In radiation therapy, it is imperative to deliver high doses of radiation to the tumor while reducing radiation to the healthy tissue. Respiratory motion is the most significant source of errors during treatment. Therefore, it is essential to accurately model respiratory motion for precise and effective radiation delivery. Many approaches exist to account for respiratory motion, such as controlled breath hold and respiratory gating, and they have been relatively successful. They still present many drawbacks. Thus, research has been expanded to tumor tracking. This paper presents a spatio-temporal model for four dimensional CT reconstruction. The method begins with a set of initial CT projections and a simultaneously acquired breathing trace. Two methods are explored to model the spatial components: principal component analysis and a pseudoinverse matrix method. An iterative approach is used to match the simulated projections to the actual projections. The simulated projections and the initial projections are evaluated using Normalized Root Mean Square Error (NRMSE). The proposed method shows simulated projections and actual projections match, and as such the model is able to accurately predict the deformation.