## Results: 9

2.

The top, middle, and bottom cutlines are used to compare the pointwise thermal image temperature and pre and post calibration finite element prediction of the temperature versus cutline distance. The profiles illustrate the effect of the heterogeneity. Uncalibrated, the cutlines are symmetric; calibrated, cutlines demonstrate an asymmetric heating. Graph lines are color coded to represent the corresponding profile for thermal image and FEM prediction.

3.

Schematic of procedure workflow. An axial slice cut from the principle treatment plane demonstrates a 2D representation of the local heating in that slice. The full field of view shown is 240mm x 240mm (scale on image in mm). Multi-planar thermal image data is projected onto a finite element representation of the prostate and used to calibrate a model of the bioheat transfer. The predictive power of the calibrated model may be exploited for further planning and treatment optimization.

4.

Time varying plots of the post-calibration pointwise error in the model prediction,

*u*–*u*, along the x-axis of and of the thermal image data along the y-axis of . The temperature and distance are given in units of Celsius and millimeter, respectively. The units of time are provided with respect to the time duration of the 5W calibration pulse = 60s = Δ^{MRTI}*t*. Iso-error lines (a) and Temperature isotherms (b) are projected onto the time-distance plane. The DICOM coordinate of the laser tip along each cutline,*x*_{0}=−3mm and*y*_{0}=−5mm, is labeled as a reference.5.

(a) A cutplane though the FE prostate model illustrating the post-calibration temperature prediction of Pennes model. The cutplane shown is intersecting and coplanar with the catheter. The temperature is given in °C. Mesh lines illustrate the mesh resolution. Profiles along the x-, y-, and z- axis are taken with respect to the displayed orientation. The thermal image history along the y-axis is shown in . The post calibration error between the predicted temperature and the thermal image temperature along the x-axis is shown in . A cutplane through the error field,

*u*–*u*, is shown in °C (b)pre- and (c)post-calibration for comparison. The plotted error is seen to be significantly reduced post-calibration.^{MRTI}6.

The number of function evaluations required for convergence of the Quasi-Newton optimization method used in the calibration study is shown. The graph is intended to convey the general convergence behavior observed from the breadth of the calibration problems studied. The PDE constrained optimization problems are seen to have converged to their minimum within an average of 20 function evaluations. This data can be used to estimate the time required for a real-time calibration. Surgery protocols should allow time to complete 20 function-gradient computations for the calibration phase. The objective function values as a function of iteration number is shown in the insert to illustrate the typical convergence behavior observed.

7.

Schematic diagram of

*in vivo*MR-guided LITT calibration procedure in a canine model of prostate. Contrast enhanced T1-W MR images have been volume rendered to better visualize the relationship of the target volume and applicator trajectory to the surrounding anatomy. As displayed, the subject was stabilized in the supine position with legs upward. A stainless steel stylet was used to insert the laser catheter consisting of a 700*μ*m core diameter, 1 cm diffusing-tip silica fiber within a 2mm diameter water-cooled catheter (light grey cylinder). A non-destructive calibration pulse is applied under MR temperature monitoring. A volume rendering of the multi-planar thermal images (in degrees Celsius) is registered and fused with the 3D anatomy to visualize the 3D volume of therapy.8.

A comparison of cutplanes through the (a) measured MR temperature image and (b) the pre and post calibration finite element prediction is shown. The cutplanes are taken at the same axial position within the anatomy; the plane is 3mm from the plane that contains the catheter. The temperature scale shown is in Celsius. A reference of the axial position is provided in the 3D insert of (a). At the time instance shown the prostate has been exposed to a dose of 5 Watts for 55 seconds, ≈ .9Δ

*t*. The calibration problem involves recovering the spatially varying thermal properties within a small neighborhood around the laser tip. The illustration shown in (b) represents the inverse problem recovery of ≈ 3700 model parameters and allows for the non isotropic heating contours shown. The top, middle, and bottom cutlines (a) are used to compare the pointwise thermal image temperature and pre and post calibration finite element prediction of the temperature versus cutline distance .9.

A summary of a calibration study using various time windows of thermal image information is shown. The power versus time profile of the calibration pulse is shown in the insert; the pulse is held constant at 5W for Δ

*t*=60 seconds then turned off. The study compares the effect of using the norms for the calibration problem. The metric of the comparison is the full space-time norm of the difference between the thermal image data and the finite element comparison. The initial pre-optimization value of the objective function is provided as a reference for the relative decrease. Different initial thermal conductivity and perfusion distributions for the heterogeneous and homogeneous solve account for the initial discrepancy in the objective function. The plot demonstrates that the optimal amount of thermal image information to use in the calibration problem is 1.5 × pulse duration. This suggests that the calibration process can be implemented in near real-time with minimal impact on latency in the feedback control paradigm.