High-intensity Focused Ultrasound - Theory

Theory

Ultrasound can be focused, either via a lens (for example, a polystyrene lens), a curved transducer, or a phased array (or any combination of the three) into a small focal zone, in a similar way to focusing light through a magnifying glass focusing light rays to a point. Using an exponential model of ultrasound attenuation (i.e. the ultrasound intensity profile is bounded by an exponentially decreasing function where the decrease in ultrasound is a function of the distance traveled through the tissue), this can be modeled as

where is the initial beam intensity, is the attenuation coefficient in units of inverse length, and z is the distance traveled through the attenuating medium.

In this model, is a measure of the power density of the heat absorbed from the ultrasound field. Sometimes, SAR is also used to express the amount of heat absorbed by a specific medium and is related to Q by dividing Q by the tissue density. Also, this demonstrates that tissue heating is proportional to the intensity and the intensity is inversely proportional to the area over which an ultrasound beam is spread, which is why focusing the beam into a sharp point (i.e. increasing the beam intensity) creates a rapid temperature rise at the focus.

The amount of damage caused in the tissue can be modeled using Cumulative Equivalent Minutes (CEM). Several formulations of the CEM equation have been suggested over the years, but the equation currently in use for most research done in HIFU therapy comes from a 1984 paper by Dewey and Sapareto:

with the integral being over the treatment time, R=2 for temperatures over 43 °C and 4 for temperatures between 43 °C and 37 °C, a reference temperature of 43 °C, and time in minutes. This formula is an empirical formula derived from experiments performed by Dewey and Sapareto by measuring the survival of cell cultures after exposure to heat.