Influence of the hole geometry on the flow distribution in ventricular catheters for hydrocephalus

Background

Hydrocephalus is a medical condition consisting of an abnormal accumulation of cerebrospinal fluid within the brain. A catheter is inserted in one of the brain ventricles and then connected to an external valve to drain the excess of cerebrospinal fluid. The main drawback of this technique is that, over time, the ventricular catheter ends up getting blocked by the cells and macromolecules present in the cerebrospinal fluid. A crucial factor influencing this obstruction is a non-uniform flow pattern through the catheter, since it facilitates adhesion of suspended particles to the walls. In this paper we focus on the effects that tilted holes as well as conical holes have on the flow distribution and shear stress.

Methods

We have carried out 3D computational simulations to study the effect of the hole geometry on the cerebrospinal fluid flow through ventricular catheters. All the simulations were done with the OpenFOAM® toolbox. In particular, three different groups of models were investigated by varying (i) the tilt angles of the holes, (ii) the inner and outer diameters of the holes, and (iii) the distances between the so-called hole segments.

Results

The replacement of cylindrical holes by conical holes was found to have a strong influence on the flow distribution and to lower slightly the shear stress. Tilted holes did not involve flow distribution changes when the hole segments are sufficiently separated, but the mean shear stress was certainly reduced.

Conclusions

The authors present new results about the behavior of the fluid flow through ventricular catheters. These results complete earlier work on this topic by adding the influence of the hole geometry. The overall objective pursued by this research is to provide guidelines to improve existing commercially available ventricular catheters.

     

Steady-state and transient electric birefringence of solutions of bent-rod macromolecules

We first calculate the steady-state birefringence, expressed in the form of specific Kerr constant, K_sp, of rigid, bent-rod macromolecules. Equations are derived for K_sp as a function of the geometric and electro-optical parameters. We also consider flexibly hinged rods and evaluate K_sp for them by averaging over the angle between the two arms, ?. Next, we turn to the time decay of the electric birefringence. The decay function for rigid bent rods is a sum of three exponential terms, and a procedure for their calculation is indicated. We observe that single-exponential decays can be found for ? > 90° or ? < 60°, in spite of the high electro-optical and hydrodynamic anisotropy of the macromolecule. Special attention is paid to the case of rods with equal arms.     

Steady-state solutions in mathematical models of atrial cell electrophysiology and their stability

The steady states of the Fenton-Karma, the Courtemanche and the Nygren cell models were studied by determining the fixed points of the dynamical system describing their cell kinetics. The linear stability of the fixed points was investigated, as well as their response to external stimuli. Symbolic calculations were carried out as far as possible in order to prove the existence of these fixed points. In the Fenton-Karma model, a unique stable fixed point was found, namely the resting state. In contrast, the Courtemanche model had an infinite number of fixed points. A bifurcation diagram was constructed by classifying these fixed points according to a conservation law. Initial conditions were identified, for which the dynamical behavior of the cell was auto-oscillatory. In its original formulation, the Nygren model had no fixed point. After having restored charge conservation, the system was found to have an infinite number of fixed points, resulting in a bifurcation diagram similar to that of the Courtemanche model. The approach proposed in this paper assists in the exploration of the high-dimensional parameter space of the cell models and the identification of the conditions leading to spontaneous pacemaker activity.     

VEGF: A potential target for hydrocephalus

Growth factors are primarily responsible for the genesis, differentiation and proliferation of cells and maintenance of tissues. Given the central role of growth factors in signaling between cells in health and in disease, it is understandable that disruption of growth factor-mediated molecular signaling can cause diverse phenotypic consequences including cancer and neurological conditions. This review will focus on the specific questions of enlarged cerebral ventricles and hydrocephalus. It is also well known that angiogenic factors, such as vascular endothelial growth factor (VEGF), affect tissue permeability through activation of receptors and adhesion molecules; hence, recent studies showing elevations of this factor in pediatric hydrocephalus led to the demonstration that VEGF can induce ventriculomegaly and altered ependyma when infused in animals. In this review, we discuss recent findings implicating the involvement of biochemical and biophysical factors that can induce a VEGF-mimicking effect in communicating hydrocephalus and pay particular attention to the role of the VEGF system as a potential pharmacological target in the treatment of some cases of hydrocephalus. The source of VEGF secretion in the cerebral ventricles, in periventricular regions and during pathologic events including hydrocephalus following hypoxia and hemorrhage is sought. The review is concluded with a summary of potential non-surgical treatments in preclinical studies suggesting several molecular targets including VEGF for hydrocephalus and related neurological disorders.     

Experimental investigation of the shock wave in a fast discharge with cylindrical geometry

The work is devoted to the registration and the study of the properties of cylindrical shock waves generated in the fast discharge (dI/dt ～ 10¹² A/s) inside the ceramic tube (Al₂O₃) filled by argon at pressures of 100 and 300 Pa. The shock wave appears at the inner wall of the insulator and moves to the discharge axis with a velocity of about (3?4) × 10⁶ cm/s with subsequent cumulation. The plasma behind the front is heated enough to produce radiation in the vacuum ultraviolet (VUV) region, which makes it possible to study its structure by means of a pinhole camera with a microchannel plate detector. The time resolution of the registration system was 10 ns. The analysis of VUV spectra of the plasma shows that the electron temperature behind the shock wave front is about several eV; after the moment of cumulation, its temperature increases to 20–30 eV.     

The bacterial flagellum as an imperfect cylindrical crystal: flagellar geometry, movement and polymorphism, and the role of partial dislocations

A pairing attraction between helical turns of subunits in a cylindrical crystal, like that in the dahlemense strain of tobacco mosaic virus, can cause the axis of the rod or crystal to become helical. This is true only if the number of helices is odd. The shape of a bacterial flagellum can be accounted for then if, as Caspar &; Holmes and Klug have suggested, rows of its subunits exhibit such a pairing interaction. Klug's thoughts on bacterial flagella are developed and extended into a model that accounts qualitatively for geometry, movement and polymorphism of flagella. If the number of helices between which there is a pairing interaction is odd, then the crystal is an imperfect cylindrical crystal. The geometry of such crystals is described. They contain a line defect, termed here an antiphase boundary, across which the pairing interaction is reversed. The boundary is a line of expansion on the convex side of a curved filament. Movement of flagella is explained by circumferential displacement of the antiphase boundary. One polymorphic form can convert to another if a dislocation passes along it. Straight flagella are perfect cylindrical crystals with no antiphase boundary.     

Inherited hydrocephalus in Csk: Wistar-Imamichi rats; Hyd strain: a new disease model for hydrocephalus

Hydrocephalic rats were found in a breeding colony of Csk: Wistar-Imamichi strain rats. In males, the hydrocephalus were serious and could be detected from 7 days after birth. Survival was 3-4 weeks. In females, the hydrocephalus was moderate, there was no abnormal external appearance, and the rats were able to mature. Ventricular dilatation was excessive in males but moderate in females. The total frequency of hydrocephalus was 34.3% in both males and females. Breeding data indicated that this disease is heritable and is single dominant and X-linked (symbol, Hyd). The female moderate hydrocephalics could be detected by progeny tests without examining brain sections. No evidence of developmental anomaly was observed in the ventricles. This hydrocephalus was classified as being of the communicating type, and this strain was named the Hyd strain as an animal model for human hydrocephalus.     

稳态视觉诱发电位神经网络间的相互作用

稳态视觉诱发电位(steady-state visual evoked potential,SSVEP)不同于瞬态视觉诱发电位,有其独特的产生机理。当用两种不同频率的闪光同时刺激时,每种频率闪光诱发的SSVEP之间是否会相互影响?它们与对应单一频率闪光刺激时产生的SSVEP的关系怎样?作者用!波段频率8.3Hz与"波段频率20Hz的闪光分别及同时刺激10个被试的双眼,发现在同时刺激时,每种频率闪光的SSVEP比对应单频刺激时的SSVEP略小,但位置分布无明显变化。这说明不同频率SSVEP的产生网络是彼此独立的,在被同时激活时,每个网络产生的信号并不相互影响。     

The pathogenesis of normal pressure hydrocephalus: A theoretical analysis

Hydrocephalus is an abnormal accumulation of cerebrospinal fluid (CSF) in the cerebral ventricles, usually caused by impaired absorption of the fluid into the bloodstream. Despite obstructed absorption and continued secretion of CSF into the ventricles at a near normal rate, the ventricular CSF pressure (VCSFP) is often normal. We attempt to understand how hydrocephalus can exist with normal VCSFP by exploring the role of the brain parenchyma in absorbing CSF in hydrocephalus. We test three theories: (1) the ventricular wall is impermeable to CSF; (2) ventricular CSF seeps into the parenchyma, from which it is efficiently absorbed; and (3) ventricular CSF seeps into the parenchyma but is absorbed inefficiently. We model the brain as a thick spherical shell consisting of a porous, elastic, solid matrix, containing interstitial fluid and blood. We modify the equations of poroelasticity, which describe flow of fluid through porous solids, to allow for parenchymal absorption. For each of the three theories we calculate the steady state changes in VCSFP and in parenchymal fluid pressure caused by an incremental defect in CSF absorption. We also calculate the steady state changes in fluid content, tissue volume, tissue displacement, and stresses caused by a small increment of VCSFP. We conclude that only the second theory—seepage of CSF with efficient parenchymal absorption—accounts for the clinical features of normal pressure hydrocephalus. These features include sustained ventricular dilatation despite normal VCSFP, increased periventricular fluid content, and localized periventricular white matter damage.     

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling’s law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.     

The geometry of evolution

Some structures are more suitable for self-organization through the Darwin-Wallace mechanism of variation and selection than others. Such evolutionary adaptability (or evolvability) can itself evolve through variation and selection, either by virtue of being associated with reliability and stability or by hitchhiking along with the advantageous traits whose appearance it facilitates. In order for a structure to evolve there must be a reasonable probability that genetic variation carries it from one adaptive peak to another; at the same time the structure should not be overly unstable to phenotypic perturbations, as this is incompatible with occupying a peak. Organizations that are complex in terms of numbers of components and interactions are more likely to meet the peak-climbing condition, but less likely to meet the stability condition. Biological structures that are characterized by a high degree of component redundancy and multiple weak interactions satisfy these conflicting pressures.     

The geometry of coexistence

Understanding the processes that maintain diversity has been the focus of extensive study, yet there is much that has not been integrated into a cohesive framework. First, there is a separation of perspective. Ecological and evolutionary approaches to diversity have progressed in largely parallel directions. Second, there is a separation of emphasis. In both ecology and population genetics, classical theories favour local explanations with emphasis on population dynamics and selection within populations, while contemporary theories favour spatial explanations, with emphasis on population structure and interactions among populations. What is lacking is a comparative approach that evaluates the relative importance of local and spatial processes in maintaining genetic and ecological diversity. I present a framework for diversity maintenance that emphasizes the comparative approach. I use a well-known but little-used mathematical approach, the perturbation theorem for dynamical systems, to identify key points of contact between ecological and population genetic theories of coexistence. These connections provide for a synthesis of several important concepts: population structure (source-sink versus extinction-colonization), spatial heterogeneity (intrinsic versus extrinsic) in fitness and competitive ability, and temporal scales over which local and spatial processes influence diversity. This framework ties together a large and diverse body of theory and data from ecology and population genetics. It yields comparative predictions that can serve as guidelines in biodiversity management.     

Steady-state modelling of metabolic pathways: A guide for the prospective simulator

Steady-state modelling and control analysis by means of computersimulation provides valuable insight into the behaviour of metabolicpathways. This review, which is aimed at the newcomer to thisfield, discusses the objectives of steady-state modelling andthe steady-state properties of the four basic metabolic structures,namely linear and branched chains, loops and cycles It is shownhow the model definition in terms of stoichiometric reactionsand rate equations leads to a set of balance equations fromwhich the conservation constraints and flux relationships canbe deduced, either informally or through a rigourous analysisof the stoichiometnc matrix The initial analysis of a steady-statemetabolic model is summarized in an algorithm. Key referencesto the literature on metabolic modelling are given.     

The geometry of shape space: application to influenza

Shape space was proposed over 20 years ago as a conceptual formalism in which to represent antibody/antigen binding. It has since played a key role in computational immunology. Antigens and antibodies are considered to be points in an abstract "shape space", where coordinates of points in this space represent generalized physico-chemical properties associated with various (unspecified) physical properties related to binding, such as geometric shape, hydrophobicity, charge, etc. Distances in shape space between points representing antibodies and (the shape complement) of antigens are assumed to be related to their affinity, with small distances corresponding to high affinity. In this paper, we provide algorithms, related to metric and ordinal multidimensional scaling algorithms first developed in the mathematical psychology literature, which construct explicit, quantitative coordinates for points in shape space given experimental data such as hemagglutination inhibition assays, or other general affinity assays. Previously, such coordinates had been conceptual constructs and totally implicit. The dimension of shape space deduced from hemagglutination inhibition assays for influenza is low, approximately five dimensional.The deduction of the explicit geometry of shape space given experimental affinity data provides new ways to quantify the similarity of antibodies to antibodies, antigens to antigens, and the affinity of antigens to antibodies. This has potential utility in, e.g. strain selection decisions for annual influenza vaccines, among other applications. The analysis techniques presented here are not restricted to the analysis of antibody-antigen interactions and are generally applicable to affinity data resulting from binding assays.     

The geometry of leaf morphogenesis: A theoretical proposition

Plant morphogenesis exhibits numerous bifurcations with particular angle values such as 41°, 53°, which, in lower plants, can be measured in the thallus, and, in higher plants, in the ribs of the leaves. An interpretation of these angles is attempted. Since they characterize the functioning of a morphogenetic field, a formalism was constructed suitable for the study of living systems. The mathematical tool devised here, named the Arithmetical Relator, combines Geometry and Arithmetic, and assumes that a general system results from the interaction between an internal cyclic structure and an environment to which this structure is adapted. The formalism described therefore takes into account partial self-reference and changes in the level of organization. Within this framework, the particular values of the ramification angles are extreme for slight shifts in the internal structure. A pattern of the relations between the genome, the cell and the organ is suggested.

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Résumé La morphogenèse végétale est le siège de nombreuses bifurcations. Celles-ci donnent naissance à des angles particuliers (41°, 53° ...) qui peuvent être mesurés au niveau du thalle des végétaux inférieurs et de la nervation foliaire des végétaux supérieurs. Une interpretation est recherchée: ces angles caractérisant le fonctionnement d'un champ morphogénétique, il a fallu bâtir un formalisme bien adapté au domaine du vivant en vue de cette étude. L'outil mathématique conçu, le Relateur Arithmétique, alliant la géométrie et l'arithmétique, interprète un systéme comme le résultat de l'interaction entre une structure interne cyclique et un environnement auquel elle est adaptée. On pent alors rendre compte d'une auto-référence partielle et d'un changement de niveau d'organisation. Les valeurs particulières des angles de ramification sont extrêmales pour une petite variation de la structure interne du systeme. Une proposition concernant les relations entre génome, cellule et organe est donnée en conclusion.

     

The grading of normal pressure hydrocephalus.

PATIENTS AND METHOD: During a period of 15 years we investigated 200 patients suspected of normal pressure hydrocephalus (NPH) by means of an intrathecal infusion test. In 107 patients (54%) the diagnosis of a normal pressure hydrocephalus could be confirmed. For the evaluation of the course of disease we used the Black-Grading-Scale for shunt assessment [1] and the clinical grading for chronic hydrocephalus (Kiefer-scale) [4] pre- and postoperatively as well as in a follow-up examination seven months after surgical treatment. The aim of our study was to find out a quick and easy-to-handle bed-side examination for the grading of NPH. DISCUSSION: The Black-Grading-Scale does not allow to distinguish between patients in an unchanged condition and those with a worsening of their symptoms. Therefore this scale is useful for patients with an obstructive hydrocephalus but not for those with a NPH. In our opinion the clinical grading of Kiefer [4] seems to be the most reliable scale for the grading and long term follow-up of a normal pressure hydrocephalus. CONCLUSION: Our own created NPH-Recovery-Rate is based on the clinical grading for chronic hydrocephalus (Kiefer-scale) [4]. It allows the interindividual comparison between the courses of disease in patients with normal pressure hydrocephalus.