2882 The Application of Kernel Principal Component Analysis in Complexity Evaluation of Radiation Therapy

H. Yan, S. Zhou, L. Marks, F. Yin

Duke University Medical Center, Durham, NC

Purpose/Objective(s): A novel tool is proposed for complexity evaluation in radiotherapy clinical outcome study. Byperforming a nonlinear Kernel Principal Component Analysis (KPCA), one can efficiently compute principal components inhigh-dimensional feature spaces, and project the data onto eigenvectors in high-dimension and use the projections as a new setof variables.

Methods: Principal Component Analysis (PCA) is an orthogonal basis transformation. The new basis is found by diagonalizingthe centered covariance matrix of a data set. The projection of the data set along the eigenvector s of the above matrix are calledprincipal components. The eigenvalue of eigenvector v of the covariance matrix equals the amount of variance in the originaldata set along the direction of v. The principal components along the first n eigenvectors retain the maximum amount ofinformation contained in the original data set.

Assume that our data is mapped into feature space and properly centered by nonlinear map�: x3 �(x), �(x1), �(x2), ..., �(xL).After an analysis of the covariance matrixC�1/L� �(xi) �(xi)T.We get eigenvalues and eigenvector s satisfying�V�CV.This implies that we may consider the equivalent system.��(xj), �ivi����(xj), Cvi�, j�1, ..., L.By defining Kij�� �(xi), �(xj)�, we get the expressionL�i�i�K�i.

for a new PCA, where � is eigenvalue and � is eigenvector. We solve the eigenvalue problem for nonzero eigenvalues. Clearly,all solutions belonging to nonzero eigenvalues is principal component in high dimensional feature space. If n is large enoughto take into account all directions belonging to eigenvector s with non-zero eigenvalue , we can reconstruct signal in featurespace rather than in input space. The projection of �(x) on span{v1, v2, ..., vn} can be calculated as

�i�� vi, �(xj)�� ��ij�� (xi),�(xj)�, i�1, ..., L.�i is the projections of �(x) on the first several eigenvector s corresponding to principle components. Note that the projection

of �(x)is not necessarily expressed explicitly in high-dimension feature space, all inner product ��(xi),�(xj)� in high-dimension can be implemented by the non-linear operators, such as polynomial, sigmoid functions.

Results: A clinical data containing 64 subjects with left-sided breast cancer treated with tangent photon fields is used as testcase. The goal is to determine the relationship between patient characteristics (including demographic and therapeuticparameters) and perfusion defect 6 month post radiotherapy treatment. The patient characteristics are first mapped to ahigh-dimensional space based on non-linear PCA, and then its projection along the eigenvector s were obtained. The resultedprojection data was finally used as inputs of a Back-Propagation neural network for prediction. The result shows that fewprinciple components of non-linear PCA possess comparable variation as those achieved by the traditional linear PCA. Theneural network prediction accuracy was improved as the new variables achieved from KPCA is used.

Conclusions: Linear PCA can extract at most N components, where N is the dimensionality of the data. KPCA, on the otherhand, allows the extraction of up to L features, where L is the number of training examples. This tool can be particular usefulfor radiotherapy clinical studies because many of the dosimetric, patient demographic variables are not explicitly linear-correlated.

Author Disclosure: H. Yan, None; S. Zhou, None; L. Marks, None; F. Yin, None.

2883 Assessment of the Relative Biological Effectiveness of Clinical Carbon Ion Beams

A. J. Chang, H. D. Suit, H. Paganetti

Massachusetts General Hospital, Boston, MA

Background: Recently, interest in carbon ion radiotherapy for the treatment of various malignancies has grown due to theirparticular physical and radiobiological properties, which provide accurate dose conformation and increased relative biologicaleffectiveness. Studies have demonstrated a 1.5- to 3-fold increase in biological effectiveness in the treatment of the distal partof the tumor volume relative to the effectiveness on the surrounding healthy tissues, which could be attributed to the high linearenergy of transfer of the carbon ion. In comparison, the relative biological effectiveness for proton therapy has beendemonstrated to be approximately at 1.1. However, large variations in RBE values for carbon beams have been observed andhave been attributed to the dependencies of RBE values on different factors such as dose, LET, and �/�.

Purpose/Objective(s): Treatment planning algorithms need to incorporate RBE modelling based on a limited set of experi-mental data. This study investigates the relationship of RBE as a function of various parameters such as dose, LET, and �/�.The data gained from this study can be incorporated into a biophysical model for future treatment planning.

Materials/Methods: The published results from twelve independent in vitro studies were reviewed and analysed. Various celllines (HSG cells, AT478 squamous carcinoma cells, BY-2 tobacco cells, NG1RGB human fibroblasts, HFL-III, LC-1 sq, A-549lung adenocarcinoma, C32TG amelanotic melanoma, SK-MG-1, KNS-89, KS-1, A-172, ONS-76, KNS-60, Becker, T98Gglioblastoma, SF126, Syrian hamster embryo Cells, Chinese hamster V79 lung cells, AG1522B fibroblasts, PS1 porcine skinfibroblasts) were utilized in these studies. All RBE values were normalized relative to 60Co. RBE values were extracted fromthe middle of the Spread Out Bragg Peak (SOBP) and plotted as a function of dose, LET and a/b.

Results: After the data from the previous studies were thoroughly analyzed, an increase in RBE values was observed withdecreasing doses. RBE values remained approximately at 1.5 at doses above 3 Gy. However, a dramatic rise in RBE values wasobserved at a dose slightly below 3 Gy with RBE values rising up to 4 at approximately 2 Gy. Furthermore, a relationshipbetween RBE and LET was identified. A trend supporting an increase in RBE value with an increase in LET was observed. RBEvalues increased from 1.5 at approximately 5 keV to approximately 3.4 at 50 keV, and then subsequently retuned approximately

S709Proceedings of the 48th Annual ASTRO Meeting

to 1.5 at 70 keV. Finally, the relationship between RBE and a/b was evaluated. Although it has been assumed that RBE increaseswith decreasing a/b, the data analysed in this study can not conclusively support the assumption.

Conclusions: Institutions that treat patients with carbon ion beams currently assume an RBE of about 3.0 in the target volume.Based on our data analysis, this assumed RBE value appears reasonable. However, large variations with dose, LET and a/b canbe expected. As generally undisputed and predicted by all biophysical models, RBE increases with LET to a maximal value andthen decreases. Also, as can be expected due to the shouldered survival curve after 60Co irradiation, RBE increases withdecreasing radiation dose. Some RBE models used in clinical applications of carbon ions are based on the assumption that thereis an increase in RBE when a/b decreases. The data support a trend but not a one-to-one correlation.

Author Disclosure: A.J. Chang, None; H.D. Suit, None; H. Paganetti, None.

2884 Treatment of Canine Bladder Cancer Using Laparoscopically Implanted Tissue Expander Radiotherapy(LITE-RT)

A. N. Gutierrez, S. M. Murphy, L. J. Forrest, T. R. Mackie

University of Wisconsin, Madison, WI

Purpose/Objective(s): The aim of this study was to use LITE-RT to isolate and target the urinary bladder in dogs withtransitional cell carcinoma and reduce acute and chronic side effects to critical structures by decreasing their dose. LITE-RTis a technique which geometrically displaces the PTV through the use of a laparoscopically-placed, custom shaped tissueexpander (TE).

Materials/Methods: Two dogs with confirmed and fully staged TCC of the bladder underwent biopsy and tumor evaluationvia cystoscopy. Custom shaped TE, 440ml and 240ml, (Spec. Surg. Products, Victor MT) were developed and placed betweenthe bladder and colon via sutures to the prepubic tendon. Laparoscopic placement was performed in one dog and laparotomyplacement in the other. A planning CT was acquired with the TE inflated. The TE was inflated with a saline/contrast mix priorto each treatment to the same volume as the planning CT. The dogs underwent fractionated radiotherapy (2.5 Gy x 18 � 45Gy). Using tomotherapy, a MVCT was done prior to each treatment and fused to the planning kVCT to ensure accurate organpositioning. The TE was removed one week after completion of therapy. Colonoscopy and cystoscopy were performed priorto therapy in 2 dogs and 1 week after therapy in 1 dog. Clinical signs of bowel and urinary habits were monitored.

Results: Pretreatment cystoscopy and ultrasonography revealed a 2.5x2.4 cm tumor surrounding the right ureter in one dog anda 5.5x5.5 cm tumor involving the majority of the ventral bladder wall and neck in the second dog. Both dogs received all 18fractions with minimal radiation side effects. Visual organ displacement and bladder isolation was adequate on the planning CT.Sutures anchoring the TE pulled through the prepubic tendon in both dogs requiring an additional surgery. One dog had aforeign body reaction to the TE forming a fibrous capsule surrounding the TE. No signs of colitis were observed in either dog.Clinical signs of pollakiuria and incontinence worsened during therapy but resolved after treatment. One week follow upcystoscopy was available in one dog, and tumor volume was significantly decreased–ureteral papilla was now visual.Colonoscopy and biopsy obtained prior to and after therapy in this dog showed no change. Three months post therapy dog iscontinent with no hematuria.

Conclusions: Use of LITE-RT is feasible in the treatment of spontaneous TCC of the canine bladder. Early results of thistechnique show promise. Lack of acute colitis in this study represents a large decrease in previously reported patient morbidities.Future studies are planned to measure the bladder motion with TE inflation and quantize the daily repositioning accuracy.

Author Disclosure: A.N. Gutierrez, None; S.M. Murphy, None; L.J. Forrest, None; T.R. Mackie, Mackie has a financial interestin TomoTherapy Inc., E. Ownership Interest.

2885 Three-Dimensional Dose Verification for Radiation Therapy

P. Guo1, J. Adamovics2, M. Oldham1

1Duke University Medical Center, Durham, NC, 2Rider University, Lawrenceville, NJ

Purpose/Objective(s): Sophisticated dose delivery techniques like intensity-modulated radiation therapy (IMRT) requiredetailed dose verification in 3D for comprehensive validation of correct implementation. Previously we presented extensive‘small volume’ studies on a new material PRESAGETM, with promise as a breakthrough material for accurate and convenient3D dosimetery. Here this work is extended, and the first comprehensive 3D dosimetric verification of both conformal and IMRTdistributions, using PRESAGETM, is presented.

S710 I. J. Radiation Oncology ● Biology ● Physics Volume 66, Number 3, Supplement, 2006