Calculation Accuracy

RAHD's MultiDimensional^TM Analysis requires an approach to calculations that can accurately handle all of the beam modifiers. We start with special care in the way beam data is stored. Measured beam data for both open fields and wedged fields, saved with an improved level of accuracy.

FINE Storage of Measured Beam Data

Measured beam data is stored using the Bentley-Milan approach with storage of tables of data corresponding to the intersection of diverging fan lines with measured cross scans. This provides an inherent geometric correction and brings inherent advantages for calculation of penumbral effects for all of the beam modifiers. One Hundred and One (101) fanlines are used for every field size. This improves accuracy for smaller fields. It also allows use of data well outside the field edge for improved accuracy in critical structures with multiple fields with MultiDimensional^TM Analysis.

The calculation of a single point:

A Central-Axis-Depth-Dose (CADD) value is determined from the measured data sets, corresponding to the field size (or equivalent square for rectangular fields). For the Central Axis calculation plane only the X-axis Off-Axis Ratio (OAR) values are used. For every point for the selected depth, this ratio is multiplied by the dose value determined at the Central Axis for the corresponding depth.

Calculating an OFF-AXIS Plane

For each point in the calculation grid, two Off-Axis-Ratios (OAR's) are used: one corresponding to the X coordinate location, the other distance corresponding to the Y coordinate location. The Y coordinate value is chosen from the same X-direction cross-scan data. Multiplication of these two values provides an Off-Axis-Ratio which is considered equivalent to the value one would measure at this location, corresponding to perfectly symmetrical beams.

Calculating the effect of Collimator Rotation

For collimator rotation additional geometric measurements are is required to determine the appropriate corresponding values for the X axis OAR and the Y axis OAR.

The CLARKSON Integration. . .

Scatter contribution is determined for each point by performing a Clarkson integration using 36 10° sectors. Beam's Eye View (BEV) shows the over-all blocking pattern for the entire field (up to 20 blocks). Each block has individually specified attenuation and the primary radiation passing through the block contributes to the scatter from under each block to every calculation point.

Blocked Beam AlgorithmTM

As a result of a RAHD calculation tool known as the Blocked Beam algorithm, the intensity is calculated to be approximately 50% of the Central Axis dose at the nominal field edge, at machine calibration distance. This dose gradually decreases under the block until it reaches the block transmission value. In all cases, radiation getting through the block or collimator contributes scatter for the Blocked-Beam-Generator^TM integration.

The dose calculated will appear to be higher than the amount expected from the block transmission factor alone, as you move away from the Central Axis, along the Y direction up or down. This is because the CT cuts are transverse cuts, while the beam geometry is diverging through the CT cuts. The RAHD ray tracing approach as originally designed for the Blocked-Beam-Generator^TM handles this effect very well. This approach also provides a firm basis for accurate calculations for MultiDimensional^TM Analysis.

Generating an EQUIVALENT BEAM. . .

The RAHD Blocked-Beam-Generator^TM Clarkson integration is performed for each of the 101 fanline intersections for measured cross scan data. This process is repeated for each depth (Dmax and others as measured). A new set of curves is generated that shows the change at Dmax as a result of blocking, and the generated equivalent cross scans for each depth. Both the original measured set and the generated set are displayed on a single graph that is scaled and normalized to the Dmax Central Axis value. Formatted scaled hard-copy may also be plotted. Curves generated very graphically show the effect of blocks in the real clinical world, such as accurately accounting for the fill-in from scatter at depth under kidney and cord blocks.

Missing Blocks . . .

Earlier systems (and some today) ignore the effect of the block pattern away from the plane being calculated. Significant errors may result during Clarkson calculation of scatter contributions if the complete block pattern is not considered. The RAHD Blocked-Beam-Generator^TMtakes into account all blocks including conformal blocks designed in the BEV as well as all other beam modifiers. This provides optimal accuracy for multiple plane calculations, allows accurate calculation of planes between the available CT slices, and provides the confidence needed for useful MultiDimensional^TM Analysis.

Shadowing of Blocks

Penumbra for Blocks and the Collimator

Blocks located at different distances within the beam can affect the dose quite differently. As collimator jaws are close to the source and the beam diverges at the greater projected distance a broad "fuzzy" penumbra results. Blocks on the tray closer to the patient and will yield a relatively "sharp" penumbra.

The location of each block (up to 20 per beam) along with the transmission value for each block provides the Blocked-Beam-Generator^TM with the data to modify both the primary and scatter contribution to each point calculated to achieve extremely accurate beam modeling.

Adding a WEDGE

Adding a wedge increases the number of Blocked-Beam-Generator^TM calculations by an additional factor of forty (40). Machine data files include measured cross scans for wedges for the range of field sizes to be treated and five depths for each field size (plus a surface scan). These data quantify the wedge's differential attenuation from toe to heel, and give the value of primary radiation transmitted. The 40 strip sectors provide 40 values of attenuation of primary radiation shadowed by that region. This changes the scatter contribution from that region to every point calculated in Blocked-Beam-Generator^TM dose calculations. With the slower processors used in the '80s, 20 wedge sectors consumed more time than most were willing to wait. With the advent of dynamic wedges the number of sectors was increased to forty (40) to improve calculation accuracy.

And the COMPENSATOR. . .

Compensators are also handled within the Blocked-Beam-Generator^TM. The compensator is displayed on the BEV graphics, along with the blocks, and if a wedge is used, the wedge icon. The compensator is displayed as a matrix of squares, each representing a 1 cm area as shadowed by direct ray tracing to the level of the isocenter. Each compensator segment is supplied with a transmission value as measured for and corresponding to the specific energy used. Ray tracing through each segment then impacts the primary radiation which is used to determine the value of scatter added into the calculation for every point calculated during the BBG^TM Clarkson integration.

This greatly increases the complexity of the calculations required. The number of operations required is directly proportional to the number of compensator segments (for a 12cm x 12cm field = 144 pieces).

The RAHD Blocked-Beam-Generator^TM was originally developed by the Department of Medical Physics at the University of Utah. Although it has been used clinically for over 12 years, one can appreciate that the elegance of this accurate approach to calculations could not really come into its own until the arrival of full 64-bit processing and super-computer power.

Now, the power and the accuracy of the RAHD Blocked-Beam-Generator^TM provides unparalleled accuracy in dose calculations and including rotated collimators and couches, conformal blocking, asymmetric jaws, dynamic wedges, and compensators. Alpha™ power, merged with the elegant RAHD Blocked-Beam-Generator^TM now provides true MultiDimensional^TM Analysis.