The temporal contrast of high-peak-power lasers is usually limited by pre-pulses, which are generally produced by post-pulses due to the nonlinearity of the active medium. The reason for the conversion between pre-pulse and post-pulse is now well known, but the mechanisms for the delay-shift and asymmetric broadening of the newly generated pre-pulse are not yet clear. In this work, a novel, to the best of our knowledge, numerical model combining the nonlinear Schrödinger equation and the Frantz-Nodvik equation is proposed to investigate the underlying mechanisms for the "distortion" of the pre-pulse. Numerical results show that the gain characteristics of Ti:sapphire amplifiers can only make a minor change on the temporal profile of the pre-pulse, but the high-order dispersion is the main cause for the delay-shift and asymmetric broadening of the pre-pulse, and the effects are more significant for the initial post-pulse with a relatively larger delay.