Symmetric image registration with directly calculated inverse deformation field

This paper presents a novel technique for a symmetric deformable image registration based on a new method for fast and accurate direct inversion of a large motion model deformation field. The proposed image registration algorithm maintain a one-to-one mapping between registered images by symmetrically warping them to each other, and by ensuring the inverse consistency criterion at each iteration. This makes the final estimation of forward and backward deformation fields anatomically plausible. The quantitative validation of the method has been performed on magnetic resonance data obtained for a pelvis area demonstrating applicability of the method to adaptive prostate radiotherapy. The experiments demonstrate the improved robustness in terms of inverse consistency error when compared to previously proposed methods for symmetric image registration

Nonparametric joint shape learning for customized shape modeling

We present a shape optimization approach to compute patient-specific models in customized prototyping applications. We design a coupled shape prior to model the transformation between a related pair of surfaces, using a nonparametric joint probability density estimation. The coupled shape prior forces with the help of application-specific data forces and smoothness forces drive a surface deformation towards a desired output surface. We demonstrate the usefulness of the method for generating customized shape models in applications of hearing aid design and pre-operative to intra-operative anatomic surface estimation

Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach

Cardiac motion estimation is an important diagnostic tool to detect heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges because of the complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate the cardiac motion using ultrafast ultrasound data. -- Our solution is based on a variational formulation characterized by the L2-regularized class. The displacement is represented by a lattice of b-splines and we ensure robustness by applying a maximum likelihood type estimator. While this is an important part of our solution, the main highlight of this paper is to combine a low-rank data representation with topology preservation. Low-rank data representation (achieved by finding the k-dominant singular values of a Casorati Matrix arranged from the data sequence) speeds up the global solution and achieves noise reduction. On the other hand, topology preservation (achieved by monitoring the Jacobian determinant) allows to radically rule out distortions while carefully controlling the size of allowed expansions and contractions. Our variational approach is carried out on a realistic dataset as well as on a simulated one. We demonstrate how our proposed variational solution deals with complex deformations through careful numerical experiments. While maintaining the accuracy of the solution, the low-rank preprocessing is shown to speed up the convergence of the variational problem. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that experience motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201

Bayesian modelling of organ deformations in radiotherapy

Moderne strålebehandling mot kreft er skreddarsydd for å gje ein høg stråledose tilpassa svulsten (målvolumet), mens så lite dose som mogleg vert gitt til det friske vevet omkring. Den totale dosen vert levert over nokre veker i daglege "fraksjonar", noko som reduserer biverknader. Under og mellom desse fraksjonane rører dei indre organa på seg heile tida på grunn av pust, fylling av blæra, tarmar si rørsle og ekstern påverknad. Likevel vert posisjonen til målvolumet og relevante risikoorgan bestemt på grunnlag av eit statisk 3D-skann som er tatt før behandlinga startar. Den vanlege måten å sikre seg mot konsekvensar av denne rørsla er å legge til marginar rundt svulsten. Slik sikrar ein å treffe målvolumet, men til gjengjeld får det friske vevet meir dose. Marginane sin storleik er fastsett ved hjelp av statistikk over tidlegare behandla pasienter. Dei statistiske metodane som vert brukte er ofte enkle, og tek berre omsyn til rigid rørsle, altså at heile kroppen rører seg i eitt. Dessutan vert det ikkje teke omsyn til rørsla til risikoorgan. For å berekne dose til risikoorgana er det vanleg å anta at forma til organa i planleggingsskannet er representative for forma deira under behandling. Arbeidet i denne avhandlinga handlar om å bruka teknikkar frå Bayesiansk statistikk for å modellere korleis organ rører og deformerer seg mellom fraksjonane. Målet er å estimere nøyaktig den statistiske fordelinga av rørsle for eit eller fleire organ til ein pasient. Fordelinga gjev innsikt i korleis organa forandre seg medan behandlinga går for seg. Denne innsikta er nyttig for evaluering av stråleterapiplanar, statistisk prediksjon av biverknader, såkalla robust planlegging og å berekna størrelsen på marginar. Metodane som vert presentert er evaluerte for endetarmen (rektum) sine rørsler hjå prostatakreftpasientar. For desse pasientane er rektum eit viktig risikoorgan, som kan bli ramma både av akutte og seine biverknader, som lekkasje, bløding og smerter. Samanlikna med eksisterande metodar har den Bayesianske tilnærminga to fordelar: For det første gir kombinasjonen av populasjonsstatistikk og individuelle data meir nøyaktige anslag av den pasientspesifikke fordelinga. For det andre estimerer dei nye metodane den såkalla systematiske feilen i tillegg til variasjonar frå fraksjon til fraksjon. Den systematiske feilen er forskjellen mellom den estimerte forma på organet under planlegging, og gjennomsnittsforma til organet under bestråling. Denne typen feil var tema for artikkel I. Her fekk vi til å redusere den systematiske feilen til rektum hjå 33 av 37 prostatakreftpasientar ved å bruke ein metode som kombinerer forma på rektum under planlegginga og gjennomsnittsforma i populasjonen. Vi vurderte og om denne forbetringa hadde påverknad på estimering av summert dose til rektum. Metoden gav ikkje signifikant forbetring for to antatt relevante parametrar (ekvivalent uniform dose og D5%), men gav signifikant reduksjon av bias på det estimerte dose-volum-histogrammet i intervallet 52.5 Gy til 65 Gy. Hovudarbeidet i dette prosjektet er publisert i artikkel II. Der presenterer vi to modellar for organrørsle basert på Bayesianske metodar. Inndata til desse metodane er organformer som er henta frå 3D-skanningar. Metodane kan ta ulikt tal slike former, og produserer meir nøyaktige resultat jo fleire former dei får. Dei gjev anslag av gjennomsnittsforma og kor stor uvissa om denne forma er, i tillegg til anslag av fordelinga av variasjon av former frå fraksjon til fraksjon. Vi evaluerte metodane etter kor godt dei kunne berekne "dekningssannsyn", altså sannsynet for at organet skal dekke eit gitt punkt i pasientkoordinatsystemet til ei gitt tid. For denne berekninga måtte titusenvis av organformer gjerast om til såkalla binærmasker, som er 3D-matriser av punkter i pasient-koordinatsystemet der verdien til eit punkt er 1 dersom punktet er inne i organet, og 0 elles. Denne berekninga var mogleg på grunn av programvare som blei implementert for dette prosjektet, og som er presentert i artikkel III. Også her var det prostatakreftpasientar sitt rektum som vart brukt til evaluering. Berekningane til dei nye metodane var likare det sanne dekningssannsynet enn tilsvarande berekningar frå tidlegare metodar, i signifikant grad, i alle fall opp til tre input. Forskjellen mellom dei to nye algoritmane er i hovudsak kompleksiteten og nøyaktigheita, og valet mellom algoritmane i ein gitt bruk vil vere ei avveging mellom desse faktorane. Vi viste ein måte modellane kan verte brukte i artikkel IV, som handlar om pasientar som får re-bestråling for tilbakefall av prostatakreft. Her brukte vi modellane til å berekne forventa akkumulert dose til rektum frå dei to behandlingane, og også uvissa rundt den forventa dosen. Metoden er basert på representative former" av rektum, altså former som rektum kan ta som er sannsynlege, men lite fordelaktige. Desse formene kan brukast som visuell hjelp for onkologar og doseplanleggjarar, og metoden kan implementerast ved hjelp av eksisterande funksjonar i programvaren for behandlingsplanlegging. Overordna gir denne avhandlinga nye løysingar for den sentrale utfordringa med å redusere konsekvensar av organrørsle i stråleterapi. Dei presenterte modellane er dei første som utnyttar statistikk for populasjonen og data frå den enkelte pasienten samstundes, og som tar omsyn til både systematiske og tilfeldige feil.Modern radiotherapy tends to be highly conformal, meaning that a high and uniform dose is delivered to the target volume and as little dose as possible to the surrounding normal tissue. The total radiation dose is delivered across several smaller daily fractions, typically spanning several weeks. During and between these fractions, internal organs are constantly in motion due to factors such as breathing, changes to bladder filling state, intestinal movement and external influences. Nevertheless, the position of the target and relevant organs at risk (OARs) are determined based on a static 3D scan acquired before start of treatment. A common safeguard which is used to take such motion into account is the addition of margins around the target. These margins reduce the chance of missing parts of the target, yet increases dose to the healthy tissue surrounding the target. The margin size is based on statistics from previous patients. However, for the most part, the statistical methods used are very simple, and typically based on an assumption of rigid patient motion. Similarly, motion of the OARs is commonly neglected. For estimation of dose to the OARs, it is common to assume that the organ shape at the static scan is representative for its shape during treatment. The work in this thesis concerns the use of techniques from Bayesian statistics for modelling inter-fraction organ motion and deformation. The goal is to estimate accurately the statistical distribution of shapes for one or more organs for a given patient. The distribution provides knowledge of how the patient's organs might move and deform during the radiotherapy course. This information is useful for the evaluation of radiotherapy plans, prediction of adverse effects, so-called motion-robust radiotherapy planning, the generation of margins and more. The methods presented in this thesis have been evaluated for predicting deformations of the rectum of prostate cancer patients. For these patients, the rectum is a crucial OAR that is affected by both early and late side effects including leakage, bleeding and pain. Compared to existing methods, the Bayesian approach developed and implemented in this thesis offers two advantages: first, combining population statistics and individual data leads to more accurate estimates of the patient-specific distribution. Secondly, the new methods estimate the distribution of the so-called systematic error in addition to variations from fraction to fraction. The systematic error is the difference between the estimated shape/position of an organ at the planning stage and its average shape/position during therapy, and was the subject of paper I. Here, we were able to reduce the systematic error of the rectum in 33 out of 37 prostate cancer patients using a straightforward method to combine the shape of the rectum at the planning CT with the population mean shape. We also evaluated the impact of this improvement on the estimation of dose to the rectum. We found no significant improvement on the estimation of two presumably relevant dose parameters (equivalent uniform dose and D5%). However, we did find significant reduction in the bias of the estimated dose-volume histogram in the range from 52.5 Gy to 65 Gy. Paper II contains the central work of this project. It presents two organ deformation models based on Bayesian methods. The input data to these algorithms are organ shapes derived from 3D scans. The methods can take a varying number of such inputs from a given patient, and will produce more accurate results the more inputs they are given. They provide an estimate of the mean shape of the organ, as well as the uncertainty of this mean, in addition to the distribution of the variation of shapes from fraction to fraction. The methods were evaluated in the task of estimating coverage probabilities, i.e. the probability that the organ will cover a certain point in the patient coordinate system, for the rectum of prostate cancer patients. For this evaluation, tens of thousands of organ shapes needed to be converted to so-called binary masks, which are 3D arrays of points in the patient coordinate system where the value of each point is 1 if the point is inside the organ and 0 if it is outside. This was enabled by the highly efficient point-in-polyhedron software presented in paper III, which was developed for this project. The models were given varying number of scans, from 1 to 10, as input, and compared to two existing (non-Bayesian) models. The estimates of the coverage probability produced by the new models were significantly more similar to the ground truth than those produced by the existing models, at least up to three input scans. The main differences between the two new algorithms are their of conceptual complexity and accuracy, and the choice of method in a given application will therefore come down to a trade-off between these qualities. An application for the models derived in paper II, concerning patients receiving re-irradiation for recurrent prostate cancer, is presented in paper IV. We introduce a way of estimating the expectation and uncertainty of the accumulated dose to the rectum from the two treatment courses. The method is based on "representative shapes" of the rectum, that is, shapes that are probable and also particularly favourable or unfavourable in terms of dose. The advantage is that these shapes can be used as a visual aid for the oncologist or dose planner, and that the method can be implemented using existing features of treatment planning systems. Overall, this thesis provides novel solutions to the central challenge of organ motion mitigation in RT. The presented models are the first to simultaneously exploit population and patient specific organ motion and addressing both systematic and random errors.Doktorgradsavhandlin

State of the Art of Level Set Methods in Segmentation and Registration of Medical Imaging Modalities

Segmentation of medical images is an important step in various applications such as visualization, quantitative analysis and image-guided surgery. Numerous segmentation methods have been developed in the past two decades for extraction of organ contours on medical images. Low-level segmentation methods, such as pixel-based clustering, region growing, and filter-based edge detection, require additional pre-processing and post-processing as well as considerable amounts of expert intervention or information of the objects of interest. Furthermore the subsequent analysis of segmented objects is hampered by the primitive, pixel or voxel level representations from those region-based segmentation. Deformable models, on the other hand, provide an explicit representation of the boundary and the shape of the object. They combine several desirable features such as inherent connectivity and smoothness, which counteract noise and boundary irregularities, as well as the ability to incorporate knowledge about the object of interest. However, parametric deformable models have two main limitations. First, in situations where the initial model and desired object boundary differ greatly in size and shape, the model must be re-parameterized dynamically to faithfully recover the object boundary. The second limitation is that it has difficulty dealing with topological adaptation such as splitting or merging model parts, a useful property for recovering either multiple objects or objects with unknown topology. This difficulty is caused by the fact that a new parameterization must be constructed whenever topology change occurs, which requires sophisticated schemes. Level set deformable models, also referred to as geometric deformable models, provide an elegant solution to address the primary limitations of parametric deformable models. These methods have drawn a great deal of attention since their introduction in 1988. Advantages of the contour implicit formulation of the deformable model over parametric formulation include: (1) no parameterization of the contour, (2) topological flexibility, (3) good numerical stability, (4) straightforward extension of the 2D formulation to n-D. Recent reviews on the subject include papers from Suri. In this chapter we give a general overview of the level set segmentation methods with emphasize on new frameworks recently introduced in the context of medical imaging problems. We then introduce novel approaches that aim at combining segmentation and registration in a level set formulation. Finally we review a selective set of clinical works with detailed validation of the level set methods for several clinical applications

Classical and all-floating FETI methods for the simulation of arterial tissues

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.Comment: 29 page

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor