Re-entry in models of cardiac ventricular tissue with scar represented as a Gaussian random field.

Introduction: Fibrotic scar in the heart is known to act as a substrate for arrhythmias. Regions of fibrotic scar are associated with slowed or blocked conduction of the action potential, but the detailed mechanisms of arrhythmia formation are not well characterised and this can limit the effective diagnosis and treatment of scar in patients. The aim of this computational study was to evaluate different representations of fibrotic scar in models of 2D 10 × 10 cm ventricular tissue, where the region of scar was defined by sampling a Gaussian random field with an adjustable length scale of between 1.25 and 10.0 mm. Methods: Cellular electrophysiology was represented by the Ten Tusscher 2006 model for human ventricular cells. Fibrotic scar was represented as a spatially varying diffusion, with different models of the boundary between normal and fibrotic tissue. Dispersion of activation time and action potential duration (APD) dispersion was assessed in each sample by pacing at an S1 cycle length of 400 ms followed by a premature S2 beat with a coupling interval of 323 ms. Vulnerability to reentry was assessed with an aggressive pacing protocol. In all models, simulated fibrosis acted to delay activation, to increase the dispersion of APD, and to generate re-entry. Results: A higher incidence of re-entry was observed in models with simulated fibrotic scar at shorter length scale, but the type of model used to represent fibrotic scar had a much bigger influence on the incidence of reentry. Discussion: This study shows that in computational models of fibrotic scar the effects that lead to either block or propagation of the action potential are strongly influenced by the way that fibrotic scar is represented in the model, and so the results of computational studies involving fibrotic scar should be interpreted carefully.

Gaussian random field-based characterization and reconstruction of cancellous bone microstructure considering the constraint of correlation structure.

The macro scale physical properties of cancellous bone materials are governed by the microstructural features, which is of great significance for the multi-scale research of cancellous bone and the inverse design of bone-mimicking materials. Therefore, it is essential to characterize the natural cancellous bone samples, and reconstruct the microstructures with the biomimetic osteointegration and mechanical properties. In this research, a novel approach for the characterization and reconstruction of cancellous bone was proposed, based on the medical image analysis and anisotropic three-dimensional Gaussian random field (GRF). The geometric similarity, i.e. the interface curvature distribution (ISD), was meticulously studied, which is important to the osteointegration ability. And the mechanical properties were validated by the stress-strain curves under the large compressive strain simulated by the smoothed particle hydrodynamic (SPH) method. In addition, the effects of the generation parameters of GRF-based biomimetic microstructures on the apparent properties were analyzed. The ISD results demonstrated that both GRF and micro-CT groups had the similar columnar morphological properties, while the latter had more hyperbolic features. And it was found that the GRF-based biomimetic microstructures and the natural bone samples based on micro-CT (MCT) had the similar failure mode. The concordance correlation coefficient between MCT and GRF pairs was 0.8685, with a Pearson ρ value of 0.8804, and significance level p<0.0001. The Bland-Altman LoA was 0.1647 MPa with 95 % (1.96SD) lower and upper bound value between -0.2892 and 0.6185 MPa. The two groups had almost the same elastic modulus with the mean absolute percentage error (MAPE) of 7.84 %. While the yield stress and total conversion energy of the GRF-based samples were lower than those of the natural bone samples, and the MAPE were 16.99 % and 16.27 %, respectively. Although it meant the lower structural efficiency, the huge design space of this approach and advanced 3D printing technology can provide great potential for the design of orthopedic implants.

Incorporating environmental heterogeneity and observation effort to predict host distribution and viral spillover from a bat reservoir.

Predicting the spatial occurrence of wildlife is a major challenge for ecology and management. In Latin America, limited knowledge of the number and locations of vampire bat roosts precludes informed allocation of measures intended to prevent rabies spillover to humans and livestock. We inferred the spatial distribution of vampire bat roosts while accounting for observation effort and environmental effects by fitting a log Gaussian Cox process model to the locations of 563 roosts in three regions of Peru. Our model explained 45% of the variance in the observed roost distribution and identified environmental drivers of roost establishment. When correcting for uneven observation effort, our model estimated a total of 2340 roosts, indicating that undetected roosts (76%) exceed known roosts (24%) by threefold. Predicted hotspots of undetected roosts in rabies-free areas revealed high-risk areas for future viral incursions. Using the predicted roost distribution to inform a spatial model of rabies spillover to livestock identified areas with disproportionate underreporting and indicated a higher rabies burden than previously recognized. We provide a transferrable approach to infer the distribution of a mostly unobserved bat reservoir that can inform strategies to prevent the re-emergence of an important zoonosis.

Discrimination between Gaussian process models: active learning and static constructions.

The paper covers the design and analysis of experiments to discriminate between two Gaussian process models with different covariance kernels, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered. First, we study sequential constructions, where successive design (observation) points are selected, either as additional points to an existing design or from the beginning of observation. The selection relies on the maximisation of the difference between the symmetric Kullback Leibler divergences for the two models, which depends on the observations, or on the mean squared error of both models, which does not. Then, we consider static criteria, such as the familiar log-likelihood ratios and the Fréchet distance between the covariance functions of the two models. Other distance-based criteria, simpler to compute than previous ones, are also introduced, for which, considering the framework of approximate design, a necessary condition for the optimality of a design measure is provided. The paper includes a study of the mathematical links between different criteria and numerical illustrations are provided.

Habitat and climatic associations of climate-sensitive species along a southern range boundary.

Climate change and habitat loss are recognized as important drivers of shifts in wildlife species' geographic distributions. While often considered independently, there is considerable overlap between these drivers, and understanding how they contribute to range shifts can predict future species assemblages and inform effective management. Our objective was to evaluate the impacts of habitat, climatic, and anthropogenic effects on the distributions of climate-sensitive vertebrates along a southern range boundary in Northern Michigan, USA. We combined multiple sources of occurrence data, including harvest and citizen-science data, then used hierarchical Bayesian spatial models to determine habitat and climatic associations for four climate-sensitive vertebrate species (American marten [Martes americana], snowshoe hare [Lepus americanus], ruffed grouse [Bonasa umbellus] and moose [Alces alces]). We used total basal area of at-risk forest types to represent habitat, and temperature and winter habitat indices to represent climate. Marten associated with upland spruce-fir and lowland riparian forest types, hares with lowland conifer and aspen-birch, grouse with lowland riparian hardwoods, and moose with upland spruce-fir. Species differed in climatic drivers with hares positively associated with cooler annual temperatures, moose with cooler summer temperatures and grouse with colder winter temperatures. Contrary to expectations, temperature variables outperformed winter habitat indices. Model performance varied greatly among species, as did predicted distributions along the southern edge of the Northwoods region. As multiple species were associated with lowland riparian and upland spruce-fir habitats, these results provide potential for efficient prioritization of habitat management. Both direct and indirect effects from climate change are likely to impact the distribution of climate-sensitive species in the future and the use of multiple data types and sources in the modelling of species distributions can result in more accurate predictions resulting in improved management at policy-relevant scales.

Spatio-temporal parse network-based trajectory modeling on the dynamics of criminal justice system.

We extend the existing group-based trajectory modeling by proposing the network-based trajectory modeling based on judicious design and analysis of a spatio-temporal parse network (STPN) as a representation of neighborhood structure that evolves in time. The STPN offers a principled qualitative specification for an explicit paradigm framework to deal with complex real-world problems. The framework is completed by developing a quantitative specification of latent field representation to merge seamlessly on or alongside the established STPN via hierarchical modeling. The models adopt spatial random effects to characterize the heterogeneity and autocorrelation over the locations where nonlinear trajectories were observed. The trajectories are then investigated in the presence of the operational constraints of the dependence structure induced by the spatial and temporal dimensions. With the framework, complex developmental trajectory problems can be discerned, communicated, diagnosed and modeled in a relatively simple way that interpretation is accessible to nontechnical audiences and quickly comprehensible to technically sophisticated audiences. The proposed modeling is applied to address the challenges of the trajectory modeling of nonlinear dynamics arising from a motivating criminal justice empirical process.

Uncertainty quantification of TMS simulations considering MRI segmentation errors.

Objective.Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation method that is used to study brain function and conduct neuropsychiatric therapy. Computational methods that are commonly used for electric field (E-field) dosimetry of TMS are limited in accuracy and precision because of possible geometric errors introduced in the generation of head models by segmenting medical images into tissue types. This paper studies E-field prediction fidelity as a function of segmentation accuracy.Approach.The errors in the segmentation of medical images into tissue types are modeled as geometric uncertainty in the shape of the boundary between tissue types. For each tissue boundary realization, we then use an in-house boundary element method to perform a forward propagation analysis and quantify the impact of tissue boundary uncertainties on the induced cortical E-field.Main results.Our results indicate that predictions of E-field induced in the brain are negligibly sensitive to segmentation errors in scalp, skull and white matter (WM), compartments. In contrast, E-field predictions are highly sensitive to possible cerebrospinal fluid (CSF) segmentation errors. Specifically, the segmentation errors on the CSF and gray matter interface lead to higher E-field uncertainties in the gyral crowns, and the segmentation errors on CSF and WM interface lead to higher uncertainties in the sulci. Furthermore, the uncertainty of the average cortical E-fields over a region exhibits lower uncertainty relative to point-wise estimates.Significance.The accuracy of current cortical E-field simulations is limited by the accuracy of CSF segmentation accuracy. Other quantities of interest like the average of the E-field over a cortical region could provide a dose quantity that is robust to possible segmentation errors.

MAXIMUM LIKELIHOOD ESTIMATION OF GAUSSIAN COPULA MODELS FOR GEOSTATISTICAL COUNT DATA.

This work investigates the computation of maximum likelihood estimators in Gaussian copula models for geostatistical count data. This is a computationally challenging task because the likelihood function is only expressible as a high dimensional multivariate normal integral. Two previously proposed Monte Carlo methods are reviewed, the Genz-Bretz and Geweke-Hajivassiliou-Keane simulators, and a new method is investigated. The new method is based on the so-called data cloning algorithm, which uses Markov chain Monte Carlo algorithms to approximate maximum likelihood estimators and their (asymptotic) variances in models with computationally challenging likelihoods. A simulation study is carried out to compare the statistical and computational efficiencies of the three methods. It is found that the three methods have similar statistical properties, but the Geweke-Hajivassiliou-Keane simulator requires the least computational effort. Hence, this is the method we recommend. A data analysis of Lansing Woods tree counts is used to illustrate the methods.

Stochastic models of dense or hollow nanoparticles and their scattering properties.

A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.

Dispersion of Recovery and Vulnerability to Re-entry in a Model of Human Atrial Tissue With Simulated Diffuse and Focal Patterns of Fibrosis.

Fibrosis in atrial tissue can act as a substrate for persistent atrial fibrillation, and can be focal or diffuse. Regions of fibrosis are associated with slowed or blocked conduction, and several approaches have been used to model these effects. In this study a computational model of 2D atrial tissue was used to investigate how the spatial scale of regions of simulated fibrosis influenced the dispersion of action potential duration (APD) and vulnerability to re-entry in simulated normal human atrial tissue, and human tissue that has undergone remodeling as a result of persistent atrial fibrillation. Electrical activity was simulated in a 10 × 10 cm square 2D domain, with a spatially varying diffusion coefficient as described below. Cellular electrophysiology was represented by the Courtemanche model for human atrial cells, with the model parameters set for normal and remodeled cells. The effect of fibrosis was modeled with a smoothly varying diffusion coefficient, obtained from sampling a Gaussian random field (GRF) with length scales of between 1.25 and 10.0 mm. Twenty samples were drawn from each field, and used to allocate a value of diffusion coefficient between 0.05 and 0.2 mm2/ms. Dispersion of APD was assessed in each sample by pacing at a cycle length of 1,000 ms, followed by a premature beat with a coupling interval of 400 ms. Vulnerability to re-entry was assessed with an aggressive pacing protocol with pacing cycle lengths decreasing from 450 to 250 ms in 25 ms intervals for normal tissue and 300-150 ms for remodeled tissue. Simulated fibrosis at smaller spatial scales tended to lengthen APD, increase APD dispersion, and increase vulnerability to sustained re-entry relative to fibrosis at larger spatial scales. This study shows that when fibrosis is represented by smoothly varying tissue diffusion, the spatial scale of fibrosis has important effects on both dispersion of recovery and vulnerability to re-entry.

An Updated Survey on Statistical Thresholding and Sample Size of fMRI Studies.

Background: Since the early 2010s, the neuroimaging field has paid more attention to the issue of false positives. Several journals have issued guidelines regarding statistical thresholds. Three papers have reported the statistical analysis of the thresholds used in fMRI literature, but they were published at least 3 years ago and surveyed papers published during 2007-2012. This study revisited this topic to evaluate the changes in this field. Methods: The PubMed database was searched to identify the task-based (not resting-state) fMRI papers published in 2017 and record their sample sizes, inferential methods (e.g., voxelwise or clusterwise), theoretical methods (e.g., parametric or non-parametric), significance level, cluster-defining primary threshold (CDT), volume of analysis (whole brain or region of interest) and software used. Results: The majority (95.6%) of the 388 analyzed articles reported statistics corrected for multiple comparisons. A large proportion (69.6%) of the 388 articles reported main results by clusterwise inference. The analyzed articles mostly used software Statistical Parametric Mapping (SPM), Analysis of Functional NeuroImages (AFNI), or FMRIB Software Library (FSL) to conduct statistical analysis. There were 70.9%, 37.6%, and 23.1% of SPM, AFNI, and FSL studies, respectively, that used a CDT of p ≤ 0.001. The statistical sample size across the articles ranged between 7 and 1,299 with a median of 33. Sample size did not significantly correlate with the level of statistical threshold. Conclusion: There were still around 53% (142/270) studies using clusterwise inference that chose a more liberal CDT than p = 0.001 (n = 121) or did not report their CDT (n = 21), down from around 61% reported by Woo et al. (2014). For FSL studies, it seemed that the CDT practice had no improvement since the survey by Woo et al. (2014). A few studies chose unconventional CDT such as p = 0.0125 or 0.004. Such practice might create an impression that the threshold alterations were attempted to show "desired" clusters. The median sample size used in the analyzed articles was similar to those reported in previous surveys. In conclusion, there seemed to be no change in the statistical practice compared to the early 2010s.

A MULTI-RESOLUTION MODEL FOR NON-GAUSSIAN RANDOM FIELDS ON A SPHERE WITH APPLICATION TO IONOSPHERIC ELECTROSTATIC POTENTIALS.

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial models for non-Gaussian random fields on a sphere based on a multi-resolution analysis. Using a special wavelet frame, named spherical needlets, as building blocks, the proposed model is constructed in the form of a sparse random effects model. The spatial localization of needlets, together with carefully chosen random coefficients, ensure the model to be non-Gaussian and isotropic. The model can also be expanded to include a spatially varying variance profile. The special formulation of the model enables us to develop efficient estimation and prediction procedures, in which an adaptive MCMC algorithm is used. We investigate the accuracy of parameter estimation of the proposed model, and compare its predictive performance with that of two Gaussian models by extensive numerical experiments. Practical utility of the proposed model is demonstrated through an application of the methodology to a data set of high-latitude ionospheric electrostatic potentials, generated from the LFM-MIX model of the magnetosphere-ionosphere system.

MULTIPLE TESTING OF LOCAL MAXIMA FOR DETECTION OF PEAKS IN RANDOM FIELDS.

A topological multiple testing scheme is presented for detecting peaks in images under stationary ergodic Gaussian noise, where tests are performed at local maxima of the smoothed observed signals. The procedure generalizes the one-dimensional scheme of [31] to Euclidean domains of arbitrary dimension. Two methods are developed according to two different ways of computing p-values: (i) using the exact distribution of the height of local maxima, available explicitly when the noise field is isotropic [9, 10]; (ii) using an approximation to the overshoot distribution of local maxima above a pre-threshold, applicable when the exact distribution is unknown, such as when the stationary noise field is non-isotropic [9]. The algorithms, combined with the Benjamini-Hochberg procedure for thresholding p-values, provide asymptotic strong control of the False Discovery Rate (FDR) and power consistency, with specific rates, as the search space and signal strength get large. The optimal smoothing bandwidth and optimal pre-threshold are obtained to achieve maximum power. Simulations show that FDR levels are maintained in non-asymptotic conditions. The methods are illustrated in the analysis of functional magnetic resonance images of the brain.

A Gaussian random field model for similarity-based smoothing in Bayesian disease mapping.

Conditionally specified Gaussian Markov random field (GMRF) models with adjacency-based neighbourhood weight matrix, commonly known as neighbourhood-based GMRF models, have been the mainstream approach to spatial smoothing in Bayesian disease mapping. In the present paper, we propose a conditionally specified Gaussian random field (GRF) model with a similarity-based non-spatial weight matrix to facilitate non-spatial smoothing in Bayesian disease mapping. The model, named similarity-based GRF, is motivated for modelling disease mapping data in situations where the underlying small area relative risks and the associated determinant factors do not vary systematically in space, and the similarity is defined by "similarity" with respect to the associated disease determinant factors. The neighbourhood-based GMRF and the similarity-based GRF are compared and accessed via a simulation study and by two case studies, using new data on alcohol abuse in Portugal collected by the World Mental Health Survey Initiative and the well-known lip cancer data in Scotland. In the presence of disease data with no evidence of positive spatial correlation, the simulation study showed a consistent gain in efficiency from the similarity-based GRF, compared with the adjacency-based GMRF with the determinant risk factors as covariate. This new approach broadens the scope of the existing conditional autocorrelation models.

Decreased resting-state interhemispheric coordination in first-episode, drug-naive paranoid schizophrenia.

BACKGROUND: Dysconnectivity hypothesis posits that schizophrenia relates to abnormalities in neuronal connectivity. However, little is known about the alterations of the interhemispheric resting-state functional connectivity (FC) in patients with paranoid schizophrenia. In the present study, we used a newly developed voxel-mirrored homotopic connectivity (VMHC) method to investigate the interhemispheric FC of the whole brain in patients with paranoid schizophrenia at rest. METHODS: Forty-nine first-episode, drug-naive patients with paranoid schizophrenia and 50 age-, gender-, and education-matched healthy subjects underwent a resting-state functional magnetic resonance imaging (fMRI) scans. An automated VMHC approach was used to analyze the data. RESULTS: Patients exhibited lower VMHC than healthy subjects in the precuneus (PCu), the precentral gyrus, the superior temporal gyrus (STG), the middle occipital gyrus (MOG), and the fusiform gyrus/cerebellum lobule VI. No region showed greater VMHC in the patient group than in the control group. Significantly negative correlation was observed between VMHC in the precentral gyrus and the PANSS positive/total scores, and between VMHC in the STG and the PANSS positive/negative/total scores. CONCLUSIONS: Our results suggest that interhemispheric resting-state FC of VMHC is reduced in paranoid schizophrenia with clinical implications for psychiatric symptomatology thus further contribute to the dysconnectivity hypothesis of schizophrenia.

Abnormal default-mode network homogeneity in first-episode, drug-naive schizophrenia at rest.

BACKGROUND: Dysconnectivity hypothesis posits that schizophrenia relates to abnormal resting-state connectivity within the default-mode network (DMN) and this aberrant connectivity is considered as contribution of difficulties in self-referential and introspective processing. However, little is known about the alterations of the network homogeneity (NH) of the DMN in schizophrenia. In the present study, we used an automatic NH method to investigate the NH of the DMN in schizophrenia patients at rest. METHODS: Forty-nine first-episode, drug-naive schizophrenia patients and 50 age-, gender-, and education-matched healthy controls underwent a resting-state functional magnetic resonance imaging (fMRI). An automated NH approach was used to analyze the data. RESULTS: Patients exhibited lower NH than controls in the left medial prefrontal cortex (MPFC) and the right middle temporal gyrus (MTG). Significantly higher NH values in the left posterior cingulate cortex (PCC) and the right cerebellum Crus I were found in the patient group than in the control group. No significant correlation was found between abnormal NH values and Positive and Negative Symptom Scale (PANSS) scores, duration of untreated psychosis (DUP), age or years of education in the patient group. CONCLUSIONS: Our findings suggest that abnormal NH of the DMN exists in first-episode, drug-naive schizophrenia and further highlight the importance of the DMN in the pathophysiology of schizophrenia.

Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization.

Obtaining an accurate three-dimensional (3D) structure of a porous microstructure is important for assessing the material properties based on finite element analysis. Whereas directly obtaining 3D images of the microstructure is impractical under many circumstances, two sets of methods have been developed in literature to generate (reconstruct) 3D microstructure from its 2D images: one characterizes the microstructure based on certain statistical descriptors, typically two-point correlation function and cluster correlation function, and then performs an optimization process to build a 3D structure that matches those statistical descriptors; the other method models the microstructure using stochastic models like a Gaussian random field and generates a 3D structure directly from the function. The former obtains a relatively accurate 3D microstructure, but computationally the optimization process can be very intensive, especially for problems with large image size; the latter generates a 3D microstructure quickly but sacrifices the accuracy due to issues in numerical implementations. A hybrid optimization approach of modelling the 3D porous microstructure of random isotropic two-phase materials is proposed in this paper, which combines the two sets of methods and hence maintains the accuracy of the correlation-based method with improved efficiency. The proposed technique is verified for 3D reconstructions based on silica polymer composite images with different volume fractions. A comparison of the reconstructed microstructures and the optimization histories for both the original correlation-based method and our hybrid approach demonstrates the improved efficiency of the approach.

Is there a cerebellar compensatory effort in first-episode, treatment-naive major depressive disorder at rest?

BACKGROUND: This study was undertaken to explore whether there is a cerebellar compensatory response in patients with first-episode, treatment-naive major depressive disorder (MDD). The cerebellar compensatory response is defined as a cerebellar hyperactivity which would be inversely correlated with both the activation of the functionally connected cerebral regions and the depression severity. METHODS: Resting-state functional magnetic resonance imaging (fMRI) data of 24 patients with MDD and 24 healthy subjects were analyzed with the fractional amplitude of low-frequency fluctuations (fALFF) and functional connectivity (FC) methods. The structural images were processed with the voxel-based morphometry (VBM) method. RESULTS: Compared to healthy controls, depressed patients had significantly increased fALFF in the left Crus I and the left cerebellar lobule VI. FC analysis of these two seeded regions found that depressed patients had increased FC between the left Crus I and the right hippocampus, but had decreased FC between the left Crus I and the left inferior parietal lobule (IPL), and between the left cerebellar lobule VI and bilateral inferior temporal gyrus. No correlation was observed between the abnormal fALFF of the seeds and their connected regions and the depression severity or the executive function. The VBM results did not show significant reduction in gray or white matter volume in any above-mentioned region. CONCLUSIONS: Our findings suggest that increased cerebellar activity at resting state may be a disease state phenomenon but not a compensatory response to the dysfunction of the default mode network (DMN) in MDD.

Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields.

This paper is concerned with sample path properties of anisotropic Gaussian random fields. We establish Fernique-type inequalities and utilize them to study the global and local moduli of continuity for anisotropic Gaussian random fields. Applications to fractional Brownian sheets and to the solutions of stochastic partial differential equations are investigated.