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.     

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.     

A computational model for tracking subsurface tissue deformationduring stereotactic neurosurgery

Recent advances in the field of sterotactic neurosurgery have made it possible to coregister preoperative computed tomography (CT) and magnetic resonance (MR) images with instrument locations in the operating field. However, accounting for intraoperative movement of brain tissue remains a challenging problem. While intraoperative CT and MR scanners record concurrent tissue motion, there is motivation to develop methodologies which would be significantly lower in cost and more widely available. The approach the authors present is a computational model of brain tissue deformation that could be used in conjunction with a limited amount of concurrently obtained operative data to estimate subsurface tissue motion. Specifically, the authors report on the initial development of a finite element model of brain tissue adapted from consolidation theory. Validations of the computational mathematics in two and three dimensions are shown with errors of 1%-2% for the discretizations used. Experience with the computational strategy for estimating surgically induced brain tissue motion in vivo is also presented. While the predicted tissue displacements differ from measured values by about 15%, they suggest that exploiting a physics-based computational framework for updating preoperative imaging databases during the course of surgery has considerable merit. However, additional model and computational developments are needed before this approach can become a clinical reality     

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.     

Augmented virtuality based on stereoscopic reconstruction in multimodal image-guided neurosurgery: methods and performance evaluation

Displaying anatomical and physiological information derived from preoperative medical images in the operating room is critical in image-guided neurosurgery. This paper presents a new approach referred to as augmented virtuality (AV) for displaying intraoperative views of the operative field over three-dimensional (3-D) multimodal preoperative images onto an external screen during surgery. A calibrated stereovision system was set up between the surgical microscope and the binocular tubes. Three-dimensional surface meshes of the operative field were then generated using stereopsis. These reconstructed 3-D surface meshes were directly displayed without any additional geometrical transform over preoperative images of the patient in the physical space. Performance evaluation was achieved using a physical skull phantom. Accuracy of the reconstruction method itself was shown to be within 1 mm (median: 0.76 mm +/- 0.27), whereas accuracy of the overall approach was shown to be within 3 mm (median: 2.29 mm +/- 0.59), including the image-to-physical space registration error. We report the results of six surgical cases where AV was used in conjunction with augmented reality. AV not only enabled vision beyond the cortical surface but also gave an overview of the surgical area. This approach facilitated understanding of the spatial relationship between the operative field and the preoperative multimodal 3-D images of the patient.     

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.     

基于稀疏特征匹配和形变传播的无缝图像拼接

该文给出了一种基于稀疏特征匹配和形变传播的无缝图像拼接方法。首先,在配准图像的重叠区域中寻找一条结构误差最小的最佳接缝,从一边的图像中选取目标区域;接着,沿着接缝在两边的图像区域中检测出显著的结构特征,并进行特征匹配,获得目标区域中接缝上的匹配特征点及与之关联的边缘特征点的结构形变矢量;然后,通过求解泊松方程,将这些稀疏的形变矢量稳定和平滑地传播到目标区域内部,得到目标区域中各点的形变矢量;最后,由形变矢量通过内插获得目标区域的梯度场,并由梯度场重构出最终结果。该方法执行方便快速,不需要复杂的特征检测,能够统一地纠正图像拼接中较大的结构错位和颜色过渡不自然,在全局上消除结构接缝和颜色接缝。与其它方法比较,该方法获得较明显的改进。     

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.      

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.     

Compensating for intraoperative soft-tissue deformations using incomplete surface data and finite elements

Image-guided liver surgery requires the ability to identify and compensate for soft tissue deformation in the organ. The predeformed state is represented as a complete three-dimensional surface of the organ, while the intraoperative data is a range scan point cloud acquired from the exposed liver surface. The first step is to rigidly align the coordinate systems of the intraoperative and preoperative data. Most traditional rigid registration methods minimize an error metric over the entire data set. In this paper, a new deformation-identifying rigid registration (DIRR) is reported that identifies and aligns minimally deformed regions of the data using a modified closest point distance cost function. Once a rigid alignment has been established, deformation is accounted for using a linearly elastic finite element model (FEM) and implemented using an incremental framework to resolve geometric nonlinearities. Boundary conditions for the incremental formulation are generated from intraoperatively acquired range scan surfaces of the exposed liver surface. A series of phantom experiments is presented to assess the fidelity of the DIRR and the combined DIRR/FEM approaches separately. The DIRR approach identified deforming regions in 90% of cases under conditions of realistic surgical exposure. With respect to the DIRR/FEM algorithm, subsurface target errors were correctly located to within 4 mm in phantom experiments.     

A Validated Model of Calf Compression and Deep Vessel Collapse During External Cuff Inflation

This paper presents a validated model of calf compression with an external pressure cuff as used for deep vein thrombosis. Magnetic resonance (MR) images of calf geometry were used to generate subject-specific finite-element (FE) models of the calf cross section. Ultrasound images of deep vessel collapse obtained through a water-filled cuff were used to validate model behavior. Calf/cuff pressure interface measurements were applied to the FE model and the resulting tissue deformation was compared with MR image in normal volunteers (three females, four males, age range 20-55) using two distinct cuffs. MR observations and the model results showed good qualitative agreement. A similar reduction in cross-sectional area of the posterior tibial veins was obtained under both symmetric compression (89%) and asymmetric compression (81%), but greater compression of the anterior tibial veins was achieved with symmetric compression. The need to account for the effective compressibility of the calf tissue suggests that external measurements of the calf tissue deformation will not accurately predict deep vessel collapse. These results have implications for the modification of venous haemodynamics by such systems and could help to improve cuff design.     

Alignment of sparse freehand 3-D ultrasound with preoperative images of the liver using models of respiratory motion and deformation

We present a method for alignment of an interventional plan to optically tracked two-dimensional intraoperative ultrasound (US) images of the liver. Our clinical motivation is to enable the accurate transfer of information from three-dimensional preoperative imaging modalities [magnetic resonance (MR) or computed tomography (CT)] to intraoperative US to aid needle placement for thermal ablation of liver metastases. An initial rigid registration to intraoperative coordinates is obtained using a set of US images acquired at maximum exhalation. A preprocessing step is applied to both the preoperative images and the US images to produce evidence of corresponding structures. This yields two sets of images representing classification of regions as vessels. The registration then proceeds using these images. The preoperative images and plan are then warped to correspond to a single US slice acquired at an unknown point in the breathing cycle where the liver is likely to have moved and deformed relative to the preoperative image. Alignment is constrained using a patient-specific model of breathing motion and deformation. Target registration error is estimated by carrying out simulation experiments using resliced MR volumes to simulate real US and comparing the registration results to a "bronze-standard" registration performed on the full MR volume. Finally, the system is tested using real US and verified using visual inspection.     

Reconstruction of 3-D head geometry from digitized point sets: an evaluation study

In this paper, we evaluate different methods to estimate patient-specific scalp, skull, and brain surfaces from a set of digitized points from the target's scalp surface. The reconstruction problem is treated as a registration problem: An a priori surface model, consisting of the scalp, skull, and brain surfaces, is registered to the digitized surface points. The surface model is generated from segmented magnetic resonance (MR) volume images. We study both affine and free-form deformation (FFD) registration, the use of average models, the averaging of individual registration results, a model selection procedure, and statistical deformation models. The registration algorithms are mainly previously published, and the objective of this paper is to evaluate these methods in this particular application with sparse data. The main interest of this paper is to generate geometric head models for biomedical applications, such as electroencephalography and magnetoencephalographic. However, the methods can also be applied to other anatomical regions and to other application areas. The methods were validated using 15 MR volume images, from which the scalp, skull, and brain were manually segmented. The best results were achieved by averaging the results of the FFD registrations of the database: the mean distance from the manually segmented target surface to a deformed a priori model surface for the studied anatomical objects was 1.68-2.08 mm, depending on the point set used. The results support the use of the evaluated methods for the reconstruction of geometric models in applications with sparse data.     

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.     

An electromechanical model of the heart for image analysis and simulation

This paper presents a new three-dimensional electromechanical model of the two cardiac ventricles designed both for the simulation of their electrical and mechanical activity, and for the segmentation of time series of medical images. First, we present the volumetric biomechanical models built. Then the transmembrane potential propagation is simulated, based on FitzHugh-Nagumo reaction-diffusion equations. The myocardium contraction is modeled through a constitutive law including an electromechanical coupling. Simulation of a cardiac cycle, with boundary conditions representing blood pressure and volume constraints, leads to the correct estimation of global and local parameters of the cardiac function. This model enables the introduction of pathologies and the simulation of electrophysiology interventions. Moreover, it can be used for cardiac image analysis. A new proactive deformable model of the heart is introduced to segment the two ventricles in time series of cardiac images. Preliminary results indicate that this proactive model, which integrates a priori knowledge on the cardiac anatomy and on its dynamical behavior, can improve the accuracy and robustness of the extraction of functional parameters from cardiac images even in the presence of noisy or sparse data. Such a model also allows the simulation of cardiovascular pathologies in order to test therapy strategies and to plan interventions.     

A framework for predictive modeling of anatomical deformations

A framework for modeling and predicting anatomical deformations is presented, and tested on simulated images. Although a variety of deformations can be modeled in this framework, emphasis is placed on surgical planning, and particularly on modeling and predicting changes of anatomy between preoperative and intraoperative positions, as well as on deformations induced by tumor growth. Two methods are examined. The first is purely shape-based and utilizes the principal modes of co-variation between anatomy and deformation in order to statistically represent deformability. When a patient's anatomy is available, it is used in conjunction with the statistical model to predict the way in which the anatomy will/can deform. The second method is related, and it uses the statistical model in conjunction with a biomechanical model of anatomical deformation. It examines the principal modes of co-variation between shape and forces, with the latter driving the biomechanical model, and thus predicting deformation. Results are shown on simulated images, demonstrating that systematic deformations, such as those resulting from change in position or from tumor growth, can be estimated very well using these models. Estimation accuracy will depend on the application, and particularly on how systematic a deformation of interest is.     

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.     

Computer-aided placement of deep brain stimulators: from planning to intraoperative guidance

In current practice, optimal placement of deep-brain stimulators (DBSs) used to treat movement disorders in patients with Parkinson's disease and essential tremor is an iterative procedure. A target is chosen preoperatively based on anatomical landmarks identified on magnetic resonance images. This point is used as an initial position that is refined intraoperatively using both microelectrode recordings and macrostimulation. In this paper, we report on our current progress toward developing a system for the computer-assisted preoperative selection of target points and for the intraoperative adjustment of these points. The system consists of a deformable atlas of optimal target points that can be used to select automatically the preoperative target, of an electrophysiological atlas, and of an intraoperative interface. Results we have obtained show that automatic prediction of target points is an achievable goal. Our results also indicate that electrophysiological information could be used to resolve structures not visible in anatomic images, thus improving both preoperative and intraoperative guidance. Our intraoperative system has reached the stage of a working prototype and we compare targeting accuracy as well as the number of paths needed to reach the targets with our system and with the method in current clinical use.     

多元经验模态分解及在SAR图像目标识别中的应用

提出基于多元模态分解的合成孔径雷达（SAR）目标识别方法。多元模态分解是传统模态分解的多元扩展,能够有效避免传统算法中的模态混叠问题。采用多元模态分解对SAR图像进行处理,获得的多层次固有模式函数（IMF）能够更为有效地反映目标的时频特性。不同IMF之间具有良好互补性,同时它们描述同一目标因而具有内在关联性。分类阶段,采用联合稀疏表示对分解得到的IMF进行表征。联合稀疏表示在多任务学习的理念下,对多个关联稀疏表示问题进行求解,可获得更为可靠的估计结果。在获得各层次IMF对应的稀疏表示系数矢量的基础上,计算不同类别对于当前测试样本多层次IMF的重构误差之和,进而判定测试样本的目标类别。基于MSTAR数据集开展实验,通过在标准操作条件、俯仰角差异、噪声干扰以及目标遮挡条件下进行对比分析,验证了提出方法的有效性。     

Imaging electrical impedance from acoustic measurements by means of magnetoacoustic tomography with magnetic induction (MAT-MI)

We have conducted computer simulation and experimental studies on magnetoacoustic-tomography with magnetic induction (MAT-MI) for electrical impedance imaging. In MAT-MI, the object to be imaged is placed in a static magnetic field, while pulsed magnetic stimulation is applied in order to induce eddy current in the object. In the static magnetic field, the Lorentz force acts upon the eddy current and causes acoustic vibrations in the object. The propagated acoustic wave is then measured around the object to reconstruct the electrical impedance distribution. In the present simulation study, a two-layer spherical model is used. Parameters of the model such as sample size, conductivity values, strength of the static and pulsed magnetic field, are set to simulate features of biological tissue samples and feasible experimental constraints. In the forward simulation, the electrical potential and current density are solved using Poisson's equation, and the acoustic pressure is calculated as the forward solution. The electrical impedance distribution is then reconstructed from the simulated pressure distribution surrounding the sample. The present computer simulation results suggest that MAT-MI can reconstruct conductivity images of biological tissue with high spatial resolution and high contrast. The feasibility of MAT-MI in providing high spatial resolution images containing impedance-related information has also been demonstrated in a phantom experiment.