Maximum geometrical hindrance to diffusion in brain extracellular space surrounding uniformly spaced convex cells

Brain extracellular space (ECS) constitutes a porous medium in which diffusion is subject to hindrance, described by tortuosity, lambda = (D/D*)1/2, where D is the free diffusion coefficient and D* is the effective diffusion coefficient in brain. Experiments show that lambda is typically 1.6 in normal brain tissue although variations occur in specialized brain regions. In contrast, different theoretical models of cellular assemblies give ambiguous results: they either predict lambda-values similar to experimental data or indicate values of about 1.2. Here we constructed three different ECS geometries involving tens of thousands of cells and performed Monte Carlo simulation of 3-D diffusion. We conclude that the geometrical hindrance in the ECS surrounding uniformly spaced convex cells is independent of the cell shape and only depends on the volume fraction alpha (the ratio of the ECS volume to the whole tissue volume). This dependence can be described by the relation lambda = ((3-alpha)/2)1/2, indicating that the geometrical hindrance in such ECS cannot account for lambda > 1.225. Reasons for the discrepancy between the theoretical and experimental tortuosity values are discussed.     

低分子数下的生命

瞬时分子信号发生在微区,这些区域通常处于一种非均一非平衡状态。在这个过程中,参与的分了数很少,通常有很大的波动。于是,了解各种分子成分的空间组织结构对理解细胞信号通路非常必要。我们利用蒙特卡洛电脑仿真的方法,结合现实的三维几何构形,来研究亚细胞结构以及神经元和突触的生理学。     

A model of effective diffusion and tortuosity in the extracellular space of the brain

Tortuosity of the extracellular space describes hindrance posed to the diffusion process by a geometrically complex medium in comparison to an environment free of any obstacles. Calculating tortuosity in biologically relevant geometries is difficult. Yet this parameter has proved very important for many processes in the brain, ranging from ischemia and osmotic stress to delivery of nutrients and drugs. It is also significant for interpretation of the diffusion-weighted magnetic resonance data. We use a volume-averaging procedure to obtain a general expression for tortuosity in a complex environment. A simple approximation then leads to tortuosity estimates in a number of two-dimensional (2D) and three-dimensional (3D) geometries characterized by narrow pathways between the cellular elements. It also explains the counterintuitive fact of lower diffusion hindrance in a 3D environment. Comparison with Monte Carlo numerical simulations shows that the model gives reasonable tortuosity estimates for a number of regular and randomized 2D and 3D geometries. Importantly, it is shown that addition of dead-end pores increases tortuosity in proportion to the square root of enlarged total extracellular volume fraction. This conclusion is further supported by the previously described tortuosity decrease in ischemic brain slices where dead-end pores were partially occluded by large macromolecules introduced into the extracellular space.     

Structural relationships between parenchymal and stromal elements in the pars intermedia of the rat adenohypophysis as demonstrated by extracellular space markers

Summary The pars intermedia (PI) of the rat adenohypophysis was studied by light and transmission electron microscopy after conventional staining as well as ruthenium red staining, and after systemic injection of horseradish peroxidase. The studies disclose a complex and constant system of two channel types (Type I and Type II channels) formed by PI cells with specific relationships to a very rich nerve supply, to each other, and to a stellate cell type proposed here to represent an element of neuroglia. The channel system could perform a function in the movement of fluids and solutes within the PI which is virtually avascular in the rat as well as in other mammals.Supported by the Medical Research Council of Canada Grant # MA6445We thank Mr. J. Jones and Mr. A.R. Morris for their expert technical assistance     

Monte Carlo Simulation of Release of Vesicular Content in Neuroendocrine Cells

The release of transmitter from the vesicle, its diffusion through the fusion pore, and the cleft and its interaction with the carbon electrode were simulated using the Monte Carlo method. According to the simulation the transmitter release is largely determined by geometric factors – the ratio of the fusion pore cross-sectional and vesicular areas, if the diffusion constant is as in the aqueous solution – but the speed of transmitter dissociation from the gel matrix plays an important role during the rise phase of release. Transmitter is not depleted near the entrance to the fusion pore and there is no cleft-to-vesicle feedback, but the depletion becomes evident if the diffusion constant is reduced, especially if the pore is wide. In general, the time course of amperometric currents closely resembles the time course of the simulated transmitter concentration in the cleft and the time course of release. Surprisingly, even a tenfold change of the electrode efficiency has only a marginal effect on the amplitude or the time course of amperometric currents. Greater electrode efficiency however lowers the cleft concentration, but only if the cleft is narrow. As the cleft widens the current amplitudes diminish and rise times lengthen, but the decay times are less affected. Moreover, the amplitude dependence of the rise and decay times becomes steeper as the cleft widens and/or as the release kinetics slows. Finally, lower diffusion constant of transmitter in the narrow cleft does not further prolong the amperometric currents, whose slow time course reflects slow release kinetics.     

Poly[N-(2-hydroxypropyl)methacrylamide] polymers diffuse in brain extracellular space with same tortuosity as small molecules

Integrative optical imaging was used to show that long-chain synthetic poly[N-(2-hydroxypropyl)methacrylamide] (PHPMA) polymers in a range of molecular weights from 7.8 to 1057 kDa were able to diffuse through the extracellular space in rat neocortical slices. Tortuosity (square root of ratio of diffusion coefficient in aqueous medium to that in brain) measured with such polymers averaged 1.57, a value similar to that obtained previously with tetramethylammonium, a small cation. When PHPMA was conjugated with bovine serum albumin (BSA) to make a bulky polymer with molecular weight 176 kDa, the tortuosity rose to 2.27, a value similar to that obtained previously with BSA alone and with 70-kDa dextran. The method of image analysis was justified with diffusion models involving spherical and nonspherical initial distributions of the molecules.     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

Guiding conformation space search with an all-atom energy potential

The most significant impediment for protein structure prediction is the inadequacy of conformation space search. Conformation space is too large and the energy landscape too rugged for existing search methods to consistently find near-optimal minima. To alleviate this problem, we present model-based search, a novel conformation space search method. Model-based search uses highly accurate information obtained during search to build an approximate, partial model of the energy landscape. Model-based search aggregates information in the model as it progresses, and in turn uses this information to guide exploration toward regions most likely to contain a near-optimal minimum. We validate our method by predicting the structure of 32 proteins, ranging in length from 49 to 213 amino acids. Our results demonstrate that model-based search is more effective at finding low-energy conformations in high-dimensional conformation spaces than existing search methods. The reduction in energy translates into structure predictions of increased accuracy.     

The use of 60Co-EDTA as an extracellular marker in frog skin

⁶⁰Co-EDTA was tested as an extracellular marker in isolated epithelia of frog skin.It was found to be non-toxic for frog skin and 0.1 mM EDTA proved to be enough to saturate any adsorption sites.Comparing with [¹⁴C]inulin, ⁶⁰Co-EDTA marks a slightly greater extracellular space and this volume is constant between 15 min and 2 h.Furthermore it is reproducible and its use simplifies the methodology of the determination of water and electrolyte contents in the cells.     

Bias in Markov models of disease

We examine bias in Markov models of diseases, including both chronic and infectious diseases. We consider two common types of Markov disease models: ones where disease progression changes by severity of disease, and ones where progression of disease changes in time or by age. We find sufficient conditions for bias to exist in models with aggregated transition probabilities when compared to models with state/time dependent transition probabilities. We also find that when aggregating data to compute transition probabilities, bias increases with the degree of data aggregation. We illustrate by examining bias in Markov models of Hepatitis C, Alzheimer’s disease, and lung cancer using medical data and find that the bias is significant depending on the method used to aggregate the data. A key implication is that by not incorporating state/time dependent transition probabilities, studies that use Markov models of diseases may be significantly overestimating or underestimating disease progression. This could potentially result in incorrect recommendations from cost-effectiveness studies and incorrect disease burden forecasts.     

Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study

Three practical methods for scatter correction of Tc-99m SPECT images are evaluated. Among these, two methods, three-energy window (TEW) methods using the trapezoidal and triangular approximations, have been described previously by investigators, and a new approximation is offered in this work. The SIMIND (SIMulation of Imaging Nuclear Detectors) Monte Carlo program is used to simulate a line source placed at on-axis and 5 cm off-axis locations, a cold-sphere/hot-background phantom, a hot-sphere/cold-background phantom, and a more clinically realistic NCAT (Nonuniform Rational B-spline-based CArdiac-Torso) phantom. For evaluation of these methods, the scatter line-spread functions and scatter fractions for the on- and off-axis line source, image contrast, signal-to-noise ratio and relative noise for the cold spheres, and recovery coefficient for the hot spheres of different diameters are compared. For the NCAT phantom, a line profile through a slice of the reconstructed image is considered before and after scatter correction, and also image contrast defined by this profile is used to compare the correction methods. The results of this study indicate that for the line source simulation the scatter fractions obtained from the proposed method are a better estimation of true scatter fractions. Also, for both the sphere simulation and NCAT simulation, the proposed method improves the image contrast as compared to the two other methods.     

Optimization of GATE simulations for whole-body planar scintigraphic acquisitions using the XCAT male phantom with 177Lu-DOTATATE biokinetics in a Siemens Symbia T2

Simulations of planar whole body acquisitions in therapeutic procedures are often extensively time-consuming and therefore rarely used. However, optimising tools and variance reduction techniques can be employed to overcome this problem. In this paper, a variety of features available in GATE are explored and their capabilities to reduce simulation time are evaluated. For this purpose, the male XCAT phantom was used as a virtual patient with ¹⁷⁷Lu-DOTATATE pharmacokinetic for whole body planar acquisition simulations in a Siemens Symbia T2 model. Activity distribution was divided into 8 compartments that were simulated separately. GATE optimization techniques included reducing the amount of time spent in both voxel and detector tracking. Some acceleration techniques led to a decrease of CPU-time by a factor of 167, while image statistics were kept constant. In that context, the simulation of therapeutic procedure imaging would still require 46 days on a single CPU, but this could be reduced to hours on a dedicated cluster.     

Astrocytes and extracellular matrix in extrasynaptic volume transmission

Volume transmission is a form of intercellular communication that does not require synapses; it is based on the diffusion of neuroactive substances across the brain extracellular space (ECS) and their binding to extrasynaptic high-affinity receptors on neurons or glia. Extracellular diffusion is restricted by the limited volume of the ECS, which is described by the ECS volume fraction α, and the presence of diffusion barriers, reflected by tortuosity λ, that are created, for example, by fine astrocytic processes or extracellular matrix (ECM) molecules. Organized astrocytic processes, ECM scaffolds or myelin sheets channel the extracellular diffusion so that it is facilitated in a certain direction, i.e. anisotropic. The diffusion properties of the ECS are profoundly influenced by various processes such as the swelling and morphological rebuilding of astrocytes during either transient or persisting physiological or pathological states, or the remodelling of the ECM in tumorous or epileptogenic tissue, during Alzheimer''s disease, after enzymatic treatment or in transgenic animals. The changing diffusion properties of the ECM influence neuron–glia interaction, learning abilities, the extent of neuronal damage and even cell migration. From a clinical point of view, diffusion parameter changes occurring during pathological states could be important for diagnosis, drug delivery and treatment.     

FLUKA simulation of target fragmentation in proton therapy

In proton therapy, secondary fragments are created in nuclear interactions of the beam with the target nuclei. The secondary fragments have low kinetic energies and high atomic numbers as compared to primary protons. Fragments have a high LET and deposit all their energy close to the generation point. For their characteristics, secondary fragments can alter the dose distribution and lead to an increase of RBE for the same delivered physical dose. Moreover, the radiobiological impact of target fragmentation is significant mostly in the region before the Bragg peak, where generally healthy tissues are present, and immediately after Bragg peak. Considering the high biological impact of those particles, especially in the case of healthy tissues or organs at risk, the inclusion of target fragmentation processes in the dose calculation of a treatment planning system can be relevant to improve the treatment accuracy and for this reason it is one of the major tasks of the MoVe IT project.In this study, Monte Carlo simulations were employed to fully characterize the mixed radiation field generated by target fragmentation in proton therapy. The dose averaged LET has been evaluated in case of a Spread Out Bragg Peak (SOBP). Starting from LET distribution, RBE has been evaluated with two different phenomenological models. In order to characterize the mixed radiation field, the production cross section has been evaluated by means of the FLUKA code. The future development of present work is to generate a MC database of fragments fluence to be included in TPS.     

Maximum Likelihood Estimation of Genetic Parameters in Cell Populations

In this paper we consider a cell population such as bacteria consisting of two types of cells, mutant and nonmutant. Under the mutation and homogeneous pure birth processes, this paper derives a maximum likelihood estimation procedure for estimating mutation rate and birth rate. The method is applied to Newcombe's data; further some Monte Carlo studies are generated. The numerical results indicate that the method is quite efficient for estimating genetic parameters in cell populations.     

Estimation of contrast agent concentration in intra- and extra-vascular spaces of brain tissue

This article presents a new method for estimating the leakage of a contrast agent out of a vessel. The proposed method is developed based on tissue homogeneity (TH) model, modified Patlak model, and Monte Carlo simulation. The analytical methods published in the literature estimate the contrast agent leakage by solving the coupled differential equations associated with the TH model under adiabatic conditions. These methods employ unrealistic simplifying assumptions and become intractable in their applications to the vessels that have a non-uniform permeability. Without making any unrealistic assumptions, our approach simply tracks the passage of the contrast agent through the capillary and its crossing of the vessel walls based on the blood flow in the vessel, the vessel's permeability, and the condition of the blood-brain barrier (BBB). These are treated as statistical processes that can be modeled reasonably well using the Monte Carlo method. In the proposed approach, the intra- and extra-vascular spaces are divided into multiple compartments, similar to the Patlak model. A real, measured arterial input function (AIF) is used as the capillary input and the concentration of the contrast agent is found as a function of time and distance, inside and outside of the capillary. This is done for normal and abnormal capillaries with uniform and non-uniform permeability. The proposed method generates concentration curves similar to those of the analytical method for simple AIF models. It also generates reasonable concentration curves for a real AIF. The proposed method does not fit a mathematical function to the measured AIF and does not make unrealistic simplifying assumptions. It is not therefore prone to the fitting errors and generates more realistic and more accurate results than the analytical methods.     

The extracellular space and blood-eye barrier in an insect retina: An ultrastructural study

Summary (1) The distribution of the extracellular space (ECS) in the outer part of the locust compound eye has been mapped with lanthanum and ruthenium red, applied to the retina. (2) In the photoreceptor zone, about 2.4% of the volume is ECS, in agreement with radiotracer and electrical estimates. Of this ECS, about 70% lies in lacunae between ommatidia, but only 1–2% adjacent to the photosensitive rhabdom. The lacunae are filled with material which binds applied tracers, and are thought to be structural spaces. (3) It has been suggested several times that such a small cation pool is insufficient to sustain more than a few large photoresponses, but this is shown to be incorrect. Enough Na⁺ lies within the rhabdomal ECS and within rapid diffusional access to it, to impose no immediate limitation. (4) The palisade vacuoles surrounding the rhabdom are intracellular, and are typical of light as well as dark-adapted eyes. (5) Tracers fail to penetrate more than about 30 m into the axon zone, in agreement with electrical, dye and radiotracer indications of a blood-eye barrier near this point. Septate and gap junctions between glial membranes proliferate at this level, the lacunae disappear, and the axonal clefts narrow, but no tight junctions were seen. Comparison is made with the barrier around the nerve cord. (6) The secondary pigment cells in the retina may function as osmotic/ionic buffers, in conjunction with the blood-eye barrier.     

Conformational space exploration of Met- and Leu-enkephalin using the MOLS method, molecular dynamics, and Monte Carlo simulation--a comparative study

We report here a comparative study of the molecular conformational energy landscape generated using the mutually orthogonal Latin squares (MOLS) method, molecular dynamics (MD), and Monte Carlo (MC) simulation. The MOLS method, as described earlier from our laboratory, uses an experimental design technique to rapidly and exhaustively sample the low energy conformations of a molecule. MD and MC simulations have been used to perform similar tasks. In the comparison reported here, the three methods were applied to a pair of neuropeptides, namely Met- and Leu-enkephalin. A set of 1500 conformations of these enkephalins were generated using these methods with CHARMM22 force field, and the resulting samples were analyzed to determine the extent and nature of coverage of the conformational space. The results indicate that the MOLS method samples a larger number of possible conformations and identifies conformations closer to the experimental structures than the MD and MC simulations.     

Monte Carlo Simulation of Fluids in Curved Three-dimensional Space

Abstract

This work describes the methods required to perform computer simulations of three-dimensional fluids confined to the surface of a four-dimensional hypersphere. The use of such non-Euclidian spaces, or spherical boundary conditions, is convenient in cases where spatial inhomogeneities occur over length-scales comparable to that of the entire system. The form of the pressure equation in curved space is discussed, and the results of Monte Carlo simulations of hard spheres confined to the surface of a hypersphere are presented. Comparison of the simulation results to the Carnahan-Starling equation of state in flat space provides a basis for determining when curvature effects can be neglected.     

Uses and misuses of progress curve analysis in enzyme kinetics

Progress curve analysis is a convenient tool for the characterization of enzyme action: a single reaction mixture provides multiple experimental measured points for continuously varying amounts of substrates and products with exactly the same enzyme and modulator concentrations. The determination of kinetic parameters from the progress curves, however, requires complex mathematical evaluation of the time-course data. Some freely available programs (e.g. FITSIM, DYNAFIT) are widely applied to fit kinetic parameters to user-defined enzymatic mechanisms, but users often overlook the stringent requirements of the analytic procedures for appropriate design of the input experiments. Flaws in the experimental setup result in unreliable parameters with consequent misinterpretation of the biological phenomenon under study. The present commentary suggests some helpful mathematical tools to improve the analytic procedure in order to diagnose major errors in concept and design of kinetic experiments.