F20Ultrasound

Resolution in Ultrasound Imaging

Sara Ong & Aqmar Md Yusoff

University of Minnesota, Methods of Experimental Physics II, Fall 2020

Abstract

This project aims to explore the optimal conditions for high spatial resolution of an ultrasound image using a 5-Mhz transducer. Spatial resolution is divided into lateral and axial resolution—the lateral resolution was determined by measuring reflected ultrasound signals of a pair of wires separated by a horizontal distance, and the axial resolution similarly but with wires separated by a vertical distance. The focal point was determined to be 73.2 ± 0.5 mm away from the transducer, where the best lateral resolution was measured to be 0.9 ± 0.3 mm and the axial resolution was measured to be 1.2 ± 0.1 mm. The theoretical resolution limits for lateral and axial are 0.5 ± 0.2 mm and 0.7 ± 0.1 mm respectively. An ultrasound image of a blackberry shows the most detail when taken at the focal point.

Introduction

Ultrasound imaging uses high-frequency sound waves, ranging from 2 MHz to 20 MHz 1, to image structures such as organs and tissues in the human body. The ultrasound waves are created by a transducer that contains piezoelectric elements which vibrate to produce the ultrasound waves whenever an electrical pulse is applied; the reflected waves are then detected by the transducer and converted from the mechanical vibration into an electrical pulse 1. The amplitude of the reflected signals, or echo signals, are converted to brightness where the echo signals with the highest amplitude are the brightest—this is known as B-mode imaging (or 2D imaging) 1. The image is constructed by varying the shades of grey of pixels at a given location that reflects the amplitude of the echo signals.

Figure 1: The diagram of an ultrasound transducer. The focal point is located at the narrowest ultrasound beam width .

Piezoelectricity refers to electricity that results from pressure and latent heat. In this project, only piezoelectricity resulting from the pressure is relevant. AC voltage is first applied onto piezoelectric elements so that it vibrates within the range of ultrasound wave frequency, producing the ultrasound wave. Fig. 1 shows the position of the piezoelectric element in a single-element ultrasound transducer. When the echo signals exert pressure onto the piezoelectric crystal, piezoelectricity is produced 2. As a result, voltage signals can be detected by an oscilloscope and processed to form an image.

Theory

Impedance mismatches between mediums allow ultrasound transducers to detect reflected pulses which can be displayed as 2D images. Spatial resolution is defined as the minimum separation distance at which two structures can be individually resolved.

Lateral Resolution

The lateral resolution is limited by the diffraction limit discovered by Ernst Abbe:

is the wavelength of the ultrasound beam, is the angle between the centre of the transducer to the radius. The diffraction limit for our system is calculated to be 0.5 ± 0.2 mm. This is the minimum resolution calculated at the focal point.

Axial Resolution

The axial resolution is described by the equation shown below:

The axial resolution is calculated to be 0.7 ± 0.1 mm.

Experimental Setup & Apparatus

A 5-MHz ultrasound transducer was connected to a 3D printer where it could be moved in the lateral and axial directions as shown in Fig. 2.

Figure 2: The ultrasound transducer is attached to the 3D printer where it can be controlled by a computer via a LabView program.

Lateral resolution

The resolution of a 0.88 mm width wire was measured at different heights. The resolution was further checked by measuring the ultrasound signal of two 0.88-mm-width wires with horizontal separations of 0.53 mm, 0.88 mm, and 1.57 mm using spacer wires. Fig. 3 shows the experimental setup of two wires with a horizontal spacer.

Figure 3: Two 0.19-mm wires are horizontally separated by a spacer.

Axial resolution

The resolution of two 0.88-mm-width wires was measured with vertical spacers of 0.53 mm, 0.88 mm, and 1.57 mm. Fig. 4 shows the experimental setup of two wires with a vertical spacer.

Figure 4: Two 0.88-mm wires are vertically separated by a spacer.

Results & Analysis

Lateral Resolution

The resolution of a single wire was compared at different heights, and the results are shown in Fig. 5. The minimum width of the wire, and therefore the best resolution found, was 0.9 ± 0.3 mm at a distance of 73.2 ± 0.5 mm (the focal point) below the transducer.

Figure 5: The resolution determined by the width of a 0.19-mm wire—the width was taken to be the FWHM value of the lateral plots of the wire.

The two-wire checks were carried out and the results are shown in Fig. 6, and the B-mode image in Fig. 7.

Figure 6: Lateral resolution plots of two wires, where only a separation distance of 0.88 and 1.57 mm were seen to have at least a 50% drop in intensity between the two wires, showing them to be individually resolvable.

Figure 7: B-mode images showing how the separation is only visible with separation distances of 0.88 and 1.57 mm.

Axial Resolution

Half of the pulse width was found to be 0.66 ± 0.05. Two-wire checks were conducted and the plot is shown in Fig. 8, with the B-mode images in Fig. 9. The spacer wires were not as effective for axial separation due to the 0.88-mm wires being difficult to manipulate, so the separation distances were calculated directly from the received signals.

Figure 8: The percentage drop in intensity between the two axially-spaced wires showing only separation distances of 1.2 ± 0.1 mm or more are definitively resolvable.

Figure 9: B-mode images showing how the separation is only visible with separation distances of 1.2 and 1.4 mm.

Blackberry

A blackberry was imaged at 3 different axial heights: below, at, and above the focal point (Fig. 10).

Figure 10: B-mode images of a blackberry showing clearest detail when imaged at the focal point.

Conclusion

Spatial Resolution

The theoretical lateral resolution was calculated to be 0.5 ± 0.2 mm, and the experimental value was found to be 0.9 ± 0.3 mm. It is possible for the experimental value to be lowered since we were limited by the widths of the spacers as well as the depths we set our wires at, so it is likely that an experimental value closer to the theoretical limit can be found with a similar experimental setup.

The theoretical axial resolution was calculated to be 0.7 ± 0.1 mm, and the experimental value was found to be 1.2 ± 0.1 mm. Again, it is possible for this experimental value to be lowered for similar reasons. Both the theoretical and experimental resolutions could also be lowered even more if deconvolution methods were employed, but we did not have time for them to be carried out in this experiment.

Future Work

It would be highly advantageous for the data collection process to be automated in future experiments and averaging done in LabVIEW; the signals from the waveform data were observed to sometimes have a quantised shift of 0.0001 milliseconds, so the correction for this should be implemented in the LabVIEW function as well to save time. This would enable data collection for more axial distances and spacer widths, which could result in finding experimental resolution limits closer to the theoretical values.

Including deconvolution methods in the data analysis would also be a viable option for lowering both the theoretical and experimental axial resolution limits.

References

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