The reference region model can quantify tumour perfusion without needing an arterial input function (AIF) and provides relative estimates, i.e. KTrans/KTrans,RR and ve/ve,RR which are usually converted to absolute KTrans and ve by using literature-based values for KTrans,RR and ve,RR. However, this approach fails to account for inter-patient variability. This study proposes a method that uses the Reference Region and AIF Tail (RRIFT) to estimate patient-specific KTrans,RR and ve,RR. The AIF tail is the post-peak part of the AIF and is easier to measure than the complete AIF. Evaluation in simulation and in-vivo showed that RRIFT provides comparable results to Tofts model, and even outperforms the Tofts model at slower temporal resolutions.