Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

Alteration of natural ³⁷Ar activity concentration in the subsurface by gas transport and water infiltration

High ³⁷Ar activity concentration in soil gas is proposed as a key evidence for the detection of underground nuclear explosion by the Comprehensive Nuclear Test-Ban Treaty. However, such a detection is challenged by the natural background of ³⁷Ar in the subsurface, mainly due to Ca activation by cosmic rays. A better understanding and improved capability to predict ³⁷Ar activity concentration in the subsurface and its spatial and temporal variability is thus required. A numerical model integrating ³⁷Ar production and transport in the subsurface is developed, including variable soil water content and water infiltration at the surface. A parameterized equation for ³⁷Ar production in the first 15 m below the surface is studied, taking into account the major production reactions and the moderation effect of soil water content. Using sensitivity analysis and uncertainty quantification, a realistic and comprehensive probability distribution of natural ³⁷Ar activity concentrations in soil gas is proposed, including the effects of water infiltration. Site location and soil composition are identified as the parameters allowing for a most effective reduction of the possible range of ³⁷Ar activity concentrations. The influence of soil water content on ³⁷Ar production is shown to be negligible to first order, while ³⁷Ar activity concentration in soil gas and its temporal variability appear to be strongly influenced by transient water infiltration events. These results will be used as a basis for practical CTBTO concepts of operation during an OSI.

Quantification of water content across a cement-clay interface using high resolution neutron radiography

In many designs for radioactive waste repositories, cement and clay will come into direct contact. The geochemical contrast between cement and clay will lead to mass fluxes across the interface, which consequently results in alteration of structural and transport properties of both materials that may affect the performance of the multi-barrier system. We present an experimental approach to study cement-clay interactions with a cell to accommodate small samples of cement and clay. The cell design allows both in situ measurement of water content across the sample using neutron radiography and measurement of transport parameters using through-diffusion tracer experiments. The aim of the high- resolution neutron radiography experiments was to monitor changes in water content (porosity) and their spatial extent. Neutron radiographs of several evolving cement-clay interfaces delivered quantitative data which allow resolving local water contents within the sample domain. In the present work we explored the uncertainties of the derived water contents with regard to various input parameters and with regard to the applied image correction procedures. Temporal variation of measurement conditions created absolute uncertainty of the water content in the order of ±0.1 (m3/m3), which could not be fully accounted for by correction procedures. Smaller relative changes in water content between two images can be derived by specific calibrations to two sample regions with different, invariant water contents.

Biochemical T2* MR quantification of ankle arthrosis in pes cavovarus

Pes cavovarus affects the ankle biomechanics and may lead to ankle arthrosis. Quantitative T2 STAR (T2*) magnetic resonance (MR) mapping allows high resolution of thin cartilage layers and quantitative grading of cartilage degeneration. Detection of ankle arthrosis using T2* mapping in cavovarus feet was evaluated. Eleven cavovarus patients with symptomatic ankle arthrosis (13 feet, mean age 55.6 years, group 1), 10 cavovarus patients with no or asymptomatic, mild ankle arthrosis (12 feet, mean age 41.8 years, group 2), and 11 controls without foot deformity (18 feet, mean age 29.8 years, group 3) had quantitative T2* MR mapping. Additional assessment included plain radiographs and the American Orthopaedic Foot and Ankle Society (AOFAS) score (groups 1 and 2 only). Mean global T2* relaxation time was significantly different between groups 1 and 2 (p = 0.001) and groups 1 and 3 (p = 0.017), but there was no significance for decreased global T2* values in group 2 compared to group 3 (p = 0.345). Compared to the medial compartment T2* values of the lateral compartment were significantly (p = 0.025) higher within group 1. T2* values in the medial ankle joint compartment of group 2 were significantly lower than those of group 1 (p = 0.019). Ankle arthrosis on plain radiographs and the AOFAS score correlated significantly with T2* values in the medial compartment of group 1 (p = 0.04 and 0.039, respectively). Biochemical, quantitative T2* MR mapping is likely effective to evaluate ankle arthrosis in cavovarus feet but further studies are required.

Diagnostic performance and accuracy of 3-D spoiled gradient-dual-echo MRI with water- and fat-signal separation in liver-fat quantification: comparison to liver biopsy

To prospectively evaluate a 3-dimensional spoiled gradient-dual-echo (3D SPGR-DE) magnetic resonance imaging (MRI) sequence for the qualitative and quantitative analysis of liver fat content (LFC) in patients with the suspicion of fatty liver disease using histopathology as the standard of reference.

Reliability and discriminatory power of methods for dental plaque quantification

This in situ study evaluated the discriminatory power and reliability of methods of dental plaque quantification and the relationship between visual indices (VI) and fluorescence camera (FC) to detect plaque.

[Ultrasonic and radiographic quantification of palmar angulation in metacarpal IV and V neck fractures]

Therapy of metacarpal neck fractures depending on radiographically measured palmar angulation is discussed controversially in the literature. Some authors describe normal hand function of malunited metacarpal neck fractures with a palmar angulation up to 70°; others define 30° as the uppermost limit to maintain normal hand function. However, the methods of measuring palmar angulation are not clearly defined. Here, we present a new method to measure palmar angulation using ultrasound. The aim of this prospective study is to compare the radiographic methods of measuring palmar angulation with the ultrasound method. PATIENTS/MATERIAL AND METHOD: 20 patients with a neck fracture of the metacarpals IV or V were treated either conservatively or operatively. 2 weeks after trauma or operation, an x-ray was performed. 2 examiners measured the palmar angulation on the oblique and lateral projections using 2 different methods (medullary canal and dorsal cortex methods). At the same time, the 2 examiners performed measurements of palmar angulation using ultrasound. The measurements obtained with the different methods as well as by the 2 examiners at 2 different terms were compared. Intra- and interobserver reliability of each method was calculated, and for the ultrasound method a test for accuracy of the measured angles was performed.

[Ethics, empiricism and uncertainty]

Accidents can lead to difficult boundary situations. Such situations often take place in the emergency units. The medical team thus often and inevitably faces professional uncertainty in their decision-making. It is essential to communicate these uncertainties within the medical team, instead of downplaying or overriding existential hurdles in decision-making. Acknowledging uncertainties might lead to alert and prudent decisions. Thus uncertainty can have ethical value in treatment or withdrawal of treatment. It does not need to be covered in evidence-based arguments, especially as some singular situations of individual tragedies cannot be grasped in terms of evidence-based medicine.

Video-based quantification of body movement during social interaction indicates the severity of negative symptoms in patients with schizophrenia

In schizophrenia, nonverbal behavior, including body movement, is of theoretical and clinical importance. Although reduced nonverbal expressiveness is a major component of the negative symptoms encountered in schizophrenia, few studies have objectively assessed body movement during social interaction. In the present study, 378 brief, videotaped role-play scenes involving 27 stabilized outpatients diagnosed with paranoid-type schizophrenia were analyzed using Motion Energy Analysis (MEA). This method enables the objective measuring of body movement in conjunction with ordinary video recordings. Correlations between movement parameters (percentage of time in movement, movement speed) and symptom ratings from independent PANSS interviews were calculated. Movement parameters proved to be highly reliable. In keeping with predictions, reduced movement and movement speed correlated with negative symptoms. Accordingly, in patients who exhibited noticeable movement for less than 20% of the observation time, prominent negative symptoms were highly probable. As a control measure, the percentage of movement exhibited by the patients during role-play scenes was compared to that of their normal interactants. Patients with negative symptoms differed from normal interactants by showing significantly reduced head and body movement. Two specific positive symptoms were possibly related to movement parameters: suspiciousness tended to correlate with reduced head movement, and the expression of unusual thought content tended to relate to increased movement. Overall, a close and theoretically meaningful association between the objective movement parameters and the symptom profiles was found. MEA appears to be an objective, reliable and valid method for quantifying nonverbal behavior, an aspect which may furnish new insights into the processes related to reduced expressiveness in schizophrenia.

Tandem mass spectrometry identification and LC-MS quantification of intact cytokinin nucleotides in K-562 human leukemia cells

We describe here a new reversed-phase high-performance liquid chromatography with mass spectrometry detection method for quantifying intact cytokinin nucleotides in human K-562 leukemia cells. Tandem mass spectrometry was used to identify the intracellular metabolites (cytokinin monophosphorylated, diphosphorylated, and triphosphorylated nucleotides) in riboside-treated cells. For the protein precipitation and sample preparation, a trichloroacetic acid extraction method is used. Samples are then back-extracted with diethyl ether, lyophilized, reconstituted, and injected into the LC system. Analytes were quantified in negative selected ion monitoring mode using a single quadrupole mass spectrometer. The method was validated in terms of retention time stabilities, limits of detection, linearity, recovery, and analytical accuracy. The developed method was linear in the range of 1-1,000 pmol for all studied compounds. The limits of detection for the analytes vary from 0.2 to 0.6 pmol.

Feature-invariant image registration method for quantification of surgical outcomes in patients with craniosynostosis: a preliminary study

Craniosynostosis consists of a premature fusion of the sutures in an infant skull that restricts skull and brain growth. During the last decades, there has been a rapid increase of fundamentally diverse surgical treatment methods. At present, the surgical outcome has been assessed using global variables such as cephalic index, head circumference, and intracranial volume. However, these variables have failed in describing the local deformations and morphological changes that may have a role in the neurologic disorders observed in the patients. This report describes a rigid image registration-based method to evaluate outcomes of craniosynostosis surgical treatments, local quantification of head growth, and indirect intracranial volume change measurements. The developed semiautomatic analysis method was applied to computed tomography data sets of a 5-month-old boy with sagittal craniosynostosis who underwent expansion of the posterior skull with cranioplasty. Quantification of the local changes between pre- and postoperative images was quantified by mapping the minimum distance of individual points from the preoperative to the postoperative surface meshes, and indirect intracranial volume changes were estimated. The proposed methodology can provide the surgeon a tool for the quantitative evaluation of surgical procedures and detection of abnormalities of the infant skull and its development.