Volumetric intraoperative brain deformation compensation: model development and phantom validation

During neurosurgery, nonrigid brain deformation may affect the reliability of tissue localization based on preoperative images. To provide accurate surgical guidance in these cases, preoperative images must be updated to reflect the intraoperative brain. This can be accomplished by warping these preoperative images using a biomechanical model. Due to the possible complexity of this deformation, intraoperative information is often required to guide the model solution. In this paper, a linear elastic model of the brain is developed to infer volumetric brain deformation associated with measured intraoperative cortical surface displacement. The developed model relies on known material properties of brain tissue, and does not require further knowledge about intraoperative conditions. To provide an initial estimation of volumetric model accuracy, as well as determine the model's sensitivity to the specified material parameters and surface displacements, a realistic brain phantom was developed. Phantom results indicate that the linear elastic model significantly reduced localization error due to brain shift, from > 16 mm to under 5 mm, on average. In addition, though in vivo quantitative validation is necessary, preliminary application of this approach to images acquired during neocortical epilepsy cases confirms the feasibility of applying the developed model to in vivo data.     

Brain shift estimation in image-guided neurosurgery using 3-D ultrasound

Intraoperative brain deformation is one of the most important causes affecting the overall accuracy of image-guided neurosurgical procedures. One option for correcting for this deformation is to acquire three-dimensional (3-D) ultrasound data during the operation and use this data to update the information provided by the preoperatively acquired MR data. For 12 patients 3-D ultrasound images have been reconstructed from freehand sweeps acquired during neurosurgical procedures. Ultrasound data acquired prior to and after opening the dura, but prior to surgery, have been quantitatively compared to the preoperatively acquired MR data to estimate the rigid component of brain shift at the first stages of surgery. Prior to opening the dura the average brain shift measured was 3.0 mm parallel to the direction of gravity, with a maximum of 7.5 mm, and 3.9 mm perpendicular to the direction of gravity, with a maximum of 8.2 mm. After opening the dura the shift increased on average 0.2 mm parallel to the direction of gravity and 1.4 mm perpendicular to the direction of gravity. Brain shift can be detected by acquiring 3-D ultrasound data during image-guided neurosurgery. Therefore, it can be used as a basis for correcting image data and preoperative planning for intraoperative deformations.     

Stereopsis-guided brain shift compensation

Brain deformation models have proven to be a powerful tool in compensating for soft tissue deformation during image-guided neurosurgery. The accuracy of these models can be improved by incorporating intraoperative measurements of brain motion. We have designed and implemented a passive intraoperative stereo vision system capable of estimating the three-dimensional shape of the surgical scene in near real-time. This intraoperative shape is compared with the cortical surface in the co-registered preoperative magnetic resonance (MR) volume for the estimation of the cortical motion resulting from the open cranial surgery. The estimated cortical motion is then used to guide a full brain model, which updates a preoperative MR volume. We have found that the stereo vision system is accurate to within approximately 1 mm. Based on data from two representative clinical cases, we show that stereopsis guidance improves the accuracy of brain shift compensation both at and below the cortical surface.     

Biomechanical modeling of the human head for physically based, nonrigid image registration

The accuracy of image-guided neurosurgery generally suffers from brain deformations due to intraoperative changes. These deformations cause significant changes of the anatomical geometry (organ shape and spatial interorgan relations), thus making intraoperative navigation based on preoperative images error prone. In order to improve the navigation accuracy, we developed a biomechanical model of the human head based on the finite element method, which can be employed for the correction of preoperative images to cope with the deformations occurring during surgical interventions. At the current stage of development, the two-dimensional (2-D) implementation of the model comprises two different materials, though the theory holds for the three-dimensional (3-D) case and is capable of dealing with an arbitrary number of different materials. For the correction of a preoperative image, a set of homologous landmarks must be specified which determine correspondences. These correspondences can be easily integrated into the model and are maintained throughout the computation of the deformation of the preoperative image. The necessary material parameter values have been determined through a comprehensive literature study. Our approach has been tested for the case of synthetic images and yields physically plausible deformation results. Additionally, we carried out registration experiments with a preoperative MR image of the human head and a corresponding postoperative image simulating an intraoperative image. We found that our approach yields good prediction results, even in the case when correspondences are given in a relatively small area of the image only.     

In vivo quantification of a homogeneous brain deformation model for updating preoperative images during surgery

Clinicians using image-guidance for neurosurgical procedures have recently recognized that intraoperative deformation from surgical loading can compromise the accuracy of patient registration in the operating room. While whole brain intraoperative imaging is conceptually appealing it presents significant practical limitations. Alternatively, a promising approach may be to combine incomplete intraoperatively acquired data with a computational model of brain deformation to update high resolution preoperative images during surgery. The success of such an approach is critically dependent on identifying a valid model of brain deformation physics. Towards this end, we evaluate a three-dimensional finite element consolidation theory model for predicting brain deformation in vivo through a series of controlled repeat-experiments. This database is used to construct an interstitial pressure boundary condition calibration curve which is prospectively tested in a fourth validation experiment. The computational model is found to recover 75%-85% of brain motion occurring under loads comparable to clinical conditions. Additionally, the updating of preoperative images using the model calculations is presented and demonstrates that model-updated image-guided neurosurgery may be a viable option for addressing registration errors related to intraoperative tissue motion.     

Self-calibrating 3D-ultrasound-based bone registration for minimally invasive orthopedic surgery

Intraoperative freehand three-dimensional (3-D) ultrasound (3D-US) has been proposed as a noninvasive method for registering bones to a preoperative computed tomography image or computer-generated bone model during computer-aided orthopedic surgery (CAOS). In this technique, an US probe is tracked by a 3-D position sensor and acts as a percutaneous device for localizing the bone surface. However, variations in the acoustic properties of soft tissue, such as the average speed of sound, can introduce significant errors in the bone depth estimated from US images, which limits registration accuracy. We describe a new self-calibrating approach to US-based bone registration that addresses this problem, and demonstrate its application within a standard registration scheme. Using realistic US image data acquired from 6 femurs and 3 pelves of intact human cadavers, and accurate Gold Standard registration transformations calculated using bone-implanted fiducial markers, we show that self-calibrating registration is significantly more accurate than a standard method, yielding an average root mean squared target registration error of 1.6 mm. We conclude that self-calibrating registration results in significant improvements in registration accuracy for CAOS applications over conventional approaches where calibration parameters of the 3D-US system remain fixed to values determined using a preoperative phantom-based calibration.     

Displacement estimation with co-registered ultrasound for image guided neurosurgery: a quantitative in vivo porcine study

Brain shift during open cranial surgery presents a challenge for maintaining registration with image-guidance systems. Ultrasound (US) is a convenient intraoperative imaging modality that may be a useful tool in detecting tissue shift and updating preoperative images based on intraoperative measurements of brain deformation. We have quantitatively evaluated the ability of spatially tracked freehand US to detect displacement of implanted markers in a series of three in vivo porcine experiments, where both US and computed tomography (CT) image acquisitions were obtained before and after deforming the brain. Marker displacements ranged from 0.5 to 8.5 mm. Comparisons between CT and US measurements showed a mean target localization error of 1.5 mm, and a mean vector error for displacement of 1.1 mm. Mean error in the magnitude of displacement was 0.6 mm. For one of the animals studied, the US data was used in conjunction with a biomechanical model to nonrigidly re-register a baseline CT to the deformed brain. The mean error between the actual and deformed CT's was found to be on average 1.2 and 1.9 mm at the marker locations depending on the extent of the deformation induced. These findings indicate the potential accuracy in coregistered freehand US displacement tracking in brain tissue and suggest that the resulting information can be used to drive a modeling re-registration strategy to comparable levels of agreement.     

Robust nonrigid registration to capture brain shift from intraoperative MRI

We present a new algorithm to register 3-D preoperative magnetic resonance (MR) images to intraoperative MR images of the brain which have undergone brain shift. This algorithm relies on a robust estimation of the deformation from a sparse noisy set of measured displacements. We propose a new framework to compute the displacement field in an iterative process, allowing the solution to gradually move from an approximation formulation (minimizing the sum of a regularization term and a data error term) to an interpolation formulation (least square minimization of the data error term). An outlier rejection step is introduced in this gradual registration process using a weighted least trimmed squares approach, aiming at improving the robustness of the algorithm. We use a patient-specific model discretized with the finite element method in order to ensure a realistic mechanical behavior of the brain tissue. To meet the clinical time constraint, we parallelized the slowest step of the algorithm so that we can perform a full 3-D image registration in 35 s (including the image update time) on a heterogeneous cluster of 15 personal computers. The algorithm has been tested on six cases of brain tumor resection, presenting a brain shift of up to 14 mm. The results show a good ability to recover large displacements, and a limited decrease of accuracy near the tumor resection cavity.     

Surgical navigation by autostereoscopic image overlay of integral videography

This paper describes an autostereoscopic image overlay technique that is integrated into a surgical navigation system to superimpose a real three-dimensional (3-D) image onto the patient via a half-silvered mirror. The images are created by employing a modified version of integral videography (IV), which is an animated extension of integral photography. IV records and reproduces 3-D images using a microconvex lens array and flat display; it can display geometrically accurate 3-D autostereoscopic images and reproduce motion parallax without the need for special devices. The use of semitransparent display devices makes it appear that the 3-D image is inside the patient's body. This is the first report of applying an autostereoscopic display with an image overlay system in surgical navigation. Experiments demonstrated that the fast IV rendering technique and patient-image registration method produce an average registration accuracy of 1.13 mm. Experiments using a target in phantom agar showed that the system can guide a needle toward a target with an average error of 2.6 mm. Improvement in the quality of the IV display will make this system practical and its use will increase surgical accuracy and reduce invasiveness.     

Tracking and finite element analysis of stripe deformation in magnetic resonance tagging

Magnetic resonance tissue tagging allows noninvasive in vivo measurement of soft tissue deformation. Planes of magnetic saturation are created, orthogonal to the imaging plane, which form dark lines (stripes) in the image. The authors describe a method for tracking stripe motion in the image plane, and show how this information can be incorporated into a finite element model of the underlying deformation. Human heart data were acquired from several imaging planes in different orientations and were combined using a deformable model of the left ventricle wall. Each tracked stripe point provided information on displacement orthogonal to the original tagging plane, i.e., a one-dimensional (1-D) constraint on the motion. Three-dimensional (3-D) motion and deformation was then reconstructed by fitting the model to the data constraints by linear least squares. The average root mean squared (rms) error between tracked stripe points and predicted model locations was 0.47 mm (n=3,100 points). In order to validate this method and quantify the errors involved, the authors applied it to images of a silicone gel phantom subjected to a known, well-controlled, 3-D deformation. The finite element strains obtained were compared to an analytic model of the deformation known to be accurate in the central axial plane of the phantom. The average rms errors were 6% in both the reconstructed shear strains and 16% in the reconstructed radial normal strain.     

Nonrigid motion modeling of the liver from 3-D undersampled self-gated golden-radial phase encoded MRI

Magnetic resonance imaging (MRI) has been commonly used for guiding and planning image guided interventions since it provides excellent soft tissue visualization of anatomy and allows motion modeling to predict the position of target tissues during the procedure. However, MRI-based motion modeling remains challenging due to the difficulty of acquiring multiple motion-free 3-D respiratory phases with adequate contrast and spatial resolution. Here, we propose a novel retrospective respiratory gating scheme from a 3-D undersampled high-resolution MRI acquisition combined with fast and robust image registrations to model the nonrigid deformation of the liver. The acquisition takes advantage of the recently introduced golden-radial phase encoding (G-RPE) trajectory. G-RPE is self-gated, i.e., the respiratory signal can be derived from the acquired data itself, and allows retrospective reconstructions of multiple respiratory phases at any arbitrary respiratory position. Nonrigid motion modeling is applied to predict the liver deformation of an average breathing cycle. The proposed approach was validated on 10 healthy volunteers. Motion model accuracy was assessed using similarity-, surface-, and landmark-based validation methods, demonstrating precise model predictions with an overall target registration error of TRE = 1.70 ± 0.94 mm which is within the range of the acquired resolution.     

In vivo quantification of retraction deformation modeling for updated image-guidance during neurosurgery

The use of coregistered preoperative anatomical scans to provide navigational information in the operating room has greatly benefited the field of neurosurgery. Nonetheless, it has been widely acknowledged that significant errors between the operating field and the preoperative images are generated as surgery progresses. Quantification of tissue shift can be accomplished with volumetric intraoperative imaging; however, more functional, lower cost alternative solutions to this challenge are desirable. We are developing the strategy of exploiting a computational model driven by sparse data obtained from intraoperative ultrasound and cortical surface tracking to warp preoperative images to reflect the current state of the operating field. This paper presents an initial quantification of the predictive capability of the current model to computationally capture tissue deformation during retraction in the porcine brain. Performance validation is achieved through comparisons of displacement and pressure predictions to experimental measurements obtained from computed tomographic images and pressure sensor recordings. Group results are based upon a generalized set of boundary conditions for four subjects that, on average, account for at least 75% of tissue motion generated during interhemispheric retraction. Individualized boundary conditions can improve the degree of data-model match by 10% or more but warrant further study. Overall, the level of quantitative agreement achieved in these experiments is encouraging for updating preoperative images to reflect tissue deformation resulting from retraction, especially since model improvements are likely as a result of the intraoperative constraints that can be applied through sparse data collection.     

Registration of 3-D intraoperative MR images of the brain using a finite-element biomechanical model

We present a new algorithm for the nonrigid registration of three-dimensional magnetic resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces of objects (cortical surface and the lateral ventricles) in the image sequence using a deformable surface matching algorithm. The volumetric deformation field of the objects is then inferred from the displacements at the boundary surfaces using a linear elastic biomechanical finite-element model. Two experiments on synthetic image sequences are presented, as well as an initial experiment on intraoperative MR images showing brain shift. The results of the registration algorithm show a good correlation of the internal brain structures after deformation, and a good capability of measuring surface as well as subsurface shift. We measured distances between landmarks in the deformed initial image and the corresponding landmarks in the target scan. Cortical surface shifts of up to 10 mm and subsurface shifts of up to 6 mm were recovered with an accuracy of 1 mm or less and 3 mm or less respectively.     

Image-Guided Intraoperative Cortical Deformation Recovery Using Game Theory: Application to Neocortical Epilepsy Surgery

During neurosurgery, nonrigid brain deformation prevents preoperatively-acquired images from accurately depicting the intraoperative brain. Stereo vision systems can be used to track intraoperative cortical surface deformation and update preoperative brain images in conjunction with a biomechanical model. However, these stereo systems are often plagued with calibration error, which can corrupt the deformation estimation. In order to decouple the effects of camera calibration from the surface deformation estimation, a framework that can solve for disparate and often competing variables is needed. Game theory, which was developed to handle decision making in this type of competitive environment, has been applied to various fields from economics to biology. In this paper, game theory is applied to cortical surface tracking during neocortical epilepsy surgery and used to infer information about the physical processes of brain surface deformation and image acquisition. The method is successfully applied to eight in vivo cases, resulting in an 81% decrease in mean surface displacement error. This includes a case in which some of the initial camera calibration parameters had errors of 70%. Additionally, the advantages of using a game theoretic approach in neocortical epilepsy surgery are clearly demonstrated in its robustness to initial conditions.      

An ultrasonic approach to localization of fiducial markers forinteractive, image-guided neurosurgery. I. Principles

Fiducial markers are reference points used in the registration of image space(s) with physical (patient) space. As applied to interactive, image-guided surgery, the registration of image space with physical space allows the current location of a surgical tool to be indicated on a computer display of patient-specific preoperative images. This intrasurgical guidance information is particularly valuable in surgery within the brain, where visual feedback is limited. The accuracy of the mapping between physical and image space depends upon the accuracy with which the fiducial markers were located in each coordinate system. To effect accurate space registration for interactive, image-guided neurosurgery, the use of permanent fiducial markers implanted into the surface of the skull is proposed in this paper. These small cylindrical markers are composed of materials that make them visible in the image sets. The challenge lies in locating the subcutaneous markers in physical space. This paper presents an ultrasonic technique for transcutaneously detecting the location of these markers. The technique incorporates an algorithm based on detection of characteristic properties of the reflected A-mode ultrasonic waveform. The results demonstrate that ultrasound is an appropriate technique for accurate transcutaneous marker localization. The companion paper to this article describes an automatic, enhanced implementation of the marker-localization theory described in this article     

Iterative principal axes registration method for analysis of MR-PETbrain images

Computerized automatic registration of MR-PET images of the brain is of significant interest for multimodality brain image analysis. Here, the authors discuss the principal axes transformation for registration of three-dimensional MR and PET images. A new brain phantom designed to test MR-PET registration accuracy determines that the principal axes registration (PAR) method is accurate to within an average of 1.37 mm with a standard deviation of 0.78 mm. Often the PET scans are not complete in the sense that the PET volume does not match the respective MR volume. The authors have developed an iterative PAR (IPAR) algorithm for such cases. Partial volumes of PET can be accurately registered to the complete MR volume using the new iterative algorithm. The quantitative and qualitative analyses of MR-PET image registration are presented and discussed. Results show that the new PAR algorithm is accurate and practical in MR-PET correlation studies     

Modelling prostate motion for data fusion during image-guided interventions

There is growing clinical demand for image registration techniques that allow multimodal data fusion for accurate targeting of needle biopsy and ablative prostate cancer treatments. However, during procedures where transrectal ultrasound (TRUS) guidance is used, substantial gland deformation can occur due to TRUS probe pressure. In this paper, the ability of a statistical shape/motion model, trained using finite element simulations, to predict and compensate for this source of motion is investigated. Three-dimensional ultrasound images acquired on five patient prostates, before and after TRUS-probe-induced deformation, were registered using a nonrigid, surface-based method, and the accuracy of different deformation models compared. Registration using a statistical motion model was found to outperform alternative elastic deformation methods in terms of accuracy and robustness, and required substantially fewer target surface points to achieve a successful registration. The mean final target registration error (based on anatomical landmarks) using this method was 1.8 mm. We conclude that a statistical model of prostate deformation provides an accurate, rapid and robust means of predicting prostate deformation from sparse surface data, and is therefore well-suited to a number of interventional applications where there is a need for deformation compensation.     

极轴式望远镜主镜支撑结构对镜面变形的影响

根据极轴式望远镜的工作特点,以口径为700 mm的极轴式望远镜主镜室系统为例,确定了一套主镜支撑方案。借助于有限元分析软件MSC.Patran详细地建立了系统的有限元模型,选取多种工况,分析了系统在自重作用下的镜面变形情况,绘制了镜面变形误差PV值和RMS值的变化曲线。结果表明:镜面变形主要受角的影响,随着的增大而减小,径向支撑效果优于轴向支撑效果,镜面变形误差满足设计指标要求。在主镜室系统竖直放置时,利用Zygo干涉仪测得带支撑结构的镜面变形误差RMS值为28.48 nm,表明主镜在该支撑结构作用下的面形接近于加工检测时的状态,同时也验证了有限元模型的准确性。     

Automatic fusion of freehand endoscopic brain images to three-dimensional surfaces: creating stereoscopic panoramas

A major limitation of the use of endoscopes in minimally invasive surgery is the lack of relative context between the endoscope and its surroundings. The purpose of this work was to fuse images obtained from a tracked endoscope to surfaces derived from three-dimensional (3-D) preoperative magnetic resonance or computed tomography (CT) data, for assistance in surgical planning, training and guidance. We extracted polygonal surfaces from preoperative CT images of a standard brain phantom and digitized endoscopic video images from a tracked neuro-endoscope. The optical properties of the endoscope were characterized using a simple calibration procedure. Registration of the phantom (physical space) and CT images (preoperative image space) was accomplished using fiducial markers that could be identified both on the phantom and within the images. The endoscopic images were corrected for radial lens distortion and then mapped onto the extracted surfaces via a two-dimensional 2-D to 3-D mapping algorithm. The optical tracker has an accuracy of about 0.3 mm at its centroid, which allows the endoscope tip to be localized to within 1.0 mm. The mapping operation allows multiple endoscopic images to be "painted" onto the 3-D brain surfaces, as they are acquired, in the correct anatomical position. This allows panoramic and stereoscopic visualization, as well as navigation of the 3-D surface, painted with multiple endoscopic views, from arbitrary perspectives.     

Sphere-filled organ model for virtual surgery system

We have been developing a virtual surgery system that is capable of simulating surgical maneuvers on elastic organs. In order to perform such maneuvers, we have created a deformable organ model using a sphere-filled method instead of the finite element method. This model is suited for real-time simulation and quantitative deformation. Furthermore, we have equipped this model with a sense of touch and a sense of force by connecting it to a force feedback device. However, in the initial stage the model became problematic when faced with complicated incisions. Therefore, we modified this model by developing an algorithm for organ deformation that performs various, complicated incisions while taking into account the effect of gravity. As a result, the sphere-filled model allowed our system to respond to various incisions that deform the organ. Thus, various physical manipulations that involve pressing, pinching, or incising an organ's surface can be performed. Furthermore, the deformation of the internal organ structures and changes in organ vasculature can be observed via the internal spheres' behavior.