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26-28 July, 2010

CMM Brain Neuromechanics Workshop

at the Fields Institute
222 College Street, Toronto

Organizing Committee:
C. Drapaca (Penn State)
JM Drake (Hospital for Sick Children, Toronto)
M. Johnston (Sunnybrook & Womens Hospital, Toronto)
S. Sivaloganathan (University of Waterloo)


James Drake, Hospital for Sick Children, Toronto

Corina S. Drapaca
, Center for Neural Engineering, Pennsylvania State University
New Developments in the Modeling of the Material Brain

In this talk we will present the first two neuro-mechanical models of the brain that establish critical interrelationships between the material structure and the electro-chemical activity of the brain. One model can predict the shrinkage of the brain tissue seen in patients with normal pressure hydrocephalus due to a change in ionic concentrations of the ventricular CSF and in the absence of an elevated intracranial pressure, and thus it opens the possibility of pharmaceutical treatment of hydrocephalus. Our second model uses neuroimaging measurements to predict stress-softening of the brain tissue when the neurons are activated. In addition we will show how one can use cine MRI to estimate the apparent stiffness of the brain in patients with chiari malformations before and after surgery. Before surgery, the brain tissue appears to be stiffer and inhomogeneous, while after the surgery, the brain becomes softer and more homogeneous. This finding could help measure the success of surgery of chiari malformations, in a non-invasive and safe way. Finally, we show a novel technique of differentiating between low and high grade gliomas based on their stiffness values obtained using information provided by image mass spectroscopy.

Patrick Drew
, Center for Neural Engineering, Pennsylvania State University
Balloons, bagpipes and blood - Imaging single vascular dynamics in the
awake mouse cortex

Increases in neural activity in the brain are followed by increases in blood flow and volume. While these changes in the flow of blood are commonly used as a surrogate for neural activity in fMRI and other imaging techniques, a detailed understanding of the underlying hemodynamic events has been lacking. One enduring controversy is what parts of the vascular network (arteries, capillaries or veins) account for the changes in blood volume during sensory stimulation. By using transcranial, two-photon laser scanning microscopy in awake mice, we were able to image spontaneous and sensory evoked changes in blood flow and volume at the level of single vessels. Sensory stimulation evoked large changes in arterial diameters, as well as slower, smaller changes in venous volumes. The changes in arteries and veins observed in awake animals were qualitatively different from those observed in anesthetized animals. These results provide a link between functional signals and their vascular origin.

Almut Eisentraeger, Oxford University Mathematical Institute
Multi-fluid poro-elastic modelling of the CSF infusion test

Ian Sobey(1), Almut Eisentraeger(1), Benedikt Wirth(2) & Marek Czosnyka (3)
(1) Mathematical Institute, University of Oxford, UK
(2) Institute for Numerical Simulation, University of Bonn, Germany
(3) Department of Clinical Neurosciences, University of Cambridge, UK

We have developed a multi-fluid model for flow of cerebro-spinal fluid (CSF) in the brain which has both general application for study of hydrocephalus and particularly here, for simulation of a CSF infusion test. Existing poro-elastic models for CSF flow treat the parenchyma and CSF as a continuum where very slow fluid flow interacts with and can affect the deformation of the underlying elastic substructure. A spherical model with CSF production at the centre of the brain, which allows flow through the aqueduct and very slow flow through the parenchyma before absorption at the outer periphery of the brain, has provided very plausible results for hydrocephalus. However, while that model provides new predictions about the interior state of the parenchyma, it is only applicable for long time scales that neglect blood pulsations on the cardiac cycle time scale. Here we describe our model which, by adding a blood compartment to the usual poro-elastic framework, allows blood pulsations to be included and so to attempt a time accurate simulation of CSF pressure fluctuations in an infusion test.

An infusion test is used to gain data about the CSF system, particularly resistance to absorption and brain compliance. In the test, a saline solution is injected into the CSF system for a fixed period to provide a temporarily elevated CSF production rate. The overall CSF pressure rises to a new plateau value, the level of which provides information about the outflow resistance, and the rate of CSF pressure rise gives information about the compliance.

In order to simulate CSF flow on short time scales we have retained the continuum poro-elastic model but extended the formulation to allow multiple compartments that do not exchange fluid in the continuum region. However, pressure fluctuations of one fluid can affect the pressure of other fluids as well as stress and deformation in the underlying elastic substructure. This results in a model where we can feed into a simulation the correct arterial pressure fluctuations (which are recorded during the infusion test) and then predict CSF pressure fluctuations and compare predictions with recorded values. By varying the physical parameters so as to fit the observed CSF pressure recording, we can provide new and additional predictions of parameters in a particular case, as well as predictions for stress, deformation and fluid content in the parenchyma during and after a test. In this presentation we will outline our multi-fluid model, discuss briefly the methods we use to solve the system of equations and present some results that compare computational predictions with clinical data using both conventional simulation and our multi-fluid model.

Joseph T. Francis, SUNY Downstate Medical Center
Erasing Sensorimotor Memories: A Novel Tool for Probing LTP's Influence on Learning and Memory

At present we are constructing a synthetic version of the sensorimotor control system of the nonhuman primate. In order to reach this goal we are utilizing electrophysiological, pharmacological and computational methods. I will present results and theory from our work aimed at generating a somatosensory neuroprosthesis, in addition to a force controlled brain machine interface, and how we are utilizing these experiments in combination with micro-infusion of the PKMzeta inhibitor ZIP into the sensorimotor cortex to further our understanding of this system. We have recently shown that such injections of ZIP erase sensorimotor memories without influencing explicit memories needed for task completion. This tool will allow us to wipe out such learning induced LTP dependent memories from our in vivo physiological system, which we can then compare with such LTP erasure in our computational models, compare, and learn.

Kristian Franze, University of Cambridge
Mechanosensitivity of CNS cells in health and disease

Nerve tissue comprises a variety of cells, blood vessels, and extracellular matrix. All of these building blocks differ in their mechanical properties; therefore, particularly during growth and migration, the local mechanical environment of motile CNS cells will change considerably. Here we show that both neurons and glial cells, the basic building blocks of nerve tissue, respond to these variations in their mechanical microenvironment. Using culture substrates incorporating gradients of mechanical properties we found that neuronal axons are repelled by stiff substrates while glial cells spread more on stiffer substrates. We have used traction force microscopy and scanning force microscopy in combination with calcium imaging to suggest a possible model for neuronal mechanosensing. During development, this mechanosensitivity might be used - in combination with biochemical signaling - to guide neuronal axons along distinct pathways. Glial cell reactivity, on the other hand, which is found in numerous pathological processes, is also triggered by mechanical cues. Neural implants for example, which are orders of magnitude stiffer than healthy CNS tissue, often cause a foreign body reaction, which is characterized by an encapsulation of the implant by reactive microglial cells and later by reactive astrocytes. This assembly of different glial cell layers around the 'foreign body' results in a serious reduction of lifetime and functionality of these devices. The mechanical mismatch between implant and tissue may trigger the encapsulation of the implant, repelling neurons while attracting glial cells. Exploiting this knowledge may ultimately lead to the development of a new generation of implants, incorporating appropriate mechanical cues which support healthy tissue structure.

Jurgen Germann
, Toronto Centre for Phenogenomics
Experience forms the brain: Using structural MRI to study training induced brain plasticity in adult mice

Previous studies have demonstrated that plastic changes associated with experience can be observed in the brains of adult humans and mice using MRI. For example, the extensive navigational experience of London taxi drivers is associated with increased hippocampal volume and learning to juggle leads to selective structural changes in the brains of young adults. The goal of this study was to investigate these experience induced structural changes more closely using MRI in mice. To induce differential plastic brain changes mice were trained in different versions of the Barnes maze. In the Barnes maze mice are placed in the centre of a highly lit platform. Along the edge of the platform there are 40 holes, one of which is connected to an escape box that gives mice the chance to escape the exposed situation. In the spatial version of the Barnes maze numerous distal landmarks are placed around the platform and mice learn to use the spatial landmarks to navigate quickly to the escape box. In the non-spatial version of the Barnes maze the escape box is moved to a different hole every trial but a flag is always placed next it. Mice learn to approach the flag to find the escape box. All images were obtained using a high-field MR scanner (7T). To investigate the time course of possible structural brain changes live imaging of anesthetized mice (125µm voxel resolution) was performed before and at various time-points during and after training. Some mice were sacrificed 10 days after training and their brain fixed and high resolution anatomical images (32µm voxel resolution) and Diffusion weighted images (150µm voxel resolution) obtained. Automated registration algorithms were used to localize subtle anatomical differences
We observed changes in specific brain regions. Learning the spatial version of the Barnes maze is associated with changes primarily in the hippocampus. Learning the non-spatial version of the Barnes maze is associated with changes primarily in the striatum. These local change can be observed in the first days of training and persist for remainder of the experiment. Additionally the variation in learning performance between mice is reflected in the amount of local structural change.

Bruce Gluckman
, Center for Neural Engineering, Pennsylvania State University
Implant damage as motivation for studying neural mechanics

A common observation in deep brain stimulation studies is that after implant patients see improvements first, then stimulation is turned on. This common effect is attributed to micro-legions. We undertook a study to map the implant damage in rats from depth electrodes placed in the ventral hippocampus. Not only did we observe damage near the implant trajectory, but we were able to track degeneration into the contralateral hippocampus. Current discussions in the invasive brain-machine-interface literature include the objective of finding better implant materials and methods for implantation that will provide long, stable recordings that minimize short term and long term tissue damage. Proposed approaches are to either find ‘softer’ materials, or ones with much smaller size format. I’ll review some of the evidence for and competing against these approaches.

Paul Janmey, Institute for Medicine and Engineering, University of Pennsylvania
Mechanosensing by neurons and astrocytes

Many cell types, including neurons and glial cells, respond strongly to changes in matrix rigidity when cultured on flexible substrates. Neurons are very unusual in that they extend processes and survive better on very soft materials than they do on stiff surfaces. In contrast, on soft gels astrocytes remain unactivated, do not spread, and have disorganized F-actin and intermediate filament systems compared to the cytoskeletons of astrocytes on hard surfaces. The stiffness range over which these cell types alter their phenotype is in the range from 50 Pa to 2000 Pa, approximately the range of elastic modulus for intact brain, when measured at small strains on a time scale of 1 s. The effects of substrate stiffness are evident when cells are grown on synthetic gels made from flexible rubberlike polymers or when they are embedded in semi-flexible biopolymer gels such as fibrin. The different responses of neurons and astrocytes enables preferential selection of cell type by altering matrix stiffness. Dissociated embryonic rat cortices grown on flexible fibrin gels, a biomaterial with potential use as an implant material, display a similar mechano-dependent difference in cell population. These data emphasize the potential importance of material substrate stiffness as a design feature in the next generation of biomaterials intended to promote neuronal regeneration across a lesion in the CNS while simultaneously minimizing the ingrowth of astrocytes into the lesion area. The length and time scales over which cells deform their substrate and alter their morphology suggest mechanisms by which these cells can sense mechanical signals.

Miles Johnston, Sunnybrook Health Sciences Centre, University of Toronto,
An alternative approach to understanding the pressure gradients in the brain that induce hydrocephalus

Hydrocephalus is a chronic brain disorder characterized by expansion of the ventricles and in some cases, significant neurological damage. Perhaps the greatest paradox in the hydrocephalus field is the failure of researchers to consistently measure transmantle pressure gradients (ventricle to subarachnoid space) in humans and in animal models of the communicating form of the disorder. Without such a gradient it is difficult to conceptualize how ventricular distention occurs. Based on the results of a mathematical model, one group has proposed that ventricular expansion may result from a relative reduction in interstitial pressure in the peri-ventricular area leading to the formation of an intra-mantle rather than a transmantle pressure gradient (Pena et al., Acta Neurochir 81: 59, 2002). Clues from studies in non-CNS tissues such as skin suggest that the dissociation of ß1 integrins with the surrounding matrix fibers results in a significant reduction of interstitial fluid pressure (Wiig et al., Acta Anaesthesiol Scand 47: 111, 2003). We examined these concepts in the rat brain and observed that the intraventricular injection of anti ß1 integrin antibodies resulted in a significant reduction in periventricular pressures to values significantly below those monitored in the ventricular system. In addition, many of these animals developed hydrocephalus (Nagra et al., Am J Physiol 297: R1312, 2009). We conclude that changes in the periventricular matrix generate pressure gradients favourable for ventricular expansion suggesting a novel mechanism for hydrocephalus development.
However, a number of issues need further clarification. If the pressures were to decline in the periventricular tissues, some removal of fluid must occur from the tissues.
We feel that Aquaporin-4 (AQP4) is a likely candidate for this effect as it is the predominant water channel in the brain. Indeed, in preliminary studies, the administration of blocking antibodies resulted in an up-regulation of AQP4 protein levels. In addition, in some experiments we negated capillary function by stopping the heart with KCL (capillary pressures = 0). Under these conditions, periventricular interstitial fluid pressures increased after anti ß1 integrin antibody administration into a lateral ventricle supporting the view that the capillary absorption of parenchymal water may play a pivotal role in the generation of pressure gradients in our hydrocephalus model.

Significance of these studies:
Apart from providing a mechanism to explain ventriculomegaly, it is of special interest to note that there are a number of ways to modulate aquaporin function using newly developed drugs and molecular techniques. This provides the exciting possibility that some forms of hydrocephalus may be treatable with pharmacological agents thus reducing the dependence on problematic shunts.

Leslie M. Loew, R.D. Berlin Center for Cell Analysis, University of Connecticut
Health Center
Design, Use and Application of Voltage Sensitive Dyes for Imaging Neuronal Physiology

The chemistry and the physics of voltage sensitive dyes should be understood and appreciated as a prerequisite for their optimal application to problems in neuroscience. This talk will provide a basic understanding of the properties of the large variety of available organic voltage sensitive dyes. The mechanisms by which the dyes respond to voltage guides the best set up of the optics for recording or imaging electrophysiological activity. The physical and chemical properties of the dyes can be tuned to optimize delivery to and staining of the cells in different experimental preparations. High resolution microscope imaging, including confocal and non-linear optical microscopy, are being used in conjunction with the voltage sensitive dyes to map electrical activity in both space and time; these optical approaches will be briefly surveyed. Applications of the dyes to optical imaging of electrical activity in individual cells and tissues will be presented to illustrate the range of problems that can be tackled with this technology. Results from microscope imaging experiments also provide data for mathematical models of the physiology. I will briefly introduce the Virtual Cell, a software system for reaction-diffusion modeling that has been used to simulate neuronal cell biology. (supported by USPHS NIH grants: U54 RR022232, R01 EB001963 and P41 RR13186)

Martin Ostoja-Starzewski, University of Illinois at Urbana-Champaign
MRI-based model of TBI vis-à-vis random fractal geometry of brain

The traumatic brain injury (TBI) presents several challenges to a mechanician. First, there is a need to translate the MRI information on the human head-brain system into a composite model with heterogeneous material properties (scalp, skull, CSF, white and gray matter). Given the MRI with one cubic milimeter voxel mesh, we construct a 3D finite element (FE) model. To validate this model, a previous cadaver experiment of frontal impact is simulated. The model is run under either of two extreme assumptions concerning the head-neck junction - either free or fixed - and the experimental measurements are well bounded by the computed pressures from the two boundary conditions. In both cases the impact gives rise not only to a fast pressure wave but also to a slow and spherically convergent shear stress wave, which is potentially more damaging to brain tissues. Such heretofore unknown wave patterns are also discovered in other head impacts. However, this rather conventional continuum-computational mechanics approach has to be contrasted with the random fractal geometry of brain. Given the material spatial randomness, the separation of scales does not hold. Here we note that the human brain surface has a fractal dimension of about 2.7-2.8, while the entire cardiovascular system has a fractal structure, and so does the pulmonary system. A possible way to deal with these challenges is to adapt a recently begun extension of continuum mechanics of fractal porous media which are specified by a mass (or spatial) fractal dimension D, a surface fractal dimension d, and a resolution length scale R. That theory is based on a dimensional regularization, in which D is also the order of fractional integrals employed to state global balance laws. In effect, the governing equations are cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order but containing coefficients involving D, d and R. This procedure allows a specification of geometry configuration of continua by 'fractal metric' coefficients, on which the continuum mechanics is subsequently constructed, with micropolar effects arising naturally. While all the derived relations depend explicitly on D, d and R, upon setting D=3 and d=2, they reduce to conventional forms of governing equations for continuous media with Euclidean geometries. Our formulation is based on a product measure, making it capable of grasping local material anisotropy, and assuring consistency of the mechanical approach to continuum mecahnics with that based on energy principles.

Katerina Papoulia, University of Waterloo
Hyperelastic vs. hypoelastic models in finite strain viscoelasticity

An Eulerian rate formulation for finite strain analysis based on the Jaumann rate of stress is proposed and is shown to be in accordance with the definition of a hypoelastic material model. Integrability conditions of the proposed hypoelastic model in the sense of Cauchy and Green elasticity are derived. A hyperelastic potential may be used to derive the model. Derived integrability conditions show that the proposed model is exactly integrable if the Jaumann rate of the Kirchhoff stress is used. Two deformation cases, rectilinear shear and closed path four-step loading, are solved. Contrary to classical hypoelasticity, results obtained do not show any sign of shear oscillation and/or elastic dissipation under simple shear motion and closed path elastic loading. The proposed model is further extended to finite strain viscoelasticity through specifying a general nonlinear viscous flow rule on the Eulerian background. Multiplicative decomposition of the deformation gradient into its elastic and inelastic parts is employed for a generalized Maxwell model and the elastic part of the left Green-Cauchy deformation tensor is consistently introduced on the Eulerian configuration. Exact deviatoric/volumetric decoupled forms for kinematic and kinetic variables are further obtained with no assumption for viscous incompressibility. The proposed finite strain viscoelastic model is then used to solve the problem of cyclic simple shear for various large shear amplitudes. Results obtained are in good agreement with reported experimental data. The proposed model is consistent with the thermodynamics of irreversible phenomena, i.e. it yields non-dissipative (reversible) stress response for purely elastic deformations and the dissipation
(irreversibility) of the model is solely determined by its viscous
(inelastic) stress response. Furthermore, the proposed model is formulated and integrated in the fixed background and no eigenvalue extraction is needed. This makes the model a good candidate for finite element implementation.

Richard Penn, Neurosurgery, University of Chicago
William of Ockham looks at theories of Hydrocephalus

Andrew Sharp
, Southern Illinois University School of Medicine
Penetration Mechanics and Mechanical Properties of Mouse Brain Tissue

Through the use of a variety of implantable devices, significant progress towards an understanding of the neuronal basis of behavior is being achieved. Also, there has been an increased interest in the use of implantable devices for the treatment of numerous neurological disorders. Unfortunately, the design of instruments to be inserted into neuronal tissue has largely been one of trial and error and has not utilized approaches to minimize tissue damage. This is largely due to the lack of understanding of the mechanics of probe insertion and the mechanical properties of neuronal tissue at the relevant length scales. Therefore, state of the art probes generally rely on rigid materials that are not suited for the study of small animals, such as mice, or for general treatment of human neurological disorders. The goal of this work is to provide a generalizable description of the micrometer scale penetration mechanics and material properties of mouse brain tissue in vivo. Cylindrical stainless steel probes were inserted into the cerebral cortex and olfactory bulb of mice under anesthesia. The effects of probe size, probe geometry, insertion rate, insertion location, animal age and the presence of the dura and pia on the resulting forces were measured continuously throughout probe insertion and removal. Material properties (modulus, cutting force, and frictional force) were extracted using mechanical analysis. Implications for future probe design strategies and insertion methodologies will be presented.

Kathleen Wilkie, University of Waterloo
The Effects of Aging on Brain Biomechanics and an Examination of the Pulsation-Damage Hypothesis for Hydrocephalus

Mathematical modelling of neurosurgery, head trauma, and conditions such as hydrocephalus usually treat infant and adult cerebrum as mechanically
equivalent. If infant mechanical properties are required, sometimes a brain-mass scaling relationship is used to find the parameters instead of determining them directly from experimental data. In this talk, we will use age-dependent shear complex modulus data to determine the mechanical properties of infant and adult cerebrum for the fractional Zener viscoelastic

Using these two sets of parameter values, we will examine the effects of CSF pulsations on the genesis and evolution of hydrocephalus in both the infant and adult cases. Specifically, we will examine the ability of CSF pulsations to damage periventricular tissue, which has been proposed as a possible causative mechanism for hydrocephalus. We will show that the material stresses induced in both the infant and adult brains are much smaller than the damage threshold for white matter, and thus we conclude that the CSF pulsations cannot be the primary cause of tissue damage or ventricular expansion in either infant or adult hydrocephalus.

Alan Wineman, University of Michigan
Some Topics from Continuum Mechanics Related to Brain Neuromechanics

A number of topics from continuum mechanics are presented that are useful in developing mathematical models of brain neuromechanics. Part I reviews basic concepts used to describe deformation or distortion of brain tissue, strains, stresses, their connection and material stiffness. Part II presents concepts from viscoelasticity used to describe the time dependent response of brain tissue such as stress relaxation, creep, response to sinusoidal loading, energy dissipation, characteristic response times and their alteration due to non-mechanical influences. Part III describes recent modeling approaches that can be used to describe microstructural changes in materials due to large deformation, disease or other non-mechanical sources.

K P Unnikrishnan, Center for Computational Medicine and Bioinformatics (CCMB) University of Michigan Medical School
Graph Discovery in Neuronal Networks

Neuroscientists are collecting activation (spike-train) data from hundreds of neurons with milli-second precision. Analysis of these large data sets poses interesting data mining challenges. We describe computational methods and associated statistical significance tests to discover patterns in multi-neuronal spike trains. By discovering these patterns, we are able to uncover the functional connectivity (graphical structure) of the underlying neuronal networks and observe their time-evolutions. We illustrate these on simulated and real data sets and compare the data mining methods with model-based estimation methods. We conclude with a brief discussion of Hebb cell assemblies and neural codes and how data mining can help discover them.


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