Fractal analysis for assessing the level of modulation of IMRT fields

Abstract

To investigate the potential of three fractal dimension (FD) analysis methods (i.e., the variation, power spectrum, and variogram methods) as metrics for quantifying the degree of modulation in planned intensity modulated radiation therapy (IMRT) treatment fields, and compare the most suitable FD method to the number of monitor units (MUs), the average leaf gap, and the 2D modulation index (2D MI) for assessing modulation. The authors implemented, validated, and compared the variation, power spectrum, and variogram methods for computing the FD. Validation of the methods was done using mathematical fractional Brownian surfaces of known FD that ranged in size from 128 × 128 to 512 × 512. The authors used a test set consisting of seven head and neck carcinoma plans (50 prescribed treatment fields) to choose an FD cut-point that ensures no false positives (100% specificity) in distinguishing between moderate and high degrees of field modulation. The degree of field modulation was controlled by adjusting the fluence smoothing parameters in the Eclipse™ treatment planning system (Varian Medical Systems, Palo Alto, CA). The moderate modulation fields were representative of the degree of modulation used clinically at the authors' institution. The authors performed IMRT quality assurance (QA) on the 50 test fields using the MapCHECK™ device. The FD cut-point was applied to a validation set consisting of four head and neck plans (28 fields). The area under the curve (AUC) from receiver operating characteristic (ROC) analysis was used to compare the ability of FD, number of MUs, average leaf gap, and the 2D MI for distinguishing between the moderate and high modulation fields. The authors found the variogram FD method to be the most suitable for assessing the modulation complexity of IMRT fields for head and neck carcinomas. Pass rates as measured by the gamma criterion for the MapCHECK™ IMRT field measurements were higher for the moderately modulated fields, and a gamma criterion with 1 mm distance-to-agreement and 1% dose difference showed a clear separation between the 94% pass rates of the moderate and high modulation groups. From the ROC analysis of the test set, the authors found the AUC of the variogram FD, number of MUs, average leaf gap, and 2D MI methods to be 0.99 (almost perfect), 0.91 (excellent), 0.91 (excellent), and 0.92 (excellent), respectively. A cut-point of FD > 2.25 correctly identified 92.8% of the high modulation fields and 100% of the moderately modulated fields in the validation set, satisfying the condition of no false positives. Of the three FD methods investigated, the variogram method is the most accurate and precise metric for identifying high modulation treatment fields. It is also more accurate and precise than the number of MUs, the average leaf gap, and the 2D MI. Although MapCHECK™ IMRT QA does a reasonable job at identifying high modulation fields, the variogram FD method provides one with the opportunity to quantitatively and accurately assess modulation and adjust overly modulated fields at the treatment planning stage before they are sent to the treatment machine for QA or patient treatment.