Ultrasonic Classification of Emboli A thesis submitted in partial fulfillment of the requirement for the degree of Bachelors of Science in Physics from The College of William and Mary by Alison M. Pouch Accepted for ______________Honors _______________ ________________________________________ Dr. Gina Hoatson, Director ________________________________________ Dr. Mark Hinders, Advisor ________________________________________ Dr. Christopher Del Negro ________________________________________ Dr. Robert Welsh Williamsburg, VA May 2, 2007 Contents Abstract ………………………………………………………………………………………….. 1 Introduction ……………………………………………………………………………………… 2 Chapter 1: Ultrasound Instrumentation and Imaging Basics ……………………………………. 4 1.1 Ultrasound and Acoustic Impedance ………………………………………………... 4 1.2 Ultrasound Instrumentation …………………………………………………………. 5 1.3 Automated Scanning and Imaging …………………………………………………... 6 1.4 Experimental Imaging and Signal Processing ………………………………………. 7 Chapter 2: Clinical Application of the Emboli Detection and Classification System …………. 14 Chapter 3: The Emboli Detection and Classification System in Experiment ………………….. 18 3.1 Experimental Specifications ……………………………………………………….. 18 3.2 The EDAC System Display ………………………………………………….…….. 18 3.3 The Experimental Circuit …………………………………………………………... 20 Chapter 4: Frequency-Domain Analysis of an Analytical Scattering Model ……………….…. 23 4.1 Analytical Scattering Model …………………………………………………….…. 23 4.2 Frequency-Domain Analysis …………………………………………….………… 26 4.3 Testing of Material Parameters …………………………………………….………. 34 4.4 Scattering Effects of a Thin Layer Surround the Embolus ……………………….... 40 Chapter 5: Time-Domain Analysis and Simulation Comparison ……………………………… 43 5.1 Analytical Time-Domain Analysis ………………………………………………… 43 5.2 Comparison of Analytical and FDTD Approaches ………………………………... 44 Chapter 6: Sizing Gaseous Microemboli ………………………………………………………. 49 6.1 Theoretical and Experimental Verification of Gaseous Embolus Sizing ………….. 49 6.2 Phase Analysis ……………………………………………………….…………..… 53 Chapter 7: Viscous-Fluid Model Analysis …………………………………………………..…. 56 Chapter 8: Acoustic Radiation Force Calculations …………………………………….………. 61 Chapter 9: Discussion …………………………………………………………………….……. 71 Acknowledgements …………………………………………………………………….………. 74 References ……………………………………………………………………………….……... 74 Appendix A: Scattering Coefficients for the Viscous-Fluid Model …………………………… 76 Appendix B: Code for Functions Implemented in MATLAB …………………………….…… 78 Abstract The goal of this thesis is to develop theoretical verification for a system that uses broadband ultrasonic pulses to characterize microemboli in cardiopulmonary bypass (CPB) circuits. This Emboli Detection and Classification (EDACTM: Luna Innovations Incorporated, Roanoke, VA)) device non-invasively tracks and classifies individual microemboli passing through extracorporeal circuits. To determine the size and composition of microemboli in the bloodstream, we begin by implementing an analytical ultrasound scattering model in MATLAB. Our frequency- and time-domain analyses are then compared to a two-dimensional scattering model based on the cylindrical acoustic finite integration technique (CAFIT), assuming axisymmetric wave propogation. Confirmed by experimental data from the EDAC device, the analytical model and CAFIT simulations indicate a linear relationship between the amplitude of backscattered echoes and diameter of gas microemboli. We extend our analytical model to account for viscosity in the microembolus and surrounding fluid, which necessitates consideration of both compressional and shear wave modes. The result, a more complicated scattering solution, will assist in better characterizing non-gaseous microemboli. Our scattering solutions are the basis for an exact analytical model to calculate the radiation force on emboli needed to optimize debubbling adjuncts to the EDAC device. Introduction In this study, the frequency-domain and time-domain analysis of ultrasound scattering from fluid spheres is applied to emboli classification. An embolus (pl. emboli) refers to a microbubble, generally of gas or lipid composition, that flows through the bloodstream. Presenting a significant health hazard, these emboli may occlude blood vessels and thereby prevent the flow of blood to surrounding tissue and vital organs. Such embolic events are of significant concern in cardiac and orthopedic surgery, commercial and military diving expeditions, high-altitude operations, and other military objectives and medical scenarios. Luna Innovations, Inc. is currently developing an ultrasonic emboli detection and classification (EDAC) device, shown in Figure 1.1, to be used as a tool for noninvasive and nondestructive examination of debris in the body’s vasculature. Figure 1.1 The EDAC device developed by Luna Innovations, Inc. The first chapter of this thesis provides an overview of the basics of ultrasound technology, including automated scanning instrumentation and foundations of imaging. In addition, it outlines experimental projects that were conducted in William and Mary’s Nondestructive Evaluation (NDE) lab to demonstrate techniques in ultrasound imaging and signal processing. The second chapter explains the clinical application of the EDAC device and its use in cardiopulmonary bypass (CPB) circuits. The experimental specifications of the EDAC device are introduced in the third chapter, along with a description of the EDAC system display and experimental circuit used to test the device. In the fourth chapter, we outline the analytical scattering model that is the basis of our frequency-domain scattering analysis. The chapter includes an analysis of material parameters and the effects a thin shell surrounding the embolus has on backscatter. In the fifth chapter, we use our analytical model to develop a time-domain scattering analysis and test the result against a two-dimensional, axisymmetric ultrasound scattering simulation based on a variant of the finite difference time domain (FDTD) technique. The sixth chapter presents a scheme for sizing gas microemboli and describes the results of a phase analysis. The seventh chapter introduces a viscous-fluid model that extends our original analytical formulation. Acoustic radiation force calculations are presented in chapter eight, and a concluding discussion follows in chapter nine. Chapter 1: Ultrasound Instrumentation and Imaging Basics 1.1 Ultrasound and Acoustic Impedance Sound in a fluid (liquid or gas) produces a wave or a series of small fluctuations manifested by changes in a material’s pressure and density. Sound audible to humans lies within the frequency range of 20 Hz to 20 kHz. Sound above a frequency of 20 kHz is referred to as ultrasound. Ultrasound is extremely useful in medical diagnostics, as its applications provide a real-time, non-ionizing, noninvasive, portable, and relatively inexpensive means of imaging anatomy. Acoustic impedance is a critical concept in ultrasound technology; it impacts the design of ultrasound transducers and the assessment of sound absorption in a medium. The acoustic impedance of a given material is defined as the product of its density and acoustic velocity. This factor must be taken into account when considering the transmission and reflection of ultrasonic pulses at the boundary of two different materials. The impedances of two materials can be used, as follows in Equation 1.1, to determine the reflection coefficient R at the boundary of two materials: (Z −Z )2 R =  2 1  (1.1) (Z +Z ) 2 1 In this expression, Z = ρ c and Z = ρ c , where Z is acoustic impedance, ρ is the material’s 1 1 1 2 2 2 density, and c is the acoustic velocity in a given material. It is evident that larger impedance mismatches result in larger reflection coefficients. Large values of R, in turn, correspond to strong echoes, indicative of greater amounts of reflected energy returned from a boundary between two materials. 1.2 Ultrasound Instrumentation All ultrasound instrumentation incorporates several fundamental components, including a transducer, a pulser-receiver, and a computer or scope display. A transducer is a device that converts energy from one form to another; in this case, electrical energy to acoustic energy and vice versa. Specifically, piezoelectric transducers (PZTs) utilize the piezoelectric effect to perform this conversion. The transducer’s active element consists of a piece of polarized material, which changes shape when an electric field is applied. The polarized molecules align themselves with the induced voltage, thus changing the material’s structural dimensions. Conversely, an electric field is generated when the material changes shape as a result of applied pressure. Figure 1.2 illustrates the basic structure of a typical acoustic piezoelectric transducer. The PZT disk, the active transducer element, consists of piezoelectric ceramics, whose thickness determines the frequency of the transducer and the wavelength of an outgoing pulse. A thin PZT element vibrates with a wavelength that is twice its thickness; thus, the thickness of a particular PZT disc is half the desired radiated wavelength. Two electrodes connected across the PZT element allow an electric field to be induced and generated by the element. Behind the PZT disk, the damping material suppresses initial vibrations of the element, while the matching layer on the opposite side of the disk prevents the impedance of ultrasonic emissions from the transducer. + electrodes - damping material PZT disk matching layer ultrasonic pulse Figure 1.2 Basic structure of an acoustic piezoelectric transducer. The pulser-receiver serves as a link between the display and transducer. The pulser in a pulser-receiver generates short, large amplitude electric pulses to the transducer. It controls both pulse length and pulse energy. In the receiver section of the instrument, the voltage signals produced by the transducer, after being received as ultrasonic pulses reflected from the scatterer, are amplified. This provides the output for the digital display or signal processing. In addition, the receiver is responsible for signal rectification, filtering returned signals, gain, and reject control. Electric information returned from the transducer provides data for the display, which can produce a variety of visual images of the anatomy under investigation. 1.3 Automated Scanning and Imaging Ultrasonic scanning systems are used for automated data acquisition and imaging. As opposed to hand-held transducers, these automated systems emit and receive ultrasonic pulses at regular, controlled intervals while moving the transducer between pulses. They are particularly useful for scanning material defects. An example of the typical scan layout for a flat surface is shown in Figure 1.3. In this case, the transducer travels along the scanning path above and parallel to the specimen’s surface. At each point in the scan configuration, the signal strength and/or the signal’s travel time are measured. These values, in turn, are plotted using varying color schemes or shading to produce detailed images of the material’s features. (a) (b) Figure 1.3 (a) Top view of a typical scan configuration for a flat specimen. The transducer travels above and parallel to the specimen and at each point measures the strength of the signal returned from the material. (b) A side view of the transducer scanning a flat specimen. Water immersion tanks are commonly used in laboratory ultrasound scanning systems. Both the transducer and specimen to be scanned are submerged in water. The water maintains consistent coupling as the transducer passes above the material in the desired configuration. Automated scanning systems are often capable of displaying ultrasound data in three of the most common image formats: A-scan, B-scan, and C-scan presentations, which correspond to A-mode, B-mode, and C-mode, respectively. The A-scan is a waveform with the echo amplitude plotted as a function of time. Since sound speed is relatively constant, the time delay, indicated on the horizontal axis of the A-scan, corresponds to the depth of the reflection. The B-scan presentation represents an anatomic cross-section in the scanning plane. The travel time of the ultrasonic pulses is displayed along the vertical axis, and the distance from the transducer to each reflecting interface is plotted along the horizontal axis. B-scan images correspond to brightness mode, in which the brightness of each point, or pixel, is determined by the strength of the echo. A B-scan is usually produced by setting a trigger gate on the corresponding A-scan; when the signal amplitude is great enough to trigger the gate, a point is