31545 Medical Imaging systems
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1 Simulation of ultrasound systems and non-linear imaging 545 Medical Imaging systems Lecture 9: Simulation of ultrasound systems and non-linear imaging Jørgen Arendt Jensen Department of Electrical Engineering (DTU Elektro) Biomedical Engineering Group Technical University of Denmark October, 8. Discussion assignment from last lecture. Simulation of ultrasound systems: Field II (a) Field II. Principles and overview (b) Simulating B-mode imaging systems and blood flow. Non-linear ultrasound imaging (a) Linear and Non-linear wave propagation (b) Why is non-linear better? 4. Exercises (a) Questions for exercises 4 (b) Questions for assignments Reading material: JAJ, Chapters.5-6 and 4., Pages 7-44 and 7-75 Reduction in signal-to-noise ratio Discussion of time and phase shift systems Calculate what you would get in a time and phase shift velocity estimation systems for the parameters given below. Assume a peak velocity of.6 m/s at an angle of 6 degrees at the center of the vessel. The center frequency of the probe is MHz, and the pulse repetition frequency is. khz. The speed of sound is 5 m/s.. How much is the time shift between two ultrasound pulse emissions?. What is the largest velocity detectable, if the cross-correlation function is calculated and searched over two wavelengths? Reduction in snr [db] 5 5. What is the highest detectable velocity for a phase shift system? 4. What is the loss in SNR for a velocity of.5 m/s based on Figure 7.5 and 8. for the two systems? f = MHz f prf =. khz B r = Velocity [m/s] Center frequency of transducer Pulse repetition frequency Relative bandwidth of pulse 4
2 Stationary echo canceling Linear Acoustic System: Spatial impulse responses 5 Reduction in snr [db] Velocity [m/s] Reduction of the signal-to-noise ratio due to the stationary echo canceling filter as a function of velocity. A Gaussian MHz pulse with a relative bandwidth of. was used. The pulse repetition frequency was. khz. Impulse response at a point in space. 5 6 Huygens Principle Ultrasound fields Emitted field: p( r, t) = ρ v(t) t h( r, t) Pulse echo field: v r ( r, t) = v pe (t) f m ( r ) h pe ( r, t) f m ( r ) = ρ( r ) c( r ) ρ c Arrival times: t = r /c Moving the point results in a new impulse response: Continuous wave fields: F {p( r, t)}, F {v r ( r, t)} Spatial Impulse Responses - h( r, t) All fields can be derived from the spatial impulse response. 7 8
3 Field II Simulation system Transducer modeled by dividing it into rectangles, triangles or bounding lines. C program interfaced to Matlab. Matlab used as front-end. Can handle any transducer geometry. Physical understanding of transducer. Pre-defined types: piston and concave single element, linear array, phased array, convex array, D matrix Any focusing, apodization, and excitation pulse. Multiple focusing and apodization. Dynamic focusing. Can calculate all types of fields (emitted, received, pulsed, CW) Can generate artificial ultrasound images (phased and linear array images with multiple receive and transmit foci). Data storage not necessary. Post-processing in Matlab. Versions for: Windows, Linux, Apple OS-X, Sun Free program at: Field II Program Organization M-files Matlab Matlab interface Transducers Calculations Signal processing Makes it possible to use Matlab for signal processing and imaging 9 Using the Field II program % Start the system and initialize the path path(path, /home/jaj/programs/field_ii/m_files ) % Initialize the field system field_init % Set parameters for transducer aperture f=5e6; % Transducer center frequency [Hz] fs=e6; % Sampling frequency [Hz] c=54; % Speed of sound [m/s] width=.5/; % Width of element element_height=/; % Height of element [m] kerf=.5/; % Kerf [m] focus=[ 6]/; % Fixed focal point [m] N_elements=64; % Number of physical elements % Set the sampling frequency Using the Field II program - PSF calculation % Make the aperture for the response aperture = xdc_linear_array (N_elements, width, element_height, kerf,,, focus); % Set the excitation of the aperture excitation=sin(*pi*f*(:/(fs):/f)); excitation=excitation.*hanning(max(size(excitation))) ; xdc_excitation (aperture, excitation); xdc_impulse (aperture, excitation); % Calculate for the points x=(-:.5:); % Lateral positions for field calculation points=[ x; x*; + x*] /; % Point for calculation disp( Finding response for array ) [h, t_start] = calc_hhp(aperture,aperture,points); set_sampling(fs);
4 Point spread function Point spread function for 64 elements array Using the Field II program - PSF calculation with apodization 9 8 % Make an other example with apodization 7 6 xdc_apodization (aperture,, hanning(n_elements) ); [h, t_start] = calc_hhp(aperture,aperture,points); really quick to make different calculations. Point spread function for 64 element linear array at mm depth without apodization (6 db between the contour lines) 4 Point spread function with apodization Realistic simulation of in-vivo imaging 9 Point spread function for 64 elements array with Hanning apodization 9 Point spread function for 64 elements array Scattered field: v r ( r, t) = v pe (t) f m ( r ) h pe ( r, t) f m ( r ) = ρ( r ) c( r ) ρ c ρ( r ) - Spatial variation in density 6 6 c( r ) - Spatial variation in speed of sound Point spread function for 64 element linear array at mm depth with apodization (left) (6 db between the contour lines) and without apodization (right) Description of spatial variation in backscattering from anatomic image: σ fm ( r ) 5 6
5 Cyst phantom Simulation result for artificial kidney Simulated kindney scan using Field II 5 4 Axial distance [mm] Axial distance [mm] Lateral distance [mm] Lateral distance [mm] Simulation can be done in parallel for multiple image lines 7 8 Flow simulation in Field II Pulse-echo model: Color flow imaging phantom 4 p r ( r, t) = v pe (t) t f m ( r ) r h pe ( r, t), The motion of the blood scatterers is modelled: r (i + ) = r (i) + T prf v( r (i), t) Axial distance [mm] Scatterers are propagated between pulses according to their velocity i - Emission number 9 9 Lateral distance [mm]
6 Pulsating velocity profiles found in the human body Profiles for the femoral artery Profiles for the carotid artery Measured and simulated spectrograms for cartoid artery.5 Measured spectrogram Velocity Velocity Frequency [khz] Simulated spectrogram - Relative radius - Relative radius Frequency [khz].5 Velocity profiles from the common femoral (left) and carotid arteries (right) at different times in the cardiac cycle The velocity data can be found on the web in the data directories Data measured using a conventional B-K Medical 55 scanner Field II Simulation system Any kind of transducer, excitation, impulse response, focusing and apodization can be simulated Simulations are done in C Scripting and pre- and post processing are done in Matlab All linear ultrasound imaging systems can be simulated including anatomic and flow systems Conventional and synthetic aperture systems can be simulated Simulations and measurements are accurate for both point spread functions, images, and flow modeling Simulations are easy to parallelize for shared disk, heterogeneous systems Field II: How to get and use it Citationware - Free to use, but you have to cite the papers J.A. Jensen: Field: A Program for Simulating Ultrasound Systems, Medical & Biological Engineering & Computing, pp. 5-5, Volume 4, Supplement, Part, 996. J.A. Jensen and N. B. Svendsen: Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers, IEEE Trans. Ultrason., Ferroelec., Freq. Contr., vol. 9, pp. 6-67, 99. Web-site: 4
7 Non-linear ultrasound imaging Linear ultrasound imaging Non-linear wave propagation Examples of non-linear waves Why is non-linear better? Linear Imaging Depth in tissue: D = ct c - Speed of sound (fixed at 54 m/s) t - Time since pulse emission ( µs at 5 cm) Optimizing resolution Pulse inversion imaging Reading material: Chapter.5 ρ - Density of medium κ - Compressibility of medium C = ρ κ 5 6 Non-linear Propagation Particle Displacement for Wave x= x= λ/ x= λ x= λ/ One wavelength Speed of sound: ( c(t) = c + B A p(t) ) ( A B +) c Z B/A - Non-linearity parameter p(t) - Acoustic pressure c - Speed of sound for linear waves ρ - Density of the undisturbed medium Z - Characteristic acoustic impedance Direction of propagation A = ρ c ( ) p B = ρ ρ Z = ρ c 7 8
8 Example B/A values From Beyer (974) and Bamber (986) Medium B/A Water Water C, atm.) 5. Blood 6. Liver 7.6 Spleen 7.8 Fat. Ultrasound wave, peak pressure of MPa in water. Maximum speed of sound: Minimum speed: c min = 54 A span of 4.6 m/s. ( c max = c + B ) ( A p(t) B +) = 54. m/s A c Z ( ) ( 5. +) = 57.7 m/s For 5 cm depth, corresponding to µs: =.46 mm. λ =..5 mm 9 Distortion of wave Harmonic Example x 5 cm x 5. 4 cm.4 x x -5 Demo x 5 cm x -5 x 5 8 cm x -4 Normalized amplitude First harmonic Second harmonic Distance [cm] Harmonics for a MHz non-linear wave in water. Peak pressure is MPa and B/A is 5.. rd 4th 5th
9 Measured Non-linear Pulses What is the Advantage? 4 x 5 cm 4 4 x 5 cm 4 4 x 5 5 cm 4 4 x 5 cm 4 4 x 6 Linear point spread function at z=6 mm 4 x 5 Pulse at 5 cm x 6 Non linear nd harmonic point spread function at z=6 mm MHz phased array. Peak intensity 9 mw/cm. Matlab demo: non linear demo.m Isolation of Second Harmonic Resolution and Bandwidth Spectrum of non linear pulse and filter Spectrum of non linear pulse Transfer function of filter Amplitude.5.5 Long pulse Normalized amplitude 4 5 Spectrum of long pulse Relative amplitude Amplitude x 6 Short pulse.5.5 Normalized amplitude Frequency [MHz] 4 5 Spectrum of short pulse Frequency [MHz] x Frequency [MHz] 5 6
10 Principle of Pulse Inversion Spectral amplitude [db].5.5 x 6 Non linear pulses at 4 cm Positive non linear pulse Negative non linear pulse Pulse inversion Relative time [s] x 6 Spectra of pulses Non linear spectrum Pulse inversion spectrum Frequency [MHz] 7 PSF for Pulse Inversion 4 x 6 Linear point spread function at z=6 mm x 6 Non linear pulse inversion point spread function at z=6 mm Matlab demo: non linear demo 8 PSF without Pulse Inversion 4 x 6 Linear point spread function at z=6 mm Summary Speed of sound is dependent on the pressure Positive pressure parts propagates faster than negative pressure parts 4 x 6 Non linear nd harmonic point spread function at z=6 mm Non-linear waves have lower side and grating lobes leading to images with higher contrast Pulse inversion gives higher axial resolution
11 Exercise 4: Spectrogram from carotid artery Exercise: signal processing in pulsed wave system. Process receive signal to get complex data (load from file). Divide into overlapping segements. Calculate power spectrum (apply compression) 4. Display the spectra as a function of time 5. Compare the spectra for different vessels 4 4 Next lecture at Rigshospitalet on Ultrasound Diagnosis In-vivo measurements. Performed in building 49, room 9. Order goes by group number. See: 8.html. Wait in the hall before being called 4. Can be done in groups or individually 5. Data will be placed in CampusNet. You can also get it on a USB stick 6. The scanning is completely voluntary and does not count towards the final grade. You can always opt out. 7. The informed consent form can be found on CampusNet/File sharing in the top directory and must be signed before the scanning 4. Time: Thursday, October 4 at 9.. Place: Rigshospitalet, Entrance. Please see the map below.. Address: Rigshospitalet, Blegdamsvej 9, Kbenhavn. 4. Contact person: PhD student, MD Tin-Quoc Nguyen, Ultrasound section, Department of Radiology. 5. Content: The visit will start with a lecture in the conference room. Afterwards we will see examples of ultrasound scanners along with the equipment used for taking and practicing biopsies. The visit will take roughly hours. 44
12 Map of Rigshospitalet 45
31545 Medical Imaging systems
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