An alternative to the pulse sequences at present used in dynamic contrast uptake MRI is the dynamic LL-EPI T(1) mapping method. This method generates T(1) estimates in a few seconds, thereby allowing dynamic studies. A particular advantage of the LL-EPI technique is that it provides the opportunity to generate spatial and temporal information about the paramagnetic contrast agent concentration independently of the inflow rate. This paper illustrates, by computer simulations, the accuracy of the estimated 1/T(1) value when using the LL-EPI technique in situations that are not supported by the model. The simulated situations not supported by the model are those in which the longitudinal and transversal relaxation rates change during the T(1) mapping. The most critical moment occurs during a bolus passage of contrast agent when the concentration gradient is large. The computer simulations of the LL-EPI T(1) mapping method in non-supported situations show that in normal perfused capillary tissue the error in the estimated 1/T(1) value is within the absolute error of 0.1 s(-1) in most simulated situations, although in a typical vessel the simulations do indicate that the stated absolute error tolerance of 0.5 s(-1) is exceeded relatively easily. However, this transgression can be rectified by a non-bolus injection of the contrast agent media.