Method of Calculating Percentage Depth Dose for Diagnostic X‑rays by iaj67571

VIEWS: 7 PAGES: 9

									Received Jan. 6, 2004;    Revision accepted May 26, 2004;       Code No. 873


     Summary




       Key words: Diagnostic X-ray, Percentage depth dose, Monte Carlo simulation
               f                                                R
                                                                                    d
                                   D d R


      D( d , R) = Dp ( d ) + Ds ( d , R)

                   Dp d                                             Ds d R




      Dp ( d ) = ∫0 max ∆Dp ( E, d ) ⋅ ω ( E ) ⋅ dE
                       E



       ∆Dp E d                               d                          E

                                                                        2
                                                         f 
      ∆Dp ( E, d ) = ∆Dp ( E, 0) ⋅ exp{− µ ( E ) ⋅ d} ⋅       
                                                         f + d


       E                                E


       E


                               Φ( E )
      ω ( E) =                                                                                                          f    f +d
                        Φ( E ) ⋅ dE
                   Emax
                   ∫
                   0


    Φ E                                  E
    E max                                                                                                                                          R


                                                                                                                    2
      Ds ( d , R) = ∫0 max ∆Ds ( E, d , R) ⋅ ω ( E ) ⋅ dE
                           E
                                                                                                           f  R⋅ f + d
                                                                                        ∆Ds ( E, d , R) =        ⋅ ∫ f 2πr ⋅ F(r ) ⋅ δ ( E, d , r ) ⋅ dr
                                                                                                           f + d 0
    ∆Ds E d R                                    E                                R
                                                            d                                     F r               r


                                             2
                         f  R⋅ f + d
      ∆Ds ( E, d , R) =        ⋅ ∫ f 2πr ⋅ δ ( E, d , r ) ⋅ dr
                         f + d 0

                                                                                                      E
       E d r                                                                  E                 ∆D p E
                                                                                                      E
d                                                 r                                                             d                                            r
                                        E d r                                                                                         E d r
                                                                                        ∆Dp E              E d r
                                                                                                   Dp d                             Ds d R
                                                                                                                            Dp d
                           ∆Ds E d R                                        E d r                 ∆Dp E
                                                                                                            Ds d R


                                                                    f       f+d                                     E               ∆Dp E
                                                      F r




    E d r




    ∆


                              ∆Dp E
            E d r




                    − =               −
=



                                                                E
                                                            E




                                                  ∆Dp E
                                          E d r




                          E       ∆D p            ×
E
                                                              =   =   ×




                                                      ×   ×



        ×        ×


                            ×                                     ×



 ×




             E
∆Dp E                           ∆Ds E d R
                                            ∆Dp
E           ∆Ds E d R



                        ×                         =
                =
=                           =       =       ×




                    ’   =               ’       =
    =       ×                   =




        ×
                    ’           =       =   =
        =   ×




=
        ×       ×           ×


                                    =
                                    =   ×




×


    ×       ×           ×
            ’   =       ’   =
    =               =




=       =
        ×
                          E d r
            F r




=                     =   ×


=           =


=                     =   ×


=                     =   ×


=       =


=                     =   ×


                  =               =


    =                                 =   ×


=


=

								
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