Brain mechanics For neurosurgery: modeling issues Stelios K. Kyriacou, Ashraf Mohamed, Karol Miller, Samuel Neff Abstract 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 quan- titative 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. 1 Introduction The mechanical behavior of brain tissue is one of the most demanding and complicated to model. Depending on the application, viscoelastic (Miller 1999; Mendis et al. 1995; Wang and Wineman 1972), poroelastic (Paulsen et al. 1999; Miga et al. 1998a; Subramaniam et al. 1995; Kaczmarek et al. 1997; Pena et al. 1999; Nagashima et al. 1990; Tenti et al. 1999; Basser 1992) and even purely elastic (Kyriacou et al. 1999; Kyriacou and Davatzikos 1998; Takizawa et al. 1994; Ferrant et al. 2000) models have been used in different analyses. The characteristic time scale is very important for choosing the material model. Impact usually is modeled with viscoelasticity, while long term processes like hy- drocephalus can be modeled using poroelasticity or mixture theory due to the need to account for interstitial fluid movement. In applications like brain image registration, even a purely elastic model may suffice. Simulating the mechanical behavior of the human brain will be an important milestone in neu- rosurgery. One example is the following: neurosurgical retraction provides traction forces at the surface of the brain to provide a better field of view during microsurgical treatments such as clipping of skull base aneurysms. A complication of the retraction, however, may be neurological impairment due to a retractor-induced injury to the tissue (Yundt et al. 1997). Thus, a reasonably accurate simulation tool to predict the level of stress within the tissue would be of high value. More specifically, a biomechanical model of brain anatomy could be used to optimize retractor-applied pressure and Biomechan Model Mechanobiol 1 (2002) 151 – 164 Ó Springer-Verlag 2002 DOI 10.1007/s10237-002-0013-0 Original paper 151 Received: 19 March 2002 / Accepted: 6 June 2002 S. K. Kyriacou (&), A. Mohamed Department of Radiology and Radiological Science The Johns Hopkins University, Baltimore, Maryland e-mail: kyriacou@cbmv.jhu.edu K. Miller Department of Mechanical and Materials Engineering The University of Western Australia, Perth S. Neff Neurosurgery, St. Christopher’s Hospital for Children, Philadelphia, Pennsylvania Work is supported by a generous grant from the Whitaker Foundation. We would like to also thank Dr. Christos Davatzikos (Johns Hopkins School of Medicine, Baltimore, Maryland) for his help.