A study on understanding the physical mechanism of change in ultrasonic envelope statistical property during temperature elevation

Purpose: Our previous studies demonstrate that the variation in ultrasonic envelope statistics is correlated with the temperature change inside scattering media. This variation is identified as the change in the scatterer structure during thermal expansion or contraction. However, no specific evidence has been verified to date. This study numerically reproduces the change in the scatterer distribution during thermal expansion or contraction using finite element simulations and also investigates how the situation is altered by different material properties. Methods: The material properties of a linear elastic solid depend on the thermal expansion coefficient, thermal conductivity, specific heat, and initial scatterer number density. Three-dimensional displacements, calculated in the simulation, were sequentially used to update the positions of the randomly distributed scatterers. Ultrasound signals from the scatterer distribution were generated by simulating a 7.5-MHz linear array transducer whose specifications were the same as those in the experimental measurements of several phantoms and excised porcine livers. To represent the change in the envelope statistical feature, the absolute value of the ratio change in the logarithmic Nakagami (NA) parameter, (Formula presented.), at each time was calculated as a value normalized with the initial NA parameter. Results: The change in the scatterer number density relates to the volume change during temperature elevation. The magnitude of the (Formula presented.) shift against the temperature change increases depending on the higher thermal expansion coefficient. In contrast, the relationship between (Formula presented.) and the scatterer number density is similar with any material property. Additionally, the changes in (Formula presented.) obtained by several experimental phantoms with low to high scatterer number densities are comparable with the numerical simulation results. Conclusions: The change in (Formula presented.) is indirectly related to the change in the scatterer number density owing to the volume change during thermal expansion or contraction.