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Biomedical Imaging by Sebastian Aeffner, Timo Aspelmeier, Tim Salditt

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D(z)=D^(z)*12πσexp(z22σ2)=12πσRpD^(z)exp((zz)22σ2)dz.(5.58)

This leads to a rather complex, but closed analytic expression for the ‘real’ proton Bragg curve D(z), including some tabulated special functions. The Bragg peak now has a finite maximum and is in very good agreement with experimental data [12]. Here, we have carried out the convolution numerically (σ = 0.16 cm). The resulting Bragg curve is plotted in Figure 5.12 (solid line). A finite spectrum of initial energies further contributes to the broadening of realistic Bragg peaks. In radiotherapy with protons, the superposition of several quasi monoenergetic beams is employed to create a so called spread out Bragg peak with an almost homogeneous dose plateau in a certain ...

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