In this paper, we present a fully automatic, fast and accurate deformable registration technique. This technique deals with free-form deformation. It minimizes an energy functional that combines both similarity and smoothness measures. By using calculus of variations, the minimization problem was represented as a set of nonlinear elliptic partial differential equations (PDEs). A Gauss-Seidel finite difference scheme is used to iteratively solve the PDE. The registration is refined by a multi-resolution approach. The whole process is fully automatic. It takes less than 3 min to register two three-dimensional (3D) image sets of size 256 x 256 x 61 using a single 933 MHz personal computer. Extensive experiments are presented. These experiments include simulations, phantom studies and clinical image studies. Experimental results show that our model and algorithm are suited for registration of temporal images of a deformable body. The registration of inspiration and expiration phases of the lung images shows that the method is able to deal with large deformations. When applied to the daily CT images of a prostate patient, the results show that registration based on iterative refinement of displacement field is appropriate to describe the local deformations in the prostate and the rectum. Similarity measures improved significantly after the registration. The target application of this paper is for radiotherapy treatment planning and evaluation that incorporates internal organ deformation throughout the course of radiation therapy. The registration method could also be equally applied in diagnostic radiology.

Convolution/superposition (C/S) is regarded as the standard dose calculation method in most modern radiotherapy treatment planning systems. Different implementations of C/S could result in significantly different dose distributions. This paper addresses two major implementation issues associated with collapsed cone C/S: one is how to utilize the tabulated kernels instead of analytical parametrizations and the other is how to deal with voxel size effects. Three methods that utilize the tabulated kernels are presented in this paper. These methods differ in the effective kernels used: the differential kernel (DK), the cumulative kernel (CK) or the cumulative-cumulative kernel (CCK). They result in slightly different computation times but significantly different voxel size effects. Both simulated and real multi-resolution dose calculations are presented. For simulation tests, we use arbitrary kernels and various voxel sizes with a homogeneous phantom, and assume forward energy transportation only. Simulations with voxel size up to 1 cm show that the CCK algorithm has errors within 0.1% of the maximum gold standard dose. Real dose calculations use a heterogeneous slab phantom, both the 'broad' (5 x 5 cm2) and the 'narrow' (1.2 x 1.2 cm2) tomotherapy beams. Various voxel sizes (0.5 mm, 1 mm, 2 mm, 4 mm and 8 mm) are used for dose calculations. The results show that all three algorithms have negligible difference (0.1%) for the dose calculation in the fine resolution (0.5 mm voxels). But differences become significant when the voxel size increases. As for the DK or CK algorithm in the broad (narrow) beam dose calculation, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 10% (7%) of the maximum dose. As for the broad (narrow) beam dose calculation using the CCK algorithm, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 1% of the maximum dose. Among all three methods, the CCK algorithm is demonstrated to be the most accurate one for multi-resolution dose calculations.

Delineating regions of interest (ROIs) on each phase of four-dimensional (4D) computed tomography (CT) images is an essential step for 4D radiotherapy. The requirement of manual phase-by-phase contouring prohibits the routine use of 4D radiotherapy. This paper develops an automatic re-contouring algorithm that combines techniques of deformable registration and surface construction. ROIs are manually contoured slice-by-slice in the reference phase image. A reference surface is constructed based on these reference contours using a triangulated surface construction technique. The deformable registration technique provides the voxel-to-voxel mapping between the reference phase and the test phase. The vertices of the reference surface are displaced in accordance with the deformation map, resulting in a deformed surface. The new contours are reconstructed by cutting the deformed surface slice-by-slice along the transversal, sagittal or coronal direction. Since both the inputs and outputs of our automatic re-contouring algorithm are contours, it is relatively easy to cope with any treatment planning system. We tested our automatic re-contouring algorithm using a deformable phantom and 4D CT images of six lung cancer patients. The proposed algorithm is validated by visual inspections and quantitative comparisons of the automatic re-contours with both the gold standard segmentations and the manual contours. Based on the automatic delineated ROIs, changes of tumour and sensitive structures during respiration are quantitatively analysed. This algorithm could also be used to re-contour daily images for treatment evaluation and adaptive radiotherapy.

Real-time knowledge of intra-fraction motion, such as respiration, is essential for four-dimensional (4D) radiotherapy. Surrogate-based and internal-fiducial-based methods may suffer from one or many drawbacks such as false correlation, being invasive, delivering extra patient radiation, and requiring complicated hardware and software development and implementation. In this paper we develop a simple non-surrogate, non-invasive method to monitor respiratory motion during radiotherapy treatments in real time. This method directly utilizes the treatment beam and thus imposes no additional radiation to the patient. The method requires a pre-treatment 4DCT and a real-time detector system. The method combines off-line processes with on-line processes. The off-line processes include 4DCT imaging and pre-calculating detector signals at each phase of the 4DCT based on the planned fluence map and the detector response function. The on-line processes include measuring detector signal from the treatment beam, and correlating the measured detector signal with the pre-calculated signals. The respiration phase is determined as the position of peak correlation. We tested our method with extensive simulations based on a TomoTherapy machine and a 4DCT of a lung cancer patient. Three types of simulations were implemented to mimic the clinical situations. Each type of simulation used three different TomoTherapy delivery sinograms, each with 800 to 1000 projections, as input fluences. Three arbitrary breathing patterns were simulated and two dose levels, 2 Gy/fraction and 2 cGy/fraction, were used for simulations to study the robustness of this method against detector quantum noise. The algorithm was used to determine the breathing phases and this result was compared with the simulated breathing patterns. For the 2 Gy/fraction simulations, the respiration phases were accurately determined within one phase error in real time for most projections of the treatment, except for a few projections at the start and end of the treatment in which beam intensities were extremely low. At 2 cGy/fraction dose level, the method can still determine the respiration phase very well with less than 10% of projections having more than two phases (approximately 1 s) error. This technique can also be applied in other delivery systems such as orthogonal x-ray systems, although in those cases it would entail the delivery of additional non-treatment radiation.