The Research Algorithm Of Deformable Image Registration Based On Demons Algorithm

The basic principle of radiation therapy is to make use of the physical properties of radiation and the radiation biology reaction of biological tissue cells to kill the tumor and achieve the objective of treatment. About70%of cancer patients need to receive radiation treatment in different periods of the disease course, such as radiotherapy alone, preoperative, postoperative and intraoperative radiotherapy or in combination with chemotherapy and so on. The goal of radiotherapy is to increase the gain ratio of radiation therapy, that is delivering sophisticated radiation treatments with precision and speed while reducing radiation exposure to surrounding healthy tissue. However, because of the patient set-up errors in fractionated radiotherapy (including External surface marker errors, the errors of Laser lights and treatment bed or the artificial operation errors), the target area shift and deformation in fractionated radiotherapy(resulting from the filling degree of organ, the weight change of cancer patient or the tumor deformation and shift), and the intrafraction target area motion(resulting from breathing, heart beats or Gastrointestinal Motility) in treatment stages will cause the position and shape change of organ. Owing to the high dose gradients during the treatment, slight changes in weight, position and anatomy of a patient may make critical organs involved in high dose area and even cause omission of target area, which will lead to a severe under-dosage of tumor or damage to the critical non-target organs. The above problems can be solved by image guided radiotherapy treatment (IGRT), which will keep target coverage and normal organ sparing. The confirmation of patient position and the tracking of organ motion all depend on the accuracy and real-time of image registration result. At the same time, according to the images obtained in every fractionated radiotherapy, the image registration technology can be used to measure the set-up errors to adjust the following radiotherapy plans. Besides, by using deformable registration, the dose distribution on planning CT can be deformed according to current anatomic structure to adjust the following radiation dose and re-optimize the treatment plan. With the development of radiotherapy technology, the deformable image registration plays an important role in the realization of the four dimensional radiotherapy. The deformable registration can be used to map the contour of the target into all other treatment images to perform automatic region-of-interest (ROI) delineation, which can save much time and labor. By using deformable registration, the cumulative dose distribution on different time phase can be mapped to the reference phase to evaluate the composite dose distribution. The use of deformation registration to realize image guided radiotherapy can improve the accuracy of the tumor radiation therapy effectively.Image registration is indeed to evaluate the similarity between two or more images, and the image registration algorithm is used to establish the relationship between two images, then the corresponding geometry transform parameters can be got to deform one of the images. With the rapid development of medical image equipment, medical image registration technology is also used widely and developed quickly, new technology and method will emerge more and more. There are two kinds of methods based on feature space, that is, methods based on gray and methods based on characteristic. The’demons’algorithm, proposed by Thirion in1998, was a fully automatic grey-scale-based deformable image registration algorithm. This algorithm only uses the gradient information of the static image to drive the deformation, however, it is inefficient when the gradient of the static image is small. In2005, Wang et al. put forth an’active demons’algorithm, in which an’active force’based on the gradient information of the moving image and an’passive force’based on the gradient information of the reference image were combined to deform the moving image to achieve more accurate and fast image registration. In2006, Rogelj et al. proposed a symmetric demons registration algorithm, which then is used in the deformable registration that based on the similarity measure. The method uses the average gradient information between the reference image and the moving image to be the demons force in order to increase the effectiveness of the registration result. Afterwards, Vercauteren et al. described a standard registration model, with a registration energy consisting of a similarity function, a transformation error function and a smoothness regularization, then the demons algorithm could be regarded as an optimization of the global energy function. The additive demons algorithm just achieves the non-rigid registration of medical images by optimizing the demons energy function, and the deformation field is updated by vector addition. Besides, they proposed that the alternate optimization scheme of the demons algorithm could be used in combination with the Lie group structure on diffeomorphic transformations.The paper introduces the theoretical knowledge of original demons algorithm, active demons algorithm and additive demons algorithm firstly, and on that basis, the registration experiment of mathematically deformed images is used to verify the advantage of additive demons algorithm. Compare to the original demons algorithm and the active demons algorithm, the additive demons algorithm achieves more accurate registration. Besides, the iteration number can be determined automatically to avoid low precision caused by too small iteration number and waste of time when the number is large. In addition, this paper also analyzes the diffeomorphic demons algorithm theoretically. The non-parametric diffeomorphic image registration algorithm indeed preserves the topology of the objects in the image by ensuring the inevitability of the output transformation. But the algorithms above only use the grey value constancy assumption and ignore the influence of gradient constancy assumption on the result of image registration.Based on Brox et al.’s gradient constancy assumption and Malis’s efficient second-order minimization (ESM) algorithm, an improved demons algorithm is proposed in this work. This assumption show that the gradient of the image grey value is not to vary due to the displacement. The gradient of the image grey value is invariant under grey value changes, which contributes to determine the displacement vector. Besides, the efficient ESM procedure uses the idea that when the images are aligned with the optimal spatial transformation s, the fixed image and the warped image as well as their gradient should be very close to each other. Thus, combining the grey value constancy assumption with the gradient constancy assumption, a grey value gradient similarity term and a transformation error term are added into the diffeomorphic demons energy function, and thus derived a formula to calculate the update of transformation field. At the same time, the algorithm is improved based on the original diffeomorphic demons algorithm in order to produce smooth invertible deformation field and ensure the topology of image. In this improved algorithm, the deformation fields is updated by exponential mapping and composition operation, which replaces the optimization process in Euclidean space in the original diffeomorphic demons algorithm. The limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm is used to optimize the demons energy function, thus the iteration number can be determined automatically. The improved registration method needs to optimize each pixel in the images, so it has a lot of calculation. The L-BFGS algorithm uses a limited memory variation of the BFGS algorithm, it is particularly well suited for optimization problems with a large number of variables. A coarse-to-fine multi-resolution approach can be used in the demons algorithm to reduce the effect of large deformation in image registration. At first, registration is performed iteratively starting with images at lower resolution with less time required. The resulting deformation field is used to initialize registration at higher resolution to achieve more accurate registration. Therefore, the multi-resolution approach can be used to realize faster convergence and higher registration accuracy.In this paper, a simple gel-balloon phantom is designed to simulate the deformation of the body organs. The CT images of the phantom are obtained to test the improved registration algorithm. The registration result of original diffeomorphic demons algorithm is not good, especially in the position of the needles, but by using the improved demons algorithm, no significant difference between the reference and the registered image is detected. Besides, the proposed method is demonstrated with mathematically deformed images and tumor images in clinic. In the experiment of mathematically deformed images, the fixed image is deformed using a known formula to get the moving image, comparing with the registration results using the DD algorithm, the IDD algorithm achieves higher precision and faster convergence speed, especially for larger deformations. To evaluate the performance of the IDD algorithm in clinical application, the CT images of a liver cancer patient are used in this experiment. In the fractionated radiotherapy, the moving image exhibits obvious deformations in patient position and tumor size. The registered image still has some error for so large deformation between the fixed image and the moving image, but the registration error of the algorithm we proposed is less than the original diffeomorphic demons algorithm. The value of the weighting coefficient γ reflects the role of the grey value gradient similarity in image registration. The extra30random trials are performed to validate the value of y, in these experiments, the weighting coefficient is set as0.1,0.15,0.3and0.35respectively, The MSE and CC are used to measure the registration result. The registration result shows that the IDD algorithm is more efficient than the DD method when the parameter γ=0.15. Besides, the registration accuracy of this value (0.15) is higher than the others (0.1,0.3, and0.35). The results of the above experiments show that the proposed method could improve the registration accuracy and increase the convergence rate, so it can realize more precise radiotherapy.