Modeling of the heat distribution in the intervertebral disk

Abstract

The heat transfer equation was used to model the heat distribution in an intervertebral disk during ultrasound (US) exposure. The influence of thermal and acoustic parameters was studied to get a quantitative understanding of the heat transfer in the system. Heating of collagen to 65 degrees C or above will lead to denaturation and is believed to stabilize and contract the outer part of the disk in a herniated disk. In our model, the US intensity was approximated by a Gaussian distribution and nonlinear propagation was excluded. The effect of self-heating and cooling of the transducer was also studied. The simulations were performed using the finite element method. From this model, it can be concluded that it is possible to heat parts of the disk to treatment temperature using a focused 5-mm diameter US probe. The physical constraints on the piezocrystal set the limit of the size of the treatment volume.