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.
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
- Action Potentials physiology MeSH
- Diffusion MeSH
- Humans MeSH
- Mathematics MeSH
- Membrane Potentials physiology MeSH
- Models, Neurological * MeSH
- Neurons physiology MeSH
- Normal Distribution MeSH
- Computer Simulation MeSH
- Poisson Distribution MeSH
- Probability MeSH
- Stochastic Processes MeSH
- Synaptic Potentials MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
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.
- MeSH
- Diffusion * MeSH
- Cybernetics MeSH
- Models, Neurological * MeSH
- Neurons * MeSH
- Stochastic Processes MeSH
- Publication type
- Journal Article MeSH
Methamphetamine (METH) abuse is known to increase the risk of Parkinson's disease (PD) due to its dopaminergic neurotoxicity. This is the rationale for the METH model of PD developed by toxic METH dosing (10 mg/kg four times every 2 h) which features robust neurodegeneration and typical motor impairment in mice. In this study, we used diffusion kurtosis imaging to reveal microstructural brain changes caused by METH-induced neurodegeneration. The METH-treated mice and saline-treated controls underwent diffusion kurtosis imaging scanning using the Bruker Avance 9.4 Tesla MRI system at two time-points: 5 days and 1 month to capture both early and late changes induced by METH. At 5 days, we found a decrease in kurtosis in substantia nigra, striatum and sensorimotor cortex, which is likely to indicate loss of DAergic neurons. At 1 month, we found an increase of kurtosis in striatum and sensorimotor cortex and hippocampus, which may reflect certain recovery processes. Furthermore, we performed tract-based spatial statistics analysis in the white matter and at 1 month, we observed increased kurtosis in ventral nucleus of the lateral lemniscus and some of the lateral thalamic nuclei. No changes were present at the early stage. This study confirms the ability of diffusion kurtosis imaging to detect microstructural pathological processes in both grey and white matter in the METH model of PD. The exact mechanisms underlying the kurtosis changes remain to be elucidated but kurtosis seems to be a valuable biomarker for tracking microstructural brain changes in PD and potentially other neurodegenerative disorders.
- MeSH
- Behavior, Animal drug effects MeSH
- Diffusion Magnetic Resonance Imaging MeSH
- Dopamine Agents toxicity MeSH
- Methamphetamine toxicity MeSH
- Disease Models, Animal MeSH
- Brain diagnostic imaging drug effects pathology MeSH
- Mice, Inbred C57BL MeSH
- Parkinson Disease, Secondary diagnostic imaging pathology MeSH
- Animals MeSH
- Check Tag
- Male MeSH
- Animals MeSH
- Publication type
- Journal Article MeSH
Purpose of this paper is to describe characteristic features of dissolution data by using homogeneous model of dissolution with initial transient phase. To achieve the goal we consider a random lag time before the homogeneous phase of the dissolution begins. The resulting dissolution profiles are characterized by sigmoidal shape commonly observed in empirical dissolution data. Furthermore, probability distribution of repeated measurements at fixed time is deduced from the model and function describing variability of the data in dependency on time is proposed. Three examples with normal, exponential and gamma probability distribution of the lag time are presented. All the models are pairwise compared with the Weibull function with high similarity between them. The result offers an alternative interpretation for the frequently found fit of the Weibull model to experimental data.
Evidence suggests that accumulation and aggregation of α-synuclein contribute to the pathogenesis of Parkinson's disease (PD). The aim of this study was to evaluate whether diffusion kurtosis imaging (DKI) will provide a sensitive tool for differentiating between α-synuclein-overexpressing transgenic mouse model of PD (TNWT-61) and wild-type (WT) littermates. This experiment was designed as a proof-of-concept study and forms a part of a complex protocol and ongoing translational research. Nine-month-old TNWT-61 mice and age-matched WT littermates underwent behavioral tests to monitor motor impairment and MRI scanning using 9.4 Tesla system in vivo. Tract-based spatial statistics (TBSS) and the DKI protocol were used to compare the whole brain white matter of TNWT-61 and WT mice. In addition, region of interest (ROI) analysis was performed in gray matter regions such as substantia nigra, striatum, hippocampus, sensorimotor cortex, and thalamus known to show higher accumulation of α-synuclein. For the ROI analysis, both DKI (6 b-values) protocol and conventional (2 b-values) diffusion tensor imaging (cDTI) protocol were used. TNWT-61 mice showed significant impairment of motor coordination. With the DKI protocol, mean, axial, and radial kurtosis were found to be significantly elevated, whereas mean and radial diffusivity were decreased in the TNWT-61 group compared to that in the WT controls with both TBSS and ROI analysis. With the cDTI protocol, the ROI analysis showed decrease in all diffusivity parameters in TNWT-61 mice. The current study provides evidence that DKI by providing both kurtosis and diffusivity parameters gives unique information that is complementary to cDTI for in vivo detection of pathological changes that underlie PD-like symptomatology in TNWT-61 mouse model of PD. This result is a crucial step in search for a candidate diagnostic biomarker with translational potential and relevance for human studies.
- MeSH
- alpha-Synuclein metabolism MeSH
- Diffusion Magnetic Resonance Imaging methods MeSH
- Humans MeSH
- Disease Models, Animal MeSH
- Brain metabolism pathology MeSH
- Mice, Transgenic MeSH
- Mice MeSH
- Parkinson Disease metabolism pathology MeSH
- Pilot Projects MeSH
- Motor Activity MeSH
- Diffusion Tensor Imaging methods MeSH
- Animals MeSH
- Check Tag
- Humans MeSH
- Male MeSH
- Mice MeSH
- Animals MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
Cíl. V práci je hodnocena vlastní zkušenost se zobrazováním gliových nádorů pomocí tenzorů difúze při vyšetření magnetickou rezonancí. Metoda. Bylo provedeno retrospektivní zhodnocení skupiny 24 nemocných s gliovými nádory. V souboru bylo zastoupeno osm nádorů gr. II, osm nádorů gr. Ill a osm nádorů gr. IV s histologicky stanovenou diagnózou. Všichni nemocní podstoupili zobrazení pomocí T2 vážených obrazů, mnohosměrných obrazů difuzního vážení (měřených v 60 nonkolineárních směrech) a TI vážených obrazů bez a po podání kontrastní látky. Použitá sekvence i programové vybavení využité k hodnocení je produktem Massachusetts General Hospital Corporation (Boston, USA, Ma). U všech nemocných byly vypočteny mapy frakční anizotropie (FA). Změny frakční anizotropie v bílé hmotě byly hodnoceny ve vlastní tkáni nádoru, na hranici nádoru a v normálně vypadající bílé hmotě v sousedství nádoru. Trojrozměrné modely traktů bílé hmoty byly využity k demonstraci prostorových vztahů nádoru s vnitřní kapsulou nebo kalózním tělesem, ke stopování traktů použito bylo prahu změny FA 0,25 a úhlu deklinace tenzoru 45 st. Hodnoceno bylo i sycení nádorové tkáně kontrastní látkou. Výsledky. Uniformní homogenní strukturu a ostré ohraničení bylo prokázáno u všech nádorů gr. II na FA mapách, široký lem intermediální FA byl u všech nádorů gr. II. Variabilní ohraničení se vyskytovalo na FA mapách u nádorů gr. IV. Pomocí hodnocení map FA bylo dosaženo senzitivity 81 % a specificity 87% pro rozlišení nízkostupňových a vysokostupňových gliálních nádorů. Pokud bylo sycení kontrastní látkou hodnoceno společně s mapami FA, bylo v souboru dosaženo 100% senzitivity i specificity. Závěr. I když pouhé hodnocení map FA není dostatečné pro hodnocení gradingu gliových nádorů, kombinace posouzení sycení kontrastní látkou a hodnocení map FA zvyšuje možnosti odlišení nízko- a vysoko stupňových gliomů. Trojrozměrné modely vláken bílé hmoty v kalózním tělese a vnitřní kapsule mohou být využity v předoperačním plánováni.
Aim. To evaluate the authors experience with the use of diffusion tensor magnetic resonance imaging (DTI) on patients with glial tumours. Methods. A retrospective evaluation of a group of 24 patients with glial tumours was performed. There were eight patients with grade II, eight patients with grade III and eight patients with grade IV tumours with a histologically proven diagnosis. All the patients underwent routine imaging including T2 weighted images, multidirectional diffusion weighted imaging (measured in 60 non-collinear directions) and Tl weighted non-enhanced and contrast enhanced images. The imaging sequence and evaluation software were produced by Massachusetts General Hospital Corporation (Boston, USA, Ma). Fractional anisotropy (FA) maps were calculated in all patients. The white matter FA changes were assessed within the tumourous tissue, on the tumourous borderline and in the normally appearing white matter adjacent to the tumour. A three-dimensional model of the white matter tract was created to demonstrate the space relationship of the tumour and the capsula interna or corpus callosum in each case using the following fibre tracing parameters: FA step 0.25 and a tensor declination angle of 45 gr. An additional assessment of the tumourous tissue enhancement was performed. Results. A uniform homogenous structure and sharp demargination of the grade II tumours and the wide rim of the intermedial FA in all grade III tumours respectively, were found during the evaluation of the FA maps. In grade IV tumours a variable demargination was noted on the FA maps. The sensitivity and specificity for the discrimination of low and high grade glial tumours using FA maps was revealed to be 81% and 87% respectively. If the evaluation of the contrast enhancement was combined with the evaluation of the FA maps, both sensitivity and specificity were 100%. Conclusion. Although the evaluation of the fractional anisotropy maps is not sufficient for glioma grading, the combination of the contrast enhancement pattern and fractional anisotropy maps evaluation improves the possibility of distinguishing low and high grade glial tumours. Three-dimensional models of the white matter fibres in the corpus callosum and the internal capsule may be used in the presurgical planning.
- MeSH
- Anisotropy MeSH
- Astrocytoma diagnosis MeSH
- Diffusion Magnetic Resonance Imaging methods utilization MeSH
- Humans MeSH
- Magnetic Resonance Imaging methods utilization MeSH
- Brain Neoplasms diagnosis pathology MeSH
- Image Processing, Computer-Assisted methods utilization MeSH
- Sensitivity and Specificity MeSH
- Neoplasm Staging methods utilization MeSH
- Imaging, Three-Dimensional methods utilization MeSH
- Check Tag
- Humans MeSH
