Rotational diffusion membrane and fluorescence anisotropy.

Structural properties of model membranes, such as lipid vesicles, may be investigated through the addition of fluorescent probes. After incorporation, the fluorescent molecules are excited with linearly polarized light and the fluorescence emission is depolarized due to translational as well as rotational diffusion during the lifetime of the excited state. The monitoring of emitted light is undertaken through the technique of time-resolved fluorescence: the intensity of the emitted light informs on fluorescence decay times, and the decay of the components of the emitted light yield rotational correlation times which inform on the fluidity of the medium. The fluorescent molecule DPH, of uniaxial symmetry, is rather hydrophobic and has collinear transition and emission moments. It has been used frequently as a probe for the monitoring of the fluidity of the lipid bilayer along the phase transition of the chains. The interpretation of experimental data requires models for localization of fluorescent molecules as well as for possible restrictions on their movement. In this study, we develop calculations for two models for uniaxial diffusion of fluorescent molecules, such as DPH, suggested in several articles in the literature. A zeroth order test model consists of a free randomly rotating dipole in a homogeneous solution, and serves as the basis for the study of the diffusion of models in anisotropic media. In the second model, we consider random rotations of emitting dipoles distributed within cones with their axes perpendicular to the vesicle spherical geometry. In the third model, the dipole rotates in the plane of the of bilayer spherical geometry, within a movement that might occur between the monolayers forming the bilayer. For each of the models analysed, two methods are used by us in order to analyse the rotational diffusion: (I) solution of the corresponding rotational diffusion equation for a single molecule, taking into account the boundary conditions imposed by the models, for the probability of the fluorescent molecule to be found with a given configuration at time t. Considering the distribution of molecules in the geometry proposed, we obtain the analytical expression for the fluorescence anisotropy, except for the cone geometry, for which the solution is obtained numerically; (II) numerical simulations of a restricted rotational random walk in the two geometries corresponding to the two models. The latter method may be very useful in the cases of low-symmetry geometries or of composed geometries.

Numerical simulation of an ethanol turbulent spray flame with RANS and diffusion combustion model

A detailed numerical simulation of ethanol turbulent spray combustion on a rounded jet flame is pre- sented in this article. The focus is to propose a robust mathematical model with relatively low complexity sub- models to reproduce the main characteristics of the cou- pling between both phases, such as the turbulence modulation, turbulent droplets dissipation, and evaporative cooling effect. A RANS turbulent model is implemented. Special features of the model include an Eulerian– Lagrangian procedure under a fully two-way coupling and a modified flame sheet model with a joint mixture fraction– enthalpy b -PDF. Reasonable agreement between measured and computed mean profiles of temperature of the gas phase and droplet size distributions is achieved. Deviations found between measured and predicted mean velocity profiles are attributed to the turbulent combustion modeling adopted

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Retrieval of trace gases vertical profile in the lower atmosphere combining. Differential Optical Absorption Spectroscopy with radiative transfer models

The motivation for the work presented in this thesis is to retrieve profile information for the atmospheric trace constituents nitrogen dioxide (NO2) and ozone (O3) in the lower troposphere from remote sensing measurements. The remote sensing technique used, referred to as Multiple AXis Differential Optical Absorption Spectroscopy (MAX-DOAS), is a recent technique that represents a significant advance on the well-established DOAS, especially for what it concerns the study of tropospheric trace consituents. NO2 is an important trace gas in the lower troposphere due to the fact that it is involved in the production of tropospheric ozone; ozone and nitrogen dioxide are key factors in determining the quality of air with consequences, for example, on human health and the growth of vegetation. To understand the NO2 and ozone chemistry in more detail not only the concentrations at ground but also the acquisition of the vertical distribution is necessary. In fact, the budget of nitrogen oxides and ozone in the atmosphere is determined both by local emissions and non-local chemical and dynamical processes (i.e. diffusion and transport at various scales) that greatly impact on their vertical and temporal distribution: thus a tool to resolve the vertical profile information is really important. Useful measurement techniques for atmospheric trace species should fulfill at least two main requirements. First, they must be sufficiently sensitive to detect the species under consideration at their ambient concentration levels. Second, they must be specific, which means that the results of the measurement of a particular species must be neither positively nor negatively influenced by any other trace species simultaneously present in the probed volume of air. Air monitoring by spectroscopic techniques has proven to be a very useful tool to fulfill these desirable requirements as well as a number of other important properties. During the last decades, many such instruments have been developed which are based on the absorption properties of the constituents in various regions of the electromagnetic spectrum, ranging from the far infrared to the ultraviolet. Among them, Differential Optical Absorption Spectroscopy (DOAS) has played an important role. DOAS is an established remote sensing technique for atmospheric trace gases probing, which identifies and quantifies the trace gases in the atmosphere taking advantage of their molecular absorption structures in the near UV and visible wavelengths of the electromagnetic spectrum (from 0.25 μm to 0.75 μm). Passive DOAS, in particular, can detect the presence of a trace gas in terms of its integrated concentration over the atmospheric path from the sun to the receiver (the so called slant column density). The receiver can be located at ground, as well as on board an aircraft or a satellite platform. Passive DOAS has, therefore, a flexible measurement configuration that allows multiple applications. The ability to properly interpret passive DOAS measurements of atmospheric constituents depends crucially on how well the optical path of light collected by the system is understood. This is because the final product of DOAS is the concentration of a particular species integrated along the path that radiation covers in the atmosphere. This path is not known a priori and can only be evaluated by Radiative Transfer Models (RTMs). These models are used to calculate the so called vertical column density of a given trace gas, which is obtained by dividing the measured slant column density to the so called air mass factor, which is used to quantify the enhancement of the light path length within the absorber layers. In the case of the standard DOAS set-up, in which radiation is collected along the vertical direction (zenith-sky DOAS), calculations of the air mass factor have been made using “simple” single scattering radiative transfer models. This configuration has its highest sensitivity in the stratosphere, in particular during twilight. This is the result of the large enhancement in stratospheric light path at dawn and dusk combined with a relatively short tropospheric path. In order to increase the sensitivity of the instrument towards tropospheric signals, measurements with the telescope pointing the horizon (offaxis DOAS) have to be performed. In this circumstances, the light path in the lower layers can become very long and necessitate the use of radiative transfer models including multiple scattering, the full treatment of atmospheric sphericity and refraction. In this thesis, a recent development in the well-established DOAS technique is described, referred to as Multiple AXis Differential Optical Absorption Spectroscopy (MAX-DOAS). The MAX-DOAS consists in the simultaneous use of several off-axis directions near the horizon: using this configuration, not only the sensitivity to tropospheric trace gases is greatly improved, but vertical profile information can also be retrieved by combining the simultaneous off-axis measurements with sophisticated RTM calculations and inversion techniques. In particular there is a need for a RTM which is capable of dealing with all the processes intervening along the light path, supporting all DOAS geometries used, and treating multiple scattering events with varying phase functions involved. To achieve these multiple goals a statistical approach based on the Monte Carlo technique should be used. A Monte Carlo RTM generates an ensemble of random photon paths between the light source and the detector, and uses these paths to reconstruct a remote sensing measurement. Within the present study, the Monte Carlo radiative transfer model PROMSAR (PROcessing of Multi-Scattered Atmospheric Radiation) has been developed and used to correctly interpret the slant column densities obtained from MAX-DOAS measurements. In order to derive the vertical concentration profile of a trace gas from its slant column measurement, the AMF is only one part in the quantitative retrieval process. One indispensable requirement is a robust approach to invert the measurements and obtain the unknown concentrations, the air mass factors being known. For this purpose, in the present thesis, we have used the Chahine relaxation method. Ground-based Multiple AXis DOAS, combined with appropriate radiative transfer models and inversion techniques, is a promising tool for atmospheric studies in the lower troposphere and boundary layer, including the retrieval of profile information with a good degree of vertical resolution. This thesis has presented an application of this powerful comprehensive tool for the study of a preserved natural Mediterranean area (the Castel Porziano Estate, located 20 km South-West of Rome) where pollution is transported from remote sources. Application of this tool in densely populated or industrial areas is beginning to look particularly fruitful and represents an important subject for future studies.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

A MICROFLUIDIC METHOD TO MEASURE DIFFUSION IN HYDROGELS

A novel microfluidic method is proposed for studying diffusion of small molecules in a hydrogel. Microfluidic devices were prepared with semi-permeable microchannels defined by crosslinked poly(ethylene glycol) (PEG). Uptake of dye molecules from aqueous solutions flowing through the microchannels was observedoptically and diffusion of the dye into the hydrogel was quantified. To complement the diffusion measurements from the microfluidic studies, nuclear magnetic resonance(NMR) characterization of the diffusion of dye in the PEG hydrogels was performed. The diffusion of small molecules in a hydrogel is relevant to applications such asdrug delivery and modeling transport for tissue-engineering applications. The diffusion of small molecules in a hydrogel is dependent on the extent of crosslinking within the gel, gel structure, and interactions between the diffusive species and the hydrogel network. These effects were studied in a model environment (semi-infinite slab) at the hydrogelfluid boundary in a microfluidic device. The microfluidic devices containing PEG microchannels were fabricated using photolithography. The unsteady diffusion of small molecules (dyes) within the microfluidic device was monitored and recorded using a digital microscope. The information was analyzed with techniques drawn from digital microscopy and image analysis to obtain concentration profiles with time. Using a diffusion model to fit this concentration vs. position data, a diffusion coefficient was obtained. This diffusion coefficient was compared to those from complementary NMR analysis. A pulsed field gradient (PFG) method was used to investigate and quantify small molecule diffusion in gradient (PFG) method was used to investigate and quantify small molecule diffusion in hydrogels. There is good agreement between the diffusion coefficients obtained from the microfluidic methods and those found from the NMR studies. The microfluidic approachused in this research enables the study of diffusion at length scales that approach those of vasculature, facilitating models for studying drug elution from hydrogels in blood-contacting applications.

Diffusion-driven transport in clayrock formations

Clay mineral-rich sedimentary formations are currently under investigation to evaluate their potential use as host formations for installation of deep underground disposal facilities for radioactive waste (e.g. Boom Clay (BE), Opalinus Clay (CH), Callovo-Oxfordian argillite (FR)). The ultimate safety of the corresponding repository concepts depends largely on the capacity of the host formation to limit the flux towards the biosphere of radionuclides (RN) contained in the waste to acceptably low levels. Data for diffusion-driven transfer in these formations shows extreme differences in the measured or modelled behaviour for various radionuclides, e. g. between halogen RN (Cl-36, I-129) and actinides (U-238,U-235, Np-237, Th-232, etc.), which result from major differences between RN of the effects on transport of two phenomena: diffusion and sorption. This paper describes recent research aimed at improving understanding of these two phenomena, focusing on the results of studies carried out during the EC Funmig IP on clayrocks from the above three formations and from the Boda formation (HU). Project results regarding phenomena governing water, cation and anion distribution and mobility in the pore volumes influenced by the negatively-charged surfaces of clay minerals show a convergence of the modelling results for behaviour at the molecular scale and descriptions based on electrical double layer models. Transport models exist which couple ion distribution relative to the clay-solution interface and differentiated diffusive characteristics. These codes are able to reproduce the main trends in behaviour observed experimentally, e.g. D-e(anion) < D-e(HTO) < D-e(cation) and D-e(anion) variations as a function of ionic strength and material density. These trends are also well-explained by models of transport through ideal porous matrices made up of a charged surface material. Experimental validation of these models is good as regards monovalent alkaline cations, in progress for divalent electrostatically-interacting cations (e.g. Sr2+) and still relatively poor for 'strongly sorbing', high K-d cations. Funmig results have clarified understanding of how clayrock mineral composition, and the corresponding organisation of mineral grain assemblages and their associated porosity, can affect mobile solute (anions, HTO) diffusion at different scales (mm to geological formation). In particular, advances made in the capacity to map clayrock mineral grain-porosity organisation at high resolution provide additional elements for understanding diffusion anisotropy and for relating diffusion characteristics measured at different scales. On the other hand, the results of studies focusing on evaluating the potential effects of heterogeneity on mobile species diffusion at the formation scale tend to show that there is a minimal effect when compared to a homogeneous property model. Finally, the results of a natural tracer-based study carried out on the Opalinus Clay formation increase confidence in the use of diffusion parameters measured on laboratory scale samples for predicting diffusion over geological time-space scales. Much effort was placed on improving understanding of coupled sorption-diffusion phenomena for sorbing cations in clayrocks. Results regarding sorption equilibrium in dispersed and compacted materials for weakly to moderately sorbing cations (Sr2+, Cs+, Co2+) tend to show that the same sorption model probably holds in both systems. It was not possible to demonstrate this for highly sorbing elements such as Eu(III) because of the extremely long times needed to reach equilibrium conditions, but there does not seem to be any clear reason why such elements should not have similar behaviour. Diffusion experiments carried out with Sr2+, Cs+ and Eu(III) on all of the clayrocks gave mixed results and tend to show that coupled diffusion-sorption migration is much more complex than expected, leading generally to greater mobility than that predicted by coupling a batch-determined K-d and Ficks law based on the diffusion behaviour of HTO. If the K-d measured on equivalent dispersed systems holds as was shown to be the case for Sr, Cs (and probably Co) for Opalinus Clay, these results indicate that these cations have a D-e value higher than HTO (up to a factor of 10 for Cs+). Results are as yet very limited for very moderate to strongly sorbing species (e.g. Co(II), Eu(III), Cu(II)) because of their very slow transfer characteristics. (C) 2011 Elsevier Ltd. All rights reserved.

Ar diffusion in K-feldspar: present and absent

The mechanisms of Ar release from K-feldspar samples in laboratory experiments and during their geological history are assessed here. Modern petrology clearly established that the chemical and isotopic record of minerals is normally dominated by aqueous recrystallization. The laboratory critique is trickier, which explains why so many conflicting approaches have been able to survive long past their expiration date. Current models are evaluated for self-consistency; especially Arrhenian non-linearity leads to paradoxes. The models’ testable geological predictions suggest that temperature-based downslope extrapolations often overestimate observed geological Ar mobility substantially. An updated interpretation is based on the unrelatedness of geological behaviour to laboratory experiments. The isotopic record of K-feldspar in geological samples is not a unique function of temperature, as recrystallisation promoted by aqueous fluids is the predominant mechanism controlling isotope transport. K-feldspar should therefore be viewed as a hygrochronometer. Laboratory degassing proceeds from structural rearrangements and phase transitions such as are observed in situ at high temperature in Na and Pb feldspars. These effects violate the mathematics of an inert Fick’s Law matrix and preclude downslope extrapolation. The similar upward-concave, non-linear shapes of Arrhenius trajectories of many silicates, hydrous and anhydrous, are likely common manifestations of structural rearrangements in silicate structures.

Brain fiber tract plasticity in experimental spinal cord injury: diffusion tensor imaging.

Diffusion tensor imaging (DTI) and immunohistochemistry were performed in spinal cord injured rats to understand the basis for activation of multiple regions in the brain observed in functional magnetic resonance imaging (fMRI) studies. The measured fractional anisotropy (FA), a scalar measure of diffusion anisotropy, along the region encompassing corticospinal tracts (CST) indicates significant differences between control and injured groups in the 3 to 4 mm area posterior to bregma that correspond to internal capsule and cerebral peduncle. Additionally, DTI-based tractography in injured animals showed increased number of fibers that extend towards the cortex terminating in the regions that were activated in fMRI. Both the internal capsule and cerebral peduncle demonstrated an increase in GFAP-immunoreactivity compared to control animals. GAP-43 expression also indicates plasticity in the internal capsule. These studies suggest that the previously observed multiple regions of activation in spinal cord injury are, at least in part, due to the formation of new fibers.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Quantitative diffusion tensor imaging detects dopaminergic neuronal degeneration in a murine model of Parkinson's disease.

Early diagnosis of Parkinson's disease (PD) is required to improve therapeutic responses. Indeed, a clinical diagnosis of resting tremor, rigidity, movement and postural deficiencies usually reflect >50% loss of the nigrostriatal system in disease. In a step to address this, quantitative diffusion tensor magnetic resonance imaging (DTI) was used to assess nigrostriatal degeneration in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) intoxication model of dopaminergic nigral degeneration. We now demonstrate increased average diffusion (p<0.005) and decreased fractional anisotropy (p<0.03) in the substantia nigra (SN) of 5- to 7-day MPTP-treated animals when compared to saline controls. Transverse diffusivity demonstrated the most significant differences (p < or = 0.002) and correlated with the numbers of SN dopaminergic neurons (r=-0.75, p=0.012). No differences were found in the striatum, corpus callosum, cerebral cortex, or ventricles. These results demonstrate that DTI may be used as a surrogate biomarker of nigral dopaminergic neuronal degeneration.

Diffusion tensor imaging of rat spinal cord in vivo

Magnetic resonance imaging, with its exquisite soft tissue contrast, is an ideal modality for investigating spinal cord pathology. While conventional MRI techniques are very sensitive for spinal cord pathology, their specificity is somewhat limited. Diffusion MRI is an advanced technique which is a very sensitive and specific indicator of the integrity of white matter tracts. Diffusion imaging has been shown to detect early ischemic changes in white matter, while conventional imaging demonstrates no change. By acquiring the complete apparent diffusion tensor (ADT), tissue diffusion properties can be expressed in terms of quantitative and rotationally invariant parameters. ^ Systematic study of SCI in vivo requires controlled animal models such as the popular rat model. To date, studies of spinal cord using ADT imaging have been performed exclusively in fixed, excised spinal cords, introducing inevitable artifacts and losing the benefits of MRI's noninvasive nature. In vivo imaging reflects the actual in vivo tissue properties, and allows each animal to be imaged at multiple time points, greatly reducing the number of animals required to achieve statistical significance. Because the spinal cord is very small, the available signal-to-noise ratio (SNR) is very low. Prior spin-echo based ADT studies of rat spinal cord have relied on high magnetic field strengths and long imaging times—on the order of 10 hours—for adequate SNR. Such long imaging times are incompatible with in vivo imaging, and are not relevant for imaging the early phases following SCI. Echo planar imaging (EPI) is one of the fastest imaging methods, and is popular for diffusion imaging. However, EPI further lowers the image SNR, and is very sensitive to small imperfections in the magnetic field, such as those introduced by the bony spine. Additionally, The small field-of-view (FOV) needed for spinal cord imaging requires large imaging gradients which generate EPI artifacts. The addition of diffusion gradients introduces yet further artifacts. ^ This work develops a method for rapid EPI-based in vivo diffusion imaging of rat spinal cord. The method involves improving the SNR using an implantable coil; reducing magnetic field inhomogeneities by means of an autoshim, and correcting EPI artifacts by post-processing. New EPI artifacts due to diffusion gradients described, and post-processing correction techniques are developed. ^ These techniques were used to obtain rotationally invariant diffusion parameters from 9 animals in vivo, and were validated using the gold-standard, but slow, spinecho based diffusion sequence. These are the first reported measurements of the ADT in spinal cord in vivo . ^ Many of the techniques described are equally applicable toward imaging of human spinal cord. We anticipate that these techniques will aid in evaluating and optimizing potential therapies, and will lead to improved patient care. ^