Ultrasound molecular imaging (USMI) is an emerging technique to monitor diseases at the molecular level by the use of novel targeted ultrasound contrast agents (tUCA). These consist of microbubbles functionalized with targeting ligands with high-affinity for molecular markers of specific disease processes, such as cancer-related angiogenesis. Among the molecular markers of angiogenesis, the vascular endothelial growth factor receptor 2 (VEGFR2) is recognized to play a major role. In response, the clinical-grade tUCA BR55 was recently developed, consisting of VEGFR2-targeting microbubbles which can flow through the entire circulation and accumulate where VEGFR2 is over-expressed, thus causing selective enhancement in areas of active angiogenesis. Discrimination between bound and free microbubbles is crucial to assess cancer angiogenesis. Currently, this is done non-quantitatively by looking at the late enhancement, about 10 min after injection, or by calculation of the differential targeted enhancement, requiring the application of a high-pressure ultrasound (US) burst to destroy all the microbubbles in the acoustic field and isolate the signal coming only from bound microbubbles. In this work, we propose a novel method based on mathematical modeling of the binding kinetics during the tUCA first pass, thus reducing the acquisition time and with no need for a destructive US burst. Fitting time-intensity curves measured with USMI by the proposed model enables the assessment of cancer angiogenesis at both the vascular and molecular levels. This is achieved by estimation of quantitative parameters related to the microvascular architecture and microbubble binding. The proposed method was tested in 11 prostate-tumor bearing rats by performing USMI after injection of BR55, and showed good agreement with current USMI methods. The novel information provided by the proposed method, possibly combined with the current non-quantitative methods, may bring deeper insight into cancer angiogenesis, and thus potentially improve cancer diagnosis and management.