End%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

116 APPENDIX B

APPENDIX B. PolyImPro

Three Dimensional Reconstruction of The Components of The Carotid Plaque

From Standard CT Medical Images

Abstract

The present study compares plaque and calcium volumes between sixteen diseased human carotid arteries. Half were from symptomatic patients, and half were from asymptomatic patients. In-house software was developed for the 3-D reconstruction of the plaque components from computerized tomography (CT) images. Results revealed higher mean total volume (TV) in the symptomatic group compared to the asymptomatic group. In contrast, the mean ratio of calcium volume (CV) to TV was lower for the symptomatic group compared to the asymptomatic group. This shows that symptomatic patients have a significantly greater plaque burden with minimal plaque calcification. The process of acquiring the data helped understand what tools/features are needed to conduct this work.

One important feature of this software is the ability to create automated regions of interest (ROI) in addition to simple manual selection/modification of the ROIs in a

GUI environment.

117 Introduction

Angiograms have been used for many years to assess the severity of carotid artery stenosis. Methods guided by North American symptomatic carotid endarterectomy trial (NASCET), European carotid surgery trial (ECST) are popular among physicians, but all those techniques measure the degree of stenosis differently

[78]. This motivated researchers to acquire CT images rather than angiograms such to obtain the 3-D geometry as well as information about plaque components.

Wintermark et al. found a 72.6% agreement between CT and histological examination in carotid plaque characterization [79]. In addition, research has shown a correlation between hypercholesterolemia (cardiovascular risk factor) and plaque components using CT images to determine plaque component volumes

[80]. The paper suggests ranges of Hounsfield units (HU) to be used to identify plaque components. Here we present the methodology for the development of software to analyze CT images to select ROI to determine plaque component volumes and construct a 3-D model of the plaque.

Methods

Software (cttech) (Figure 62) was written in MATLAB (The MathWorksTM, Natick,

MA) to analyze medical images (CT, MRI). The software is user-friendly and allows for manual modification of automated functions. This software gives greater control than some commercially available software packages for image segmentation.

The software draws polygons on the images to identify the ROIs (Figure 62). An auto-polygon feature can be used to identify regions that fall within a certain

118 intensity range selected by the user. The polygons can then be edited manually, a feature not present in other software of the same genre. Otherwise the polygons can be drawn completely manually. The software allows the user to copy one or many polygons to another image. The intensity of each individual pixel can be displayed. The software also lets the user smooth the polygons using a moving average technique. Parameters such as number of points, number of new points created, and number of iterations can be varied to get the desired level of smoothing. The software provides a tool to create new slices with polygons in between the existing image slices through linear interpolation of the images and polygons. An increase in the number of images can improve the quality of the 3-D geometry. A distance measuring tool is also available. Information about the image

(no. of pixels, pixel size, slice thickness, spacing between slices) is displayed on screen.

Sixteen diseased carotids were analyzed, half of which are symptomatic and half asymptomatic. Polygons were drawn on each image to identify the lumen, outer wall, and regions with high levels of calcium. The area of each ROI was multiplied by the spacing between slices to obtain the ROI volume of that slice. Volumes for the various components were obtained by summing the volume contribution for each slice. To create the 3D geometry of the plaque components (Figure 64), the polygons were used to create binary images with the ROI white and the rest black

(Figure 63). This technique reduced ROI selection time when using SEGMENT

(Medviso AB, Lund, Sweden) to create the 3D structures of each plaque component. The geometries were further processed using GEOMAGIC

119 (Geomagic, Research Triangle Park, NC) for smoothing and to be exported in initial graphics exchange specification (IGES) format Figure 64. Mean volumes of plaque components such as TV and CV were computed by cttech for both symptomatic and asymptomatic groups.

Results

TV and CV of all the sixteen carotids were computed and compared. Both symptomatic and asymptomatic patient groups were selected based on the criterion that their NASCET scores were similar (73.8% and 60.9%, respectively).

However, the present study revealed greater TV and CV difference between the two patient groups. Mean TV was observed to be higher (64.6%) in symptomatic patients than in asymptomatic patients (1706.9 ± 723.7 vs. 1037.1 ± 310.3 mm3, p

< 0.05) (Figure 65a and Table 7). In contrast, mean CV was slightly lower (21.9%) in symptomatic patients than in asymptomatic patients (183.8 vs. 235.3 mm3).

However, the mean ratio of CV to TV was lower in symptomatic patients than in asymptomatic patients (8.9 ± 7.3 vs. 22.6 ± 13.9%, p < 0.05) (Figure 65b and Table

7).

120 Figure 62: Screenshot of cttech with polygons encompassing ROIs in one typical medical CT image of a diseased carotid artery.

(a) (b) (c)

Figure 63: Binary images output from software cttech for healthy internal carotid (a), maximum stenosed internal carotid (b) and healthy common carotid artery (c).

121 (a )

(b )

Figure 64: 3D reconstructed diseased carotid artery bifurcation, front and back view with plaque components (external carotid artery is not shown).

2500 40

Mean Total Plaque Volume 35 2000 Mean Percent Calcium Volume ) ) 30 3 3

1500 25 20 1000 15 Volume (mm Volume Volume (mm Volume 10 500 5

0 0 Asymptomatic Symptomatic Asymptomatic Symptomatic (a) (b)

Figure 65: Comparison of mean TV (a) and mean percent CV (b) between symptomatic and asymptomatic groups.

122

Table 7: NASCET scores, and volumes of plaque (total and calcium) of asymptomatic and symptomatic patients (eight each). Total % Calcium Patient Wall Stenosis Volume %Calcium Types Volume NASCET [mm3] [mm3] 50 1272 355 28

51 648 257 40 70 1319 141 11 76 604 29 5 78 931 52 6 79 876 332 38

Asymptomatic 87 1341 386 29 89 1305 330 25 AVG 72 1037 235 23 STD 15 310 142 14

60 999 53 5 69 1402 195 14

69 1272 0 0 71 2344 268 11 80 2440 138 6

Symptomatic 84 626 6 1 91 2510 538 21 92 2061 273 13 AVG 77 1707 184 9 STD 12 724 179 7

%Difference 6.45 65% -22% -60%

Discussion

The present analysis provides a measure of TV and CV for symptomatic and asymptomatic carotid arteries. Physicians make decision on patients with carotid disease based on the ratio of the peak velocities in their internal carotid to that in their common carotid arteries and their NACET scores. However, the composition of plaque is thought to be important in the likelihood of plaque rupture or ischemic

123 events. Knowledge of the morphologic composition of the plaque allows determination of mechanical stresses exerted on the protective fibrous cap, which may be of importance in the assessment of plaque vulnerability [81]. 3-D volumetric reconstruction of CT axial images allows for better characterization of plaque geometry and spatial distribution of plaque structural components. Here we show that symptomatic patients have a significantly greater plaque burden with minimal plaque calcification. Further development of the software includes automatic generation of the healthy adventitia and media provided the outer wall is defined. The software also has the potential to be used for phase contrast MRIs but this feature is still under development.

124 Fluid Dynamic Analysis of Upper Airway of an Obstructive Sleep Apnea Patient

Pre and Post Surgery

Abstract

The present study compares flow parameters (pressure drop, velocity, and shear stress) in the upper airway between pre- and post- bariatric surgery obstructive sleep apnea (OSA) patients. CT images of the upper airway were obtained prior to and six months post bariatric surgery in patients with a comorbid OSA. In-house software was used to reconstruct 3D geometric models of the upper airway, and fluid flow simulations were conducted using commercial computational fluid dynamics (CFD) software. Results show that pressure drop in the upper airway and velocity at the throat decrease post-surgery. Shear stress on the airway walls also decreased markedly. These trends were expected, however more patients must be analyzed and correlations must be drawn between these fluid dynamic parameters and the pathophysiology of the upper airway in OSA.

Introduction

Up to 93% of obese persons presenting for bariatric surgery are affected by OSA

[82-86]. OSA is a disorder of the upper airway, often closely related to obesity because of associated changes in the soft tissues of the neck. Decreased muscle tone together with increased adipose tissue around the neck predisposes the upper airway to collapse during sleep. This results in an increase in airflow resistance and work of breathing during sleep. Weight loss is considered a treatment method for mild to moderate OSA, and is an adjunct to continuous

125

positive airway pressure (CPAP) treatment in more severe OSA. Roux-en-Y gastric bypass (RYGB) is a type of bariatric surgery capable of inducing a profound weight loss via both restriction (decreasing stomach size) and malabsorption

(bypassing portions of the small intestine). Post-surgical weight loss subsequently elicits marked decreases in total body fat, including the adipose tissues surrounding the upper airway.

This study compares the fluid dynamics and geometric changes to the upper airways of patients with OSA who underwent RYGB surgery. CFD has been used to characterize airflow of the upper airway in several previous investigations [87-

89], but comparisons of airflow between pre- and post- bariatric surgery patients with OSA, has not been done. The present study may contribute to our understanding of the airflow restrictions seen in the upper airways of obese patients with OSA, and lead to development of improved, quantitative diagnostic tools for evaluating OSA and bariatric surgery outcomes.

Methods

Patients with known OSA planning on undergoing RYGB at the Summa Health

System Bariatric Care Center, (Akron City Hospital, Akron, OH) were recruited to participate in the study. CT images of the upper airway were obtained directly prior to, and six months after RYGB. Software (PolyImPro) for analyzing and segmenting the images was developed using Matlab (The MathWorksTM, Natick,

MA). Specifically, this software retains the ability to draw polygons on the images to identify the region of interest (ROI) (upper airway in this case) based on the

126 brightness intensity distribution in each image and outputs the ROI as a binary image (Figure 66, Figure 67, Figure 68 and Figure 69). This process allows for a more robust reconstruction of the wall surface of the upper airway using Segment

(Medviso AB, Lund, Sweden) (Figure 70). The wall surface of each case was exported from Segment in STL format , then smoothed to remove pixilation artifact, closed to form a volume, and converted to IGES format in Geomagic Studio

(Geomagic, Research Triangle Park, NC) (Figure 71 and Figure 72). The geometries were meshed using a combination of Gambit and Tgrid and air flow was simulated using Fluent (ANSYS Inc., Canonsburg, PA).

Figure 66: Step 1 – Load images and adjust contrast to make the ROI prominent.

127 Figure 67: Step 2 – Identify the ROI with a polygon and smooth it.

Figure 68: Step 3 – Convert to black and white and save as DICOM.

128 Figure 69: Preview of the 3-dimensional structure

129 Figure 70: Segmentation of the DICOM images to build a steriolithographic model.

130

Figure 71: 3D reconstructed upper airway (pre-surgery).

Figure 72: 3D reconstructed upper airway (post-surgery).

131

Figure 73: Tetrahedral mesh at inlet bounded by prism boundary layer cells.

132 Figure 74: Unsteady flow waveform used as inlet boundary condition

For the purpose of this analysis, the upper airway wall was assumed to be rigid and air flow in both cases was assumed to be laminar. A sinusoidal velocity profile

(Figure 74) was imposed at the model inlet to simulate inhalation and exhalation, similar to a single breathing cycle. The maximum air flow rate was taken to be 10

L/min. The model outlet was set as a zero pressure.

Results

Transient pressure drop over the length of the upper airway was calculated for each case. Peak pressure drop during inspiration, in the post-surgery (~41 dynes/cm2) case was found to be less than that in the pre-surgery (~87 dynes/cm2)

133

case (53%) (Figure 75, Figure 76 and Figure 77). The post-surgery case also presents less wall shear stress (Figure 80 and Figure 81) and velocity (Figure 78 and Figure 79) near the obstructed region. There was an approximately 40% decrease in peak velocity observed in the post surgery case.

Figure 75: Unsteady pressure drop in pre and post surgery upper airway for one breathing cycle

134

Figure 76: Pressure distribution in pre-surgery upper airway.

135 Figure 77: Pressure distribution in post-surgery upper airway.

136

Figure 78: Velocity distribution in pre-surgery upper airway.

137

Figure 79: Velocity distribution in post-surgery upper airway

138

Figure 80: Strain rate distribution in pre-surgery upper airway walls.

139

Figure 81: Strain rate distribution in post-surgery upper airway walls.

140 %NASCET vs. Total Volume 3000

2500 ) 3

2000

1500

1000 Total Volume (mm Volume Total 500

0 40 50 60 70 80 90 100 % NASCET

Figure 82: Comparison of total wall volume of the diseased internal carotid artery to the %NASCET scores.

% NASCET vs. Calcium Volume 600

) 500 3

400

300

200

Calcium Volume(mm 100

0 40 50 60 70 80 90 100 % NASCET

Figure 83: Comparison of calcium volume of the diseased internal carotid artery to the %NASCET scores.

141 % NASCET vs. % Calcium 45

40

35

30

25

20

% Calcium 15

10

5

0 40 50 60 70 80 90 100 % NASCET

Figure 84: Comparison of %calcium volume (calcium volume/total wall volume) of the diseased internal carotid artery to the %NASCET scores.

Discussion

Airway pressure drop, velocity, and shear stress were computed and compared between the pre- and post-operative conditions. Software to reconstruct the 3D anatomy from CT images was developed and used. This comparison showed a reduction in pressure drop post operatively. This was felt to cause the decrease in collapse of the upper airway that was noted at the postoperative time point. It should be noted, however, that this study is exploratory in nature, and that a number of assumptions have been made in order to streamline the analytic process. Though the results show an expected trend, the magnitudes may not be physiological. For example, pressure drop during inspiration might be larger than what the rigid model simulation predicts because of the compliance of the upper

142 airway. Had the upper airway been compliant, it would have been narrower during inspiration, thus causing a greater drop in pressure and increased diameter during expiration (thus causing less pressure drop). Hence this study is limited to a qualitative rather than quantitative analysis. The anatomy of upper airway in vivo is likely to vary based on the position of the head and neck, conscious state (sleep vs. wake) and the respiratory cycle. In future iterations of this study, we intend to use patient specific flow waveforms, obtained during sleep, this will allow better modeling of what occurs in the airway of OSA patients. Conversion from a rigid to a compliant wall model will also be performed, further adding to validity. The

Reynolds numbers at inlets for pre- and post- surgery cases, respectively, are calculated as 759 and 811 while those at the narrowest regions of the flow domain are 3319 and 1626. In this study, laminar flow was assumed, which is not expected to be true, at these Reynolds numbers. Turbulent flow necessitates the use of CFD solvers, such as nek5000 (Paul Fischer, Argonne National Laboratory, Lemont, IL) which is more suitable for transitional flows because of its use of spectral elements.

Nek5000 only accepts hexahedral elements, however it is difficult to mesh complex geometries such as the one described herein, with hexahedral elements. Whereas meshing with tetrahedral elements is comparatively easy. So we will mesh the geometry using tetrahedral elements and then convert them to hexahedral. A software to convert tetrahedral meshes (such as those used in this study), to hexahedral meshes, is under development, and will enable future use of nek5000.

A comparison with experimental results conducted through use of a respiratory pump (Harvard Apparatus, Holliston, MA) will provide validation.

143 APPENDIX C

APPENDIX C. MGPtracker

Automated quantification of radial movement of microglial cells

The object of this study was to quantify the movement of microglial cells towards an injury site created by laser at Emory University, Atlanta, and compare quantitatively between control and drug cases. Image processing of the result in an automatic repeatable way can provide some parameters that may be useful in quantifying the effect of various drugs in the microglial cell experiment. By tracking the front of the cells as they move toward the injury site at the center, we can get various geometry parameters about the front-polygon that is detected at each time point. First, we noted that the front-polygon reached the injury at the center faster for the control case compared to the drug case. This is shown in Figure 85, Figure

86, Figure 87, Figure 88 and Figure 89. Next, we could quantify the distance between front-polygon and edge of injury site as well area of the front-polygon and show how this changes with time (Figure 89 and Figure 90). The problem with this data is that the injury site area is larger to start for the control case compared to the drug case (1019.2 vs. 320.4 square microns). This can be seen in Figure 86 and Figure 88. Distances start at 47 and 24 microns for drug and control cases, respectively. In addition, the initial gray scale of the image can affect the starting

144 positions as well. We can also compute the velocity with this data (Figure 95) however; cell movement in the azimuthal direction creates erroneous radial velocities. It is probably best to look at the slope of the radial distances in Figure

89 to get an idea of how fast they move. Using a least square fit on the first 9 min shows that the two fronts actually move very much at the same radial velocity

(Vcontrol= 1.56 and Vdrug = 1.35 microns/min). From 12 to 24 min, the control case seems to move slower at these times while the drug is still moving fast (Vcontrol=

0.38 and Vdrug = 1.45 microns/min). Finally, the control has reached the injury but the drug case has not. Still, at this point, the drug case velocity looks similar to that of the control (Vdrug = 0.63 microns/min). Since the drug started out further away, this implies that the velocity is dependent on the distance the front is from the injury site. We believe Stefka already told this but we are not sure. If we plot the drug case with a time shift representing a time delay until the front has reached the same location as the control case, the two plots line up rather well (Figure 89,

Figure 90, Figure 91 and Figure 92). We also compared the shape index between the Drug and Control cases to see if there were anything interesting from a shape point of view (Figure 92). These plots show the drug case is much less circular than the control case. Not sure how important this but might be, it is interesting to see if it is repeatable.

Detailed Method:

Multiframe TIFF images were obtained that portrayed the movement of the microglial cells. As the very first step the multiframe TIFF image was broken down to individual frames using ImageJ software (National Institutes of Health). Matlab

145

(The MathWorksTM, Natick, MA) was used for the whole analysis henceforth. The images were in grayscale with intensities ranging from 0 – 255. The grayscale images were converted to binary image, taking the range 100 – 255 to be representative of the cells of interest in this study. However the threshold values can be changed by the operator to match his/her understanding of the microglial cell physiology/structure. In the binary images, white represented the cells and black represented void space. Next a unique center pixel was selected that represented the center of the injury, which as observed, were different for the two cases. A coordinate transformation was then performed on the pixel locations, i.e. all pixel locations were saved as r-θ coordinates. The image was divided into 36 subareas (polygons) in the radial and azimuthal directions. Pixel locations in each polygon subarea are stored and number of bright pixels in each element is computed. For each time step, the vertices of front were identified in each of the angular sectors as the radial location beyond the injury site where more than 10 pixels are bright. When this is done for all the sectors, a front-polygon is formed with the vertices for that particular time step (Figure 85, Figure 86, Figure 87 and

Figure 88). The frames with the front-polygon are saved as JPEG images that are later used to create a GIF animation. Parameters like average radius (Figure 89), average velocity (Figure 91, Figure 95 and Figure 96), area (Figure 90), angular distance (Figure 93 and Figure 94) and shape index (Figure 92) were calculated from the saved front-polygons and plotted with time. Velocity and radius are also plotted for all the angular sectors for all the different time points. For all these calculations the time difference between the frames is taken as 3 minutes and pixel

146 size is taken as 0.5814 micron. Calculation of radial velocity is not always accurate since cells also move in the azimuthal direction. This leads to erroneous values in the radial velocity calculation.

Figure 85: The front of cell movement is indicated as the read line (polygon) for the Drug case at the first time point (t=1). Front-polygon geometry is non-circular with some vertices far from center and some near depending on the angle.

147

Figure 86: The front of cell movement is indicated as the read line (polygon) for the Drug case at the time point where the cells have reached the injury site in the center (t=18).

148

Figure 87: The front of cell movement is indicated as the read line (polygon) for the Control case at the first time point (t=1). Front-polygon geometry is non-circular but less so compared with the Drug case.

149

Figure 88: The front of cell movement is indicated as the read line (polygon) for the Control case at the time point where the cells have reached the injury site in the center (t=11).

150

Figure 89: Comparison between the Drug and Control cases for average distance between the front-polygon and the outer edge of the injury site at the center as a function of time. Note that the average distance for the control case reaches the edge of center injury site faster than the drug case.

Figure 90: Comparison between the Drug and Control cases for area between the front-polygon and the outer edge of the injury site at the center as a function of time. Note that the area for the control case is much smaller than the drug case. This could be affected by the fact that control case injury area is larger than that of the drug case. Also, differences in gray scale could impact this relationship.

151 Figure 91: Comparison between the Drug and Control cases for average radial velocity of the front-polygon towards the outer edge of the injury site at the center as a function of time. These values are affected greatly by noise or cell angular movement.

Figure 92: Comparison between the Drug and Control cases for shape index of the front-polygon as a function of time. These plots show the drug case is much less circular than the control case.

152 Figure 93: Control case for each individual angular distance between the front- polygon and the outer edge of the injury site at the center as a function of angle at each time point.

Figure 94: Drug case for each individual angular distance between the front- polygon and the outer edge of the injury site at the center as a function of angle at each time point.

153 Figure 95: Control case for each individual radial velocity between the front- polygon and the outer edge of the injury site at the center as a function of angle at each time point.

Figure 96: Drug case for each individual radial velocity between the front-polygon and the outer edge of the injury site at the center as a function of angle at each time point.

154 APPENDIX D

APPENDIX D. TRANSITION TO TURBULENCE IN ACCELERATING AND DECELERATING

UNSTEADY FLOW

Pulsatile flow consists of an acceleration period followed by a deceleration period.

During the flow acceleration, the Recr is delayed while during deceleration it is not.

This was observed by accelerating and decelerating blood at different rates. In the

first part of this study, Re was increased from 0 – 4500 and back to 0 in 360 s (180

s each phase). In the second part of the study, Re was increased from 0 – 4500

and back to 0 in 10 s (5 s each phase).

In the case of the slower acceleration and deceleration, the Recr were similar, Re

= 2800 and 3000, respectively (Figure 1). In the case of faster acceleration and

deceleration, the Recr were different, Re = 3400 during acceleration and Re = 2400

during deceleration (Figure 2).

155 Figure 97: Measured centerline velocity and theoretical centerline velocity (dotted line) by accelerating and decelerating flow between Re = 0 and Re = 4500 in 180 s.

156 5s 500 Theory Ramp-UP Ramp-DOWN 400

300

200

100 Centerline velocity [cm/s] Centerline

0 0 1000 2000 3000 4000 5000 Reynolds number

Figure 98: Measured centerline velocity and theoretical centerline velocity (dotted line) by accelerating and decelerating flow between Re = 0 and Re = 4500 in 5 s.

157 APPENDIX E

APPENDIX E. CURRICULUM VITAE

NAME Dipankar Biswas

DATE OF March 4th, 1980 BIRTH

PLACE OF Kolkata, West Bengal, India BIRTH

EDUCATION Master of Science, Mechanical Engineering - July-2009 Northern Illinois University, DeKalb, IL

Bachelor of Science, Power Engineering - December 2004 Jadavpur University, Kolkata, West Bengal, India

EMPLOYMENT The University of Akron, Akron, OH Teaching Assistant, 2009 – Present

Northern Illinois University, Dekalb, IL Teaching Assistant, 2007 – 2008 Research Assistant, 2008 – 2009

Development Consultants Private Limited, Kolkata, West Bengal, India Design Engineer, 2004 – 2007

RESEARCH Northern Illinois University in collaboration with Argonne National Laboratory (TRACC), 2007 – 2009

The University of Akron, Biofluids Laboratory, 2009 – Present

MASTERS Biswas D., Development Of an Iterative Scouring Procedure THESIS for Implementation in CFD Code for Open Channel Flow Under Different Bridge Flooding Conditions, Mechanical

158 Engineering Department, Northern Illinois University, Dekalb IL (July 2009) TEACHING Gas Turbine Laboratory

Fluid Mechanics, Heat Transfer, Fundamentals of vibration, Introduction to Aerodynamics and Fundamentals of Compressible Flow

PEER Gyoneva S., Davalos D., Biswas D., Garnier E., Loth F, REVIEWED Akassoglou K, and Traynelis S. F., Activated Microglia Display JOURNAL a Slower Response to Tissue Damage in Vivo, GLIA 2014; 62: 1345 - 1360

Biswas D., Casey D., Crowder D. C., Steinman D.A., Yun Y.H., Loth F., Characterization of Transition to Turbulence for Blood in a Straight Pipe under Steady Flow Conditions, accepted, Journal of Biomechanical Engineering

Biswas D., Casey D., Crowder D. C., Steinman D.A., Yun Y.H., Loth F., Characterization of Transition to Turbulence for Blood in a S-shaped Pipe under Steady Flow Conditions, in preparation, Journal of Biomechanical Engineering

Casey D., Biswas D., Crowder D. C., Steinman D.A., Yun Y.H., Loth F., Characterization of Transition to Turbulence for Blood in a Stenosed Pipe under Steady Flow Conditions, in preparation, Journal of Biomechanical Engineering

CONFERENCE Biswas D., Casey D. M., Smith Jr. K. W., Kay I., Crowder D. C., Jones S. A., Yun Y. H., Loth F., Transition to turbulence for whole blood in a straight pipe for accelerating flows, Proceedings of the 2014 Midwest American Society of Biomechanics Regional Meeting (Podium) (2014)

Casey D. M., Biswas D., Smith K. W. Jr., Crowder D. C., Yun Y. H., Loth F., Importance of Temperature on the Rheological Properties of Blood, Proceedings of the 2014 Midwest American Society of Biomechanics Regional Meeting (Poster) (2014)

Biswas D., Casey D. M., Crowder D. C., Yun Y. H., Loth F., In Vitro Flow System for Hemodynamic Evaluation Using Doppler Ultrasound, Proceedings of the 14th Biennial Meeting of the International Society for Applied Cardiovascular Biology (Poster) (2014)

159 Biswas D., Casey D. M., Smith Jr. K. W., Kay I., Crowder D. C., Jones S. A., Yun Y. H., Loth F., Doppler Ultrasound Measurements of Transition to Turbulence for Porcine Blood in a Straight Pipe, Proceedings of the 7th World Congress of Biomechanics (Poster) (2014)

Biswas D., Loth F., Krauza M. L., Pohle-Krauza R. J., Fluid Dynamic Analysis of Upper Airway of an Obstructive Sleep Apnea Patient Pre and Post Surgery, Proceedings of the ASME 2012 Summer Bioengineering Conference (Poster) (2012)

Ambati N., Biswas D., Loth F., Rittgers S. E., Jones S. A., Flow System to Detect Transitional Flow Based on Pulsed Doppler Ultrasound Velocity Profiles, Proceedings of the ASME 2012 Summer Bioengineering Conference (Poster) (2012)

Biswas D., Loth, F., McCormick S., Bassiouny H., Three Dimensional Reconstruction of the Components of the Carotid Plaque from Standard CT Medical Images, Proceedings of the ASME 2011 Summer Bioengineering Conference (Podium) (2011)

M. Kostic, P. Majumdar, D. Biswas, Bridges and Environment: Development of an Iterative scouring Procedure for Implementation in CFD Code for Different Bridge Flooding Conditions, Proceedings of the 3rd WSEAS Int. Conf. on Energy Planning, Energy Saving, Environmental Education (2009)

INVENTIONS A New Design of Prosthetic Venous Valve, an Effort Towards Reducing Venous Reflux While Permitting Normal Antegrade Flow, Invention Disclosure Form

Device and Method for Reduction of Intra Cranial Peak Pressure, Invention Disclosure Form

Software MGPtracker to quantify microglia cell movement towards laser induced injury site, Invention Disclosure Form, being licensed by MBF Bioscience

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