Jared Catenacci

Volumetric Thermoacoustic Imaging over Large Fields of View

The thermoacoustic (TA) contrast mechanism relies on rapid tissue heating and subsequent thermal expansion. TA computerized tomography (TCT) is therefore inverse source imaging. The TA contrast mechanism provides information complementary to that revealed by current diagnostic imaging techniques, but has been limited to just a few centimeters depth penetration. In this article, whole organ TCT is demonstrated on a large swine kidney. TA sinograms show that TA signal generated by high-power, very high frequency (VHF) electromagnetic pulses is detectable after travel through 6 cm of soft tissue. Reconstructed images provide resolution sufficient to track progression of calyces throughout the kidney. Because VHF electromagnetic energy can easily penetrate the abdomen of large adults, our results indicate that whole organ TA imaging is feasible in vivo, provided an ultrasound array can be placed near the region of interest. Pulses of 22 to 25 kW with carrier frequency 108 MHz and 900 ns pulse width were applied at a 100-Hz pulse repetition frequency to generate a 13-kV/m electric field and TA signal. Only 2 to 5 mJ was absorbed in the kidney per pulse, causing temperature and pressure jumps of only 5e-6°C and 4 Pa averaged throughout the 141-g specimen. TA pulses were detected by focused, single-element transducers (V306, Panametrics), amplified by 54 dB and averaged 64 times to reduce electronic noise. Data were measured over a cylindrical measurement aperture of radius 5 cm and length 6 cm, by rotating the specimen 1.8 degrees between tomographic views and translating 2 mm between slices. Reconstruction via filtered backprojection yields in-plane resolution better than 5 mm, but suffers significant blurring between planes. Both in-plane resolution and slice sensitivity profile could be improved by applying shorter irradiation pulsewidths and using less directional transducers. Both hardware changes would be recommended for a clinical prototype.

Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems

Abstract Normalized differences of several adjacent observations, referred to as pseudo-measurement errors in this paper, are used in so-called difference-based estimation methods as building blocks for the variance estimate of measurement errors. Numerical results demonstrate that pseudo-measurement errors can be used to serve the role of measurement errors. Based on this information, we propose the use of pseudo-measurement errors to determine an appropriate statistical model and then to subsequently investigate whether there is a mathematical model misspecification or error. We also propose to use the information provided by pseudo-measurement errors to quantify uncertainty in parameter estimation by bootstrapping methods. A number of numerical examples are given to illustrate the effectiveness of these proposed methods.

Asymptotic Properties of Probability Measure Estimators in a Nonparametric Model

We consider probability measure estimation in a nonparametric model using a least-squares approach under the Prohorov metric framework. We summarize the computational methods and related convergence results that were recently developed by our group. New results are presented on the bias and the variance due to the approximation and new pointwise asymptotic normality of the approximated probability measure estimator. We propose the use of a model selection criterion to balance the bias and the variance, and compare the new pointwise confidence bands constructed using the asymptotic normality results with those obtained by Monte Carlo simulations.

Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance

Abstract We investigate the feasibility of quantifying properties of a composite dielectric material through the reflectance, where the permittivity is described by the Lorentz model in which an unknown probability measure is placed on the model parameters. We summarize the computational and theoretical framework (the Prohorov metric framework) developed by our group in the past two decades for nonparametric estimation of probability measures using a least-squares method, and point out the limitation of the existing computational algorithms for this particular application. We then improve the algorithms, and demonstrate the feasibility of our proposed methods by numerical results obtained for both simulated data and experimental data for inorganic glass when considering the resonance wavenumber as a distributed parameter. Finally, in the case where the distributed parameter is taken as the relaxation time, we show using simulated data how the addition of derivative measurements improves the accuracy of the method.

Quantifying the degradation in thermally treated ceramic matrix composites

Reflectance spectroscopy obtained from a thermally treated silicon nitride carbon based ceramic matrix composite is used to quantity the oxidation products SiO2 and SiN. The data collection is described in detail in order to point out the potential biasing present in the data processing. A probability distribution is imposed on select model parameters, and then non-parametrically estimated. A non-parametric estimation is chosen since the exact composition of the material is unknown due to the inherent heterogeneity of ceramic composites. The probability distribution is estimated using the Prohorov metric framework in which the infinite dimensional optimization is reduced to a finite dimensional optimization using an approximating space composed of linear splines. A weighted least squares estimation is carried out, and uncertainty quantification is performed on the model parameters, including a piecewise asymptotic confidence band for the estimated probability density. Our estimation results indicate a distinguishable increase in the SiO2 present in the samples which were heat treated for 100 hours compared to 10 hours.

Thermoacoustic Imaging with VHF Signal Generation: A New Contrast Mechanism for Cancer Imaging Over Large Fields of View

Ex vivo thermoacoustic (TA) imaging of large porcine specimens demonstrates the feasibility of performing whole organ TA imaging. A smaller system optimized for ex vivo prostate cancer imaging has been developed and is currently in use to determine whether the TA contrast mechanism can visualize prostate cancer.

Decomposition of permittivity contributions from reflectance using mechanism models

In this paper, we investigate the properties of a complex nonmagnetic material through the reflectance, where the permittivity is described by a mechanism model in which an unknown probability measure is placed on the model parameters. Specifically, we consider whether or not this unknown probability measure can be determined from the reflectance or the derivatives of the reflectance, and we also investigate the effect of measurement noise on the estimation. The numerical results demonstrate that if only the reflectance can be observed, then the distribution form cannot be recovered even in the case where the measurement noise level is small. However, if both the reflectance and the derivative of the reflectance can be observed, then the estimated distribution is reasonably close to the true one even in the case where the measurement noise level is relatively high.

A comparison of stochastic systems with different types of delays

In this article, we investigate the effects of different types of delays, a fixed delay and a random delay, on the dynamics of stochastic systems as well as their relationship with each other in the context of a just-in-time network model. The specific example on which we focus is a pork production network model. We numerically explore the corresponding deterministic approximations for the stochastic systems with these two different types of delays. Numerical results reveal that the agreement of stochastic systems with fixed and random delays depend on the population size and the variance of the random delay, even when the mean value of the random delay is chosen the same as the value of the fixed delay. When the variance of the random delay is sufficiently small, the histograms of state solutions to the stochastic system with a random delay are similar to those of the stochastic model with a fixed delay regardless of the population size. We also compared the stochastic system with a Gamma distributed random delay to the stochastic system constructed based on the Kurtzs limit theorem from a system of deterministic delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the second system appear more dispersed than the corresponding ones obtained for the first case. In addition, we found that there is more agreement between the histograms of these two stochastic systems as the variance of the Gamma distributed random delay decreases.

Stochastic vs. Deterministic Models for Systems with Delays

Abstract We consider population models with nodal delays which result in dynamical systems with delays. For small population models the appropriate models are discrete stochastic systems with delays. We consider these delay systems and present new theoretical and computational results for such systems. In particular, in this note we summarize results on the effects of different types of delays (a fixed delay and a random delay) on the dynamics of stochastic system as well as their relationship with each other in the context of a just-in-time network model. In addition, we numerically explore the corresponding deterministic approximations for the stochastic systems with these two different types of delays.

Aggregate data and the Prohorov Metric Framework: Efficient gradient computation

Abstract We discuss efficient methods for computing gradients in inverse problems for estimation of distributions for individual parameters in models where only aggregate or population level data is available. The ideas are illustrated with two examples arising in applications.