A realistic model of the anatomical texture from the pulmonary interstitium was developed with the goal of extending the capability of anthropomorphic computational phantoms (e.g., XCAT, Duke University), allowing for more accurate image quality assessment. Contrast-enhanced, high dose, thorax images for a healthy patient from a clinical CT system (Discovery CT750HD, GE healthcare) with thin (0.625 mm) slices and filtered back- projection (FBP) were used to inform the model. The interstitium which gives rise to the texture was defined using 24 volumes of interest (VOIs). These VOIs were selected manually to avoid vasculature, bronchi, and bronchioles. A small scale Hessian-based line filter was applied to minimize the amount of partial-volumed supernumerary vessels and bronchioles within the VOIs. The texture in the VOIs was characterized using 8 Haralick and 13 gray-level run length features. A clustered lumpy background (CLB) model with added noise and blurring to match CT system was optimized to resemble the texture in the VOIs using a genetic algorithm with the Mahalanobis distance as a similarity metric between the texture features. The most similar CLB model was then used to generate the interstitial texture to fill the lung. The optimization improved the similarity by 45%. This will substantially enhance the capabilities of anthropomorphic computational phantoms, allowing for more realistic CT simulations.