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Maximizing instrument-limited SNR by optimum choice of transducer frequency
ABSTRACTS,
ULTRASONIC
IMAGING
AND TISSUE
CHARACTERIZATION
SYMPOSIUM
Several of us at the previous Tissue Characterization Symposium proposed a method for utilizing the phase information present in an echo waveform and for incorporating this information into an image [l]. We termed such a process FM Imaging since it was based on our observation that an A-line ultrasound waveform is a frequency modulated as well as an amplitude modulated signal. In this context we termed conventional B-mode ultrasonography, AM Imaging. In this paper, we provide a theoretical basis for FM Imaging and show additional clinical results. It is shown that the echo waveform predicted by a tissue model in which scattering is produced by fluctuations in density and compressibility is, in reality, both an amplitude and a frequency modulated signal. The frequency modulation is directly relatable to the distribution and the statistics of the scatterers. Additional studies suggests that FM Imaging may offer --in viva higher resolution over a greater depth of field than would be available with convential imaging. [l] Ferrari, L., Jones, I., Gonzalez, V., and Behren, M., Ultrasonic Imaging 4, 178 (1982) (Abstract only). MAXIMIZING INSTRUMENT-LIMITED SNR BY OPTIMUM CHOICE OF TRANSDUCER FREQUENCY, S. W. Smith'**, R. F. Wagner', and 0. T. van Ramm3 'National Center for Devices and Radiological Health, FDA, Rockville, MD 20857, and Departments of *Radiology, 3Biomedical Engineering and 3Medicine, Duke University Medical Center, Durham, NC 27706. We use our previously-derived signal-to-noise ratios (SNR's) for signal detection to establish a program for optimizing ultrasound B-scanners according to the specific task requirement. For tissue parenchyma and tissue mimicking phantoms, the image signal is determined by the frequency-dependent backscatter, the frequency-dependent and the transducer frequency response. The image noise consists of the attenuation, For strong backscatmultiplicative speckle noise and the additive instrument noise. tered signals, the additive noise is negligible, and the SNR is optimized not by but simply by diminishing the speckle cell size further increases in signal strength, by means of the resolution cell size, or by compounding. However, if the backscattered signal is weak compared to the instrument noise, then the SNR can be maximized by selecting a transducer center frequency corresponding to a maximum response to the and tissue attenuation. If one assumes tissue is product of backscattered signal the acoustic backscatter coefficient (intensity) is composed of spherical scatterers, while the frequency-dependent tissue attenuaproportional to f4 (Rayleigh dependence), tion of ultrasound intensity is proportional to exp(-48fR), where R is the range to the scatterers in the object volume and B is the tissue attenuation coefficient. For the peak response occurs at f, % 1/8.R and a continuous wave or Gaussian pulse model, zero bandwidth. If one assumes a moderate average attenuation value of 8 = 0.046 nepers/cm/MHz equivalent to 0.4 dB/cm/MHz for abdominal or cardiac imaging, the peak frequency response occurs at f 9 1.5 MHz for a range of about 15 cm. DIFFR4CTION-LIMITED LATERAL RESOLUTION OF ULTRASONIC PHASED ARRAYS, R. Martin Arthur, Biomedical Computer Laboratory and Department of Electrical Engineering, Washington University, St. Louis, MO 63130. The value of a given ultrasonic tissue property is a spatial average of that property over the resolution cell of the measurement system. Cell size is primarily limited by lateral resolution. The lateral resolution fixed by transducer geometry was calculated for a 'typical' linear array driven by an exponentially-damped 2.25 MHz sinusoid. The simulated array consisted of 16 rectangular elements with a width of 0.9 h and a height of 12 h, separated by 1.8 A. The impulse response of each element at a given target was found using the method of Lockwood and Willette [I]. The impulse response of the array was found by combining element responses using appropriate delays for beam steering and either point or axicon focusing. After convolution and differentiation to get the pressure at a target, the signal reflected to the array was found assuming reciprocity. Both point and axicon focusing were applied to the received signals. Resolution was determined at ranges of 2, 5, 10, 15, and 20 cm and at 5 to 9 off-axis angles from 0 to 40 degrees at each range. To estimate resolution, the peak of the received signal was calculated as two point targets with various if the reflection from either target had to be separations were scanned. For example, 3 dB greater than that from any look direction between the two targets, lateral resolution varied from about 1.5 mm at ranges of 2 and 5 cm at off-axis angles from 0 to 30 degrees to 20 mm at a range of 20-cm at 40 degrees off axis for point focus on both transmit and receive. This work was supported in part by the NIH under Grants RR00396 and RR01362 from __ the Division of Resources and by Washington University. [l] Lockwood, J. C. and Willette, J. G., J- Acoust. Sot. Am. 53, 735-741 (1973). ---
191
ULTRASONIC
IMAGING
AND TISSUE
CHARACTERIZATION
SYMPOSIUM
Several of us at the previous Tissue Characterization Symposium proposed a method for utilizing the phase information present in an echo waveform and for incorporating this information into an image [l]. We termed such a process FM Imaging since it was based on our observation that an A-line ultrasound waveform is a frequency modulated as well as an amplitude modulated signal. In this context we termed conventional B-mode ultrasonography, AM Imaging. In this paper, we provide a theoretical basis for FM Imaging and show additional clinical results. It is shown that the echo waveform predicted by a tissue model in which scattering is produced by fluctuations in density and compressibility is, in reality, both an amplitude and a frequency modulated signal. The frequency modulation is directly relatable to the distribution and the statistics of the scatterers. Additional studies suggests that FM Imaging may offer --in viva higher resolution over a greater depth of field than would be available with convential imaging. [l] Ferrari, L., Jones, I., Gonzalez, V., and Behren, M., Ultrasonic Imaging 4, 178 (1982) (Abstract only). MAXIMIZING INSTRUMENT-LIMITED SNR BY OPTIMUM CHOICE OF TRANSDUCER FREQUENCY, S. W. Smith'**, R. F. Wagner', and 0. T. van Ramm3 'National Center for Devices and Radiological Health, FDA, Rockville, MD 20857, and Departments of *Radiology, 3Biomedical Engineering and 3Medicine, Duke University Medical Center, Durham, NC 27706. We use our previously-derived signal-to-noise ratios (SNR's) for signal detection to establish a program for optimizing ultrasound B-scanners according to the specific task requirement. For tissue parenchyma and tissue mimicking phantoms, the image signal is determined by the frequency-dependent backscatter, the frequency-dependent and the transducer frequency response. The image noise consists of the attenuation, For strong backscatmultiplicative speckle noise and the additive instrument noise. tered signals, the additive noise is negligible, and the SNR is optimized not by but simply by diminishing the speckle cell size further increases in signal strength, by means of the resolution cell size, or by compounding. However, if the backscattered signal is weak compared to the instrument noise, then the SNR can be maximized by selecting a transducer center frequency corresponding to a maximum response to the and tissue attenuation. If one assumes tissue is product of backscattered signal the acoustic backscatter coefficient (intensity) is composed of spherical scatterers, while the frequency-dependent tissue attenuaproportional to f4 (Rayleigh dependence), tion of ultrasound intensity is proportional to exp(-48fR), where R is the range to the scatterers in the object volume and B is the tissue attenuation coefficient. For the peak response occurs at f, % 1/8.R and a continuous wave or Gaussian pulse model, zero bandwidth. If one assumes a moderate average attenuation value of 8 = 0.046 nepers/cm/MHz equivalent to 0.4 dB/cm/MHz for abdominal or cardiac imaging, the peak frequency response occurs at f 9 1.5 MHz for a range of about 15 cm. DIFFR4CTION-LIMITED LATERAL RESOLUTION OF ULTRASONIC PHASED ARRAYS, R. Martin Arthur, Biomedical Computer Laboratory and Department of Electrical Engineering, Washington University, St. Louis, MO 63130. The value of a given ultrasonic tissue property is a spatial average of that property over the resolution cell of the measurement system. Cell size is primarily limited by lateral resolution. The lateral resolution fixed by transducer geometry was calculated for a 'typical' linear array driven by an exponentially-damped 2.25 MHz sinusoid. The simulated array consisted of 16 rectangular elements with a width of 0.9 h and a height of 12 h, separated by 1.8 A. The impulse response of each element at a given target was found using the method of Lockwood and Willette [I]. The impulse response of the array was found by combining element responses using appropriate delays for beam steering and either point or axicon focusing. After convolution and differentiation to get the pressure at a target, the signal reflected to the array was found assuming reciprocity. Both point and axicon focusing were applied to the received signals. Resolution was determined at ranges of 2, 5, 10, 15, and 20 cm and at 5 to 9 off-axis angles from 0 to 40 degrees at each range. To estimate resolution, the peak of the received signal was calculated as two point targets with various if the reflection from either target had to be separations were scanned. For example, 3 dB greater than that from any look direction between the two targets, lateral resolution varied from about 1.5 mm at ranges of 2 and 5 cm at off-axis angles from 0 to 30 degrees to 20 mm at a range of 20-cm at 40 degrees off axis for point focus on both transmit and receive. This work was supported in part by the NIH under Grants RR00396 and RR01362 from __ the Division of Resources and by Washington University. [l] Lockwood, J. C. and Willette, J. G., J- Acoust. Sot. Am. 53, 735-741 (1973). ---
191