by Simon Hackl
I’m a PhD student at the Industrial Mathematics Institute at JKU Linz, working on improving ultrasound images. With my work, I contribute to the CD-Laboratory MaMSi, where researchers from JKU, RICAM, University of Vienna, and Medical University of Vienna collaborate on improving ultrasound imaging. Our industry partner GE Healthcare is a very important part of this project, contributing scientifically with their practical expertise on ultrasound system design and performance.
How ultrasound imaging works
Ultrasound imaging begins with an array of transducers at the tip of the ultrasound probe, which emit short acoustic pulses into the body, see top of Figure 1 . In order to obtain an ultrasound image, focusing is required in the following two crucial steps: First, during transmission, the individual transducer elements emit waves at slightly different times to create a transmit focus, see the top left of Figure 1. These delays ensure that all waves arrive simultaneously at a focus point, where the emitted waves interfere constructively, see bottom of Figure 1. Once inside the body, the acoustic wave scatters at inhomogeneities. This especially happens at interfaces between different tissues, such as skin-fat, fat-muscle, or soft tissue-bone boundaries, where a part of the wave is reflected back toward the ultrasound transducer. The transducer array subsequently detects these backscattered signals, shown in the top right of Figure 1. During receive focusing, the system applies precise time delays to the different signals received at the individual transducer elements, and subsequently adds them up. This process compensates for the different times of flight from each scattering point back to the transducer elements. By repeating this receive focusing procedure for every pixel in the image, the system reconstructs the final ultrasound image – though at considerable computational cost.
The problem: sound speed variations distort images
The focusing processes described above require a time of flight calculation from each transducer element to every pixel in the ultimate image. Due to the massive computational demands of processing ultrasound data in real-time, imaging systems make a simplifying assumption: they treat sound speed as constant throughout the body, which works well in homogeneous media. In reality, however, different tissue types have different sound speeds, which causes the actual times of flight to differ from those calculated under the constant sound-speed assumption. These errors accumulate over large-scale inhomogeneities, causing the received signals to be misaligned during image reconstruction. The result is a collection of image artifacts such as blurring and geometric distortions, shown in Figure 2. The problem becomes particularly severe in areas with large regions containing body fat, such as abdominal imaging or in obese patients. And even the plastic cap covering the transducer array can introduce noticeable aberrations if not properly accounted for.
The solution: A more precise time of flight calculation
To overcome this problem, my colleagues and I have developed a method based on geometrical acoustics that corrects for aberrations in layered media with varying sound speeds. Instead of assuming a constant sound speed, we calculate more accurate times of flight by treating sound propagation as acoustic rays traveling perpendicular to the wavefront – a standard assumption in geometrical acoustics, see the top of Figure 2. The key insight is decomposing the total propagation path into individual layer segments, each consisting of a straight line due to the constant sound speed in each medium layer. Summing these layer-wise times of flight yields the correct total time of flight through the layered medium. Incorporating these corrected delays into the ultrasound image reconstruction significantly reduces aberrations, as shown on the bottom of Figure 2.
improved time of flight calculation, bottom: our method applied in ultrasound
image aberration correction in a phantom-based experimental setting
Future work
Despite its accuracy, our method is too slow for real-time ultrasound imaging, where a single image requires approximately one billion calculations within roughly 20 milliseconds. Unfortunately, this is beyond our algorithm’s current speed. However, we now have a precise baseline method and have identified several promising strategies to accelerate the computation while keeping errors below the threshold that would reintroduce aberrations. A second challenge is that our method requires knowing the layered structure of the medium in advance. This is straightforward for the transducer cover, where geometry and materials are known. For patient tissue, however, the situation appears paradoxical: reconstructing an accurate image requires correct times of flight, which in turn require knowing the medium structure itself.
Fortunately, the tissue structure need only be known at coarse resolution – a large-scale approximation suffices. Reconstructing this coarse tissue map is an inverse problem, which happens to be our institute’s area of expertise. We’re now working on combining our time of flight correction method with inverse problem techniques to broaden its potential field of application.
This work represents an important step toward aberration correction in layered media, with ongoing research addressing the computational and inverse problem challenges outlined above. For more applications of mathematics to medical imaging and other industrial problems, visit the website of our Industrial Mathematics Institute. For a preprint containing our work and for further literature on the topic follow this link on arxiv. We thank GE Healthcare for providing the ultrasound device image of the Voluson family, shown at the beginning of this blog entry.