1. Overview
The effect of TLV on the dose distributions observed by the target and the surrounding
tissue was computed using 3D convolution and demonstrated on two test cases: an ideal,
computergenerated, spherically symmetric target and dose distribution; and a 2arc,
10fraction treatment plan used to treat a representative lung lesion in a human subject.

2. ComputerGenerated Target and Dose Model
A 3D, spherically symmetric dose distribution was created to simulate the ideal dose
field size for a 12 mm diameter, spherical lesion. The dose field consisted of a uniform
dose at the center of the target region that fell off as a function of r3 at the target
edge according to the equation:
Dmax = peak dose within the target, Rt = target radius, and R90 = radius of the flat
central plateau at maximum dose. R90 is defined such that the dose at the target edge
becomes 90% in the presence of the r3 falloff. For Dmax = 110% and Rt = 6 mm, R90
becomes 4.4 mm. To simulate the effects of varying the treatment margin size, R90 was
increased or decreased, while Dmax and Rt were kept at fixed values.


3. Lung Lesion Treatment Plan
A ~12 mmdiameter tumor was chosen that was located posteriorlyinferiorly in a patient’s
left lung. The treatment plan consisted of 6MV Xrays administered in two 110degree arcs
separated from each other by 20 degrees. Each arc was administered daily at 2.5 Gy/fraction,
during independent ~15second breathholds, and repeated daily over 10 days of treatment,
for a total of 50 Gy.
(the isodose contours at 90, 80, 50, and 30% of maximal dose are shown) 

4. Optimization of (Positive) Margins
For the computergenerated dataset, for each margin size and TLV, the resulting tumor DVH
and minimal tumor dose were computed. The margin size was adjusted in onetenth millimeter
increments; the optimal margin value was found by iteration that achieved a minimum tumor
dose of 90%. For the lung lesion plan, dose distributions were first generated for margins
of 28 mm, and for the 7x7x10 mm marginplan used for the actual radiotherapy treatment,
and the corresponding optimal TLV values were then determined by iteration.

5. Optimization of Very Small (& Negative) Margins
When using very small margins, dose blurring effect will significantly shift the DVH curve
for the target down and to the left, giving unfavorable results. Based upon the dose
broadening simulations for each margin, a scaling factor can be computed and applied to
the dose distribution such that the minimum tumor dose will be identical to the desired
therapeutic minimum dose. The criterion used for comparing several different margin sizes
after scaling was the minimization of lung volume receiving 80% of the maximum dose.
