Map data to high dimensional space where it is easier to classify with linear decision surfaces: reformulate problem so that data is mapped implicitly to this space.Extend the above definition for non-linearly separable problems: have a penalty term for misclassifications.Define an optimal hyperplane: maximize margin.(cases) that define the hyperplane are the support vectors. Even at its present state of development, hyperthermia planning for regional hyperthermia delivers valuable information, not only for clinical practice, but also for further technologic improvements.A Support Vector Machine (SVM) performs classification byįinding the hyperplane that maximizes the margin between the two classes. Further improvements in the implemented models, FE and FDTD, are required. The hyperthermia planning system HyperPlan could be validated for a number of the 30 patients. However, gross fluctuations exist from patient to patient. There are also statistically provable differences among the tumor entities regarding the attained specific absorption rate, temperatures, and volume loads in normal tissue. The results of the FE and FDTD methods are comparable, although slight differences exist resulting from the differences in the underlying models. Tumor temperatures can only be estimated, because of the rather variable perfusion conditions. We could show sufficient agreement between the calculations and measurements for power density (specific absorption rate) within the range of assessed precision. Segmentation, grid generation, E-field, and temperature calculation can be carried out in clinical practice at an acceptable time expenditure of about 1-2 days.Īll 30 patients we analyzed with cervical, rectal, and prostate carcinoma exhibit a good correlation between the model calculations and the attained clinical data regarding acute toxicity (hot spots), prediction of easy-to-heat or difficult-to-heat patients, and the dependency on various other individual parameters. In both methods, temperature distributions are calculated on the tetrahedral grid by solving the bioheat transfer equation with the FE method. The FDTD method, on the other hand, calculates the E-field on a cubical grid, but also requires a tetrahedral grid for correction at electrical interfaces. The FE method necessitates, primarily, this tetrahedral grid for the calculation of the E-field. A tetrahedral grid is generated from the segmented tissue boundaries, consisting of approximately 80,000 tetrahedrons per patient. Both methods base their calculations on segmented (contour based) CT or MR image data. Two numeric methods, FE and FDTD, are implemented in HyperPlan for solving Maxwell's equations. A number of hyperthermia-specific modules are provided, enabling the creation of three-dimensional tetrahedral patient models suitable for treatment planning. This system already contains powerful algorithms for image processing, geometric modeling, and three-dimensional graphics display. The planning system HyperPlan is built on top of the modular, object-oriented platform for visualization and model generation AMIRA. Data and observations obtained from clinical hyperthermia are compared with the numeric methods FE (finite element) and FDTD (finite difference time domain), respectively.
![hyperplan equation hyperplan equation](https://i.stack.imgur.com/6H2gI.jpg)
The main aim is to prove the clinical practicability of the hyperthermia treatment planning system HyperPlan on a beta-test level.