Effects of inhomogeneities within the brain on EEG and MEG

The influence of ventricles and lesions on MEG and EEG is studied. The ventricles have an intricate shape and are filled with cerebrospinal fluid. Lesions can have various shapes and their conductivity is unknown. A realistically shaped three-compartment model is used, describing the scalp, skull and brain, which includes the realistically shaped ventricles or a spherical lesion. The potential is computed by means of the finite-element method, and the magnetic field by applying the law of Biot-Savart (Broek, S.P.v.d., Zhou, H. and Peters, M.J. 1996, computation of neuromagnetic fields using finite-element method and Biot-Savart law, Med. Biol. Eng. Comput., 34,21-26). An influence of the ventricles on the potential is only noticeable for dipoles that are within a few centimetres of a ventricle and on the relatively weak potentials on the opposite side of the head. The 'radial' component of the magnetic field generated by superficial dipoles is not influenced by the ventricles in a healthy subject. The influence on the other components, and on the field generated by dipoles near the ventricles can be large. A lesion has a large effect on the potential for sources near the lesion. The effects on the MEG are smaller, but noticeable. Care should be taken in explaining abnormalities in EEGs and MEGs, as it is possible that they are caused by the presence of an inhomogeneity

The influence of inhomogeneities in a head model on EEG and MEG

A realistically shaped model of the head, consisting of tetrahedral elements, is used to investigate the influence of inhomogeneities in the volume conductor (e.g., ventricles and holes) on EEG and MEG. The potential is computed using the finite-element method. The magnetic field is calculated from this potential distribution, applying the law of Biot-Savart. In order to study the influence of the ventricles, computations are carried out using two models: one in which the elements within the ventricles are given the same conductivity as the brain and one in which these elements have a higher conductivity. The influence of holes in the skull layer is examined by giving some elements in the skull layer the same conductivity as that of the brain. The geometry of compartments is obtained semiautomatically from Magnetic Resonance Imaging (MRI) scans. The surface of the ventricles is obtained by manually selecting points on the interface between ventricle and brain. The computation time depends on the total number of tetrahedrons. Therefore, the vertices are distributed in, such a way that a sufficiently high accuracy is obtained with as few tetrahedrons as possible

Bio-inks for 3D bioprinting : recent advances and future prospects

In the last decade, interest in the field of three-dimensional (3D) bioprinting has increased enormously. 3D bioprinting combines the fields of developmental biology, stem cells, and computer and materials science to create complex bio-hybrid structures for various applications. It is able to precisely place different cell types, biomaterials and biomolecules together in a predefined position to generate printed composite architectures. In the field of tissue engineering, 3D bioprinting has allowed the study of tissues and organs on a new level. In clinical applications, new models have been generated to study disease pathogenesis. One of the most important components of 3D bio-printing is the bio-ink, which is a mixture of cells, biomaterials and bioactive molecules that creates the printed article. This review describes all the currently used bio-printing inks, including polymeric hydrogels, polymer bead microcarriers, cell aggregates and extracellular matrix proteins. Amongst the polymeric components in bio-inks are: natural polymers including gelatin, hyaluronic acid, silk proteins and elastin; and synthetic polymers including amphiphilic block copolymers, PEG, poly(PNIPAAM) and polyphosphazenes. Furthermore, photocrosslinkable and thermoresponsive materials are described. To provide readers with an understanding of the context, the review also contains an overview of current bio-printing techniques and finishes with a summary of bio-printing applications

The structure of large random graphs

We obtain universality results on the structure of random graphs from two different angles. Naturally, there is a trade-off between the generality of the assumptions on a model and the specificity of the results one may obtain. The strength of the first work is its generality: we obtain non-asymptotic universal tail bounds on the height of random trees that do not require any assumptions on e.g. the tail behaviour of the degrees. In the second work, we need stronger assumptions, but our description of the structure is more specific: we do not study a real-valued statistic of the random graph model, but show convergence in distribution under rescaling of the graph itself, which entails the convergence of a whole panoply of such statistics. Firstly, we obtain new non-asymptotic universal tail bounds for the height of uniformly random trees with a given degree sequence. We also obtain universal tail bounds for the height of simply generated trees and conditioned Bienaymé trees (the family trees of branching processes) that settle several conjectures from the literature. Moreover, we define a partial ordering on degree sequences and show that it induces a stochastic ordering on the heights of uniformly random trees with given degree sequences. The latter result implies that sub-binary random trees are stochastically the tallest trees with a given number of vertices and leaves. Secondly, we consider the strongly connected components (SCCs) of a uniform directed graph on n vertices with i.i.d. in- and out-degree pairs distributed as (D−, D+), with E[D^+] = E[D^_−] = μ. We condition on equal total in- and out-degree. A phase transition for the emergence of a giant SCC is known to occur at the critical point where E[D^−D^+] = μ. We study the model at this critical point and show that, under some additional finite moment conditions, the SCCs ranked by decreasing number of edges with distances rescaled by n^{−1/3} converge in distribution to a sequence of finite strongly connected directed multigraphs with edge lengths, and that these are either 3-regular or loops almost surely. This is the first universality result for the scaling limit of a critical directed graph model and the first quantitative result on the directed configuration model at criticality