Ultrasound Echoes Turn Lung Scars Into Numbers With Random Matrix Physics

Ultrasound is one of medicine’s most trusted tools, yet it has a well-known blind spot: organs that are so full of tiny interfaces that sound waves bounce around chaotically before returning to the probe. The lung is the classic example. Its millions of air-filled alveoli act as dense acoustic scatterers, and the resulting multiple scattering scrambles the clean echo patterns that conventional echolocation-based imaging relies on. A team at North Carolina State University and the University of North Carolina at Chapel Hill has now turned this apparent weakness into a measurement strategy, showing that the statistics of multiply scattered ultrasound can quantify structural changes in complex biological media. In a study published in Frontiers in Acoustics, the researchers demonstrate that two simple numbers extracted from backscattered signals correlate with the severity of pulmonary fibrosis in living rats.

The approach rests on a piece of mathematics borrowed from an unlikely field: the analysis of wireless communication channels. When a multi-element ultrasound array fires a pulse from each of its elements in turn and records the echoes on every element, the result is a data structure called the Inter-element Response Matrix, or IRM. Each entry of this matrix describes the signal that travels from one transducer element into the tissue and back to another element. Because the probe both emits and receives, the configuration is purely backscattering, meaning all the information comes from waves that have interacted with the medium and returned. Once the IRM is formed, a mathematical operation known as singular value decomposition, or SVD, breaks it down into a set of singular values that summarize how the medium redistributes acoustic energy among the array elements.

Earlier work by Prada and Fink showed that when point-like scatterers are randomly distributed in a homogeneous medium, each scatterer corresponds to a non-zero singular value of the propagation matrix in the frequency domain. Building on this, Aubry and Derode applied results from Random Matrix Theory, a framework originally developed to describe the statistical properties of large random matrices in physics and telecommunications, to the singular values of acoustic propagation matrices. Their central insight was that when multiple scattering dominates a medium, the distribution of singular values converges to a characteristic shape known as the Quarter Circle Law. The closer the measured distribution hugs this quarter circle, the more the wave field has been randomized by repeated scattering events rather than by simple single reflections.

The North Carolina team exploited this principle by computing a probability density function of the singular values from each IRM and tracking two parameters of that distribution. The first, called E(X), is the expected value of the singular value distribution. The second, called lambda-max, is the peak of the probability density function, that is, the most frequently represented singular value. Theory predicts that as multiple scattering becomes more dominant, E(X) should increase while lambda-max should decrease, because the distribution spreads out and flattens toward the quarter-circle shape. Changes in the microstructure of the medium, such as the density of scatterers, should therefore leave a measurable fingerprint in these two numbers.

To test this idea, the researchers began with computer simulations. They generated two-dimensional numerical structures containing monodisperse circular scatterers made of either plastic or aluminum, randomly distributed in water, with the scatterer area fraction varied from 5 to 25 percent in steps of 5 percent. A simulated 128-element array transducer emitting a 5 MHz Gaussian pulse probed each structure, and the finite-difference time-domain solver SimSonic computed the full wave physics. The results showed that as scatterer density increased, E(X) rose and lambda-max fell, with both metrics reaching a plateau once the area fraction exceeded roughly 15 percent. Beyond that density, multiple scattering had become so dominant that the singular value distribution no longer changed appreciably, a limitation the authors attribute to the saturation predicted by the Quarter Circle Law. Notably, the two metrics could also distinguish between plastic and aluminum scatterers, indicating sensitivity to material properties as well as density.

The team then moved from simulation to laboratory phantoms. Gelatin-glass bead phantoms were fabricated with glass beads embedded at volume fractions of 3 and 10 percent, mimicking highly scattering media in which the scatterer size is comparable to the ultrasound wavelength. Two linear array transducers with central frequencies of 5.1 and 7.8 MHz interrogated these samples, and the singular value distributions were compared against the theoretical quarter circle. At the lower frequency, both E(X) and lambda-max clearly separated the low-density from the high-density phantoms. At the higher frequency, multiple scattering dominated for both densities and the sensitivity of the metrics diminished, reinforcing the simulation finding that the method works best before full scattering saturation sets in.

A second family of phantoms probed a different question: whether the metrics respond to changes in the speed of sound rather than to scattering strength. Polydimethylsiloxane, a soft silicone matrix, was loaded with barium titanate particles at five different mass ratios, producing composites in which the scatterers were much smaller than the wavelength and therefore only weakly scattering, but in which the acoustic velocity varied substantially with particle concentration. The measurements showed that E(X) and lambda-max could differentiate between these weakly scattering media only at the lower particle concentrations. At higher concentrations the trends became difficult to estimate, and conventional speed-of-sound measurements tracked the composition more reliably. The authors note that speed of sound is often hard to measure in biological settings, where through-transmission geometries are rarely practical, which is precisely why backscattering-based metrics could be valuable.

The decisive test came in living animals. The researchers studied thirty-two Sprague Dawley rats: six with healthy lungs serving as controls, eighteen with pulmonary fibrosis of varying severity induced by instilling bleomycin into the airway, and eight fibrotic rats treated with the antifibrotic drug Nintedanib. Under anesthesia, a sternotomy exposed both lungs, and a 128-element array operating at 7.8 MHz recorded five IRMs per animal to ensure reproducibility. After the ultrasound sessions, the lungs were excised, inflation-fixed, sectioned, and stained, and a veterinary pathologist blinded to the animal groups scored fibrosis severity on the modified Ashcroft scale, which ranges from 0 for healthy tissue to 8 for the most severe fibrosis, though no slide in this study scored above 4.

The in vivo results showed statistically significant correlations between both metrics and the histology scores. E(X) decreased with increasing fibrosis severity, while lambda-max increased, a pattern consistent with the underlying physics: fibrotic thickening of the alveolar walls reduces the density of healthy air-filled alveoli, which are the strongest scatterers in lung tissue. Fewer strong scatterers means less multiple scattering, shifting the singular value distribution away from the quarter circle in the direction of lower E(X) and higher lambda-max. The correlations were moderate rather than strong, and the authors examined time windows of 2, 4, 6, and 8 microseconds without finding significant differences, suggesting the result is robust to that processing choice.

The study positions singular value statistics as a potential complement to existing quantitative ultrasound tools such as the backscatter coefficient and envelope statistics, which the same group has previously used to stage interstitial lung disease in rodents. Because the IRM can be acquired with standard multi-element arrays in a backscattering geometry, the approach does not require access to the far side of the organ, a major practical advantage over transmission-based speed-of-sound measurements. The authors caution that only two scatterer volume fractions were tested in the highly scattering phantoms and that the plateau behavior limits sensitivity once multiple scattering fully dominates. They also emphasize that true validation must come from biological tissue, ideally in vivo, which the rat study provides a first step toward. If the moderate correlations seen here can be strengthened and translated to larger animals and eventually patients, the chaotic echoes that once defeated ultrasound imaging of the lung may become a quantitative window into its microstructure.

Subject of Research: Quantifying ultrasound multiple scattering to characterize complex biological media and assess pulmonary fibrosis

Article Title: Characterizing random complex biological media by quantifying ultrasound multiple scattering

Article References: Yousefian, O., Dashti, A., Geithner, H., Karbalaeisadegh, Y., Yao, S., Blackwell, J., Ali, M., Montgomery, S., Zhu, Y., Egan, T., & Muller, M. (2025). Characterizing random complex biological media by quantifying ultrasound multiple scattering. Frontiers in Acoustics, 3, Article 1545057. https://doi.org/10.3389/facou.2025.1545057

Image Credits: AI Generated

DOI: 10.3389/facou.2025.1545057

Keywords: ultrasound, multiple scattering, random matrix theory, singular value decomposition, pulmonary fibrosis, quantitative ultrasound, tissue characterization, lung microstructure, biomedical acoustics, phantoms, in vivo rodent study, Inter-element Response Matrix