Impact of uncertainties in biometric parameters on intraocular lens power formula predicted refraction using a Monte-Carlo simulation

PURPOSE

The purpose of this study was to investigate the uncertainty in the formula predicted refractive outcome REFU after cataract surgery resulting from measurement uncertainties in modern optical biometers using literature data for within-subject standard deviation Sw.

METHODS

This Monte-Carlo simulation study used a large dataset containing 16 667 preoperative IOLMaster 700 biometric measurements. Based on literature Sw values, REFU was derived for both the Haigis and Castrop formulae using error propagation strategies. Using the Hoya Vivinex lens (IOL) as an example, REFU was calculated both with (WLT) and without (WoLT) consideration of IOL power labelling tolerances.

RESULTS

WoLT the median REFU was 0.10/0.12 dpt for the Haigis/Castrop formula, and WLT it was 0.13/0.15 dpt. WoLT REFU increased systematically for short eyes (or high power IOLs), and WLT this effect was even more pronounced because of increased labelling tolerances. WoLT the uncertainty in the measurement of the corneal front surface radius showed the largest contribution to REFU, especially in long eyes (and low power IOLs). WLT the IOL power uncertainty dominated in short eyes (or high power IOLs) and the uncertainty of the corneal front surface in long eyes (or low power IOLs).

CONCLUSIONS

Compared with published data on the formula prediction error of refractive outcome after cataract surgery, the uncertainty of biometric measures seems to contribute with ⅓ to ½ to the entire standard deviation. REFU systematically increases with IOL power and decreases with axial length.

Direct bioanalysis or indirect calculation of target engagement and free drug exposure: do we apply double standards?

Analysis of "free" drug/target concentrations is important to set up appropriate pharmacokinetic-pharmacodynamic models, to evaluate active-drug exposure and target engagement. Such "free-analyte" determination could be done by direct bioanalysis using an appropriate "free-analyte" assay. Development of "free" assays is often considered challenging from a technological and regulatory perspective. The application of a "total-total" approach, where the "free-analyte" concentration is determined mathematically, is considered a more convenient option. In this perspective, we examine and discuss the challenges of this "total-total" approach, from the affinity data, the importance of applying an appropriate "total" assay, the impact of additional binding partners and the variability of the total drug/target assays and their impact on the quality and variability of the final "free-analyte" dataset.

Simultaneous Measurement of Strain and Temperature Distributions Using Optical Fibers with Different GeO2 and B2O3 Doping

Compensating for the effects of temperature is a crucial issue in structural health monitoring when using optical fiber sensors. This study focused on the change in sensitivity due to differences in GeO2 and B2O3 doping and then verified the accuracy when measuring the strain and temperature distributions simultaneously. Four types of optical fiber sensors were utilized to measure the strain and temperature in four-point bending tests, and the best combination of the sensors resulted in strain and temperature errors of 28.4 μϵ and 1.52 °C, respectively. Based on the results obtained from the four-point bending tests, we discussed the error factors via an error propagation analysis. The results of the error propagation analysis agreed well with the experimental results, thus indicating the effectiveness of the analysis as a method for verifying accuracy and error factors.

Error quantification in multi-parameter mapping facilitates robust estimation and enhanced group level sensitivity

Multi-Parameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates R₁ and R₂^*, proton density PD, and magnetization transfer saturation MT_sat) that are sensitive to microstructural tissue properties such as iron and myelin content. Their capability to reveal microstructural brain differences, however, is tightly bound to controlling random noise and artefacts (e.g. caused by head motion) in the signal. Here, we introduced a method to estimate the local error of PD, R₁, and MT_sat maps that captures both noise and artefacts on a routine basis without requiring additional data. To investigate the method's sensitivity to random noise, we calculated the model-based signal-to-noise ratio (mSNR) and showed in measurements and simulations that it correlated linearly with an experimental raw-image-based SNR map. We found that the mSNR varied with MPM protocols, magnetic field strength (3T vs. 7T) and MPM parameters: it halved from PD to R₁ and decreased from PD to MT_sat by a factor of 3-4. Exploring the artefact-sensitivity of the error maps, we generated robust MPM parameters using two successive acquisitions of each contrast and the acquisition-specific errors to down-weight erroneous regions. The resulting robust MPM parameters showed reduced variability at the group level as compared to their single-repeat or averaged counterparts. The error and mSNR maps may better inform power-calculations by accounting for local data quality variations across measurements. Code to compute the mSNR maps and robustly combined MPM maps is available in the open-source hMRI toolbox.

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized by a conformally mapped generalized Polynomial Chaos (gPC) algorithm. The studied random deformations of the array are elliptical and are described by different Beta distributions. To successfully capture the erratic deviations in DOA estimates that occur at larger deformations, specifically at the edges of the distributions, a novel conformal map is introduced, based on the hyperbolic tangent function. The application of this new map is compared to regular gPC and Monte Carlo sampling as a reference. A significant increase in convergence rate is observed. The numerical experiments show that the UCA root-MUSIC algorithm is robust to the considered array deformations, since the resulting errors on the DOA estimates are limited to only 2 to 3 degrees in most cases.

Using Conventional Cameras as Sensors for Estimating Confidence Intervals for the Speed of Vessels from Single Images

In this paper, we describe an image-based approach for estimating the speed of a moving vessel using the wakes that remain on the surface of water after the vessel has passed. The proposed method calculates the speed of the vessel using only one RGB image. In this study, we used the vanishing line of the mean water plane, the camera height concerning the level of the tide, and the intrinsic parameters of the camera to perform geometric rectification on the surface plane of the water. We detected the location of troughs on one of the wake arms and computed the distance between them in the rectified image to estimate the speed of the vessel as a so-called inverse ship wake problem. We used a radar that was designed to monitor ships to validate the proposed method. We used statistical studies to determine the reliability and error propagation of the estimated values throughout the calculation process. The experiments showed that the proposed method produced precise and accurate results that agreed with the actual radar data when using a simple capture device, such as a conventional camera.

Optimizing the Energy Efficiency of Unreliable Memories for Quantized Kalman Filtering

This paper presents a quantized Kalman filter implemented using unreliable memories. We consider that both the quantization and the unreliable memories introduce errors in the computations, and we develop an error propagation model that takes into account these two sources of errors. In addition to providing updated Kalman filter equations, the proposed error model accurately predicts the covariance of the estimation error and gives a relation between the performance of the filter and its energy consumption, depending on the noise level in the memories. Then, since memories are responsible for a large part of the energy consumption of embedded systems, optimization methods are introduced to minimize the memory energy consumption under the desired estimation performance of the filter. The first method computes the optimal energy levels allocated to each memory bank individually, and the second one optimizes the energy allocation per groups of memory banks. Simulations show a close match between the theoretical analysis and experimental results. Furthermore, they demonstrate an important reduction in energy consumption of more than 50%.

Error Propagation in the Simulation of Atherosclerotic Plaque Growth and the Prediction of Atherosclerotic Disease Progression

Assessments of coronary artery disease can be achieved using non-invasive computed tomography coronary angiography (CTCA). CTCA can be further used for the 3D reconstruction of the coronary arteries and the development of computational models. However, image acquisition and arterial reconstruction introduce an error which can be propagated, affecting the computational results and the accuracy of diagnostic and prognostic models. In this work, we investigate the effect of an imaging error, propagated to a diagnostic index calculated using computational modelling of blood flow and then to prognostic models based on plaque growth modelling or binary logistic predictive modelling. The analysis was performed utilizing data from 20 patients collected at two time points with interscan period of six years. The collected data includes clinical and risk factors, biological and biohumoral data, and CTCA imaging. The results demonstrated that the error propagated and may have significantly affected some of the final outcomes. The calculated propagated error seemed to be minor for shear stress, but was major for some variables of the plaque growth model. In parallel, in the current analysis SmartFFR was not considerably affected, with the limitation of only one case located into the gray zone.

Using fractal self-similarity to increase precision of shrub biomass estimates

We show that aerial tips are self-similar fractals of whole shrubs and present a field method that applies this fact to improves accuracy and precision of biomass estimates of tall-shrubs, defined here as those with diameter at root collar (DRC) ≥ 2.5 cm. Power function allometry of biomass to stem diameter generates a disproportionate prediction error that increases rapidly with diameter. Thus, biomass should be modeled as a single measure of stem diameter only if stem diameter is less than a threshold Dmax . When stem diameter exceeds Dmax , then the stem internode should be treated as a conic frustrum requiring two additional measures: a second, node-adjacent diameter and a length. If the second diameter is less than Dmax , then the power function allometry can be applied to the aerial tip; otherwise an additional internode is measured. This "two-component" allometry-internodes as frustra and aerial tips as shrubs-can reduce estimated biomass error propagated to the plot-level by as much as 50% or more where very large shrubs are present Dmax is any diameter such that the ratio of single-component to two-component uncertainty exceeds the ratio of two-component to single-component measurement time. Guidelines for estimating Dmax based on pilot field data are provided. Tall shrubs are increasing in abundance and distribution across Arctic, alpine, boreal, and dryland ecosystems. Estimating their biomass is important for both ecological studies and carbon accounting. Reducing field-sample prediction error increases precision in multi-stage modeling because additional measures efficiently improve plot-level biomass precision, reducing uncertainty for shrub biomass estimates.

Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment.

Error propagation in constraint-based modeling of Chinese hamster ovary cells

Chinese hamster ovary (CHO) cells are the most popular mammalian cell factories for the production of glycosylated biopharmaceuticals. To further increase titer and productivity and ensure product quality, rational system-level engineering strategies based on constraint-based metabolic modeling, such as flux balance analysis (FBA), have gained strong interest. However, the quality of FBA predictions depends on the accuracy of the experimental input data, especially on the exchange rates of extracellular metabolites. Yet, it is not standard practice to devote sufficient attention to the accurate determination of these rates. In this work, we investigated to what degree the sampling frequency during a batch culture and the measurement errors of metabolite concentrations influence the accuracy of the calculated exchange rates and further, how this error then propagates into FBA predictions of growth rates. We determined that accurate measurements of essential amino acids with low uptake rates are crucial for the accuracy of FBA predictions, followed by a sufficient number of analyzed time points. We observed that the measured difference in growth rates of two cell lines can only be reliably predicted when both high measurement accuracy and sampling frequency are ensured.

Analytical Assessment of the Propagation of Colored Sensor Noise in Strapdown Inertial Navigation

Knowledge of the propagation of sensor errors in strapdown inertial navigation is crucial for the design of inertial and integrated navigation systems. The propagation of initialization errors and deterministic sensor errors is well covered in the literature. If considered at all, the propagation of inertial sensor noise has typically been assessed for un-correlated (white) Gaussian noise. Real inertial sensor noise, however, is time-correlated (colored) and best described by a combination of different stochastic processes. In this paper, we demonstrate how a navigation system's response to colored noise input differs from the response to bias-like or white noise inputs. We present a method for assessing the navigation error from various inertial sensor noise processes without the need for time-consuming Monte Carlo simulations and demonstrate its application and validity with real sensor data. The proposed method is used to determine in which scenarios the sensor's real noise can be approximated by simple white Gaussian noise. The results indicate that neglecting colored sensor noise is justified for many applications, but should be checked individually for each sensor configuration and mission.

Assessment of Position Repeatability Error in an Electromagnetic Tracking System for Surgical Navigation.Sensors (Basel). 2020;20. [PMID: 32053941 DOI: 10.3390/s20040961]

In this paper we present a study of the repeatability of an innovative electromagnetic tracking system (EMTS) for surgical navigation, developed to overcome the state of the art of current commercial systems, allowing for the placement of the magnetic field generator far from the operating table. Previous studies led to the development of a preliminary EMTS prototype. Several hardware improvements are described, which result in noise reduction in both signal generation and the measurement process, as shown by experimental tests. The analysis of experimental results has highlighted the presence of drift in voltage components, whose effect has been quantified and related to the variation of the sensor position. Repeatability in the sensor position measurement is evaluated by means of the propagation of the voltage repeatability error, and the results are compared with the performance of the Aurora system (which represents the state of the art for EMTS for surgical navigation), showing a repeatability error about ten times lower. Finally, the proposed improvements aim to overcome the limited operating distance between the field generator and electromagnetic (EM) sensors provided by commercial EM tracking systems for surgical applications and seem to provide a not negligible technological advantage.

Multispectral Sensor Calibration and Characterization for sUAS Remote Sensing

This paper focuses on the calibration of multispectral sensors typically used for remote sensing. These systems are often provided with “factory” radiometric calibration and vignette correction parameters. These parameters, which are assumed to be accurate when the sensor is new, may change as the camera is utilized in real-world conditions. As a result, regular calibration and characterization of any sensor should be conducted. An end-user laboratory method for computing both the vignette correction and radiometric calibration function is discussed in this paper. As an exemplar, this method for radiance computation is compared to the method provided by MicaSense for their RedEdge series of sensors. The proposed method and the method provided by MicaSense for radiance computation are applied to a variety of images captured in the laboratory using a traceable source. In addition, a complete error propagation is conducted to quantify the error produced when images are converted from digital counts to radiance. The proposed methodology was shown to produce lower errors in radiance imagery. The average percent error in radiance was −10.98%, −0.43%, 3.59%, 32.81% and −17.08% using the MicaSense provided method and their “factory” parameters, while the proposed method produced errors of 3.44%, 2.93%, 2.93%, 3.70% and 0.72% for the blue, green, red, near infrared and red edge bands, respectively. To further quantify the error in terms commonly used in remote sensing applications, the error in radiance was propagated to a reflectance error and additionally used to compute errors in two widely used parameters for assessing vegetation health, NDVI and NDRE. For the NDVI example, the ground reference was computed to be 0.899 ± 0.006, while the provided MicaSense method produced a value of 0.876 ± 0.005 and the proposed method produced a value of 0.897 ± 0.007. For NDRE, the ground reference was 0.455 ± 0.028, MicaSense method produced 0.239 ± 0.026 and the proposed method produced 0.435 ± 0.038.

Uncertainties in Model-Based Diesel Particulate Filter Diagnostics Using a Soot Sensor

Monitoring the filtration efficiency of the diesel particulate filter (DPF), is a legislative requirement for minimizing particulate matter (PM) emissions from diesel engines of passenger cars and heavy-duty vehicles. To reach this target, on-board diagnostics (OBD) in real-time operation are required. Such systems in passenger cars are often utilizing a soot sensor, models for PM emissions simulation and algorithms for diagnosis. Their performance is associated with a series of challenges related to the accuracy and effectiveness of involved models, algorithms and hardware. This paper analyzes the main influencing factors and their impact on the effectiveness of the OBD system. The followed method comprised an error propagation analysis to quantify the error of detection during a New European Driving Cycle (NEDC). The results of the study regarding the performance of the OBD model showed that the total error of diagnosis is ±28%. This performance can be improved by increasing the sensor accuracy and the soot model, which can make the model appropriate for even tighter legislation limits and other approaches such as on-board monitoring (OBM).

Optimization of b-value schemes for estimation of the diffusion coefficient and the perfusion fraction with segmented intravoxel incoherent motion model fitting

PURPOSE

Intravoxel incoherent motion (IVIM) modeling for estimation of the diffusion coefficient (D) and perfusion fraction (f) is increasingly popular, but no consensus on standard protocols exists. This study provides a framework for optimization of b-value schemes for reduced estimation uncertainty of D and f from segmented model fitting.

THEORY

Analytical expressions for uncertainties of D and f from segmented model fitting were derived as Cramer-Rao lower bounds (CRLBs).

METHODS

Optimized b-value schemes were obtained for 3 to 12 acquisitions and in the limit of infinitely many acquisitions through constrained minimization of the CRLBs, with b-values constrained to be 0 or 200 to 800 s/mm² . The optimized b-value scheme with eight acquisitions was compared with b-values linearly distributed in the allowed range using simulations and in vivo liver data from seven healthy volunteers.

RESULTS

All optimized b-value schemes contained exactly three unique b-values regardless of the total number of acquisitions (0, 200, and 800 s/mm² ) with repeated acquisitions distributed approximately as 1:2:2. Compared with linearly distributed b-values, the variability of estimates of D and f was reduced by approximately 30% as seen both in simulations and in repeated in vivo measurements.

CONCLUSION

The uncertainty of IVIM D and f estimates can be reduced by the use of optimized b-value schemes.

Effects of gleno-humeral joint centre mislocation on gleno-humeral kinematics and kinetics

The gleno-humeral (GH) rotation centre is typically estimated using predictive or functional methods, however these methods may lead to location errors. This study aimed at determining a location error threshold above which statistically significant changes in the values of kinematic and kinetic GH parameters occur. The secondary aims were to quantify the effects of the direction of mislocation (X, Y or Z axis) of the GH rotation centre on GH kinematic and kinetic parameters. Shoulder flexion and abduction movements of 11 healthy volunteers were recorded using a standard motion capture system (Vicon, Oxford Metrics Ltd, Oxford, UK), then GH kinematic and kinetic parameters were computed. The true position of the GH rotation centre was determined using a low dose x-ray scanner (EOS™ imaging, France) and this position was transferred to the motion data. GH angles and moments were re-computed for each position of the GH rotation centre after errors of up to ± 20 mm were added in increments of ± 5 mm to each axis. The three-dimensional error range was 5 mm to 34.65 mm. GH joint angle and moment values were significantly altered from 10 mm of three-dimensional error, and from 5 mm of error on individual axes. However, errors on the longitudinal and antero-posterior axes only caused very small alterations of GH joint angle and moment values respectively. Future research should develop methods of GH rotation centre estimation that produce three-dimensional location errors of less than 10 mm to reduce error propagation on GH kinematics and kinetics.

Error Budget for Geolocation of Spectroradiometer Point Observations from an Unmanned Aircraft System

We investigate footprint geolocation uncertainties of a spectroradiometer mounted on an unmanned aircraft system (UAS). Two microelectromechanical systems-based inertial measurement units (IMUs) and global navigation satellite system (GNSS) receivers were used to determine the footprint location and extent of the spectroradiometer. Errors originating from the on-board GNSS/IMU sensors were propagated through an aerial data georeferencing model, taking into account a range of values for the spectroradiometer field of view (FOV), integration time, UAS flight speed, above ground level (AGL) flying height, and IMU grade. The spectroradiometer under nominal operating conditions (8∘ FOV, 10 m AGL height, 0.6 s integration time, and 3 m/s flying speed) resulted in footprint extent of 140 cm across-track and 320 cm along-track, and a geolocation uncertainty of 11 cm. Flying height and orientation measurement accuracy had the largest influence on the geolocation uncertainty, whereas the FOV, integration time, and flying speed had the biggest impact on the size of the footprint. Furthermore, with an increase in flying height, the rate of increase in geolocation uncertainty was found highest for a low-grade IMU. To increase the footprint geolocation accuracy, we recommend reducing flying height while increasing the FOV which compensates the footprint area loss and increases the signal strength. The disadvantage of a lower flying height and a larger FOV is a higher sensitivity of the footprint size to changing distance from the target. To assist in matching the footprint size to uncertainty ratio with an appropriate spatial scale, we list the expected ratio for a range of IMU grades, FOVs and AGL heights.

Quantification of Intrinsically Disordered Proteins: A Problem Not Fully Appreciated

Protein quantification is essential in a great variety of biochemical assays, yet the inherent systematic errors associated with the concentration determination of intrinsically disordered proteins (IDPs) using classical methods are hardly appreciated. Routinely used assays for protein quantification, such as the Bradford assay or ultraviolet absorbance at 280 nm, usually seriously misestimate the concentrations of IDPs due to their distinct and variable amino acid composition. Therefore, dependable method(s) have to be worked out/adopted for this task. By comparison to elemental analysis as the gold standard, we show through the example of four globular proteins and nine IDPs that the ninhydrin assay and the commercial Qubit^TM Protein Assay provide reliable data on IDP quantity. However, as IDPs can show extreme variation in amino acid composition and physical features not necessarily covered by our examples, even these techniques should only be used for IDPs following standardization. The far-reaching implications of these simple observations are demonstrated through two examples: (i) circular dichroism spectrum deconvolution, and (ii) receptor-ligand affinity determination. These actual comparative examples illustrate the potential errors that can be incorporated into the biophysical parameters of IDPs, due to systematic misestimation of their concentration. This leads to inaccurate description of IDP functions.

Data-Driven Hazardous Gas Dispersion Modeling Using the Integration of Particle Filtering and Error Propagation Detection

The accurate prediction of hazardous gas dispersion process is essential to air quality monitoring and the emergency management of contaminant gas leakage incidents in a chemical cluster. Conventional Gaussian-based dispersion models can seldom give accurate predictions due to inaccurate input parameters and the computational errors. In order to improve the prediction accuracy of a dispersion model, a data-driven air dispersion modeling method based on data assimilation is proposed by applying particle filter to Gaussian-based dispersion model. The core of the method is continually updating dispersion coefficients by assimilating observed data into the model during the calculation process. Another contribution of this paper is that error propagation detection rules are proposed to evaluate their effects since the measured and computational errors are inevitable. So environmental protection authorities can be informed to what extent the model output is of high confidence. To test the feasibility of our method, a numerical experiment utilizing the SF₆ concentration data sampled from an Indianapolis field study is conducted. Results of accuracy analysis and error inspection imply that Gaussian dispersion models based on particle filtering and error propagation detection have better performance than traditional dispersion models in practice though sacrificing some computational efficiency.

The Application of Social Characteristic and L1 Optimization in the Error Correction for Network Coding in Wireless Sensor Networks

One of the remarkable challenges about Wireless Sensor Networks (WSN) is how to transfer the collected data efficiently due to energy limitation of sensor nodes. Network coding will increase network throughput of WSN dramatically due to the broadcast nature of WSN. However, the network coding usually propagates a single original error over the whole network. Due to the special property of error propagation in network coding, most of error correction methods cannot correct more than C/2 corrupted errors where C is the max flow min cut of the network. To maximize the effectiveness of network coding applied in WSN, a new error-correcting mechanism to confront the propagated error is urgently needed. Based on the social network characteristic inherent in WSN and L1 optimization, we propose a novel scheme which successfully corrects more than C/2 corrupted errors. What is more, even if the error occurs on all the links of the network, our scheme also can correct errors successfully. With introducing a secret channel and a specially designed matrix which can trap some errors, we improve John and Yi’s model so that it can correct the propagated errors in network coding which usually pollute exactly 100% of the received messages. Taking advantage of the social characteristic inherent in WSN, we propose a new distributed approach that establishes reputation-based trust among sensor nodes in order to identify the informative upstream sensor nodes. With referred theory of social networks, the informative relay nodes are selected and marked with high trust value. The two methods of L1 optimization and utilizing social characteristic coordinate with each other, and can correct the propagated error whose fraction is even exactly 100% in WSN where network coding is performed. The effectiveness of the error correction scheme is validated through simulation experiments.

Data Quality and Assessment, Validation Methods and Error Propagation through the Simulation Software: Report from the Round-Table Discussion at the 10th World Congress of Chemical Engineering in Barcelona (October 1-5, 2017)

The issues of data quality and propagation of data uncertainties into process design and plant specifications are of great current interest. Hence, two Working Parties of the European Federation of Chemical Engineers (EFCE) organized a Round Table Discussion on the topic, as part of the World Congress of Chemical Engineering (WCCE10) in Barcelona, in October 2017. The discussion was guided by industrial and academic experts, with the audience as a key part of the discussion, trying to find some answers in three areas: Data acquisition and evaluation of experimental uncertainties, tools for data reconciliation to improve their quality, and impact of data uncertainties on the process at the end. Several concrete stories are presented that demonstrate the importance of considering data quality and all possible contributions to the uncertainty of chemical process design. Difficulties associated with data quality are discussed at various levels: (1) the experimentalists (measurement issues, evaluation of uncertainties, use of consistency analysis tools); (2) model developers (capture of adequate physics, parameter regression strategies, uncertainty propagation), (3) vendors of process simulation software, and (4) process engineers (who are responsible at the end). Paths for improvements were proposed through better and more efficient communication among different participants, as well as through education.

Analysis of the Precision of Variable Flip Angle T1 Mapping with Emphasis on the Noise Propagated from RF Transmit Field Maps

In magnetic resonance imaging, precise measurements of longitudinal relaxation time (T₁) is crucial to acquire useful information that is applicable to numerous clinical and neuroscience applications. In this work, we investigated the precision of T₁ relaxation time as measured using the variable flip angle method with emphasis on the noise propagated from radiofrequency transmit field ([Formula: see text]) measurements. The analytical solution for T₁ precision was derived by standard error propagation methods incorporating the noise from the three input sources: two spoiled gradient echo (SPGR) images and a [Formula: see text] map. Repeated in vivo experiments were performed to estimate the total variance in T₁ maps and we compared these experimentally obtained values with the theoretical predictions to validate the established theoretical framework. Both the analytical and experimental results showed that variance in the [Formula: see text] map propagated comparable noise levels into the T₁ maps as either of the two SPGR images. Improving precision of the [Formula: see text] measurements significantly reduced the variance in the estimated T₁ map. The variance estimated from the repeatedly measured in vivoT₁ maps agreed well with the theoretically-calculated variance in T₁ estimates, thus validating the analytical framework for realistic in vivo experiments. We concluded that for T₁ mapping experiments, the error propagated from the [Formula: see text] map must be considered. Optimizing the SPGR signals while neglecting to improve the precision of the [Formula: see text] map may result in grossly overestimating the precision of the estimated T₁ values.

A Theoretical Analysis for Assessing the Variability of Secondary Model Thermal Inactivation Kinetic Parameters

Traditionally, for the determination of the kinetic parameters of thermal inactivation of a heat labile substance, an appropriate index is selected and its change is measured over time at a series of constant temperatures. The rate of this change is described through an appropriate primary model and a secondary model is applied to assess the impact of temperature. By this approach, the confidence intervals of the estimates of the rate constants are not taken into account. Consequently, the calculated variability of the secondary model parameters can be significantly lower than the actual variability. The aim of this study was to demonstrate the influence of the variability of the primary model parameters in establishing the confidence intervals of the secondary model parameters. Using a Monte Carlo technique and assuming normally distributed DT values (parameter associated with a primary inactivation model), the error propagating on the DTref and z-values (secondary model parameters) was assessed. When DT confidence intervals were broad, the secondary model's parameter variability was appreciably high and could not be adequately estimated through the traditional deterministic approach that does not take into account the variation on the DT values. In such cases, the proposed methodology was essential for realistic estimations.

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Data-driven optimized flip angle selection for T1 estimation from spoiled gradient echo acquisitions

PURPOSE

Define criteria for selection of optimal flip angle sets for T1 estimation and evaluate effects on T1 mapping.

THEORY AND METHODS

Flip angle sets for spoiled gradient echo-based T1 mapping were selected by minimizing T1 estimate variance weighted by the joint density of M0 and T1 in an initial acquisition. The effect of optimized flip angle selection on T1 estimate error was measured using simulations and experimental data in the human and rat brain.

RESULTS

For two-point acquisitions, optimized angle sets were similar to those proposed by other groups and, therefore, performed similarly. For multipoint acquisitions, optimal angle sets for T1 mapping in the brain consisted of a repetition of two angles. Implementation of optimal angles reduced T1 estimate variance by 30-40% compared with a multipoint acquisition using a range of angles. Performance of the optimal angle set was equivalent to that of a repetition of the two-angle set selected using criteria proposed by other researchers.

CONCLUSION

Repetition of two carefully selected flip angles notably improves the precision of resulting T1 estimates compared with acquisitions using a range of flip angles. This work provides a flexible and widely applicable optimization method of particular use for those who repeatedly perform T1 estimation. Magn Reson Med 76:792-802, 2016. © 2015 Wiley Periodicals, Inc.

Use of exocentric and egocentric representations in the concurrent planning of sequential saccades

The concurrent planning of sequential saccades offers a simple model to study the nature of visuomotor transformations since the second saccade vector needs to be remapped to foveate the second target following the first saccade. Remapping is thought to occur through egocentric mechanisms involving an efference copy of the first saccade that is available around the time of its onset. In contrast, an exocentric representation of the second target relative to the first target, if available, can be used to directly code the second saccade vector. While human volunteers performed a modified double-step task, we examined the role of exocentric encoding in concurrent saccade planning by shifting the first target location well before the efference copy could be used by the oculomotor system. The impact of the first target shift on concurrent processing was tested by examining the end-points of second saccades following a shift of the second target during the first saccade. The frequency of second saccades to the old versus new location of the second target, as well as the propagation of first saccade localization errors, both indices of concurrent processing, were found to be significantly reduced in trials with the first target shift compared to those without it. A similar decrease in concurrent processing was obtained when we shifted the first target but kept constant the second saccade vector. Overall, these results suggest that the brain can use relatively stable visual landmarks, independent of efference copy-based egocentric mechanisms, for concurrent planning of sequential saccades.

Maximum likelihood estimation of FRET efficiency and its implications for distortions in pixelwise calculation of FRET in microscopy

Ratiometric determination of the efficiency of fluorescence or Förster resonance energy transfer (FRET) is one of the most widespread methods for the characterization of protein clustering and conformation. Low photon numbers, often present in pixel-by-pixel determination of FRET efficiency in digital microscopy, result in large uncertainties in the derived FRET parameter. Here, we propose a method based on maximum likelihood estimation (MLE) of FRET efficiency using photon counting detectors to overcome this limitation. Intensities measured in the donor, FRET, and acceptor channels were all assumed to follow Poisson statistics as a result of detector shot noise. The joint probability of photon numbers detected in the donor, FRET, and acceptor channels was derived using an equation describing the relationship between the three measured intensities. The FRET efficiency generating the measured photon numbers with the largest likelihood was determined iteratively providing a single FRET value for all pixels in the calculation. Since as few as 100 pixels are sufficient to provide a maximum likelihood estimate for FRET, biological variability in FRET values can be revealed by performing the analysis for regions of interests in an image. Since the algorithm provides the probability of a combination of donor, FRET, and acceptor intensities observed in each individual pixel given a certain FRET efficiency, outlier pixels with low probabilities could be excluded from the analysis. Simulations carried out with low photon numbers in the presence and absence of outlier pixels revealed that the proposed approach can reliably and reproducibly estimate FRET efficiency. In addition, systematic evaluation of the simulation results showed that the distribution of pixel-by-pixel FRET efficiencies is skewed, and the mean of these FRET values is a biased and unreliable estimate of the FRET efficiency. In the absence of outlier pixels, FRET calculated from summed donor, FRET, and acceptor intensities proved to be as reliable as MLE. We conclude that MLE of FRET outperforms calculations using summed and pixel-by-pixel intensities in biologically relevant situations involving low photon numbers and outlier pixels. © 2014 International Society for Advancement of Cytometry.

The sensitivity of backscattering coefficients to elastic scattering cross-sections and electron stopping powers

The sensitivity of Monte Carlo estimates of backscattering coefficients η to the accuracy of their input data is examined by studying the percentage change in η due to changes of 10% and 20% in the differential elastic scattering cross-section dσ/dΩ and corresponding changes in the stopping power S(E) in the primary energy range 200-10,000 eV. To a good approximation equivalent elastic and inelastic scattering changes produce equal and opposite shifts in η, a result consistent with predictions of transport theory. For medium to high atomic numbers an x% error in the specification of either S(E) or dσ/dΩ produces a percentage change in η significantly less than x%, while at low atomic number Δη/η increases approximately linearly with ln E so that Monte Carlo predictions are then more sensitive to parameter precision at high energy.

Error Analysis and Propagation in Metabolomics Data Analysis

Error analysis plays a fundamental role in describing the uncertainty in experimental results. It has several fundamental uses in metabolomics including experimental design, quality control of experiments, the selection of appropriate statistical methods, and the determination of uncertainty in results. Furthermore, the importance of error analysis has grown with the increasing number, complexity, and heterogeneity of measurements characteristic of 'omics research. The increase in data complexity is particularly problematic for metabolomics, which has more heterogeneity than other omics technologies due to the much wider range of molecular entities detected and measured. This review introduces the fundamental concepts of error analysis as they apply to a wide range of metabolomics experimental designs and it discusses current methodologies for determining the propagation of uncertainty in appropriate metabolomics data analysis. These methodologies include analytical derivation and approximation techniques, Monte Carlo error analysis, and error analysis in metabolic inverse problems. Current limitations of each methodology with respect to metabolomics data analysis are also discussed.

On the translational error theory of aging

Theoretical treatments of error feedback in translation have revealed that two different modes of behavior are possible, depending on the values of certain parameters. In mode I, the error frequency will rise steadily toward randomness, inevitably reaching whatever value is catastrophic for cell survival; the "error catastrophe" theory of aging implicitly assumes this mode of behavior. In mode II, the error frequency will converge to a stable value, which may or may not have toxic consequences. We have performed an experimental test of the behavior of the translation system in Escherichia coli cells: we altered the system's intrinsic fidelity by means of the error-promoting drug streptomycin, and monitored the kinetics of change in error frequency by means of a specific assay of one kind of mistranslation (incorporation of cysteine into flagellin). We find that the system behaves according to mode II. Moreover, E. coli cells in which the error frequency has stabilized at a value as high as 50 times greater than normal continue to proliferate, albeit abnormally slowly, and their viability is not detectably reduced. Earlier results by Gorini and his associates point in the same direction. These observations diminish the plausibility of the error catastrophe theory of aging.