Simulated Annealing of the Radionuclide Distribution

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.


  • At this point in the calibration process you should have completed all of the tasks described in the Central Axis Measurements section.
  • In the BEBIG calibration dialog, click the Surface Measurements tab.
  • In the Show group click the Meas. (% center) button.
  • The picture of the plaque should match the protocol sheet orientation. If not, rotate the picture or sheet as necessary.
  • Enter the meas. height of the BEBIG surface measurements, this is typically 1 mm from the surface of the plaque.
  • Enter the central, and 3 rings of surface measurements 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 can not be used for simulated annealing, so the outermost ring of the protocol sheet (values of 2, 5, 6 etc...) in this example will not be entered, nor will the measurement at 9 o'clock (6) situated directly over the notch.
  • Fill in all remaining simulated annealing control points for which measurements are not provided, provided those points are over the plaque surface. Set all unused simulated annealing fields to zero (0.00).
  • Enter the radius of the PS outermost ring as 8.3mm. From the protocol sheet the diameter of the 3rd ring (that corresponds to the PS outermost ring) is defined as 17.1 mm. Dividing this by 2 yields a radius of 8.55 mm. However, in the PS model of the plaque, that would place the point over the exact edge of the plaque where there are no underlying radionuclide patches, so subtract 0.25mm to make sure the ring sits above a radionuclide patch source in the PS model.
  • Equally space the inner and middle ring radii between the center and outermost ring. In this case the radii were rounded to 2.75 and 5.5 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 0.10 (ie 10%) 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 a patch range of 7. The radionuclide patches are modeled as hexagons. The value of 7 is the number of patches that include a hexagon and its adjoining hexagons. The surface annealing algorithm will redistribute source strength equally to the 7 closest patches to a measurement point until the upper or lower limits are reached. After the 7 closest patches have reached their strength limits, nighboring patches will be included sorted by distance from the measurement point.
  • Start with 150 iterations of the surface annealing process in random order.
  • Check the Enable nonuniform activity checkbox and then click the Solve button to begin the redistribution of radionuclide strength via a surface annealing process.
BEBIGProtocolSurfaceData

The BEBIG protocol sheet 2 of near-surface measurments. The measurements highlighted in yellow are the ones that will be entered into PS.

COBSurface2a

The PS Surface Measurements tab.

COBSurface2b

In this figure, the near-surface measurement points from the BEBIG protocol sheet are overlayed onto their corresponding PS data entry fields. The most distal ring of the protocol sheet, beyond the edge of the plaque, is not used by PS. Any PS data entry fields for which measurements are not provided on the protocol sheet MUST be approximated, for instance, by interpolating the measured points, or set to zero if they are outside the plaque perimeter or are not over a portion of the plaque where radionuclide is deposited.


  • Repeat the Solve button until the RMS error no longer decreases.
  • The brighness of the patches is proportional to their redistributed source strength.
  • In this example, after clicking the solve button twice (ie 300 iterations total), the RMS error fell from 30.507 to 9.208. If you attempt to reproduce this example, your RMS error may vary slightly because the simulated annealing order involves some randomness. The poorer central axis fit seen in the dose profile window will be corrected in the next step.
  • Proceed to manual fine-tuning of the central axis calibration.
COBCalibration4
COBDoseProfile4

Click on this link to proceed to Manual fine-tuning of the central axis calibration.


Calibration | Certificates | Axial Measurements | Surface Measurements | Manual Tuning | Fine-Tuning Steps
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