Simulated Annealing of the Radionuclide Distribution


At this point in the calibration process you should have completed all of the tasks described in the Central Axis Measurements section.

In this section of the tutorial we will modify the initial PS model that assumed a uniform distribution of patch-source strength over the surface of the plaque to instead create a nonuniform distribution of source strength which better reproduces the near-surface measurements provided on BEBIG protocol sheet 2.

This will be accomplished by first entering the surface measurement data and then launching a simulated annealing process which iteratively redistributes source strength amongst the patches with the objective of reducing the RMS % error between the calculated and measured dose at the near-surface measurement points.


The BEBIG protocol sheet 2 of near-surface measurments. The measurements highlighted in yellow, pink and blue are the ones that will be entered in the BEBIG Surface Measurements tab. The measurements highlighted in purple will NOT be used.

Set annealing parameters
  • In the BEBIG calibration window, click the Surface Measurements tab.
  • The picture of the plaque should match the protocol sheet orientation. If not, rotate the picture (click the Rotate button) to match the sheet.
  • In the Meas. height text field, enter the height above the concave surface of the plaque of the BEBIG surface measurements. By default, this height is 1 mm from the surface of the plaque, and is representative of retina dose.
  • From the protocol sheet the chord diameter of the 3rd ring (that corresponds to the blue tinted PS outermost ring) is defined as 13.0 mm for this plaque. Enter this value into the Outermost ring diameter text field. The outermost ring of point overlays should move to the edge of the plaque, at or slightly beyond the surface patches, as illustrated by the red arrow in the figure to the right.
  • Click the Autofill button to calculate the chord diameters of the innermost and middle rings, or enter values manually. The rings are assumed to be equiangularly spaced across the curved face of the plaque. The autofill function will calculate the angle subtended by the outermost ring and from that derive the angles and diameters of the innermost and middle rings. In this case the diameters are calculated to be 4.6 and 9 mm respectively.
  • The patch lower limit is the minimum fraction that a patch can decrease to, in this example no patch can be reduced to less than 0.20 (ie 20%) of its original (uniform distribution) strength.
  • The patch upper limit is the maximum fraction that a patch can increase to, in this example no patch can exceed twice (2.0) its original strength.
  • Start with 150 iterations of the surface annealing process in random order.

The Surface Measurements tab.




Enter surface measurements
  • The picture of the plaque should match the protocol sheet orientation. If not, rotate the picture (click the Rotate button) to match the sheet.
  • In the Show group click the Meas. (% center) button.
  • In the Picture group enable Show meas. pts and Label meas. pts by clicking the checkboxes as necessary.
  • Click the Enable nonuniform activity checkbox to enable the Solve button.
  • Enter the central measurement, and the 3 rings of surface measurements (tinted white, yellow, pink and blue in the figure above) from the protocol sheet into the simulated annealing control point fields as illustrated.
  • Near-surface measurements that are not directly above the silver surface of the plaque (tinted purple in the figure above) can not be used for simulated annealing, so the outermost ring from the protocol sheet (values of 2, 5, 10 etc...) in this example will not be entered, nor will the measurements at 9 o'clock (4 and 14) situated directly over the notch.Set all unused simulated annealing text fields to zero (0.00).
  • Fill in all the remaining simulated annealing control points for which measurements are not provided, provided those points are above the plaque surface. You may optionally use the Autofill function to interpolate the presumed missing elements of the middle and outer rings.
  • In this figure, the near-surface measurement points from the BEBIG protocol sheet are overlayed onto their corresponding data entry fields. Only the measurements that are highlighted in yellow, pink and blue are to be entered. Measurements beyond the edge of the plaque, highlighted in purple, corresponding to the most distal ring of the protocol sheet and measurements above the notch, are not used by PS. Any PS data entry fields for which measurements are not provided on the protocol sheet MUST be estimated, for example, by interpolating between the surrounding measured points, and may optionally be set to zero if they are outside the plaque perimeter or are not over a portion of the plaque where radionuclide is deposited except for optic nerve notches. The two missing measurements of the middle ring located at roughly 7 and 11 o'clock had to be manually estimated since the missing measurements are near a notch.
  • To perform the simulated annealing, PS calculates a control point (the hundreds of small black cubes and text in figure to right) 1 mm above the center of each patch source (illustrated as hexagons) and angularly interpolates normalized dose rate target values from the measured data points (the larger blue cubes with larger text labels in the figure).

    • Optionally, click the Distribute Activity Uniformly button to clear the results of a previous solution.
    • Set the annealing order to Random.
    • Click the Solve button to redistribute the radionuclide strength via a surface annealing process. A progress window will appear. Simulated annealing of the many hundreds of patches is a lengthy process and can take many minutes to complete.
    • Optionally repeat the Solve button until the RMS error no longer decreases. In this tutorial, two (2) passes of 150 iterations each were employed. The first reduced the surface RMS % error from 9% to 4.634%. The second pass further reduced the error to 4.567%.
    • You can follow the annealing process by observing the brightness of the patches which vary as a function of their source strength.
    • Note the final RMS error.

    • You may optionally experiment between the From center and random annealing orders by repeating the step above using the From center setting instead of Random.
    • Proceed to manual fine-tuning of the central axis calibration.
    • If you attempt to reproduce this example, your RMS error may vary slightly because the simulated annealing order involves some randomness.
    • The poor central axis fit seen in the dose profile window will be corrected in the next step by manually fine-tuning the central axis calibration.