Detailed internal information of lung morphology is made possible by the advent of four-dimensional computed tomography (4D-CT) and fast magnetic resonance imaging (MRI). Motion information is needed, and may be vital, in radiotherapy for lung cancer treatment, where having a very accurate modeling of the organ motion and deformation due to breathing is a challenging task. Deformable registration methods can be used to estimate deformations between 3D-CT images corresponding to different anatomical states. In this work our goal is to propose a motion model that follows lung and tumor displacements and deformations in order to extract and analyze physiological parameters like nonlinearity and hysteresis of motion during free breathing. We used a lagrangian approach tu build the motion model from vector fields computed between the reference end-of-exhale phase and all others. The motion model was evaluated for accuracy and consistency. Non-linearity and hysteresis of the lung motion were than estimated. To evaluate motion hysteresis, we introduce a measure inspired by the Frechet distance from computational geometry. Results demonstrate that lung motion during free-breathing is prone to nonlinearity and hysteresis, and that these physiological effects vary across different regions within the lung. However, for 3D-CTs with a 2.5 mm inter-slice distance, motion between end-exhale and end-inhale is well approximated with a straight-line trajectory for approximately 95% of both lungs for patients 1 and 3, and approximately 80% of both lungs for patient 2. Physiological information like nonlinearity and hysteresis of lung motion could be integrated to create a general lung atlas, with multiple clinical applications like inter-patient breathing studies, detection of specific (abnormal or not) breathing situations, and precise dosimetry study in radiotherapy.