Quantitative Ultrasound for Periodontal Soft Tissue Characterization.

Periodontal diseases affect 45.9\% of adults aged 30 or older in the United States. Current diagnostic methods for clinical assessment of these diseases are visual examination and bleeding on probing that are subjective, qualitative, and/or invasive. Thus, there is a critical need for research on noninvasive modalities for periodontal tissue characterization. Quantitative Ultrasound (QUS) has shown promising results in noninvasive characterization of various soft tissues; however, it has not been used in periodontics. This study is among initial investigations into the application of QUS for periodontal tissue characterization in the literature. Here, QUS analysis of oral soft tissues (alveolar mucosa and gingiva) is performed in an in vivo animal study including 10 swine. US scanning was performed at the first molar of all four oral quadrants, resulting in a total of 40 scans. We investigated first order speckle statistics of oral tissues by using the two-parameter Burr (power-law b and scale factor l) and Nakagami models (shape factor m and scale factor $\alpha$). Parametric imaging of these parameters was created using a sliding kernel method sweeping regions of interest with a kernel size of 10 wavelengths from a phantom study. Results showed that the difference between gingiva and alveolar mucosa were statistically significant using Burr and Nakagami parameters ($p-value<0.0001$). The Burr b and Nakagami m were higher in gingiva while the Burr l and Nakagami {$\alpha$} were higher in alveolar mucosa. Findings from QUS analyses agreed with observation from histology that showed denser stains for gingiva. Linear classifications of these tissues using 2D parameter spaces of the Burr and Nakagami models resulted in a segmentation accuracy of 93.51\% and 90.91\%, respectively. We propose that QUS holds promising potentials as an augmented tool for disease diagnosis in periodontology.

Comprehensive experimental assessments of rheological models' performance in elastography of soft tissues.

Elastography researchers have utilized several rheological models to characterize soft tissue viscoelasticity over the past thirty years. Due to the frequency-dependent behavior of viscoelastic parameters as well as the different techniques and frequencies employed in various studies of soft tissues, rheological models have value in standardizing disparate techniques via explicit mathematical representations. However, the important question remains: which of the several available models should be considered for widespread adoption within a theoretical framework? We address this by evaluating the performance of three well established rheological models to characterize ex vivo bovine liver tissues: the Kelvin-Voigt (KV) model as a 2-parameter model, and the standard linear solid (SLS) and Kelvin-Voigt fractional derivative (KVFD) models as 3-parameter models. The assessments were based on the analysis of time domain behavior (using stress relaxation tests) and frequency domain behavior (by measuring shear wave speed (SWS) dispersion). SWS was measured over a wide range of frequency from 1 Hz to 1 kHz using three different tests: (i) harmonic shear tests using a rheometer, (ii) reverberant shear wave (RSW) ultrasound elastography scans, and (iii) RSW optical coherence elastography scans, with each test targeting a distinct frequency range. Our results demonstrated that the KVFD model produces the only mutually consistent rendering of time and frequency domain data for liver. Furthermore, it reduces to a 2-parameter model for liver (correspondingly to a 2-parameter "spring-pot" or power-law model for SWS dispersion) and provides the most accurate predictions of the material viscoelastic behavior in time (>98% accuracy) and frequency (>96% accuracy) domains. STATEMENT OF SIGNIFICANCE: Rheological models are applied in quantifying tissues viscoelastic properties. This study is unique in presenting comprehensive assessments of rheological models.

Generalized formulations producing a Burr distribution of speckle statistics.

Purpose: The study of speckle from imaging systems has a rich history, and recently it was proposed that a fractal or power law distribution of scatterers in vascularized tissue will lead to a form of the Burr probability distribution functions for speckle amplitudes. This hypothesis is generalized and tested in theory, simulations, and experiments. Approach: We argue that two broadly applicable conjectures are sufficient to justify the applicability of the Burr distribution for speckle from a number of acoustical, optical, and other pulse-echo systems. The first requirement is a multiscale power law distribution of weak scatterers, and the second is a linear approximation for the increase in echo intensity with size over some range of applicability. Results: The Burr distribution for speckle emerges under a wide variety of conditions and system parameters, and from this one can estimate the governing power law parameter, commonly in the range of 2 to 6. However, system effects including the imaging point spread function and the degree of focusing will influence the Burr parameters. Conclusions: A generalized pair of conditions is sufficient for producing Burr distributions across a number of imaging systems. Simulations and some theoretical considerations indicate that the estimated Burr power law parameter will increase with increasing density of scatters. For studies of speckle from living tissue or multiscale natural structures, the Burr distribution should be considered as a long tail alternative to classical distributions.

Clusters of Ultrasound Scattering Parameters for the Classification of Steatotic and Normal Livers.

The study of ultrasound tissue interactions in fatty livers has a long history with strong clinical potential for assessing steatosis. Recently we proposed alternative measures of first- and second-order statistics of echoes from soft tissues, namely, the H-scan, which is based on a matched filter approach, to quantify scattering transfer functions and the Burr distribution to model speckle patterns. Taken together, these approaches produce a multiparameter set that is directly related to the fundamentals of ultrasound propagation in tissue. To apply this approach to the problem of assessing steatotic livers, these analyses were applied to in vivo rat livers (N=21) under normal feeding conditions or after receiving a methionine- and choline-deficient diet that produces steatosis within a few weeks. Ultrasound data were acquired at baseline and again at weeks 2 and 6 before applying the H-scan and Burr analyses. Furthermore, a classification technique known as the support vector machine was then used to find clusters of the five parameters that are characteristic of the different steatotic liver conditions as confirmed by histologic processing of excised liver tissue samples. With the in vivo multiparametric ultrasound measurement approach and determination of clusters, steatotic can be discriminated from normal livers with 100% accuracy in a rat animal model.

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.

Speckle from branching vasculature: dependence on number density.

Purpose: Recent theories examine the role of the fractal branching vasculature as a primary site of Born scattering from soft normal tissues. These derivations postulate that the first-order statistics of speckle from soft tissue, such as the liver, thyroid, and prostate, will follow a Burr distribution with a power law parameter that can be related back to the underlying power law, which governs the branching network. However, the issue of scatterer spacing, or the number of cylindrical vessels per sample volume of the interrogating pulse, has not been directly addressed. Approach: Speckle statistics are examined with a 3D simulation that varies the number density and the governing power law parameter of an ensemble of different sized cylinders. Several in vivo liver scans are also analyzed for confirmation across different conditions. Results: The Burr distribution is found to be an appropriate model for the histogram of amplitudes from speckle regions, where the parameters track the underlying power law and scatterer density conditions. These results are also tested in a more general model of rat liver scans in normal versus abnormal conditions, and the resulting Burr parameters are also found to be appropriate and sensitive to underlying scatterer distributions. Conclusions: These preliminary results suggest that the classical Burr distribution may be useful in the quantification of scattering of ultrasound from soft vascularized tissues and as a tool in tissue characterization.

Validations of the microchannel flow model for characterizing vascularized tissues.

The microchannel flow model postulates that stress-strain behavior in soft tissues is influenced by the time constants of fluid-filled vessels related to Poiseuille's law. A consequence of this framework is that changes in fluid viscosity and changes in vessel diameter (through vasoconstriction) have a measurable effect on tissue stiffness. These influences are examined through the theory of the microchannel flow model. Then, the effects of viscosity and vasoconstriction are demonstrated in gelatin phantoms and in perfused tissues, respectively. We find good agreement between theory and experiments using both a simple model made from gelatin and from living, perfused, placental tissue ex vivo.