Kalman Filtered MR Temperature Imaging for Laser Induced Thermal Therapies

The feasibility of using a stochastic form of Pennes bioheat model within a 3-D finite element based Kalman filter (KF) algorithm is critically evaluated for the ability to provide temperature field estimates in the event of magnetic resonance temperature imaging (MRTI) data loss during laser induced thermal therapy (LITT). The ability to recover missing MRTI data was analyzed by systematically removing spatiotemporal information from a clinical MR-guided LITT procedure in human brain and comparing predictions in these regions to the original measurements. Performance was quantitatively evaluated in terms of a dimensionless
$L_{2}$
(RMS) norm of the temperature error weighted by acquisition uncertainty. During periods of no data corruption, observed error histories demonstrate that the Kalman algorithm does not alter the high quality temperature measurement provided by MR thermal imaging. The KF-MRTI implementation considered is seen to predict the bioheat transfer with
${\hbox {RMS ~error}} < {4}$
for a short period of time,
$\Delta t < 10~{\rm s}$
, until the data corruption subsides. In its present form, the KF-MRTI method currently fails to compensate for consecutive for consecutive time periods of data loss
$\Delta t > 10~{\rm sec}$
.