Physiological parameters associated with blood perfusion, such as blood flow, blood volume, vascular transit times and blood vessel leakiness, can potentially provide diagnostic and prognostic information about the pathological tissue. These microcirculatory parameters can be extracted from dynamic contrast enhanced (DCE) images. Recent developments in imaging technologies have allowed significant improvements in both the spatial and temporal resolutions of DCE imaging datasets. For quantitative analysis of such datasets, more realistic models of tissue microcirculation can be developed. In this study, distributed-parameter (DP) tracer kinetics models were developed and applied to clinical DCE X-ray Computed Tomography data for various tumors. A multiple-compartment, mammillary DP model that accounts for more than one kinetically distinct compartment within the tissue interstitial, was developed. This model has been further enhanced by including the distribution of capillary transit times to account for different capillary lengths in the tissue. These models were tested using clinical DCE images to study their applicability in the clinical setting. A comparative study of distributed- and lumped-parameter compartmental models was also performed. This work demonstrates that these DP models can be practically applied for analysis of tumor DCE imaging data, and encourages the use of such models on clinical DCE imaging datasets.