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In a Computed Tomography Angiography (CTA) exam, synchronization of contrast peak in the vasculature and the x-ray aperture is highly desirable. The current existing method of moving CT scanner table constantly is far from ideal and needs large amount of contrast material for compensation. We propose an adaptive bolus chasing method, which ensures a high Contrast to Noise Ratio (CNR) of the vascular images in CTA and potentially reduces the radiation exposure and contrast usage. The proposed method is based on a local time and space parameter varying model of the contrast bolus. Optimal scan time for the next segment of the vasculature is estimated and predicted in real time and guides the CT scanner table movement which guarantees that each segment of the vasculature is scanned with the maximum possible enhancement. Simulation and experimental results show that the proposed bolus-chasing method outperforms the conventional constant-speed method substantially.