Patent Abstract:
the invention relates to a method for evaluating treatment - relevant spatial anatomical information among different data sets of the heart , the method comprising the steps of :— determining a reference anatomical 3 dimensional data set of the heart ,— providing a first anatomical 3 dimensional data set of the heart , the first anatomical 3 dimensional data set comprising first treatment - relevant spatial anatomical information ,— providing a second anatomical 3 dimensional data set of the heart , the second anatomical 3 dimensional data set comprising second treatment - relevant spatial anatomical information ,— registering the reference data set to the first and the second data sets ,— transferring the treatment relevant spatial anatomical information of the first and the second data set to the reference data set in order to generate a first transferred treatment - relevant spatial anatomical information on the reference data set and a second transferred treatment - relevant spatial anatomical information on the reference data set — evaluating the first and the second transferred treatment - relevant spatial anatomical information .

Detailed Description:
we present a novel method to investigate this problem by comparing pre - planned ablation lines defined by an experienced clinician . although actual ablation lines may differ from their targets , a comparison among desirable ablation lines does provide insight into how much ablation lines may vary along certain parts of the left atrium . we propose a framework for transfer of ablation planning information among different left atria heart models . initially , a statistical shape model of the left atrium is generated to serve as a common basis . this approach is possible to transfer ( spatially organized ) annotations from input data to the previously computed common model . by projecting the different annotations onto to the common model , we can compare the different annotations and extract common features . by way of example , this makes it possible to compare different planning structures used in the context for atrial fibrillation ablation . further on , it can be used as basis for an automatic planning approach . when applied to planning an atrial fibrillation ablation , different anatomical configurations of the left atrium have to be considered . this could be addressed by using a common basis for each configuration , e . g . for pulmonary veins , a common pulmonary vein or supernumerary vein . the left atria are segmented from 3 - d data sets ( ct , c - arm ct , mri ) and modeled as triangle meshes . the correspondence between different left - atrial models is calculated via non - rigid registration of the model . transfer of planning lines from the mesh - model a to mesh - model b is carried out as follows : first , model a is registered to model b . afterwards , the planning data from model a is projected to model b . the proposed solution can contain the following contributions : first of all , it uses a non - rigid point cloud based registration algorithm , for example coherent point drift , to generate a statistical shape model of the left atrium . secondly , spatially organized information , e . g . pulmonary vein isolation ablation planning lines are transferred and merged across multiple specific anatomies . the statistical shape model of the left atrium can be used as a reference model to perform rf ablation planning , e . g . for pulmonary vein isolation ( pvi ). the second aspect enables us to transfer these annotations onto new unseen mesh models . this functionality can be used for automatic procedure planning . this invention proposes a method for left atrium shape modeling using non - rigid point cloud registration . in our approach , we generate the shape model from 3 - d magnetic resonance imaging ( mri ) volume data sets . we exclusively used data sets of left atria with four pulmonary veins , which reflects the most common anatomic configuration [ 10 ]. first , the relevant structure was segmented and represented as triangle mesh . then we used the coherent point drift ( cpd ) algorithm [ 11 ] to pairwise align meshes via non - rigid point cloud registration . basically , cpd registration is performed based on a gaussian mixture model ( gmm ) framework and a regularization of the displacement field . benefits of the cpd algorithm are the generation of smooth deformation fields while being robust against noise and outliers [ 11 ]. left atrium mesh models of ten subjects were extracted from contrast enhanced 3 - d mri volume data sets . the mri data sets were acquired with a resolution of 256 × 256 × 68 voxels . the in - plane pixel spacing was 1 . 23 × 1 . 23 mm and the slice thickness 1 . 5 mm . the left atrium was segmented from mri voxel data sets using a semi - automatic segmentation software ( syngo inspace ep , siemens ag , forchheim , germany ). the segmentation process is initialized by manually selecting a point inside the left atrium . based on this seedpoint , the complete left atrium is segmented automatically . the segmentation results are represented as triangle meshes . for registration , let us consider the mesh as a point cloud m consisting of n points x i ∈ r 3 m ≡ m =[ x 1 t , . . . , x n t ] t ∈ r 3n ( 1 ) in a first step , we selected one left atrium mesh model as a reference mesh . the reference mesh was chosen based on visual inspection to clearly express the la anatomy . the reference mesh m ref is then registered to a set of sample meshes { m t } t t = 1 , with t = 9 , using the cpd algorithm . all meshes have the same anatomical orientation , and are zero centered before applying the registration . we used the coherent point drift ( cpd ) algorithm to register the reference mesh to the set of sample meshes . cpd follows a probabilistic approach by considering the alignment of the two point sets as a probability density estimation problem . the basic idea is to fit the gmm centroids , represented by the points of the reference mesh m ref , to the sample mesh m t , by maximizing the likelihood . this optimization is performed with the expectation maximization algorithm . during the optimization process , the gmm centroids are forced to move coherently as a group , to ensure preservation of the topological structure of the point set . the displacement function v for the reference mesh is defined as with m ref as the initial centroid positions , { circumflex over ( m )} ref and v , respectively are obtained by minimizing the following energy function [ 12 ]: where φ ( v ) is a regularization to ensure the displacement field to be smooth . x n denotes a point of the mesh m t , y m a point of the transformed mesh { circumflex over ( m )} ref , respectively . n and m refer to the number of points within the respective mesh . the parameter λ determines the trade - off between data fitting and smoothness of the deformation field . we empirically determined a suitable value for this parameter ( λ = 2 . 0 ). the reference mesh m ref is registered to every sample mesh m t . the transformed mesh { circumflex over ( m )} ref is labeled y t for ease of use . the training set is defined as v ={ m ref , v 1 , . . . , v t }. we used a principle component analysis ( pca ) approach [ 13 ] to compute the modes of variation . applying pca to the covariance matrix of the centered version of v yields a set of eigenvectors e 1 describing the principle modes of variation in the training data set . the eigenvectors are ordered in descending order based on the value of their corresponding eigenvalue . the p largest eigenvectors are stored in the matrix φ =[ e 1 , . . . , e p ]∈ r 3n × p . a linear combination of the p principal modes of variation , with b ∈ r p as weighting factors , spans a subset of linearized mesh models composed of the given modes of variation : for quantitative evaluation of the proposed framework , we used ten clinical data sets with manually annotated pulmonary veins ( pv ) ostia . these landmarks are labeled rspv ( right superior pulmonary veins ), ripv ( right inferior pulmonary veins ), lspv ( left superior pulmonary veins ), and lipv ( left inferior pulmonary veins ). the quality of the registration is measured based on residual landmark distances and mesh - to - mesh distance . the residual landmark error is defined as the euclidean distance of the center of corresponding pv ostia and measured after non - rigid cpd registration . quantitative registration results are shown in fig5 and discussed in more detail below . fig5 ( a ) shows the average mesh - to - mesh distance , as well as the initial and residual landmark offset per data set . the initial and residual offsets per landmark are shown in fig5 ( b ) . the average mesh - to - mesh distance is between 2 . 5 and 5 . 1 mm , the average landmark offset is between 2 . 9 and 13 . 9 mm . the highest mesh - to - mesh distance occurs at the end of the pulmonary veins . in this case especially on the right inferior pv . we described a method for left atrium shape modeling using non - rigid point cloud registration . the overall performance of the mesh registration shows a mean mesh - to - mesh error of 3 . 4 mm over all data sets . the coherent point drift algorithm was capable of dealing with high variations in anatomy . the highest residual mesh - to - mesh distance results from different extents of the pulmonary veins . the average landmark offset was 8 . 5 mm . landmarks on the right side of the left atrium , namely rspv and ripv , show a lower residual error compared to left sided landmarks lspv and lipv . this might be due to the additional pouch on the left side of the left atrium , the left atrial appendage , which is anterior to the pv ostia . the mesh models of the left atrium also contained a large part of the connected pulmonary veins . removing or trimming these extensions might improve the accuracy , since these structures show a high variation in shape and size . for the modeling of the atrium , short pulmonary vein ostia would be sufficient . this work is a first step towards our goal of automatic planning of ablation regions for atrial fibrillation procedures . planning structures could be transferred to augmented fluoroscopy systems used to guide the procedure and overlaid to the x - ray images . it has been found that the highest mesh - to - mesh distance occurs at the end of the pulmonary veins . in the following , the comparison of pre - planned ablation lines for the treatment of atrial fibrillation using a common reference model is discussed in more detail . we used left atrial ( la ) surface models of seven different patients to build up a common reference shape . the mesh models are represented as a triangulated mesh structure . the models cover the left atrium as well as a certain extent of the attached pulmonary veins . the length of the pulmonary veins varies from data set to data set for consistency , a pre - processing step has been applied to all la mesh models . the attached pulmonary veins have been removed from the mesh about 2 cm distal to the la antrum . the common reference shape is generated via pairwise non - rigid registration of the la models . for registration , the mesh is seen as point cloud m consisting of n points x i ∈ r 3 m ≡ m =[ x 1 t , . . . , x n t ] t ∈ r 3n . ( 6 ) all meshes have the same anatomical orientation , and are zero centered before applying the registration . we used the coherent point drift ( cpd ) algorithm [ 12 ] to perform the non - rigid point cloud registration . the main benefit of the cpd algorithm is the robustness against nose and outliers while generating smooth deformation fields . a pivot mesh m pivot is registered to template meshes m t i . the variables t i are used to refer to each of the t = 7 template meshes . below , we describe how to derive a common reference model . then we establish mean ablation lines . afterwards , we evaluate how individual pre - planned ablation lines vary around their mean as we move around the left and right ipsilateral pvs . in the first step , we selected one left atrium mesh model as pivot element , in the next step , we registered the pivot mesh to the remaining template meshes { m t 2 , . . . , m t t }. we used the coherent point drift algorithm to compute the non - rigid transformation between the pivot mesh and the other left atrial mesh models . cpd follows a probabilistic approach by considering the alignment of the two point sets as a probability density estimation problem . the basic idea is to fit the gaussian mixture model ( gmm ) centroids , represented by the points of the pivot mesh m pivot , to the template mesh m t i , by maximizing the likelihood . this optimization is performed with the expectation maximization algorithm . during the optimization the gmm centroids are forced to move coherently as a group , to ensure preservation of the topological structure of the point set . for each template mesh m t i , the estimated deformation field μ t i ∈ r 3n is calculated by registration of the pivot mesh m pivot to m t i . the transformed pivot mesh can then be described as the common reference model or reference data set is defined as the mean shape given by putting ( 8 ) and ( 9 ) together , it is easy to see that the reference mesh is comprised of the selected pivot mesh , and a mean deformation field . in other words , the selection of a proper pivot mesh is important , because it determines the basic shape of the resulting mean mesh . this is why we carefully selected the pivot mesh , making sure that all relevant landmarks , namely the pulmonary veins and left atrium appendage , were clearly expressed . planning lines l are represented as a set of points l ={ x 1 , . . . x p } with x ∈ r 3 . each template mesh m t i has two planning lines l t i , r and l t i , l attached . they represent desirable ablation lines for right and left sided ipsilateral pulmonary veins , respectively . the planning lines are a subset of the corresponding template mesh , i . e . { l t i , r , l t i , l }⊂ m t i . to transfer the planning lines from a template mesh onto the reference model , m ref is registered to m t i using cpd . after registration , the two mesh models are optimally aligned based on the optimization criterion stated in ( 5 ). the planning lines { l t i , r , l t i , l } are now projected onto the transformed reference model { tilde over ( m )} t i with a nearest neighbor approach . by applying the inverse deformation field , the lines can be mapped onto the reference model m ref . there , they are labeled { circumflex over ( l )} t i , r and { circumflex over ( l )} t i , l for right and left sided planning , respectively . the mean planning lines are derived from the set of re - mapped ablation lines defined as l ={{ circumflex over ( l )} t i , r ,{ circumflex over ( l )} t i , l } t i = . ( 11 ) initially , each planning line consists of an arbitrary number of points . for consistency , each line l was interpolated with a cubic spline , and equidistantly sampled with a fixed number of sample points p l . to investigate the spread and distribution among the pre - planned ablation lines , a common orientation and labeling was enforced . each planning line represents a closed loop encircling the la . the point closest to the top is defined as the starting point , and the remaining points are traversed in anterior direction . after correct alignment of l , mean reference lines l ref , r and l ref , l are generated by averaging corresponding points along the interpolated lines . in fig1 , a schematic view of a left atrium 10 is shown including the pulmonary veins 11 , 12 , 13 , 14 . an example of ipsilateral ablation planning lines 15 and 16 is shown . in fig3 , several pre - planned ablation lines transferred from different meshes are shown . in fig3 three different ablation lines 15 a - 15 c and 16 a - 16 c are shown . in fig4 in addition to the ablation lines already shown in fig3 , estimated mean ablation lines 17 and 18 are shown , which were calculated as discussed above . we evaluated our approach on t = 7 la meshes with attached planning lines . the pre - planned ablation lines were placed by an experienced clinician . the registration accuracy of the non - rigid registration of the reference model to the template meshes in terms of residual average mesh - to - mesh error is shown in fig6 . the mean residual mesh - to - mesh error calculated over all meshes was 2 . 0 mm . data set 1 was selected as pivot mesh for the reference mesh generation . as can be seen in ( 8 ), the reference mesh is comprised of the pivot mesh with an additive deformation term . hence , non - rigid registration of the reference mesh onto data set 1 is possible with a very low residual error , as illustrated in the first column of fig6 . the deviation of the re - mapped planning lines from their respective mean is evaluated as follows . for each point of the reference planning lines l ref , r and l ref , l , the distance to the re - mapped planning lines { circumflex over ( l )} t i , r , { circumflex over ( l )} t i , l with i = 1 . . . t is calculated . for further , more anatomically oriented evaluations , the planning lines were divided into eight equally spaced segments , as depicted in fig8 , in which a clock schema is used to divide the substantial circular planning lines into different segments . based on this convention , we present the mean deviation of the individual planning lines per line segment in fig7 . line segment 1 and 2 are located on the roof of the la . 5 and 6 are below the inferior pv , and 7 and 8 are on the posterior side of the la . note that there is an additional pouch on the left side of the la , the left atrial appendage ( laa ). the laa is located anterior the left - sided pvs , separated from them by an arrow ridge . the laa runs on the left side along segments 2 to 5 . the average distance of the re - mapped ablation lines to the reference ablation line was 2 . 9 ± 1 . 9 mm and 1 . 8 ± 1 . 5 mm for right and left sided planning lines , respectively . the maximum distance of a single planning point to the reference planning line was 8 . 5 mm and 7 . 6 mm for right and left side , respectively . according to our analysis , the average deviation over all individual planning lines that were part of our data set was 2 . 4 ± 1 . 8 mm . this results in a region for pre - planned ablation lines that is approximately twice this width . the smallest deviation was encountered in line segments 2 and 3 . we believe that this is due to the presence of the ridge between left atrial appendage and left pvs , that leaves limited space for setting up pre - planned ablation lines . based on feedback from physicians in this field , our findings appear plausible . in a nutshell , by comparing pre - planned ablation lines placed by an experienced clinician on la models of actual patients , we found that one seems to have some 5 mm of “ wiggle room ” despite the presence of prominent anatomical structures . after analyzing the inter - patient variance of manually placed planning lines and learning a general planning pattern , the design of an algorithm for fully automatic pre - planning of ablation lines will be the next step . in fig9 , we summarize the method for evaluating treatment - relevant spatial anatomical information on a reference data set . an example for the treatment - relevant spatial anatomical information are the ablation planning lines in the left atrium . the method starts in step s 90 . in a step s 91 , a reference three - dimensional data set of the atrium is provided . in step s 92 , further three - dimensional data sets with treatment - relevant spatial anatomical information are provided , e . g . a first data set , a second data set and eventually further data sets . in step s 93 , the reference data set is registered to each of the data sets provided in step s 92 . in step s 94 , the treatment - relevant spatial anatomical information of each of the data sets provided in step s 92 is transferred on the reference data set so that transferred treatment - relevant spatial anatomical information is attached to the reference data set . in step s 95 , the transferred treatment - relevant spatial anatomical information attached to the reference data set is compared and evaluated . this means that by way of example , a mean and a standard deviation of the planning lines transferred to the reference data set is determined . in the next step s 96 , a reference treatment - relevant spatial anatomical information is determined , e . g . reference treatment planning lines . the method ends in step s 97 . in fig1 , a flow chart is shown comprising the steps which can be carried out to compute a reference three - dimensional data set . the method starts in step s 100 . in another step s 101 , the different three - dimensional anatomical data sets are provided . in step s 102 , a pivot data set is selected . this pivot data set may be selected based on visual inspection of the different data sets and serves as basis for the generated reference data set . in step s 103 , the pivot data set is registered to every of the other three - dimensional data sets . in step s 104 , it is possible to determine a statistical shape model , e . g . a mean shape as explained in more detail above . in step s 105 , a reference model or reference data set of the left atrium can be determined as mentioned above in equation 10 . as discussed above , the reference model can be comprises of the selected pivot data set and a mean deformation field . in fig1 , a flow chart is shown comprising the steps which can be used to plan an interventional treatment in an atrium . the method starts in step 110 . in the method shown in fig1 , the transferred treatment - relevant spatial anatomical information is applied to a new data set . in step s 111 , the reference three - dimensional data set is provided . furthermore , reference treatment - relevant spatial anatomical information on the reference data set is provided , e . g . as reference treatment planning lines ( step s 112 ). in step s 113 , the new three - dimensional image data set is provided for which the planning lines should be determined . in step s 114 , the left atrium in the new data set is segmented and in step s 115 , the reference data set is registered to the new data set . in step s 116 , the reference treatment - relevant spatial anatomical information is transferred to the new data set to determine planning lines for the new data set . the method ends in step s 117 . in fig2 , a system is schematically shown with which ablation lines can be evaluated and with which a planning of ablation lines is possible . the three - dimensional images can be generated with an imaging system 21 , which can be an mr or ct scanner . the different three - 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