Scalar Metrics Research Articles

Application of fractal dimension for quantifying noise texture in computed tomography images.

Evaluation of noise texture information in CT images is important for assessing image quality. Noise texture is often quantified by the noise power spectrum (NPS), which requires numerous image realizations to estimate. This study evaluated fractal dimension for quantifying noise texture as a scalar metric that can potentially be estimated using one image realization. The American College of Radiology CT accreditation phantom (ACR) was scanned on a clinical scanner (Discovery CT750, GE Healthcare) at 120kV and 25 and 90mAs. Images were reconstructed using filtered back projection (FBP/ASIR 0%) with varying reconstruction kernels: Soft, Standard, Detail, Chest, Lung, Bone, and Edge. For each kernel, images were also reconstructed using ASIR 50% and ASIR 100% iterative reconstruction (IR) methods. Fractal dimension was estimated using the differential box-counting algorithm applied to images of the uniform section of ACR phantom. The two-dimensional Noise Power Spectrum (NPS) and one-dimensional-radially averaged NPS were estimated using established techniques. By changing the radiation dose, the effect of noise magnitude on fractal dimension was evaluated. The Spearman correlation between the fractal dimension and the frequency of the NPS peak was calculated. The number of images required to reliably estimate fractal dimension was determined and compared to the number of images required to estimate the NPS-peak frequency. The effect of Region of Interest (ROI) size on fractal dimension estimation was evaluated. Feasibility of estimating fractal dimension in an anthropomorphic phantom and clinical image was also investigated, with the resulting fractal dimension compared to that estimated within the uniform section of the ACR phantom. Fractal dimension was strongly correlated with the frequency of the peak of the radially averaged NPS curve, having a Spearman rank-order coefficient of 0.98 (P-value<0.01) for ASIR 0%. The mean fractal dimension at ASIR 0% was 2.49 (Soft), 2.51 (Standard), 2.52 (Detail), 2.57 (Chest), 2.61 (Lung), 2.66 (Bone), and 2.7 (Edge). A reduction in fractal dimension was observed with increasing ASIR levels for all investigated reconstruction kernels. Fractal dimension was found to be independent of noise magnitude. Fractal dimension was successfully estimated from four ROIs of size 64×64 pixels or one ROI of 128×128 pixels. Fractal dimension was found to be sensitive to non-noise structures in the image, such as ring artifacts and anatomical structure. Fractal dimension estimated within a uniform region of an anthropomorphic phantom and clinical head image matched that estimated within the ACR phantom for filtered back projection reconstruction. Fractal dimension correlated with the NPS-peak frequency and was independent of noise magnitude, suggesting that the scalar metric of fractal dimension can be used to quantify the change in noise texture across reconstruction approaches. Results demonstrated that fractal dimension can be estimated from four, 64×64-pixel ROIs or one 128×128 ROI within a head CT image, which may make it amenable for quantifying noise texture within clinical images.

Co-Optimization of Communication and Sensing for Multiple Unmanned Aerial Vehicles in Cooperative Target Tracking

In this paper, we consider motion-planning for multiple unmanned aerial vehicles (UAVs) that oversee cooperative target tracking in realistic communication environments. We present a novel multi-UAVs cooperative target tracking algorithm based on co-optimization of communication and sensing strategy, which can generate information-gathering trajectories considering the multi-hops communication reliability. Firstly, a packet-erasure channel model is used to describe the realistic wireless communication links, in which the probability of a successful information transmission is modeled as a function of the signal-to-noise ratio (SNR). Secondly, the Fisher information matrix (FIM) is used to quantify the information gained in target tracking. Thirdly, a scalar metric is used for trajectories panning over a finite time horizon. This scalar metric is a utility function of the expected information gain and the probability of a successful information transmission. With the combining of the sensing and communication into a utility function, the co-optimization of communication and sensing is reflected in the tradeoffs between maximizing information gained and improving communication reliability. The results of comparison simulations show that the proposed algorithm effectively improved estimation performance compared to the method that does not consider communication reliability.

Concussion classification via deep learning using whole-brain white matter fiber strains.

Developing an accurate and reliable injury predictor is central to the biomechanical studies of traumatic brain injury. State-of-the-art efforts continue to rely on empirical, scalar metrics based on kinematics or model-estimated tissue responses explicitly pre-defined in a specific brain region of interest. They could suffer from loss of information. A single training dataset has also been used to evaluate performance but without cross-validation. In this study, we developed a deep learning approach for concussion classification using implicit features of the entire voxel-wise white matter fiber strains. Using reconstructed American National Football League (NFL) injury cases, leave-one-out cross-validation was employed to objectively compare injury prediction performances against two baseline machine learning classifiers (support vector machine (SVM) and random forest (RF)) and four scalar metrics via univariate logistic regression (Brain Injury Criterion (BrIC), cumulative strain damage measure of the whole brain (CSDM-WB) and the corpus callosum (CSDM-CC), and peak fiber strain in the CC). Feature-based machine learning classifiers including deep learning, SVM, and RF consistently outperformed all scalar injury metrics across all performance categories (e.g., leave-one-out accuracy of 0.828–0.862 vs. 0.690–0.776, and .632+ error of 0.148–0.176 vs. 0.207–0.292). Further, deep learning achieved the best cross-validation accuracy, sensitivity, AUC, and .632+ error. These findings demonstrate the superior performances of deep learning in concussion prediction and suggest its promise for future applications in biomechanical investigations of traumatic brain injury.

Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.

Spatial Separation of Closely-Located Users in Measured Massive MIMO Channels

We investigate the ability of Massive multiple-input multiple-output (MIMO) systems to spatially separate up to eighteen users located close to one another in line-of-sight (LOS) propagation conditions, in both indoor and outdoor environments. For that, we use fully-synchronous measured channels at 2.6 GHz of single-antenna users moving within a small area and concurrently communicating with a base station (BS) equipped with a compact 128-port array. To quantify the degree of spatial user separability, we use three scalar metrics, namely, the achievable sum-rates, the condition number of the channel matrix, and the angle to interference factor. Our results show that Massive MIMO with zero-forcing (ZF) or regularized ZF (RZF) can spatially separate nine, even eighteen, concurrent users at practical SNR values even in the challenging case of dominant LOS propagation. In particular, signal-to-noise ratio losses relative to ideal (non-interfering and equally strong) channels can be reduced dramatically compared with standard multiuser MIMO systems, which typically have the same number of users as BS antennas. Our findings suggest that with RZF or ZF the ratio of BS antennas to number of served users should be at least three to four, to harvest most of the available spatial gains that the environment can offer. Although orthogonality and array gains complement each other, for the suggested ratios of antennas to users, the main contribution to improving system performance, measured in sum-rates, comes from the orthogonality gain.

What Is Better Than Coulomb Failure Stress? A Ranking of Scalar Static Stress Triggering Mechanisms from 105 Mainshock‐Aftershock Pairs

AbstractAftershocks may be triggered by the stresses generated by preceding mainshocks. The temporal frequency and maximum size of aftershocks are well described by the empirical Omori and Bath laws, but spatial patterns are more difficult to forecast. Coulomb failure stress is perhaps the most common criterion invoked to explain spatial distributions of aftershocks. Here we consider the spatial relationship between patterns of aftershocks and a comprehensive list of 38 static elastic scalar metrics of stress (including stress tensor invariants, maximum shear stress, and Coulomb failure stress) from 213 coseismic slip distributions worldwide. The rates of true‐positive and false‐positive classification of regions with and without aftershocks are assessed with receiver operating characteristic analysis. We infer that the stress metrics that are most consistent with observed aftershock locations are maximum shear stress and the magnitude of the second and third invariants of the stress tensor. These metrics are significantly better than random assignment at a significance level of 0.005 in over 80% of the slip distributions. In contrast, the widely used Coulomb failure stress criterion is distinguishable from random assignment in only 51–64% of the slip distributions. These results suggest that a number of alternative scalar metrics are better predictors of aftershock locations than classic Coulomb failure stress change.

Diffusion Kurtosis Imaging in the Assessment of Peritumoral Brain Edema in Glioblastomas and Brain Metastases

Aim: to explore the opportunities of application of diffusionkurtosis imaging (DKI) for assessment and estimation of diffusion scalar metrics in different locations of peritumoral edema for extra- and intracerebral tumors and in contralateral normal tissue.Materials and methods. 38 patients with supratentorial brain tumors were investigated: 24 (63%) patients with primarily revealed glioblastomas (GB) and 14 (37%) patients with solitary cancer brain metastasis (MTS). MRI was performed on 3.0 T MR-scanner (Signa HDxt, General Electric, USA) with the standard protocols for brain tumor and additional protocol for DKI. The standard protocol for brain tumor included: T1-, T2-weighted images, T2-FLAIR, DWI, T1 with contrast enhancement. Diffusion kurtosis MRI based on SE EPI with TR = 10000 ms, TE = 102 ms, FOV = 240 mm, isotropic voxel size 3 × 3 × 3 mm3, 60 noncoplanar diffusion directions. We used three b-values: 0, 1000 and 2500 s/mm2. Аcquisition time was 22 min. Total acquisition time was near 40 min. This study was approved by Ethical committee of Burdenko National Scientific and Practical Center for Neurosurgery. Parametric maps were constructed for the following diffusion coefficients: mean (MK), transverse / radial (RK), longitudinal / axial (AK) kurtozis; medium (MD), transverse / radial (RD) and longitudinal / axial (AD) diffusion; fractional anisotropy (FA) and a bi-exponential diffusion model coefficients: axonal water fractions (AWF), axial (AxEAD) and radial (RadEAD) extra-axonal water diffusion and the water molecules trajectory tortuosity index (TORT). Normative quantitative indicators were obtained for the six regions of the peritumoral zone as they moved away from the tumor (region 2) to the edema periphery (regions 4–5), as well as in the normal brain on the contralateral hemisphere (C/L) (zone 7). A comparative analysis of these indicators was conducted for cases with GB and MTS. DKI scalar metrics were estimated using Explore DTI (http://www.exploredti.com/).Results. Anatomic MRI (T1 without/with contrast enhancement) for all cases with GB and MTS visualized a contrast enhancement tumor. The peritumoral edema, spreading mainly over the brain white matter, was well visualized on T2-FLAIR. Diffusion kurtosis coefficients decreased in the near peritumoral edema (regions 2–3) and a gradually increased to the edema periphery (regions 5–6). In Region 2, MK in both GB and MTS groups were MKGB(2) = 0.637 ± 0.140 and MKMTS(2) = 0.550 ± 0.046; RK in this region were RKGB(2) = 0.690 ± 0.154 and RKMTS (2) = 0.584 ± 0.051. Differences both MK and RK coefficients in patients with GB and MTS of region 2 were significant (p &lt; 0.001). There were no differences in AK values for GB and MTS in region 2 (p &gt; 0.05), but in regions 3 and 4 differences were observed (p &lt; 0.01). The minimum value of AK in the central edema (regions 3–4) was AKMTS(3–4) = 0.433 ± 0.063 in patients with MTS. The values of MK and RK on the contralateral side in patients with MTS were significantly higher than in the GB group (p &lt; 0.02); MKC/LMTC = 0.954 ± 0.140, RKC/LMTC = 1.257 ± 0.308 and MKC/LGB = 0.829 ± 0.146, RKc/LGB = 0.989 ± 0.282. There was no significant difference for contralateral AK between the groups.Conclusions. We found that DKI scalar metrics are the sensitive tumor biomarkers. It allows us to perform a robust differentiation between the infiltrating GB tumor and purely vasogenic edema of МТS. The obtained results will allow further differential diagnosis of extra- and intracerebral tumors and can be used to plan surgical / radiosurgical treatment for brain tumors.

Differentiation of glioma malignancy grade using diffusion MRI

Modern diffusion MR protocols allow one to acquire the multi-shell diffusion data with high diffusion weightings in a clinically feasible time. In the present work we assessed three diffusion approaches based on diffusion and kurtosis tensor imaging (DTI, DKI), and neurite orientation dispersion and density imaging (NODDI) as possible biomarkers for human brain glioma grade differentiation based on the one diffusion protocol. We used three diffusion weightings (so called b-values) equal to 0, 1000, and 2500s/mm2 with 60 non-coplanar diffusion directions in the case of non-zero b-values. The patient groups of the glioma grades II, III, and IV consist of 8 subjects per group. We found that DKI, and NODDI scalar metrics can be effectively used as glioma grade biomarkers with a significant difference (p<0.05) for grading between low- and high-grade gliomas, in particular, for glioma II versus glioma III grades, and glioma III versus glioma IV grades. The use of mean/axial kurtosis and intra-axonal fraction/orientation dispersion index metrics allowed us to obtain the most feasible and reliable differentiation criteria. For example, in the case of glioma grades II, III, and IV the mean kurtosis is equal to 0.31, 0.51, and 0.90, and the orientation dispersion index is equal to 0.14, 0.30, and 0.59, respectively. The limitations and perspectives of the biophysical diffusion models based on intra-/extra-axonal compartmentalisation for glioma differentiation are discussed.

Validation of DWI pre-processing procedures for reliable differentiation between human brain gliomas

Diffusion magnetic resonance imaging (dMRI) is a powerful tool in clinical applications, in particular, in oncology screening. dMRI demonstrated its benefit and efficiency in the localisation and detection of different types of human brain tumours. Clinical dMRI data suffer from multiple artefacts such as motion and eddy-current distortions, contamination by noise, outliers etc. In order to increase the image quality of the derived diffusion scalar metrics and the accuracy of the subsequent data analysis, various pre-processing approaches are actively developed and used. In the present work we assess the effect of different pre-processing procedures such as a noise correction, different smoothing algorithms and spatial interpolation of raw diffusion data, with respect to the accuracy of brain glioma differentiation. As a set of sensitive biomarkers of the glioma malignancy grades we chose the derived scalar metrics from diffusion and kurtosis tensor imaging as well as the neurite orientation dispersion and density imaging (NODDI) biophysical model. Our results show that the application of noise correction, anisotropic diffusion filtering, and cubic-order spline interpolation resulted in the highest sensitivity and specificity for glioma malignancy grading. Thus, these pre-processing steps are recommended for the statistical analysis in brain tumour studies.

MJO simulation in CMIP5 climate models: MJO skill metrics and process-oriented diagnosis

The Madden-Julian Oscillation (MJO) simulation diagnostics developed by MJO Working Group and the process-oriented MJO simulation diagnostics developed by MJO Task Force are applied to 37 Coupled Model Intercomparison Project phase 5 (CMIP5) models in order to assess model skill in representing amplitude, period, and coherent eastward propagation of the MJO, and to establish a link between MJO simulation skill and parameterized physical processes. Process-oriented diagnostics include the Relative Humidity Composite based on Precipitation (RHCP), Normalized Gross Moist Stability (NGMS), and the Greenhouse Enhancement Factor (GEF). Numerous scalar metrics are developed to quantify the results. Most CMIP5 models underestimate MJO amplitude, especially when outgoing longwave radiation (OLR) is used in the evaluation, and exhibit too fast phase speed while lacking coherence between eastward propagation of precipitation/convection and the wind field. The RHCP-metric, indicative of the sensitivity of simulated convection to low-level environmental moisture, and the NGMS-metric, indicative of the efficiency of a convective atmosphere for exporting moist static energy out of the column, show robust correlations with a large number of MJO skill metrics. The GEF-metric, indicative of the strength of the column-integrated longwave radiative heating due to cloud-radiation interaction, is also correlated with the MJO skill metrics, but shows relatively lower correlations compared to the RHCP- and NGMS-metrics. Our results suggest that modifications to processes associated with moisture-convection coupling and the gross moist stability might be the most fruitful for improving simulations of the MJO. Though the GEF-metric exhibits lower correlations with the MJO skill metrics, the longwave radiation feedback is highly relevant for simulating the weak precipitation anomaly regime that may be important for the establishment of shallow convection and the transition to deep convection.

On the lower bounds of the $L^2$-norm of the Hermitian scalar curvature

On a pre-quantized symplectic manifold, we show that the symplectic Futaki invariant, which is an obstruction to the existence of constant Hermitian scalar curvature almost-Kahler metrics, is actually an asymptotic invariant. This allows us to deduce a lower bound for the L^2-norm of the Hermitian scalar curvature as obtained by S. Donaldson \cite{Don} in the Kahler case.

Infinite loop spaces and positive scalar curvature

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary index map from the space of positive scalar metrics to a suitable space from the real $K$-theory spectrum. Our main results concern the nontriviality of this map. We prove that for $2n \geq 6$, the natural $KO$-orientation from the infinite loop space of the Madsen--Tillmann--Weiss spectrum factors (up to homotopy) through the space of metrics of positive scalar curvature on any $2n$-dimensional spin manifold. For manifolds of odd dimension $2n+1 \geq 7$, we prove the existence of a similar factorisation. When combined with computational methods from homotopy theory, these results have strong implications. For example, the secondary index map is surjective on all rational homotopy groups. We also present more refined calculations concerning integral homotopy groups. To prove our results we use three major sets of technical tools and results. The first set of tools comes from Riemannian geometry: we use a parameterised version of the Gromov--Lawson surgery technique which allows us to apply homotopy-theoretic techniques to spaces of metrics of positive scalar curvature. Secondly, we relate Hitchin's secondary index to several other index-theoretical results, such as the Atiyah--Singer family index theorem, the additivity theorem for indices on noncompact manifolds and the spectral-flow index theorem. Finally, we use the results and tools developed recently in the study of moduli spaces of manifolds and cobordism categories. The key new ingredient we use in this paper is the high-dimensional analogue of the Madsen--Weiss theorem, proven by Galatius and the third named author.

Analysis of the effects of noise, DWI sampling, and value of assumed parameters in diffusion MRI models.

PurposeThis study was a systematic evaluation across different and prominent diffusion MRI models to better understand the ways in which scalar metrics are influenced by experimental factors, including experimental design (diffusion‐weighted imaging [DWI] sampling) and noise.MethodsFour diffusion MRI models—diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), mean apparent propagator MRI (MAP‐MRI), and neurite orientation dispersion and density imaging (NODDI)—were evaluated by comparing maps and histogram values of the scalar metrics generated using DWI datasets obtained in fixed mouse brain with different noise levels and DWI sampling complexity. Additionally, models were fit with different input parameters or constraints to examine the consequences of model fitting procedures.ResultsExperimental factors affected all models and metrics to varying degrees. Model complexity influenced sensitivity to DWI sampling and noise, especially for metrics reporting non‐Gaussian information. DKI metrics were highly susceptible to noise and experimental design. The influence of fixed parameter selection for the NODDI model was found to be considerable, as was the impact of initial tensor fitting in the MAP‐MRI model.ConclusionAcross DTI, DKI, MAP‐MRI, and NODDI, a wide range of dependence on experimental factors was observed that elucidate principles and practical implications for advanced diffusion MRI. Magn Reson Med 78:1767–1780, 2017. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Neurite density index is sensitive to age related differences in the developing brain

PurposeWhite matter development during childhood and adolescence is characterised by increasing white matter coherence and organisation. Commonly used scalar metrics, such as fractional anisotropy (FA), are sensitive to multiple mechanisms of white matter change and therefore unable to distinguish between mechanisms that change during development. We investigate the relationship between age and neurite density index (NDI) from neurite orientation dispersion and density imaging (NODDI), and the age-classification accuracy of NDI compared with FA, in a developmental cohort. MethodDiffusion-weighted imaging data from 72 children and adolescents between the ages of 4–19 was collected (M=10.42, SD=3.99, 36 male). We compared NODDI metrics against conventional DTI metrics (fractional anisotropy [FA], mean diffusivity [MD], axial diffusivity [AD] and radial diffusivity [RD]) in terms of their relationship to age. An ROC analysis was also performed to assess the ability of each metric to classify older and younger participants. ResultsNDI exhibited a stronger relationship with age (median R2=.60) compared with MD (median R2=.39), FA (median R2=.27), AD (median R2=.14), and RD (median R2=.35) in a high proportion of white matter tracts. When participants were divided into an older and younger group, NDI achieved the best classification (median area under the curve [AUC]=.89), followed by MD (median AUC=.81), FA (median AUC=.80), RD (median AUC=.81), and AD (median AUC=.64). ConclusionOur results demonstrate the sensitivity of NDI to age-related differences in white matter microstructural organisation over development. Importantly, NDI is more sensitive to such developmental changes compared to commonly used DTI metrics. This knowledge provides justification for implementing NODDI metrics in developmental studies.

A Severity Function Approach to Scenario Selection

The function approach (abbreviated SFA) is a method of selecting adverse from a multivariate density. It requires the scenario user (e.g. an agency that runs banking sector stress tests) to specify a severity function, which maps candidate into a scalar metric. The higher the value of this metric, the more harmful a scenario is. In selecting a scenario the SFA proceeds as follows: First, it isolates a set of equally severe scenario candidates. This set is determined by the condition that more severe only occur with some user-specified probability. Second, from this set it selects the candidate with the highest probability density, i.e. the most plausible scenario. The approach hence operationalizes the mantra that scenarios should be severe yet plausible.

Preoperative automated fibre quantification predicts postoperative seizure outcome in temporal lobe epilepsy.

Approximately one in every two patients with pharmacoresistant temporal lobe epilepsy will not be rendered completely seizure-free after temporal lobe surgery. The reasons for this are unknown and are likely to be multifactorial. Quantitative volumetric magnetic resonance imaging techniques have provided limited insight into the causes of persistent postoperative seizures in patients with temporal lobe epilepsy. The relationship between postoperative outcome and preoperative pathology of white matter tracts, which constitute crucial components of epileptogenic networks, is unknown. We investigated regional tissue characteristics of preoperative temporal lobe white matter tracts known to be important in the generation and propagation of temporal lobe seizures in temporal lobe epilepsy, using diffusion tensor imaging and automated fibre quantification. We studied 43 patients with mesial temporal lobe epilepsy associated with hippocampal sclerosis and 44 healthy controls. Patients underwent preoperative imaging, amygdalohippocampectomy and postoperative assessment using the International League Against Epilepsy seizure outcome scale. From preoperative imaging, the fimbria-fornix, parahippocampal white matter bundle and uncinate fasciculus were reconstructed, and scalar diffusion metrics were calculated along the length of each tract. Altogether, 51.2% of patients were rendered completely seizure-free and 48.8% continued to experience postoperative seizure symptoms. Relative to controls, both patient groups exhibited strong and significant diffusion abnormalities along the length of the uncinate bilaterally, the ipsilateral parahippocampal white matter bundle, and the ipsilateral fimbria-fornix in regions located within the medial temporal lobe. However, only patients with persistent postoperative seizures showed evidence of significant pathology of tract sections located in the ipsilateral dorsal fornix and in the contralateral parahippocampal white matter bundle. Using receiver operating characteristic curves, diffusion characteristics of these regions could classify individual patients according to outcome with 84% sensitivity and 89% specificity. Pathological changes in the dorsal fornix were beyond the margins of resection, and contralateral parahippocampal changes may suggest a bitemporal disorder in some patients. Furthermore, diffusion characteristics of the ipsilateral uncinate could classify patients from controls with a sensitivity of 98%; importantly, by co-registering the preoperative fibre maps to postoperative surgical lacuna maps, we observed that the extent of uncinate resection was significantly greater in patients who were rendered seizure-free, suggesting that a smaller resection of the uncinate may represent insufficient disconnection of an anterior temporal epileptogenic network. These results may have the potential to be developed into imaging prognostic markers of postoperative outcome and provide new insights for why some patients with temporal lobe epilepsy continue to experience postoperative seizures.

Probabilistic biomechanical finite element simulations: whole-model classical hypothesis testing based on upcrossing geometry

Statistical analyses of biomechanical finite element (FE) simulations are frequently conducted on scalar metrics extracted from anatomically homologous regions, like maximum von Mises stresses from demarcated bone areas. The advantages of this approach are numerical tabulability and statistical simplicity, but disadvantages include region demarcation subjectivity, spatial resolution reduction, and results interpretation complexity when attempting to mentally map tabulated results to original anatomy. This study proposes a method which abandons the two aforementioned advantages to overcome these three limitations. The method is inspired by parametric random field theory (RFT), but instead uses a non-parametric analogue to RFT which permits flexible model-wide statistical analyses through non-parametrically constructed probability densities regarding volumetric upcrossing geometry. We illustrate method fundamentals using basic 1D and 2D models, then use a public model of hip cartilage compression to highlight how the concepts can extend to practical biomechanical modeling. The ultimate whole-volume results are easy to interpret, and for constant model geometry the method is simple to implement. Moreover, our analyses demonstrate that the method can yield biomechanical insights which are difficult to infer from single simulations or tabulated multi-simulation results. Generalizability to non-constant geometry including subject-specific anatomy is discussed.

Fiber up-sampling and quality assessment of tractograms - towards quantitative brain connectivity.

Background and PurposeDiffusion MRI tractography enables to investigate white matter pathways noninvasively by reconstructing estimated fiber pathways. However, such tractograms remain biased and nonquantitative. Several techniques have been proposed to reestablish the link between tractography and tissue microstructure by modeling the diffusion signal or fiber orientation distribution (FOD) with the given tractogram and optimizing each fiber or compartment contribution according to the diffusion signal or FOD. Nevertheless, deriving a reliable quantification of connectivity strength between different brain areas is still a challenge. Moreover, evaluating the quality of a tractogram and measuring the possible error sources contained in a specific reconstructed fiber bundle also remains difficult. Lastly, all of these optimization techniques fail if specific fiber populations within a tractogram are underrepresented, for example, due to algorithmic constraints, anatomical properties, fiber geometry or seeding patterns.MethodsIn this work, we propose an approach which enables the inspection of the quality of a tractogram optimization by evaluating the residual error signal and its FOD representation. The automated fiber quantification (AFQ) is applied, whereby the framework is extended to reflect not only scalar diffusion metrics along a fiber bundle, but also directionally dependent FOD amplitudes along and perpendicular to the fiber direction. Furthermore, we also present an up‐sampling procedure to increase the number of streamlines of a given fiber population. The introduced error metrics and fiber up‐sampling method are tested and evaluated on single‐shell diffusion data sets of 16 healthy volunteers.Results and ConclusionAnalyzing the introduced error measures on specific fiber bundles shows a considerable improvement in applying the up‐sampling method. Additionally, the error metrics provide a useful tool to spot and identify potential error sources in tractograms.

Comparison of parameter uncertainty analysis techniques for a TOPMODEL application

Parameter uncertainty in hydrologic modeling is crucial to the flood simulation and forecasting. The Bayesian approach allows one to estimate parameters according to prior expert knowledge as well as observational data about model parameter values. This study assesses the performance of two popular uncertainty analysis (UA) techniques, i.e., generalized likelihood uncertainty estimation (GLUE) and Bayesian method implemented with the Markov chain Monte Carlo sampling algorithm, in evaluating model parameter uncertainty in flood simulations. These two methods were applied to the semi-distributed Topographic hydrologic model (TOPMODEL) that includes five parameters. A case study was carried out for a small humid catchment in the southeastern China. The performance assessment of the GLUE and Bayesian methods were conducted with advanced tools suited for probabilistic simulations of continuous variables such as streamflow. Graphical tools and scalar metrics were used to test several attributes of the simulation quality of selected flood events: deterministic accuracy and the accuracy of 95 % prediction probability uncertainty band (95PPU). Sensitivity analysis was conducted to identify sensitive parameters that largely affect the model output results. Subsequently, the GLUE and Bayesian methods were used to analyze the uncertainty of sensitive parameters and further to produce their posterior distributions. Based on their posterior parameter samples, TOPMODEL’s simulations and the corresponding UA results were conducted. Results show that the form of exponential decline in conductivity and the overland flow routing velocity were sensitive parameters in TOPMODEL in our case. Small changes in these two parameters would lead to large differences in flood simulation results. Results also suggest that, for both UA techniques, most of streamflow observations were bracketed by 95PPU with the containing ratio value larger than 80 %. In comparison, GLUE gave narrower prediction uncertainty bands than the Bayesian method. It was found that the mode estimates of parameter posterior distributions are suitable to result in better performance of deterministic outputs than the 50 % percentiles for both the GLUE and Bayesian analyses. In addition, the simulation results calibrated with Rosenbrock optimization algorithm show a better agreement with the observations than the UA’s 50 % percentiles but slightly worse than the hydrographs from the mode estimates. The results clearly emphasize the importance of using model uncertainty diagnostic approaches in flood simulations.

Quantification of MDL-induced signal degradation in MIMO-OFDM mode-division multiplexing systems

Mode-division multiplexing (MDM) transmission over few-mode optical fiber has emerged as a promising technology to enhance transmission capacity, in which multiple-input-multiple-output (MIMO) digital signal processing (DSP) after coherent detection is used to demultiplex the signals. Compared with conventional single-mode systems, MIMO-MDM systems suffer non-recoverable signal degradation induced by mode-dependent loss (MDL). In this paper, the MDL-induced signal degradation in orthogonal-frequency-division-multiplexing (OFDM) MDM systems is theoretically quantified in terms of mode-average error vector magnitude (EVM) through frequency domain norm analysis. A novel scalar MDL metric is proposed considering the probability distribution of the practical MDM input signals, and a closed-form expression for EVM measured after zero-force (ZF) MIMO equalization is derived. Simulation results show that the EVM estimations utilizing the novel MDL metric remain unbiased for unrepeated links. For a 6 × 100 km 20-mode MDM transmission system, the estimation accuracy is improved by more than 90% compared with that utilizing traditional condition number (CN) based MDL metric. The proposed MDL metric can be used to predict the MDL-induced SNR penalty in a theoretical manner, which will be beneficial for the design of practical MIMO-MDM systems.