Individual prediction of cognitive decline in mild cognitive impairment using support vector machine-based analysis of diffusion tensor imaging data.

Although cross-sectional diffusion tensor imaging (DTI) studies revealed significant white matter changes in mild cognitive impairment (MCI), the utility of this technique in predicting further cognitive decline is debated. Thirty-five healthy controls (HC) and 67 MCI subjects with DTI baseline data were neuropsychologically assessed at one year. Among them, there were 40 stable (sMCI; 9 single domain amnestic, 7 single domain frontal, 24 multiple domain) and 27 were progressive (pMCI; 7 single domain amnestic, 4 single domain frontal, 16 multiple domain). Fractional anisotropy (FA) and longitudinal, radial, and mean diffusivity were measured using Tract-Based Spatial Statistics. Statistics included group comparisons and individual classification of MCI cases using support vector machines (SVM). FA was significantly higher in HC compared to MCI in a distributed network including the ventral part of the corpus callosum, right temporal and frontal pathways. There were no significant group-level differences between sMCI versus pMCI or between MCI subtypes after correction for multiple comparisons. However, SVM analysis allowed for an individual classification with accuracies up to 91.4% (HC versus MCI) and 98.4% (sMCI versus pMCI). When considering the MCI subgroups separately, the minimum SVM classification accuracy for stable versus progressive cognitive decline was 97.5% in the multiple domain MCI group. SVM analysis of DTI data provided highly accurate individual classification of stable versus progressive MCI regardless of MCI subtype, indicating that this method may become an easily applicable tool for early individual detection of MCI subjects evolving to dementia.

High b-value Diffusion-weighted Imaging: A Sensitive Method to Reveal White Matter Changes in Schizophrenia

Background: b-value is the parameter characterizing the intensity of the diffusion weighting during image acquisition. Data acquisition is usually performed with low b value (b~1000 s/mm2). Evidence shows that high b-values (b>2000 s/mm2) are more sensitive to the slow diffusion compartment (SDC) and maybe more sensitive in detecting white matter (WM) anomalies in schizophrenia.Methods: 12 male patients with schizophrenia (mean age 35 +/-3 years) and 16 healthy male controls matched for age were scanned with a low b-value (1000 s/mm2) and a high b-value (4000 s/mm2) protocol. Apparent diffusion coefficient (ADC) is a measure of the average diffusion distance of water molecules per time unit (mm2/s). ADC maps were generated for all individuals. 8 region of interests (frontal and parietal region bilaterally, centrum semi-ovale bilaterally and anterior and posterior corpus callosum) were manually traced blind to diagnosis.Results: ADC measures acquired with high b-value imaging were more sensitive in detecting differences between schizophrenia patients and healthy controls than low b-value imaging with a gain in significance by a factor of 20- 100 times despite the lower image Signal-to-noise ratio (SNR). Increased ADC was identified in patient's WM (p=0.00015) with major contributions from left and right centrum semi-ovale and to a lesser extent right parietal region.Conclusions: Our results may be related to the sensitivity of high b-value imaging to the SDC believed to reflect mainly the intra-axonal and myelin bound water pool. High b-value imaging might be more sensitive and specific to WM anomalies in schizophrenia than low b-value imaging

Prospective and retrospective motion correction in diffusion magnetic resonance imaging of the human brain.

Diffusion-weighting in magnetic resonance imaging (MRI) increases the sensitivity to molecular Brownian motion, providing insight in the micro-environment of the underlying tissue types and structures. At the same time, the diffusion weighting renders the scans sensitive to other motion, including bulk patient motion. Typically, several image volumes are needed to extract diffusion information, inducing also inter-volume motion susceptibility. Bulk motion is more likely during long acquisitions, as they appear in diffusion tensor, diffusion spectrum and q-ball imaging. Image registration methods are successfully used to correct for bulk motion in other MRI time series, but their performance in diffusion-weighted MRI is limited since diffusion weighting introduces strong signal and contrast changes between serial image volumes. In this work, we combine the capability of free induction decay (FID) navigators, providing information on object motion, with image registration methodology to prospectively--or optionally retrospectively--correct for motion in diffusion imaging of the human brain. Eight healthy subjects were instructed to perform small-scale voluntary head motion during clinical diffusion tensor imaging acquisitions. The implemented motion detection based on FID navigator signals is processed in real-time and provided an excellent detection performance of voluntary motion patterns even at a sub-millimetre scale (sensitivity≥92%, specificity>98%). Motion detection triggered an additional image volume acquisition with b=0 s/mm2 which was subsequently co-registered to a reference volume. In the prospective correction scenario, the calculated motion-parameters were applied to perform a real-time update of the gradient coordinate system to correct for the head movement. Quantitative analysis revealed that the motion correction implementation is capable to correct head motion in diffusion-weighted MRI to a level comparable to scans without voluntary head motion. The results indicate the potential of this method to improve image quality in diffusion-weighted MRI, a concept that can also be applied when highest diffusion weightings are performed.

Diffusion tensor echo planar imaging using surface coil transceiver with a semiadiabatic RF pulse sequence at 14.1T.

Diffusion magnetic resonance studies of the brain are typically performed using volume coils. Although in human brain this leads to a near optimal filling factor, studies of rodent brain must contend with the fact that only a fraction of the head volume can be ascribed to the brain. The use of surface coil as transceiver increases Signal-to-Noise Ratio (SNR), reduces radiofrequency power requirements and opens the possibility of parallel transmit schemes, likely to allow efficient acquisition schemes, of critical importance for reducing the long scan times implicated in diffusion tensor imaging. This study demonstrates the implementation of a semiadiabatic echo planar imaging sequence (echo time=40 ms, four interleaves) at 14.1T using a quadrature surface coil as transceiver. It resulted in artifact free images with excellent SNR throughout the brain. Diffusion tensor derived parameters obtained within the rat brain were in excellent agreement with reported values.

Characterizing the connectome in schizophrenia with diffusion spectrum imaging.

Schizophrenia is a complex psychiatric disorder characterized by disabling symptoms and cognitive deficit. Recent neuroimaging findings suggest that large parts of the brain are affected by the disease, and that the capacity of functional integration between brain areas is decreased. In this study we questioned (i) which brain areas underlie the loss of network integration properties observed in the pathology, (ii) what is the topological role of the affected regions within the overall brain network and how this topological status might be altered in patients, and (iii) how white matter properties of tracts connecting affected regions may be disrupted. We acquired diffusion spectrum imaging (a technique sensitive to fiber crossing and slow diffusion compartment) data from 16 schizophrenia patients and 15 healthy controls, and investigated their weighted brain networks. The global connectivity analysis confirmed that patients present disrupted integration and segregation properties. The nodal analysis allowed identifying a distributed set of brain nodes affected in the pathology, including hubs and peripheral areas. To characterize the topological role of this affected core, we investigated the brain network shortest paths layout, and quantified the network damage after targeted attack toward the affected core. The centrality of the affected core was compromised in patients. Moreover the connectivity strength within the affected core, quantified with generalized fractional anisotropy and apparent diffusion coefficient, was altered in patients. Taken together, these findings suggest that the structural alterations and topological decentralization of the affected core might be major mechanisms underlying the schizophrenia dysconnectivity disorder. Hum Brain Mapp, 36:354-366, 2015. © 2014 Wiley Periodicals, Inc.

Estimation of a maximum Lu diffusion rate in a natural eclogite garnet

Lutetium zoning in garnet within eclogites from the Zermatt-Saas Fee zone, Western Alps, reveal sharp, exponentially decreasing central peaks. They can be used to constrain maximum Lu volume diffusion in garnets. A prograde garnet growth temperature interval of 450-600 A degrees C has been estimated based on pseudosection calculations and garnet-clinopyroxene thermometry. The maximum pre-exponential diffusion coefficient which fits the measured central peak is in the order of D-0= 5.7*10(-6) m(2)/s, taking an estimated activation energy of 270 kJ/mol based on diffusion experiments for other rare earth elements in garnet. This corresponds to a maximum diffusion rate of D (600 A degrees C) = 4.0*10(-22) m(2)/s. The diffusion estimate of Lu can be used to estimate the minimum closure temperature, T-c, for Sm-Nd and Lu-Hf age data that have been obtained in eclogites of the Western Alps, postulating, based on a literature review, that D (Hf) < D (Nd) < D (Sm) a parts per thousand currency sign D (Lu). T-c calculations, using the Dodson equation, yielded minimum closure temperatures of about 630 A degrees C, assuming a rapid initial exhumation rate of 50A degrees/m.y., and an average crystal size of garnets (r = 1 mm). This suggests that Sm/Nd and Lu/Hf isochron age differences in eclogites from the Western Alps, where peak temperatures did rarely exceed 600 A degrees C must be interpreted in terms of prograde metamorphism.

Understanding diffusion MR imaging techniques: from scalar diffusion-weighted imaging to diffusion tensor imaging and beyond.

The complex structural organization of the white matter of the brain can be depicted in vivo in great detail with advanced diffusion magnetic resonance (MR) imaging schemes. Diffusion MR imaging techniques are increasingly varied, from the simplest and most commonly used technique-the mapping of apparent diffusion coefficient values-to the more complex, such as diffusion tensor imaging, q-ball imaging, diffusion spectrum imaging, and tractography. The type of structural information obtained differs according to the technique used. To fully understand how diffusion MR imaging works, it is helpful to be familiar with the physical principles of water diffusion in the brain and the conceptual basis of each imaging technique. Knowledge of the technique-specific requirements with regard to hardware and acquisition time, as well as the advantages, limitations, and potential interpretation pitfalls of each technique, is especially useful.

Diffusion of influenza during the winter of 1889-90 in Switzerland

The influenza of the winter of 1889-90 was one of the first epidemics to spread all over the world. At the time, several people hypothesized that the railway was one of the main vectors of diffusion of this influenza. This hypothesis was defended in Switzerland especially by Schmid, Chief of the Swiss Office of Health, who collected an impressive body of material about the spread of the epidemic in that country. These data on influenza combined with data about the structure of the railway are used in this paper in order to test the hypothesis of a mixed diffusion process, first between communes interconnected by the railway, and secondly, between those communes and neighbouring communes. An event history analysis model taking into account diffusion effects is proposed and estimated. Results show that the hypothesis is supported if the railway network in Switzerland is not taken as a whole but if a distinction between railway companies is made.

Long-term monitoring of post-stroke plasticity after transient cerebral ischemia in mice using in vivo and ex vivo diffusion tensor MRI.

WE USED A MURINE MODEL OF TRANSIENT FOCAL CEREBRAL ISCHEMIA TO STUDY: 1) in vivo DTI long-term temporal evolution of the apparent diffusion coefficient (ADC) and diffusion fractional anisotropy (FA) at days 4, 10, 15 and 21 after stroke 2) ex vivo distribution of a plasticity-related protein (GAP-43) and its relationship with the ex vivo DTI characteristics of the striato-thalamic pathway (21 days). All animals recovered motor function. In vivo ADC within the infarct was significantly increased after stroke. In the stroke group, GAP-43 expression and FA values were significantly higher in the ipsilateral (IL) striatum and contralateral (CL) hippocampus compared to the shams. DTI tractography showed fiber trajectories connecting the CL striatum to the stroke region, where increased GAP43 and FA were observed and fiber tracts from the CL striatum terminating in the IL hippocampus.Our data demonstrate that DTI changes parallel histological remodeling and recovery of function.

Comparison of central macular thickness (CMT) measurement between time domain and spectral domain (SD) optical coherence tomography (OCT) and reproducibility of SD OCT in active neovascular AMD

Purpose: To evaluate the reproducibility of Cirrus-SD OCT measurements and to compare central macular thickness (CMT) measurements between TD-Stratus and SD-Cirrus OCT in patients with active exudative AMD. Methods: Consecutive case series of patients with active exudative AMD seen in the Medical Retina Department. Patients underwent 1 scan with Stratus (macular thickness map protocol) and 5 scans with Cirrus (Macular Cube protocol) at the same visit by the same experienced examiner. To be included, patients best-corrected visual acuity (BCVA) had to be >20/200 while all scans had to be of sufficient quality, well-centered and at least one Cirrus scan with CMT >300 microns. The repeatability of the SD Cirrus was estimated by using all 5 CMT measurements and the mean of the Cirrus measurements was compared with the CMT obtained by TD Stratus. Results: Cirrus OCT demonstrated high intraobserver repeatability at the central foveal region (ICC 96%). The mean of the CMT measurements was 321microns for Stratus and 387 microns for Cirrus. The average difference was 65m (SD=30). The coefficient of concordance between Stratus and Cirrus CMT measurements was rho=0,749 with a high precision and a moderate accuracy. The equation of the line of regression between Stratus and meanCirrus is given by the following: M_stratus = 0,848 x m_cirrus - 4,496 (1).Conclusions: The Cirrus macular cube protocol allows reproducible CMT measurements in patients with active exudative AMD. In cases of upgrading from TD to SD use and vice versa, there is the possibility to predict the measurements by using the equation (1). These real life data and conclusions can help in improving our clinical management of patients with neovascular AMD.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Artificial evolution on network structures : how time and space influence dynamics

Abstract The main objective of this work is to show how the choice of the temporal dimension and of the spatial structure of the population influences an artificial evolutionary process. In the field of Artificial Evolution we can observe a common trend in synchronously evolv¬ing panmictic populations, i.e., populations in which any individual can be recombined with any other individual. Already in the '90s, the works of Spiessens and Manderick, Sarma and De Jong, and Gorges-Schleuter have pointed out that, if a population is struc¬tured according to a mono- or bi-dimensional regular lattice, the evolutionary process shows a different dynamic with respect to the panmictic case. In particular, Sarma and De Jong have studied the selection pressure (i.e., the diffusion of a best individual when the only selection operator is active) induced by a regular bi-dimensional structure of the population, proposing a logistic modeling of the selection pressure curves. This model supposes that the diffusion of a best individual in a population follows an exponential law. We show that such a model is inadequate to describe the process, since the growth speed must be quadratic or sub-quadratic in the case of a bi-dimensional regular lattice. New linear and sub-quadratic models are proposed for modeling the selection pressure curves in, respectively, mono- and bi-dimensional regu¬lar structures. These models are extended to describe the process when asynchronous evolutions are employed. Different dynamics of the populations imply different search strategies of the resulting algorithm, when the evolutionary process is used to solve optimisation problems. A benchmark of both discrete and continuous test problems is used to study the search characteristics of the different topologies and updates of the populations. In the last decade, the pioneering studies of Watts and Strogatz have shown that most real networks, both in the biological and sociological worlds as well as in man-made structures, have mathematical properties that set them apart from regular and random structures. In particular, they introduced the concepts of small-world graphs, and they showed that this new family of structures has interesting computing capabilities. Populations structured according to these new topologies are proposed, and their evolutionary dynamics are studied and modeled. We also propose asynchronous evolutions for these structures, and the resulting evolutionary behaviors are investigated. Many man-made networks have grown, and are still growing incrementally, and explanations have been proposed for their actual shape, such as Albert and Barabasi's preferential attachment growth rule. However, many actual networks seem to have undergone some kind of Darwinian variation and selection. Thus, how these networks might have come to be selected is an interesting yet unanswered question. In the last part of this work, we show how a simple evolutionary algorithm can enable the emrgence o these kinds of structures for two prototypical problems of the automata networks world, the majority classification and the synchronisation problems. Synopsis L'objectif principal de ce travail est de montrer l'influence du choix de la dimension temporelle et de la structure spatiale d'une population sur un processus évolutionnaire artificiel. Dans le domaine de l'Evolution Artificielle on peut observer une tendence à évoluer d'une façon synchrone des populations panmictiques, où chaque individu peut être récombiné avec tout autre individu dans la population. Déjà dans les année '90, Spiessens et Manderick, Sarma et De Jong, et Gorges-Schleuter ont observé que, si une population possède une structure régulière mono- ou bi-dimensionnelle, le processus évolutionnaire montre une dynamique différente de celle d'une population panmictique. En particulier, Sarma et De Jong ont étudié la pression de sélection (c-à-d la diffusion d'un individu optimal quand seul l'opérateur de sélection est actif) induite par une structure régulière bi-dimensionnelle de la population, proposant une modélisation logistique des courbes de pression de sélection. Ce modèle suppose que la diffusion d'un individu optimal suit une loi exponentielle. On montre que ce modèle est inadéquat pour décrire ce phénomène, étant donné que la vitesse de croissance doit obéir à une loi quadratique ou sous-quadratique dans le cas d'une structure régulière bi-dimensionnelle. De nouveaux modèles linéaires et sous-quadratique sont proposés pour des structures mono- et bi-dimensionnelles. Ces modèles sont étendus pour décrire des processus évolutionnaires asynchrones. Différentes dynamiques de la population impliquent strategies différentes de recherche de l'algorithme résultant lorsque le processus évolutionnaire est utilisé pour résoudre des problèmes d'optimisation. Un ensemble de problèmes discrets et continus est utilisé pour étudier les charactéristiques de recherche des différentes topologies et mises à jour des populations. Ces dernières années, les études de Watts et Strogatz ont montré que beaucoup de réseaux, aussi bien dans les mondes biologiques et sociologiques que dans les structures produites par l'homme, ont des propriétés mathématiques qui les séparent à la fois des structures régulières et des structures aléatoires. En particulier, ils ont introduit la notion de graphe sm,all-world et ont montré que cette nouvelle famille de structures possède des intéressantes propriétés dynamiques. Des populations ayant ces nouvelles topologies sont proposés, et leurs dynamiques évolutionnaires sont étudiées et modélisées. Pour des populations ayant ces structures, des méthodes d'évolution asynchrone sont proposées, et la dynamique résultante est étudiée. Beaucoup de réseaux produits par l'homme se sont formés d'une façon incrémentale, et des explications pour leur forme actuelle ont été proposées, comme le preferential attachment de Albert et Barabàsi. Toutefois, beaucoup de réseaux existants doivent être le produit d'un processus de variation et sélection darwiniennes. Ainsi, la façon dont ces structures ont pu être sélectionnées est une question intéressante restée sans réponse. Dans la dernière partie de ce travail, on montre comment un simple processus évolutif artificiel permet à ce type de topologies d'émerger dans le cas de deux problèmes prototypiques des réseaux d'automates, les tâches de densité et de synchronisation.

Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.

Quantifying the time for accurate EEG decoding of single value-based decisions.

BACKGROUND: Recent neuroimaging studies suggest that value-based decision-making may rely on mechanisms of evidence accumulation. However no studies have explicitly investigated the time when single decisions are taken based on such an accumulation process. NEW METHOD: Here, we outline a novel electroencephalography (EEG) decoding technique which is based on accumulating the probability of appearance of prototypical voltage topographies and can be used for predicting subjects' decisions. We use this approach for studying the time-course of single decisions, during a task where subjects were asked to compare reward vs. loss points for accepting or rejecting offers. RESULTS: We show that based on this new method, we can accurately decode decisions for the majority of the subjects. The typical time-period for accurate decoding was modulated by task difficulty on a trial-by-trial basis. Typical latencies of when decisions are made were detected at ∼500ms for 'easy' vs. ∼700ms for 'hard' decisions, well before subjects' response (∼340ms). Importantly, this decision time correlated with the drift rates of a diffusion model, evaluated independently at the behavioral level. COMPARISON WITH EXISTING METHOD(S): We compare the performance of our algorithm with logistic regression and support vector machine and show that we obtain significant results for a higher number of subjects than with these two approaches. We also carry out analyses at the average event-related potential level, for comparison with previous studies on decision-making. CONCLUSIONS: We present a novel approach for studying the timing of value-based decision-making, by accumulating patterns of topographic EEG activity at single-trial level.

Quantitative Analysis of Myelin and Axonal Remodeling in the Uninjured Motor Network After Stroke.

Contralesional brain connectivity plasticity was previously reported after stroke. This study aims at disentangling the biological mechanisms underlying connectivity plasticity in the uninjured motor network after an ischemic lesion. In particular, we measured generalized fractional anisotropy (GFA) and magnetization transfer ratio (MTR) to assess whether poststroke connectivity remodeling depends on axonal and/or myelin changes. Diffusion-spectrum imaging and magnetization transfer MRI at 3T were performed in 10 patients in acute phase, at 1 and 6 months after stroke, which was affecting motor cortical and/or subcortical areas. Ten age- and gender-matched healthy volunteers were scanned 1 month apart for longitudinal comparison. Clinical assessment was also performed in patients prior to magnetic resonance imaging (MRI). In the contralesional hemisphere, average measures and tract-based quantitative analysis of GFA and MTR were performed to assess axonal integrity and myelination along motor connections as well as their variations in time. Mean and tract-based measures of MTR and GFA showed significant changes in a number of contralesional motor connections, confirming both axonal and myelin plasticity in our cohort of patients. Moreover, density-derived features (peak height, standard deviation, and skewness) of GFA and MTR along the tracts showed additional correlation with clinical scores than mean values. These findings reveal the interplay between contralateral myelin and axonal remodeling after stroke.