Y. Guo, J. W. Trobaugh, and R. M. Arthur, "A Framework for Temperature Imaging using the Change in Backscattered Ultrasonic Signals", Ultrasonic Imaging, vol. 31, pp. 74-75, 2009.

Abstract

In thermal treatments, such as hyperthermia and HIFU, control of heat delivery would benefit from non-invasive, safe, inexpensive and convenient thermometry based on ultrasound. We proposed a theoretical model for the change in the backscattered energy (CBE) from individual scatterers, which predicted that CBE increased or decreased monotonically with temperature depending on scatterer type [1]. CBE calculated as a ratio of backscattered signals confirmed these predictions in 1D, 2D and 3D experiments with multiple tissue types both in vitro and in vivo, implying that CBE is a potentially useful thermometer. To date, CBE has been computed in a straightforward but ad hoc manner based on statistics of the energy ratio. Although these previous measures have proven useful, we wanted to systematize our approach to temperature imaging using backscattered signals. Here we 1) model temperature imaging via a probabilistic framework, 2) formalize computational methods, 3) develop procedures for precise computation of CBE and accurate estimation of temperature, and 4) employ approaches using changes in the backscattered signals in addition to the energy ratio.

By extending our original CBE model for a single scatterer to a random phasor sum representation [2], images can be represented as collections of temperature-dependent random variables. We model temperature imaging as a problem of estimating temperature from the resulting random processes. We pursued several approaches to temperature imaging based on the joint distribution of measurement variables x_T and x_T0 at temperatures T and T₀. One approach was to estimate temperature from the ratio of x_T and x_T0. In fact, current computation of what we call positive CBE and negative CBE can be defined as the mean of this ratio over values larger than or less than 1, respectively. Assuming uniformly distributed tissue scatterers, the probability density function (pdf) of the ratio can be found analytically and was used to estimate CBE precisely even in low signal-to-noise ratio (SNR) conditions. The ability to estimate CBE from noisy signals enables us to achieve accurate temperature imaging even when SNR varies. A second approach is to use the complex difference of x_T and x_T0, for which a maximum likelihood estimator for temperature has been developed. Additionally, temperature may be estimated using approaches based directly on the joint distribution, such as mutual information (MI). In simulations with uniformly distributed scatterers, MI can be estimated accurately by removing the noise effect. Estimation error using the MI-base method was less than ± 0.3^oC even when calibration curves and data used for temperature estimation were obtained under different SNRs.

In this work we modeled CBE-based temperature imaging as an estimation problem using the statistical properties of random process formed by backscattered signals. We formalized the computation and characterization of CBE as the ratio between signals and developed a maximum likelihood estimator for temperature, whose analytical form allows us to analyze its performance theoretically. We also demonstrated the use of mutual information for temperature estimation. Furthermore, this framework can be extended to incorporate other parameters for robust estimation of temperature.

1) WL Straube and RM Arthur, UMB, 20:915-922, 1994.

2) JW Trobaugh and RM Arthur, IEEE Trans on UFFC, 47:1520-1529, 2000.

Support: R21-CA90531, R01-CA107558 and the Wilkinson Trust at Washington University, St. Louis.