Liver Backscatter and the Hepatic Vasculature’s Autocorrelation Function

Real-time imaging of nanobubble ultrasound contrast agent flow, extravasation, and diffusion through an extracellular matrix using a microfluidic model

Lipid shell-stabilized nanoparticles with a perfluorocarbon gas-core, or nanobubbles, have recently attracted attention as a new contrast agent for molecular ultrasound imaging and image-guided therapy. Due to their small size (∼275 nm diameter) and flexible shell, nanobubbles have been shown to extravasate through hyperpermeable vasculature (e.g., in tumors). However, little is known about the dynamics and depth of extravasation of intact, acoustically active nanobubbles. Accordingly, in this work, we developed a microfluidic chip with a lumen and extracellular matrix (ECM) and imaging method that allows real-time imaging and characterization of the extravasation process with high-frequency ultrasound. The microfluidic device has a lumen and is surrounded by an extracellular matrix with tunable porosity. The combination of ultrasound imaging and the microfluidic chip advantageously produces real-time images of the entire length and depth of the matrix. This captures the matrix heterogeneity, offering advantages over other imaging techniques with smaller fields of view. Results from this study show that nanobubbles diffuse through a 1.3 μm pore size (2 mg mL-1) collagen I matrix 25× faster with a penetration depth that was 0.19 mm deeper than a 3.7 μm (4 mg mL-1) matrix. In the 3.7 μm pore size matrix, nanobubbles diffused 92× faster than large nanobubbles (∼875 nm diameter). Decorrelation time analysis was successfully used to differentiate flowing and extra-luminally diffusing nanobubbles. In this work, we show for the first time that combination of an ultrasound-capable microfluidic chip and real-time imaging provided valuable insight into spatiotemporal nanoparticle movement through a heterogeneous extracellular matrix. This work could help accurately predict parameters (e.g., injection dosage) that improve translation of nanoparticles from in vitro to in vivo environments.

Power laws prevail in medical ultrasound

Major topics in medical ultrasound rest on the physics of wave propagation through tissue. These include fundamental treatments of backscatter, speed of sound, attenuation, and speckle formation. Each topic has developed its own rich history, lexicography, and particular treatments. However, there is ample evidence to suggest that power law relations are operating at a fundamental level in all the basic phenomena related to medical ultrasound. This review paper develops, from literature over the past 60 years, the accumulating theoretical basis and experimental evidence that point to power law behaviors underlying the most important tissue-wave interactions in ultrasound and in shear waves which are now employed in elastography. The common framework of power laws can be useful as a coherent overview of topics, and as a means for improved tissue characterization.

Local Burr distribution estimator for speckle statistics

Speckle statistics in ultrasound and optical coherence tomography have been studied using various distributions, including the Rayleigh, the K, and the more recently proposed Burr distribution. In this paper, we expand on the utility of the Burr distribution by first validating its theoretical framework with numerical simulations and then introducing a new local estimator to characterize sample tissues of liver, brain, and skin using optical coherence tomography. The spatially local estimates of the Burr distribution's power-law or exponent parameter enable a new type of parametric image. The simulation and experimental results confirm the potential for various applications of the Burr distribution in both basic science and clinical realms.

Speckle statistics of biological tissues in optical coherence tomography

The speckle statistics of optical coherence tomography images of biological tissue have been studied using several historical probability density functions. Here, we propose a new theoretical framework based on power-law functions, where we hypothesize that an underlying power-law distribution governs scattering from tissues. Thus, multi-scale scattering sites including the fractal branching vasculature will contribute to power-law probability distributions of speckle statistics. Specifically, these are the Burr type XII distribution for speckle amplitude, the Lomax distribution for intensity, and the generalized logistic distribution for log amplitude. Experimentally, these three distributions are fitted to histogram data from nine optical coherence tomography scans of various samples and biological tissues, in vivo and ex vivo. The distributions are also compared with classical models such as the Rayleigh, K, and gamma distributions. The results indicate that across OCT datasets of various tissue types, the proposed power-law distributions are more appropriate models yielding novel parameters for characterizing the physics of scattering from biological tissue. Thus, the overall framework brings to the field new biomarkers from OCT measures of speckle in tissues, grounded in basic biophysics and with wide applications to diagnostic imaging in clinical use.

Scattering Signatures of Normal versus Abnormal Livers with Support Vector Machine Classification

Fifty years of research on the nature of backscatter from tissues has resulted in a number of promising diagnostic parameters. We recently introduced two analyses tied directly to the biophysics of ultrasound scattering: the H-scan, based on a matched filter approach to distinguishing scattering transfer functions, and the Burr distribution for quantification of speckle patterns. Together, these analyses can produce at least five parameters that are directly linked to the mathematics of ultrasound in tissue. These have been measured in vivo in 35 rat livers under normal conditions and after exposure to compounds that induce inflammation, fibrosis, and steatosis in varying combinations. A classification technique, the support vector machine, is employed to determine clusters of the five parameters that are signatures of the different liver conditions. With the multiparametric measurement approach and determination of clusters, the different types of liver pathology can be discriminated with 94.6% accuracy.

Burr, Lomax, Pareto, and Logistic Distributions from Ultrasound Speckle

After 100 years of theoretical treatment of speckle patterns from coherent illumination, there remain some open questions about the nature of ultrasound speckle from soft vascularized tissues. A recent hypothesis is that the fractal branching vasculature is responsible for the dominant echo pattern from organs such as the liver. In that case, an analysis of cylindrical scattering structures arranged across a power law distribution of sizes is warranted. Using a simple model of echo strength and basic transformation rules from probability, we derive the first order statistics of speckle considering the amplitude, the intensity, and the natural log of amplitude. The results are given by long tailed distributions that have been studied in the statistics literature for other fields. Examples are given from simulations and animal studies, and the theoretical fit to these preliminary data support the overall framework as a plausible model for characterizing ultrasound speckle statistics.