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In this paper we perform a numerical study of the tranverse expansion ofhadronic scattering amplitudes in the dipole picture of high energy QCD. We gobeyond the mean field approximation by including fluctuations and also wavefunction saturation effects, and the evolution with both a fixed and a runningcoupling is investigated. We also study the nonperturbative aspects, and as hasbeen predicted earlier, our results indicate that the Froissart-Martin bound issaturated once confinement effects are included in the evolution. Thus thetotal cross section increases proportional to the square of the logarithm ofthe cms energy. Furthermore it is seen that we obtain a reasonable value forthe proportionality coefficient. The impact of saturation and non-leadingeffects on this coefficient is also studied.

On the High Energy Behaviour of The Total Cross Section in the QCD Dipole Model