EE 5345 Biomedical Instrumentation Lecture 6: slides 129-147 Carlos E. Davila, Electrical Engineering Dept. Southern Methodist University slides can be viewed at: http:// www.seas.smu.edu/~cd/ee5345.html EE 7345/5345, SMU Electrical Engineering Department, 2000 129
Transducer Properties (cont.) transducer d nf φ D λ λ or 2 4 d nf = near-field distance = φ = divergence angle: wave fronts D 2 4λ sinφ. λ = 12 D EE 5345, SMU Electrical Engineering Department 130
Transducer Properties (cont.) λ λ or 2 4 ~ E = Acos(2πf t) c = f λ crystal will vibrate at same frequency, f, as that of the applied voltage. c: speed of sound in tissue: about 1500 m/s λ: wavelength of sound EE 5345, SMU Electrical Engineering Department 131
Transducer Properties (cont.) S = change in crystal thickness/original crystal thickness = ge E: applied electric field g: constant Material g (m/v)x10-12 quartz 2.3 barium titanate 60-190 lead zirconate titanate (PET-4) 290 lead zirconate titanate (PET-5) 370 EE 5345, SMU Electrical Engineering Department 132
Transducer Properties (cont.) If crystal undergoes mechanical compression, a voltage is generated proportional to the compression. In imaging, the piezoelectric crystal is used to generate ultrasound, which is transmitted into the tissue. Some of the ultrasound is reflected by the tissue. Voltage is turned off and the crystal is then used to convert the reflected pressure waves to a voltage. The information in the reflected pressure waves can be used to image tissue. EE 5345, SMU Electrical Engineering Department 133
Basic Ultrasonic Imaging Configuration transducer 2αct cte T R ~ p ( t ) signal processing patient pulse generator p(t) monitor EE 5345, SMU Electrical Engineering Department 134
Ultrasound Attennuation in Tissue due to: Divergence of wavefronts in the far-field. Convergence of wave energy to heat (exponential with distance): p( z) = p e o αz p(z): sound pressure at distance z from transducer face α: attenuation coefficient p 0 : sound pressure at transducer face EE 5345, SMU Electrical Engineering Department 135
Attenuation Coefficients at 1MHz Material α (db/cm) Air 10 Blood 0.18 Bone 3-10 Lung 40 Muscle 1.65-1.75 Other soft tissues 1.35-1.68 Water 0.002 source: Medical Imaging Systems, A. Macovsky, Prentice Hall EE 5345, SMU Electrical Engineering Department 136
Ultrasound Scattering due to: Rayleigh scattering: due to acoustic impedance irregularities (i.e. red blood cells) Specular reflection at planar interfaces: tissue characterized by acoustic impedance Z. Z ρ: density = ρc c: speed of sound in tissue sound waves encountering tissue boundary having different acoustic impedances is partially reflected at the interface. EE 5345, SMU Electrical Engineering Department 137
Propagation Velocity Tissue Mean Velocity (m/s) Air 330 Fat 1450 Aqueous Humor of eye 1500 Vitreous Humor of eye 1520 Brain 1541 Liver 1549 Kidney 1561 Blood 1570 Lens of eye 1620 Skull bone 4080 Muscle 1585 Spleen 1566 source: Medical Imaging Systems, A. Macovsky, Prentice Hall EE 5345, SMU Electrical Engineering Department 138
Models for Ultrasounic Backscatter (Reflection) Specular reflection: incident θ i θ r θ t z transmitted reflected Z 1 Z 2 tissue interface EE 5345, SMU Electrical Engineering Department 139
Specular Reflection (cont.) R: reflectivity = reflected pressure incident pressure = Z Z cosθ cosθ Z + Z 2 i 1 2 i 1 cosθ cosθ t t Materials at Interface Reflectivity (θ i = θ t = 0) Brain-skull bone 0.66 Fat-bone 0.69 Fat-blood 0.08 Fat-kidney 0.08 Fat- muscle 0.10 Fat-liver 0.09 Lens-aqueous humor 0.10 Lens-vitreous humor 0.09 Muscle-blood 0.03 Muscle-kidney 0.03 Muscle-liver 0.01 soft tissue-air 0.9995 soft tissue-pzt5 crystal 0.89 source: Medical Imaging Systems, A. Macovsky, Prentice Hall EE 5345, SMU Electrical Engineering Department 140
Models for Ultrasonic Backscatter (cont.) Isotropic scattering 1-D model assumptions: transmitted ultrasound assumed to consist of planar waves (no diffraction). sound propagates with uniform velocity c. attennuation coefficient α is uniform throught body. body is modeled as an array of isotropic (invariant with respect to direction) scatterers. EE 5345, SMU Electrical Engineering Department 141
Isotropic scattering 1-D model (cont.): Reflected ultrasound has convolution property: 2αz ~ e p( t) = r( z) p t z 2z c dz ~ p ( t ) : reflected ultrasound pressure wave p( t) r( z) ( ) r z = 1 4z : transmitted ultrasound pressure wave : reflectivity profile ( ) δz z δz 2αz e 1 z :attennuation due to heat loss :attennuation due to reflected wave divergence (diffraction spreading) EE 5345, SMU Electrical Engineering Department 142
Comparison of Backscatter Models Note that if Z(z) is a step function, Z 1 h(z) is an impulse function and corresponds to specular reflection. ~ p ( t ) = p ( t ) Z 2 z Isotropic scattering model is more general, it considers gradual changes in reflectivity. Attennuation is compensated for by electronics. EE 5345, SMU Electrical Engineering Department 143
Imaging Modalities: based on measurement of backscatter A-Mode Scan (eye, cataract detection): transmitted pulse t reflected pulses (one per tissue boundry) t tissue boundries EE 5345, SMU Electrical Engineering Department 144
Imaging Modalities (cont.) M-Mode Scan: at t = t 1 : at t = t 2 : M etc. t t A-mode scans Can image moving tissue boundaries by stacking A- mode scans obtained at different times on top of each other. Used to image heart valves. Trandsucer is stationary. EE 5345, SMU Electrical Engineering Department 145
Imaging Modalities (cont.) B-Mode Scan (sonograms) t A-mode scans t EE 5345, SMU Electrical Engineering Department 146
Noise Sources in Ultrasound Scans Additive White Noise: due to piezoelectric materials and semiconductor material in instrumentation amplifiers. Speckle Noise: reflected ultrasound is coming from an array of randomly positioned point scatterers (reflectors), reflected wave fronts add constructively and destructively. Speckle can be reduced by averaging several images together. EE 5345, SMU Electrical Engineering Department 147