SIAM News Blog

Hybrid Pulmonary Imaging Methodology Combines USCT and EIT Techniques to Boost Scan Results

By Lina Sorg

Thoracic ultrasound scans assess structures and organs within the chest, including the lungs and pleural cavity. Traditional B-mode ultrasound imaging uses bright dots to represent ultrasound echoes and forms a cone-shaped pattern as waves propagate throughout the domain. However, the technique does have certain drawbacks. “The thing with using traditional ultrasound for pulmonary imaging is that greater than 99.9 percent of the incident wave is actually reflected back at the pleura-lung boundary,” Melody Alsaker of Gonzaga University said. “The wave does not penetrate the pleura very well, and you can’t actually see into the lungs.” Instead, technicians decipher medically relevant information from artifact appearance—which is very difficult to interpret—rather than directly from the images themselves. 

Ultrasound-computed tomography (USCT) is an imaging modality that relies on the transmission of ultrasonic energy and provides much richer acoustic data than classic B-mode ultrasounds, which rely on reflected signals. The resulting data has a significantly higher resolution and is also easier to interpret. USCT applies low-frequency ultrasound waves through an array of transducers on the boundary of the organ in question. Trigonometric acoustic wave patterns travel through the domain, allowing clinicians to measure the resulting acoustic boundary pressure. They then use the boundary data to reconstruct a sound speed map within the plane of transducers. 

The principle of USCT is fairly similar to electrical impedance tomography (EIT), during which technicians apply trigonometric current patterns (instead of acoustic waves) via electrodes (instead of transducers). After the current moves through the domain, practitioners measure the resulting surface voltages and utilize this boundary data to reconstruct the connectivity map within the plane of electrodes.

Though USCT and EIT are complimentary imaging approaches, each has different strengths. USCT supplies good spatial information and a higher resolution of organ boundaries, but EIT offers better data about regional ventilation and perfusion distributions that allow clinicians to clearly see lung pathologies. During a minisymposium presentation at the 2021 SIAM Annual Meeting, which took place virtually this week, Alsaker presented a hybrid pulmonary imaging methodology that combines USCT and EIT techniques to exploit the strengths of each modality. The resulting hybrid reconstructions can be used in tandem for diagnostic purposes.

Figure 1. Sound speed and conductivity phantoms. Top to bottom: a small pneumothorax on the side of the lung, a larger pneumothorax, and air trapping.
First, Alsaker provided a brief mathematical background of the USCT reconstruction methodology. For the sake of simplicity, she assumed constant density within the domain. “Given knowledge of that instant wave and pressure on the boundaries, we’re going to reconstruct the sound speed inside the domain,” she said. To do so, Alsaker used k-wave—an open-source MATLAB acoustics toolbox—to employ the distorted Born iterative method (DBIM). Then she overviewed EIT, which utilizes the D-bar reconstruction method. Dirichlet-to-Neumann mapping transforms the boundary voltages to boundary current densities. “Given knowledge of that DN map, we want to recover the conductivity within the domain,” Alsaker said. It is also important to note that she was able to include priors in both the DBIM and D-bar methods based on a priori information. 

Over the last few years, Alsaker has been working with a priori approaches to yield sharpened images. To initiate her hybrid methodology, she introduced numerically simulated thoracic phantoms for sound speed and conductivity. The three types of phantoms in Figure 1 represent three different thoracic injuries: a small pneumothorax on the side of the lung, a larger pneumothorax, and air trapping. The sound speed phantoms—used for ultrasound reconstruction—require the corresponding conductivity phantoms, which employ slightly different organ boundaries to make things more realistic. Alsaker simulated the sound speed phantoms with 32 transducers on the boundary, solved the forward problem via k-wave, and added one percent Gaussian noise (which is standard for USCT simulations). She simulated the conductivity phantoms with 32 electrodes on the boundary, solved the forward problem via the finite element method and a complete electrode model, and added 0.1 percent Gaussian noise (which is standard for EIT simulations).

Alsaker then outlined the procedure that she used to obtain the hybrid reconstructions that combine information from the USCT and EIT scans. First, she computed an initial USCT reconstruction using DBIM. Next, she used the USCT to construct a prior for D-bar, which involved segmenting organ boundaries from the reconstruction and assigning optimized conductivity values to them. Afterwards, Alsaker used D-bar to compute an EIT reconstruction with the USCT prior. Finally, she utilized the EIT reconstruction to construct a prior for DBIM, which ultimately yields an updated ultrasound reconstruction.

Figure 2. Results of the sound speed phantoms for the small pneumothorax (top), larger pneumothorax (middle), and air trapping (bottom). Left to right: true organ boundaries for the phantom, standard EIT (D-bar) reconstruction with no priors, ultrasound reconstruction (DBIM) with no priors, D-bar reconstruction with priors, and DBIM with priors.

Alsaker concluded her presentation with a comparison of various reconstructions of the sound speed phantoms—original EIT reconstruction (with D-bar), original USCT (with DBIM), EIT with priors, and USCT with priors—for the aforementioned three thoracic injuries (see Figure 2). She began with the small pneumothorax. Though the original ultrasound scan does seem to have sharper boundaries, it does not effectively recover certain organs. However, adding priors via a priori data for both the USCT and EIT scan yielded good results. “Look at how well these features are showing up that were not visible in the original EIT scan,” she said. The pathology popped out quite distinctly in the USCT scan as well.

The outcome was slightly different for the larger pneumothorax. “I’m honestly not sure if the ultrasound scan is improved much with the EIT prior,” she said. “There’s some speckle in the reconstruction when you put the prior in there.” However, the EIT scan is much sharper than what one would expect from a typical EIT scan. And in the case of air trapping, the pathology showed up much more clearly in both reconstructions with priors.

Ultimately, Alsaker’s results suggest that the complementary use of priors and combination of EIT and USCT data could significantly improve thoracic imaging. Sharper results could lead to more accurate diagnoses and treatment plans for patients with pulmonary disease.

Lina Sorg is the managing editor of SIAM News.
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