Planning of Radiation Treatment

  • Udo Ebert
Part of the The IBM Research Symposia Series book series (IRSS)


The aim of radiotherapy is to destroy a malignant tumour. In accomplishing this goal one has to spare the healthy tissue and organs as much as possible since otherwise they could perish. Thus, the total irradiation time should be short.

These considerations lead to a mathematical model in which constraints reflect the restrictions on the dosage — lower bounds in the tumour and upper bounds in the healthy tissue. The time of irradiation becomes the objective function of the optimization problem. By fixing some of the possible parameters of the treatment one gets a model in which the velocity of the source of radiation can be determined. This solution is approximated, solving a linear and quadratic or parametric programming problem. The model is implemented as a programming system for radiation-treatment planning. An example is given showing its application to a kidney tumour.


Radiation Treatment Healthy Tissue Target Point Kidney Tumour Polygonal Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1].
    U.Ebert: Optimale Auslegung von Bestrahlungsplanen, Schriftenreihe des Rechenzentrums der Universitat Munster, Nr. 19, 1976Google Scholar
  2. [2]
    U.Ebert: Computation of Optimal Radiation Treatment plans, to appearGoogle Scholar
  3. [3]
    U.Ebert: A System for Calculating Optimal Radiation Treatment Plans, to appearGoogle Scholar
  4. [4]
    IBM Application Program, Mathematical Programming System /360: Control Language, User’s Manual, IBM-Form H20–02 90–1Google Scholar
  5. [5]
    IBM Application Program, Mathematical Programming System /360 Version 2: Linear and Separable Programming – User’s Manual, IBM–Form GH20–0476–2Google Scholar
  6. [6]
    IBM System /360 Operating System, PL/I(F): Language Reference Manual, IBM–Form GC28–8201–3Google Scholar
  7. [7].
    C.E.Lemke: Bimatrix Equilibrium Points and Mathematical Programming, Management Science 11 (1965), 681–689CrossRefGoogle Scholar
  8. [8].
    S.Matschke, J.Richter, K.Welker: Physikalische und technische Grundlagen der Bestrahlungsplanung, Leipzig 1968Google Scholar
  9. [9].
    H.Pudlatz: GEOMAP - ein FORTRAN-Programm zur Erzeu-gung von Choroplethen-und Isolinienkarten auf dem Schnelldrucker, Schriftenreihe des Rechenzentrums der Universitat Munster, Nr. 16, 1976Google Scholar
  10. [10].
    A.Ravindran: A Computer Routine for Quadratic and Linear Programming Problems (alg.431), Communications of the ACM 15 (1972), 818–820Google Scholar
  11. [11].
    M.Simmonard: Linear Programming, Englewoods Cliffs, 1966Google Scholar
  12. [12].
    T.D.Sterling, H.Perry, L.Katz: Automation of Radiation Treatment Planning, IV. Derivation of a mathematical expression for the per cent depth dose surface of cobalt 60 beams and visualisation of multiple field dose distributions, British Journal of Radiology 37 (1964), 554–550CrossRefGoogle Scholar
  13. [13]
    T.D.Sterling, H.Perry, J.J.Weinkam: Automation of Radiation Treatment Planning, V. Calculation and visualisation of the total treatment volume, British Journal of Radiology 38 (1965), 906–913CrossRefGoogle Scholar
  14. [14]
    T.D.Sterling, H.Perry, J.J.Weinkam: Automation of Radiation Treatment Planning, VI. A general field equation to calculate per cent depth dose in the irradiated volume of a cobalt 60 beam, British Journal of Radiology 40 (1967), 463–468CrossRefGoogle Scholar
  15. [15]
    J.J.Weinkam, A.Kolde: Radiation Treatment Planning System Manual, Saint LouisGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Udo Ebert
    • 1
  1. 1.Computing CenterUniversity of MünsterWest Germany

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