One of the most powerful features of the dynamic contrast-enhanced (DCE) MRI technique is its capability to quantitatively measure the physiological or pathophysiological environments assessed by the passage of contrast agent by means of model-based pharmacokinetic analysis. The widely used two-compartment pharmacokinetic model developed by Brix and colleges fits tumor data well in most cases, but fails to explain the biexponential arterial input function. In this work, this problem has been attacked from a theoretical point of view, showing that this problem can be solved by adopting a more realistic model assumption when simplifying the general solutions of the two-compartment pharmacokinetic equations. Pharmacokinetic parameters derived from our model were demonstrated to have comparative tissue specificity to Ktrans from Larsson's model, better than those from Brix's model and the empirical area-under-the-curve (AUC). Tissue-type classifier constructed with the arterial input function–decomposed kep-kpe pair from our model was also demonstrated to have superior performance than any other classifier based on DCE-MRI pharmacokinetic parameters or empirical AUC. The feature that this classifier has a near-zero false-negative rate makes it a highly desirable tool for clinical diagnostic and response assessment applications.