diffusion process
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In stochastic neuronal models, an interspike interval corresponds to the time interval during which the process imitating the membrane potential reaches a threshold from an initial depolarization. For neurons with an extensive dendritic structure, a stochastic process combining diffusion and discontinuous development of its trajectory is considered a good description of the membrane potential. Due to a lack of analytical solutions of the threshold passage distribution for such a process, a method for computer simulation is introduced here. For the diffusion Ornstein-Uhlenbeck process with exponentially distributed moments of constant jumps a program is given. The relation between the simulation step, accuracy of simulation and amount of computing time required is discussed.
Statistical properties of spike trains as well as other neurophysiological data suggest a number of mathematical models of neurons. These models range from entirely descriptive ones to those deduced from the properties of the real neurons. One of them, the diffusion leaky integrate-and-fire neuronal model, which is based on the Ornstein-Uhlenbeck (OU) stochastic process that is restricted by an absorbing barrier, can describe a wide range of neuronal activity in terms of its parameters. These parameters are readily associated with known physiological mechanisms. The other model is descriptive, Gamma renewal process, and its parameters only reflect the observed experimental data or assumed theoretical properties. Both of these commonly used models are related here. We show under which conditions the Gamma model is an output from the diffusion OU model. In some cases, we can see that the Gamma distribution is unrealistic to be achieved for the employed parameters of the OU process.
- Klíčová slova
- First-passage-time problem, Leaky integrate-and-fire, Stein’s neuronal model,
- MeSH
- difuze * MeSH
- kybernetika MeSH
- modely neurologické * MeSH
- neurony * MeSH
- stochastické procesy MeSH
- Publikační typ
- časopisecké články MeSH
The Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein's model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined. Solving the first-passage-time problem for the Jacobi process, we found closed-form expressions for mean, variance, and third moment that are easy to implement numerically. The first two moments are used here to determine the role played by the parameters of the neuronal model; namely, the effect of multiplicative noise on the output of the Jacobi neuronal model with input-dependent parameters is examined in detail and compared with the properties of the generic Jacobi diffusion. It appears that the dependence of the model parameters on the rate of inhibition turns out to be of primary importance to observe a change in the slope of the response curves. This dependence also affects the variability of the output as reflected by the coefficient of variation. It often takes values larger than one, and it is not always a monotonic function in dependency on the rate of excitation.
- Publikační typ
- časopisecké články MeSH
Pathology of neurodegenerative diseases can be correlated with intra-neuronal as well as extracellular changes which lead to neuronal degeneration. The central nervous system (CNS) is a complex structure comprising of many biological barriers. These microstructural barriers might be affected by a variety of pathological processes. Specifically, changes in the brain tissue's microstructure affect the diffusion of water which can be assessed non-invasively by diffusion weighted (DW) magnetic resonance imaging (MRI) techniques. Diffusion tensor imaging (DTI) is a diffusion MRI technique that considers diffusivity as a Gaussian process, i.e. does not account for any diffusion hindrance. However, environment of the brain tissues is characterized by a non-Gaussian diffusion. Therefore, diffusion kurtosis imaging (DKI) was developed as an extension of DTI method in order to quantify the non-Gaussian distribution of water diffusion. This technique represents a promising approach for early diagnosis of neurodegenerative diseases when the neurodegenerative process starts. Hence, the purpose of this article is to summarize the ongoing clinical and preclinical research on Parkinson's, Alzheimer's and Huntington diseases, using DKI and to discuss the role of this technique as an early stage biomarker of neurodegenerative conditions.
- Klíčová slova
- Alzheimer’s disease, Diffusion kurtosis imaging, Huntington’s disease, Neurodegenerative disorders, Neuroimaging, Parkinson’s disease,
- MeSH
- časná diagnóza MeSH
- lidé MeSH
- mozek diagnostické zobrazování MeSH
- neurodegenerativní nemoci diagnostické zobrazování MeSH
- počítačové zpracování obrazu MeSH
- zobrazování difuzních tenzorů metody MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- přehledy MeSH
The process of diffusion of sodium hyaluronate and its hydrophobically modified alkyl derivatives in water was studied by measuring the kinetics of solid polymer film swelling. The following fundamental thermodynamic parameters of the swelling process were calculated: the apparent diffusion coefficient of swelling by water D(s) determined at three temperatures (25, 37, and 45 degrees C), the activation enthalpy of diffusion connected with the swelling DeltaH(D,s) and the activation enthalpy of the swelling process DeltaH(s). The thermodynamic activity of the solvent for the given sodium hyaluronate and its four alkyl derivatives has been expressed through the internal quantity RA(delta,s), that is expansion work of polymer coil accomplished by the action of the internal pressure.
- MeSH
- časové faktory MeSH
- difuze MeSH
- hydrofobní a hydrofilní interakce MeSH
- kyselina hyaluronová analogy a deriváty chemie MeSH
- povrchové vlastnosti MeSH
- teplota MeSH
- termodynamika MeSH
- tlak MeSH
- uhlovodíky chemie MeSH
- voda MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Názvy látek
- kyselina hyaluronová MeSH
- uhlovodíky MeSH
- voda MeSH
Estimating structural connectivity from diffusion-weighted magnetic resonance imaging is a challenging task, partly due to the presence of false-positive connections and the misestimation of connection weights. Building on previous efforts, the MICCAI-CDMRI Diffusion-Simulated Connectivity (DiSCo) challenge was carried out to evaluate state-of-the-art connectivity methods using novel large-scale numerical phantoms. The diffusion signal for the phantoms was obtained from Monte Carlo simulations. The results of the challenge suggest that methods selected by the 14 teams participating in the challenge can provide high correlations between estimated and ground-truth connectivity weights, in complex numerical environments. Additionally, the methods used by the participating teams were able to accurately identify the binary connectivity of the numerical dataset. However, specific false positive and false negative connections were consistently estimated across all methods. Although the challenge dataset doesn't capture the complexity of a real brain, it provided unique data with known macrostructure and microstructure ground-truth properties to facilitate the development of connectivity estimation methods.
- Klíčová slova
- Challenge, Connectivity, Diffusion MRI, Microstructure, Monte carlo simulation, Numerical substrates, Tractography,
- MeSH
- difuzní magnetická rezonance * metody MeSH
- fantomy radiodiagnostické MeSH
- lidé MeSH
- metoda Monte Carlo MeSH
- mozek diagnostické zobrazování MeSH
- počítačové zpracování obrazu * metody MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Research Support, N.I.H., Extramural MeSH
Diffusion is a mass transport phenomenon caused by chaotic thermal movements of molecules. Studying the transport in specific domain is simplified by using evolutionary differential equations for local concentration of the molecules instead of complete information on molecular paths [1]. Compounds in a fluid mixture tend to smooth out its spatial concentration inhomogeneities by diffusion. Rate of the transport is proportional to the concentration gradient and coefficient of diffusion of the compound in ordinary diffusion. The evolving concentration profile c(x,t) is then solution of evolutionary partial differential equation deltac/deltat=DDeltac where D is diffusion coefficient and Delta is Laplacian operator. Domain of the equation may be a region in space, plane or line, a manifold, such as surface embedded in space, or a graph. The Laplacian operates on smooth functions defined on given domain. We can use models of diffusion for such diverse tasks as: a) design of method for precise measurement of receptors mobility in plasmatic membrane by confocal microscopy [2], b) evaluation of complex geometry of trabeculae in developing heart [3] to show that the conduction pathway within the embryonic ventricle is determined by geometry of the trabeculae.
Robust voxelwise analysis using tract-based spatial statistics (TBSS) together with permutation statistical method is standardly used in analyzing diffusion tensor imaging (DTI) of brain. A similar analytical method could be useful when studying DTI of cervical spinal cord. Based on anatomical data of sixty-four healthy volunteers, white (WM) and gray matter (GM) masks were created and subsequently registered into DTI space. Using TBSS, two skeleton types were created (single line and dilated for WM as well as GM). From anatomical data, percentage rates of overlap were calculated for all skeletons in relation to WM and GM masks. Voxelwise analysis of fractional anisotropy values depending on age and sex was conducted. Correlation of fraction anisotropy values with age of subjects was also evaluated. The two WM skeleton types showed a high overlap rate with WM masks (~94%); GM skeletons showed lower rates (56% and 42%, respectively, for single line and dilated). WM and GM areas where fraction anisotropy values differ between sexes were identified (p < .05). Furthermore, using voxelwise analysis such WM voxels were identified where fraction anisotropy values differ depending on age (p < .05) and in these voxels linear dependence of fraction anisotropy and age (r = -0.57, p < .001) was confirmed by regression analysis. This dependence was not proven when using WM anatomical masks (r = -0.21, p = .10). The analytical approach presented shown to be useful for group analysis of DTI data for cervical spinal cord.
- Klíčová slova
- Diffusion tensor imaging, Spinal cord, Voxelwise analysis,
- MeSH
- algoritmy * MeSH
- anizotropie MeSH
- bílá hmota diagnostické zobrazování MeSH
- difuzní magnetická rezonance * MeSH
- dospělí MeSH
- krční mícha diagnostické zobrazování MeSH
- lidé středního věku MeSH
- lidé MeSH
- počítačové zpracování obrazu metody MeSH
- zdraví dobrovolníci pro lékařské studie MeSH
- Check Tag
- dospělí MeSH
- lidé středního věku MeSH
- lidé MeSH
- mužské pohlaví MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
The amorphous polymer film swelling in a liquid solvent below the glass transition temperature was characterized by a few kinetic parameters (especially the mutual diffusion coefficient of swelling and its mean value) obtained by interference of monochromatic light in the wedge arrangement. This interferometric method allows one to determine the concentration field in the swollen surface layer and consequently to compute the concentration-dependent diffusion coefficient. A software system developed at the Department of Physics and Material Engineering at TBU in Zlin has been used for the evaluation of the main kinetic parameters of the swelling process. The software can be used for the on-line analyses of interferograms during the swelling process. The main application outputs are the computation of the concentration profile, the concentration gradient, the mutual diffusion coefficient of the swelling by the solvent and its mean value.
- Klíčová slova
- concentration profile, diffusion, hyaluronan, image analyses, interferometry, swelling,
- MeSH
- difuze MeSH
- interferometrie * MeSH
- kinetika MeSH
- kyselina hyaluronová chemie MeSH
- polymery chemie MeSH
- rozpouštědla chemie MeSH
- software MeSH
- teplota MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Názvy látek
- kyselina hyaluronová MeSH
- polymery MeSH
- rozpouštědla MeSH
Leaky integrate-and-fire neuronal models with reversal potentials have a number of different diffusion approximations, each depending on the form of the amplitudes of the postsynaptic potentials. Probability distributions of the first-passage times of the membrane potential in the original model and its diffusion approximations are numerically compared in order to find which of the approximations is the most suitable one. The properties of the random amplitudes of postsynaptic potentials are discussed. It is shown on a simple example that the quality of the approximation depends directly on them.
- MeSH
- akční potenciály fyziologie MeSH
- difuze MeSH
- lidé MeSH
- matematika MeSH
- membránové potenciály fyziologie MeSH
- modely neurologické * MeSH
- neurony fyziologie MeSH
- normální rozdělení MeSH
- počítačová simulace MeSH
- Poissonovo rozdělení MeSH
- pravděpodobnost MeSH
- stochastické procesy MeSH
- synaptické potenciály MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
