Ursula van Rienen

Adhesion of osteoblasts to a nanorough titanium implant surface

This work considers the adhesion of cells to a nanorough titanium implant surface with sharp edges. The basic assumption was that the attraction between the negatively charged titanium surface and a negatively charged osteoblast is mediated by charged proteins with a distinctive quadrupolar internal charge distribution. Similarly, cation-mediated attraction between fibronectin molecules and the titanium surface is expected to be more efficient for a high surface charge density, resulting in facilitated integrin mediated osteoblast adhesion. We suggest that osteoblasts are most strongly bound along the sharp convex edges or spikes of nanorough titanium surfaces where the magnitude of the negative surface charge density is the highest. It is therefore plausible that nanorough regions of titanium surfaces with sharp edges and spikes promote the adhesion of osteoblasts.

Modeling the Field Distribution in Deep Brain Stimulation: The Influence of Anisotropy of Brain Tissue

The neurosurgical method of deep brain stimulation (DBS) is used to treat symptoms of movement disorders like Parkinsons disease by implanting stimulation electrodes in deep brain areas. The aim of this study was to examine the field distribution in DBS and the role of heterogeneous and anisotropic material properties in the brain areas where stimulation is applied. Finite element models of the human brain were developed comprising tissue heterogeneity and anisotropy. The tissue data were derived from averaged magnetic resonance imaging and diffusion tensor imaging datasets. Unilateral stimulation of the subthalamic nucleus (STN) was computed using an accurate model of an electrode used in clinical treatment of DBS extended with an encapsulation layer around the electrode body. Computations of anisotropic and isotropic brain models, which consider resistive tissue properties for unipolar and bipolar electrode configurations, were carried out. Electrode position was varied within an area around the stimulation center. Results have shown a deviation of 2 % between anisotropic and isotropic field distributions in the vicinity of the STN. The sensitivity of this deviation referring to the electrode position remained small, but increased when the electrode position approached areas of high anisotropy.

Chapter Nine – A Comparison of the Hodgkin–Huxley Model and the Soliton Theory for the Action Potential in Nerves

Abstract We describe the origin and significance of electrical and mechanical observations on nerves. To this end, we compare two models for neural activity, which are the established Hodgkin–Huxley model and the more recent soliton theory, respectively. While the Hodgkin–Huxley model focuses particularly on the electrical aspects of the neural membranes, the soliton model is based on hydrodynamic and thermodynamic properties of the membrane, thus including changes in all thermodynamic variables.

Generalized stern models of the electric double layer considering the spatial variation of permittvity and finite size of ions in saturation regime

The interaction between a charged metal implant surface and a surrounding body fluid (electrolyte solution) leads to ion redistribution and thus to formation of an electrical double layer (EDL). The physical properties of the EDL contribute essentially to the formation of the complex implant-biosystem interface. Study of the EDL began in 1879 by Hermann von Helmholtz and still today remains a scientific challenge. The present mini review is focused on introducing the generalized Stern theory of an EDL, which takes into account the orientational ordering of water molecules. To ascertain the plausibility of the generalized Stern models described, we follow the classical model of Stern and introduce two Langevin models for spatial variation of the relative permittivity for point-like and finite sized ions. We attempt to uncover the subtle interplay between water ordering and finite sized ions and their impact on the electric potential near the charged implant surface. Two complementary effects appear to account for the spatial dependency of the relative permittivity near the charged implant surface — the dipole moment vectors of water molecules are predominantly oriented towards the surface and water molecules are depleted due to the accumulation of counterions. At the end the expressions for relative permittivity in both Langevin models were generalized by also taking into account the cavity and reaction field.

Algebraic multigrid for complex symmetric matrices and applications

This paper is concerned with the numerical study of an algebraic multigrid preconditioner for complex symmetric system matrices. We use several different Krylov subspace methods as an outer iteration, namely the QMR method proposed by Freund and Nachtigal, the BiCGCR method of Clemens, and the CSYM method of Bunse-Gerstner and Stoever. In addition, we compare the results with the standard Jacobi preconditioner for complex symmetric problems. We test our approach on the numerical simulation of high-voltage insulators.

Impact of uncertain head tissue conductivity in the optimization of transcranial direct current stimulation for an auditory target

OBJECTIVE Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique to modify neural excitability. Using multi-array tDCS, we investigate the influence of inter-individually varying head tissue conductivity profiles on optimal electrode configurations for an auditory cortex stimulation. APPROACH In order to quantify the uncertainty of the optimal electrode configurations, multi-variate generalized polynomial chaos expansions of the model solutions are used based on uncertain conductivity profiles of the compartments skin, skull, gray matter, and white matter. Stochastic measures, probability density functions, and sensitivity of the quantities of interest are investigated for each electrode and the current density at the target with the resulting stimulation protocols visualized on the head surface. MAIN RESULTS We demonstrate that the optimized stimulation protocols are only comprised of a few active electrodes, with tolerable deviations in the stimulation amplitude of the anode. However, large deviations in the order of the uncertainty in the conductivity profiles could be noted in the stimulation protocol of the compensating cathodes. Regarding these main stimulation electrodes, the stimulation protocol was most sensitive to uncertainty in skull conductivity. Finally, the probability that the current density amplitude in the auditory cortex target region is supra-threshold was below 50%. SIGNIFICANCE The results suggest that an uncertain conductivity profile in computational models of tDCS can have a substantial influence on the prediction of optimal stimulation protocols for stimulation of the auditory cortex. The investigations carried out in this study present a possibility to predict the probability of providing a therapeutic effect with an optimized electrode system for future auditory clinical and experimental procedures of tDCS applications.

Modeling of an Optimized Electrostimulative Hip Revision System Under Consideration of Uncertainty in the Conductivity of Bone Tissue

Since several years, the number of total hip arthroplasty revision surgeries is substantially growing. One of the main reasons for this procedure to become necessary is the loosening or damage of the prothesis, which is facilitated by bone necrosis at the implant-bone interface. Electrostimulation is one promising technique, which can accelerate the growth of bone cells and, therefore, enhance the anchorage of the implant to the bone. We present computational models of an electrostimulative total hip revision system to enhance bone regeneration. In this study, the influence of uncertainty in the conductivity of bone tissue on the electric field strength and the beneficial stimulation volume for an optimized electrode geometry and arrangement is investigated. The generalized polynomial chaos technique is used to quantify the uncertainty in the stimulation volumes with respect to the uncertain conductivity of cancellous bone, bone marrow, and bone substitute, which is used to fill defective areas. The results suggest that the overall beneficial stimulation areas are only slightly sensitive to the uncertainty in conductivity of bone tissue. However, in the proximity of tissue boundaries, larger uncertainties, especially in the transition between beneficial and understimulation areas, can be expected.

Evaluation of electric field distribution in electromagnetic stimulation of human femoral head.

Electromagnetic stimulation is a common therapy used to support bone healing in the case of avascular necrosis of the femoral head. In the present study, we investigated a bipolar induction screw system with an integrated coil. The aim was to analyse the influence of the screw parameters on the electric field distribution in the human femoral head. In addition, three kinds of design parameters (the shape of the screw tip, position of the screw in the femoral head, and size of the screw insulation) were varied. The electric field distribution in the bone was calculated using the finite element software Comsol Multiphysics. Moreover, a validation experiment was set up for an identical bone specimen with an implanted screw. The electric potential of points inside and on the surface of the bone were measured and compared to numerical data. The electric field distribution within the bone was clearly changed by the different implant parameters. Repositioning the screw by a maximum of 10 mm and changing the insulation length by a maximum of 4 mm resulted in electric field volume changes of 16% and 7%, respectively. By comparing the results of numerical simulation with the data of the validation experiment, on average, the electric potential difference of 19% and 24% occurred when the measuring points were at a depth of approximately 5 mm within the femoral bone and directly on the surface of the femoral bone, respectively. The results of the numerical simulations underline that the electro-stimulation treatment of bone in clinical applications can be influenced by the implant parameters.

Spatial Variation of Permittivity near a Charged Membrane in Contact with Electrolyte Solution

Abstract The interaction between a charged membrane bilayer surface and an electrolyte solution causes the formation of an electrical double layer, which has been a subject of extensive study for more than a century. This chapter provides a statistical mechanical description of orientational ordering of water molecules and of excluded volume effect of ions near the charged membrane surface. The space variation of the permittivity of the electrolyte solution near the charged membrane surface obtained by statistical mechanical model is then included in a phenomenological model for the membrane surface potential for highly charged membranes.

Fast Calculation of Space Charge in Beam Line Tracking by Multigrid Techniques

Numerical prediction of charged particle dynamics in accelerators is essential for the design and understanding of these machines. The calculation of space charge forces influencing the behaviour of a particle bunch is still a bottleneck of existing tracking codes.