Objective assessment of medical image quality can be performed with mathematical model observers matched to radiologists. Foveated channelized Hotelling observer models (FCHO) have been shown to be more accurate predictors of the human search performance in simulated 3D images than standard model observers such as the ideal observer or the non-prewhitening observer with eye filter. However, nothing is known about the performance of FCHOs with the computed tomography (CT) modality as well as with images extracted from real patients. Patient-extracted images are smaller than simulated images and their size could be limiting for FCHOs as peripheral vision is modeled by an increasing spatial extent of channels. This study has two aims: to extend a foveated model observer to 2D anatomical liver CT images and to find channel parameters enabling the FCHO to match human performance. Regions of interest (ROIs) were automatically extracted from CT images of five patients’ livers and their size was of 100x100 pixels, a balance between the anatomical constraints and the modeling of peripheral vision. Two radiologist-validated small low-contrast hypodense hepatic metastases were simulated to generate signal-present ROIs. The signal diameters were of 1 cm relatively to the patient and their contrast of -50 HU. The foveated model observer used was a FCHO with dense difference-of-Gaussians channels that were optimized to the size of the extracted ROIs. The performance of the optimized FCHO could reproduce human performance for a detection task in anatomical liver CT images within standard error up to 9 degrees of visual angle. This study shows that optimized FCHOs could be used in more anthropomorphic assessments of image quality of CT units.