Transconvolution and the virtual positron emission tomograph--a new method for cross calibration in quantitative PET∕CT imaging

PURPOSE Positron emission tomography (PET)∕computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET∕CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET∕CT in the context of multicenter trials. METHODS To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET∕CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET∕CT systems, a dedicated solid-state phantom incorporating (68)Ge∕(68)Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET∕CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. RESULTS The proposed Transconvolution method matched different PET∕CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. CONCLUSIONS By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.

Cardiovascular magnetization transfer ratio imaging compared with histology: A postmortem study

Cardiovascular magnetization transfer ratio (MTR) imaging by steady state free precession is a promising imaging method to assess microstructural changes within the myocardium. Hence, MTR imaging was correlated to histological analysis. Three postmortem cases were selected based on a suspicion of myocardial infarction. MTR and T2 -weighted (T2w ) imaging was performed, followed by autopsy and histological analysis. All tissue abnormalities, identified by autopsy or histology, were retrospectively selected on visually matched MTR and T2w images, and corresponding MTR values compared with normal appearing tissue. Regions of elevated MTR (up to approximately 20%, as compared to normal tissue), appearing hypo-intense in T2w -images, revealed the presence of fibrous tissue in microscopic histological analysis. Macroscopic observation (autopsy) described scar tissue only in one case. Regions of reduced MTR (up to approximately 20%) corresponded either to (i) the presence of edema, appearing hyperintense in T2w -images and confirmed by autopsy, or to (ii) inflammatory granulocyte infiltration at a microscopic level, appearing as hypo-intense T2w -signal, but not observed by autopsy. Findings from cardiovascular MTR imaging corresponded to histology results. In contrast to T2w -imaging, MTR imaging discriminated between normal myocardium, scar tissue and regions of acute myocardial infarction in all three cases. J. Magn. Reson. Imaging 2013. © 2013 Wiley Periodicals, Inc.

A hybrid method for large-scale short-term scheduling of make-and-pack production processes

Due to the ongoing trend towards increased product variety, fast-moving consumer goods such as food and beverages, pharmaceuticals, and chemicals are typically manufactured through so-called make-and-pack processes. These processes consist of a make stage, a pack stage, and intermediate storage facilities that decouple these two stages. In operations scheduling, complex technological constraints must be considered, e.g., non-identical parallel processing units, sequence-dependent changeovers, batch splitting, no-wait restrictions, material transfer times, minimum storage times, and finite storage capacity. The short-term scheduling problem is to compute a production schedule such that a given demand for products is fulfilled, all technological constraints are met, and the production makespan is minimised. A production schedule typically comprises 500–1500 operations. Due to the problem size and complexity of the technological constraints, the performance of known mixed-integer linear programming (MILP) formulations and heuristic approaches is often insufficient. We present a hybrid method consisting of three phases. First, the set of operations is divided into several subsets. Second, these subsets are iteratively scheduled using a generic and flexible MILP formulation. Third, a novel critical path-based improvement procedure is applied to the resulting schedule. We develop several strategies for the integration of the MILP model into this heuristic framework. Using these strategies, high-quality feasible solutions to large-scale instances can be obtained within reasonable CPU times using standard optimisation software. We have applied the proposed hybrid method to a set of industrial problem instances and found that the method outperforms state-of-the-art methods.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

Virtual tissue alignment and cutting plane definition--a new method to obtain optimal longitudinal histological sections.

Histomorphometric evaluation of the buccal aspects of periodontal tissues in rodents requires reproducible alignment of maxillae and highly precise sections containing central sections of buccal roots; this is a cumbersome and technically sensitive process due to the small specimen size. The aim of the present report is to describe and analyze a method to transfer virtual sections of micro-computer tomographic (CT)-generated image stacks to the microtome for undecalcified histological processing and to describe the anatomy of the periodontium in rat molars. A total of 84 undecalcified sections of all buccal roots of seven untreated rats was analyzed. The accuracy of section coordinate transfer from virtual micro-CT slice to the histological slice, right-left side differences and the measurement error for linear and angular measurements on micro-CT and on histological micrographs were calculated using the Bland-Altman method, interclass correlation coefficient and the method of moments estimator. Also, manual alignment of the micro-CT-scanned rat maxilla was compared with multiplanar computer-reconstructed alignment. The supra alveolar rat anatomy is rather similar to human anatomy, whereas the alveolar bone is of compact type and the keratinized gingival epithelium bends apical to join the junctional epithelium. The high methodological standardization presented herein ensures retrieval of histological slices with excellent display of anatomical microstructures, in a reproducible manner, minimizes random errors, and thereby may contribute to the reduction of number of animals needed.

The modified coronally advanced tunnel combined with an enamel matrix derivative and subepithelial connective tissue graft for the treatment of isolated mandibular Miller Class I and II gingival recessions: a report of 16 cases.

OBJECTIVES To clinically evaluate the healing of mandibular Miller Class I and II isolated gingival recessions treated with the modified coronally advanced tunnel (MCAT) in conjunction with an enamel matrix derivative (EMD) and subepithelial connective tissue graft (SCTG). METHOD AND MATERIALS Sixteen healthy patients (13 women and 3 men) exhibiting one isolated mandibular Miller Class I and II gingival recessions of a depth of ≥ 3 mm, were consecutively treated with the MCAT in conjunction with EMD and SCTG. Treatment outcomes were assessed at baseline and at 12 months postoperatively. The primary outcome variable was complete root coverage (CRC) (eg, 100% root coverage). RESULTS Postoperative pain and discomfort were low and no complications such as postoperative bleeding, allergic reactions, abscesses, or loss of SCTG were observed. At 12 months, statistically significant (P < .0001) root coverage was obtained in all 16 defects. CRC was measured in 12 out of the 16 cases (75%) while in the remaining 4 defects root coverage amounted to 90% (in two cases) and 80% (in two cases), respectively. Mean root coverage was 96.25%. Mean keratinized tissue width increased from 1.98 ± 0.8 mm at baseline to 2.5 ± 0.9 mm (P < .0001) at 12 months, while mean probing depth did not show any statistically significant changes (ie, 1.9 ± 0.3 mm at baseline vs 1.8 ± 0.2 mm at 12 months). CONCLUSION Within their limits, the present results indicate that the described treatment approach may lead to predictable root coverage of isolated mandibular Miller Class I and II gingival recessions.

Temporal evolution of strut light intensity after implantation of bioresorbable polymeric intracoronary scaffolds in the ABSORB cohort B trial-an application of a new quantitative method based on optical coherence tomography.

BACKGROUND Quantitative light intensity analysis of the strut core by optical coherence tomography (OCT) may enable assessment of changes in the light reflectivity of the bioresorbable polymeric scaffold from polymer to provisional matrix and connective tissues, with full disappearance and integration of the scaffold into the vessel wall. The aim of this report was to describe the methodology and to apply it to serial human OCT images post procedure and at 6, 12, 24 and 36 months in the ABSORB cohort B trial. METHODS AND RESULTS In serial frequency-domain OCT pullbacks, corresponding struts at different time points were identified by 3-dimensional foldout view. The peak and median values of light intensity were measured in the strut core by dedicated software. A total of 303 corresponding struts were serially analyzed at 3 time points. In the sequential analysis, peak light intensity increased gradually in the first 24 months after implantation and reached a plateau (relative difference with respect to baseline [%Dif]: 61.4% at 12 months, 115.0% at 24 months, 110.7% at 36 months), while the median intensity kept increasing at 36 months (%Dif: 14.3% at 12 months, 75.0% at 24 months, 93.1% at 36 months). CONCLUSIONS Quantitative light intensity analysis by OCT was capable of detecting subtle changes in the bioresorbable strut appearance over time, and could be used to monitor the bioresorption and integration process of polylactide struts.

Comparison of (31)P saturation and inversion magnetization transfer in human liver and skeletal muscle using a clinical MR system and surface coils.

(31)P MRS magnetization transfer ((31)P-MT) experiments allow the estimation of exchange rates of biochemical reactions, such as the creatine kinase equilibrium and adenosine triphosphate (ATP) synthesis. Although various (31)P-MT methods have been successfully used on isolated organs or animals, their application on humans in clinical scanners poses specific challenges. This study compared two major (31)P-MT methods on a clinical MR system using heteronuclear surface coils. Although saturation transfer (ST) is the most commonly used (31)P-MT method, sequences such as inversion transfer (IT) with short pulses might be better suited for the specific hardware and software limitations of a clinical scanner. In addition, small NMR-undetectable metabolite pools can transfer MT to NMR-visible pools during long saturation pulses, which is prevented with short pulses. (31)P-MT sequences were adapted for limited pulse length, for heteronuclear transmit-receive surface coils with inhomogeneous B1 , for the need for volume selection and for the inherently low signal-to-noise ratio (SNR) on a clinical 3-T MR system. The ST and IT sequences were applied to skeletal muscle and liver in 10 healthy volunteers. Monte-Carlo simulations were used to evaluate the behavior of the IT measurements with increasing imperfections. In skeletal muscle of the thigh, ATP synthesis resulted in forward reaction constants (k) of 0.074 ± 0.022 s(-1) (ST) and 0.137 ± 0.042 s(-1) (IT), whereas the creatine kinase reaction yielded 0.459 ± 0.089 s(-1) (IT). In the liver, ATP synthesis resulted in k = 0.267 ± 0.106 s(-1) (ST), whereas the IT experiment yielded no consistent results. ST results were close to literature values; however, the IT results were either much larger than the corresponding ST values and/or were widely scattered. To summarize, ST and IT experiments can both be implemented on a clinical body scanner with heteronuclear transmit-receive surface coils; however, ST results are much more robust against experimental imperfections than the current implementation of IT.

Experimental and Calculated Spectra of π-Stacked Mild Charge-Transfer Complexes: Jet-Cooled Perylene·(Tetrachloroethene) n , n = 1,2

The S0 ↔ S1 spectra of the mild charge-transfer (CT) complexes perylene·tetrachloroethene (P·4ClE) and perylene·(tetrachloroethene)2 (P·(4ClE)2) are investigated by two-color resonant two-photon ionization (2C-R2PI) and dispersed fluorescence spectroscopy in supersonic jets. The S0 → S1 vibrationless transitions of P·4ClE and P·(4ClE)2 are shifted by δν = −451 and −858 cm–1 relative to perylene, translating to excited-state dissociation energy increases of 5.4 and 10.3 kJ/mol, respectively. The red shift is ∼30% larger than that of perylene·trans-1,2-dichloroethene; therefore, the increase in chlorination increases the excited-state stabilization and CT character of the interaction, but the electronic excitation remains largely confined to the perylene moiety. The 2C-R2PI and fluorescence spectra of P·4ClE exhibit strong progressions in the perylene intramolecular twist (1au) vibration (42 cm–1 in S0 and 55 cm–1 in S1), signaling that perylene deforms along its twist coordinate upon electronic excitation. The intermolecular stretching (Tz) and internal rotation (Rc) vibrations are weak; therefore, the P·4ClE intermolecular potential energy surface (IPES) changes little during the S0 ↔ S1 transition. The minimum-energy structures and inter- and intramolecular vibrational frequencies of P·4ClE and P·(4ClE)2 are calculated with the dispersion-corrected density functional theory (DFT) methods B97-D3, ωB97X-D, M06, and M06-2X and the spin-consistent-scaled (SCS) variant of the approximate second-order coupled-cluster method, SCS-CC2. All methods predict the global minima to be π-stacked centered coplanar structures with the long axis of tetrachloroethene rotated by τ ≈ 60° relative to the perylene long axis. The calculated binding energies are in the range of −D0 = 28–35 kJ/mol. A second minimum is predicted with τ ≈ 25°, with ∼1 kJ/mol smaller binding energy. Although both monomers are achiral, both the P·4ClE and P·(4ClE)2 complexes are chiral. The best agreement for adiabatic excitation energies and vibrational frequencies is observed for the ωB97X-D and M06-2X DFT methods.

Development of a rapid column-switching LC-MS/MS method for the quantification of THCCOOH and THCCOOH-glucuronide in whole blood for assessing cannabis consumption frequency

The concentration of 11-nor-9-carboxy-Δ(9)-tetrahydrocannabinol (THCCOOH) in whole blood is used as a parameter for assessing the consumption behavior of cannabis consumers. The blood level of THCCOOH-glucuronide might provide additional information about the frequency of cannabis use. To verify this assumption, a column-switching liquid chromatography-tandem mass spectrometry (LC-MS/MS) method for the rapid and direct quantification of free and glucuronidated THCCOOH in human whole blood was newly developed. The method comprised protein precipitation, followed by injection of the processed sample onto a trapping column and subsequent gradient elution to an analytical column for separation and detection. The total LC run time was 4.5 min. Detection of the analytes was accomplished by electrospray ionization in positive ion mode and selected reaction monitoring using a triple-stage quadrupole mass spectrometer. The method was fully validated by evaluating the following parameters: linearity, lower limit of quantification, accuracy and imprecision, selectivity, extraction efficiency, matrix effect, carry-over, dilution integrity, analyte stability, and re-injection reproducibility. All acceptance criteria were analyzed and the predefined criteria met. Linearity ranged from 5.0 to 500 μg/L for both analytes. The method was successfully applied to whole blood samples from a large collective of cannabis consumers, demonstrating its applicability in the forensic field.

Circulating matrix metalloproteinase 9 levels in relation to sampling methods, femoral and carotid atherosclerosis.

OBJECTIVES To examine whether circulating levels of matrix metalloproteinase 9 (MMP-9) were associated with ultrasound-assessed intima-media thickness (IMT) and echolucent plaques in the carotid and femoral arteries. To examine preanalytical sources of variability in MMP-9 concentrations related to sampling procedures. SUBJECTS AND DESIGN Plasma and serum MMP-9 levels were compared with ultrasound assessed measures of femoral and carotid atherosclerosis, in a cross-sectional study of 61-year-old men (n = 473). Preanalytical sources of variability in MMP-9 levels were examined in 10 healthy subjects. Main outcome measures were circulating levels of MMP-9 in serum and plasma, IMT of the carotid and femoral arteries, and plaque status based on size and echolucency. SETTING Research unit at university hospital. RESULTS Plasma concentrations of total and active MMP-9 were associated with femoral artery IMT independently of traditional cardiovascular risk factors, and were higher in subjects with moderate to large femoral plaques. Plasma MMP-9 concentration was higher in men with echolucent femoral plaques (P = 0.006) compared with subjects without femoral plaques. No similar associations were found for carotid plaques. MMP-9 concentrations were higher in serum than in plasma, and higher when sampling was performed with Vacutainer than with syringe. MMP-9 levels in serum were more strongly associated with peripheral neutrophil count compared with MMP-9 levels in plasma. CONCLUSIONS Plasma MMP-9 levels were associated with atherosclerosis in the femoral artery, and total MMP-9 concentration was higher in men with echolucent femoral plaques. The choice of sample material and sampling method affect the measurements of circulating MMP-9 levels.

1D.03: Inactive Matrix Gla Protein is Assocated with Renal Resistive Index in a Population-Based Study

OBJECTIVE Renal resistive index (RRI) varies directly with renal vascular stiffness and pulse pressure. RRI correlates positively with arteriolosclerosis in damaged kidneys and predicts progressive renal dysfunction. Matrix Gla-protein (MGP) is a vascular calcification inhibitor that needs vitamin K to be activated. Inactive MGP, known as desphospho-uncarboxylated MGP (dp-ucMGP), can be measured in plasma and has been associated with various cardiovascular (CV) markers, CV outcomes and mortality. In this study we hypothesize that increased RRI is associated with high levels of dp-ucMGP. DESIGN AND METHOD We recruited participants via a multi-center family-based cross-sectional study in Switzerland exploring the role of genes and kidney hemodynamics in blood pressure regulation. Dp-ucMGP was quantified in plasma samples by sandwich ELISA. Renal doppler sonography was performed using a standardized protocol to measure RRIs on 3 segmental arteries in each kidney. The mean of the 6 measures was reported. Multiple regression analysis was performed to estimate associations between RRI and dp-ucMGP adjusting for sex, age, pulse pressure, mean pressure, renal function and other CV risk factors. RESULTS We included 1035 participants in our analyses. Mean values were 0.64 ± 0.06 for RRI and 0.44 ± 0.21 (nmol/L) for dp-ucMGP. RRI was positively associated with dp-ucMGP both before and after adjustment for sex, age, body mass index, pulse pressure, mean pressure, heart rate, renal function, low and high density lipoprotein, smoking status, diabetes, blood pressure and cholesterol lowering drugs, and history of CV disease (P < 0.001). CONCLUSIONS RRI is independently and positively associated with high levels of dp-ucMGP after adjustment for pulse pressure and common CV risk factors. Further studies are needed to determine if vitamin K supplementation can have a positive effect on renal vascular stiffness and kidney function.

Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.

Influence of sample matrix on the alkaline extraction of Cr(VI) in soils and industrial materials

An accurate and efficient determination of the highly toxic Cr(VI) in solid materials is important to determine the total Cr(VI) inventory of contaminated sites and the Cr(VI) release potential from such sites into the environment. Most commonly, total Cr(VI) is extracted from solid materials following a hot alkaline extraction procedure (US EPA method 3060A) where a complete release of water-extractable and sparingly soluble Cr(VI) phase is achieved. This work presents an evaluation of matrix effects that may occur during the hot alkaline extraction and in the determination of the total Cr(VI) inventory of variably composed contaminated soils and industrial materials (cement, fly ash) and is compared to water-extractable Cr(VI) results. Method validation including multiple extractions and matrix spiking along with chemical and mineralogical characterization showed satisfying results for total Cr(VI) contents for most of the tested materials. However, unreliable results were obtained by applying method 3060A to anoxic soils due to the degradation of organic material and/or reactions with Fe2+-bearing mineral phases. In addition, in certain samples discrepant spike recoveries have to be also attributed to sample heterogeneity. Separation of possible extracted Cr(III) by applying cation-exchange cartridges prior to solution analysis further shows that under the hot alkaline extraction conditions only Cr(VI) is present in solution in measurable amounts, whereas Cr(III) gets precipitated as amorphous Cr(OH)3(am). It is concluded that prior to routine application of method 3060A to a new material type, spiking tests are recommended for the identification of matrix effects. In addition, the mass of extracted solid material should to be well adjusted to the heterogeneity of the Cr(VI) distribution in the material in question.

Using the contribution matrix to evaluate complex study limitations in a network meta-analysis: a case study of bipolar maintenance pharmacotherapy review.

BACKGROUND Limitations in the primary studies constitute one important factor to be considered in the grading of recommendations assessment, development, and evaluation (GRADE) system of rating quality of evidence. However, in the network meta-analysis (NMA), such evaluation poses a special challenge because each network estimate receives different amounts of contributions from various studies via direct as well as indirect routes and because some biases have directions whose repercussion in the network can be complicated. FINDINGS In this report we use the NMA of maintenance pharmacotherapy of bipolar disorder (17 interventions, 33 studies) and demonstrate how to quantitatively evaluate the impact of study limitations using netweight, a STATA command for NMA. For each network estimate, the percentage of contributions from direct comparisons at high, moderate or low risk of bias were quantified, respectively. This method has proven flexible enough to accommodate complex biases with direction, such as the one due to the enrichment design seen in some trials of bipolar maintenance pharmacotherapy. CONCLUSIONS Using netweight, therefore, we can evaluate in a transparent and quantitative manner how study limitations of individual studies in the NMA impact on the quality of evidence of each network estimate, even when such limitations have clear directions.