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Background: Cognitive impairment is common in multiple sclerosis (MS). Interpretation of neuropsychological tests requires the use of normative data. Traditionally, normative data have been reported for discrete categories such as age. More recently continuous norms have been developed using multivariable regression equations that account for multiple demographic factors. Regression-based norms have been developed for use in the Canadian population for tests included in the MACFIMS and BICAMS test batteries. Establishing the generalizability of these norms is essential for application in clinical and research settings.Objectives: We aimed to (i) test the performance of previously published Canadian regression-based norms in an independently collected sample of Canadian healthy controls; (ii) compare the ability of Canadian and non-Canadian regression-based norms to discriminate between healthy controls and persons with MS; and (iii) develop regression-based norms for several cognitive tests drawn from batteries commonly used in MS that incorporated race/ethnicity in addition to age, education, and sex.Methods: We included 93 adults with MS and 96 healthy adults in this study, with a replication sample of 104 (MS) and 39 (healthy adults). Participants reported their sociodemographic characteristics, and each was administered the oral Symbol Digit Modalities Test (SDMT), the California Verbal Learning Test (CVLT-II), and the Brief Visuospatial Memory Test-Revised (BVMT-R). From the healthy control data, we developed regression-based norms incorporating race, age, education and sex. We then applied existing discrete norms and regression-based norms for the cognitive tests to the healthy controls, and generated z-scores which were compared using Spearman rank and concordance coefficients. We also used receiver operating characteristic (ROC) curves to compare the ability of each set of norms to discriminate between participants with and without MS. Within the MS samples we compared the ability of each set of norms to discriminate between differing levels of disability and employment status using relative efficiency.Results: When we applied the published regression norms to our healthy sample, impairment classification rates often differed substantially from expectations (7%), even when the norms were derived from a Canadian (Ontario) population. Most, but not all of the Spearman correlations between z-scores based on different existing published norms for the same cognitive test exceeded 0.90. However, concordance coefficients were often lower. All of the norms for the SDMT reliably discriminated between the MS and healthy control groups. In contrast, none of the norms for the CVLT-II or BVMT-R discriminated between the MS and healthy control groups. Within the MS population, the norms varied in their ability to discriminate between disability levels or employment status; locally developed norms for the SDMT and CVLT-II had the highest relative efficiency.Conclusion: Our findings emphasize the value of local norms when interpreting the results of cognitive tests and demonstrate the need to consider and assess the performance of regression-based norms developed in other populations when applying them to local populations, even when they are from the same country. Our findings also strongly suggest that the development of regression-based norms should involve larger, more diverse samples to ensure broad generalizability.

Explicit mechanisms describing the complex degradation pathways of atmospheric volatile organic compounds (VOCs) are important, since they allow the study of the contribution of individual VOCS to secondary pollutant formation. They are computationally expensive to solve however, since they contain large numbers of species and a wide range of time-scales causing stiffness in the resulting equation systems. This paper and the following companion paper describe the application of systematic and automated methods for reducing such complex mechanisms, whilst maintaining the accuracy of the model with respect to important species and features. The methods are demonstrated via application to version 2 of the Leeds Master Chemical Mechanism. The methods of Jacobian analysis and overall rate sensitivity analysis proved to be efficient and capable of removing the majority of redundant reactions and species in the scheme across a wide range of conditions relevant to the polluted troposphere. The application of principal component analysis of the rate sensitivity matrix was computationally expensive due to its use of the decomposition of very large matrices, and did not produce significant reduction over and above the other sensitivity methods. The use of the quasi-steady state approximation (QSSA) proved to be an extremely successful method of removing the fast time-scales within the system, as demonstrated by a local perturbation analysis at each stage of reduction. QSSA species were automatically selected via the calculation of instantaneous QSSA errors based on user-selected tolerances. The application of the QSSA led to the removal of a large number of alkoxy radicals and excited Criegee bi-radicals via reaction lumping. The resulting reduced mechanism was shown to reproduce the concentration profiles of the important species selected from the full mechanism over a wide range of conditions, including those outside of which the reduced mechanism was generated. As a result of a reduction in the number of species in the scheme of a factor of 2, and a reduction in stiffness, the computational time required for simulations was reduced by a factor of 4 when compared to the full scheme.

This paper presents a formal method of species lumping that can be applied automatically to intermediate compounds within detailed and complex tropospheric chemical reaction schemes. The method is based on grouping species with reference to their chemical lifetimes and reactivity structures. A method for determining the forward and reverse transformations between individual and lumped compounds is developed. Preliminary application to the Leeds Master Chemical Mechanism (MCMv2.0) has led to the removal of 734 species and 1777 reactions from the scheme, with minimal degradation of accuracy across a wide range of test trajectories relevant to polluted tropospheric conditions. The lumped groups are seen to relate to groups of peroxy acyl nitrates, nitrates, carbonates, oxepins, substituted phenols, oxeacids and peracids with similar lifetimes and reaction rates with OH. In combination with other reduction techniques, such as sensitivity analysis and the application of the quasi-steady state approximation (QSSA), a reduced mechanism has been developed that contains 35% of the number of species and 40% of the number of reactions compared to the full mechanism. This has led to a speed up of a factor of 8 in terms of computer calculation time within box model simulations.