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Focal liver lesions (FLLs) are usually quantitatively assessed by time-intensity curves (TICs) extracted from contrast-enhanced ultrasound (CEUS) image sequences. To overcome the subjectivity of manual region of interest (ROI) selection and automatically extract TICs, a novel factor analysis method called replace approximation (RA) was proposed. Assuming that the two factors are the arterial and portal vein phases, respectively, the high-dimensional time-series data are mapped into 1-D space, where the TIC at each pixel in the image becomes a point along a one-dimensional axis. The RA method aims to seek two apexes corresponding to the factor curves (the targeted TICs) in the subspace. This method was tested on 18 free-breathing datasets with respiratory motion correction. The experimental results showed that the RA method extracted physiological factor curves and the corresponding factor images efficiently. The mean correlation coefficient between the factor curves and the corresponding ROI measurements was 0.95 ± 0.02. Furthermore, the wash-in time ratio indexes of FLLs derived from the factor curves were used to perform parametric imaging, which could represent the characteristics of different types of FLLs. These results indicate that two-factor analysis has the potential to perform quantitative analysis of hepatic perfusion, which would be helpful to the differential diagnosis of FLLs.