The Pennsylvania State University
The Graduate School
Graduate Program in Acoustics
CYCLIC AND RADIAL VARIATION OF ULTRASONIC BACKSCATTER
FROM FLOWING PORCINE BLOOD
A Thesis in
Acoustics
by
Dong-Guk Paeng
2002 Dong-Guk Paeng
Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
August 2002
We approve the thesis of Dong-Guk Paeng.
Date of Signature
K. Kirk Shung Distinguished Professor of Bioengineering Thesis Advisor Chair of Committee
John M. Tarbell Distinguished Professor of Chemical Engineering and Bioengineering
Victor W. Sparrow Associate Professor of Acoustics
Nadine Barrie Smith Assistant Professor of Bioengineering
Anthony A. Atchley Professor of Acoustics Head of Graduate Program in Acoustics
iii
ABSTRACT
The ultrasonic backscattering from flowing blood was investigated using several hemodynamic parameters and a physiological parameter. An emphasis was placed on the cyclic variation of the backscattering power and the origin and mechanisms responsible for it. Acceleration was hypothesized to enhance the aggregation of red blood cells (RBCs), and this is the first time that acceleration is suggested and experimentally verified as having an effect on aggregation of RBC. Two interesting phenomena, the ‘Black Hole (BH)’ phenomenon and the ‘Bright Collapsing Ring (BCR)’ phenomenon, were observed under pulsatile flow in B-mode cross sectional images. The BH phenomenon describes a dark hypoechoic hole at the center of the tube surrounded by a bright hyperechoic zone in B-mode cross sectional images, and the BCR phenomenon describes the appearance of a bright hyperechoic ring at the periphery of the tube at early systole and its convergence from the periphery to the center of the tube, finally collapsing as flow develops. These two phenomena were analyzed by the RBC aggregation due to the combined effects of the shear rate and acceleration, and this analysis could provide an integrated explanation of the cyclic and radial variation of the backscattered power. The origin of the Doppler power variation was investigated using a 10 MHz pulsed Doppler system with a single element transducer from three different fluid media: a rigid polystyrene microsphere solution, deformable porcine RBC suspension, and aggregating porcine whole blood. The Doppler power variation was observed only from porcine whole blood, which led to a conclusion that the ultrasonic backscattering was mainly dependent on the RBC aggregation under steady and pulsatile flow. The pattern of the cyclic variation of the Doppler power to have a maximum power at peak systole was mainly due to the enhanced rouleaux formation by acceleration. The BCR phenomenon was observed from the cyclic variation pattern of the Doppler power at different radial positions; the Doppler power peak was observed at early systole at the periphery of the tube and lagged the flow as close from the periphery to the center of the tube. The BH iv
phenomenon from the Doppler power measurements was also observed during some parts of a cycle. The BCR phenomenon from porcine whole blood in a mock flow loop was further examined in real time in B-mode images under pulsatile flow. The BCR phenomenon was found to be dependent on the flow speed, stroke rate and hematocrit, but independent on the transducer frequency from 9 to 13 MHz. The BCR phenomenon was stronger as systolic peak speed at the center of the tube increased from 10 to 25 cm/s, and as stroke rate decreased from 60 to 20 BPM. At low hematocrit of 12 %, no BCR phenomenon was discernable although it was observed at higher hematocrits. The pattern of the nonlinear relationship between echogenicity and hematocrit varied with radial positions. The BH phenomenon was also observed under certain hemodynamic conditions and varied over a pulsatile cycle. The BCR phenomenon was also observed from human carotid arteries from 10 subjects only in the harmonic images. In order to better understand these phenomena, the cyclic and radial variation of echogenicity under oscillatory flow was measured and the results showed a different pattern from that under pulsatile flow. The echogenicity at the center of the tube was enhanced during acceleration and degraded during deceleration, while the expansion and collapse of the ‘Bright Ring’ was observed twice per cycle. The cyclic and radial variation of echogenicity was dependent on stroke volume, stroke rate, mean steady flow added to the pure oscillatory flow, and transducer angle. The rouleaux distribution and orientation across the tube during flow acceleration were proposed based on the experimental results of the transducer angle, reaching a maximum of the echogenicity variation at about 25°. The cyclic variation of echogenicity was also observed from the porcine RBC suspensions, independent of the transducer angle and stroke rate but changed with the mean steady flow added to the pure oscillatory flow. The strong variation of echogenicity from oscillatory flow seemed to be caused by the rouleaux formation in addition to the echogenicity variations from one cell based deformation of RBC suspensions. v
TABLE OF CONTENTS
LIST OF FIGURES ...... viii LIST OF TABLES...... xiv ACKNOWLEDGMENTS ...... xv Chapter 1 INTRODUCTION...... 1 1.1 Background...... 1 1.2 Previous Studies...... 4 1.2.1 Shear Rate...... 5 1.2.2 Hematocrit and Flow Turbulence ...... 5 1.2.3 Cyclic Variation of the Backscattered Power from Blood...... 6 1.2.4 The ‘Black Hole’ Phenomenon...... 7 1.2.5 The ‘Collapsing Ring’ Phenomenon...... 7 1.3 Specific Aims...... 8 1.4 Thesis Outlines...... 11
Chapter 2 BACKGROUND FOUNDATIONS ...... 12 2.1 Blood Properties and Blood Rheology ...... 12 2.2 Hemodynamics ...... 13 2.2.1 Steady Flow...... 13 2.2.2 Oscillatory and Pulsatile Flow...... 16 2.3 Ultrasonic Scattering from Blood ...... 18 2.3.1 Scattering from a Single Scatterer ...... 18 2.3.2 Multiple Scattering in Blood...... 20
Chapter 3 ORIGIN OF THE DOPPLER POWER VARIATION...... 22 3.1 Introduction...... 22 3.2 Materials and Methods...... 24 3.2.1 Preparation Of Porcine Blood And Polystyrene Microspheres .....24 3.2.2 Mock Flow Loop...... 25 3.2.3 Doppler Instrument ...... 27 3.2.4 Data acquisition and analysis...... 28 3.2.5 Transfer Function of the Doppler System...... 29 3.3 Results...... 30 3.3.1 Steady Flow Experiments ...... 30 3.3.2 Pulsatile Flow Experiments ...... 34 3.4 Discussion...... 41 3.4.1 Doppler Power from Microspheres and RBC Suspensions ...... 41 3.4.2 Aggregation Effects on Doppler Power from Whole Blood...... 43 vi
3.4.3 Acceleration and Deceleration...... 44 3.5 Conclusions...... 45
Chapter 4 CYCLIC AND RADIAL VARIATION OF THE DOPPLER POWER...... 47 4.1 Introduction...... 47 4.2 Experiments ...... 47 4.3 Results and Discussion ...... 49 4.3.1 Steady Flow Experimental Results ...... 49 4.3.2 Stroke Rate Dependence at the Tube Center ...... 53 4.3.3 Cyclic and Radial Variation of the Doppler Power ...... 55 4.4 Conclusions...... 61
Chapter 5 THE ECHOGENICITY VARIATION UNDER PULSATILE FLOW: THE ‘BRIGHT COLLAPSING RING’ PHENOMENON ...... 63 5.1 Introduction...... 63 5.2 Materials and Methods...... 64 5.2.1 GE LOGIQ 700 Expert System ...... 64 5.2.2 Blood Preparation and Mock Flow Loop...... 65 5.3 Results...... 66 5.3.1 The ‘Bright Collapsing Ring’ Phenomenon ...... 66 5.3.2 Speed Dependence...... 66 5.3.3 Stroke Rate Dependence...... 75 5.3.4 Frequency Dependence...... 79 5.3.5 Hematocrit Dependence...... 79 5.4 Discussion...... 91 5.4.1 Effects of Acceleration and Shear Rate on the Echogenicity ...... 91 5.4.2 Comparison of the Echogenicity with the Doppler Power ...... 94 5.4.3 The Cyclic Variation of the ‘Black Hole’ Phenomenon...... 95 5.5 Human Subject Experiment ...... 95 5.6 Conclusions...... 100
Chapter 6 CYCLIC AND RADIAL VARIATIONS OF ECHOGENICITY UNDER OSCILLATORY FLOW...... 101 6.1 Introduction...... 101 6.2 Materials and Methods...... 102 6.3 Results from Whole Blood Experiments ...... 103 6.3.1 Stroke Volume Dependence...... 103 6.3.2 Mean Steady Flow Dependence...... 110 6.3.3 Stroke Rate Dependence...... 111 6.3.4 Transducer Angle Dependence...... 115 6.4 Discussion for Whole Blood Experiments...... 119 vii
6.4.1 The Cyclic Variation Pattern ...... 119 6.4.2 ‘Black Hole’ Phenomenon from Oscillatory Flow ...... 124 6.4.3 Shear Rate and Acceleration...... 125 6.4.4 Radial Distribution of Rouleaux ...... 126 6.5 RBC Suspension Experiments ...... 126 6.5.1 Steady Mean Flow Dependence...... 127 6.5.2 Transducer Angle Dependence...... 131 6.5.3 Stroke Rate Dependence...... 132 6.6 Conclusions...... 136
Chapter 7 CONCLUSIONS AND SUGGESTIONS...... 138 7.1 Conclusions...... 138 7.2 Suggestions for Future Studies ...... 140
BIBLIOGRAPHY...... 143
viii
LIST OF FIGURES
1.1 A schematic diagram of the blood circulation system in the human body (Jensens 1996)...... 3 1.2 Parameters to affect the backscattering from flowing blood under pulsatile flow ...... 9 2.1 Diagrammatic representation of the effects of red cell aggregation and red cell deformation on the shear dependence of blood viscosity (Lowe 1988)...... 14 2.2 Velocity profiles computed by the Womersley equation for the different Womersley numbers (α) (Fung 1997) ...... 17 2.3 Velocity profiles measured from the descending thoracic aorta of an anesthetized dog (Milner 1989) ...... 17 3.1 Experimental arrangement for steady and pulsatile flow conditions...... 26 3.2 Frequency responses of the Doppler power and the RF power measured with the Doppler instrument at a sampling frequency of 39.06 kHz using electronic injection. The dashed line denotes the frequency response of Doppler power and the solid line the RF power ...... 31 3.3 The RF and Doppler power from polystyrene microspheres under steady flow. The solid line and dotted lines are for the RF power and the Doppler power from the small size of microspheres (1-35 µm diameter) respectively, the dashed line is the Doppler power from large microspheres (20-130 µm diameter) ...... 32 3.4 The Doppler power from porcine whole blood and red blood cell (RBC) suspensions under steady flow. The solid line is for whole blood and the dotted line is for RBC suspensions. These results represent the averages from 3 different porcine blood samples. Standard deviations are shown as the error bars. Hematocrit of whole blood and RBC suspensions is 20%...... 33 3.5 Comparison between the RF power and the Doppler power under steady flow. All the results represent the mean values from 3 experiments and the standard deviations are not shown for comparison. The solid thin line is for the Doppler power from whole blood and the dotted thick line is the RF power for whole blood. The dashed thin line is for the Doppler power from RBC suspension and the broken thick line for the RF power from RBC suspension...... 35 ix
3.6. The Doppler power for microspheres (1-35 µm diameter) over a cycle under pulsatile flow. The Doppler power spectrum is the average over 100 cycles. The panels in each column represent the results for one stroke rate (20, 40 and 60 BPM from left to right), the panels in the upper row illustrate the Doppler power in dB and the lower panels the mean Doppler velocity in m/s for each stroke rate. Four different speeds were used to produce the results at 40 BPM to show velocity dependence...... 36 3.7 The Doppler power from RBC suspensions over a cycle under pulsatile flow at 3 stroke rates (20, 40, and 60 BPM from left to right) for 3 speed levels (30, 50, and 120 cm/s from top to bottom for peak speed). Each data point is the average over 50 cycles. The mean and the standard deviations from 3 different blood samples are shown as solid lines and error bars. The left vertical axes are the Doppler power in dB and the right vertical axes are the mean Doppler velocity in m/s. The dotted lines are the mean Doppler velocity, and the standard deviations are not shown (< 5 cm/s) for clarity. Hematocrit is 40%...... 38. 3.8 The Doppler power for whole blood over a cycle under pulsatile flow at 3 stroke rates (20, 40, and 60 BPM from left to right) for 3 speed levels (30, 50, and 120 cm/s from top to bottom for peak speed). The mean and the standard deviations from 4 different blood samples are shown as solid lines and error bars. The rest are the same as in Fig. 3.7...... 39 3.9 Comparison between the RF power and the Doppler power for whole blood under pulsatile flow. The RF power is the average over 20 cycles. The stroke rate is 20 BPM and hematocrit is 40%. The Doppler power and velocity is shown as a reference by the dotted line and the dash-dotted line, respectively.....42 4.1 Experimental arrangement for steady and pulsatile flow conditions...... 48 4.2 Transducer movements for different radial positions ...... 50 4.3 Compensation curve for radial positions obtained from RBC suspensions...... 50 4.4 Steady flow experiments. The lines and error bars are the mean and standard deviation from 5 different blood samples. v1~v6: Poiseuille flow peak velocity profiles ...... 51 4.5 Stroke rate dependence of the Doppler power at the center of the tube. The mean value was obtained from 4 different blood samples...... 54 4.6 Temporal variations of the Doppler power at different radial positions at 20 BPM. The mean value was obtained from 4 different blood samples...... 56 4.7 Radial variations of the Doppler power at different times within a cycle at 20 BPM ...... 57 4.8 The same as in Fig. 4.6 except at 40 BPM...... 59 4.9 The same as in Fig. 4.6 except at 60 BPM...... 60 x
5.1 The snap shots of the ‘Bright Collapsing Ring’ Phenomenon development during a pulsatile cycle in B-mode cross sectional images and the corresponding normalized echogenicity across the tube diameter along the horizontal lines of the tube center. The grayscale and the echogenicity were normalized with the maximum grayscale, 255 ...... 67 5.2 The spectrograms of three different speed levels within a sampling volume obtained at the tube center as shown in Fig. 5.3. The black lines represent the mean speed profiles computed from the mean frequencies of the spectrogram. The speed levels at peak systole are about 10, 15 and 25 cm/s from the top to bottom panel...... 70 5.3 The temporal mean echogenicity over a pulsatile cycle inside the tube for three different speed levels and the corresponding normalized echogenicity across the horizontal tube diameter...... 71 5.4 The cyclic variation of the total echogenicity across the horizontal tube diameter for three speed levels and the corresponding speed profiles. The lines in the gray images are the distributions of echogenicity across the tube diameter at different times ...... 72 5.5 The cyclic variation of the deviation from the temporal mean echogenicity obtained by subtraction of temporal mean echogenicity in Fig. 5.2 from Fig. 5.4 for three speed levels ...... 73 5.6 The cyclic variation of the total echogenicity at different radial positions for three speed levels ...... 74 5.7 The temporal mean echogenicity over a pulsatile cycle across the horizontal tube diameter for three stroke rates, 20, 40, and 60 beats/min (BPM) ...... 76 5.8 The cyclic variation of the total echogenicity across the horizontal tube diameter for three stroke rates and the corresponding speed profiles...... 77 5.9 The cyclic variation of the deviation from the temporal mean echogenicity across the horizontal tube diameter for three stroke rates and the corresponding speed profiles ...... 78 5.10 The temporal mean echogenicity over a pulsatile cycle across the horizontal tube diameter for three transducer frequencies, 9, 11, and 13 MHz...... 80 5.11 The cyclic variation of the total echogenicity across the horizontal tube diameter synchronized with the speed profile for three transducer frequencies....81 5.12 The cyclic variation of the deviation from the temporal mean echogenicity across the horizontal tube diameter synchronized with the speed profile for three transducer frequencies ...... 82 5.13 The temporal mean echogenicity over a pulsatile cycle inside the tube in B- mode images for eight hematocrits (12, 15, 20, 25, 29, 38, 40, 46%)...... 85 xi
5.14 The temporal mean echogenicity over a pulsatile cycle across the horizontal tube diameter for eight hematocrits ...... 86 5.15 The cyclic variation of the total echogenicity across the horizontal tube diameter synchronized with the speed profile for eight hematocrits ...... 87 5.16 The cyclic variation of the deviation from the temporal mean echogenicity across the horizontal tube diameter synchronized with the speed profile for eight hematocrits...... 88 5.17 The echogenicity as a function of hematocrit at different radial positions of the tube...... 89 5.18 The cyclic variation of echogenicity with hematocrit synchronized with the speed profile at different radial positions...... 90 5.19 The snap shots of the ‘Bright Collapsing Ring’ Phenomenon development from a human carotid artery during a heart cycle in harmonic cross sectional images and the corresponding normalized echogenicity across the horizontal vessel diameter...... 98 5.20 The cyclic variation of the total echogenicity and the deviation from the temporal mean echogenicity from a human carotid artery across the horizontal vessel diameter synchronized with the speed profile over a heart cycle ...... 99 6.1 The spectrograms of four different stroke volumes within a sampling volume obtained at the tube center. The black lines represent the mean speed profiles computed from the mean frequencies of the spectrogram. The stroke volumes are about 15, 20, 30, and 40 cc/stroke from the top to bottom panel ....105 6.2 The temporal mean echogenicity over an oscillatory cycle inside the tube in B- mode images for four stroke volumes...... 106 6.3 The temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for four stroke volumes...... 107 6.4 The cyclic variation of the total echogenicity across the horizontal tube diameter for four stroke volumes and the corresponding speed profiles. The lines in the gray images are the distributions of echogenicity across the tube diameter at different times ...... 108 6.5 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for four stroke volumes and the corresponding speed profiles ...... 109 6.6 The temporal mean echogenicity over an oscillatory cycle inside the tube in B-mode images for three different mean steady flow speeds and the corresponding normalized echogenicity across the horizontal tube diameter .....112 xii
6.7 The cyclic variation of the total echogenicity across the horizontal tube diameter for three different mean steady flow speeds and the corresponding speed profiles ...... 113 6.8 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for four stroke volumes and the corresponding speed profiles ...... 114 6.9 The temporal mean echogenicity over an oscillatory cycle inside the tube in B-mode images for three stroke rates and the corresponding normalized echogenicity across the horizontal tube diameter ...... 116 6.10 The cyclic variation of the total echogenicity across the horizontal tube diameter for three stroke rates and the corresponding speed profiles...... 117 6.11 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for three stroke rates and the corresponding speed profiles ...... 118 6.12 The temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for five transducer angles (0, 10, 15, 25, and 40°)...... 120 6.13 The cyclic variation of the total echogenicity across the horizontal tube diameter for five transducer angles and the corresponding speed profiles...... 121 6.14 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for five transducer angles and the corresponding speed profiles...... 122 6.15 A schematic diagram of rouleaux distribution across the tube and the definition of transducer angle ...... 123 6.16 The temporal mean echogenicity from porcine red blood cell (RBC) suspensions over an oscillatory cycle inside the tube in B-mode images for two different mean steady flow speed levels and the corresponding normalized echogenicity across the horizontal tube diameter ...... 128 6.17 The cyclic variation of the total echogenicity from porcine RBC suspensions across the horizontal tube diameter for two different mean steady flow speed levels and the corresponding speed profiles ...... 129 6.18 The cyclic variation of the deviation from the temporal mean echogenicity from porcine RBC suspensions over an oscillatory cycle across the horizontal tube diameter for two different mean steady flow speed levels and the corresponding speed profiles ...... 130 6.19 The temporal mean echogenicity from porcine RBC suspensions over an oscillatory cycle across the horizontal tube diameter for four transducer angles (10, 20, 30, and 45°) ...... 133 xiii
6.20 The cyclic variation of the deviation from the temporal mean echogenicity from RBC suspensions over an oscillatory cycle across the horizontal tube diameter for four transducer angles synchronized with the speed profile ...... 134 6.21 The cyclic variation of the deviation from the temporal mean echogenicity from RBC suspensions over an oscillatory cycle across the horizontal tube diameter for three stroke rates and the corresponding speed profiles...... 135 7.1 The ‘Black Hole’ phenomenon observed from in vivo experiments on pigs (Lin 1997) ...... 142
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LIST OF TABLES
3.1 Summary of cyclic variation of the Doppler power from porcine whole blood and RBC suspension. The numbers are all in dB scale of the Doppler power except for peak speed. Ave denotes the mean Doppler power over a cycle, Min the minimum power and ∆ the difference between the minimum and the maximum power in a cycle...... 40
xv
ACKNOWLEDGMENTS
“The blood is the life.” (Deuteronomy 12:23) How many times I recited this Bible verse while I was performing the experiments with pig’s blood, especially while cleaning the bloody experimental equipments! One day, I could suddenly realize that the blood refers Jesus’ sacrificial blood that gives us eternal life as shown in the following verses. “Whoever eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day. For my flesh is real food and my blood is real drink. Whoever eats my flesh and drinks my blood remains in me, and I in him.” (John 6:54-56) Therefore the blood is the life in both physical and spiritual senses, and I praise the Lord. I really appreciate my advisor, Dr. Shung for leading me to this world of blood and biomedical ultrasound. He has trusted me throughout the whole years with lots of support and showed indefatigable patience. One day in class, I could see the image of my father overlapped with him in a very short moment and have felt the same reliance of my father. I also thank my committee members, Dr. Tarbell, Dr. Sparrow, and Dr. Smith. All their comments and guidance have been helpful for me to be a better scholar. Without the ultrasonic transducer group and biomedical ultrasound group, I could not attain my goal. Dr. Cao’s creative suggestions and comments were always of great help. I believe that he was sent for me as an answer of my prayer. I also thank the staffs of Acoustics and Bioengineering Program, Carolyn, Karen, Brenda, Rita, and Doretta. Special thanks go to Gene for his help for experimental setups, slaughterhouses such as A.J. Peachey’s in Belliville for providing the free fresh blood with kindness, and janitors for cleaning bloody lab. David Summers and Richard James, were very kind to proofread my thesis and journal papers but the challenges from their lives were much more precious to me. It’s a cherishable time for me to share HIS works in our lives and pray together with Bill Saxton and ICF members as well as Mark Ogden. Church members and pastor in State College Korean Church were supportive and especially Kang Kim’s help both as an acoustician and as a brother in HIM was always unforgettable. My mother, brother, two sisters, and in-laws as well as my father and a brother who are not in this world any longer, showed their love all the time and support me in every way. No words are appropriate to express my thanks to them. I also appreciate my parents and two brothers-in-law for their care and love. Most of all, I dedicate all my works to my beloved wife, KyoungHee Lee and twin daughters, Heemang and Somang for their love and support. 1
Chapter 1
INTRODUCTION
1.1 Background
William Harvey, who discovered the basic principles of the circulation of the blood, was so impressed by its complexity that he stated that the motion of the heart and blood was to be comprehended only by God in the first chapter of his book in 1628 (Sheperd and Vanhoutte 1979). Much more knowledge has been gained since then, but even to date the complexity in the human blood circulation system is not fully understood yet, especially their pathological aspects. One example is red blood cell (RBC) aggregation, the phenomenon in which RBCs form a pile or network by electrostatic interactions mediated by macromolecules in the plasma. The pile or network formed by RBCs is called a ‘rouleau’ (rouleaux for plural). In spite of the fact that this phenomenon of stickiness of RBCs has been known for a long time, it is only in the past few decades that its causes have been studied, and even now its significance to normal and abnormal physiology is not entirely clear (Rampling 1988). The prime rheological effect of RBC aggregation is the rapid increase in blood viscosity as the shear rate falls. The shear-dependence of blood viscosity is of considerable potential importance in cardiovascular diseases, in which reduction in flow and shear forces may result in (1) a greater dependence of flow on rheological factors, and (2) local increases in blood viscosity, which may perpetuate flow disturbances (Lowe 1988). Pathological levels of RBC aggregation also play a role in microcirculatory flow disorders and vascular thrombosis (Chien 1975; Bicher 1972). In the clinical situation, excessive RBC aggregation may play an important role in a broad spectrum of diseases such as atherosclersosis (Ernst et al. 1991; Koenig and Ernst 1992; Le Devehat et al. 1990; Schmid-Schonbein and Volger 1976; Volger 1981), diabetes (Le Devehat et al. 2
1990; MacRury et al. 1993; Schmid-Schobein and Volger 1976; Tanahashi et al. 1993), cardiovascular disease (Hahn et al. 1989; Neumann et al. 1991; Razavian et al. 1992; Resch et al. 1991; Tanahashi et al. 1989), hyperlipidemia (Razavian et al. 1994), malignancies (Khan et al. 1995; Miller and Heilmann 1989; Sharma et al. 1992), and obesity (Poggi et al. 1994). Therefore, measurements of red cell aggregation and plasma viscosity are useful in the diagnosis and monitoring of some diseases (Lowe 1988). Most techniques for measuring the extent of RBC aggregation are only applicable under in vitro or ex vivo conditions. The single exception is ultrasound measurements. Ultrasound can provide real-time observations of aggregate formation in vivo (Wang et el. 1992), characterization of the rouleau formation kinetics (Kim et al. 1989; Kitamura et al. 1995), and the shear rate dependence of erythrocyte aggregation (Shehada et al. 1994; Van Der Heiden et al. 1995; Cloutier et al. 1996). Ultrasound is one of four major modalities in medical imaging techniques, along with X-ray, Magnetic Resonance Imaging (MRI), and Radionuclide imaging (Shung et al. 1992). Modern commercial ultrasonic systems have several imaging techniques such as B-mode, color Doppler, and power Doppler, displaying an image or a duplex and triplex image with a conventional pulsed Doppler spectrogram. Recently tissue harmonic imaging and B-Flow imaging techniques have been developed. Each imaging method has its own advantage depending on the clinical applications. However, interactions between ultrasound and RBCs from flowing blood are so complicated that further advance of the present knowledge of the ultrasonic scattering properties of whole blood must be pursued. The human cardiovascular system as shown in Fig. 1.1 was simulated using a simple mock flow loop in which hemodynamic parameters could be better controlled to study the ultrasonic backscattering characteristics from flowing blood in this research. Porcine blood was used to mimic human blood, and its physiological property was also controlled and changed. The Doppler power signals from a single element transducer and the commercial B-mode images from a linear array transducer were used for the research. 3
Figure 1.1 A schematic diagram of the blood circulation system in the human body (Jensens 1996). 4
The results may lead to a better understanding of blood rheology and hemodynamics, resulting in the ability to monitor physiological conditions for some diseases of humans in real time in the future and demonstrate the usefulness of ultrasound as a tool for the visualization of blood flow.
1.2 Previous Studies
Red cell aggregation, as one of the determinants of blood viscosity, plays an important role in both blood rheology (Knisely 1965) and blood echogenicity (Shung et al. 1984, 1992; Yuan and Shung 1988a, b; Cloutier et al. 1996). Shear rate seems to be the most important factor in affecting rouleaux formation in the moving blood in the vessels (Sigel et al. 1982, 1983). Machi et al. (1983) manipulated the shear rate in animals with surgically exposed vena cava, aorta and portal veins, and observed marked changes in echogenicity with the flow change in vivo. They could explain 57% of the total variation of echogenicity in relation to RBC aggregation. This seems highly significant and corresponds to in vitro studies (Razavian et al. 1994). Fibrinogen is another important factor which affects red cell aggregation. This is consistent with the previous results that stressed the effect of fibrinogen over other factors such as age and sex, or other hematologic parameters (Pignon et al. 1994). Kitamura and Kawasaki (1997) showed that the echogenicity was significantly associated with plasma fibrinogen, even though the echogenicity was correlated with other hematological factors, such as serum total cholesterol, and serum protein fraction excluding albumin, and serum total triglyceride. They concluded that ultrasound measurements of red cell aggregation seemed to be useful for the assessment not only of a part of the rheological condition of the blood, but also concomitant changes in plasma macromolecules. Another factor to be considered in RBC aggregation is hematocrit, since the rate and magnitude of rouleaux formation increase with increasing hematocrit (Lowe 1988). Kitamura et al. (1995) reported that hematocrit appears to determine the rate of aggregate 5
formation, and fibrinogen concentration appears to determine the size of the aggregate scatterers. Relevant to the focus of this research, one highly useful review paper concerning ultrasound backscattering from non-aggregating and aggregating erythrocytes was written by Cloutier and Qin (1997). After a review of scattering theories and theoretical models on ultrasound backscattering by RBC, they discussed the influence of the experimental factors, such as the volume of the scatterers, ultrasound frequency, hematocrit, orientation of the scatterers, flow turbulence, flow pulsatility, and concentration of fibrinogen and dextran. Among them, shear rate, flow turbulence, and hematocrit will be reviewed briefly in the following sections, because they are more related to this research. Then emphases will be placed on the cyclic variation of the backscattered power from blood under pulsatile flow, the ‘Black Hole (BH)’ phenomenon, and the ‘Collapsing Ring’ phenomenon.
1.2.1 Shear Rate Sigel et al. (1982, 1983) first showed that the ultrasonic echogenicity was dependent on shear rate. They suggested that RBC aggregation was a major cause of the increased echogenicity from blood. Yuan and Shung (1988) also reported that the backscattered power of porcine whole blood decreased as the shear rate was increased. Since then many studies have been published (Shehada et al. 1994; Van Der Heiden et al. 1995; Razavian et al. 1995; Cloutier et al. 1996; Qin et al. 1998; Lin and Shung 1999). In summery, it was found that there was a certain threshold shear rate that gave a maximum echogenicity. The echogenicity decreases as the shear rate was further increased and became independent at higher shear rates. However, the threshold shear rate for a maximum echogenicity and the shear rate limit where all rouleaux were broken up to individual cells range from 0.5 to 25 s–1 and from 20 to 150 s–1, respectively, depending on the flow conditions.
1.2.2 Hematocrit and Flow Turbulence 6
Shung et al. (1976) first measured the nonlinear relations between the backscatter and hematocrit, in which the backscatter from human blood suspension reached a maximum at about 26% of hematocrit. Shung and his associates (Shung et al. 1984; Yuan and Shung 1988a, b; Shung et al. 1992) observed further that the backscatter maximum could appear between 10% and 30 % of hematocrit depending on the flow conditions. Shung et al. (1984) also first demonstrated that flow turbulence increased the ultrasound basckscattered power. Several researchers (Bascom et al. 1993; Coutier et al. 1995, 1996; Bascom and Cobbold 1995) have further investigated the mechanism which is not fully understood yet; however, all agree that turbulence produces randomness in the spatial and temporal arrangement of RBC that leads to an increase in the backscattered power. Twersky and his collaborators (Twersky 1987; Lucas and Twersky 1987; Berger et al. 1991) introduced two parameters in his theoretical model considering the particle shape, correlation among particles, and the variance of the particle size, in order to better explain the hematocrit nonlinear relation and the increase of backscattering by turbulence.
1.2.3 Cyclic Variation of the Backscattered Power from Blood At first, there was a controversy as to the existence of cyclic variation of the backscattered power from blood. Later several studies confirmed the cyclic variation of the power during a cycle. Luckman (1987) reported no variation during a cardiac cycle in Doppler signal from blood in an adult carotid artery with an 8 MHz pulsed-wave Doppler system, while Thompson et al. (1985), Bascom et al. (1988) and de Kroon et al. (1991) observed a cyclic variation of Doppler power in in vitro experiments and backscatter in vivo in human iliac arteries. More recent results (Wu and Shung 1996; Missaridis and Shung 1999) have shown the existence of the cyclic variation of Doppler power from whole blood in vitro. Lin and Shung (1999) also observed the variation of the backscattered power from porcine blood using a 20 MHz intravascular transducer. The results on the cyclic variation of RBC and microsphere suspensions were also reported at some flow conditions (Cloutier and Shung 1993a). The results from whole blood under pulsatile flow indicated that the maximum Doppler power occurred near the peak velocity 7
for whole blood (Cloutier and Shung 1993b; Wu and Shung 1996; Missaridis and Shung 1999), whereas the Doppler power from RBC and microsphere suspensions was found to be minimal near the peak velocity (Cloutier and Shung 1993a) over a pulsatile cycle. The pattern of cyclic variation of echogenicity was also varied with flow conditions and radial positions.
1.2.4 The ‘Black Hole’ Phenomenon Yuan and Shung (1989) first reported the ‘Black Hole (BH)’ phenomenon, a dark hypoechoic hole at the center of the tube surrounded by a bright hyperechoic zone, which was observed from porcine whole blood experiments in cross-sectional ultrasonic B- mode images. Subsequent studies (Mo et al. 1991; Shehada et al. 1994; Qin et al. 1998; Cao et al. 2001) were undertaken to investigate the origin and the mechanism responsible for this phenomenon. They found that the low aggregation at the center of the tube was attributed to this hypoechoic zone. The parameters in their investigations were shear rate (mean flow velocity), entrance length, fibrinogen concentration, and insonification angles. Shehada et al. (1994) suggested the mechanism as low shear rate (< 0.05 s-1) at the center of the tube for less aggregation compared to the maximum aggregation between 0.05 and 2 s-1 of shear rate at surrounding area. The other mechanism suggested by Qin et al. (1998) was the structural organization and orientation of RBC rouleaux across the tube based on the experimental results by different transducer angles. Cao et al. (2001) could observe this phenomenon under pulsatile flow and found that the BH phenomenon was enhanced as hematocrit increased from 23 to 60%, as peak speed decreased, as stroke rate increased from 20 to 60 BPM at a fixed peak systolic speed, and as the entrance length increased.
1.2.5 The ‘Collapsing Ring’ Phenomenon Reyner (1995) first observed an interesting phenomenon, namely, the “Collapsing Ring’ phenomenon, from the porcine whole blood in the B-mode cross sectional images under pulsatile cycle. The bright hyperechoic ring appeared at the periphery of the tube at early systole and converged from the periphery to the center and finally collapsed as flow 8 developed. He presented the shear rate and the spatial rate of echogenicity across the tube diameter as a function of time to show the links between the ‘Collapsing Ring’ phenomenon and the shear rate. No further investigation and analysis were carried out.
1.3 Specific Aims
Fig. 1.2 shows the most important parameters that affect the backscattering power from flowing blood under pulsatile flow. The backscatter from blood is a function of hematocrit, backscattering cross section of a red blood cell, and packing factor which characterizes how RBCs pack together. The packing factor is affected by hematocrit, the flow disturbance, and a RBC aggregation tendency. Since backscattering cross section is proportionate to square of the scatterer volume at a given frequency for blood assuming the same physical properties (density and compressibility), rouleaux in blood increase the backscattering significantly. The aggregation is mainly dependent on hematocrit, plasma protein concentration, and hemodynamic conditions such as shear rate and acceleration. Under pulsatile and oscillatory flow, the shear rate and acceleration vary with time and radial position during a cycle. Since shear rate and acceleration are not measurable parameters, flow speed and stroke rate are the main hemodynamic parameters to investigate the backscatter from blood in this thesis in addition to a physiological parameter, hematocrit, in order to better understand these complicated inter-relationships under pulsatile flow. Although initial studies seemed to debate whether there is any variation of the backscattered power during a flow cycle, a number of recent studies have demonstrated that the backscatter of blood changes as a function of time during a pulsatile flow cycle. Even among investigators who were able to observe the cyclic variation of the backscattering power, the cyclic variation pattern was inconsistent; the peak Doppler power was observed at different phases of the flow. Shear rate was cited as the reason to explain the cyclic variation pattern, but the explanation was incomplete. Consequently the cyclic pattern of the backscattering power and the fundamental mechanisms responsible for it were the subjects of primary interest of this thesis. The origin of the 9
Pulsatile Flow
Flow Speed
Shear Rate Acceleration Stroke Rate
Turbulence Aggregation Fibrinogen
Backscattering Hematocrit Packing Factor cross section
Backscatter
Figure 1.2 Parameters to affect the backscattering from flowing blood under pulsatile flow.
10 cyclic variation was investigated through three different fluid media: a rigid polystyrene microsphere solution, deformable porcine RBC suspensions, and aggregating porcine whole blood. The shear rate is one of the most important hemodynamic parameters to be applied to explain the backscattering pattern from flowing blood in relations with red cell aggregation. Many studies performed under steady flow have been interpreted and analyzed using variation in the shear rate as a basis for the variation of backscattering. There have been some studies performed under pulsatile flow, but the basis of analysis and the interpretation of the data was still the shear rate. Some phenomena can be explained well by the shear rate analysis but others cannot. Temporal mean backscattering over a cycle can be explained well by the mean shear rate. However the instantaneous backscattering variation during a cycle cannot be fully understood by the shear rate since shear rate changes within a cycle. One of the phenomena is the pattern of cyclic variation of backscattering power under a pulsatile cycle. The observed backscattering power showed high echogenicity during systole, which contradicts the analysis by the shear rate. Therefore, other mechanisms in addition to the shear rate must be introduced to explain the conflicts, considering the change of shear rate during a pulsatile cycle. Recent results (Cao et al. 2001; Paeng et al. 2001) suggested the possible effect of flow acceleration on the aggregation. Experiments were conducted to investigate the effect of acceleration on the backscattering power using the Doppler power and the B- mode images. Allard et al. (1996) and Qin et al. (1998) have proposed the possible distribution of rouleaux across the tube diameter based on the shear rate analysis under steady flow. The shear rate changes over a pulsatile cycle so that the radial distribution of rouleaux must vary within a cycle. Therefore, the radial redistribution of rouleaux during a pulsatile cycle was also investigated in this research. Two interesting phenomena in the B-mode images were observed in our laboratory for the first time. Both the BH and the ‘Collapsing Ring’ phenomena were observed under pulsatile flow and the origin and mechanisms of the two phenomena were investigated in this thesis. The BH phenomenon has been recently observed from 11 pulsatile flow (Cao et al. 2001), but the cyclic variation of the phenomenon was not reported. The other interesting phenomenon, the ‘Collapsing Ring’, was reported by Reyner (1995) under pulsatile flow, but no further reports and analyses have been found.
1.4 Thesis Outline
Chapter 2 provides relevant background information in this thesis such as blood properties, hemorheology, hemodynamics, and ultrasonic scattering theories. Brief summaries in each field are given. Chapter 3 presents the experimental results obtained from an investigation of the Doppler power variation from flowing porcine whole blood and RBC suspensions, and polystyrene microsphere suspensions under steady and pulsatile flow at the center of the rigid tube. Three fluid media were used to investigate the origin of the Doppler power variation. The calibration and validation of the Doppler system and the experimental setups are described in detail in this chapter. Chapter 4 is dedicated to the description of experimental results obtained on the cyclic variation of the Doppler power at different radial positions in the tube for a further clarification of the role of acceleration in enhancing the rouleaux formation. Chapter 5 discusses the two interesting phenomena, namely the BH phenomenon and the ‘Bright Collapsing Ring (BCR)’ phenomenon, from the B-mode cross-sectional images under pulsatile flow. The cyclic and radial variations of echogenicity were observed and analyzed with several parameters including flow speed, stroke rate, hematocrit, and transmitting frequency. The BCR phenomenon was also observed from human carotid arteries in harmonic images. Chapter 6 reports the experimental results on the cyclic and radial variation of echogenicity under oscillatory flow. Both porcine whole blood and RBC suspensions were used as flow media to study the origin and mechanisms of the echogenicity variation. Chapter 7 summarizes the findings in this research concerning the variation of ultrasonic backscattering from flowing blood and suggests possible future research. 12
Chapter 2
BACKGROUND FOUNDATIONS
The background information relevant to this thesis is given in this chapter so as to better describe the rationale of the current research.
2.1 Blood Properties and Blood Rheology
Blood is a marvelous fluid that nurtures life, contains many enzymes and hormones, and transports oxygen and carbon dioxide between the lungs and the cells of the tissues (Fung 1993). Blood is mainly composed of red cells (erythrocytes, ~ 45% of total blood volume) and plasma, with small amount of white cells (leukocytes, 1/600th of the cellular volume) and platelets (thrombocytes, 1/800th of cellular volume). Plasma is a saline solution of three major types of protein, namely, albumin, globulin, and fibrinogen. The volume portion of cellular elements in the whole blood is defined as hematocrit and represented in %. The shape of human erythrocytes is a biconcave disc with a diameter of about 8 µm and thickness of about 1~3 µm. The mean volume is about 87 µm3. The shape is controlled by the osmolarity difference between the interior and exterior of the membrane, and it is also deformed by high shear rate. Plasma is a Newtonian viscous fluid whose viscosity is about 1.2 cP, but whole blood behaves like a non-Newtonian fluid whose viscosity varies with hematocrit, the protein concentration of the plasma, the deformability of the blood cells, and the tendency of the blood cells to aggregate (Fung 1997). The viscosity of whole blood increases when the shear rate of the flow and temperature decrease, and when the hematocrit increases. Aggregation and hardening of the cells increase the viscosity. These factors are all affected by various states of health and disease. Blood rheology plays a vital role in circulation because the coefficient of viscosity of blood affects resistance of 13
flow and therefore flow rate. This non-Newtonian property of whole blood is usually modeled by Casson’s equation. Erythrocyte aggregation is known to be responsible for this increase of viscosity under low flow conditions. Red blood cells of humans and some of other domestic animals in plasma can form aggregates known as rouleaux (Lowe 1988). Red cell aggregation results from the action of large plasma proteins, mainly fibrinogen and some
serum globulins such as α2-macroglobulin and immunoglobulins, which form bridges between adjacent red cells and overcome their mutual repulsion due to negative charges on their surfaces due primarily to sialic acid residues. Rouleaux formation is primarily dependent on the shear rate and hematocrit in addition to fibrinogen concentration. As shear rate rises, the aggregates are torn apart until no aggregates remain when shear rate reaches about 100 s-1. With increasing hematocrit, the rate and size of rouleaux will increase rapidly. The shear dependence of viscosity in whole blood increases very rapidly with hematocrit to reach a maximum at about 70%. High viscosity at low shear rate due to rouleaux formation produced by the fibrinogen led to blunting of the flow profile and a significant influence on flow rate. Red cell deformation as well as red cell aggregation also affects the shear dependence of blood viscosity as shown in Fig. 2.1.
2.2 Hemodynamics
2.2.1 Steady Flow The steady flow of a Newtonian fluid in a long cylindrical rigid tube is described well by Poiseuille’s equation. The velocity profile across the tube is a parabola and proportional to the square of the tube radius and the pressure gradient. The assumptions of Poiseuille’s flow are a Newtonian incompressible flow in the straight long rigid tube with a constant radius and a fully developed flow so that flow is independent of flow direction for laminar flow. The velocity profile across the tube radius is
14
Figure 2.1 Diagrammatic representation of the effects of red cell aggregation and red cell deformation on the shear dependence of blood viscosity (Lowe 1988).
2 2 ∆Pa2 r r v(r) = 1− = v0 1− (2.1) 4µL a a
where v(r) is velocity at radial position r, v0 is the maximum velocity at the center of the tube, ∆P is pressure difference, a is the internal radius of the tube, µ is the dynamic viscosity of the liquid, and L is the length of the tube. The shear rate (γ) is defined as the velocity gradient with respect to radial position. The shear rate for Poiseuille’s flow, which is a Newtonian fluid, dv 2rv τ γ ≡ − = 0 ≡ − (2.2) dr a2 µ 15
where τ is the shear stress. The relationship between the shear stress and shear rate is important for the category of the flow. A characteristic of Newtonian flow is the linear relation between the shear stress and shear rate as shown in Poiseuille’s flow. Whole blood is known as a non-Newtonian fluid whose viscosity decreases exponentially with shear rate at lower shear rate depending on hematocrits and temperature as mentioned in the previous section. For a small shear rate less than 10 s-1, and for hematocrit less than 40%, whole blood can be described approximately by Casson’s model,
τ = τ y + cγ (2.3)
-1 where τy is a yield stress and c is a constant. At a higher shear rate (>500 s ), whole blood behaves like a Newtonian fluid. For an intermediate shear rate, a power law model is usually used, τ = cγn. Casson’s flow gives a plug speed profile in a rigid cylindrical long tube for steady flow, while a Newtonian flow has a parabola shape profile of speed. 2 Reynolds number (Re in cm /s) is the ratio of inertia force to the viscous force to indicate whether the flow is laminar or turbulent and defined as following, 2aρV R = ≅ 52Va (2.4) e µ where ρ is the density of the blood and V is the mean velocity of flow. The approximate value is calculated with the kinematic viscosity, ν=µ/ρ= 0.038 cm2/s. Flow is usually considered as a laminar flow for less than a Reynolds number of 2000 and a turbulent flow for higher Reynolds numbers. The flow develops from a plug profile to a parabolic shape of speed as the steady
flow flows from the entrance of the tube. The entrance or inlet length (Le), the distance for flow to establish a laminar flow to have the parabolic shape from a flat profile at the start, was determined experimentally as following, 2kρVa2 L = = kaR ≅ 4.2Va2 (2.5) e µ e where k is a derived constant ranging from 0.057 to 0.13 and k=0.08 is reasonable for oscillatory flow (Chang and Atabek 1961; Nichols and O’rourke 1998). The inlet length 16 for the steady flow component in arteries is taken as the last approximate equation with kinematic viscosity, ν= 0.038 cm2/s, and k=0.08.
2.2.2 Oscillatory and Pulsatile Flow Womersley (1955) analyzed an oscillatory flow in a rigid cylindrical tube. He assumed the laminar flow of an incompressible Newtonian fluid with a single frequency sinusoidal pressure gradient, |A|cos(ωt - φ). Then the axial velocity (v) and the volume flow rate (Q) are respectively,
3 / 2 r 2 J 0 ( j α ) 2 ' − ja A a jωt | A | a M 0 ' v(t,r) = Re 1− e = ⋅ sin(ωt −φ + ε 0 ) (2.6) µα 2 J ( j3 / 2α) µ α 0
2 3 / 2 4 ' − jπa A 2J1( j α) jωt | A | πa M10 ' Q(t) = Re 1− 3 / 2 3 / 2 e = ⋅ 2 sin(ωt −φ + ε10 ) (2.7) ωρ j αJ0 ( j α) µ α where J0 and J1 are the Bessel functions of order zero and one respectively, Re stands for
' ' " " the real part of complex number, and the Womersley parameters, α, M10 , ε10 , M10 , ε10 are defined as follows,
1/ 2 ω α ≡ a (2.8) µ
3 / 2 r J 0 ( j α ) 3 / 2 ' " 2J ( j α) M ' e jε10 ≡ 1− a M " e jε10 ≡ 1− 1 (2.9) 0 J ( j3 / 2α) 10 j3 / 2αJ ( j3 / 2α) 0 0 As α goes to zero (low frequency asymptotes), the flow gives a time varying parabolic velocity profile with pressure gradient and velocity in phase. At higher frequency flow (α >10), the core flow is inviscid and the effects of viscosity are confined to the Stokes layer on the wall, so that the profile is flat in the middle (outside the Stokes layer) and lags the pressure gradient by 90°. Fig. 2.2 shows the theoretical velocity profiles for the different Womersley numbers that were computed using Equation 2.6. If the dimensions of the 17
Figure 2.2 Velocity profiles computed by the Womersley equation for the different Womersley numbers (α) (Fung 1997).
Figure 2.3 Velocity profiles measured from the descending thoracic aorta of an anesthetized dog (Milner 1989).
18 tube, the viscosity of the fluid, and the pressure gradient are known, the physiological pulsatile flow can be calculated by adding the harmonic components of frequencies in a velocity profile, which exists in vivo, assuming a linear system. However, the Womersley equation cannot be rigorously applied to arteries (Nichols and O’Rourke 1998), since several assumptions such as a Newtonian fluid, laminar flow, a long tube with constant diameter, and a single sinusoidal flow are not exactly satisfied in the arteries. The computed velocity profiles using the Womersley equation are somewhat different from the measured ones from the thoracic aorta of an anesthetized dog, which showed markedly blunting of the central portions as shown in Fig. 2.3, since entrance effects might not be fully satisfied and the nonlinear terms were omitted from the linearized equation. Nevertheless, the Womersley equation is almost certainly as close to, or closer than, a practical approximation as Poiseuille’s equation is for steady flow in arteries (Nicholes and O’Rourke 1998).
2.3 Ultrasonic Scattering from Blood
2.3.1 Scattering from a Single Scatterer The inhomogeneous linear wave equation is written in the following form (Morse and
Ingard 1969),
2 2 2 1 ∂ p γ κ ∂ p ∇ p − 2 2 = ∇ • (γ ρ∇p) + 2 2 (2.10) c0 ∂t c0 ∂t
ρ − ρ0 κ − κ0 1 γ ρ = ,γ κ = ,κ ≡ 2 (2.11) ρ κ0 ρc where p is the fluctuating acoustic pressure, ρ is the density, c is the sound speed, κ is the compressibility, and the subscript 0 is the ambient quantity. The 1st term and the 2nd term on the right hand side of the Equation 2.10 are the dipole and the monopole scattering source terms, respectively. The total acoustic pressure p is the sum of incident pressure pi and scattered pressure ps, that is p = pi + ps. If the total pressure is plugged in the above 19
Equation 2.10 and the incident pressure is subtracted, the scattering wave equation is obtained.
2 2 2 1 ∂ ps γ κ ∂ p ∇ ps − 2 2 = ∇ • (γ ρ∇p) + 2 2 (2.12) c0 ∂t c0 ∂t Integrating by the Green’s theorem with the Sommerfeld radiation condition, the scattered field is obtained,
p (r ) = k 2G(r − r )γ (r ) p(r ) + γ (r )∇p(r ) • ∇G(r − r ) dV (2.13) s ∫[]0 0 κ 0 0 ρ 0 0 0 0 V0 where k0 is the acoustic wave number of the ambient fluid, and G is a Green’s function, r0 represents the source position, and V0 is the volume of a scatterer. It is impossible to solve the scattering field for an arbitrary shape of an object using this integral method. Since red blood cells are weak scatterers, whose acoustic properties of the scatterers are similar with the surrounding medium so that ps << pi and p ≈ pi, the Born approximation can be applied and the far field approximation of Rayleigh scatterers (low frequency or long wavelength for ka <<1) is given by eikr p (r,θ ) ≅ k 2V [γ − γ cosθ ] (2.14) s 4πr 0 e κ ρ The backscattering cross section is obtained from this equation with an angle 180°,
2 2 2 4 2 2 | ps (r,π ) | π f Ve κe − κ0 ρe − ρ0 σ bs = r 2 = 4 − (2.15) | pi | c0 κ0 ρe where Ve is the volume of a red blood cell, f is the frequency of the transmitted ultrasonic wave, and the subscripts e and 0 represent the red blood cell and the ambient fluid media, respectively. The backscattering cross section is a function of the intrinsic properties of red blood cells in the brackets of the equation, the transmitting frequency of ultrasound, the speed of sound, and the red cell volume. Since the intrinsic properties of red blood cells and the speed of sound in the media do not vary much, the backscattering cross section is mainly dependent on the volume of a red blood cell, at a fixed frequency. Considering rouleaux 20 formation in whole blood at certain hemodynamic conditions, the volume of a scatterer varies greatly depending on the size of rouleaux.
2.3.2 Multiple Scattering in Blood The RBCs are so densely packed in normal human blood that they interact strongly and cannot be treated as independent scatterers. Two stochastic models were first proposed to simulate the density and compressibility function of the packed RBCs at high hematocrit blood, which is a random medium. The particle model used the backscattered wavelets from an individual RBC, and the continuum model used the density and compressibility fluctuation of the medium as source terms in an inhomegeneous wave equation as in Equation 2.10. These two models were later integrated in the hybrid model (Mo and Cobbold 1992). Mo and Cobbold (1986) proposed a general particle scattering model assuming blood as a suspension of RBC aggregates and that all scatterers in the blood sample have RBCs of identical size. The backscattering coefficient (BSC) is given by H BSC = σ bs W (2.16) Ve where W is a packing factor. In the continuum model, BSC is defined by the following expression, assuming scattering is considered to arise from spatial fluctuations in the density and compressibility of the continuum, var(n) BSC = σ bs (2.17) Ω0 where Ω0 is an elemental blood volume known as a voxel, σ bs is the average backscattering cross section in the random medium, and var(n) is the variance in the number of scatterers in Ω0 obtained by averaging over space and time. The two models were integrated in the hybrid model by Mo and Cobbold (1992), who combined the influence of the mean number of scatterers per voxel and its variation in number as a function of time. BSC in this hybrid model is given as 21
var(n) n BSC = σ bs = σ bs W (2.17) Ω0 Ω0 where n is the mean number of scatterers in the voxels Ω0. The concept of the packing factor (W) was first brought up by Twersky and his associates (Berger et al. 1991) to consider the correlation of scatterers. They could find the relationship by theoretical approaches, shown in the following equation:
2 2 2 H(1− H ) 2 4dbH (1− H ) d bH W = 2 (1− H ) + (1− H )H + (2.18) []1+ (d −1)H 1+ 5d 1+ 4b where d is the parameter for shape (d =1 for slab, d =2 for cylinder, d =3 for sphere, d >3 for convex particles such as erythrocytes), b is the variance of size distribution. Parameter d is also influenced by the correlation among particles. A decrease of parameter d corresponds to less correlation or higher fluctuation such as seen in turbulent flow and tends to shift the maximum of the backscattering power versus hematocrit curve toward a higher hematocrit, at a fixed b value. Recently, a new theoretical model was proposed by Bascom and Cobbold (1995) using a factional packing dimension to represent the packing method, and the packing factor is given by (1− H )m+1 W (m) = (2.20) (1+ H[m −1])m−1 where m is the fractional packing dimension related to the physical dimension and the packing symmetry of the scatterers, the absolute temperature, Boltzmann’s constant, the pressure and the variation of the pressure of the isothermal compressibility of the fluid, and the flow condition. For porcine RBC suspensions under steady flow, m = 2.54. All these models can calculate the nonlinear relations between backscattering and hematocrit. The backscattering coefficient from blood is computed as nonlinearly proportional to the hematocrit having a maximum at a hematocrit around 13~20% and then dropping off at higher hematocrits. 22
Chapter 3
ORIGIN OF THE DOPPLER POWER VARIATION
3.1 Introduction Although a number of recent studies have demonstrated that the echogenicity of blood varies as a function of time under pulsatile flow, the fundamental mechanisms responsible for it are still uncertain. In order to better understand this phenomenon, the Doppler power from porcine blood and polystyrene microsphere suspensions was measured at the center of the tube as functions of two crucial parameters, flow velocity and stroke rate (for pulsatile flow), under steady and pulsatile flow in a mock flow loop. In this chapter, the experimental results were obtained with a 10 MHz pulsed Doppler system whose frequency response was estimated more accurately by electronic injection and validated by comparing to the Radio Frequency (RF) signal acquired from the same Doppler instrument. Doppler power imaging has become a routine procedure in diagnostic ultrasound since 1994 (Rubin et al. 1994). Doppler power imaging has several advantages over conventional color Doppler imaging even though it does not carry the velocity information. It gives a higher signal to noise ratio (SNR), is less angle dependent, has no aliasing artifact, and is easier to implement. This technique allows the imaging of smaller vessels because of the higher SNR. Although commercial Doppler devices including scanners capable of power Doppler imaging are now widely available, the interaction between blood and ultrasound that produces the Doppler signal is still not clearly understood in spite of much effort that has been put forth by many investigators in the past. Luckman (1987) reported no variation during a cardiac cycle in Doppler signal from blood in an adult carotid artery with an 8 MHz pulsed-wave Doppler system, while Thompson et al. (1985), Bascom et al. (1988) 23 and de Kroon et al. (1991) observed a cyclic variation of Doppler power in in vitro experiments and backscatter in vivo in human iliac arteries. More recent results (Wu and Shung 1996; Missaridis and Shung 1999) have shown the existence of the cyclic variation of Doppler power from whole blood in vitro whereas the results on the cyclic variation of RBC and microsphere suspensions were inconclusive (Cloutier and Shung 1993a). The results from whole blood under pulsatile flow indicated that the maximum Doppler power occurred near the peak velocity for whole blood (Cloutier and Shung 1993b; Wu and Shung 1996; Missaridis and Shung 1999) whereas the Doppler power from RBC and microsphere suspensions was found to be minimal near the peak velocity (Cloutier and Shung 1993a) over a pulsatile cycle. In the present study using a more accurate method for estimating the transfer function of the Doppler instrument, Doppler power from the whole blood as well as microsphere and RBC suspensions was measured under similar experimental conditions so as to shed more light on these findings. The rationale for re-examining these issues arises from the fact that in calculating the Doppler power, the transfer function of the Doppler system, which is rather difficult to accurately estimate, must be known. The results are affected to a significant degree by the transfer function used. Several methods have been reported to estimate the transfer function previously (Cloutier and Shung 1993a; Cloutier et al. 1995; Wu and Shung 1996; Missaridis and Shung 1999). In this chapter, electronic injection was used to estimate the transfer function of a Doppler system. Its validity was established by comparison to the backscattered signal for the RBC suspension, which is known to be independent of flow speed in a mock circulation flow loop (Yuan and Shung 1988a). It is known that a number of hematological and hemodynamic parameters could affect the Doppler power from flowing blood. These parameters include RBC aggregation, hematocrit, and the distribution of the blood cells in the blood stream, which can be represented by the so-called packing factor in several publications (Twersky 1988; Berger et al. 1991; Shung et al. 1984; Mo and Cobbold 1992; Lim and Cobbold 1999). The packing factor is a function of the hematocrit, cell shape and correlation among cells, and the variance of the cell size. The correlation among the cells is affected by the flow conditions. It has also been shown that turbulent flow that reduces correlation among 24 cells increased the Doppler power (Shung et al. 1984, 1992). Spatial shear rate is another important factor that may affect the Doppler power because the formation and the size of the RBC aggregation are known to be highly dependent on the shear rate. This chapter investigates the variation of the Doppler power from porcine blood and polystyrene microspheres mainly using two flow parameters, speed and stroke rate (for pulsatile flow), under steady and pulsatile flow in a mock flow loop.
3.2 Materials and Methods
3.2.1 Preparation Of Porcine Blood And Polystyrene Microspheres Porcine blood is similar to human blood in red cell aggregation tendency (Yuan and Shung 1988a). Fresh porcine blood was obtained from slaughterhouses in 4 liter bottles which were prepared with 12 g of dipotassium salt (EDTA) dissolved in 120 ml of saline for anticoagulation. The blood was filtered through paper filters with 30 µm pore size to remove any flesh or clots and then centrifuged to separate the RBCs from the plasma. The buffy coat layer including white blood cells, platelets and other minor cells was removed. The concentrated RBCs and plasma were stored in a refrigerator at about 4 oC and the desired hematocrit was obtained at a later time by mixing of the concentrated RBCs with plasma for whole blood experiments. Red blood cell suspensions were used because RBC aggregation does not occur in a RBC suspension. To prepare the RBC suspension, the plasma and buffy coat were removed and the red cells were washed twice with 0.9% normal saline solution buffered to pH 7.4. Then the washed concentrated RBCs were reconstituted with 0.85% saline solution to the desired hematocrit. In order to prevent crenation of the red cells, 0.5% bovine albumin was added to the saline solution. Blood was circulated in the loop for at least 1 hour before making any measurements in order to remove the bubbles inside the loop and to allow the blood to reach the room temperature. The hematocrit was determined by reading RBC portions of capillary tubes after 4 minutes of centrifuging at 8000 rpm with a microcentrifuge (Clay Adams, Readacrit, Fisher Scientific, Pittsburgh, PA). 25
The polystyrene microspheres (Duke Scientific, Palo Alto, 1-35 µm and 20-130 µm of diameter distributions of microspheres) were suspended in a 16.5% glycerol and saline solution at a concentration of 1g/100ml. The density of microspheres is 1.261 g/cm3. The neutral buoyancy was checked visually after several hours as to whether the microspheres had settled down or risen to the surface. The reason that microspheres of two different size ranges were used is to investigate the effect of the scatterer sizes on the Doppler power qualitatively.
3.2.2. Mock Flow Loop The mock flow loop used in the experiments is shown in Fig. 3.1. For the steady flow loop, two reservoirs were used and the flow speed was controlled using the hydrostatic pressure difference between the two reservoirs. The reservoirs also reduced the speed fluctuations and removed bubbles. A magnetic stirrer at the bottom of each reservoir prevented the blood from settling. The inlet length to the measuring site for polyurethane tube (ID: 12.7 mm, OD: 15.9 mm, Nalgene, Rochester, NY) was 1 m, which was necessary for the development of laminar flow at the measuring site. A polypropylene tube (ID: 6.4 mm, OD: 7.9 mm, Cole Parmer, Chicago, IL) was used only for the experiments that used the large microspheres to obtain higher speeds under steady flow. The instantaneous maximum Reynolds number was kept below 1,683 calculated assuming a blood viscosity of 4 cP under both steady and pulsatile flow so as to maintain laminar flow in all experiments. A T-shape plastic connector of an appropriate size with a closed end and a hole on the side for transducer mounting was attached at the end of the tube, so that the transducer would be in direct contact with the scattering media in order to achieve higher SNR. The flow might be disturbed by the connector, but this effect could be assumed minimal for a low speed experiment. This minimal effect was demonstrated by the experimental results. A peristaltic pump (Cole Parmer, Chicago, IL) was used to refill the top reservoir from the lower one. For a pulsatile flow, only one reservoir in front of a pulsatile pump (Harvard Apparatus, Holliston, MA) was used to remove bubbles and to store blood. A bifurcation from the pump was constructed because the pump stroke volume was too large. The flow 26
Electromagnetic 10 MHz Pulsed Flowmeter Doppler
Flow
1 m Water tank
Flow Reservoir Magnetic stirrer Harvard Pulsatile Pump or Masterflex Peristaltic Pump
Jiffy Jack
Figure 3.1 Experimental arrangement for steady and pulsatile flow conditions. 27 speed was controlled by opening and blocking this bifurcation. A square-wave electromagnetic flowmeter (Carolina Medical Electronics, Model 501, Kings, NC) was used to trigger flow cycles which initiated the signal acquisition from the same phase of each cycle for ensemble averaging. The tube used in the pulsatile experiments was a polypropylene tube (ID: 6.4 mm, OD: 7.9 mm, Cole Parmer Chicago, IL). No acoustic window was used to mount the transducer for maintaining a direct contact with the fluid in pulsatile flow experiments. These tubing materials are known to have good resistance to many chemicals and hydrolytic degradation but they have poor acoustic properties, which may cause beam distortion. The beam profiles with/without the polypropylene tube were measured using a needle type hydrophone. There was about a 3 dB difference of on axis intensity near the focal point, and the –3 dB beam width with the tube was about 1.5 mm greater. However, beam distortion should not affect the experimental results significantly because the relative changes of the Doppler power from moving blood scatterers were measured.
3.2.3 Doppler Instrument The 10 MHz pulsed Doppler system built by Dr. Craig Hartley at Baylor College of Medicine was modified to allow the collection of the radio frequency (RF) signal from the instrument in addition to the Doppler signal. The RF signal was acquired from the RF board after the RF amplifier and before demodulation. In order to minimize interference from other components of the experimental arrangements, the A/D board needed for acquiring the RF signal was disconnected when the Doppler signal was collected, and vice versa. The 10 MHz single element transducer whose diameter is 3.0 mm was excited with a short pulse of 4 cycles of the 10 MHz signal and a pulse repetition frequency (PRF) of 39.06 kHz. The axial spatial length of the sampling volume with this transmitted signal is 0.54 mm. The sampling volume for the Doppler measurements was positioned at the center of the tube. The center position was determined after identifying both walls by controlling the range gate and positioned at the midpoint of the two walls.
28
3.2.4 Data acquisition and analysis A National Instrument A/D board (PC-MIO-16E-4, Austin, TX) along with the LABVIEW system was used to collect the Doppler data. The audio time signal from the Doppler meter was collected at 40.96 kHz sampling frequency and divided into 1024 point segments (25 ms) for analysis. A Kaiser-Bessel windowed signal (β=5) for each segment was taken for a 1024 point FFT and squared for the power spectrum. These power spectra were ensemble averaged over 50 or 100 cycles in the frequency domain through LABVIEW G programming. The ensemble averaged power spectrum was transferred to the computer through the A/D board. The post-processing was done in the MATLAB® software for compensation of the transfer function and filtering out the noise. After the transfer function was compensated, the Doppler power was obtained by summing up the power spectrum over all frequencies above a certain threshold so that noise could be minimized. This threshold was taken as a number 20 dB below the peak value. The Doppler power was smoothed by a median filter and a running average in order to determine low frequency variations of the Doppler power. The power spectra from 40 segments (one second) were averaged for the steady flow experiments without ensemble averaging. The Doppler mean velocity (V) and the Doppler power (P) within the sample volume were calculated using following equations:
c f ⋅ p( f ) V = ∑ i i (3.1) 2 f 0 cosθ ∑ p( fi ) 1 P =10⋅log10 ∑ p( fi ) (3.2) N where c is the sound speed in blood (1570 m/s), f0 the carrier frequency (10 MHz), θ the angle between the flow and transducer axial direction (60°), p(fi) the power in a bandwidth (∆f = 40 Hz) between fi and fi+1, and N is the number of points in the frequency domain (1024). The RF signal was collected using a Signatec A/D board (DA500A, Corona, CA) mounted in another computer. The sampling frequency was 100 MHz for each line, which was triggered with a gate signal. Each line had 2208 points of data and 254 consecutive lines were collected. From each line, a 512 point FFT was taken near the 29 center of tube in order to include the pulsed Doppler sample volume. The RF power was averaged over 254 lines in the frequency domain for the steady flow experiments. For pulsatile flow, the sampling started with the trigger signal from the electromagnetic flow meter for ensemble averaging over the flow cycles as a post-process. The sampling frequency was 200 MHz for 500 lines and each line had 1248 points. Because a small tube was used for pulsatile experiments, 512 sampling points with a 200 MHz sampling frequency for each line covered almost the entire lumen.
3.2.5 Transfer Function of the Doppler System The transfer function of the pulsed Doppler system has been analyzed by a variety of methods including string phantom, electronic or acoustic injection, and flow phantom (AIUM 1993). The pulsed Doppler system consists of a number of electronic components including a signal source, an RF amplifier/filter, a pair of coherent quadrature demodulators, a sample/hold, and an ultrasonic transducer. In this study, electronic injection with swept sine waves was used as opposed to previous studies where noise injection was used (Wu and Shung 1996; Missaridis and Shung 1999). The transmitted signals were disabled, and the sinusoidal signals from a function generator were used as the input. Quadrature audio output signals were collected while the output signals were monitored with an oscilloscope to determine whether there were cluttered signals or high level input signals. The FFT of the signals was taken, and the power spectrum was obtained. In this way the transfer function of the whole system was obtained excluding the effect of the transducer and the acoustic medium. This is a reasonable method because the 3 dB bandwidth of the transducer is 1.2 MHz so that the frequency response can be considered flat 20 kHz above or below the 10 MHz carrier frequencies. The effect of the acoustic medium may also be neglected because the travel distance is short and the difference in attenuation due to the minor frequency shift is minimal. The transfer function was inverted and multiplied with the Doppler power spectrum before the calculation of the Doppler power for compensation of the energy loss at higher frequencies. 30
To validate this approach, the Doppler power acquired and compensated was compared to the power of the backscattered radio frequency signals collected from the same Doppler system at the output of the RF amplifier before demodulation via a high frequency A/D board. The results for Doppler power before compensation are shown in Fig. 3.2 which indicates that the backscattered RF power did not change with Doppler frequency or flow speed while the Doppler power did change with flow speed in frequency for a polystyrene microsphere suspension (diameter distribution: 1-35 µm, Concentration: 1g/100ml) under steady flow. Since it is known that the backscatter from microsphere and RBC suspension does not change with flow speed (Yuan and Shung 1988a), these results clearly demonstrated the necessity for compensation. The Doppler power from polystyrene microsphere suspensions following compensation is shown to be independent of flow speed in Fig. 3.3.
3.3 Results
3.3.1 Steady flow experiments In order to further investigate the effects of flow speed on the Doppler power under steady flow, three types of scattering media, polystyrene microsphere suspensions of varying diameter, porcine RBC suspensions, and whole blood, were used. No Doppler power variation with speed from suspensions of different sizes of microspheres was observed up to 165 cm/s under steady flow. All speeds given in this chapter are the mean velocity (V) in the sample volume estimated by the Doppler flow meter. As expected, the Doppler power from the larger microspheres was about 7 dB higher than the power from the smaller ones. The dependence of the Doppler power upon flow speed was also examined using RBC suspensions and whole porcine blood. The hematocrit was kept at 20% for obtaining the highest Doppler power for RBC suspensions. The whole blood experiments were performed with 4 different hematocrits (6, 20, 30, 42%) but only the results from 20% hematocrit were shown in Fig. 3.4 for comparison. The hematocrit dependence is
31
1
0
-1
-2
B) d ( -3
-4
ed power -5 aliz m -6 Nor -7
-8
-9 RF power Doppler Power -10 0 2 4 6 8 10 12 14 16 18 20 Frequency(kHz)
Figure 3.2 Frequency responses of the Doppler power and the RF power measured with the Doppler instrument at a sampling frequency of 39.06 kHz using electronic injection. The dashed line denotes the frequency response of Doppler power and the solid line the RF power. 32
100 RF power(1-35um) DP( 1- 35um) DP(20-130um) 90
B) d ( 80 power RF
or 10 Doppler 0
-10 0 20 40 60 80 100 120 140 160 180 Speed(cm/s)
Figure 3.3 The RF and Doppler power from polystyrene microspheres under steady flow. The solid line and dotted lines are for the RF power and the Doppler power from the small size of microspheres (1-35 µm diameter) respectively, the dashed line is the Doppler power from large microspheres (20-130 µm diameter). 33
0 Whole Blood RBC suspension
-5
B) d ( -10 Power
-15 Doppler
-20
-25 0 5 10 15 20 25 30 35 40 Speed(cm/s)
Figure 3.4 The Doppler power from porcine whole blood and red blood cell (RBC) suspensions under steady flow. The solid line is for whole blood and the dotted line is for RBC suspensions. These results represent the averages from 3 different porcine blood samples. Standard deviations are shown as the error bars. Hematocrit of whole blood and RBC suspensions is 20%.
34 consistent with the theoretical packing factor which indicates the backscatter reaches a maximum around 20% and decreasing at higher and lower hematocrits. The experiments were performed on 3 different porcine blood samples. The mean and standard deviations are shown as lines and error bars, respectively. The Doppler power from the RBC suspension did not change (< 2 dB) appreciably with speed up to 37 cm/s, while the power from whole blood decreased with speed, yielding an almost 13 dB difference from 3 to 33 cm/s. At 33 cm/s, the Doppler power differed by only 3 dB between whole blood and RBC suspension. The standard deviation of the Doppler power from different RBC suspensions was small (< 1 dB), but that from whole blood was larger and became smaller with speed (2-4 dB). For these steady flow experiments using porcine blood, an acoustic window in a large tube was used to increase the SNR for comparison with the RF signal. In order to avoid the flow disturbance by the acoustic window, only low flow speeds were generated. The RF data were also collected and compared with the Doppler power in Fig. 3.5. The RF and Doppler power were normalized to the peak RF and Doppler power from whole blood for comparison. The patterns were similar for whole blood and RBC suspensions. The RF power from the RBC suspension did not change, but the power from whole blood decreased with speed. The differences between the RF and the Doppler power from whole blood and RBC suspensions were minimal near 35 cm/s.
3.3.2 Pulsatile Flow Experiments The Doppler power variation under pulsatile flow was also measured from polystyrene microsphere suspensions, whole porcine blood, and porcine RBC suspensions. The power was measured over a pulsatile cycle at 3 stroke rates (20, 40, and 60 BPM) at several flow speeds. The diameter distribution of microspheres used in the pulsatile flow experiment was 1-35 µm. The Doppler power from the microspheres did not change appreciably over a cycle (< 2 dB) in all 3 stroke rates as shown in Fig. 3.6. There were no distinct differences of the Doppler power from 4 different speed levels at 40 BPM. Therefore it is safe to say that the Doppler power from microspheres does not change over a cycle under pulsatile flow. 35
1 DPWB 0.9 RFWB DPRBC RFRBC 0.8 le a c
s 0.7
0.6 in linear 0.5
ed power 0.4 aliz
m 0.3 Nor 0.2
0.1
0 0 5 10 15 20 25 30 35 40 Speed(cm/s)
Figure 3.5 Comparison between the RF power and the Doppler power under steady flow. All the results represent the mean values from 3 experiments and the standard deviations are not shown for comparison. The solid thin line is for the Doppler power from whole blood and the dotted thick line is the RF power for whole blood. The dashed thin line is for the Doppler power from RBC suspension and the broken thick line for the RF power from RBC suspension.
36
20 BPM 40 BPM 60 BPM 15 15 15
)
dB 14 14 14 ( r e 13 13 13 ow p
ler 12 12 12 pp 11 11 11 Do
10 10 Peak 0.5 m/s 10 0 1 2 0 P0.eak5 1.0 1m/s 0 0.5 1 Peak 1.5 m/s Peak 2.0 m/s 2.5 2.5 2.5
2 2 2
) 1.5 1.5 1.5
m/s y( t i 1 1 1
Veloc 0.5 0.5 0.5
0 0 0 0 1 2 0 0.5 1 0 0.5 1 Time(s)
Figure 3.6 The Doppler power for microspheres (1-35 µm diameter) over a cycle under pulsatile flow. The Doppler power spectrum is the average over 100 cycles. The panels in each column represent the results for one stroke rate (20, 40 and 60 BPM from left to right), the panels in the upper row illustrate the Doppler power in dB and the lower panels the mean Doppler velocity in m/s for each stroke rate. Four different speeds were used to produce the results at 40 BPM to show velocity dependence. 37
In Fig. 3.7, the Doppler power from RBC suspensions is shown with the mean Doppler velocity for 3 stroke rates and 3 speed levels. The mean and standard deviation of the Doppler power from 3 experiments are shown while only the mean Doppler velocity is shown. The standard deviations of velocity are not shown for a better comparison and are less than 5 cm/s. The Doppler power changed minimally, remaining approximately at the same level (–5dB to –3 dB) at all stroke rates and at all speed levels over a pulsatile cycle. The standard deviations from 3 experiments were within 1 dB, except for the lowest speed experiment at 20 BPM (left top panel). The results for Doppler power from whole blood are shown in Fig. 3.8. Four experiments were performed. The hematocrit was adjusted to approximately 40%, which is similar to physiological conditions, for all pulsatile experiments. The aggregation is also known to be maximized at this hematocrit (Deng et al. 1994; Fontaine et al. 1999). The cyclic variations in the Doppler power were quite apparent at 20 and 40 BPM and at all speed levels. There were about 10~14 dB differences in the Doppler power at 20 BPM and about 4~6 dB differences at 40 BPM over a pulsatile cycle. The Doppler power was minimized at late diastole and became greater during the acceleration phase, reaching a maximum near peak systole. The Doppler power decreased again during the deceleration phase and reached a minimum at late diastole. After reaching its maximum near peak systole at lower peak speed levels, the Doppler power remained at those higher levels even to early diastole, while the power from higher speed experiments dropped quickly during the deceleration phase. The cyclic variation became weaker as the stroke rate was increased and no obvious cyclic variation was observed at 60 BPM. The Doppler power levels from whole blood at all stroke rates and all speed levels are summarized in Table 1. The Doppler power from the RBC suspension is shown only for one speed level as a reference. The mean Doppler power over a cycle decreased as the peak speed level was increased at all stroke rates. The minimum Doppler power at late diastole at 20 BPM was much smaller than the average power from the RBC suspension as seen in Table 1. The standard deviation was quite large for whole blood, especially at the lower peak speed levels. There was almost a 10 dB difference among samples at lower peak speed levels and a 5 dB difference at higher peak speed levels for all stroke rates. 38
20 BPM 40 BPM 60 BPM 0 1.5
-3 1
-6 0.5
-9 0
0 1 2 3 0 0.5 1 1.5 0 0.5 1 )
) 0 1.5 m/s dB ( y( t -3 1 i Power
-6 0.5 Veloc ler ler pp pp
-9 0 o Do 0 1 2 3 0 0.5 1 1.5 0 0.5 1
0 1.5 - D
-3 1
-6 0.5
-9 0 0 1 2 3 0 0.5 1 1.5 0 0.5 1 Time(s)
Figure 3.7 The Doppler power from RBC suspensions over a cycle under pulsatile flow at 3 stroke rates (20, 40, and 60 BPM from left to right) for 3 speed levels (30, 50, and 120 cm/s from top to bottom for peak speed). Each data point is the average over 50 cycles. The mean and the standard deviations from 3 different blood samples are shown as solid lines and error bars. The left vertical axes are the Doppler power in dB and the right vertical axes are the mean Doppler velocity in m/s. The dotted lines are the mean Doppler velocity, and the standard deviations are not shown (< 5 cm/s) for clarity. Hematocrit is 40%.
39
20 BPM 40 BPM 60 BPM 15 10 10 0.4
0 0 0 0.2
-15 -10 -10 0
0 1 2 3 0 0.5 1 1.5 0 0.5 1 )
) 15 10 10 1 m/s dB ( y( t i
0 0 0 0.5 Power ler ler Veloc pp -15 -10 -10 0 pp
Do 0 1 2 3 0 0.5 1 1.5 0 0.5 1
15 10 10 1.5 - Do
5 1 0 0 -5 0.5
-15 -10 -10 0 0 1 2 3 0 0.5 1 1.5 0 0.5 1 Time(s)
Figure 3.8 The Doppler power for whole blood over a cycle under pulsatile flow at 3 stroke rates (20, 40, and 60 BPM from left to right) for 3 speed levels (30, 50, and 120 cm/s from top to bottom for peak speed). The mean and the standard deviations from 4 different blood samples are shown as solid lines and error bars. The rest are the same as in Fig. 3.7.
40
Table 1. Summary of cyclic variation of the Doppler power from porcine whole blood and RBC suspension. The numbers are all in dB scale of the Doppler power except for peak speed. Ave denotes the mean Doppler power over a cycle, Min the minimum power and ∆ the difference between the minimum and the maximum power in a cycle.
Fluid Peak 20 BPM 40 BPM 60 BPM speed Ave ∆ Min Ave ∆ Min Ave ∆ Min (cm/s) Whole 30 1.3 14.3 - 8.7 3.1 5.7 -0.8 3.1 1.1 2.6 Blood 50 -3.2 13.0 -10.1 0.0 4.5 -2.0 0.2 2.6 -1.4 120 -5.0 10.2 -10.1 -2.9 3.5 -3.9 -3.3 2.0 -3.8 RBC 120 -3.7 1.1 - 4.2 -3.5 0.4 -3.7 -3.4 0.4 -3.6 suspension
41
The RF signal was also collected from the same Doppler system from a whole blood experiment to see whether the cyclic variation of the power could be measured. The RF power and the corresponding Doppler velocity at the center of the tube are shown in Fig. 3.9. The RF power was ensemble averaged over 20 cycles at 20 BPM. There was a cyclic variation and the pattern was similar to the Doppler power. The RF power reached maximum at peak systole and minimum at diastole.
3.4 Discussion
3.4.1 Doppler Power from Microspheres and RBC Suspensions The backscattering from the red blood cells and microspheres is known to be dependent on the size of scatterers, the density, and the compressibility of the scatterers for a given frequency. Since the red blood cells and microspheres do not aggregate in suspensions and the sizes of scatterers remain the same, it appears reasonable to assume that the backscattering variation from the suspensions with speed and stroke rate (only for pulsatile flow) should be minimal in a laminar flow condition. The experimental results from microspheres and RBC suspensions seem to support this hypothesis under both steady and pulsatile flow. These results are in disagreement with those from previous studies (Cloutier and Shung, 1993a), which indicate that the Doppler power from microsphere and RBC suspensions reached a minimum at peak systole. This discrepancy may be attributed to two factors: the speed range of previous experiments was high (up to 3 m/s) and the compensation for Doppler system transfer function was inadequate. The previous results suggested a 3 dB difference in frequency response over one half PRF (20 kHz) of the Doppler system. The new transfer function in Fig. 3.2 indicates that there may be more than 8 dB difference over the same frequency range, which may explain these differences. In particular, when the velocity difference between diastole and systole is large, the compensation of the transfer function has a significant effect on the Doppler power calculations. Therefore the minimum power at peak systole could be from the fact that the Doppler power at higher speeds was inadequately compensated. 42
75 10 1
5
) /s
m B) ) ( d ( ty dB i ( loc
74 0 0.5 e v Power RF Power Doppler Doppler
-5
73 -10 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(s)
Figure 3.9 Comparison between the RF power and the Doppler power for whole blood under pulsatile flow. The RF power is the average over 20 cycles. The stroke rate is 20 BPM and hematocrit is 40%. The Doppler power and velocity is shown as a reference by the dotted line and the dash-dotted line, respectively.
43
3.4.2 Aggregation Effects on Doppler Power from Whole Blood The Doppler power from whole blood under steady flow decreased with speed as shown in Fig. 3.4. There is about a 13 dB difference from 3 to 33 cm/s. This result is in good agreement with previous results (Yuan and Shung 1988a; Cloutier et al. 1996). This phenomenon has been attributed to the shear rate dependent RBC aggregation at low flow speed. Because the backscattering power is proportional to the 2nd power of the volume of the scatterers, the size of the rouleaux of red cells affects the Doppler power. From the observation that there was only a 3 dB difference between the power from whole blood and that from RBC suspensions at 33 cm/s, it could be concluded that the aggregation is minimal at higher flow speeds because of the high shear rate. The Doppler power from whole blood samples varied greatly, in contrast to the RBC suspensions, because aggregation tendency and fibrinogen concentration of blood could vary substantially from sample to sample (Yuan and Shung 1988b; Wu and Shung 1999). For the pulsatile flow experiments, the mean Doppler power over a pulsatile cycle decreased with speed at all stroke rates shown in Fig. 3.8 and in Table 1. There is almost a 3 dB difference of the mean Doppler power over a cycle from 30 to 50 cm/s peak speed and another 3 dB difference from 50 to 120 cm/s. This decrease with speed can be considered to result from a reduction in aggregation, as seen under steady flow. The dependence on the stroke rate was negligible. The aggregation effect was minimal at a peak speed of 120 cm/s, because there were no significant differences of the mean Doppler power levels from RBC suspensions shown in Table 1. The Doppler power from the center stream was observed to be maximal near peak systole over a cycle of pulsatile flow. This result is in agreement with previous results (Cloutier and Shung 1993b; Wu and Shung 1996; Missaridis and Shung 1999) and differs from those by Lin and Shung (1999) who observed the backscattering peak led the peak of the Doppler flow peak with a 10 MHz catheter-mounted intravascular transducer. The reason for this is that the sampled blood volume in the study by Lin and Shung (1999) was not located at the center of the tube. This phenomenon that Doppler power leads or 44 coincides with the flow peak could be accounted for a threshold of shear rate for the maximum enhancement of RBC aggregation (Wu and Shung 1996; Lin and Shung 1999). The measured RF signal from whole blood under pulsatile flow is shown in Fig. 3.9. A cyclic variation was also observed. However, the difference of the RF power between maximum and minimum (1 dB) over a cycle was much smaller than that of the Doppler power (13 dB). This could be caused by the fact that the RF power was measured over the whole diameter of the tube, which could result in less variation, while the Doppler power was measured at the center.
3.4.3 Acceleration and Deceleration The Doppler power was observed to be higher near peak systole over a cycle of pulsatile flow, while it was smaller at higher speed under steady flow. This phenomenon cannot be explained by aggregation due to shear rate alone and it seems to be contradictory, because the shear rate is greater at higher speed. A high shear rate would break up the rouleaux and give a smaller power. Even though ideally the shear rate is zero at the center of the tube according to the Womersley theory, there is still a finite non-negligible shear rate within the sampling volume of 0.5 mm3. Moreover, computational results obtained with a fluid dynamics package using finite element analysis, FIDAPTM (Fluid Dynamics International, Evanson, IL), showed that some degree of shear rate existed at the center of the tube under steady flow (Table 3, Lin and Shung 1999). Thus shear rate would change during a pulsatile cycle and this was also confirmed by computational results using FIDAPTM. Therefore, at the center of the tube the shear rate and shear rate change may be small but the acceleration could still be significant. It is proposed that the increase of the Doppler power from whole blood during early systole under pulsatile flow is the result of the acceleration of red cells along with aggregation. When the flow is accelerating, there are more chances for red cells to interact to form larger rouleaux, giving greater scattering. Rouleaux of different sizes may experience different accelerations depending on their size and mass during early systole (Cao et al. 2000), which affect the chances for collision of cells (Lim et al. 1997). 45
Red cells may easily come into contact with each other because of the compressional forces during acceleration. However the rouleaux may be disrupted because of the tensile forces on the rouleaux and the instability of flow during deceleration (Yellin 1966; Milnor 1989). A faster and slower drop of the Doppler power during deceleration at higher and lower peak speed level, respectively, might also be explained by the intensity of the disturbances depending on the magnitude of deceleration (Yellin 1966). If the large sizes of rouleaux are broken into smaller sizes, the backscattering would decrease. This may be a reason for the pattern of cyclic variation at the center of the tube, with maximum power near peak systole and minimum at late diastole, under pulsatile flow. However, this pattern may change as the sample volume is moved away from the center of the tube, where the shear rate may more affect the Doppler power compared to acceleration. The minimum Doppler power from whole blood at late diastole at 20 BPM was much smaller (-10 to 14 dB) than that from RBC suspension. The reason is unclear. One possibility is that there is some energy loss due to the high pass filter of the Doppler meter for very low speed because the flow speed is lower for whole blood due to higher viscosity under the same pump conditions. Further investigation is required to ascertain the acceleration effects and the very low Doppler power at late diastole at low stroke rate. This cyclic variation is less likely to occur at higher stroke rate (60 BPM) because the time for cells to collide to form larger rouleaux and vice versa may be insufficient in a cycle (Sennaoui et al. 1997; Lim et al. 1997; Lin and Shung, 1999). However aggregation still happens at low peak speed, which gives higher mean power compared to that at higher peak speed level in Table 1.
3.5 Conclusions
In this chapter, the variation of the Doppler power from microsphere and porcine blood was investigated using two parameters, flow speed and stroke rate (for pulsatile flow only), under steady flow and pulsatile flow. The transfer function of the Doppler system was estimated using electronic injection. The RF power from the scattering media was also measured simultaneously with the same Doppler system and compared to the 46
Doppler power to verify the frequency response. The RF power and the Doppler power from microsphere and porcine blood following compensation showed the same pattern. The Doppler power from microspheres and RBC suspensions showed no distinct variation under both steady and pulsatile flow. The Doppler power from whole porcine blood under steady flow was found to decrease with speed, with about a 13 dB difference from 3 to 33 cm/s. Only a 3 dB difference was observed between Doppler power from whole blood and RBC suspensions at 33 cm/s indicating that there was minimal RBC aggregation at this speed. The Doppler power from whole blood under pulsatile flow showed cyclic variation at 20 and 40 BPM but no cyclic variation at 60 BPM. The Doppler power increased at early systole, reaching a maximum near peak systole, and decreased slowly during late systole. The Doppler power continued to decrease at diastole and reached a minimum at late diastole. This cyclic variation became obvious as stroke rate and flow speed decreased, and the mean Doppler power over a cycle decreased as peak speed level increased. It is proposed that the high Doppler power near peak systole at the center of the tube is caused by the enhanced aggregation due to acceleration while the decrease of the mean Doppler power over a cycle with speed is due to the shear rate.
47
Chapter 4
CYCLIC AND RADIAL VARIATIONS OF THE DOPPLER POWER
4.1 Introduction
It was presented in the previous chapter that the Doppler power from whole porcine blood varied with hemodynamic conditions and the origin of the Doppler power variation was red cell aggregation. Red cells aggregate to form rouleaux at low shear rate, giving higher Doppler power, but rouleaux torn apart at higher shear rate. The Doppler power was measured only at the center of the tube where shear rate change was minimal. However, the shear rate also changes with radial position. The shear rate increases dramatically with radius under steady flow, and changes with time at a fixed radial position over a pulsatile flow cycle. The Doppler power variation at different radial positions under steady and pulsatile flow is reported in this chapter. The Doppler power and velocity were measured at different radial positions, so that the Doppler power as a function of shear rate under steady flow and its cyclic variation under pulsatile flow were analyzed. Acceleration was suggested to enhance the rouleaux at the center of the tube. This hypothesis needs to be validated by repeating the previous measurements at different radial positions. In this chapter, an emphasis will be placed on the effects of the shear rate change with time and radial position on the Doppler power during a pulsatile cycle.
4.2 Experiments Fig. 4.1 shows the mock flow loop for the experiments in this chapter. In order to avoid errors due to the wall filter at very low speed as reported in the previous chapter, the pulsatile flow was generated by adding oscillation from a piston pump to the mean
48
10 MHz Pulsed Doppler Reservoir Electromagnetic Flowmeter
Flow
Magnetic 1 m stirrer
Flow
Peristaltic Pump
Figure 4.1 Experimental arrangements for steady and pulsatile flow conditions. 49 steady flow generated by the height differences between two reservoirs. The mean flow was set to 36 cm/s for peak speed at the center of the tube. The stroke volume was set to 15 cc/stroke, and the output phase ratio of systole was 43. The other details of the experimental setups and system, preparation of blood, and data collection and analysis were the same as described in the previous chapter. Hematocrit was kept to about 40% for all experiments in this chapter. In order to investigate the cyclic and radial variation of the Doppler power, a 10 MHz single element transducer was positioned in a measuring window at an angle of 60° relative to a rigid polyurethane tube (ID: 12.7 mm, OD: 15.9 mm) which was filled with whole porcine blood. Both walls were identified when no sound was heard from a speaker of a pulsed Doppler system and the center was taken to be halfway between the two positions. Special care was taken to keep the transducer at the same position for each experiment. The range gate was set to 20 mm, and the transducer was moved back and forth with 1 mm increments as shown in Fig. 4.2. The data were collected from 0 to 6 mm, but the data from 6 mm was hardly used because of the loss due to the wall filter at very low speed. Since the beam travel distance (L) through porcine blood changed with radial position, the attenuation from blood was different. Another possible loss is from the beam distortion and interference through the tube wall at different beam positions. Therefore the losses need to be compensated, which was done with the curve shown in Fig. 4.3 with an assumption that the backscattering from RBC suspensions is independent of shear rate and speed (Yuan and Shung 1988; Paeng et al. 2001). Since the backscattering from porcine RBC suspensions should be the same regardless of radial position, the loss toward the center was added to the experimental results to maintain a flat response.
4.3 Results and Discussion
4.3.1 Steady Flow Experimental Results Fig. 4.4 shows the experimental results from the whole porcine blood under steady flow. Hematocrit was 40%. The dots and error bars are the means and standard deviations 50
60° 6.35 mm 20 mm L 0 mm
Figure 4.2 Transducer movements for different radial positions.
0.0
-1.0
y = 0.535x - 5.3575 2 -2.0 R = 0.9795
-3.0
-4.0 Doppler Power (dB)
-5.0
-6.0 0 1 2 3 4 5 6 Radius (mm)
Figure 4.3 Compensation curve for radial positions obtained from RBC suspensions. 51
0.8
) 0.6 /s m ( 0.4 ty i c o l
e 0.2 V
0 0 1 2 3 4 v1 5 v2 Radius(mm) 20 v3
) v4 B
d v5 ( 10 v6 power 0
Doppler -10 0 1 2 3 4 5 Radius(mm) 0.0 mm 20 0.9 mm
)
B 1.8 mm d ( 10 2.7 mm 3.6 mm
power 4.5 mm 0
Doppler -10 0 50 100 150 Shear Rate(/s)
Figure 4.4 Steady flow experiments. The lines and error bars are the mean and standard deviation from 5 different blood samples. v1~v6: Poiseuille flow peak velocity profiles. 52 from 5 different blood samples, respectively. The six lines for peak speeds ranging from 0.6 to 60 cm/s in the top panel are the velocity profiles computed from Poiseuille flow as shown in Equation 2.1. The experimental results were in good agreement with the computed ones. The middle panel shows the Doppler power corresponding to each velocity profile. The Doppler power decreased by about 10 dB from the center to a radial position of 4.5 mm at a speed of 0.6 cm/s. The radial variation of the Doppler power became less prominent (about 3 dB at a speed of 60 cm/s) as the speed increased. The Doppler power at the tube center decreased by about 15 dB as the speed increased from 0.6 to 60 cm/s, and at a radial position of 4.5 mm, the Doppler power decreased by about 10 dB over the same range of speed. The Doppler power as a function of the shear rate computed from the Poiseuille flow profile is shown in the bottom panel. The Doppler power decreased exponentially with shear rate regardless of the radial position except near the tube center, and this is similar to other experimental results (Yuan and Shung 1988; Van Der Heiden et al. 1995; Cloutier et al. 1996). The increased Doppler power at low shear rate is undoubtedly by the red cell aggregates. The Doppler power was almost independent above 80 s-1 shear rate, so that rouleaux seemed to be torn apart totally at this higher shear rate. The shear rate change was minimal at the center, but the Doppler power changed about 15 dB from 0.6 to 60 cm/s of the peak speed range. The rapid decrease of the Doppler power with the shear rate was shown even at the 0.9 mm radial position. Therefore, other mechanisms in addition to the shear rate could contribute to this dramatic change of the Doppler power with shear rate near the center. One possible reason is that the rouleaux size and orientation may be distributed along a certain preferential direction across the tube, as suggested by Qin et al. (1998), and this pattern may change with speed. One clue was found in the middle panel where the slopes of the Doppler power with radial position between the center and 0.9 mm were different from those at the rest of the radial positions at v3 and v4 (about 20 to 40 cm/s peak speed). The ‘Black Hole (BH)’ phenomenon was observed from some blood samples at these speed levels, even though it is not clearly shown in this figure since the experimental results from 5 blood samples were taken averaged. For higher speed, most rouleaux may be 53 disrupted so that the phenomenon was not observed. However, it is interesting to notice that there was no BH phenomenon observed for lower speed, where aggregation occurred maximally. The reason was not clear but this may be another clue that rouleaux distribution or orientation across the tube may be changed with speed.
4.3.2 Stroke Rate Dependence at the Tube Center Even though the stroke rate dependence of the Doppler power was examined in the previous chapter, some errors were included due to the wall filter for very low speed during diastole. The peak speed levels were kept the same, but the speed during diastole was changed at different stroke rates. Considering a highly sensitive change of the Doppler power with speed at lower speed during diastole in addition to errors by the wall filter, fluctuation was added to the mean steady flow in order to avoid the very low speed during diastole. The stroke rate of the piston pump was changed for fluctuation without controlling the amplitude of fluctuation while the steady mean flow was kept the same. Fig. 4.5 shows the cyclic variation of the Doppler power at the center of the tube at different stroke rates from 20 to 60 BPM (beats/min) under pulsatile flow. All data were ensemble averaged over 30 cycles for each blood sample, and the data from 4 different blood samples were averaged. Only the mean values are shown in this figure. The peak systolic flow speed was synchronized in time and the corresponding Doppler power was plotted at different stroke rates. The amplitude of the flow speed fluctuation became larger at higher stroke rates, but the overall Doppler power and the power fluctuation amplitude remained the same. The Doppler power variation due to higher shear rate fluctuation may be hindered by short time duration at higher stroke rates, so that the overall Doppler power was not changed significantly. Another possible explanation is that the reduced aggregation due to higher mean shear rate may be compensated by the enhanced aggregation due to higher mean acceleration at higher stroke rate. However, the phases between the peak systole and the peak Doppler power were changed with stroke rate. At 20 BPM, the peak of the Doppler power was measured at diastole, which was in good agreement with the results from steady flow that show the 54
20 BPM 0.6 4 3 2
0 1 1 2 30 BPM 3 4 0.6 4 3 2
0 1 1 2 3 4 40 BPM .6 4 er(dB) m/s)
( 3 2
elocity 0 1 V 1 2 3 4 50 BPM Doppler pow .6 4 3 2 0 1 1 2 60 BPM 3 4 0.6 4 3 2 0 1 1 2 3 4 Time(s)
Figure 4.5 Stroke rate dependence of the Doppler power at the center of the tube. The mean value was obtained from 4 different blood samples.
55 inverse relationship of the power with shear rate. As the stroke rate was increased, the peak of the Doppler power was shifted toward the peak systole and eventually the two peaks coincided at 60 BPM. This observation that the peak of the Doppler power occurred at different phases relative to the peak systole cannot be explained only by shear rate. There are two possible explanations. The Doppler power at 20 BPM might be governed by the shear rate when the acceleration was small. However, the acceleration became more important compared to the shear rate as the stroke rate was increased. The combined effects of shear rate and acceleration may change the pattern of cyclic variation of the Doppler power at different stroke rates as suggested in the previous chapter. The other reason may be due to the change of the radial distribution of the power near the center of the tube during a cycle, which will become clearer in the next section when the cyclic variation of the Doppler power at different radial positions is considered.
4.3.3 Cyclic and Radial Variation of the Doppler Power In order to investigate the radial variation of the Doppler power during a pulsatile cycle, the Doppler signals were obtained and analyzed at six different radial positions. The stroke rate was also changed to 20, 40, and 60 BPM. Figure 4.6 shows the temporal speed change and the Doppler power variation during a cycle at different radial positions at 20 BPM. The radial change of the Doppler power was dominant (about 6 dB) from the center to a 4.5 mm radial position mainly due to the shear rate. The cyclic variations were observed to be about 2 dB near the center and became smaller away from the center. The peak of the Doppler power was shifted from the late systole to early systole as the radial position changed from the center toward the wall. The Doppler power at the center of the tube was smaller than that in the adjacent area over certain systolic phase of the flow (between 1.5 and 2.5 s). This is the BH phenomenon, the appearance of a central hypoechoic zone surrounded by a hyperechoic zone in a tube (Yuan and Shung 1988a; Qin et al. 1998; Cao et al. 2001). However, the BH phenomenon disappeared during diastole. The radial variation 56
0.6
) .4 (m/s ty i
loc .2 Ve
0 0.0mm 0.5 1 1.5 2 2.5 3 4 1.0.89m m 1.8mm 2.7mm 3.6mm 4.5mm 4 dB) ( r e 2 pow er 0 Doppl -2
0.5 1 1.5 2 2.5 3 3.5 4 Time(s)
Figure 4.6 Temporal variations of the Doppler power at different radial positions at 20 BPM. The mean value was obtained from 4 different blood samples.
57
t=0.38 s t=0.75 s t=1.13 s 0.6 6 0.6 6 0.6 6
0.4 3 0.4 3 0.4 3
0.2 0 0.2 0 0.2 0
0 -3 0 -3 0 -3 0 2 4 0 2 4 0 2 4 t=1.50 s t=1.88 s t=2.25 s 0.6 6 0.6 6 0.6 6
0.4 3 0.4 3 0.4 3
0.2 0 0.2 0 0.2 0 Velocity(m/s)
0 -3 0 -3 0 -3 Doppler power (dB) 0 2 4 0 2 4 0 2 4 t=2.63 s t=3.00 s t=3.38 s 0.6 6 0.6 6 0.6 6
0.4 3 0.4 3 0.4 3
0.2 0 0.2 0 0.2 0
0 -3 0 -3 0 -3 0 2 4 0 2 4 0 2 4 Radius(mm)
Figure 4.7 Radial variations of the Doppler power at different times within a cycle at 20 BPM.
58 of the Doppler power at different time phases within a cycle was plotted in Fig. 4.7 in order to see the BH phenomenon more clearly. The obvious BH phenomenon appeared at 1.50, 1.88, and 2.25 s but disappeared at other times during a cycle. This cyclic variation of the BH phenomenon was not observed by Cao et al. (2001), even though they could observe the phenomenon under pulsatile flow. As suggested, their ultrasonic system with a 7.5 MHz linear transducer may not be sensitive enough to observe this variation. The pattern of the radial variation of the Doppler power was significantly changed with time near the center of the tube but was similar outside the center. This is a clue that the rouleaux distributions or orientations across the tube may be changed during a cycle, especially near the center of the tube. This redistribution of rouleaux and their orientations during a cycle may affect the different pattern of the Doppler power with stroke rate. In Fig. 4.8, the distribution of the Doppler power during a pulsatile cycle at a 40 BPM stroke rate is similar to that shown in Fig. 4.6 in terms of the cyclic and radial variations of the Doppler power and the peak shift of the Doppler power. The BH was also observed but existed shorter. However, the cyclic variation of the power was larger at the center, became small at a certain radial position outside the center, and increased again near the wall. This tendency was more obvious at 60 BPM as shown in Fig. 4.9. The peak shift of the Doppler power was observed more clearly at 60 BPM, but the BH phenomenon was weak. One speculation for the larger cyclic variation at the center and periphery of the tube is that the acceleration at both radial positions may be more important than the shear rate in affecting the Doppler power during a cycle. The acceleration is larger at the center when the shear rate is smaller. Near the tube wall, the shear rate may be too high to change the power, and the acceleration becomes important. This different pattern of cyclic variation of the Doppler power at different radial positions may be due to combined effects of shear rate and acceleration. This pattern was also observed from B- mode images that will be shown in the next chapter. The peak shift of the Doppler power from the center toward the wall of the tube was reported in Wu and Shung (1996), but the minimal cyclic variation at a certain radial 59
0.6 ) 0.4 ty(m/s loci
e 0.2 V
0 0.0mm 0.2 1 1.4 1. 2 0.6 1.0.89m m 6 1.8mm 2.7mm 6 3.6mm 4.5mm
) 4 dB ( r 2 powe r
e 0
Doppl -2
0.2 0.6 1 1.4 1.8 2
Time(s) Figure 4.8 The same as in Fig. 4.6 except at 40 BPM.
60
0.6
0.4
Velocity(m/s) 0.2
0 0.2 0.6 1 1.4 1.8 2 0.0mm 0.9mm 1.8mm 6 2.7mm 3.6mm
4.5mm 4
2
0 Doppler power(dB)
-2-
0.2 0.6 1 1.4 1.8 2 Time(s)
Figure 4.9 The same as in Fig. 4.6 except at 60 BPM. 61 position was not observed. The peak of the Doppler power appeared during an earlier systolic phase at the periphery of the tube, and the peak lagged closer to the center of the tube. This is another representation of the ‘Bright Collapsing Ring (BCR)’ phenomenon, even though it was not noticed by Wu and Shung (1996). When it is observed from B- mode images, a bright hyperechoic ring appears at the periphery of the tube at early systole and converged from the periphery to the center, finally collapsing as flow developed. The BCR was observed from real time B-mode images and will be analyzed in the next chapter. The peak shift and the BCR phenomenon during systole were explained by the shear rate change (Reyner 1995; Wu and Shung 1996). However, the shear rate varies with time during a pulsatile cycle and becomes higher at systole. The shear rate change is also different at different radial positions. Therefore, the explanation is incomplete accounting for shear rate only, so acceleration is speculated to be another factor to affect the red cell aggregation as described earlier. This peak shift and the BCR phenomenon due to the combined effects of shear rate and acceleration will be discussed in more detail in the next chapter.
4.4 Conclusions
Under steady flow the Doppler power was decreased exponentially with shear rate, but the shear rate dependence of the power was different near the center of the tube where other mechanisms such as the BH phenomenon and radial distribution of the rouleaux across the tube might be involved. For pulsatile flow, the Doppler power was observed to show cyclic variation over a pulsatile cycle, and the cyclic variation exhibited a different behavior at different radial positions across the tube. The Doppler power varied with stroke rate at the center of the tube. The peak of the Doppler power was observed during diastole at 20 BPM, but the peak was closer to the peak systole as stroke rate increased and eventually coincided with the peak systole at 60 BPM. This peak shift toward the peak systole with stroke rate may 62 be speculated to result from the aggregation enhanced by acceleration and the redistribution of the rouleaux during a cycle. The radial variation of the Doppler power was dominant (about 6dB) for all stroke rates (20, 40, and 60 BPM) from the center to 4.5 mm radial positions within a tube of 6.35 mm radius. The cyclic variation was observed to be small (about 2 dB) at the center and became smaller away from the center to reach a minimum at an intermediate radial position, and then increased again near the tube wall. The temporal positions of the peaks of the Doppler power shifted with radial position in such a way that the Doppler peak appeared at early systole at the periphery of the tube and lagged the flow closer to the center of the tube. This is another manifestation of the BCR phenomenon. The BH phenomenon was observed over some portions of the flow cycle, and the phenomenon became weaker as stroke rate increased in terms of the contrast of the Doppler power. The duration of existence of the phenomenon was also decreased with increasing stroke rate. The peak shift of the Doppler power with radial position and stroke rate at the center of the tube relative to the flow cycle was speculated due to the combined effects of acceleration with shear rate. Further experimental results were found to support the hypothesis that the acceleration may enhance the aggregation, so that the cyclic and radial variation of the Doppler power could be understood more clearly in this chapter.
63
Chapter 5
THE ECHOGENICITY VARIATIONS UNDER PULSATILE FLOW: THE ‘BRIGHT COLLAPSING RING’ PHENOMENON
5.1. Introduction
Backscattering from flowing blood in a vessel is so complicated that some phenomena cannot be explained fully. One example is the ‘Black Hole (BH)’ phenomenon, which was defined as a central hypoechoic zone surrounded by a hyperechoic zone in the cross sectional view of a B-mode image (Yuan and Shung 1989). Much has been put forth to explain the phenomenon by several investigators (Mo et al. 1991; Shehada et al. 1994; Lim et al. 1997; Qin et al. 1998; Cao et al. 2001) since it was first reported in 1989. This phenomenon was explained mainly by lack of aggregation at the center of the tube, while the more enhanced aggregation in regions surrounding the tube center resulted from a certain shear rate. Recently this BH phenomenon was observed under pulsatile flow where the shear rate was changed temporally and radially (Cao et al. 2001). They observed the BH phenomenon under different hemodynamic conditions, three stroke rates (20, 40, and 60 BPM), different velocity levels, and different entrance lengths. They also investigated how hematocrit affected the phenomenon. However, they were not able to observe the cyclic variation of the phenomenon and indicated that the sensitivity of their system perhaps was not good enough to observe the cyclic variation. In this paper, the cyclic variation of echogenicity from porcine blood was investigated with a more sensitive B-mode imaging system. Reyner (1995) observed another interesting phenomenon, the ‘Collapsing Ring’, which was defined such that a bright hyperechoic ring appeared at the periphery of the tube, converged from the periphery to the center, and finally collapsed at the center in the cross sectional B-mode images as the pulsatile flow developed. He attempted to analyze 64 it in terms of aggregation. However, his observation and analysis were limited and no other studies have been reported in the literature. A more thorough study is needed with a more sensitive system in this chapter. The previous two chapters were dedicated to investigating the cyclic and radial variation of the Doppler power during a pulsatile cycle. While the Doppler power is a good method to investigate the echogenicity from flowing blood because of the small dynamic range (Cloutier 1998), the Doppler power method has some drawbacks. No radial variation could be observed in real time with a single gate system, and the signals from low velocity were affected by band pass filters. There are also some expected errors due to the intrinsic broadening of the spectrum, positioning of the sample volume, and the transfer function of the system. B-mode images could overcome some of these drawbacks if the strong signals from tissue could be removed, thereby increasing the sensitivity to smaller signals from blood. Then the cyclic variation across the whole tube diameter could be measured in real time and be analyzed using B-mode images. In this chapter, the echogenicity from flowing blood in B-mode images is investigated. The focuses are placed on observing the ‘Bright Collapsing Ring (BCR)’ and the BH phenomena and investigating the cyclic and radial variation of echogenicity as a function of several hemodynamic parameters including speed, stroke rate, hematocrit, and frequency of transducer. The BCR phenomenon is also observed in human carotid arteries, and the results are given in the last section of this chapter.
5.2. Materials and Methods
5.2.1. GE LOGIQ 700 Expert System A LOGIQ 700 Expert system (GE, Milwaukee, WI) with an M12L linear transducer was used to study the backscattering from porcine whole blood in a rigid tube, mainly in B-mode images. Power Doppler images, color Doppler images, harmonic images, and B- Flow images as well as B-mode images were also obtained and stored as references for most of the experiments. The linear array transducer has multiple frequencies from 6 to 13 MHz, but a frequency of 13 MHz was mainly used, except when three frequencies (9, 11, and 13 MHz) were used to investigate the effects of transducer frequency on these 65 phenomena. Video images were stored on video tapes and digitized into 608×464 pixels with 29.97 frames/second using a video editing system in a personal computer. The digitized image data were stored and processed in MATLAB using an image processing tool. Duplex images with B-mode and a Doppler spectrogram were used to synchronize the echogenicity with the flow cycle. In order to increase the signal to noise ratio, ensemble averaging over 10 cycles were taken in MATLAB during post-processing. Harmonic images were used to investigate the backscattering from human carotid arteries instead of B-mode images, since harmonic images reduced the grayscale contrast between tissue and blood so that a more detailed variation of echogenicity from blood could be observed.
5.2.2. Blood Preparation and Mock Flow Loop The procedures to obtain the fresh porcine blood and the pre-processes to prepare the blood were the same as described in Chapter 3. Only porcine whole blood was used for the experiments and the hematocrit of the blood was kept to 40%. The experiments were completed within 36 hours after collecting the blood. The mock flow loop used in this experiment was the same as shown in Fig. 3.1 for the pulsatile flow experiments. The electromagnetic flowmeter was not used since the velocity in the sampling volume could be monitored by the Doppler spectrogram in Duplex images in the GE LOGIQ 700 Expert system. An M12L linear array replaced the 10 MHz Doppler transducer. One reservoir was used to mount the blood and to remove bubbles. A magnetic stirrer at the bottom of the reservoir prevented the blood from settling. The inlet length of a polystyrene tube (ID: 9.5 mm, OD: 11.1 mm, Nalgene, Rochester, NY) was 1 m, which was necessary for the development of laminar flow at the measuring site. The instantaneous maximum Reynolds number was kept below 1,235, calculated assuming a kinematic viscosity of 0.038 cm2/s under pulsatile flow, so as to maintain laminar flow in all experiments. A piston pulsatile pump (Harvard Apparatus, Holliston, MA) was used to generate the pulsatile flow. A bifurcation of the tube was constructed in order that the flow speed could be controlled by opening and closing this bifurcation. 66
5.3. Results
5.3.1. The ‘Bright Collapsing Ring’ phenomenon The BCR phenomenon, a bright hyperechoic ring converging from the periphery to the center of the tube and eventually collapsing during a pulsatile cycle in the cross sectional B-mode images, was observed under certain hemodynamic conditions. The left panels in Fig. 5.1 show the Duplex images including the cross sectional B-mode images with the corresponding pulsed Doppler spectrograms at 4 different phases during a pulsatile cycle. In the early systole as shown in the top panel, the hyperechoic ‘Bright Ring’ appeared at the periphery of the tube. At the peak systole, the ring converged toward the center of the tube and finally collapsed at the late systole as shown in the bottom duplex image. The BCR phenomenon is also shown clearly in the corresponding line plots across the tube diameter as shown in the right panels in Fig. 5.1. The echogenicity across the tube diameter near the center of the tube was obtained from the corresponding B-mode images in the left panels. About 10 vertical pixels were averaged along the horizontal line of the tube center. The echogenicity was normalized with the maximum gray scale. The BCR phenomenon was observed quite strongly when the flow stopped for a while and then started to pump. However, the BCR phenomenon was also observed with a weaker contrast even when the flow continued to circulate under certain flow conditions. This BCR phenomenon was investigated with several parameters, such as speed and stroke rate of the pulsatile flow, frequency of the transmitted signal, and hematocrits.
5.3.2. Speed Dependence The flow speed under pulsatile flow was controlled by opening or closing the branch tube to generate 3 levels of speed. The Doppler spectrograms of 3 speed levels at the center of the tube are shown in Fig. 5.2. The black lines in the spectrograms are the mean speed profiles computed from the corresponding spectrograms within the sampling volume which was taken at the center of the tube as shown in Fig. 5.3. The peak speed 67
Figure 5.1 The snap shots of the ‘Bright Collapsing Ring’ Phenomenon development during a pulsatile cycle in B-mode cross sectional images and the corresponding normalized echogenicity across the tube diameter along the horizontal lines of the tube center. The grayscale and the echogenicity were normalized with the maximum grayscale, 255.
68 levels at peak systole were approximately 10 cm/s, 15 cm/s, and 25 cm/s. With respect to the duplex images on a video tape, the BCR could be observed with the eyes but the phenomenon was not clear enough when it was digitized using a video editing system, due to degraded resolution. In order to increase the SNR to see the clear BCR phenomenon, an ensemble average over 10 pulsatile cycles was taken. The echogenicity from the ensemble averaged B-mode images was averaged over a pulsatile cycle, and the results are shown in the B-mode images in the left panels of Fig. 5.3. As the peak speed increased from 10 to 25 cm/s, the overall gray scale inside the tube turned darker and indicated lower echogenicity of the blood. The line plots across the horizontal tube diameter were obtained and plotted by the same way described in the previous section in the right panels for each speed level. The BH phenomenon, a dark hypoechoic spot surrounded by a bright hyperechoic zone is shown clearly at the center of the tube from the images of the two lower speed levels. The echogenicity near the center decreased from 0.7 to 0.5 as peak speed increased from 10 to 25 cm/s. The decrease of the mean echogenicity with speed is thought to be caused by disaggregation due to the higher mean shear rate. In order to see the temporal variation of echogenicity across the tube, line plots across the tube diameter were taken from all B-mode images during a whole cycle and plotted as a function of time in Fig. 5.4. The bottom panel shows the synchronized velocity profiles in cm/s which were computed from the Doppler spectrograms. All x- axes represent the time which was normalized over one pulsatile cycle for 20 BPM, namely 3 seconds. Y-axes represent the tube diameter, and the gray scales show normalized echogenicity for the top three panels. In order to see more detailed features of the echogenicity variations, the black lines are added to the gray images, and manifest the distributions of echogenicity across the horizontal tube diameter at different times. The overall echogenicity decreased with speed, but the temporal variation of echogenicity during a cycle was larger at higher speed levels. There was almost no temporal variation at 10 cm/s, and some weak variation was observed during systole at 15 cm/s. The temporal variation became obvious at a peak speed of 25 cm/s during systole. Another thing to be noticed in this figure is that the BH phenomenon was observed at the center of the tube, but this phenomenon became weak or disappeared for some time during the systole at the 15 cm/s peak speed as shown in the line plots of distributions of 69 echogenicity across the horizontal tube diameter. This cyclic variation of the BH was observed from pulsatile flow for the first time. In order to isolate the deviation over the temporal mean echogenicity, the averaged echogenicity over a pulsatile cycle as shown in the line plots of Fig. 5.3 was subtracted from Fig. 5.4 and plotted in Fig. 5.5. All the axes and grayscale are the same as in Fig. 5.4, except the amplitude of the gray scale, which is about 10 % of the total echogenicity. At a peak speed of 10 cm/s, the cyclic and radial variations of echogenicity were observed to be minimal, and the pattern was different from that at higher speeds. The cyclic and radial variations became obvious as speed increased. High echogenicity developed near the tube wall at early systole and converged toward the center as the flow developed at 15 cm/s; this is another manifestation of the BCR phenomenon. When this phenomenon was observed in real time in the cross sectional view of the B mode images, the ‘Bright Ring’ converged from the periphery to the center of the tube and eventually collapsed as the pulsatile flow developed. The BCR phenomenon was apparently present at the two higher speed levels. The variation was stronger at a peak speed of 25 cm/s so that the higher contrast ‘Bright Ring’ started at an earlier systolic phase of the flow. At the center of the tube, higher echogenicity was observed during the acceleration phase for 15 cm/s, while higher echogenicity was observed during both acceleration and deceleration phase for 25 cm/s. However, the cyclic variation of echogenicity was minimal right outside the tube center. In order to see the cyclic and radial variations of echogenicity at different radial positions, 5 normalized radial positions were taken from the center (r=0) toward the tube wall (r=0.7), and the averaged echogenicity from 6 bins around the normalized radial positions was plotted as a function of time in Fig. 5.6. The plot for a peak speed of 10 cm/s was not shown since there was little cyclic variation. Echogenicity decreased with radius dramatically due to the higher shear rate near the tube wall. These radial variations of echogenicity appeared at all speed levels. The shear rate was small at the center, allowing rouleaux to form and giving higher echogenicity, but the shear rate was higher near the tube wall, thus breaking the rouleaux and giving weak echogenicity. As the speed increased, the cyclic variation was stronger so that cyclic variations were apparent at all 5 radial positions for a peak speed of 25 cm/s. The cyclic variation showed different patterns at different radial positions, and these patterns were similar to those from the Doppler power variation as 70
Peak Speed: 10 cm/s
Peak Speed: 15 cm/s
Peak Speed: 25 cm/s
Figure 5.2 The spectrograms of three different speed levels within a sampling volume obtained at the tube center as shown in Fig. 5.3. The black lines represent the mean speed profiles computed from the mean frequencies of the spectrogram. The speed levels at peak systole are about 10, 15 and 25 cm/s from the top to bottom panel. 71
Peak Speed: 10 cm/s Peak Speed: 10 cm/s 1 0.8
0.6
0.5 0.4
0.2
0 0 0 0.5 1 Peak Speed: 15 cm/s Peak Speed: 15 cm/s 1 0.8 y t ci i n 0.6 oge h c
0.5 E 0.4 ed z i l a 0.2 m r o N 0 0 0 0.5 1 Peak Speed: 25 cm/s Peak Speed: 25 cm/s 1 0.8
0.6
0.5 0.4
0.2
0 0 0 0.5 1 Normalized Diameter
Figure 5.3 The temporal mean echogenicity over a pulsatile cycle inside the tube for three different speed levels and the corresponding normalized echogenicity across the horizontal tube diameter. 72
Peak Speed: 10 cm/s 1 0.5
0 0 Peak Speed: 15 cm/s r e
et 1 am
i 0.5 D d e z i al m r
o 0
N 0 Peak Speed: 25 cm/s 1 0.5
0 0
30 10 cm/s
s) 15 cm/s / 20
m 25 cm/s c ( y
t 10 ci o l
e 0 V -10 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Pulsatile Cycle for 20 BPM
Figure 5.4 The cyclic variation of the total echogenicity across the horizontal tube diameter for three speed levels and the corresponding speed profiles. The lines in the gray images are the distributions of echogenicity across the tube diameter at different times. 73
Peak Speed: 10 cm/s 0.06 1 0.04
0.02
0 0 -0.02 Peak Speed: 15 cm/s r
e 0.06 t
e 1 m
a 0.04 Di d 0.02 e z i l a 0 m r 0
No -0.02 Peak Speed: 25 cm/s 0.06 1 0.04
0.02
0 0 -0.02
30 10 cm/s )
s 15 cm/s / 20
m 25 cm/s c ( y
t 10 i c o l 0 Ve -10 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Pulsatile Cycle for 20 BPM
Figure 5.5 The cyclic variation of the deviation from the temporal mean echogenicity obtained by subtraction of temporal mean echogenicity in Fig. 5.2 from Fig. 5.4 for three speed levels. 74
Peak Speed: 15 cm/s
0.6
0.5
0.4
0.3 y t
i 0.2 c i
0.1
hogen 0 Peak Speed: 25 cm/s r= 0.01 c r= 0.2 E r= 0.4 ed z i 0.6 r= 0.6 al r= 0.7 m r o 0.5 N
0.4
0.3
0.2
0.1 0 0.2 0.4 0.6 0.8 1 30 15 cm/s s) / 20 25 cm/s m c ( y
t 10 ci o l 0 Ve -10 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Pulsatile Cycle for 20 BPM
Figure 5.6 The cyclic variation of the total echogenicity at different radial positions for three speed levels. 75 shown in Fig. 4.6. At the center of the tube, the echogenicity reached a maximum during the acceleration and deceleration phases of the flow at 25 cm/s. The peak echogenicity at different radial positions occurred at different phases of the flow cycle. The peak echogenicity lagged behind the flow peak near the center but led the flow peak near the wall. All these patterns of cyclic and radial variations of echogenicity, except the BH phenomenon, were also observed with the Doppler power measurements in Chapter 4.
5.3.3. Stroke Rate Dependence Three stroke rates were generated, 20, 40, and 60 BPM. Even though the stroke volume was the same, the speed changed with stroke rate so that the peak speed at peak systole was about 25 cm/s for 20 BPM, 35 cm/s for 40 BPM, and 40 cm/s for 60 BPM. In Fig. 5.7, the echogenicity averaged over a cycle across the horizontal tube center was plotted. The temporal mean echogenicity over a cycle was higher near the center at 20 BPM and became smaller at higher stroke rates. The BH phenomenon appeared at 20 BPM but became weaker with stroke rate. As the stroke rate increased, the velocity was higher, so that lower echogenicity at higher stroke rates could be explained by the higher mean shear rate. The weaker BH phenomenon at higher stroke rates was also observed in Cao et al. (2001) and was explained in terms of the shear rate and disaggregation of red blood cells. Echogenicity across the tube diameter along the horizontal central tube line was plotted as a function of time in Fig. 5.8. At 20 BPM, some variations of echogenicity were observed during systole, and the BH phenomenon was shown obviously at the center of the tube. This BH phenomenon disappeared or became weaker during early systole. The BH phenomenon and the overall echogenicity became weaker as the stroke rate increased. However, a cyclic variation of echogenicity was still observed at higher stroke rates. The deviations from the temporal mean echogenicity over a cycle were also calculated by subtracting the line plots in Fig. 5.7 from Fig. 5.8 and are shown in Fig. 5.9. The BCR was clearly observed at 20 BPM. As the stroke rate increased, the BCR phenomenon was less obvious in terms of contrast.
76
0.6 20 BPM 40 BPM 60 BPM
0.4
0.2 Normalized echogenicity
0 0 0.2 0.4 0.6 0.8 1 Normalized Diameter
Figure 5.7 The temporal mean echogenicity over a pulsatile cycle across the horizontal tube diameter for three stroke rates, 20, 40, and 60 beats/min (BPM). 77
Figure 5.8 The cyclic variation of the total echogenicity across the horizontal tube diameter for three stroke rates and the corresponding speed profiles. 78
Figure 5.9 The cyclic variation of the deviation from the temporal mean echogenicity across the horizontal tube diameter for three stroke rates and the corresponding speed profiles.
79
5.3.4. Frequency Dependence An M12L linear array transducer has multiple frequencies from 6 to 13 MHz and three frequencies, 9, 11, and 13 MHz from the transducer were used to investigate the frequency dependence of the echogenicity. The mean echogenicity over a cycle was plotted as lines for different frequencies across the central tube diameter in Fig. 5.10. The BH phenomenon was clearly seen for all three frequencies. The echogenicity increased as the frequency increased from 9 to 13 MHz at all radial positions. This increase was expected since backscattering from Rayleigh scatterers is proportional to the 4th power of frequency as shown in Equation 2.15, although the echogenicity amplitudes were only qualitative. The temporal variation of the total echogenicity across the central tube diameter is shown in Fig. 5.11. The higher the frequency, the stronger the observed echogenicity. The BH phenomenon was shown at the center of the tube but became weaker or disappeared for some time during systole. Even though the total echogenicity increased with frequency, the BCR phenomenon did not change much with frequency, as shown in Fig. 5.12 from the deviations over the temporal mean echogenicity. Both the BH and the BCR phenomena were clearly observed for all three frequencies, and they were independent of frequency even though the overall echogenicity decreased. This indicates that these two phenomena arise for hemorheological reasons, which are independent of the frequency of the transducer.
5.3.5. Hematocrit Dependence In order to investigate the hematocrit dependence of echogenicity, 8 hematocrits were generated from 12 to 46 %. The stroke rate was 20 BPM, and the transducer frequency was 13 MHz. The mean echogenicity over a cycle is shown in B-mode images in Fig. 5.13 for 8 hematocrits, and the corresponding line plots across the horizontal tube diameter are shown in Fig. 5.14. Even though the stroke volume and stoke rate did not change, the velocity would be changed because of different viscosity for each hematocrit.
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Figure 5.10 The temporal mean echogenicity over a pulsatile cycle across the horizontal tube diameter for three transducer frequencies, 9, 11, and 13 MHz. 81
Figure 5.11 The cyclic variation of the total echogenicity across the horizontal tube diameter synchronized with the speed profile for three transducer frequencies. 82
Figure 5.12 The cyclic variation of the deviation from the temporal mean echogenicity across the horizontal tube diameter synchronized with the speed profile for three transducer frequencies. 83
However, the velocity change was observed to be small so that the main echogenicity difference can be assumed to be mainly due to hematocrit. At low hematocrits up to 15 %, the BH phenomenon was not observed from Fig. 5.13 and barely observed in Fig. 5.14, while the phenomenon was obvious for higher hematocrits. This hematocrit dependence is similar to the results of Cao et al. (2001), where the BH was enhanced as hematocrit increased from 23 to 60 %. In Fig. 5.14, as the hematocrit increased from 12 to 46 %, the echogenicity profile across the tube diameter was changed from a parabolic shape for lower hematocrit to a linear decrease with radius. The echogenicity near the center at 12 % hematocrit was less than 0.6 and became larger at 15 and 20 %, then remained almost the same for higher hematocrits, while the echogenicity became smaller near the half radius as the hematocrit increased. Therefore the red cells’ interaction and distribution inside the tube seemed to be altered as the hematocrit changed. In order to investigate the temporal variation of echogenicity during a pulsatile cycle at different hematocrits, the echogenicity across the horizontal tube diameter was shown as a function of time in Fig. 5.15. Only one velocity profile was shown for synchronization in the two bottom panels. The BH seemed be weak at lower hematocrits and became more obvious throughout the cycle as the hematocrit increased. The overall echogenicity was small and temporal variation was minimal over a pulsatile cycle for low hematocrits. Some variations of echogenicity were shown during systole for higher hematocrits. The BH phenomenon seemed to vary with time during systole, which was not observed in a previous paper by Cao et al. (2001). Since their imaging system was old and used at 7.5 MHz, the sensitivity might not be good enough to observe this subtle cyclic variation, as discussed in their paper. In order to look at the deviation over the temporal mean echogenicity, the average over a cycle was subtracted from the total echogenicity and the deviation was plotted in Fig. 5.16. At 12 % hematocrit, the cyclic variation of echogenicity was minimal and showed a different pattern from the others, and no BCR phenomenon was observed. At 15 % Hematocrit, some variation was observed near peak systole, but the variation was weak. As the hematocrit increased, this variation during systole became more obvious. Strong bright echogenicity was shown at the periphery at early systole and converged from the periphery to the center as the flow cycle continued from early systole to early diastole. As hematocrits increased, the BCR phenomenon 84 seemed to become more prominent. Fig. 5.17 shows the hematocrit dependence of the echogenicity at different radial positions for the temporal mean echogenicity over a cycle. The patterns of hematocrit dependence of echogenicity were dramatically different at different radial positions. Echogenicity increased with hematocrit from 12 to 20 % and remained the same for higher hematocrits near the center of the tube, and the pattern of having a plateau was also measured by Shung et al. (1992) from the Doppler power under steady flow. This is different from the well-known nonlinear pattern of the backscattering from red cell suspensions as a function of hematocrit, which reaches a maximum around 10 ~ 20 % and decreases at lower and higher hematocrits. However, outside the center of the tube, the nonlinear pattern of backscattering, reaching a maximum at near 15 % hematocrit, was observed. Right outside the tube center, echogenicity reached a maximum near 20% and decreased slowly as hematocrit increased. Further toward the periphery of the tube, the echogenicity became a maximum at 15 % and decreased rapidly with hematocrit. This nonlinear pattern of echogenicity with hematocrit near the periphery can be explained by the packing factor in Equation 2.18, considering the correlation of scatterers at different flow conditions. However, the independence of echogenicity with hematocrits up to 46 % near the center cannot be explained by this theory, which does not explicitly include the effects of aggregation. One possible reason may be due to different aggregation tendencies at different hematocrits. Aggregation is known to occur maximally at about 40% (Deng et al. 1994; Fontaine et al. 1999) and near the center of the tube. Therefore it is possible that the decreased echogenicity at higher hematocrits is compensated by enhanced rouleaux formation, so that the echogenicity remains the same at higher hematocrits. The different nonlinear patterns of echogenicity at different radial positions suggest that hemodynamic parameters are very important factors in considering scattering, which may change the hematocrit dependence. Fig. 5.18 shows the temporal variation of echogenicity with hematocrits at different radial positions in order to investigate how the echogenicity variation is affected by hematocrit under different flow conditions. The cyclic variation of echogenicity at all hematocrits was minimal near the center as shown in the first two top panels, while the echogenicity 85
Figure 5.13 The temporal mean echogenicity over a pulsatile cycle inside the tube in B- mode images for eight hematocrits (12, 15, 20, 25, 29, 38, 40, 46%). 86
Figure 5.14 The temporal mean echogenicity over a pulsatile cycle across the horizontal tube diameter for eight hematocrits. 87
Figure 5.15 The cyclic variation of the total echogenicity across the horizontal tube diameter synchronized with the speed profile for eight hematocrits. 88
Figure 5.16 The cyclic variation of the deviation from the temporal mean echogenicity across the horizontal tube diameter synchronized with the speed profile for eight hematocrits. 89
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Figure 5.17 The echogenicity as a function of hematocrit at different radial positions of the tube. 90
Figure 5.18 The cyclic variation of echogenicity with hematocrit synchronized with the speed profile at different radial positions. 91 was enhanced during systole outside the center at higher hematocrits. At r = 0.6, the enhanced echogenicity appeared earlier and disappeared quickly. Close to the center of the tube, high echogenicity appeared late and lasted longer. This is believed to result from the fact that the overall shear rate is higher and the acceleration is smaller near the tube wall, so that the enhanced aggregation due to acceleration is offset by the high shear rate. Closer to the center, the acceleration is higher and the shear rate is lower, so that the acceleration’s role in affecting aggregation is more important and may allow higher echogenicity to last longer. The shorter duration of high echogenicity near the tube wall may also be due to the higher shear rate breaking rouleaux faster. For lower and higher hematocrits, the temporal variation was minimal, and the cyclic variation of echogenicity became a maximum between 20 and 30 %, except near the center of the tube during a whole cycle.
5.4. Discussion
5.4.1. Effects of Acceleration and Shear Rate on the Echogenicity Rouleaux are formed when the flow stops and remains still in porcine whole blood. These rouleaux are broken when a shear force is applied. Generally, it is believed that the aggregation of red cells occurs maximally at a certain shear rate, ranging from 0.1~10 s-1 for steady laminar flow (Shehada et al. 1994; Van Der Heiden et al. 1995; Coutier et al. 1996). Coutier et al. (1998) obtained a higher shear rate, reaching a maximum Doppler power at about 20 s-1 near the tube wall within the sampling volume of the pulsed Doppler system for steady flow. Copley et al. (1975) and Usami et al. (1975) found that the rouleaux consisted of about 10~15 red cells at a shear rate of 1~10-1 for steady flow and at 1 Hz flow frequency for sinusoidal flow. However, Lin and Shung (1999) estimated a threshold shear rate of about 150 s-1 in the sample volume at half the radius of the tube for sinusoidal flow. The shear rate was computed from a computational fluid dynamics software using finite element analysis for this estimation. Except for Lin and Shung’s results, the aggregation reaches a maximum at a shear rate in the range about 1~10 s-1 for normal physiological flow. According to the results from steady flow in Fig. 92
4.2, the Doppler power decreases as shear rate increases for speed levels from 10 to 60 cm/s at the center of the tube. In the experiments reported in this chapter, the shear rate should be higher outside the tube center for the same speed at the center, considering the smaller diameter used in this experiment compared to the Doppler experiment in Chapter 4. Therefore we can assume that the backscattering power decreased as the flow speed increased all across the tube, due to higher shear rate within the experimental speed range. From Figs. 5.3, 5.4, 5.7 and 5.8, the overall echogenicity decreased as the peak speed and stroke rate increased. It is reasonable to believe that this decrease of echogenicity is due to the increase of mean shear rate. As the peak speed and stroke rate increased, the mean shear rate increased and reduced the rouleaux formation, giving smaller echogenicity. As the speed and stroke rate increased, the BH phenomenon became weaker at the center of the tube, in good agreement with Cao et al. (2001). However, the BCR phenomenon became more obvious as the peak speed increased from 10 to 25 cm/s as shown in Fig. 5.5. The variation in shear rate can explain the decrease of mean echogenicity with speed, but the temporal variation of echogenicity during a cycle cannot be explained by shear rate alone. For low speed levels, no obvious cyclic variation was observed even though the shear rate changed during a cycle. The shear rate increased during early systole and decreased during late systole, but the echogenicity remained the same. For higher speed levels, the echogenicity was stronger during systole when the shear rate was higher compared to the diastolic phase. As the speed increased, the BCR phenomenon became obvious. All of these observations cannot be understood by the variation in shear rate alone, since a higher shear rate breaks down the rouleaux. Acceleration may be another factor enhancing the aggregation, since all these instances of enhanced echogenicity happened during the systole of the flow. Acceleration may increase the possibility of red cell collisions due to different inertia and compressional forces (Cao et al. 2001; Paeng et al. 2001). At lower speed levels, the acceleration is small during early systole so that it may compensate for the amount of the reduced aggregation due to the high shear rate. As the speed increases, the acceleration becomes larger so that the enhanced aggregation due to acceleration may become important and overcome the reduced aggregation due to high shear rate. This may explain the stronger variation of echogenicity at higher speed during 93 systole. There were also phase changes of peak echogenicity compared to the flow phase between the 15 and 25 cm/s peak speeds. High echogenicity was observed to occur late for 15 cm/s and earlier for 25 cm/s. This may be further evidence that a certain level of acceleration may be needed to give higher echogenicity to compensate for the shear rate. The echogenicity was stronger during acceleration for peak speeds of 10 and 25 cm/s at the center of the tube, where the shear rate change was minimal. Immediately next to the center, the cyclic variation of echogenicity was a minimum. In this region, the acceleration and shear rate may compensate each other to give a minimal change of echogenicity, in the same reason of minimal change of echogenicity for 10 cm/s peak speed due to the offset effect of shear rate and acceleration effects. The higher echogenicity was observed at both the periphery of the tube and the center of the tube at the same time during acceleration. The reason for this may be that the shear rate was too high near the tube wall, so that acceleration became more important, in the same way as the shear rate change was minimal and acceleration became important at the center of the tube. At other radial positions, the lower echogenicity might be explained by the combined effects of acceleration and shear rate. Considering the late appearance and longer duration of high echogenicity toward the center as shown in Fig. 5.18, the combined effects of the enhanced aggregation due to acceleration and the degraded aggregation due to high shear rate seem to be supported. As the acceleration becomes larger toward the center, more rouleaux may be formed and last longer since the shear rate is smaller, and vice versa. However, the acceleration may not always enhance the aggregation. When the speed was much higher than these levels, about 100 cm/s peak speed, the BCR phenomenon was not observed (these results were not shown here). Another clue could be found in Fig. 5.8 for the stroke rate dependence. As the stroke rate increased, the acceleration should be increased during systole, but the BCR phenomenon became weaker. Therefore acceleration may not enhance the aggregation in all flow conditions. There are several factors to be considered. A certain amount of time is required to form rouleaux. Even though the acceleration is higher for higher stroke rate, the time for rouleaux formation may not be satisfied. Acceleration should be thought of in combination with shear rate, rather than acceleration only. The contribution of both shear rate and acceleration to 94 aggregation and its importance may result in complex BCR phenomenon and cyclic variation of echogenicity. More thorough studies are required for the confirmation of this hypothesis and to quantify the acceleration and shear rate levels. Another factor to be considered is that the radial distribution of rouleaux changed during a pulsatile cycle. The rouleaux alignments and rotation may change with the flow, and these changes of rouleaux distribution during a cycle may contribute to these complex phenomena. These concepts will be discussed in more detail in the next chapter on the oscillatory flow experiment.
5.4.2. Comparison of the Echogenicity with the Doppler Power As mentioned in the previous chapter, the phase change of the peak Doppler power at different radial positions compared to the flow is a manifestation of the BCR phenomenon as shown in Fig. 5.6. At a peak speed of 25 cm/s, the pattern of echogenicity variation was similar to the pattern of the Doppler power variation as shown in Fig. 4.6. Peak echogenicity near the tube wall occurred earlier in systole and the peak echogenicity lagged behind at radii close to the center of the tube. This phase difference of the peak Doppler power was also observed by Wu and Shung (1998), and they tried to explain this phenomenon by the different shear rate variation at different radial positions during a flow cycle. They computed the temporal variation of shear rate along the radial positions from the Womersley model for oscillatory flow. This was an initial qualitative explanation with the purpose to determine whether a phase delay of zero shear rate existed due to shear rate variation across the diameter. Their underlying assumption was that the minimum shear rate that gives the maximum Doppler power occurs at different times at different radial positions. This may be true for oscillatory flow but their experimental results were from pulsatile flow, where the minimum shear rate occurred during diastole. The BCR phenomenon was observed during systole where the shear rate was higher than a threshold shear rate, resulting in the inverse relationship between shear rate and echogenicity. A possible reason to account for this discrepancy was given in the previous section by the combined effects of acceleration and shear rate on aggregation.
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5.4.3. The Cyclic Variation of the ‘Black Hole’ Phenomenon In Fig. 5.7, the BH phenomenon was apparent at 20 BPM and became weaker for higher stroke rates. The BH phenomenon also became weaker with speed as shown in Fig. 5.3 and 5.4. These results are in good agreement with those of Cao et al. (2001). The BH phenomenon was also independent of frequency and was observed throughout the flow cycle, while the BCR phenomenon was observed only during systole as shown in Figs. 5.10 and 5.11. The BH phenomenon was seen under steady flow but the BCR was not. Therefore these two can be thought of as independent physiological phenomena. However, these two phenomena do interact each other during systole, so that the BH phenomenon was weak or disappeared when the BCR phenomenon enhanced the echogenicity at the center of the tube as shown in Figs. 5.4, 5.11, and 5.12. The cyclic variation of the BH phenomenon seems to be mainly due to the enhanced aggregation of the BCR phenomenon and the change of radial distribution of rouleaux at the center of the tube during the acceleration and deceleration phases of the flow. The BH phenomenon was clearly observed during diastole but disturbed during systole in terms of contrast between the surrounding hyperechoic zone and the central hypoechoic zone. The size of the BH was also enlarged during diastole and shrunk or disappeared during systole. These variations were observed in Figs. 5.4, 5.8, 5.11, and 5.15, even though Cao et al. (2001) did not observe the variation of the BH phenomenon during a pulsatile cycle. As they suggested in their paper, the sensitivity of their system might not have been good enough to observe the cyclic variation of this BH phenomenon, while the GE LOGIQ 700 expert system has a much higher sensitivity.
5.5. Human Subject Experiment The human subject experiment was approved by the Internal Review Board (IRB) under Food and Drug Administration (FDA) regulations at The Pennsylvania State University. 8 males and 3 females were the volunteers for this experiment. Their ages were between early twenties and early forties. Their heart beats were between 65 and 90 BPM, and the peak systole speeds estimated from the Doppler measurements were between 55 cm/s and 100 cm/s. The images were taken from their carotid arteries using a GE LOGIQ 700 Expert system with a M12L linear array transducer. Even though several 96 imaging methods such as B-mode, B-Flow mode, power Doppler mode, and color Doppler mode were used to investigate, the harmonic imaging technique was used since the BCR phenomenon was observed only with this imaging approach. Backscattering from tissue is much higher than that from blood, so that the grayscale from blood in B- mode images looked dark everywhere inside the vessels and no variation was observed. The dynamic range of the echoes was too big to observe the cyclic variation of echogenicity from vessel lumen lying under the tissue from B-mode images. However, harmonic imaging from the M12L transducer reduces this dynamic range, so that the grayscale contrast between tissue and blood is smaller, allowing observation of the cyclic variation of echogenicity from the blood. Harmonic imaging from the M12L transducer in the GE LOGIQ 700 Expert system uses multiple transmit codes to extract the harmonic signals (Haider and Chiao 1999). When harmonic imaging is used to image moving tissue or blood, decorrelation between the multiple firings caused fundamental echoes to leak through and be visible. Therefore the M12L harmonic images are obtained from the combination of the 3rd harmonic signals from the tissue and the leaked fundamental signals from the blood at 9 MHz (Haider and Chiao 1999). The harmonic signals are much smaller than the fundamental signals so that the strong backscattered signal from the tissue is reduced by harmonic signals, while the weak signals from the blood maintain the strong fundamental signal. This is the reason that harmonic images reduce the dynamic range, so that cyclic variation of echogenicity from blood under tissue could be observed. Therefore, harmonic imaging seems to be a good tool to study backscattering from human blood vessels in vivo. The snap shots of the BCR phenomenon from a human carotid artery were plotted in the Duplex images in the left panels of Fig. 5.19 as a pulsatile cycle developed from late diastole to early diastole from the top to bottom panels. The Doppler spectrograms show the flow phases. The right panels illustrate the corresponding mean echogenicity across the vessel at the center of the vessel, which was taken from the left panels. The echogenicity from blood was still small compared to the harmonic signals from tissue. The normalized echogenicity was small (about 0.3) in the top panels at late diastole just before the systole started, and was enhanced to about 0.5 at the early systole inside the whole vessel lumen. The enhanced echogenicity became weaker at late systole, especially 97 at the center of the vessel, and then the echogenicity near the vessel wall became weak at early diastole. The digitized video signals from one subject were analyzed in the same way that other B-mode images were analyzed. The top panel in Fig. 5.20 is the total echogenicity across the tube diameter as a function of time during a heart cycle and the middle panel is the deviation over the temporal mean echogenicity. An ensemble average over 10 cycles was taken for this figure. The bottom panel shows the velocity profile computed from the Doppler spectrogram within the sampling volume at the center of the tube as shown in Fig. 5.19. The heart beat was about 68 BPM. The artery vessel expansion during a systole can be observed from the top panel. The high echogenicity was obvious all across the vessel diameter during systole and this bright hyperechoic zone was asymmetric. However, the variation was closer to symmetric when the temporal mean was subtracted. The variation of echogenicity was about 25 % of the total echogenicity. The ‘Bright Ring’ was obvious but collapsing phenomenon was barely observed, partly because the time resolution was not good enough to see the detailed collapsing phase of the bright ring. This hyperechoic ring disappeared during diastole without much variation. The BCR phenomenon was seen in 10 human subjects but was not observed in one subject. No detailed information about the health condition of the cardiovascular system of the subject was available, but all subjects were healthy to work every day. The possibility of inexperience of the researcher in detecting the phenomenon cannot be excluded since the researcher was not trained as a professional sonographer. The observance of the BCR phenomenon from the human carotid artery was only demonstrated in harmonic images in this study. Harmonic imaging turns out to be a good tool to study echogenicity from human arteries. Therefore, more systematic and thorough studies are required to investigate further the BCR phenomenon in human carotid arteries and to extract more meaningful information. Further study may lead to the development of a technique to diagnose diseases related to blood aggregation or the health condition of the cardiovascular system.
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Figure 5.19 The snap shots of the ‘Bright Collapsing Ring’ Phenomenon development from a human carotid artery during a heart cycle in harmonic cross sectional images and the corresponding normalized echogenicity across the horizontal vessel diameter. 99
Figure 5.20 The cyclic variation of the total echogenicity and the deviation from the temporal mean echogenicity from a human carotid artery across the horizontal vessel diameter synchronized with the speed profile over a heart cycle. 100
5.6. Conclusions
Two interesting phenomena, the BCR and the BH phenomenon, were observed from B-mode images of a state-of-the-art ultrasonic imaging system. The two phenomena were analyzed with several parameters including flow speed, stroke rate, transducer frequency, and hematocrit. As peak speed increased from 10 to 25 cm/s, the BCR phenomenon was enhanced, while the mean echogenicity and the BH phenomenon became weaker with speed. As stroke rate increased from 20 to 60 BPM, both the mean echogenicity and the cyclic variation were decreased, and the BH phenomenon became weaker. As the frequency of the transducer decreased from 13 to 9 MHz, the mean echogenicity was decreased, while the BCR and BH phenomena remained the same. The BCR and the BH phenomena were only observed above 15 % hematocrit, and the echogenicity as a function of hematocrit changed dramatically with radial position. The BH varied during a cycle, and this cyclic variation of the BH phenomenon was observed for the first time. High shear rate was the main reason of decrease of the mean echogenicity as speed and stroke rate increased, while acceleration was hypothesized to enhance echogenicity during systole to give the cyclic patterns of echogenicity. The complicated patterns of cyclic variation of echogenicity at different radial positions could be explained to a certain extent by the combined effects of acceleration and shear rate on echogenicity variation. The change of radial distribution of rouleaux during a cycle may be another important factor for explaining the complicated cyclic and radial variations of echogenicity under pulsatile flow. The BCR phenomenon was observed from 10 human carotid arteries in harmonic images and further studies are necessary to draw meaningful conclusions.
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Chapter 6
CYCLIC AND RADIAL VARIATIONS OF ECHOGENICITY UNDER OSCILLATORY FLOW
6.1 Introduction
In the last chapter, the ‘Bright Collapsing Ring (BCR)’ and the ‘Black Hole (BH)’ phenomena were observed and analyzed with several parameters under pulsatile flow. An explanation was suggested for the cyclic and radial variation of echogenicity during a pulsatile cycle, involving the change of shear rate, acceleration, and radial distribution of rouleaux during a cycle. In order to analyze the cyclic and radial variation of echogenicity further, oscillatory flow was generated in a series of experiments and the results were compared with those from pulsatile flow. Several studies of human red cell aggregation under steady and oscillatory shear have been performed in which the dynamic processes of aggregation and disaggregation of red cells at hematocrit of 45% were monitored by the use of photomicrographic methods and the microcinematographic technique (Copley et al. 1975; Usami et al. 1975; Chien et al. 1975). They concluded that the oscillatory flow motion greatly accelerates aggregation and rouleau formation. They observed that the individual rouleaux consisted of about 10-15 red cells at a frequency of 1 Hz with a peak shear rate of about 3 s-1. For a steady shear rate, each rouleau consisted of about 10 red cells at a shear rate of 1 s-1, and the number of red cells in each rouleau increased to about 15 when the shear rate increased to 10 s-1. Some rouleaux were reoriented and aligned with the laminar flow at these shear rates. In this chapter, echogenicity from porcine whole blood was used to investigate the rouleaux formation under oscillatory flow in a mock flow loop. The parameters used to investigate the rouleaux formation were stroke volume, mean flow speed, stroke rate, and transducer angle. The underlying assumption is that echogenicity from flowing blood is 102 mainly determined by rouleaux size, since each red blood cell can be considered as a Rayleigh scatterer, and backscattering from a Rayleigh scatterer is mainly affected by the scatterer volume at a fixed frequency. In order to investigate the origin of the cyclic variation of echogenicity, the echogenicity from porcine RBC suspensions was also measured and compared with the results from whole blood.
6.2 Materials and Methods
A LOGIQ 700 Expert system (GE, Milwaukee, WI) with an M12L linear transducer (6-13 MHz) was also used for this study. Power Doppler images, color Doppler images, harmonic images, and B-Flow images as well as B-mode images were collected and stored as references, but only B-mode images were used for the analysis. The transducer frequency was set to 13 MHz. The post-processing was the same as described in Chapter 6. The preparation of the porcine whole blood was the same as in Chapter 3, and the hematocrits were kept to 40% for all experiments. In order to investigate the origin of the cyclic variation of echogenicity, red blood cell suspensions were used because rouleaux were not formed in RBC suspensions, since the macromolecules needed for aggregation were removed with the plasma. The preparation of the RBC suspension was also described in Chapter 3. The mock flow loop used in this experiment was similar to the one shown in Fig. 4.1. A piston pump was modified to generate the fluctuation of pure oscillatory flow by removing the ball from the head. A mean flow was added to the pure oscillatory flow in order to investigate the effects of the mean steady flow on echogenicity. The mean steady flow was generated by the hydrostatic pressure difference of two reservoirs. These reservoirs were also useful for mounting the blood and for reducing the speed fluctuations and removing bubbles. Instead of the 10 MHz single element Doppler transducer in Fig. 4.1, an M12L linear array transducer was used with a GE LOGIQ 700 Expert system. Electromagnetic flow was removed in this experiment. A magnetic stirrer at the bottom of each reservoir prevented the blood from settling. The inlet length of a 103 polystyrene tube (ID: 9.5 mm, OD: 11.1 mm, Nalgene, Rochester, NY) was 1 m to ensure the development of laminar flow at the measuring site.
6.3 Results from Whole Blood Experiments
The echogenicity of porcine whole blood displayed radial and cyclic variation during an oscillatory cycle. However, the patterns of the variation over an oscillatory cycle were different from those over a pulsatile cycle. The echogenicity varied mainly near the center of the tube over a whole oscillatory cycle, while the echogenicity during a pulsatile cycle varied throughout the whole diameter from the periphery to the center, mainly during systolic flow. The echogenicity variation was investigated for several different flow conditions under oscillatory flow. Stroke volume, stroke rate, mean flow over oscillatory flow, and transducer angle were tested as parameters for echogenicity variation over an oscillatory cycle.
6.3.1 Stroke Volume Dependence The stroke volume was changed from 15 to 40 cc/stroke with zero mean flow while the stroke rate was set to 20 BPM in order to investigate the influence of stroke volume on echogenicity. The resulting Doppler spectrograms are shown in Fig. 6.1; the mean speed was calculated from the spectrum and plotted in black lines on the spectra. The spectrograms were taken in the cross sectional view with a minimum sampling volume at the center of the tube, and the angle was set to 73o. The ratio of systole to diastole was 50/50. In Fig. 6.2, the temporal mean echogenicity over a whole cycle is shown in the cross sectional views; the mean echogenicity was weaker as the stroke volume increased, due to the increase of the mean shear rate. No BH phenomenon was observed and in fact a rather bright hyperechoic zone was observed at the center of the tube for all stroke volumes. Fig. 6.3 shows the line plots near the center of the tube across the tube diameter, which were taken from the average of 10 rows near the center of the tube along the central horizontal line to avoid the attenuation loss at different axial positions as seen in Fig. 6.2. The echogenicity was higher at lower stroke volume and decreased as the stroke 104 volume increased. The decrease of echogenicity with stroke volume was about 0.2 at the center of the tube and became smaller near the tube wall. No BH phenomenon from the temporal mean echogenicity was observed under oscillatory flow at any stroke volume. In order to see the temporal variation of echogenicity, the ensemble-averaged echogenicity over 10 cycles across the tube diameter was plotted as a function of time during an oscillatory cycle for different stroke volumes in Fig. 6.4. The x-axes represent the normalized time over a cycle for 20 BPM and y-axes are the normalized diameter of the tube. The bottom line plots were calculated for the mean speed in cm/s from the spectrograms shown in Fig. 6.1. The velocity profiles at different stroke volumes were synchronized in time with the other panels in order to see the cyclic variation of echogenicity. At 15 cc/stroke, the echogenicity near the center was high throughout a cycle, and the temporal variation within a cycle was minimal. The high echogenicity zone shrunk towards the center, and temporal variation seemed to appear at 20 cc/stroke. The echogenicity at 30 cc/stroke showed strong cyclic variation. Near the center, the echogenicity was high during acceleration, while the echogenicity was low during deceleration at the center. During deceleration, a similar phenomenon to the BCR under pulsatile flow was shown. The high echogenic ring started to appear near the center at the maximum flow speed and expanded during the deceleration phase, reaching its largest radius half of the tube at speed zero. The largest ring shrank to the center later in the deceleration phase and collapsing at the minimum speed. The echogenicity at the center remained high during the acceleration phase of the flow. This ‘Bright Ring’ was also observed during acceleration but was too weak to be seen clearly in this figure. The BH phenomenon was observed during deceleration phase only at this stroke volume. At 40 cc/stroke, the echogenicity variation pattern was similar to the one from 30 cc/stroke, but with weaker strength and wider radial variation. The echogenicity deviation from the mean over an oscillatory cycle was calculated by subtracting the mean line plots shown in Fig. 6.3 from Fig. 6.4 in order to see the cyclic variation more clearly in Fig. 6.5. All axes are the same except for the grayscale. The maximum grayscale is about 20% of the total echogenicity. The radial and cyclic variation was stronger as the stroke volume increased and reached a maximum at 30 cc/stroke, then became weaker at higher stroke volume. 105
Figure 6.1 The spectrograms of four different stroke volumes within a sampling volume obtained at the tube center. The black lines represent the mean speed profiles computed from the mean frequencies of the spectrogram. The stroke volumes are about 15, 20, 30, and 40 cc/stroke from the top to bottom panel. 106
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Figure 6.2 The temporal mean echogenicity over an oscillatory cycle inside the tube in B-mode images for four stroke volumes.
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Figure 6.3 The temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for four stroke volumes. 108
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m 20 20 cc c ( 30 cc y
t 0
ci 40 cc o l -20 e V -40 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.4 The cyclic variation of the total echogenicity across the horizontal tube diameter for four stroke volumes and the corresponding speed profiles. The lines in the gray images are the distributions of echogenicity across the tube diameter at different times. 109
15 cc/stroke 1 0.1
0
-0.1 0 20 cc/stroke
1 0.1
0 r e
et -0.1 m 0 a i
D 30 cc/stroke d e z
i 1 0.1 al m r
o 0 N -0.1 0 40 cc/stroke 1 0.1
0
-0.1 0
40 )
s 15 cc /
m 20 20 cc c ( 30 cc y
t 0 i
c 40 cc o l -20 Ve -40 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.5 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for four stroke volumes and the corresponding speed profiles. 110
The high echogenic ring in addition to the higher echogenic zone at the center during the acceleration phase at 30 cc/stroke is shown more clearly in this figure. The ‘Bright Ring’ appeared twice over one cycle, during both the acceleration phase and the deceleration phase, while the echogenicity at the center of the tube varied once over a whole cycle. The echogenicity at the center of the tube was enhanced during the acceleration phase and decreased during the deceleration phase.
6.3.2 Mean Steady Flow Dependence The amplitude of the speed fluctuation in oscillatory flow, which was controlled by the stroke volume, turned out to affect the echogenicity in the previous section. An investigation of the influences of the mean steady flow on echogenicity was pursued in this section with a fixed stroke volume, 30 cc/stroke. The left panels in Fig. 6.6 show the temporal mean echogenicity over a cycle in B-mode cross sectional images of the tube for different mean steady flows. The right panels are the corresponding line plots of the radial variation of the mean echogenicity across the tube diameter, which was obtained along the horizontal line at the center of the tube and averaged from the 10 rows around the line in the left panels. There was no BH phenomenon observed from pure oscillatory flow with zero mean speed in the top panels, while the BH phenomenon was clearly observed as mean steady flow was added. The distribution of echogenicity across the tube diameter was also different between pure oscillatory flow and steady plus oscillatory flow. For pure oscillatory flow the distribution looked more like a parabolic shape, while the echogenicity was higher near the center and decreased almost linearly with radius for steady plus oscillatory flow. As mean steady flow was increased from 10 to 20 cm/s speed at the center of the tube, the overall echogenicity was weaker for steady plus oscillatory flow. Fig. 6.7 shows the temporal variation of echogenicity across the tube center for different mean steady flows and the corresponding mean velocity profiles in the bottom panel. When 10 cm/s of mean steady flow was added to pure oscillatory flow, it looked like physiological pulsatile flow as shown in the velocity profiles. The pure oscillatory flow gave higher echogenicity near the center of the tube during acceleration and lower echogenicity during the deceleration phase of the flow. When a mean flow of 10 cm/s was added to pure oscillatory flow, the BH phenomenon appeared at the center 111 of the tube over a cycle and some obvious temporal variation was observed during the acceleration phase of the flow. When the mean flow was increased further to 20 cm/s, the BH phenomenon became more obvious, but the echogenicity was lower and less temporal variation was observed during acceleration of the flow. Fig. 6.8 shows the variation alone, where the temporal mean over a cycle was subtracted from Fig. 6.7. There were very different temporal variation patterns between the pure oscillatory flow and the steady plus oscillatory flow. The temporal variation of echogenicity was stronger for pure oscillatory flow, even though the overall echogenicity was smaller. The echogenicity was larger during acceleration and smaller during deceleration. The overall temporal variation of echogenicity was smaller for steady plus oscillatory flow. The BCR phenomenon was clearly shown when mean flow of 10 cm/s was added. As the mean speed increased to 20 cm/s, the BCR phenomenon became weaker. For 10 cm/s of steady plus pure oscillatory flow, the BCR phenomenon and the cyclic and radial variation of echogenicity were similar to those from pulsatile flow in the previous chapter. When 20 cm/s of steady flow was added, the high echogenicity appeared at early systole and lasted a long time, until right after the peak systole, but the hyperechoic ring appeared late just before the peak systole at the periphery of the tube. This pattern is different from the results from physiological pulsatile flow.
6.3.3 Stroke Rate Dependence In order to investigate the influence of stroke rate on echogenicity under pure oscillatory flow, the stroke rate was changed to 20, 40, and 60 BPM with a fixed stroke volume, 30 cc/stroke. In Fig. 6.9, the temporal mean echogenicity over a cycle in the cross sectional view and the corresponding radial distribution of echogenicity across the tube near the center are shown. The echogenicity near the center of the tube decreased with increasing stroke rate, while there was no obvious change of echogenicity near the tube wall. No BH phenomenon was observed at these three stroke rates under oscillatory flow. The temporal variation of echogenicity during a cycle across the tube diameter at 112
Figure 6.6 The temporal mean echogenicity over an oscillatory cycle inside the tube in B-mode images for three different mean steady flow speeds and the corresponding normalized echogenicity across the horizontal tube diameter. 113
Mean Velocity : 0 cm/s 1
0.4
0.2
0 0 Mean Velocity : 10 cm/s r e t 1 e m a 0.4 Di d e z i l
a 0.2 m r
No 0 0 Mean Velocity : 20 cm/s 1
0.4
0.2
0 0
30 0 cm/s
s) 10 cm/s / 20
m 20 cm/s c ( y
t 10 i c o l 0 Ve -10 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.7 The cyclic variation of the total echogenicity across the horizontal tube diameter for three different mean steady flow speeds and the corresponding speed profiles. 114
Mean Velocity : 0 cm/s 0.1 1
0.05
0
0 -0.05 Mean Velocity : 10 cm/s
r 0.1 e t 1 e m a 0.05 Di d e z i l 0 a m r 0 No -0.05 Mean Velocity : 20 cm/s 0.1 1
0.05
0
0 -0.05
30 0 cm/s )
s 10 cm/s / 20
m 30 cm/s c ( y
t 10 i c o l 0 Ve -10 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.8 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for four stroke volumes and the corresponding speed profiles. 115 the three stroke rates is shown with the corresponding velocity profiles in Fig. 6.10. All x-axes represent the normalized time over a cycle for 20 BPM and the y-axes represent the normalized diameter of the tube. Both the cyclic variation and the overall echogenicity became weaker as the stroke rate increased. The deviation from the mean echogenicity over a cycle was calculated by subtraction of the corresponding mean echogenicity shown in the line plots in Fig. 6.9 from Fig. 6.10 and was plotted in Fig. 6.11. The prominent cyclic and radial variation at 20 BPM is shown. The echogenicity variation at higher stroke rate became weaker but expanded over the whole diameter up to the tube wall. However, this tendency is not only from the stroke rate but also from the speed change. As the stroke rate increased, the speed also increased as shown in the velocity profiles. At 20 BPM the strong variation was constrained mainly to the center of the tube, but as the stroke rate increased, the variation expanded to the whole diameter. One other thing to be mentioned is that there were some phase shifts between the flow cycle and the echogenic variation at 60 BPM. While the minimum echogenicity at the center appeared at the peak speed at 20 BPM, the minimum echogenicity occurred behind the peak speed at 40 BPM. The phase lag between the flow and the echogenicity variation was larger at 60 BPM.
6.3.4 Transducer Angle Dependence Allard et al. (1996) and Qin et al. (1998) suggested the possibility of having radial distributions of different orientation of rouleaux, because of the fact that the Doppler power was dependent on angle when the BH phenomenon was investigated. If the temporal and radial variation of echogenicity is mainly due to the rouleaux and their alignment or orientation, the echogenicity may be changed with transducer angle, assuming that there is some orientation of rouleaux alignment during certain phases of the flow. Therefore the echogenicity from flowing porcine whole blood was observed with different angles of transducer under oscillatory flow to investigate the radial distribution of rouleaux orientation. The angle between the tube axis and the transducer perpendicular to the flow direction was set to zero when the transducer was perpendicular 116
Figure 6.9 The temporal mean echogenicity over an oscillatory cycle inside the tube in B- mode images for three stroke rates and the corresponding normalized echogenicity across the horizontal tube diameter. 117
Figure 6.10 The cyclic variation of the total echogenicity across the horizontal tube diameter for three stroke rates and the corresponding speed profiles. 118
20 BPM 0.1 1
0
0 -0.1 40 BPM r
e 0.1 t 1 e m a Di d
e 0 z i l a m r 0 No -0.1 60 BPM 0.1 1
0
0 -0.1
50 20 BPM )
s 40 BPM /
m 60 BPM c ( y
t 0 i c o l Ve -50 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.11 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for three stroke rates and the corresponding speed profiles. 119 to the tube. The angle increased when the transducer slanted towards the tube while the transducer remained in the cross sectional view as shown in Fig. 6.15. In order to minimize the errors due to the travel distance of transmitted signals, an enlarged window in duplex images kept the same at a certain depth, and the transducer was adjusted to see the images of the whole tube in that window. The mean echogenicity over a cycle across the tube is shown in line plots in Fig. 6.12. Overall echogenicity was similar for all transducer angles except 10 and 40°. When the transducer angle was 40°, more of the beam might have been reflected and diffracted from the tube, resulting in weaker echogenicity, but a reason for the higher echogenicity at 10° was not known. Figs. 6-13 and 14 show the temporal variation of the total echogenicity and the deviation from the mean respectively across the horizontal tube diameter at different angles from 0 to 40°. There was no obvious cyclic variation of echogenicity at the normal angle (0°). However, the cyclic variation of echogenicity became obvious as the transducer angle increased, reached a maximum at 25°, and almost disappeared at an angle of 40°. The echogenicity at the center was enhanced during the acceleration phase and degraded during the deceleration. The ‘Bright Ring’ phenomenon was observed at angles from 10 to 25° during deceleration of the flow. The amplitude of variation in Fig. 6.14 was about 25% of the total echogenicity. The duration of high echogenicity at the center of the tube during acceleration changed with transducer angle, and the reason for this is not clear at present.
6.4 Discussion for Whole Blood Experiments
6.4.1 The Cyclic Variation Pattern The pattern of cyclic variation from oscillatory flow was different from that from pulsatile flow. Both the expansion and collapse of the ‘Bright Ring’ were observed from oscillatory flow, while only the collapsing phenomenon of the ‘Bright Ring’ was observed from pulsatile flow. The echogenicity varied over a full cycle for oscillatory flow, while echogenicity variation was observed mainly during systole of pulsatile flow. The variation of amplitude at the tube center was much stronger than that outside of the tube center for oscillatory flow, while the amplitude variation was similar all over the 120
Figure 6.12 The temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for five transducer angles (0, 10, 15, 25, and 40°). 121
Angle : 0 1 0.4 0.2 0 0 Angle : 10 1 0.4 0.2 r
e 0 0 et Angle : 15 am
i 1 D
d 0.4 e z i
al 0.2 m r 0 o 0
N Angle : 25 1 0.4 0.2 0 0 Angle : 40 1 0.4 0.2 0 0 ) s
/ 20 m c ( y
t 0 i c o l -20 Ve 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.13 The cyclic variation of the total echogenicity across the horizontal tube diameter for five transducer angles and the corresponding speed profiles.
122
Angle : 0 1 0.1
0
0 -0.1 Angle : 10 1 0.1
0
0 -0.1 er Angle : 15 et
m 0.1
a 1 i D d
e 0 z i l a m r 0 -0.1 o Angle : 25 N 1 0.1
0
0 -0.1 Angle : 40 1 0.1
0
0 -0.1 ) s
/ 20 m c ( y
t 0 i c o l -20 Ve 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.14 The cyclic variation of the deviation from the temporal mean echogenicity over an oscillatory cycle across the horizontal tube diameter for five transducer angles and the corresponding speed profiles. 123
Angle
0 mm
9. 5 mm
Figure 6.15 A schematic diagram of rouleaux distribution across the tube and the definition of transducer angle. 124 tube for pulsatile flow. The echogenicity at the center of the tube varied with the frequency of the flow, but the echogenicity outside of the center varied twice in a cycle of the oscillatory flow. The ‘Bright Ring’ from oscillatory flow was observed to vary from the center to half the tube radius, not to the periphery of the tube. The main reasons for these differences are probably the existence of the reverse flow and the short time duration of the diastolic phase that is necessary to form rouleaux for oscillatory flow. Another reason is that the speed variation may be too small for the echogenicity variation to reach up to the periphery of the tube, since the trend was observed that the variation expanded towards the tube wall as the stroke volume and stroke rate increased. The symmetric flow cycle for oscillatory flow would be another reason to give a different pattern of echogenicity variation. The amplitude of the variation over the mean echogenicity was almost up to 25% of the total echogenicity for oscillatory flow, while the variation was about 10% for pulsatile flow. The rouleaux formation seemed to be enhanced by the oscillatory motion, especially near the center of the tube. Another reason would be that the effects of rouleaux formation on the echogenicity variation from oscillatory flow may be summed to the cyclic variation of echogenicity by one cell based variation from RBC suspensions, which will be discussed later in this chapter. The cyclic variation pattern at the center of the tube shows enhanced echogenicity during acceleration and weaker echogenicity during deceleration; this pattern will be discussed later in this chapter when acceleration is considered.
6.4.2 ‘Black Hole’ Phenomenon from Oscillatory Flow The BH was observed in a very limited flow condition (i.e., during deceleration at 30cc/stroke) from oscillatory flow, while the BH phenomenon was observed more easily from both steady and pulsatile flow (Yuan and Shung 1989; Cao et al. 2001). The dynamics and the mechanisms of the BH phenomenon have been investigated by several investigators (Mo et al. 1991; Shehada et al. 1994; Lim et al. 1997; Qin et al. 1998; Cao et al. 2001). It has been suggested that this phenomenon is caused by less aggregation of RBCs at the center of the tube due to minimal shear rate. Inlet length, fibrinogen concentration, hematocrit, angular dependence, and hemodynamic conditions such as flow speed and stroke rate also play a role in affecting aggregation. Certainly time is also 125 involved in forming and disrupting the rouleaux. Since oscillatory flow has reverse flow during a cycle, there may be no time to form a structure or distribution of rouleaux for the BH near the center of the tube similar to the situation that occurs with a short entrance length, although there should be enough time to form rouleaux at the center of the tube. However, the time needed to form the structure of rouleaux for the BH should be long enough for pulsatile flow, because of less or no reverse flow and a long diastolic phase of flow. Therefore this is a possible reason that the BH phenomenon occurs for pulsatile flow under certain flow conditions.
6.4.3 Shear Rate and Acceleration The temporal mean echogenicity over a cycle decreased with increasing stroke volume, stroke rate, and mean steady flow speed. All of these can be well explained by the higher shear rate breaking up rouleaux when the stroke volume, stroke rate, and mean steady flow speed increased. The distribution of mean echogenicity across the tube diameter, showing lower echogenicity near the tube wall and higher echogenicity at the center of the tube, can also be explained by shear rate. However, the cyclic variation of echogenicity cannot be explained by shear rate, and in fact it conflicts with tendencies due to shear rate. The shear rate increases during acceleration so that rouleaux should be broken, giving weaker echogenicity, but the observations showed the opposite. In particular, the shear rate change was minimal at the center of the tube so that shear rate change cannot explain the maximum echogenicity variation at the center of the tube, while acceleration and deceleration were maximal at the center of the tube and may give a reason for this maximum cyclic variation. Acceleration may increase the collision rate of red cells (Cao et al. 2001; Paeng et al. 2001). Then acceleration could enhance the rouleaux formation, giving higher echogenicity during the acceleration phase, while deceleration may increase instability, breaking up the rouleaux and giving weaker echogenicity. However, this criterion does not apply to all results obtained in this study. The echogenicity variation was turned to decrease at a stroke volume of 40 cc/stroke and at higher stroke rates where acceleration and deceleration increased. Further studies must be pursued to arrive at a conclusion as to the role of acceleration in enhancing red cell aggregation, and to quantify what level of acceleration enhances the rouleaux formation. 126
6.4.4 Radial Distribution of Rouleaux The experimental results as shown in Figs. 6.12~14 showed the transducer angular dependence of the cyclic variation of echogenicity. These results suggest that the rouleaux distribution and alignment across the tube diameter may have certain angle preferences during the acceleration period. A schematic representation of the distributions of rouleaux across the tube diameter with a direction of transducer angle is shown in Fig. 6.15. The large rouleaux were formed and aligned at the center of the tube at an angle of about 25° with respect to the tube axis during the acceleration period. Except for the BH phenomenon at the center of the tube, this conclusion is similar with the conclusion of Qin et al. (1998) that rouleaux have an orientation of 25°, although their experiments to measure the Doppler power were performed using horse blood under steady flow. These rouleaux formations and alignments would be disrupted during the deceleration period, giving weak echogenicity.
6.5 RBC Suspension Experiments
In order to investigate the origin of the cyclic variation of echogenicity, porcine RBC suspensions were used to perform a series of experiments. A RBC suspension is a non- aggregating fluid since the macromolecules needed for the aggregation of cells were removed with the plasma and replaced with phosphate buffered saline solutions. Therefore, the origin of the cyclic variation of echogenicity can be determined, in particular whether individual cells or rouleaux contributes to this variation of echogenicity, if the experimental results from the porcine whole blood and RBC suspensions are compared. This is a motivation for this study to investigate the cyclic variation of echogenicity from porcine RBC suspensions. Under pulsatile flow, no cyclic variation of echogenicity from porcine RBC suspensions was observed under any flow conditions in our experiments. However, the echogenicity from RBC suspensions varied with a cycle under pure oscillatory flow.
127
6.5.1 Steady Mean Flow Dependence Pure oscillatory flow with zero mean steady flow was generated with a piston pump and the mean steady flow of about 10 cm/s in the sampling volume at the tube center was added to this pure oscillatory flow using the hydrostatic difference between two reservoirs. The temporal mean echogenicity over a cycle is shown in Fig. 6.16. The top panels are the averaged B-mode images over a cycle, and the bottom panels are the corresponding mean echogenicity across the tube diameter represented in line plots. The left panels are from the pure oscillatory flow and the right panels are from the oscillatory plus mean steady flow. The echogenicity was distributed uniformly across the tube diameter except near the tube wall. Since there are no rouleaux in the RBC suspensions, the radial variation of echogenicity should be minimal. The backscattering from RBC suspensions was shown to be independent of the shear rate in Chapter 3. Therefore the uniform echogenicity distribution across the tube diameter supports the fact that backscattering from RBC suspensions is independent of shear rate. The normalized echogenicity was about 0.43 for two different mean steady flows and was independent of the mean steady flow speed. The temporal variation of echogenicity across the tube diameter was plotted as a function of normalized time for 40 BPM in Fig. 6.17. The bottom panels are the velocity profiles in cm/s in the sampling volume at the center of the tube as shown in Fig. 6.16. Surprisingly, cyclic variation of echogenicity was observed from oscillatory flow, while no variation was observed from the oscillatory plus mean steady flow. The temporal mean echogenicity was subtracted from Fig. 6.17 and the deviation from the mean is shown in Fig. 6.18. The amplitude of the cyclic variation from pure oscillatory flow was about 0.04 and constituted about 10 % of total echogenicity. The echogenicity was enhanced during acceleration and was weaker during deceleration. The possibility of aggregation of RBCs is excluded in RBC suspensions, so that the variation might have something to do with cell deformation. Each cell may be stretched during acceleration and the accumulation of the stretching of individual cells may result in the enhanced echogenicity. Another possible explanation can be deduced from the fact that the correlation of RBCs affects the backscattering through a packing factor as suggested by the Twersky group’s theoretical approach (Twersky 1987; Lucas and Twersky 1987; Berger et al. 1991). RBCs may be less correlated during acceleration but 128
Figure 6.16 The temporal mean echogenicity from porcine red blood cell (RBC) suspensions over an oscillatory cycle inside the tube in B-mode images for two different mean steady flow speed levels and the corresponding normalized echogenicity across the horizontal tube diameter.
129
Mean Speed : 0 cm/s 1 0.4
0.2
r 0 e
t 0 e am i Mean Speed : 10 cm/s D d e
z 1 i al 0.4 m r o N
0.2
0 0
60 0 cm/s 10 cm/s 40 ) s / m
c 20 ( y t ci
o 0 l Ve -20
-40 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 40 BPM
Figure 6.17 The cyclic variation of the total echogenicity from porcine RBC suspensions across the horizontal tube diameter for two different mean steady flow speed levels and the corresponding speed profiles. 130
Mean Speed : 0 cm/s 0.05 1
0 r e t
e 0
m -0.05 a Di d
e Mean Speed : 10 cm/s z i l 0.05 a 1 m r No
0
0 -0.05
60 0 cm/s 10 cm/s 40 s) / m
c 20 ( y t ci
o 0 l e V -20
-40 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 40 BPM
Figure 6.18 The cyclic variation of the deviation from the temporal mean echogenicity from porcine RBC suspensions over an oscillatory cycle across the horizontal tube diameter for two different mean steady flow speed levels and the corresponding speed profiles.
131 more correlated during deceleration. A third possible reason is that each cell may rotate or align with the flow during acceleration. Since RBCs are known to rotate in the small tube (Goldsmith 1986), each cell may rotate once over an oscillatory cycle in such a way that the long biconcave axis may be parallel with the flow direction during acceleration, but perpendicular to the flow direction during deceleration. Even though an individual RBC can be treated as a Rayleigh scatterer up to 20~30 MHz according to numerical computations considering the shape (Kuo and Shung 1994; Coussios and Williams 2001), the possibility of some backscattering variation from RBC suspensions depending on the view of the transmitting angle for a biconcave shape may not be excluded considering the high frequency of the transducer, 13 MHz. However, this explanation is not supported by the experimental results of the echogenicity variation with transducer angle in the next section. The possibility of introducing turbulence to explain the higher echogenicity during acceleration was excluded for two reasons. The Reynolds number was small throughout all the experiments and the entrance length was long enough to develop the laminar flow, so that the possibility of generation of turbulent flow was very slight. Deceleration is also known to generate more disturbances compared to acceleration so that the echogenicity pattern should be opposite, if turbulence was playing a role. When the mean steady flow of 10 cm/s at the tube center was added to the pure oscillatory flow, there was no cyclic variation. Even though it is not shown, no echogenicity variation was observed from physiological pulsatile flow. It is very interesting that there was no echogenicity variation even when a small magnitude of mean steady flow was added to the pure oscillatory flow so that the reverse flow still existed. No plausible reason can be found except that the symmetry of flow may be important for this cyclic variation of echogenicity from RBC suspensions.
6.5.2 Transducer Angle Dependence The transducer was positioned at different angles while keeping the same distance, as explained in the previous whole blood experiment. The temporal mean echogenicity across the tube at the center of the tube was plotted in lines in Fig. 6.19. The mean echogenicity varied less than 0.1 with transducer angle across the tube, while the variation from whole blood with angle was about 0.2. This angular variation of 132 echogenicity may be due to the different diffraction and reflection of the beam from the tube wall. In Fig. 6.20, the echogenicity variation over the temporal mean across the tube diameter is shown as a function of normalized time for 40 BPM. There was a clear cyclic variation for all angles, but the variation pattern was independent of transducer angle. The amplitude of variation was about 10 % of the total echogenicity and this amplitude was about half that from the whole blood experiments. Therefore the cyclic variation of echogenicity from whole blood under pure oscillatory flow was partly from cells themselves and partly from aggregation. This also explains the fact that the cyclic variation of echogenicity under pure oscillatory flow (about 25% of total echogenicity) was larger compared to that under pulsatile flow (about 10% of total echogenicity). The echogenicity variation based on one red blood cell is independent of the transducer angle, so that this independence of angle excludes the explanation in the previous section that cell alignments or rotation of cells during a cycle may contribute to the cyclic variation. If the echogenicity variation arises from the rotation or alignments of cells, there should be an angular dependence.
6.5.3 Stroke Rate Dependence The dependence on stroke rate of the cyclic variation of echogenicity was also investigated from RBC suspensions and the deviation from the mean is shown in Fig. 6.21. The mean echogenicity inside the tube, except near the tube wall, was about 0.4. No obvious stroke rate dependence was observed, although cyclic variation was obvious for all three stroke rates. Since the speed level was changed with stroke rate, the cyclic variation of echogenicity from RBC suspensions should be independent of the speed or stroke volume. Therefore the weaker variation over a cycle from whole blood at higher stroke rates should be related to the time needed to form rouleaux during a cycle. The amplitude of the echogenicity variation from RBC suspensions over the total echogenicity was small compared to the result from whole porcine blood, so that the echogenicity variation from whole blood under pure oscillatory flow was the summation of the variations based on rouleaux and individual cell deformation.
133
Figure 6.19 The temporal mean echogenicity from porcine RBC suspensions over an oscillatory cycle across the horizontal tube diameter for four transducer angles (10, 20, 30, and 45°). 134
Angle : 10 0.05 1
0
0 -0.05 Angle : 20 0.05 1 r
e 0 t e m a i 0
D -0.05 d
e Angle : 30 iz l 0.05 a 1 rm o
N 0
0 -0.05 Angle : 45 0.05 1
0
0 -0.05
) 40 s /
m 20 (c y
t 0 i c
lo -20 e
V -40 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 40 BPM
Figure 6.20 The cyclic variation of the deviation from the temporal mean echogenicity from RBC suspensions over an oscillatory cycle across the horizontal tube diameter for four transducer angles synchronized with the speed profile. 135
20 BPM 1 0.05
0
0 -0.05 40 BPM r 0.05 e 1 et am i D
d 0 e z i al m r o 0 N -0.05 60 BPM 1 0.05
0
0 -0.05
50 20 BPM
s) 40 BPM /
m 60 BPM c ( y
t 0 ci o l e V -50 0 0.2 0.4 0.6 0.8 1 Normalized Time over a Cycle for 20 BPM
Figure 6.21 The cyclic variation of the deviation from the temporal mean echogenicity from RBC suspensions over an oscillatory cycle across the horizontal tube diameter for three stroke rates and the corresponding speed profiles.
136
6.6 Conclusions
Echogenicity variation from porcine whole blood and RBC suspensions during an oscillatory cycle was observed and analyzed in this chapter by varying certain hemodynamic parameters such as stroke volume, stroke rate, mean steady flow speed, and transducer angle. The variation amplitude of the echogenicity from whole blood was observed to be as large as 25 % of the total echogenicity. The pattern of cyclic variation showed higher echogenicity during acceleration and weaker echogenicity during deceleration near the center of the tube, and this pattern was explained by the enhancement of aggregation mainly due to acceleration of the flow. The ‘Bright Ring’ was observed under certain flow conditions but expanded and shrank twice over one cycle. These variations were restricted to the central zone of the tube for oscillatory flow. The BH phenomenon was observed in a very limited flow condition (during deceleration at 30 cc/stroke) under oscillatory flow, and a plausible reason was that there might be insufficient time for cells to form a structure of rouleaux for the BH, since reverse flow exists during an oscillatory cycle. The cyclic variation of echogenicity became obvious with increasing stroke volume, reaching a maximum at 30 cc/stroke, and became weaker at further higher stroke volume. When a mean steady flow was added to pure oscillatory flow, the cyclic variation pattern was changed dramatically and became similar to the variation pattern from pulsatile flow. The higher the stroke rate, the weaker the variation of echogenicity that was observed over an oscillatory cycle. The radial distributions of rouleaux and their alignments across the tube diameter were proposed to explain the angular dependence of the echogenicity variation over an oscillatory cycle. The rouleaux may be aligned at an angle of about 25° with the tube axis during the acceleration phase. The cyclic variation of echogenicity from RBC suspensions was observed under pure oscillatory flow. The echogenicity was enhanced during acceleration and became weaker during deceleration across the tube. This variation of echogenicity was independent of stroke rate, speed, and transducer angle for pure oscillatory flow. Possible reasons for the echogenicity variation may be cell stretching and decreased correlation of cells during acceleration. The amplitude of variation was about 10 % of the total echogenicity, and this variation from the RBC suspensions might contribute partly to the large variation of 137 echogenicity from whole blood. However, no cyclic variation of echogenicity from RBC suspensions was observed when a mean steady flow was added to the pure oscillatory flow, or under physiological pulsatile flow.
138
Chapter 7
CONCLUSIONS AND SUGGESTIONS
7.1. Conclusions This research has investigated the backscattering characteristics from flowing blood in a mock flow loop. The backscattering variation was studied using several hemodynamic parameters such as flow speed, stroke rate and mean steady flow, a physiological parameter, hematocrit, and transducer angle and frequency. Emphasis was placed on the cyclic and radial variation of echogenicity from whole porcine blood under pulsatile flow and their mechanisms. The origin of the echogenicity variation was also explored using three different fluid media: rigid polystyrene microsphere suspensions, deformable porcine red blood cell (RBC) suspensions, and aggregating whole blood. Red cell aggregation was the only important factor to change the backscattering power from blood under steady and pulsatile flow when a 10 MHz Doppler system was used to study the backscattered Doppler power. The change of individual cell size, shape, rotation, and deformation did not affect the backscattering under steady and pulsatile flow. However, at 13 MHz, B-mode images obtained by a GE LOGIQ 700 Expert system were able to measure the echogenicity variation from the porcine RBC suspensions only under pure oscillatory flow. It indicates that the deformation, alignment, and rotation of individual red blood cells under oscillatory flow may also contribute to the cyclic variation of the echogenicity. Under steady flow, the Doppler power from flowing whole blood measured at the center of the tube was decreased with the increasing mean shear rate. The temporal mean echogenicity over a cycle was decreased with the increasing flow speed, and the echogenicity decreased with radius and increasing stroke rate under pulsatile flow and oscillatory flow. All of this decreased backscattering could be explained well by the higher shear rate. 139
Along with the variation of the mean backscattering, the cyclic and radial variation of the backscattered power from whole blood was observed with both the Doppler power method and the GE commercial B scanner system. The pattern of the cyclic variation showed the peak backscattering power occurred some time during systole of pulsatile flow or during acceleration phase for pure oscillatory flow, but the backscatter peak occurred at different phases of the flow depending on the flow conditions and the radial positions. This pattern that shows a maximum backscatter during systole and during the acceleration phase cannot be explained by the shear rate alone. Acceleration of the flow was hypothesized as a mechanism to enhance the aggregation, since the collision rate of the red blood cells would be increased during acceleration because the force applied during acceleration is of compression in nature. Therefore the shear rate primarily affects the mean echogenicity variation over a cycle and the radial variation, while acceleration may contribute to the cyclic variation pattern. The ‘Black Hole (BH)’ and the ‘Bright Collapsing Ring (BCR)’ phenomena were observed with both the Doppler power measurements and the B-mode images under pulsatile flow. The parameters that affect the BH phenomenon were the flow speed, stroke rate, and hematocrit as shown by others. The variation of the BH phenomenon over a pulsatile cycle was first observed mainly during the systolic phase. The BH variation seemed to arise from radial redistribution of rouleaux during a cycle. The BH and the BCR phenomenon were independently observed but the BH variation during a systole was affected by the BCR phenomenon. The BCR phenomenon was enhanced by the increasing peak speed from 10 to 25 cm/s, the decreasing stroke rate from 60 to 20 BPM, and increasing hematocrit. The BCR phenomenon could be explained by the combined effects between the shear rate and acceleration. The pattern of the BCR phenomenon and the cyclic and radial variation of the echogenicity were different under pure oscillatory flow. The cyclic variation at the center of the tube was the strongest and occurred once per cycle, but outside of the center the variation was weak and showed the expanding and collapsing ‘Bright Ring’ twice a cycle. The radial distribution of the rouleaux across the tube was constructed based on the measurements obtained at different transducer angles during the acceleration phase under oscillatory flow. The rouleaux at the center of the tube was proposed to be aligned at an 140 angle of about 25° relative to the flow direction during acceleration so as to give a maximum variation of echogenicity at that angle. The rouleaux were broken during the deceleration phase to give weak echogenicity. The nonlinear relations between the echogenicity and hematocrit were highly dependent on the radial positions in the tube. The pattern that gives a maximum at about 10 to 20 % of hematocrit was observed near the tube wall, but near the tube center, the echogenicity reached a maximum and had a plateau above 20 % of hematocrit. The echogenicity became a maximum at lower hematocrits as close to the tube wall and decreased more dramatically with higher hematocrit. There was no obvious change of the nonlinear patterns over a cycle, although echogenicity was enhanced during systole for all hematocrits. The BCR phenomenon was observed from 10 human carotid arteries in the harmonic images. The variation was strong up to about 25 % of whole echogenicity. Their heart beats were between 65 to 90 BPM, and the peak speed levels were between 55 to 100 cm/s. The phenomenon could not be observed from one of the eleven subjects.
7.2. Suggestions for Future Studies Flow acceleration was hypothesized in this thesis as a factor to enhance the aggregation under pulsatile flow and oscillatory flow, but further investigations are required to validate this assumption. In particular, all the measurements and analyses have been done qualitatively up to now, since the flow profiles across the whole tube were not obtained over a full cycle. A multigate Doppler system should allow the measurement of the flow profile across the tube diameter in real time (Tortoli et al. 1996, 1997, 2001), so that the Doppler power and the velocity in a sampling volume can be obtained at the same time. The shear rate and acceleration distribution across the tube diameter can be calculated from the velocity profiles, and compared with the Doppler power variation. The shear rate and acceleration level may be quantified to show how much of velocity or acceleration would contribute to the Doppler power variation. Another possible approach is to compute the velocity profile from color Doppler images. The shear rate and acceleration can be calculated from this velocity profile and compared with the B-mode echogenicity. However this may involve some inherent errors, since the 141 quantification of the velocity from the color Doppler images is inaccurate due to wall filter and low resolution of the color scale. Computer simulation to assess the shear rate and acceleration inside a vessel under pulsatile flow and their contributions to the rouleaux formation should be helpful to quantify the two hemodynamic parameters and to understand the mechanisms. There are several challenges in doing this. One is the ability of simulating the high hematocrit over 40% that is similar to normal human blood conditions but is not available at present. There are also some difficulties to develop the accurate computational models for the backscattering calculations from the packed blood in a vessel, considering rouleaux formation in highly varying dynamic conditions under pulsatile flow. It is hard to develop an integrated model to include all these complicated effects, but the simple model to simulate the contribution of shear rate and acceleration in affecting the collision rate of red cells may be possible and worthy of investigation. The BH phenomenon has not been reported from in vivo experiments yet. The measurements of the BH phenomenon from veins may be possible since the velocity level is slow in veins, which is the similar velocity range to most of in vitro experiments that were performed to observe the BH phenomenon. In fact, the BH phenomenon was observed and shown from in vivo experimental results on pigs as shown in Fig. 7.1, which was taken from Lin (1997). However, the BH phenomenon was not noticed or mentioned in his dissertation. Therefore, further in vivo measurements of echogenicity at different veins may be able to observe the BH phenomenon. Even though the BCR phenomenon was observed from human carotid arteries, this observation was preliminary and cannot be correlated to any other health information and conditions. The observation was not taken by a professional sonographer but by a researcher who is not trained as a sonographer. Further research about this BCR phenomenon is necessary. Since this BCR phenomenon and the BH phenomenon are highly related to red cell aggregation, correlating these two phenomena to blood disorders may lead to diagnosis of certain diseases noninvasively using real time ultrasonic images. Clinical applications of the two phenomena are worthy of pursuit considering the importance of red blood cell aggregation in some diseases (Lowe 1988).
142
Figure 7.1 The ‘Black Hole’ phenomenon observed from in vivo experiments on pigs (Lin 1997)
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VITA
Dong-Guk Paeng was born in GoiSan-Gun, ChungBook, Korea on March 3, 1966 in lunar month. He moved to Seoul at his age of 10 and studied there during high school days. He entered the department of Earth and Marine Sciences in HanYang University in 1985. After junior he joined to the army and served 18 months for a naval head base in Seoul. He returned to the school and finished his B.S. in 1991. He joined the graduate school to pursue his M.S. to further study Physical Oceanography and received his M.S. degree in the same university in August 1993. Then he had short work experiences in DaeWoo Shipbuilding and Machinery Ltd. and KORDI (Korea Ocean Research and Development Institute) before he came to the United States for further study.
He joined the department of Ocean Engineering at MIT in 1995 and earned another M. S. in the area of ocean acoustics in August 1997. After spending a year to do research in the area of ocean tomography as a visiting scientist at MIT, he moved to the State College to join the Graduate Program in Acoustics at The Pennsylvania State University in 1998 in order to study the Biomedical Ultrasound for his Ph. D. degree.
During a long journey of his study, he published two papers as an author and one paper as a co-author in refereed academic journals. He submitted one paper to the IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, and now prepares two more papers to submit to Ultrasound in Medicine and Biology from his dissertation. He also presented six talks as an author and two talks as a co-author in several conferences, such as ASA (Acoustical Society of America), AIUM (America Institute of Ultrasound in Medicine), IEEE Ultrasonic symposium during his pursuit of Ph. D. degree. Currently he is a student member of ASA and AIUM.