One-Dimensional Inverse Problem of Passive Acoustic Thermometry Using the Heat Conductivity Equation: Computer and Physical Simulation

Abstract

An algorithm for reconstructing the time-varying one-dimensional distribution of the deep temperature of the human body under local heating is proposed and experimentally tested on a model. The algorithm requires that the temperature obey the heat conduction equation, the integration of which with a weight that takes into account absorption in the object, makes it possible to obtain the time dependence of the acoustic brightness temperature (measured signal), which in turn is determined by the parameters of the equation. The desired temperature is obtained by solving the heat conduction equation with the found parameters. The algorithm reconstructs two parameters: blood flow and the amplitude of the heating source, which are not determined each time anew, but only refined. In this case, the integration time increases, but the temporal resolution does not suffer: new results can be obtained after any period of time. After 2 min of heating, it is possible to reconstruct the temperature and size of the heated region with an accuracy acceptable for medical applications: 0.5°C and 0.5 mm, respectively.