We have developed a non-invasive imaging tracer kinetic model for blood flow which takes into account the distribution of capillaries in tissue. Each individual capillary is assumed to follow the adiabatic tissue homogeneity model. The main strength of our new model is in its ability to quantify the functional distribution of capillaries by the standard deviation in the time taken by blood to pass through the tissue. We have applied our model to the human prostate and have tested two different types of distribution functions. Both distribution functions yielded very similar predictions for the various model parameters, and in particular for the standard deviation in transit time. Our motivation for developing this model is the fact that the capillary distribution in cancerous tissue is drastically different from in normal tissue. We believe that there is great potential for our model to be used as a prognostic tool in cancer treatment. For example, an accurate knowledge of the distribution in transit times might result in an accurate estimate of the degree of tumour hypoxia, which is crucial to the success of radiation therapy.