Lung cancer is the most rampant killer among cancer types, taking more American lives per year than automobile accidents. This staggering annual death toll, along with our citizenry's unwillingness to cease smoking, has lead to a research emphasis on lung cancer treatment techniques. Real-time treatment of a lung tumor requires accurate tracking of both the Planning Target Volume and the nearby healthy radiosensitive tissues. An imaging modality called 4DCT (Four-Dimensional Computed Tomography) provides accurate tracking by taking a 3D image of the lungs at each phase of the breathing cycle. Once these images are taken, a method is required to link the many phases together and track changes between them. This method is called Image Registration. Standard techniques of Image Registration track these changes using rigid motions. Lungs move in a more complicated fashion than rigid methods can handle. A more detailed form of registration, Deformable Image Registration, is required for 4DCT tracking. Many deformable image registration algorithms exist. One must be chosen. The purpose of this paper is to experimentally compare four well-studied deformable image registration algorithms (Horn-Schunk Optical Flow, Thirion's Demons, and Yang's Inverse-Consistent versions of each) as they apply to 4DCT DICOM lung images. These four algorithms were coded in MATLAB with only user-created functionality. The algorithms, codes, and functions are explained in complete detail and alternative methods are provided. The algorithms were applied to ten patient data sets. Standard conditions for parameters were taken from previous recommendations. Tests were performed using Sum of Square Differences measurements to determine each algorithm's quantitative potential. The algorithms were also timed, and their final resulting images were saved for qualitative analysis. The results demonstrate that the optimal choice for Deformable Image Registration in 4DCT DICOM lung images, especially for small deformations, is the Inverse-Consistent version of Thirion's Demons algorithm. Inverse-Consistent Demons provided high quality images, a satisfactory computation speed, and the best quantitative potential.