We introduce and validate four adaptive models (AMs) to perform a physiologically based Nested-Model-Selection (NMS) estimation of such microvascular parameters as forward volumetric transfer constant, Ktrans, plasma volume fraction, vp, and extravascular, extracellular space, ve, directly from Dynamic Contrast-Enhanced (DCE) MRI raw information without the need for an Arterial-Input Function (AIF). In sixty-six immune-compromised-RNU rats implanted with human U-251 cancer cells, DCE-MRI studies estimated pharmacokinetic (PK) parameters using a group-averaged radiological AIF and an extended Patlak-based NMS paradigm. One-hundred-ninety features extracted from raw DCE-MRI information were used to construct and validate (nested-cross-validation, NCV) four AMs for estimation of model-based regions and their three PK parameters. An NMS-based a priori knowledge was used to fine-tune the AMs to improve their performance. Compared to the conventional analysis, AMs produced stable maps of vascular parameters and nested-model regions less impacted by AIF-dispersion. The performance (Correlation coefficient and Adjusted R-squared for NCV test cohorts) of the AMs were: 0.914/0.834, 0.825/0.720, 0.938/0.880, and 0.890/0.792 for predictions of nested model regions, vp, Ktrans, and ve, respectively. This study demonstrates an application of AMs that quickens and improves DCE-MRI based quantification of microvasculature properties of tumors and normal tissues relative to conventional approaches.