Verification of helical tomotherapy delivery using autoassociative kernel regressiona)
Raw detector sinogram data for helical tomotherapy treatment delivery. The left panel shows a macroscopic view of the detector data, and the right panel shows an enlarged view of six projections. All MLC leafs are closed at the beginning and the end of each projection. The intensity is modulated by adjusting the time that each MLC leaf is open for each projection.
Diagram depicting the kernel regression process. First, the distance between the query inputs and the historical memory exemplars is calculated. Next, the distances are converted into weights or similarities using the kernel function. Finally, the similarities of the query to each of the input exemplars are combined with the output exemplars to obtain estimates of the output.
Examples of some common kernel functions.
Example Gaussian kernels. Gaussian kernel with the smaller bandwidth will only generate large weights when the distance is very close to zero, while the kernel with the larger bandwidth is less specific and will assign significant weights for a larger range of distances.
Illustration of (a) inferential, (b) heteroassociative, and (c) autoassociative model architectures. In the inferential architecture, inputs are used to predict a single output. A heteroassociative model uses inputs to predict outputs. In an autoassociative model, the input exemplars perform the same action as the output exemplars.
MLC positional error for the prostate test case (A) without known errors and (B) with known errors. In this example, the AAKR technique correctly identified that a MLC leaf opened late and closed early from compressed exit detector data that were attenuated by an anthropomorphic phantom.
MLC positional error for the H and N test case (A) with known errors and (B) without known errors. In this example, the AAKR technique correctly identified a MLC timing errors of .
MLC positional error for the lung test case (A) with known errors and (B) without known errors. In this example, the model was developed with detector data from the (1) No error with only the couch in the path of the beam, and (3) No error with a cylindrical phantom in the path of the beam. The model was then tested with detector data from the error and error-free deliveries with the motion phantom in the path of the beam. Using deliveries with stationary objects in the path of the beam to develop the model, and then testing the motion with data from deliveries that had motion, illustrates that the model will not be degraded by changes in a patient’s breathing pattern or patient motion during the treatment.
AAKR Model Predictions for Projection 212 of the prostate. (a) Error with a cylindrical phantom in the path of the beam sinogram detector data and (b) no error with a cylindrical phantom in the path of the beam sinogram detector data illustrating how the model can detect machine output errors. This error was not purposely inserted and was caused by a temporary decrease in the accelerator’s output.
AAKR Model Predictions with their 95% Prediction Intervals for Projection 310 of the prostate “Error with a cylindrical phantom in the path of the beam” sinogram. No distinguishable errors were present in this sinogram, which is also reflected in the low uncertainty values. This low uncertainty is evidence of the model’s accuracy.
Doses were recalculated in the tomotherapy planning system to show the dose difference for the lung case with errors vs the lung case without errors. The 0.1% dose difference isodose lines and the DVHs for both cases are shown.
Key for the errors that were purposefully inserted into the delivery sequence from actual patient treatment plans. The resulting error did not only depend on the percent reduction in the individual MLC leaf’s closing time, but also on how long the leaf was originally open in the projection and its position in the given projection.
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