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PubMed2005

Predicting clinical variable from MRI features: application to MMSE in MCI.

The ability to predict a clinical variable from automated analysis of single, cross-sectional T1-weighted (T1w) MR scans stands to improve the management of patients with neurological diseases. We present a methodology for predicting yearly Mini-Mental Score Examination (MMSE) changes in Mild Cognitive Impairment (MCI) patients. We begin by generating a non-pathological, multidimensional reference space from a group of 152 healthy volunteers by Principal Component Analyses of (i) T1w MR intensity of linearly registered Volumes of Interest (VOI); and (ii) trace of the deformation fields of nonlinearly registered VOIs. We use multiple regression to build linear models from eigenvectors where the projection eigencoordinates of patient data in the reference space are highly correlated with the clinical variable of interest. In our cohort of 47 MCI patients, composed of 16 decliners, 26 stable and 5 improvers (based on MMSE at 1 yr follow-up), there was a significant difference (P = 0.0003) for baseline MMSE scores between decliners and improvers, but no other differences based on age or sex. First, we classified our three groups using leave-one-out, forward stepwise linear discriminant analyses of the projection eigencoordinates with 100% accuracy. Next, we compared various linear models by computing F-statistics on the residuals of predicted vs actual values. The best model was based on 10 eigenvectors + baseline MMSE, with predicted yearly changes highly correlated (r = 0.6955) with actual data. Prospective study of an independent cohort of patients is the next logical step towards establishing this promising technique for clinical use.

Artificial Intelligence↗

PubMed2000

[A field study of health effects of aircraft noise in adults around Komatsu Air Base (1998)].

OBJECTIVE: To ascertain the effects of aircraft noise on complaints about life disturbances and on psychological and physical symptoms in adults around Komatsu air base. METHODS: From April to June 1998, a questionnaire was answered by 203 persons (from 89.8% of families) in 2 areas without aircraft noise, and by 412 persons (from 89.0% of families) in 5 areas with a weighted equivalent continuous perceived noise level (WECPNL) of 75 or more. The questionnaire covered age, gender, work location, noise exposure time, past experience with noisy work and ear disease, complaints about noisiness and life disturbances, and psychological and physical symptoms. Multivariate linear models by JMP (SAS institute Inc.) were applied to analyze the relationships between the above factors including noise level and complaints or symptoms. RESULTS: Subjects in the areas with noise had more complaints about noisiness than 5 years before, although replies were less in areas without noise. Subjects in areas with a WECPNL of 75 or more had more complaints and symptoms than those in areas without noise. Moreover, subjects experiencing higher noise levels gave higher responses for most of complaints and symptoms. The JMP linear models showed that aircraft noise was positively related to complaints and symptoms after taking the effects of age, gender and past experience with noisy work and ear disease into consideration. Higher noise levels and longer exposure times were related more strongly to most complaints and symptoms. CONCLUSION: This study shows that aircraft noise with a WECPNL of 75 or more is related to various complaints and psychological and physical symptoms in adults around Komatsu air base, after considering the effects of age, gender and past experience with noisy work and ear disease. It also shows that higher noise levels and longer exposure times are related more strongly to many complaints and symptoms. The results also suggest that responses to aircraft noise have become more severe than in the past.

Adult↗

PubMed1998

Trait-based analysis in dairy cattle using blood group polymorphisms.

The potential of trait-based analysis to detect quantitative trait loci was investigated using blood group polymorphisms as the marker systems and milk and type traits in Holstein cattle as the quantitative traits. Within large half-sib families, animals were ranked on their predicted transmitted abilities or phenotypes, and blood group allele frequencies were compared between the upper and lower 5% tails of the distributions. Genotype frequencies within large families were also examined for evidence of selection. All of the major effects that had previously been detected using linear model analyses were identified by the trait-based analyses of a C blood group effect on rump angle, an L effect on milk yield and composition traits, an S effect on milk fat yield, and a direct effect of the M locus on milk and protein yields. These results provide additional support for the biological validity of these associations and also demonstrate the utility of trait-based analysis for the detection of quantitative trait loci within existing dairy breeding programs. However, just as in the linear model analyses, an analytical strategy should be utilized that allows the identification of the effects that are consistent across environments and genetic backgrounds.

Alleles↗

PubMed2000

Prediction of rates of inbreeding in populations selected on best linear unbiased prediction of breeding value.

Predictions for the rate of inbreeding (DeltaF) in populations with discrete generations undergoing selection on best linear unbiased prediction (BLUP) of breeding value were developed. Predictions were based on the concept of long-term genetic contributions using a recently established relationship between expected contributions and rates of inbreeding and a known procedure for predicting expected contributions. Expected contributions of individuals were predicted using a linear model, u(i)(()(x)()) = alpha + betas(i), where s(i) denotes the selective advantage as a deviation from the contemporaries, which was the sum of the breeding values of the individual and the breeding values of its mates. The accuracy of predictions was evaluated for a wide range of population and genetic parameters. Accurate predictions were obtained for populations of 5-20 sires. For 20-80 sires, systematic underprediction of on average 11% was found, which was shown to be related to the goodness of fit of the linear model. Using simulation, it was shown that a quadratic model would give accurate predictions for those schemes. Furthermore, it was shown that, contrary to random selection, DeltaF less than halved when the number of parents was doubled and that in specific cases DeltaF may increase with the number of dams.

Animal Husbandry↗

PubMedDate not supplied

Salivary concentration of secretory leukocyte protease inhibitor, an antimicrobial protein, is decreased with advanced age.

BACKGROUND: Secretory leukocyte protease inhibitor (SLPI) exhibits antimicrobial activities that, in addition to other well-characterized proteins such as lysozyme and lactoferrin, is thought to play a critical role in mucosal defenses. Although elderly individuals are particularly susceptible to mucosal infections, salivary production of SLPI has not been assessed in an aged cohort. OBJECTIVES: Hypothesizing that oral SLPI concentrations are reduced with advanced age, this cross-sectional study compared SLPI concentrations to concentrations of lysozyme, lactoferrin and total protein in unstimulated salivary secretions of healthy, community-dwelling 79+-year-old and younger adults. METHODS: Study participants were 45 non-hospitalized dentate adults aged 79-89 (23 elderly) or 21-51 years (22 non-elderly). Home-based interviews and clinical examinations determined dentate status and confirmed the absence of dentures, oral mucosal disease, anti-infective medication use, irradiation therapy for head and neck cancer and self-perceived xerostomia. Whole unstimulated saliva was collected from all subjects and analyzed for antimicrobial protein concentration by enzyme-linked immunosorbent assay and for total protein content by the bicinchoninic acid method. Bivariate and multivariate (generalized linear modeling) analyses evaluated the relationships between age, gender and salivary protein concentrations. RESULTS: Mean salivary levels of SLPI and lysozyme were lower in elderly compared with non-elderly subjects (p < 0.001), unlike lactoferrin and total protein levels. Similar results were obtained when concentrations of the individual proteins were normalized to the total protein concentration, suggesting that glandular production of SLPI and lysozyme preferentially decreases with aging. Gender differences were detected only for SLPI concentrations; males had lower SLPI levels than females regardless of age (p < 0.01). Generalized linear models confirmed that age (p < 0.001) and gender (p < 0.05) were each associated with the SLPI concentration and together accounted for 50% of the variation in SLPI concentration in this population. CONCLUSION: These findings indicate that SLPI production is diminished among healthy community-dwelling older adults, particularly elderly males. Further investigation should determine the impact of decreased local SLPI production on the increased risk of oral mucosal disease with advanced age.

Adult↗

PubMed2006

Transportation of juvenile tambaqui (Colossoma macropomum) in a closed system.

The objective of this study was to investigate the effect of density, duration and the use of additives to the water during the transportation of juvenile tambaqui (Colossoma macropomum) and use of this data to establish a safe transportation protocol for the species. The tested products and dosages were: salt (1000, 2000 and 3000 mg/L), gypsum (100, 300 and 500 mg/L) and benzocaine (10, 20 and 30 mg/L). Fish were transported in closed systems (plastic bag) at different densities and time periods of up to 24 h. Fish survival (FS) and water quality parameters were monitored immediately after transportation. The remaining fish were kept in floating cages in order to evaluate mortality which occurred up to 96 h after transportation (S96). The best fish density, additives dosages and time period of the transportation was estimated with a general linear model. The effect of the condition factor on FS and S96 was also evaluated. As expected, FS and S96 were significantly related to time and density. FS but not S96, were also were significantly related to treatment. FS with gypsum treatment was not different from controls and FS with table salt and benzocaine treatments were significantly reduced. The condition factor was not related to either FS or S96. FS was inversely correlated with carbon dioxide concentration. It was concluded that the additives did not improve fish transportation survival. Linear models were developed to predict the best transportation densities as a function of time.

Animals↗

PubMed2000

Prediction of rates of inbreeding in populations selected on best linear unbiased prediction of breeding value

Journal Article↗

PubMed2002

Predictive value of linear-quadratic model in the treatment of cervical cancer using high-dose-rate brachytherapy.

PURPOSE: To determine whether a dose-response relationship exists between the biologic effective dose (BED) at Point A and the bladder and rectum and the clinical outcomes in our experience with external beam radiotherapy (EBRT) and high-dose-rate brachytherapy in the treatment of cervical carcinoma. METHODS AND MATERIALS: This was a retrospective study. A total of 49 patients with cervical cancer were treated with a combination of EBRT (median 45 Gy, range 41.4-50.4) and high-dose-rate brachytherapy (median 18 Gy; range 18-19, in two fractions). Twenty-three patients received concomitant cisplatin-based chemotherapy. The cumulative BEDs were calculated at Point A (BED10) and at bladder and rectal reference points (BED3) using the linear-quadratic equation. The BED10 values, after incorporating a time factor (BED10tf) in the formula, were also calculated. RESULTS: In patients treated with RT alone, the local failure rate was 10% (1 of 10) and 19% (3 of 16) in patients receiving a BED10 >89 Gy10 or <89 Gy10 to Point A, respectively (p = 0.2). The corresponding local failure rates were 20% (3 of 15) and 0% (0 of 8) in patients treated with concomitant chemotherapy (p = 0.3). In patients treated with RT alone, the local failure rate was 7.7% (1 of 13) and 23% (3 of 13) in patients with a BED10tf >64 Gy10 or <64 Gy10 (p = 0.1), respectively. The median BED3 values at the rectal and bladder point was 95.5 Gy3 and 103.6 Gy3, respectively. Only 1 case of Grade 2 late rectal toxicity (2%) and no late bladder toxicity occurred. CONCLUSION: In patients treated with RT alone, a BED10 >89 Gy and a BED10tf >64 Gy indicated a trend toward a better local control rate. This difference was not observed in patients receiving chemotherapy. A BED3 <100 Gy3 was associated with negligible late toxicity. Although the BED10 in our study was about 10-15 Gy10 less than that in the published data, the 4-year local control rate of 80% and 83% and disease-free survival rate of 75% and 70% with and without chemotherapy, respectively, compare well with the rates in other studies in the literature.

Adenocarcinoma↗

PubMed2006

Count data in psychological applied research.

As some authors have noticed in fields other than psychology, level of measurement and distributional characteristics of count data are commonly not taken into account, so that they are analysed as normally distributed continuous variables, and therefore some general linear model is applied. In this work, we review a random sample of 457 articles published in the last four years in journals with the highest impact factor in the Journal Citation Reports (JCR Social Sciences Edition) of the Institute for Scientific Information. The goals are to know how often count variables appear in psychological applied research and which data analyses are used when dealing with count response variables. Examination showed that there is a notable presence of count variables, especially in some topics in psychology and a remarkable misapplication of the general linear model. One deals with causes and consequences of this approach to data analysis and suggests the use of specific models to analyse count data.

Humans↗

PubMed2000

Anticipation in inflammatory bowel disease: a phenomenon caused by an accumulation of confounders.

Inflammatory bowel disease (IBD) has a definite genetic component as documented by epidemiological and linkage evidence. It shows an earlier onset of disease in children of affected patients than in their parents. This has lead to speculations about genetic anticipation in this disorder. 2,007 IBD patients with sporadic disease and 472 multiplex familial cases (including 103 affected parents and 99 children of affected patients) were evaluated with a multi-item questionnaire as part of a study of inflammatory bowel disease genetics. The Mann-Whitney U-test and the general linear model were used for analysis. Clinical characteristics such as presence of fistulae, stenoses, extraintestinal manifestations, and other parameters, which are related to the severity of the disease, were found to be similar between familial and sporadic cases of IBD (corrected P > or = 0.31 for all tests). The mean-age-of onset in children of affected patients was 19.4 years earlier than in their parents. However, the age of the parental cohort was significantly higher (27 years) and the diagnostic interval also longer (1.7 years). If these confounders are corrected in a general linear model, no significant difference is evident for the age-of-onset between the groups (P > or = 0.52). There is no evidence for genetic anticipation in inflammatory bowel disease. The absence of genetic anticipation is consistent with the clinical similarity of familial and sporadic inflammatory bowel disease. This finding justifies the primary genetic analysis of familial disease under the assumption that their genetic background will be representative for all presentations of IBD.

Adult↗

PubMed2000

Outcomes monitoring and the testing of new psychiatric treatments: work therapy in the treatment of chronic post-traumatic stress disorder.

OBJECTIVE: To evaluate the effectiveness of a work therapy intervention, the Department of Veterans Affairs (VA) Compensated Work Therapy program (CWT), in the treatment of patients suffering from chronic war-related post-traumatic stress disorder (PTSD); and to demonstrate methods for using outcomes monitoring data to screen previously untested treatments. DATA SOURCES/STUDY SETTING: Baseline and four-month follow-up questionnaires administered to 3,076 veterans treated in 52 specialized VA inpatient programs for treatment of PTSD at facilities that also had CWT programs. Altogether 78 (2.5 percent) of these patients participated in CWT during the four months after discharge. STUDY DESIGN: The study used a pre-post nonequivalent control group design. DATA COLLECTION/EXTRACTION METHODS: Questionnaires documented PTSD symptoms, violent behavior, alcohol and drug use, employment status, and medical status at the time of program entry and four months after discharge from the hospital to the community. Administrative databases were used to identify participants in the CWT program. Propensity scores were used to match CWT participants and other patients, and hierarchical linear modeling was used to evaluate differences in outcomes between treatment groups on seven outcomes. PRINCIPAL FINDINGS: The propensity scaling method created groups that were not significantly different on any measure. No greater improvement was observed among CWT participants than among other patients on any of seven outcome measures. CONCLUSIONS: Substantively this study suggests that work therapy, as currently practiced in VA, is not an effective intervention, at least in the short term, for chronic, war-related PTSD. Methodologically it illustrates the use of outcomes monitoring data to screen previously untested treatments and the use of propensity scoring and hierarchical linear modeling to adjust for selection biases in observational studies.

Chronic Disease↗

PubMed1998

Directionality and inhibition in crayfish tangential cells.

The purpose of this study was to characterize the inhibitory mechanism(s) associated with directionally selective motion detection (DS) in nonspiking tangential cells of crayfish optic lobe. The experiments employed intracellular recording of synaptic potentials elicited with sinewave gratings and pharmacological techniques. Previous studies established that tangential cells are subject to bicuculline-sensitive GABA-mediated inhibition. In this study DS was reduced by 90% by bicuculline. The reduction in DS was accompanied by a substantial increase in the response to null-direction motion. Bicuculline also altered the response to pulses of illumination. The magnitude and time course of inhibition were derived from the time varying difference between the control light response and that elicited during bicuculline perfusion. Both the inhibitory delay (relative to excitation) and the inhibitory amplitude are close to the expectations of a linear model of DS. The inhibition is not prolonged with respect to excitation but its risetime is approximately 2.5 times longer. The result implies a longer time constant in the inhibitory pathway relative to that in the excitatory pathway and places limits on the frequency response of inhibition and DS. The velocity-dependence of DS is related to the time course of inhibition. The stimulus drift velocity eliciting maximum directionality is inversely proportional to the inhibitory delay. Bicuculline did not influence orientation selectivity. It is concluded that the quantitative features of bicuculline-sensitive, GABA-mediated inhibition are consistent with a linear model of DS.

Animals↗

PubMed2001

Human tissue valves in aortic position: determinants of reoperation and valve regurgitation.

BACKGROUND: Human tissue valves for aortic valve replacement have a limited durability that is influenced by interrelated determinants. Hierarchical linear modeling was used to analyze the relation between these determinants of durability and valve regurgitation measured by serial echocardiography. METHODS AND RESULTS: In adult patients, 218 cryopreserved aortic allografts were implanted with the subcoronary (85) or the root replacement technique (133), and 81 patients had root replacement with a pulmonary autograft. Mean follow-up was 4.2 years (SD 2.7; range, 0 to 10.5). Patient age, operator experience with subcoronary implantation, and allograft diameter were independent predictors for reoperation. With repeated color Doppler echocardiography, the severity of aortic regurgitation was assessed by the jet length method and the jet diameter ratio. Multilevel hierarchical linear modeling was used to estimate initial aortic regurgitation (intercept), its change over time (slope), and the effect of 11 potential determinants of durability on aortic regurgitation. With the jet length method, the intercept was 0.94 grade and the slope was 0.11 grade per year. With the jet diameter ratio, the intercept was 0.34 and the annual increase was 0.01. Subcoronary implanted valves had more initial aortic regurgitation, but progression of aortic valve regurgitation did not differ from root replacement. At midterm follow-up, recipient age <40 years was the only independent predictor of aortic regurgitation. CONCLUSIONS: Subcoronary implantation has a learning curve, resulting in more initial aortic regurgitation and early reoperation compared with root replacement. In both techniques, progression of aortic regurgitation over time is small but accelerated in young adults.

Adolescent↗

PubMed2005

Effects of EPI readout bandwidth on measured activation map and BOLD response in fMRI experiments.

The purpose of this study was to evaluate the effects of echo planar imaging (EPI) readout bandwidth and its interaction with data processing procedures on the measured blood oxygenation level dependent (BOLD) response and activation in fMRI experiments. Seventeen healthy subjects were scanned during a brief visual stimulation paradigm with two EPI pulse sequences having 'high' (1953 Hz/pixel) and 'low' (780 Hz/pixel) readout bandwidth. Functional data were analyzed with a general linear model including temporal filtering and a basic correlation model following (1) no preprocessing, (2) realignment, or (3) realignment and spatial smoothing. A range of statistical thresholds were used to generate activation maps. Despite slightly higher BOLD signal detected with the high bandwidth sequence from matched ROIs in the primary visual cortex, results showed that the low bandwidth pulse sequence was more sensitive under most conditions evaluated. That is, the low bandwidth sequence detected greater numbers of activated voxels with lower cluster average BOLD signal (e.g., low bandwidth detected 1.4 times more voxels, with average BOLD signal 30% lower compared to high bandwidth for P = 0.05 (corrected) with the 3rd preprocessing procedure using the general linear model). However, there was significant interaction between bandwidth and data preprocessing procedures. Of particular interest, the sensitivity advantage of the low bandwidth pulse sequence decreased for the smoothed data as the activation threshold became less conservative. For the frequently used threshold of P = 0.001 (uncorrected) and cluster size of at least 5 voxels, the bandwidth advantage became insignificant. These findings demonstrate that the effects of bandwidth should be considered carefully in the design, analysis, and interpretation of BOLD fMRI studies.

Adult↗

PubMed1998

Prostate-specific antigen levels are higher in African-American than in white patients in a multicenter registration study: results of RTOG 94-12.

PURPOSE: To compare serum prostate-specific antigen (PSA) levels in a national sample of African-American and white men with prostate cancer, and to attempt to explain any differences by using self-reported individual-level socioeconomic status adjustments. METHODS AND MATERIALS: During 4 1/2 months in 1994-95, 709 patients with nonmetastatic prostate cancer were enrolled in this prospective study; 17.5% were African-American and 82.5% were white. Information about clinical stage, tumor grade, pretreatment PSA, type of insurance, and educational and income status was obtained. Serum PSA levels were measured and racial differences were found; how the differences were influenced by other patient- or tumor-related factors and if the differences could be explained by socioeconomic status disparities were determined. In univariate analyses, factors associated with the mean PSA levels were studied; log-converted values were used to yield a normal distribution. Multivariate analyses were done on log-linear models for description of association patterns among various categorical variables; a perfectly fitted model should have a correlation value (CV) of 1.0. RESULTS: The mean PSA level was higher in African-Americans (14.68 ng/ml) than in whites (9.82 ng/ml) (p = 0.001). Clinical stage (p = 0.001), Gleason sum tumor grade (p = 0.0001), educational level (p = 0.001), and household income (p = 0.03) were also associated with mean PSA levels; age, type of biopsy, and insurance status were not. Disease stage (p = 0.0001), grade (p = 0.0001), education (p = 0.07), and income (p = 0.02) were all associated with PSA levels for whites, but none of these factors were important for African-Americans (all p values > 0.1). The best fitted log-linear model (CV = 0.99) contained PSA (< 10, 10-20, and > 20), Gleason sum grade (2-5, 6-7, and 8-10), race, and two interactions: PSA by race (p = 0.0012) and PSA by Gleason sum (p = 0.0001). Models replacing race for either income (CV = 0.82) or education (CV = 0.82) or both (CV = 0.78) did not fit as well. CONCLUSIONS: African-Americans with nonmetastatic prostate cancer have higher serum PSA levels at diagnosis than whites, implying a higher tumor cell burden. Individual-level household income, education, or insurance status alone or in combination account for racial differences, but only partially.

Analysis of Variance↗

PubMed1994

National diabetes programs. Application of capture-recapture to count diabetes?

OBJECTIVE: To evaluate the utility of capture-recapture methods using multiple, routinely collected, computerized data sources to estimate the numbers and prevalence of diabetes. Methods employed for regional and national monitoring of diabetes have been too inaccurate or too expensive. RESEARCH DESIGN AND METHODS: A survey was undertaken that used four sources of ascertainment to identify prevalent cases of known diabetes in community of Northern Italy: diabetic clinic and family physicians, hospital discharges, prescriptions, and reagent strips and insulin syringes. Capture-recapture methods were employed to estimate the number of missing cases and to adjust for undercount to accurately estimate the number of people who had diabetes. RESULTS: We identified 2,069 unique prevalent cases of known diabetes with the intensive case-finding procedure. The diabetic clinic and family physicians data source identified the largest number of cases. The evaluation of the two sample capture-recapture estimates showed that they were all biased downward because of dependencies between sources. Log-linear modeling was employed to take into account the dependence among all data sources and the heterogeneity of diabetic patients. This method estimated that 2,586 cases existed, resulting in an ascertainment-adjusted prevalence of 2.77% (95% confidence interval, 2.44-3.10). Thus, despite the active case identification, approximately 20% could not be identified. However, the number of cases and rates could easily be adjusted using capture-recapture. CONCLUSIONS: The study shows that a two-sample capture-recapture estimate could be very biased if the investigator is not assured that the sources are independent. However, if at least three data sources are employed, log-linear models allow estimation of the number and prevalence rate adjusted for the degree of undercount (in spite of both the dependence of data sources and the heterogeneity of the diabetic population). The critical factor, however, is that the application of multiple sources with capture-recapture methods could be applied across broad geographical areas and across time to have cost-effective monitoring of diabetes at local and national level.

Adolescent↗

PubMed1997

Wherein lies the truth? Assessment of agreement between parent proxy and child respondents.

BACKGROUND: The epidemiological study of diseases of childhood presents a special situation in that the principal respondent is almost always a person other than the index. Use of proxy respondents in paediatric epidemiology has been little studied compared with the use of surrogate respondents for adults. METHODS: Agreement between responses from children and their parents to identical questions about the children was assessed in a case-control study of childhood melanoma in Queensland, Australia. Weighted kappa and log-linear modelling techniques were used to measure agreement for ordinal data. RESULTS: Highest agreement was found for reports of unchanging physical characteristics such as eye colour (kappa = 0.88), hair colour (kappa = 0.76), and for history of residing on a farm (kappa = 0.84). Moderate agreement was seen for density of facial freckling (kappa = 0.62), propensity to sunburn (kappa = 0.46) and tanning ability (kappa = 0.47). Variables with low levels of agreement between parent proxy and child respondents included density of freckling on the shoulders (kappa = 0.28) and degree of moliness of the skin at age 5 years (kappa = 0.24). Agreement did not vary according to age or sex of the children. Log-linear modelling was performed to determine the type and magnitude of components of agreement. CONCLUSIONS: Agreement between responses from children and parent proxies depends largely upon the type of information sought, rather than characteristics of the respondents.

Adolescent↗

PubMed2002

Eigenmobilities in background electrolytes for capillary zone electrophoresis. I. System eigenpeaks and resonance in systems with strong electrolytes.

A background electrolyte system for capillary zone electrophoresis which is composed of three strong univalent ionic constituents is investigated. The ion 1 is considered as a counter-ion and two ions, 2 and 3, are considered as co-ions in relation to the analyte ion 4. We investigate the linearized model of electromigration in such a system and calculate the eigenvalues of a corresponding matrix. The model is formulated in such a way that the eigenvalues of the system are certain mobilities, which we call eigenmobilites, which characterize specific features of the electtrophoretic migration. One of the eigenmobilities is the system eigenmobility u(s) causing the rise of the system peak, called here the system eigenpeak. A situation when the analyte has the same mobility as the system eigenmobility, u(4) = u(s), is analyzed in detail. We show that it leads to the resonance-the mutual jump in the concentration profile of both co-ions, 2 and 3, has a shape of the spatial derivation of the originally sampled analyte profile and, moreover, it grows linearly with time. After a sufficiently long time it can be "amplified" to any value. The resonance has then a great impact on signals of indirect detection methods, like indirect UV detection or conductivity detection. In the framework of the linearized model the relative velocity slope S(x), a measure of electromigration dispersion, is expressed as S(x) = F(u(1) + u(4))(u(2) - u(4))(u(3) - u(4))/[u(4)(u(s) - u(4))], where u(i) is the mobility of the ith ion and F is the Faraday constant. As in practice the concentration of the analyte is not infinitely small and has a certain finite value, the analyte will be at the resonance severely dispersed to a much broader spatial interval. When a specific detector is used, the signal of such an analyte can apparently be missed without any notice.

Electrolytes↗