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Study Of The Unequal Spheres Packing Problem: An Application To Radiosurgery Treatment

Author

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  • S. P. LI

    (Institute of Physics, Academia Sinica, Nankang Taipei, Taiwan 115, R.O.C)

  • KA-LOK NG

    (Department of Bioinformatics, Taichung Healthcare and Management University, No. 500, Lioufeng Road, Wufeng Shiang, Taichung, Taiwan 413, R.O.C)

Abstract

We employ the Monte Carlo method to study a constrained optimization problem — packing hard spheres with unequal radii(r2> r1)into a 3D bounded region and discuss its connection with the Gamma Knife radiosurgery treatment planning. Selection of the best fit solution is based on the Boltzmann factor,e-ΔE/T, which allows us to search for the global optimal solution. As an illustration we determined the least number (≤15) of packed spheres that will occupy the largest volume for three different hypothetical tumor sizes (4115, 10 000 and 36 000 voxels). For the bounded regions and the sizes of the packed spheres that we studied here, the optimal volume packing ratio ranges from 41.3 to 48.7%. From our study, using a lowerr2/r1ratio is more desirable due to the ≤15 radiation shots constraint. The optimal volume packing ratio can be obtained within a relative short CPU computing time and could provide a good starting point for the radiosurgery treatment planning.

Suggested Citation

  • S. P. Li & Ka-Lok Ng, 2003. "Study Of The Unequal Spheres Packing Problem: An Application To Radiosurgery Treatment," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 815-823.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:06:n:s0129183103004966
    DOI: 10.1142/S0129183103004966
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    References listed on IDEAS

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    1. A. Sutou & Y. Dai, 2002. "Global Optimization Approach to Unequal Global Optimization Approach to Unequal Sphere Packing Problems in 3D," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 671-694, September.
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