Limitations of a convolution method for modeling geometric uncertainties in radiation therapy. II. The effect of a finite number of fractions

Abstract

Convolution methods can be used to model the effect of geometric uncertainties on the planned dose distribution in radiation therapy. This requires several assumptions, including that the patient is treated with an infinite number of fractions, each delivering an infinitesimally small dose. The error resulting from this assumption has not been thoroughly quantified. This is investigated by comparing dose distributions calculated using the Convolution method with the result of Stochastic simulations of the treatment. Additionally, the dose calculated using the conventional Static method, a Corrected Convolution method, and a Direct Simulation are compared to the Stochastic result. This analysis is performed for single beam, parallel opposed pair, and four-field box techniques in a cubic water phantom. Treatment plans for a simple and a complex idealized anatomy were similarly analyzed. The average maximum error using the Static method for a 30 fraction simulation for the three techniques in phantoms was 23%, 11% for Convolution, 10% for Corrected Convolution, and 10% for Direct Simulation. In the two anatomical examples, the mean error in tumor control probability for Static and Convolution methods was 7% and 2%, respectively, of the result with no uncertainty, and 35% and 9%, respectively, for normal tissue complication probabilities. Convolution provides superior estimates of the delivered dose when compared to the Static method. In the range of fractions used clinically, considerable dosimetric variations will exist solely because of the random nature of the geometric uncertainties. However, the effect of finite fractionation appears to have a greater impact on the dose distribution than plan evaluation parameters.

PTV margin for dose‐escalated radiation therapy of prostate cancer with daily online realignment using internal fiducial markers: Monte Carlo approach and dose population histogram (DPH) analysis

“…( 14 , 15 ) For each voxel, dose was converted to the normalized total dose (NTD), (16) which is the biologically equivalent dose in 2 Gy/fraction. The formula used to convert dose to one voxel for the i th fraction to NTD is ${\text{NTD}}_{i}MJX-TeXAtom-ORD\frac{d_{MJX-TeXAtom-ORDi}[\alpha /\beta +d_{MJX-TeXAtom-ORDi}]}{\alpha /\beta +2\text{Gy}},$ where α and β are the parameters in the linear‐quadratic model.…”

Quantifying the interplay effect in prostate IMRT delivery using a convolution‐based method

“…8 The Calypso system ͑Calypso Medical Technologies, Inc., Seattle, WA͒ is capable of real-time tracking of the intrafraction prostate motion, 9 therefore the actual dose delivered in the presence of intrafraction motion can be evaluated by convolving the static dose distribution with the motion probability density function ͑PDF͒. Similar approaches have been reported previously [10][11][12][13][14][15][16][17][18] to account for setup errors and organ motion in other tumor sites. The conventional convolution approach uses the PDF generated by population-based motion data, 15 e.g., an entire fraction, an entire treatment course of a patient, or even an entire patient population.…”

A predictive method of calculating the dosimetric effect of 1-D motion on narrow multileaf collimated segments

“…A caveat being that our method is restricted to homogeneous media by the inherent nature of the convolution. In heterogeneous media shift invariance becomes a problem (24,25) and therefore our particular approach assumes there is no distortion in the volume and that there are no heterogeneities in the irradiated material.…”