Karol Miller

Mechanical properties of brain tissue in tension

This paper contains experimental results of in vitro, uniaxial tension of swine brain tissue in finite deformation as well as proposes a new hyper-viscoelastic constitutive model for the brain tissue. The experimental results obtained for two loading velocities, corresponding to strain rates of 0.64 and 0.64 x 10(-2)s(-1), are presented. We believe that these are the first ever experiments of this kind. The applied strain rates were similar to those applied in our previous study, focused on explaining brain tissue properties in compression. The stress-strain curves are convex downward for all extension rates. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. Swine brain tissue was found to be considerably softer in extension than in compression. Previously proposed in the literature brain tissue constitutive models, developed based on experimental data collected in compression are shown to be inadequate to explain tissue behaviour in tension. A new, non-linear, viscoelastic model based on the generalisation of the Ogden strain energy hyper-elastic constitutive equation is proposed. The new model accounts well for brain tissue deformation behaviour in both tension and compression (natural strain in <-0.3,0.2>) for strain rates ranging over five orders of magnitude.

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.

Constitutive modelling of brain tissue: experiment and theory

Recent developments in computer-integrated and robot-aided surgery--in particular, the emergence of automatic surgical tools and robots--as well as advances in virtual reality techniques, call for closer examination of the mechanical properties of very soft tissues (such as brain, liver, kidney, etc.). The ultimate goal of our research into the biomechanics of these tissues is the development of corresponding, realistic mathematical models. This paper contains experimental results of in vitro, uniaxial, unconfined compression of swine brain tissue and discusses a single-phase, non-linear, viscoelastic tissue model. The experimental results obtained for three loading velocities, ranging over five orders of magnitude, are presented. The applied strain rates have been much lower than those applied in previous studies, focused on injury modelling. The stress-strain curves are concave upward for all compression rates containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. The use of the single-phase model is recommended for applications in registration, surgical operation planning and training systems as well as a control system of an image-guided surgical robot. The material constants for the brain tissue are evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude.

Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.

Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot

An optimal kinematic design method suited for parallel manipulators is developed. The kinematic optimization process yields a design that delivers the best compromise between manipulability and a new performance index, space utilisation. It is shown that the exhaustive search minimization algorithm is effective for as many as four independent design variables and presents a viable alternative to advanced nonlinear programming methods. The proposed kinematic optimization method is applied to the Linear Delta: a three degree of freedom translational manipulator. The kinematics of the Linear Delta are solved via the polynomial method. The mobility, workspace and manipulability characteristics are examined. It is shown that the Linear Deltas manipulability generally exhibits relatively little variation when compared to space utilization. The tendency exists for the solution to converge on a zero workspace size architecture when manipulability is optimized alone. The inclusion of the space utilization index in the cost function is crucial for obtaining realistic design candidates.

Constitutive modelling of abdominal organs.

Abdominal organs are very susceptible to trauma. In order to protect them properly against car crash and other impact consequences, we need to be able to simulate the abdominal organ deformation. Such simulation should account for proper stress-strain relation as well as stress dependence on strain rate. As the step in this direction, this paper presents three-dimensional, non-linear, viscoelastic constitutive models for liver and kidney tissue. The models have been constructed basing on in vivo experiments conducted in Highway Safety Research Institute and the Medical Centre of The University of Michigan (Melvin et al., 1973). The proposed models are valid for compressive nominal strains up to 35% and fast (impact) strain rates between 0.2 and 22.5 s(-1). Similar models can find applications in computer and robot assisted surgery, e.g. the realistic simulation of surgical procedures (including virtual reality) and non-rigid registration.

Optimal Design and Modeling of Spatial Parallel Manipulators

Parallel manipulators offer much higher rigidity and smaller mobile mass than their serial counterparts, thus allowing much faster and more precise manipulations. The main disadvantage of parallel robots is their small workspace in comparison to serial arms of similar size. Furthermore, the manipulability of parallel robots is often poor in some regions of the (already small) workspace. Another problematic issue is effective modeling of parallel robot dynamics, often needed for control algorithms. Dynamic algorithms developed for serial robots or general closed-loop mechanisms cannot be easily applied to parallel robots when the objective is real-time, dynamicmodelbased control. Therefore, in this work we investigate how to design parallel manipulators so that their workspace size and manipulability are maximized, and how to model parallel robot dynamics effectively. We develop a new performance index that combines measures of manipulability and workspace size, and a kinematic optimization process yielding a design that delivers the best compromise between manipulability and space utilization. Two examples are considered: the New University of Western Australia Robot (NUWAR) and the Linear Delta robot. Our experience in optimal design studies shows that the exhaustive search minimization algorithm is effective for as many as four independent design variables and presents a viable alternative to advanced non-linear programming methods. We develop a method based on Hamilton’s canonical equations to solve both the inverse and direct problems of dynamics for parallel robots. The method uses carefully chosen dependent coordinates, called here the coordinates of the extended space. The approach is shown to be computationally more efficient than the more common acceleration-based methods.

On the unimportance of constitutive models in computing brain deformation for image-guided surgery

Imaging modalities that can be used intra-operatively do not provide sufficient details to confidently locate the abnormalities and critical healthy areas that have been identified from high-resolution pre-operative scans. However, as we have shown in our previous work, high quality pre-operative images can be warped to the intra-operative position of the brain. This can be achieved by computing deformations within the brain using a biomechanical model. In this paper, using a previously developed patient-specific model of brain undergoing craniotomy-induced shift, we conduct a parametric analysis to investigate in detail the influences of constitutive models of the brain tissue. We conclude that the choice of the brain tissue constitutive model, when used with an appropriate finite deformation solution, does not affect the accuracy of computed displacements, and therefore a simple linear elastic model for the brain tissue is sufficient.

How to test very soft biological tissues in extension

Mechanical properties of very soft tissues, such as brain, liver and kidney, until recently have largely escaped the attention of researchers because these tissues do not bear mechanical loads. However, developments in Computer-Integrated and Robot-Aided Surgery - in particular, the emergence of automatic surgical tools and robots - as well as advances in Virtual Reality techniques, require closer examination of the mechanical properties of very soft tissues and, ultimately, the construction of corresponding, realistic mathematical models. A body of knowledge about mechanical properties of very soft tissues, assembled in recent years, has been almost exclusively based on the results of compression, indentation and impact tests. There are no results of tensile tests available. This state of affairs, in the authors opinion, is caused by the lack of analytical solution relating a measured quantity - machine head displacement - to strain in simple extension experiments of cylindrical samples with low aspect ratio. In the paper this important solution is presented. The theoretical solution obtained is valid for isotropic, incompressible materials for moderate deformations (<30%) when it can be assumed that planes initially perpendicular to the direction of applied extension remain plane. Two astonishing results are obtained: (i) deformed shape of a cylindrical sample subjected to uniaxial extension is independent on the form of constitutive law, (ii) vertical extension in the plane of symmetry lambda(z) is proportional to the total change of height for strains as large as 30%. The importance and relevance of these results to testing procedures in Biomechanics is highlighted.

Brain shift computation using a fully nonlinear biomechanical model

In the present study, fully nonlinear (i.e. accounting for both geometric and material nonlinearities) patient specific finite element brain model was applied to predict deformation field within the brain during the craniotomy-induced brain shift. Deformation of brain surface was used as displacement boundary conditions. Application of the computed deformation field to align (i.e. register) the preoperative images with the intraoperative ones indicated that the model very accurately predicts the displacements of gravity centers of the lateral ventricles and tumor even for very limited information about the brain surface deformation. These results are sufficient to suggest that nonlinear biomechanical models can be regarded as one possible way of complementing medical image processing techniques when conducting nonrigid registration. Important advantage of such models over the linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain tissue stress-strain relationship is linear.