Mathematical Analysis of Arterial Enhancement and Optimization of Bolus Geometry for CT Angiography Using the Discrete Fourier Transform

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Abstract
The goal of this work was to develop a clinically applicable mathematical algorithm to analyze and optimize individual arterial enhancement in CT angiography (CTA). Assuming a time-invariant linear system, the discrete Fourier transform was used to calculate the transfer function of the system ("patient function") from the arterial time-attenuation response to a test bolus. The patient function was subsequently used to predict aortic enhancement in five select patients and to calculate optimized biphasic injection protocols in two of these patients undergoing CTA of the abdominal aorta. Arterial time-attenuation curves were accurately predicted in all patients. Optimized biphasic contrast agent injection protocols resulted in uniform aortic enhancement at the predefined level over the entire scanning period in both subjects despite markedly different contrast agent volumes and injection rates used. Fourier analysis of the time-attenuation response to a test bolus is a simple and feasible approach to optimize arterial enhancement in CTA.