Lecture #5: Using Nonlinearity: Harmonic and Contrast-enhanced Ultrasound. Lecturer: Paul Sheeran

Transcription

1 Lecture #5: Using Nonlinearity: Harmonic and Contrast-enhanced Ultrasound Lecturer: Paul Sheeran

2 Lecture Schedule 2 Jan. 7: Ultrasound and bioeffects: safety regulations and limits, ultrasound-mediated therapy; Topical review Jan. 14: Ultrasound hands-on lab Jan. 21: Exam take-up

3 pressure Review: Time and Frequency 3 From lecture 1: the frequency of a sinusoidal signal is the inverse of its period, or the number of cycles per second period (T) [s] time frequency ( f ) = 1/T [s -1 or Hz]

4 pressure amplitude Review: Time and Frequency 4 However, this is ONLY true for an infinite sine wave An infinite sine wave has a single frequency component time frequency e.g. 5 MHz

5 pressure amplitude Review: Time and Frequency 5 Conversely, an infinitely short pulse in the time domain has infinite frequency components An infinitely short impulse contains EVERY frequency time frequency

6 pressure amplitude Review: Time and Frequency 6 Any finite pulse contains some distribution of frequencies. Shorter pulses in the time domain are broader in the frequency domain. 10 MHz single cycle pulse 10 MHz time frequency

7 pressure amplitude Review: Time and Frequency 7 Any finite pulse contains some distribution of frequencies. Shorter pulses in the time domain are broader in the frequency domain. 7 MHz Gaussian pulse 7 MHz time frequency

8 pressure amplitude Review: Time and Frequency 8 Any finite pulse contains some distribution of frequencies. Shorter pulses in the time domain are broader in the frequency domain. 7 MHz Gaussian pulse Fourier transform time 7 MHz frequency

9 Review: The Doppler Shift 9 Stationary transducer Reflector remains stationary Frequency unchanged Reflector moves towards transducer Frequency increases Reflector moves away from transducer Frequency decreases

10 Review: The Doppler Equation 10 F D 2f o v cosθ c F D is the Doppler shift frequency f o is the transmission (source) frequency v is the speed of the reflector q is the Doppler angle c is the speed of sound in the medium

11 Review: Continuous Wave Doppler 11 Continuous wave (CW) Doppler requires two dedicated transducers: One transducer continuously transmits ultrasound One transducer continuously receives the ultrasound echoes The area where the two beams intersect determines the location of blood velocity measurement Transmit beam Receive beam Region of overlap = region of detection

12 Review: Pulsed Wave Doppler 12 Pulsed-wave (PW) Doppler: Same transducer used for transmission and detection The operator can control at what depth the measurement occurs (Depth selection) Relatively short pulses used -> maintain axial resolution Depth selected sample volume Depth control: returning echoes are electronically time-gated to isolate signal localized to the region of interest (gate window). B-mode scout image Sample length (pulse width)

13 Review: Pulsed Wave Doppler 13 Doppler spectrum in sample volume shows time-dependent changes in scatterer velocity (Doppler shift frequency) Sample Volume Spectral Display

14 Review: Colour Doppler 14 Doppler frequency shift is encoded and displayed as a colour overlay over an anatomical B-mode image Colour encoding depends on the average flow velocity and direction of flow relative to the transducer Flow towards from transducer = red Flow away from transducer = blue

15 Review: Power Doppler 15 Power Doppler displays the total Doppler signal amplitude at each pixel Direction independent; no regions of ambiguity as with colour Doppler Much more sensitive than colour Doppler for detecting small vessels Colour Doppler of kidney Power Doppler of kidney

16 Today s Lecture 16 Linearity and nonlinearity Nonlinear propagation in tissue Harmonic imaging principles Imaging improvements Case examples Nonlinearity from contrast agents Contrast-enhanced ultrasound Physical principles and detection strategies Applications

17 Amplitude Spectral Energy (arbitrary) Linearity and Nonlinearity 17 The ultrasound imaging we ve discussed to this point are examples of linear imaging Process echoes assuming only changes in amplitude and time delay compared to transmitted waveform Assume no re-distribution of frequency content Linear Changes: Time Domain Transmitted Received Linear Changes: Frequency Domain Transmitted Received Time (microseconds) Frequency (MHz)

18 Amplitude Spectral Energy (arbitrary) Linearity and Nonlinearity 18 What if something in the imaging field changes the signal in a nonlinear way? Distorts time domain waveform Introduces new frequency content Nonlinear Changes: Time Domain 70 Nonlinear Changes: Frequency Domain Transmitted Received Transmitted Received Time (microseconds) Frequency (MHz)

19 The Born Approximation 19 Simplifications for modeling and image formation Assumption 1: Multi-path scattering does not greatly contribute to the received signal Assumption 2: The waveform is not distorted by the medium as it propagates Physicist Max Born

20 The truth, part 1 20 Multi-path scattering DOES matter in ultrasound Much research on methods to remove artifacts produced by multi-scattering From JJ Dahl, Reverberation clutter from subcutaneous tissue layers: Simulation and in vivo demonstrations, UMB 2014

21 Left: Fundamental B-mode of ovarian cancer; Right: Harmonic imaging of the same From: Tranquart et al., UMB 1999, 25(6): The truth, part 2 21 The ultrasound pulse is distorted as it propagates in tissue This is the source of image improvement using Harmonic imaging mode

22 Wave influence on speed of sound 22 Sound energy propagates as a longitudinal compressional wave

23 Wave influence on speed of sound 23 In regions of positive pressure, higher density Higher speed of sound Regions of negative pressure, lower density Lower speed of sound Peak (high pressure) Higher speed of sound Trough (low pressure) Lower speed of sound

24 Wave influence on speed of sound 24 Particles move faster with greater pressures, influence local speed of sound c c 0 + β v p c 0 = bulk speed of sound β = coefficient of nonlinearity v p = particle velocity Coefficient of nonlinearity β = 1 + B 2A Each tissue has a different nonlinearity coefficient, measured experimentally Sometimes referred to as B/A parameter

25 Nonlinearity by tissue type 25 Each tissue has a different nonlinearity coefficient, measured experimentally From: Diagnostic Ultrasound Imaging: Inside Out, Elsevier Academic Press.

26 Nonlinearity by tissue type 26 Each tissue has a different nonlinearity coefficient, measured experimentally From Varray, PhD Thesis 2011.

27 Wave distortion 27 As a result of these local density/speed of sound changes, the wave distorts Negative troughs slow down, positive peaks speed up Effect increases with increasing output pressure Effect accumulates with depth From Varray, PhD Thesis 2011.

28 Wave distortion: Harmonics 28 As a result of these local density/speed of sound changes, the wave distorts Results in generation of harmonics (energy in multiples of transmit frequency) From Varray, PhD Thesis 2011.

29 Nonlinear propagation of 2 MHz pulse in water measured at 70 cm. From Baker and Humphrey, JASA 1992 Shock waves 29 In the extreme, results in shock wave formation (positive pressure spike) Doesn t occur at diagnostic output levels due to attenuation

30 Shock waves 30 Shock wave formation (positive pressure spike) Same phenomenon that produces sonic boom, whip crack, etc Image courtesy nasa.gov

31 Harmonic development and imaging 31 So, changes in the time domain produce new frequency content in the traveling wave Re-distributes energy into harmonics of the transmitted frequency Once it has developed, this new frequency content is scattered and reflected by the tissue being imaged Means specular and non-specular reflection return new information to the transducer

32 Harmonic Imaging 32 Harmonics can be isolated to produce images of the tissue: Harmonic Imaging Also known as Tissue Harmonic Imaging (THI) From: Sonography Principles and Instruments, Elsevier Academic Press 2011.

33 From Varray, PhD Thesis Harmonic development with depth 33 More importantly, harmonics develop with increasing depth, even for lower pressures

34 Harmonic development with depth 34 From Varray, PhD Thesis What would you expect to be different about images produced from the Fundamental vs. 2 nd harmonic?

35 Imaging improvements 35 Improvement 1: Reducing clutter from superficial structures Harmonics only develop after sufficient depth Improvement 2: Better resolution Making images at twice the transmitted frequency

36 Imaging improvements 36 Reducing near-field clutter Fundamental frequency interacts with superficial layers Harmonics develop later & scatter/reflect back to transducer From Khokhlova et al., Acoustical Physics Contour Plots of Transmitted Pressure White indicates highest pressure Each line is 12.5% less pressure Large pressure field near face of transducer Significantly reduced pressure field

37 Imaging improvements 37 How does this help? Imagine problematic structures in the near field: ribs, fat, connective tissue, air Which case is likely to produce an image free of the near-field interference? From Khokhlova et al., Acoustical Physics 2006.

38 Imaging improvements 38 Image resolution Which component will produce better resolution by focusing the imaging energy more tightly? From Khokhlova et al., Acoustical Physics Contour Plots of Transmitted Pressure White indicates highest pressure Each line is 12.5% less pressure

39 HI and Resolution 39 Intuitively, imaging at a higher frequency SHOULD produce better resolution (remember definitions of axial and lateral resolution) There s more here: Transducer is already sensitive to 2 nd harmonic. Why don t we just transmit/receive at that frequency to maximize resolution?

40 HI and Resolution 40 Intuitively, imaging at a higher frequency SHOULD produce better resolution (remember definitions of axial and lateral resolution) There s more here: Transducer is already sensitive to 2 nd harmonic. Why don t we just transmit/receive at that frequency to maximize resolution? 1. Clutter reduction in near-field 2. Better penetration: Transmit low ( attenuation) -> Receive high ( resolution) High frequency component (more highly attenuated) only travels 1-way instead of 2-way

41 HI Examples 41 Examples Harmonic Imaging B-mode 2.5 MHz B-mode 4 MHz From Shapiro et al., AJR 1998.

42 HI Examples 42 Harmonic Imaging B-mode 2.5 MHz B-mode 4 MHz From Shapiro et al., AJR 1998.

43 HI Examples 43 B-mode 4.5 MHz Harmonic Imaging From Rosen and Soo, J. Clin. Im

44 HI Examples 44 B-mode 4.5 MHz Harmonic Imaging From Rosen and Soo, J. Clin. Im

45 HI Examples 45 B-mode 2.5 MHz Harmonic Imaging From Kornbluth et al., JASE 1998.

46 HI Examples 46 B-mode 2.5 MHz Harmonic Imaging From Kornbluth et al., JASE 1998.

47 HI Imaging Strategies 47 Can simply filter received echoes to isolate 2 nd harmonic Maximizes frame rate (no need to acquire additional information) However, commonly overlap in fundamental and 2 nd harmonic response image degradation Fundamental Which filter cutoff? 2 nd Harmonic From Duck, UMB 2002

48 HI Imaging Strategies 48 Multi-pulse sequences can better isolate harmonic Drawbacks: Lower max frame-rate, more susceptible to motion One implementation: Pulse inversion Transmit Pulse Receive Pulse 1 + Transmit -(Pulse) Receive Pulse 2 Adapted from Duck, UMB 2002

49 HI Imaging Strategies 49 One implementation: Pulse inversion Linear scatterer cancels, nonlinear scatterer preserved Linear Echo Nonlinear Echo Pulse Pulse 2 Adapted from Duck, UMB 2002 = = Only nonlinear echo 2x frequency

50 PI Harmonic Imaging 50 B-mode 3.4 MHz Harmonic Imaging From Hohl et al., Eur. Radiol

51 PI Harmonic Imaging 51 B-mode 3.4 MHz PI Harmonic Imaging From Schmidt et al., AJR 2003.

52 HI Summary 52 In summary Fundamental frequency interacts with superficial layers Harmonics develop later scatter back across superficial layers Harmonic imaging is good at reducing reverberation/clutter Harmonic imaging also improves resolution Applicability depends on depth, nonlinearity of the tissue Main applications in breast, abdomen, heart

53 HI and the Born Approximation 53 Remember the two half-truths of the Born approximation Multi-scattering doesn t happen Wave propagation is linear However, we know they do impact imaging An interesting consideration: Harmonic imaging counteracts multi-scattering using nonlinear propagation

54 Nonlinearity: Part 2 54 Harmonic imaging takes advantage of the way in which tissue acts nonlinearly What if an exogenous source within the tissue acts in a highly nonlinear way relative to tissue? Contrast-enhanced ultrasound imaging

55 Ultrasound Imaging of Blood Vessels 55 Conventional Ultrasound Colour Doppler 10-15% of our total blood volume is contained in liver Only 40% is contained in the large vessels

56 Ultrasound Imaging of Blood Vessels 56 Observations: Blood is a weak scatterer compared to tissue Large vessels - visible Small vessels - invisible Conclusion: Conventional ultrasound cannot image small vessels and the microcirculation Vessels too small + flow speeds too slow

57 Ultrasound Contrast Agents 57 5 m High molecular wt. gas Biocompatible shell (lipid, polymer, albumin) Microbubble Red blood cell Bubble responding to ultrasound Microbubble Tracer Properties Same size as red blood cells = Intravascular = a blood pool agent Bubbles can be discriminated from tissue using bubble specific imaging (e.g. Harmonic Imaging, Pulse Inversion) Measured signal is proportional to number of bubbles (concentration) Bubbles can be disrupted

58 Microbubble Size Distribution 58 Microbubble Activation In vitro Size Distribution of Definity Modern clinical agents are made by mechanical agitation Significance Microbubble size determines its acoustic response

59 59 Blood Perfusion Enhanced with Microbubbles Video Examples:

60 Microbubble Scattering 60 From module: Pressure scattered from a spherical particle distance Size Freq. Speed of sound Compressibility Density Angle p s ~ p i e jkd d k 2 r 3 3 κ v κ o + 3(ρ v ρ o ) cos(θ) κ o ρ o Distance (d), angle (ϴ), pressure it is exposed to (p i ), the wave number (k=2πf/c), the particle radius (r), the compressibility (κ v ) and density (ρ v ) of the particle, and the compressibility (κ o ) and density (ρ o ) of the surrounding media.

61 Microbubble Scattering 61 From module: Assuming equal size, same angle, same ultrasound pulse p s ~ A κ v κ o κ o 3(ρ v ρ o ) ρ o Compressibility Difference Density Difference Density (kg/m 3 ) Compressibility (GPa -1 ) Water Red blood cell Steel sphere Air bubble

62 Microbubble Scattering 62 From module: Assuming equal size, same angle, same ultrasound pulse p s ~ A κ v κ o κ o 3(ρ v ρ o ) ρ o Compressibility Difference Density Difference The steel sphere scatters a factor of 42.8 times more pressure than a red blood cell The air bubble scatters a factor of 30,643 times more pressure than a red blood cell!

63 63 Added Complexity: Microbubbles are Mechanical Oscillators Electrical Oscillator Mechanical Oscillator Bubble C, k Capacitance Spring stiffness Gas pressure L, m Inductance Mass, inertia Liquid mass R Electrical resistance Dash-pot, friction Viscocity, radiation

64 Bubble Equation of Motion 64 Polytropic gas Assumptions Almost incompressible medium (water) Small viscous damping Variable shell properties [Marmottant 2005] Bubble dynamics Compressibility correction Viscosity correction ρ R R R2 = P 0 + 2σ R 0 R 0 R 3κ 1 3κ c R P 0 P ext t 4μ l R R 4κ s R R 2 2σ(R) R Gas pressure and polytropic gas law Far field pressure Shell effects

65 Why Shell Properties Matter 65 Lipid distribution on bubble surface Marmottant et al., JASA, 118:3499 (2005) Lipid mono-layer responsible for enhanced nonlinear behaviour Finite surface area buckles or ruptures when compressed and stretched to its limits Understanding how shell properties impact bubble behaviour is important for new applications: tuned bubbles, drug delivery, targeted imaging. Ferrara, Pollard & Borden, Annu. Rev. Biomed. Eng., 9: (2007)

66 Resonant Frequency [MHz] Microbubble Resonance 66 f 0 = 1 2π 3γp l ρr S p ρr 0 3 Bubble resting radius Shell properties Bubble Diameter [m] Microbubbles resonate at diagnostic ultrasound frequencies Resonance determined primarily by the bubble radius Shell properties (stiffness, surface tension, etc.) tune the resonance

67 Low Pressure Linear Response 67 Excitation Pulse Bubble Response (15 kpa) Pressure [Pa] Pressure [Pa] Scattered (Detected) Echo Time [s] Conditions Keller-Miksis model of bubble oscillation Free bubble: R o = 2 um, MHz, in water

68 Linear Bubble Oscillation Example 68 With low acoustic pressures, sinusoidal oscillation occurs Returned energy primarily at same frequencies transmitted 5.3 µm bubble 1 MHz, 8 cycle pulse 50 kpa Video courtesy Brandon Helfield and Flordeliza Villanueva, University of Pittsburgh Video at 10.7 million frames per second

69 Amplitude [db] Pressure [Pa] Low Pressure Linear Response 69 Harmonic Spectrum Scattered (detected) Echo Fundamental Time [s] Frequency [MHz]

70 70 Moderate Pressure Nonlinear Response Excitation Pulse Bubble Response (40 kpa) Pressure [Pa] Pressure [Pa] Scattered Echo Conditions Keller-Miksis model of bubble oscillation Free bubble: R o = 2 um, MHz, in water

71 Nonlinear Bubble Oscillation 71 At moderate pressures, nonlinear oscillation (expansion or compression dominated) Scatters energy in harmonics of transmitted wave 2.9 µm bubble 1 MHz, 8 cycle pulse 250 kpa Video courtesy Brandon Helfield and Flordeliza Villanueva, University of Pittsburgh Video at 10.8 million frames per second

72 Amplitude [db] Low Pressure Linear Response 72 Harmonic Spectrum Scattered (detected) Echo Fundamental Harmonics Frequency [MHz]

73 Nonlinear Bubble Oscillation 73 Nonlinear oscillation video example 2: Shape modes 7 µm bubble 1 MHz, 8 cycle pulse 100 kpa Video courtesy Brandon Helfield and Flordeliza Villanueva, University of Pittsburgh Video at 10.8 million frames per second

74 Detection Strategies 74 Bubble detection is based on bubble response to ultrasound compared to tissue Received Spectral Content

75 Detection Strategies 75 Harmonic imaging: Filter-based technique 2nd harmonic (primarily bubble echoes) is bandpass filtered Limitations: Trade-off between resolution (bandwidth) and image contrast Tissue harmonics are present

76 Pulse Inversion (Coded Excitation) 76 Transmit Receive Summation Residual Pulse 1 Tissue Bubble Pulse 2 (inverse of Pulse 1) Coded excitation - Full bandwidth operation Various flavours: Pulse inversion, amplitude modulation, frequency chirps, Golay codes Burns, Wilson & Simpson, Investigative Radiology. 35(1):58, (2000)

77 Coded Excitation 77 Contrast Specific Ultrasound Conventional Ultrasound Coded excitation - Full bandwidth operation Various flavours: Pulse inversion, amplitude modulation, frequency chirps, Golay codes Burns, Wilson & Simpson, Investigative Radiology. 35(1):58, (2000)

78 78 High Pressures: Microbubble Destruction High speed optical photo of a bubble in a high energy acoustic field 2.4 MHz, 1.2 MPa Microbubble Disruption - The Negative Bolus After contrast has fully perfused, destroy contrast inplane and watch re-perfusion Unique phenomenon destroyed by same source used to image Cannot be done with other tracers Can be used to introduce a bolus into tissue with high spatial specificity Chomas et al., APL, v7(77), p.1057, (2000)

79 Bubble Fragmentation/Destruction 79 At high pressures, fragmentation and destruction occur Returns energy across broad range of frequencies Can interact highly with tissue (jetting/streaming) 3.9 µm bubble 1 MHz, 8 cycle pulse 500 kpa Video courtesy Brandon Helfield and Flordeliza Villanueva, University of Pittsburgh Video at 10.7 million frames per second

80 Signal Intensity 80 Measuring Flow with Microbubble Disruption Procedure of Disruption-Replenishment 1) Performed during a constant infusion of microbubbles 2) High pressure disrupts the agent within the imaging plane (negative bolus) 3) The scan plane is replenished at a rate determined by blood flow Disrupt bubbles within image slice Transducer Bubbles replenish image slice Time Intensity Curve Combination of components Elevation beam width Disruption - Replenishment Flow velocity Transit path Components of individual transit paths Time after disruption

81 81 Video Example: Disruption Replenishment

82 82 Video Example: Disruption Replenishment Clinical Example Contrast Specific Imaging Conventional Imaging Human renal cell carcinoma 1 cm Rate of enhancement is related to the local flow velocity Relative intensity of a region is related to the local blood volume

83 Quantification: Time Intensity Curve 83 Region of Interest Replenishment Time Intensity Curve Region of interest (ROI) quantification performed on linearized image data Microvascular determinants of the replenishment time-intensity curve: Plateau intensity Blood volume Rate of replenishment Flow velocity Transition region Vascular organization

84 Bubble Backscatter Intensity [Normalized] Quantifying Anti-Angiogenic Response 84 Data Model Drop in Blood Volume Decreasing replenishment time Time After Disruption [s]

85 85 3D Contrast-Enhanced Ultrasound

86 Molecular Imaging 86 By decorating bubbles with targeting ligands, adhere to site of expression Ex: Angiogenesis Strategies usually distinguish targeted from free-flowing bubbles Targeted bubble signal in a malignant glioma (mouse) From Willmann et al., Radiology 2006

87 Contrast-Enhanced Doppler 87 Bubbles boost SNR of blood, aid Doppler segmentation from tissue In combination with ultrafast imaging, allows simultaneous measurement of perfusion, flow, and vascular morphology Tumour Kidney Contrast-enhanced Color Doppler (red/blue), perfusion (green) segmentation in a rabbit kidney Principal curvature segmentation of ultrasound Power Doppler Courtesy Charles Tremblay-Darveau, University of Toronto

88 Vessel segmentation 88 Other approaches at vessel segmentation: Dual-frequency capture harmonics well outside of tissue range using a second transducer B-mode Acoustic Angiography Vessel segmentation of a tumour in the mammary pad of a mouse From Shelton et al., UMB 2015

89 Vessel segmentation 89 Other approaches at vessel segmentation: Capturing sparse bubble echoes to super-localize location (beating the diffraction resolution limits) Ultrasound super-localization in a living mouse brain using clinical frequencies. Resolution ~ 10 µm. From Errico et al., Nature 2015

90 Next Lecture 90 Safety and Bioeffects: Heat and Cavitation Biological interactions Regulatory limits: Definitions and dependence on imaging target (Mechanical Index, Thermal Index, etc ) How do we measure transducer output?

91 Next Lecture 91 Harnessing bioeffects for therapy Microbubble-aided therapy