A computational model for tracking subsurface tissue deformation during stereotactic neurosurgery

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.

Modeling of retraction and resection for intraoperative updating of images

OBJECTIVE

Intraoperative tissue deformation that occurs during the course of neurosurgical procedures may compromise patient-to-image registration, which is essential for image guidance. A new approach to account for brain shift, using computational methods driven by sparsely available operating room (OR) data, has been augmented with techniques for modeling tissue retraction and resection.

METHODS

Modeling strategies to arbitrarily place and move an intracranial retractor and to excise designated tissue volumes have been implemented within a computationally tractable framework. To illustrate these developments, a surgical case example, which uses OR data and the preoperative neuroanatomic image volume of the patient to generate a highly resolved, heterogeneous, finite-element model, is presented. Surgical procedures involving the retraction of tissue and the resection of a left frontoparietal tumor were simulated computationally, and the simulations were used to update the preoperative image volume to represent the dynamic OR environment.

RESULTS

Retraction and resection techniques are demonstrated to accurately reflect intraoperative events, thus providing an approach for near-real-time image-updating in the OR. Information regarding subsurface deformation and, in particular, changing tumor margins is presented. Some of the current limitations of the model, with respect to specific tissue mechanical responses, are highlighted.

CONCLUSION

The results presented demonstrate that complex surgical events such as tissue retraction and resection can be incorporated intraoperatively into the model-updating process for brain shift compensation in high-resolution preoperative images.

Serial intraoperative magnetic resonance imaging of brain shift

OBJECTIVE

A major shortcoming of image-guided navigational systems is the use of preoperatively acquired image data, which does not account for intraoperative changes in brain morphology. The occurrence of these surgically induced volumetric deformations ("brain shift") has been well established. Maximal measurements for surface and midline shifts have been reported. There has been no detailed analysis, however, of the changes that occur during surgery. The use of intraoperative magnetic resonance imaging provides a unique opportunity to obtain serial image data and characterize the time course of brain deformations during surgery.

METHODS

The vertically open intraoperative magnetic resonance imaging system (SignaSP, 0.5 T; GE Medical Systems, Milwaukee, WI) permits access to the surgical field and allows multiple intraoperative image updates without the need to move the patient. We developed volumetric display software (the 3D Slicer) that allows quantitative analysis of the degree and direction of brain shift. For 25 patients, four or more intraoperative volumetric image acquisitions were extensively evaluated.

RESULTS

Serial acquisitions allow comprehensive sequential descriptions of the direction and magnitude of intraoperative deformations. Brain shift occurs at various surgical stages and in different regions. Surface shift occurs throughout surgery and is mainly attributable to gravity. Subsurface shift occurs during resection and involves collapse of the resection cavity and intraparenchymal changes that are difficult to model.

CONCLUSION

Brain shift is a continuous dynamic process that evolves differently in distinct brain regions. Therefore, only serial imaging or continuous data acquisition can provide consistently accurate image guidance. Furthermore, only serial intraoperative magnetic resonance imaging provides an accurate basis for the computational analysis of brain deformations, which might lead to an understanding and eventual simulation of brain shift for intraoperative guidance.

In Vivo Analysis of Heterogeneous Brain Deformation Computations for Model-Updated Image Guidance

Neurosurgical image-guidance has historically relied on the registration of the patient and preoperative imaging series with surgical instruments in the operating room (OR) coordinate space. Recent studies measuring intraoperative tissue motion have suggested that deformation-induced misregistration from surgical loading is a serious concern with such systems. In an effort to improve registration fidelity during surgery, we are pursuing an approach which uses a predictive computational model in conjunction with data available in the OR to update the high resolution preoperative image series. In previous work, we have developed an in vivo experimental system in the porcine brain which has been used to investigate a homogeneous finite element rendering of consolidation theory as a tissue deformation model. In this paper, our computational approach has been extended to include heterogeneous tissue property distributions determined from an image-to-grid segmentation scheme. Results produced under two different loading conditions show that heterogeneity in the stiffness properties and interstitial pressure gradients varied over a range of physiologically reasonable values account for 1-3% and 5-8% of the predicted tissue motion, respectively, while homogeneous linear elasticity is responsible for 60-70% of the surgically-induced motion that has been recoverable with our model-based approach.

Quantification of, visualization of, and compensation for brain shift using intraoperative magnetic resonance imaging

OBJECTIVE

Modern neuronavigation systems lack spatial accuracy during ongoing surgical procedures because of increasing brain deformation, known as brain shift. Intraoperative magnetic resonance imaging was used for quantitative analysis and visualization of this phenomenon.

METHODS

For a total of 64 patients, we used a 0.2-T, open-configuration, magnetic resonance imaging scanner, located in an operating theater, for pre- and intraoperative imaging. The three-dimensional imaging data were aligned using rigid registration methods. The maximal displacements of the brain surface, deep tumor margin, and midline structures were measured. Brain shift was observed in two-dimensional image planes using split-screen or overlay techniques, and three-dimensional, color-coded, deformable surface-based data were computed. In selected cases, intraoperative images were transferred to the neuronavigation system to compensate for the effects of brain shift.

RESULTS

The results demonstrated that there was great variability in brain shift, ranging up to 24 mm for cortical displacement and exceeding 3 mm for the deep tumor margin in 66% of all cases. Brain shift was influenced by tissue characteristics, intraoperative patient positioning, opening of the ventricular system, craniotomy size, and resected volume. Intraoperative neuronavigation updating (n = 14) compensated for brain shift, resulting in reliable navigation with high accuracy.

CONCLUSION

Without brain shift compensation, neuronavigation systems cannot be trusted at critical steps of the surgical procedure, e.g., identification of the deep tumor margin. Intraoperative imaging allows not only evaluation of and compensation for brain shift but also assessment of the quality of mathematical models that attempt to describe and compensate for brain shift.

Mechanical properties of brain tissue in-vivo: experiment and computer simulation

Realistic computer simulation of neurosurgical procedures requires incorporation of the mechanical properties of brain tissue in the mathematical model. Possible applications of computer simulation of neurosurgery include non-rigid registration, virtual reality training and operation planning systems and robotic devices to perform minimally invasive brain surgery. A number of constitutive models of brain tissue, both single-phase and bi-phasic, have been proposed in recent years. The major deficiency of most of them, however, is the fact that they were identified using experimental data obtained in vitro and there is no certainty whether they can be applied in the realistic in vivo setting. In this paper we attempt to show that previously proposed by us hyper-viscoelastic constitutive model of brain tissue can be applied to simulating surgical procedures. An in vivo indentation experiment is described. The force-displacement curve for the loading speed typical for surgical procedures is concave upward containing no linear portion from which a meaningful elastic modulus might be determined. In order to properly analyse experimental data, a three-dimensional, non-linear finite element model of the brain was developed. Magnetic resonance imaging techniques were used to obtain geometric information needed for the model. The shape of the force-displacement curve obtained using the numerical solution was very similar to the experimental one. The predicted forces were about 31% lower than those recorded during the experiment. Having in mind that the coefficients in the model had been identified based on experimental data obtained in vitro, and large variability of mechanical properties of biological tissues, such agreement can be considered as very good. By appropriately increasing material parameters describing instantaneous stiffness of the tissue one is able, without changing the structure of the model, to reproduce experimental curve almost perfectly. Numerical studies showed also that the linear, viscoelastic model of brain tissue is not appropriate for the modelling brain tissue deformation even for moderate strains.

Model-Updated Image-Guided Neurosurgery: Preliminary Analysis Using Intraoperative MR

In this paper, initial clinical data from an intraoperative MR system are compared to calculations made by a three-dimensional finite element model of brain deformation. The preoperative and intraoperative MR data was collected on a patient undergoing a resection of an astrocytoma, grade 3 with non-enhancing and enhancing regions. The image volumes were co-registered and cortical displacements as well as subsurface structure movements were measured retrospectively. These data were then compared to model predictions undergoing intraoperative conditions of gravity and simulated tumor decompression. Computed results demonstrate that gravity and decompression effects account for approximately 40% and 30%, respectively, totaling a 70% recovery of shifting structures with the model. The results also suggest that a non-uniform decompressive stress distribution may be present during tumor resection. Based on this preliminary experience, model predictions constrained by intraoperative surface data appear to be a promising avenue for correcting brain shift during surgery. However, additional clinical cases where volumetric intraoperative MR data is available are needed to improve the understanding of tissue mechanics during resection.

Updated neuroimaging using intraoperative brain modeling and sparse data

A strategy to update preoperative imaging for image-guided surgery using readily available intraoperative information has been developed and implemented. A patient-specific three-dimensional finite element model of the brain is generated from preoperative MRI and used to simulate deformation resulting from multiple surgical processes. Intraoperatively obtained sparse imaging data, such as from digital cameras or ultrasonography, is then used to prescribe the displacement of selected points within the model. Interpolation to the resolution of preoperative imaging may then be performed based upon the model. The algorithms for generation of the finite element model and for its subsequent deformation have been successfully validated using a pig brain model, and preliminary clinical application in the operating room has demonstrated feasibility.

In vivo modeling of interstitial pressure in the brain under surgical load using finite elements

Current brain deformation models have predominantly reflected solid constitutive relationships generated from empirical ex vivo data and have largely overlooked interstitial hydrodynamic effects. In the context of a technique to update images intraoperatively for image-guided neuronavigation, we have developed and quantified the deformation characteristics of a three-dimensional porous media finite element model of brain deformation in vivo. Results have demonstrated at least 75-85 percent predictive capability, but have also indicated that interstitial hydrodynamics are important. In this paper we investigate interstitial pressure transient behavior in brain tissue when subjected to an acute surgical load consistent with neurosurgical events. Data are presented from three in vivo porcine experiments where subsurface tissue deformation and interhemispheric pressure gradients were measured under conditions of an applied mechanical deformation and then compared to calculations with our three-dimensional brain model. Results demonstrate that porous-media consolidation captures the hydraulic behavior of brain tissue subjected to comparable surgical loads and that the experimental protocol causes minimal trauma to porcine brain tissue. Working values for hydraulic conductivity of white and gray matter are also reported and an assessment of transient pressure gradient effects with respect to deformation is provided.

Sources of error in comparing functional magnetic resonance imaging and invasive electrophysiological recordings

OBJECT

Several authors have recently reported studies in which they aim to validate functional magnetic resonance (fMR) imaging against the accepted gold standard of invasive electrophysiological monitoring. The authors have conducted a similar study, and in this paper they identify and quantify two characteristics of these data that can make such a comparison problematic.

METHODS

Eight patients in whom surgery for epilepsy was performed and five healthy volunteers underwent fMR imaging to localize the part of the sensorimotor cortex responsible for hand movement. In the patient group subdural electrode mats were subsequently implanted to identify eloquent regions of the brain and the epileptogenic zone. The fMR imaging data were processed to correct for motion during the study and then registered with a postimplantation computerized tomography (CT) scan on which the electrodes were visible. The motion during imaging in the two groups studied, and the deformation of the brain between the preoperative images and postoperative scans were measured. The patients who underwent epilepsy surgery moved significantly more during fMR imaging experiments than healthy volunteers performing the same motor task. This motion had a particularly increased out-of-plane component and was significantly more correlated with the stimulus than in the volunteers. This motion was especially increased when the patients were performing a task on the side affected by the lesion. The additional motion is hard to correct and substantially degrades the quality of the resulting fMR images, making it a much less reliable technique for use in these patients than in others. Also, the authors found that after electrode implantation, the brain surface can shift more than 10 mm relative to the skull compared with its preoperative location, substantially degrading the accuracy of the comparison of electrophysiological measurements made in the deformed brain and fMR studies obtained preoperatively.

CONCLUSIONS

These two findings indicate that studies of this sort are currently of limited use for validating fMR imaging and should be interpreted with care. Additional image analysis research is necessary to solve the problems caused by patients' motion and brain deformation.

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.

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.

An overlapping subzone technique for MR-based elastic property reconstruction

A finite element-based nonlinear inversion scheme for magnetic resonance (MR) elastography is detailed. The algorithm operates on small overlapping subzones of the total region of interest, processed in a hierarchical order as determined by progressive error minimization. This zoned approach allows for a high degree of spatial discretization, taking advantage of the data-rich environment afforded by the MR. The inversion technique is tested in simulation under high-noise conditions (15% random noise applied to the displacement data) with both complicated user-defined stiffness distributions and realistic tissue geometries obtained by thresholding MR image slices. In both cases the process has proved successful and has been capable of discerning small inclusions near 4 mm in diameter. Magn Reson Med 42:779-786, 1999.

Model-updated image guidance: initial clinical experiences with gravity-induced brain deformation

Image-guided neurosurgery relies on accurate registration of the patient, the preoperative image series, and the surgical instruments in the same coordinate space. Recent clinical reports have documented the magnitude of gravity-induced brain deformation in the operating room and suggest these levels of tissue motion may compromise the integrity of such systems. We are investigating a model-based strategy which exploits the wealth of readily-available preoperative information in conjunction with intraoperatively acquired data to construct and drive a three dimensional (3-D) computational model which estimates volumetric displacements in order to update the neuronavigational image set. Using model calculations, the preoperative image database can be deformed to generate a more accurate representation of the surgical focus during an operation. In this paper, we present a preliminary study of four patients that experienced substantial brain deformation from gravity and correlate cortical shift measurements with model predictions. Additionally, we illustrate our image deforming algorithm and demonstrate that preoperative image resolution is maintained. Results over the four cases show that the brain shifted, on average, 5.7 mm in the direction of gravity and that model predictions could reduce this misregistration error to an average of 1.2 mm.

Model-Updated Image-Guided Neurosurgery Using the Finite Element Method: Incorporation of the Falx Cerebri

Surgeons using neuronavigation have realized the value of image guidance for feature recognition as well as for the precise application of surgical instruments. Recently, there has been a growing concern about the extent of intraoperative misregistration due to tissue deformation. Intraoperative imaging is currently under evaluation but limitations related to cost effectiveness and image clarity have made its wide spread adoption uncertain. As a result, computational model-guided techniques have generated considerable appeal as an alternative approach. In this paper, we report our initial experience with enhancing our brain deformation model by explicitly adding the falx cerebri. The simulations reported show significant differences in subsurface deformation with the falx serving to damp the communication of displacement between hemispheres by as much as 4 mm. Additionally, these calculations, based on a human clinical case, demonstrate that while cortical shift predictions correlate well with various forms of the model (70-80% of surface motion recaptured), substantial differences in subsurface deformation occurs suggesting that subsurface validation of model-guided techniques will be important for advancing this concept.

Nonlinear elastic registration of brain images with tumor pathology using a biomechanical model

A biomechanical model of the brain is presented, using a finite-element formulation. Emphasis is given to the modeling of the soft-tissue deformations induced by the growth of tumors and its application to the registration of anatomical atlases, with images from patients presenting such pathologies. First, an estimate of the anatomy prior to the tumor growth is obtained through a simulated biomechanical contraction of the tumor region. Then a normal-to-normal atlas registration to this estimated pre-tumor anatomy is applied. Finally, the deformation from the tumor-growth model is applied to the resultant registered atlas, producing an atlas that has been deformed to fully register to the patient images. The process of tumor growth is simulated in a nonlinear optimization framework, which is driven by anatomical features such as boundaries of brain structures. The deformation of the surrounding tissue is estimated using a nonlinear elastic model of soft tissue under the boundary conditions imposed by the skull, ventricles, and the falx and tentorium. A preliminary two-dimensional (2-D) implementation is presented in this paper, and tested on both simulated and patient data. One of the long-term goals of this work is to use anatomical brain atlases to estimate the locations of important brain structures in the brain and to use these estimates in presurgical and radiosurgical planning systems.

Error analysis for a free-hand three-dimensional ultrasound system for neuronavigation

Image-guided neurosurgery that is directed by a preoperative imaging study, such as magnetic resonance (MR) imaging or computerized tomography (CT) scanning, can be very accurate provided no significant changes occur during surgery. A variety of factors known to affect brain tissue movement are not reflected in the preoperative images used for guidance. To update the information on which neuronavigation is based, the authors propose the use of three-dimensional (3-D) ultrasound images in conjunction with a finite-element computational model of the deformation of the brain. The 3-D ultrasound system will provide real-time information on the displacement of deep structures to guide the mathematical model. This paper has two goals: first, to present an outline of steps necessary to compute the location of a feature appearing in an ultrasound image in an arbitrary coordinate system; and second, to present an extensive evaluation of this system's accuracy. The authors have found that by using a stylus rigidly coupled to the 3-D tracker's sensor, they were able to locate a point with an overall error of 1.36 ± 1.67 mm (based on 39 points). When coupling the tracker to an ultrasound scanhead, they found that they could locate features appearing on ultrasound images with an error of 2.96 ± 1.85 mm (total 58 features). They also found that when registering a skull phantom to coordinates that were defined by MR imaging or CT scanning, they could do so with an error of 0.86 ± 0.61 mm (based on 20 coordinates). Based on their previous finding of brain shifts on the order of 1 cm during surgery, the accuracy of their system warrants its use in updating neuronavigation imaging data.

Initial In-Vivo Analysis of 3D Heterogeneous Brain Computations for Model-Updated Image-Guided Neurosurgery

Registration error resulting from intraoperative brain shift due to applied surgical loads has long been recognized as one of the most challenging problems in the field of frameless stereotactic neurosurgery. To address this problem, we have developed a 3-dimensional finite element model of the brain and have begun to quantify its predictive capability in an in vivo porcine model. Previous studies have shown that we can predict the average total displacement within 15% and 6.6% error using intraparenchymal and temporal deformation sources, respectively, under relatively simple model assumptions. In this paper, we present preliminary results using a heterogeneous model with an expanding temporally located mass and show that we are capable of predicting an average total displacement to 5.7% under similar model initial and boundary conditions. We also demonstrate that our approach can be viewed as having the capability of recapturing approximately 75% of the registration inaccuracy that may be generated by preoperative-based image-guided neurosurgery.