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.

Brain biomechanics has been investigated for more than 30 years. In particular, finite element analyses and other powerful computational methods have long been used to provide quantitative results in the investigation of dynamic processes such as head trauma. Nevertheless, the potential of these methods to simulate and predict the outcome of quasi-static processes such as neurosurgical procedures and neuropathological processes has only recently been explored. Some inherent difficulties in modeling brain tissues, which have impeded progress, are discussed in this work. The behavior of viscoelastic and poroelastic constitutive models is compared in simple 1-D simulations using the ABAQUS finite element platform. In addition, the behaviors of quasi-static brain constitutive models that have recently been proposed are compared. We conclude that a compressible viscoelastic solid model may be the most appropriate for modeling neurosurgical procedures.

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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.

Abstract.The finite element method is applied to the biomechanics of brain tissue deformation. Emphasis is given to the deformations induced by the growth of tumors, and to the deformable registration of anatomical atlases with patient images. A uniform contraction of the tumor is first used to obtain an estimate of the shape of the brain prior to the growth of the tumor. A subsequent nonlinear regression method is used to improve on the above estimate. The resulting deformation mapping is finally applied to an atlas, yielding the registration of the atlas with the tumor-deformed anatomy. A preliminary 2D implementation that includes inhomogeneity and a nonlinear elastic material model is tested on simulated data as well as a patient image. The long-term scope of this work is its application to surgical planning systems.

It is advantageous in mechanics to identify experiments that correspond to tractable boundary value problems—this facilitates data reduction and interpretation. Increasingly more situations are arising, however, wherein experimentalists cannot dictate the geometry or applied loads during testing. Inverse finite element methods are, therefore, becoming essential tools for calculating material parameters. In this paper, we present numerical and experimental results that show that one such inverse finite element method is very useful in characterizing the mechanical behavior of neo-Hookean (rubber) membranes subjected to axisymmetric and nonaxisymmetric finite inflations.

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