Benchmarking therapeutic drug monitoring software: A review of available computer tools

Therapeutic drug monitoring (TDM) aims to optimize treatments by individualizing dosage regimens based on the measurement of blood concentrations. Dosage individualization to maintain concentrations within a target range requires pharmacokinetic and clinical capabilities. Bayesian calculations currently represent the gold standard TDM approach but require computation assistance. In recent decades computer programs have been developed to assist clinicians in this assignment. The aim of this survey was to assess and compare computer tools designed to support TDM clinical activities. The literature and the Internet were searched to identify software. All programs were tested on personal computers. Each program was scored against a standardized grid covering pharmacokinetic relevance, user friendliness, computing aspects, interfacing and storage. A weighting factor was applied to each criterion of the grid to account for its relative importance. To assess the robustness of the software, six representative clinical vignettes were processed through each of them. Altogether, 12 software tools were identified, tested and ranked, representing a comprehensive review of the available software. Numbers of drugs handled by the software vary widely (from two to 180), and eight programs offer users the possibility of adding new drug models based on population pharmacokinetic analyses. Bayesian computation to predict dosage adaptation from blood concentration (a posteriori adjustment) is performed by ten tools, while nine are also able to propose a priori dosage regimens, based only on individual patient covariates such as age, sex and bodyweight. Among those applying Bayesian calculation, MM-USC*PACK© uses the non-parametric approach. The top two programs emerging from this benchmark were MwPharm© and TCIWorks. Most other programs evaluated had good potential while being less sophisticated or less user friendly. Programs vary in complexity and might not fit all healthcare settings. Each software tool must therefore be regarded with respect to the individual needs of hospitals or clinicians. Programs should be easy and fast for routine activities, including for non-experienced users. Computer-assisted TDM is gaining growing interest and should further improve, especially in terms of information system interfacing, user friendliness, data storage capability and report generation.

Interpretation of partial fingermarks using an automated fingerprint identification system

Abstract : In the subject of fingerprints, the rise of computers tools made it possible to create powerful automated search algorithms. These algorithms allow, inter alia, to compare a fingermark to a fingerprint database and therefore to establish a link between the mark and a known source. With the growth of the capacities of these systems and of data storage, as well as increasing collaboration between police services on the international level, the size of these databases increases. The current challenge for the field of fingerprint identification consists of the growth of these databases, which makes it possible to find impressions that are very similar but coming from distinct fingers. However and simultaneously, this data and these systems allow a description of the variability between different impressions from a same finger and between impressions from different fingers. This statistical description of the withinand between-finger variabilities computed on the basis of minutiae and their relative positions can then be utilized in a statistical approach to interpretation. The computation of a likelihood ratio, employing simultaneously the comparison between the mark and the print of the case, the within-variability of the suspects' finger and the between-variability of the mark with respect to a database, can then be based on representative data. Thus, these data allow an evaluation which may be more detailed than that obtained by the application of rules established long before the advent of these large databases or by the specialists experience. The goal of the present thesis is to evaluate likelihood ratios, computed based on the scores of an automated fingerprint identification system when the source of the tested and compared marks is known. These ratios must support the hypothesis which it is known to be true. Moreover, they should support this hypothesis more and more strongly with the addition of information in the form of additional minutiae. For the modeling of within- and between-variability, the necessary data were defined, and acquired for one finger of a first donor, and two fingers of a second donor. The database used for between-variability includes approximately 600000 inked prints. The minimal number of observations necessary for a robust estimation was determined for the two distributions used. Factors which influence these distributions were also analyzed: the number of minutiae included in the configuration and the configuration as such for both distributions, as well as the finger number and the general pattern for between-variability, and the orientation of the minutiae for within-variability. In the present study, the only factor for which no influence has been shown is the orientation of minutiae The results show that the likelihood ratios resulting from the use of the scores of an AFIS can be used for evaluation. Relatively low rates of likelihood ratios supporting the hypothesis known to be false have been obtained. The maximum rate of likelihood ratios supporting the hypothesis that the two impressions were left by the same finger when the impressions came from different fingers obtained is of 5.2 %, for a configuration of 6 minutiae. When a 7th then an 8th minutia are added, this rate lowers to 3.2 %, then to 0.8 %. In parallel, for these same configurations, the likelihood ratios obtained are on average of the order of 100,1000, and 10000 for 6,7 and 8 minutiae when the two impressions come from the same finger. These likelihood ratios can therefore be an important aid for decision making. Both positive evolutions linked to the addition of minutiae (a drop in the rates of likelihood ratios which can lead to an erroneous decision and an increase in the value of the likelihood ratio) were observed in a systematic way within the framework of the study. Approximations based on 3 scores for within-variability and on 10 scores for between-variability were found, and showed satisfactory results. Résumé : Dans le domaine des empreintes digitales, l'essor des outils informatisés a permis de créer de puissants algorithmes de recherche automatique. Ces algorithmes permettent, entre autres, de comparer une trace à une banque de données d'empreintes digitales de source connue. Ainsi, le lien entre la trace et l'une de ces sources peut être établi. Avec la croissance des capacités de ces systèmes, des potentiels de stockage de données, ainsi qu'avec une collaboration accrue au niveau international entre les services de police, la taille des banques de données augmente. Le défi actuel pour le domaine de l'identification par empreintes digitales consiste en la croissance de ces banques de données, qui peut permettre de trouver des impressions très similaires mais provenant de doigts distincts. Toutefois et simultanément, ces données et ces systèmes permettent une description des variabilités entre différentes appositions d'un même doigt, et entre les appositions de différents doigts, basées sur des larges quantités de données. Cette description statistique de l'intra- et de l'intervariabilité calculée à partir des minuties et de leurs positions relatives va s'insérer dans une approche d'interprétation probabiliste. Le calcul d'un rapport de vraisemblance, qui fait intervenir simultanément la comparaison entre la trace et l'empreinte du cas, ainsi que l'intravariabilité du doigt du suspect et l'intervariabilité de la trace par rapport à une banque de données, peut alors se baser sur des jeux de données représentatifs. Ainsi, ces données permettent d'aboutir à une évaluation beaucoup plus fine que celle obtenue par l'application de règles établies bien avant l'avènement de ces grandes banques ou par la seule expérience du spécialiste. L'objectif de la présente thèse est d'évaluer des rapports de vraisemblance calcul és à partir des scores d'un système automatique lorsqu'on connaît la source des traces testées et comparées. Ces rapports doivent soutenir l'hypothèse dont il est connu qu'elle est vraie. De plus, ils devraient soutenir de plus en plus fortement cette hypothèse avec l'ajout d'information sous la forme de minuties additionnelles. Pour la modélisation de l'intra- et l'intervariabilité, les données nécessaires ont été définies, et acquises pour un doigt d'un premier donneur, et deux doigts d'un second donneur. La banque de données utilisée pour l'intervariabilité inclut environ 600000 empreintes encrées. Le nombre minimal d'observations nécessaire pour une estimation robuste a été déterminé pour les deux distributions utilisées. Des facteurs qui influencent ces distributions ont, par la suite, été analysés: le nombre de minuties inclus dans la configuration et la configuration en tant que telle pour les deux distributions, ainsi que le numéro du doigt et le dessin général pour l'intervariabilité, et la orientation des minuties pour l'intravariabilité. Parmi tous ces facteurs, l'orientation des minuties est le seul dont une influence n'a pas été démontrée dans la présente étude. Les résultats montrent que les rapports de vraisemblance issus de l'utilisation des scores de l'AFIS peuvent être utilisés à des fins évaluatifs. Des taux de rapports de vraisemblance relativement bas soutiennent l'hypothèse que l'on sait fausse. Le taux maximal de rapports de vraisemblance soutenant l'hypothèse que les deux impressions aient été laissées par le même doigt alors qu'en réalité les impressions viennent de doigts différents obtenu est de 5.2%, pour une configuration de 6 minuties. Lorsqu'une 7ème puis une 8ème minutie sont ajoutées, ce taux baisse d'abord à 3.2%, puis à 0.8%. Parallèlement, pour ces mêmes configurations, les rapports de vraisemblance sont en moyenne de l'ordre de 100, 1000, et 10000 pour 6, 7 et 8 minuties lorsque les deux impressions proviennent du même doigt. Ces rapports de vraisemblance peuvent donc apporter un soutien important à la prise de décision. Les deux évolutions positives liées à l'ajout de minuties (baisse des taux qui peuvent amener à une décision erronée et augmentation de la valeur du rapport de vraisemblance) ont été observées de façon systématique dans le cadre de l'étude. Des approximations basées sur 3 scores pour l'intravariabilité et sur 10 scores pour l'intervariabilité ont été trouvées, et ont montré des résultats satisfaisants.

Benchmarking therapeutic drug monitoring software: A systematic evaluation of available computer tools

Introduction: Therapeutic drug monitoring (TDM) aims at optimizing treatment by individualizing dosage regimen based on measurement of blood concentrations. Maintaining concentrations within a target range requires pharmacokinetic and clinical capabilities. Bayesian calculation represents a gold standard in TDM approach but requires computing assistance. In the last decades computer programs have been developed to assist clinicians in this assignment. The aim of this benchmarking was to assess and compare computer tools designed to support TDM clinical activities.¦Method: Literature and Internet search was performed to identify software. All programs were tested on common personal computer. Each program was scored against a standardized grid covering pharmacokinetic relevance, user-friendliness, computing aspects, interfacing, and storage. A weighting factor was applied to each criterion of the grid to consider its relative importance. To assess the robustness of the software, six representative clinical vignettes were also processed through all of them.¦Results: 12 software tools were identified, tested and ranked. It represents a comprehensive review of the available software's characteristics. Numbers of drugs handled vary widely and 8 programs offer the ability to the user to add its own drug model. 10 computer programs are able to compute Bayesian dosage adaptation based on a blood concentration (a posteriori adjustment) while 9 are also able to suggest a priori dosage regimen (prior to any blood concentration measurement), based on individual patient covariates, such as age, gender, weight. Among those applying Bayesian analysis, one uses the non-parametric approach. The top 2 software emerging from this benchmark are MwPharm and TCIWorks. Other programs evaluated have also a good potential but are less sophisticated (e.g. in terms of storage or report generation) or less user-friendly.¦Conclusion: Whereas 2 integrated programs are at the top of the ranked listed, such complex tools would possibly not fit all institutions, and each software tool must be regarded with respect to individual needs of hospitals or clinicians. Interest in computing tool to support therapeutic monitoring is still growing. Although developers put efforts into it the last years, there is still room for improvement, especially in terms of institutional information system interfacing, user-friendliness, capacity of data storage and report generation.

Benchmarking therapeutic drug monitoring software: A systematic evaluation of available computer tools

Objectives: Therapeutic drug monitoring (TDM) aims at optimizing treatment by individualizing dosage regimen based on blood concentrations measurement. Maintaining concentrations within a target range requires pharmacokinetic (PK) and clinical capabilities. Bayesian calculation represents a gold standard in TDM approach but requires computing assistance. The aim of this benchmarking was to assess and compare computer tools designed to support TDM clinical activities.¦Methods: Literature and Internet were searched to identify software. Each program was scored against a standardized grid covering pharmacokinetic relevance, user-friendliness, computing aspects, interfacing, and storage. A weighting factor was applied to each criterion of the grid to consider its relative importance. To assess the robustness of the software, six representative clinical vignettes were also processed through all of them.¦Results: 12 software tools were identified, tested and ranked. It represents a comprehensive review of the available software characteristics. Numbers of drugs handled vary from 2 to more than 180, and integration of different population types is available for some programs. Nevertheless, 8 programs offer the ability to add new drug models based on population PK data. 10 computer tools incorporate Bayesian computation to predict dosage regimen (individual parameters are calculated based on population PK models). All of them are able to compute Bayesian a posteriori dosage adaptation based on a blood concentration while 9 are also able to suggest a priori dosage regimen, only based on individual patient covariates. Among those applying Bayesian analysis, MM-USC*PACK uses a non-parametric approach. The top 2 programs emerging from this benchmark are MwPharm and TCIWorks. Others programs evaluated have also a good potential but are less sophisticated or less user-friendly.¦Conclusions: Whereas 2 software packages are ranked at the top of the list, such complex tools would possibly not fit all institutions, and each program must be regarded with respect to individual needs of hospitals or clinicians. Programs should be easy and fast for routine activities, including for non-experienced users. Although interest in TDM tools is growing and efforts were put into it in the last years, there is still room for improvement, especially in terms of institutional information system interfacing, user-friendliness, capability of data storage and automated report generation.

Mynodbcsv: Lightweight Zero-Config Database Solution for Handling Very Large CSV Files.

Volumes of data used in science and industry are growing rapidly. When researchers face the challenge of analyzing them, their format is often the first obstacle. Lack of standardized ways of exploring different data layouts requires an effort each time to solve the problem from scratch. Possibility to access data in a rich, uniform manner, e.g. using Structured Query Language (SQL) would offer expressiveness and user-friendliness. Comma-separated values (CSV) are one of the most common data storage formats. Despite its simplicity, with growing file size handling it becomes non-trivial. Importing CSVs into existing databases is time-consuming and troublesome, or even impossible if its horizontal dimension reaches thousands of columns. Most databases are optimized for handling large number of rows rather than columns, therefore, performance for datasets with non-typical layouts is often unacceptable. Other challenges include schema creation, updates and repeated data imports. To address the above-mentioned problems, I present a system for accessing very large CSV-based datasets by means of SQL. It's characterized by: "no copy" approach - data stay mostly in the CSV files; "zero configuration" - no need to specify database schema; written in C++, with boost [1], SQLite [2] and Qt [3], doesn't require installation and has very small size; query rewriting, dynamic creation of indices for appropriate columns and static data retrieval directly from CSV files ensure efficient plan execution; effortless support for millions of columns; due to per-value typing, using mixed text/numbers data is easy; very simple network protocol provides efficient interface for MATLAB and reduces implementation time for other languages. The software is available as freeware along with educational videos on its website [4]. It doesn't need any prerequisites to run, as all of the libraries are included in the distribution package. I test it against existing database solutions using a battery of benchmarks and discuss the results.

Clinical neurophysiology in disorders of consciousness: brain function monitoring in the ICU and beyond.

Over the past two decades, electrophysiology has undergone unprecedented changes thanks to technical improvements, which simplify measurement and analysis and allow more compact data storage. This book covers in detail the spectrum of electrophysiology applications in patients with disorders of consciousness. Its content spans from clinical aspects of the management of subjects in the intensive care unit, including EEG, evoked potentials and related implications in terms of prognosis and patient management to research applications in subjects with ongoing consciousness impairment. While the first section provides up-to-date information for the interested clinician, the second part highlights the latest developments in this exciting field. The book comprehensively combines clinical and research information related to neurophysiology in disorder-of- consciousness patients, making it an easily accessible reference for neuro-ICU specialists, epileptologists and clinical neurophysiologists as well as researchers utilizing EEG and event-related potentials.

Numerical analysis of wave-induced fluid flow effects on seismic data: Application to monitoring of CO2 storage at the Sleipner Field

In this work we analyze how patchy distributions of CO2 and brine within sand reservoirs may lead to significant attenuation and velocity dispersion effects, which in turn may have a profound impact on surface seismic data. The ultimate goal of this paper is to contribute to the understanding of these processes within the framework of the seismic monitoring of CO2 sequestration, a key strategy to mitigate global warming. We first carry out a Monte Carlo analysis to study the statistical behavior of attenuation and velocity dispersion of compressional waves traveling through rocks with properties similar to those at the Utsira Sand, Sleipner field, containing quasi-fractal patchy distributions of CO2 and brine. These results show that the mean patch size and CO2 saturation play key roles in the observed wave-induced fluid flow effects. The latter can be remarkably important when CO2 concentrations are low and mean patch sizes are relatively large. To analyze these effects on the corresponding surface seismic data, we perform numerical simulations of wave propagation considering reservoir models and CO2 accumulation patterns similar to the CO2 injection site in the Sleipner field. These numerical experiments suggest that wave-induced fluid flow effects may produce changes in the reservoir's seismic response, modifying significantly the main seismic attributes usually employed in the characterization of these environments. Consequently, the determination of the nature of the fluid distributions as well as the proper modeling of the seismic data constitute important aspects that should not be ignored in the seismic monitoring of CO2 sequestration problems.

Prospective motion correction of 3D echo-planar imaging data for functional MRI using optical tracking.

We evaluated the performance of an optical camera based prospective motion correction (PMC) system in improving the quality of 3D echo-planar imaging functional MRI data. An optical camera and external marker were used to dynamically track the head movement of subjects during fMRI scanning. PMC was performed by using the motion information to dynamically update the sequence's RF excitation and gradient waveforms such that the field-of-view was realigned to match the subject's head movement. Task-free fMRI experiments on five healthy volunteers followed a 2×2×3 factorial design with the following factors: PMC on or off; 3.0mm or 1.5mm isotropic resolution; and no, slow, or fast head movements. Visual and motor fMRI experiments were additionally performed on one of the volunteers at 1.5mm resolution comparing PMC on vs PMC off for no and slow head movements. Metrics were developed to quantify the amount of motion as it occurred relative to k-space data acquisition. The motion quantification metric collapsed the very rich camera tracking data into one scalar value for each image volume that was strongly predictive of motion-induced artifacts. The PMC system did not introduce extraneous artifacts for the no motion conditions and improved the time series temporal signal-to-noise by 30% to 40% for all combinations of low/high resolution and slow/fast head movement relative to the standard acquisition with no prospective correction. The numbers of activated voxels (p<0.001, uncorrected) in both task-based experiments were comparable for the no motion cases and increased by 78% and 330%, respectively, for PMC on versus PMC off in the slow motion cases. The PMC system is a robust solution to decrease the motion sensitivity of multi-shot 3D EPI sequences and thereby overcome one of the main roadblocks to their widespread use in fMRI studies.

Toward interoperable bioscience data.

To make full use of research data, the bioscience community needs to adopt technologies and reward mechanisms that support interoperability and promote the growth of an open 'data commoning' culture. Here we describe the prerequisites for data commoning and present an established and growing ecosystem of solutions using the shared 'Investigation-Study-Assay' framework to support that vision.

Comparability of clinical wear measurements by optical 3D laser scanning in two different centers.

OBJECTIVE: The purpose of this study was to compare the use of different variables to measure the clinical wear of two denture tooth materials in two analysis centers. METHODS: Twelve edentulous patients were provided with full dentures. Two different denture tooth materials (experimental material and control) were placed randomly in accordance with the split-mouth design. For wear measurements, impressions were made after an adjustment phase of 1-2 weeks and after 6, 12, 18, and 24 months. The occlusal wear of the posterior denture teeth of 11 subjects was assessed in two study centers by use of plaster replicas and 3D laser-scanning methods. In both centers sequential scans of the occlusal surfaces were digitized and superimposed. Wear was described by use of four different variables. Statistical analysis was performed after log-transformation of the wear data by use of the Pearson and Lin correlation and by use of a mixed linear model. RESULTS: Mean occlusal vertical wear of the denture teeth after 24 months was between 120μm and 212μm, depending on wear variable and material. For three of the four variables, wear of the experimental material was statistically significantly less than that of the control. Comparison of the two study centers, however, revealed correlation of the wear variables was only moderate whereas strong correlation was observed among the different wear variables evaluated by each center. SIGNIFICANCE: Moderate correlation was observed for clinical wear measurements by optical 3D laser scanning in two different study centers. For the two denture tooth materials, wear measurements limited to the attrition zones led to the same qualitative assessment.

Gene expression databases and data mining.

The DNA microarray technology has arguably caught the attention of the worldwide life science community and is now systematically supporting major discoveries in many fields of study. The majority of the initial technical challenges of conducting experiments are being resolved, only to be replaced with new informatics hurdles, including statistical analysis, data visualization, interpretation, and storage. Two systems of databases, one containing expression data and one containing annotation data are quickly becoming essential knowledge repositories of the research community. This present paper surveys several databases, which are considered "pillars" of research and important nodes in the network. This paper focuses on a generalized workflow scheme typical for microarray experiments using two examples related to cancer research. The workflow is used to reference appropriate databases and tools for each step in the process of array experimentation. Additionally, benefits and drawbacks of current array databases are addressed, and suggestions are made for their improvement.

Conditioning of stochastic 3-D fracture networks to hydrological and geophysical data

The geometry and connectivity of fractures exert a strong influence on the flow and transport properties of fracture networks. We present a novel approach to stochastically generate three-dimensional discrete networks of connected fractures that are conditioned to hydrological and geophysical data. A hierarchical rejection sampling algorithm is used to draw realizations from the posterior probability density function at different conditioning levels. The method is applied to a well-studied granitic formation using data acquired within two boreholes located 6 m apart. The prior models include 27 fractures with their geometry (position and orientation) bounded by information derived from single-hole ground-penetrating radar (GPR) data acquired during saline tracer tests and optical televiewer logs. Eleven cross-hole hydraulic connections between fractures in neighboring boreholes and the order in which the tracer arrives at different fractures are used for conditioning. Furthermore, the networks are conditioned to the observed relative hydraulic importance of the different hydraulic connections by numerically simulating the flow response. Among the conditioning data considered, constraints on the relative flow contributions were the most effective in determining the variability among the network realizations. Nevertheless, we find that the posterior model space is strongly determined by the imposed prior bounds. Strong prior bounds were derived from GPR measurements and helped to make the approach computationally feasible. We analyze a set of 230 posterior realizations that reproduce all data given their uncertainties assuming the same uniform transmissivity in all fractures. The posterior models provide valuable statistics on length scales and density of connected fractures, as well as their connectivity. In an additional analysis, effective transmissivity estimates of the posterior realizations indicate a strong influence of the DFN structure, in that it induces large variations of equivalent transmissivities between realizations. The transmissivity estimates agree well with previous estimates at the site based on pumping, flowmeter and temperature data.

Multi-modal Change Detection, Application to the Detection of Flooded Areas: Outcome of the 2009-2010 data fusion contest

The 2009-2010 Data Fusion Contest organized by the Data Fusion Technical Committee of the IEEE Geoscience and Remote Sensing Society was focused on the detection of flooded areas using multi-temporal and multi-modal images. Both high spatial resolution optical and synthetic aperture radar data were provided. The goal was not only to identify the best algorithms (in terms of accuracy), but also to investigate the further improvement derived from decision fusion. This paper presents the four awarded algorithms and the conclusions of the contest, investigating both supervised and unsupervised methods and the use of multi-modal data for flood detection. Interestingly, a simple unsupervised change detection method provided similar accuracy as supervised approaches, and a digital elevation model-based predictive method yielded a comparable projected change detection map without using post-event data.

Fracture imaging within a granitic rock aquifer using multiple-offset single-hole and cross-hole GPR reflection data

The sparsely spaced highly permeable fractures of the granitic rock aquifer at Stang-er-Brune (Brittany, France) form a well-connected fracture network of high permeability but unknown geometry. Previous work based on optical and acoustic logging together with single-hole and cross-hole flowmeter data acquired in 3 neighbouring boreholes (70-100 m deep) has identified the most important permeable fractures crossing the boreholes and their hydraulic connections. To constrain possible flow paths by estimating the geometries of known and previously unknown fractures, we have acquired, processed and interpreted multifold, single- and cross-hole GPR data using 100 and 250 MHz antennas. The GPR data processing scheme consisting of timezero corrections, scaling, bandpass filtering and F-X deconvolution, eigenvector filtering, muting, pre-stack Kirchhoff depth migration and stacking was used to differentiate fluid-filled fracture reflections from source generated noise. The final stacked and pre-stack depth-migrated GPR sections provide high-resolution images of individual fractures (dipping 30-90°) in the surroundings (2-20 m for the 100 MHz antennas; 2-12 m for the 250 MHz antennas) of each borehole in a 2D plane projection that are of superior quality to those obtained from single-offset sections. Most fractures previously identified from hydraulic testing can be correlated to reflections in the single-hole data. Several previously unknown major near vertical fractures have also been identified away from the boreholes.

On the use of spatially discrete data to compute energy and mass balance

In many practical applications the state of field soils is monitored by recording the evolution of temperature and soil moisture at discrete depths. We theoretically investigate the systematic errors that arise when mass and energy balances are computed directly from these measurements. We show that, even with no measurement or model errors, large residuals might result when finite difference approximations are used to compute fluxes and storage term. To calculate the limits set by the use of spatially discrete measurements on the accuracy of balance closure, we derive an analytical solution to estimate the residual on the basis of the two key parameters: the penetration depth and the distance between the measurements. When the thickness of the control layer for which the balance is computed is comparable to the penetration depth of the forcing (which depends on the thermal diffusivity and on the forcing period) large residuals arise. The residual is also very sensitive to the distance between the measurements, which requires accurately controlling the position of the sensors in field experiments. We also demonstrate that, for the same experimental setup, mass residuals are sensitively larger than the energy residuals due to the nonlinearity of the moisture transport equation. Our analysis suggests that a careful assessment of the systematic mass error introduced by the use of spatially discrete data is required before using fluxes and residuals computed directly from field measurements.