Analysis of functional magnetic resonance imaging time series by independent component analysis

Independent Component Analysis, Time Series Analysis, Functional Magnetic Resonance Imaging

Objective analysis of gait coordination for total knee arthroplasty outcome

Introduction: Coordination is a strategy chosen by the central nervous system to control the movements and maintain stability during gait. Coordinated multi-joint movements require a complex interaction between nervous outputs, biomechanical constraints, and pro-prioception. Quantitatively understanding and modeling gait coordination still remain a challenge. Surgeons lack a way to model and appreciate the coordination of patients before and after surgery of the lower limbs. Patients alter their gait patterns and their kinematic synergies when they walk faster or slower than normal speed to maintain their stability and minimize the energy cost of locomotion. The goal of this study was to provide a dynamical system approach to quantitatively describe human gait coordination and apply it to patients before and after total knee arthroplasty. Methods: A new method of quantitative analysis of interjoint coordination during gait was designed, providing a general model to capture the whole dynamics and showing the kinematic synergies at various walking speeds. The proposed model imposed a relationship among lower limb joint angles (hips and knees) to parameterize the dynamics of locomotion of each individual. An integration of different analysis tools such as Harmonic analysis, Principal Component Analysis, and Artificial Neural Network helped overcome high-dimensionality, temporal dependence, and non-linear relationships of the gait patterns. Ten patients were studied using an ambulatory gait device (Physilog®). Each participant was asked to perform two walking trials of 30m long at 3 different speeds and to complete an EQ-5D questionnaire, a WOMAC and Knee Society Score. Lower limbs rotations were measured by four miniature angular rate sensors mounted respectively, on each shank and thigh. The outcomes of the eight patients undergoing total knee arthroplasty, recorded pre-operatively and post-operatively at 6 weeks, 3 months, 6 months and 1 year were compared to 2 age-matched healthy subjects. Results: The new method provided coordination scores at various walking speeds, ranged between 0 and 10. It determined the overall coordination of the lower limbs as well as the contribution of each joint to the total coordination. The difference between the pre-operative and post-operative coordination values were correlated with the improvements of the subjective outcome scores. Although the study group was small, the results showed a new way to objectively quantify gait coordination of patients undergoing total knee arthroplasty, using only portable body-fixed sensors. Conclusion: A new method for objective gait coordination analysis has been developed with very encouraging results regarding the objective outcome of lower limb surgery.

The application of chemometrics on Infrared and Raman spectra as a tool for the forensic analysis of paints

The aim of this work is to evaluate the capabilities and limitations of chemometric methods and other mathematical treatments applied on spectroscopic data and more specifically on paint samples. The uniqueness of the spectroscopic data comes from the fact that they are multivariate - a few thousands variables - and highly correlated. Statistical methods are used to study and discriminate samples. A collection of 34 red paint samples was measured by Infrared and Raman spectroscopy. Data pretreatment and variable selection demonstrated that the use of Standard Normal Variate (SNV), together with removal of the noisy variables by a selection of the wavelengths from 650 to 1830 cm−1 and 2730-3600 cm−1, provided the optimal results for infrared analysis. Principal component analysis (PCA) and hierarchical clusters analysis (HCA) were then used as exploratory techniques to provide evidence of structure in the data, cluster, or detect outliers. With the FTIR spectra, the Principal Components (PCs) correspond to binder types and the presence/absence of calcium carbonate. 83% of the total variance is explained by the four first PCs. As for the Raman spectra, we observe six different clusters corresponding to the different pigment compositions when plotting the first two PCs, which account for 37% and 20% respectively of the total variance. In conclusion, the use of chemometrics for the forensic analysis of paints provides a valuable tool for objective decision-making, a reduction of the possible classification errors, and a better efficiency, having robust results with time saving data treatments.

Statistical evaluation of the reproducibility and the influence of paper on the analysis of black gel pen ink using laser desorption ionisation mass spectrometry

Laser desorption ionisation mass spectrometry (LDI-MS) has demonstrated to be an excellent analytical method for the forensic analysis of inks on a questioned document. The ink can be analysed directly on its substrate (paper) and hence offers a fast method of analysis as sample preparation is kept to a minimum and more importantly, damage to the document is minimised. LDI-MS has also previously been reported to provide a high power of discrimination in the statistical comparison of ink samples and has the potential to be introduced as part of routine ink analysis. This paper looks into the methodology further and evaluates statistically the reproducibility and the influence of paper on black gel pen ink LDI-MS spectra; by comparing spectra of three different black gel pen inks on three different paper substrates. Although generally minimal, the influences of sample homogeneity and paper type were found to be sample dependent. This should be taken into account to avoid the risk of false differentiation of black gel pen ink samples. Other statistical approaches such as principal component analysis (PCA) proved to be a good alternative to correlation coefficients for the comparison of whole mass spectra.

Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the RodriguesTriple Junction in the Indian Ocean were studied applying classical statistical methods(fuzzy c-means clustering, linear mixing model, principal component analysis) for theextraction of endmembers and evaluating the spatial and temporal variation ofgeochemical signals. Three main factors of sedimentation were expected by the marinegeologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. Thedisplay of fuzzy membership values and/or factor scores versus depth providedconsistent results for two factors only; the ultra-basic component could not beidentified. The reason for this may be that only traditional statistical methods wereapplied, i.e. the untransformed components were used and the cosine-theta coefficient assimilarity measure.During the last decade considerable progress in compositional data analysis was madeand many case studies were published using new tools for exploratory analysis of thesedata. Therefore it makes sense to check if the application of suitable data transformations,reduction of the D-part simplex to two or three factors and visualinterpretation of the factor scores would lead to a revision of earlier results and toanswers to open questions . In this paper we follow the lines of a paper of R. Tolosana-Delgado et al. (2005) starting with a problem-oriented interpretation of the biplotscattergram, extracting compositional factors, ilr-transformation of the components andvisualization of the factor scores in a spatial context: The compositional factors will beplotted versus depth (time) of the core samples in order to facilitate the identification ofthe expected sources of the sedimentary process.Kew words: compositional data analysis, biplot, deep sea sediments

Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuouslycored boreholes, 100 to 220m deep were drilled in the northern part of the PoPlain by Regione Lombardia in the last five years. Quantitative provenanceanalysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carriedout by using multivariate statistical analysis (principal component analysis, PCA,and similarity analysis) on an integrated data set, including high-resolution bulkpetrography and heavy-mineral analyses on Pleistocene sands and of 250 majorand minor modern rivers draining the southern flank of the Alps from West toEast (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations,metamorphic and quartzofeldspathic detritus from the Western and Central Alpswas carried from the axial belt to the Po basin longitudinally parallel to theSouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenariorapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset ofthe first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA andsimilarity analysis from core samples show that the longitudinal trunk river at thistime was shifted southward by the rapid southward and westward progradation oftransverse alluvial river systems fed from the Central and Southern Alps.Sediments were transported southward by braided river systems as well as glacialsediments transported by Alpine valley glaciers invaded the alluvial plain.Kew words: Detrital modes; Modern sands; Provenance; Principal ComponentsAnalysis; Similarity, Canberra Distance; palaeodrainage

Intelligent PCA contribution analysis for quality estimation in batch processes. Application in a sequencing batch reactor for wastewater treatment

En aquest treball, es proposa un nou mètode per estimar en temps real la qualitat del producte final en processos per lot. Aquest mètode permet reduir el temps necessari per obtenir els resultats de qualitat de les anàlisi de laboratori. S'utiliza un model de anàlisi de componentes principals (PCA) construït amb dades històriques en condicions normals de funcionament per discernir si un lot finalizat és normal o no. Es calcula una signatura de falla pels lots anormals i es passa a través d'un model de classificació per la seva estimació. L'estudi proposa un mètode per utilitzar la informació de les gràfiques de contribució basat en les signatures de falla, on els indicadors representen el comportament de les variables al llarg del procés en les diferentes etapes. Un conjunt de dades compost per la signatura de falla dels lots anormals històrics es construeix per cercar els patrons i entrenar els models de classifcació per estimar els resultas dels lots futurs. La metodologia proposada s'ha aplicat a un reactor seqüencial per lots (SBR). Diversos algoritmes de classificació es proven per demostrar les possibilitats de la metodologia proposada.

Diagnosing Patients Combining Principal Components Analysis and Case Based Reasoning

This paper addresses the application of a PCA analysis on categorical data prior to diagnose a patients data set using a Case-Based Reasoning (CBR) system. The particularity is that the standard PCA techniques are designed to deal with numerical attributes, but our medical data set contains many categorical data and alternative methods as RS-PCA are required. Thus, we propose to hybridize RS-PCA (Regular Simplex PCA) and a simple CBR. Results show how the hybrid system produces similar results when diagnosing a medical data set, that the ones obtained when using the original attributes. These results are quite promising since they allow to diagnose with less computation effort and memory storage

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

Transcriptional analysis of left-sided colitis, pancolitis, and ulcerative colitis-associated dysplasia

BACKGROUND: It is unknown why patients with extensive ulcerative colitis (UC) have a higher risk of colorectal cancer compared with patients with left-sided UC. This study characterizes the inflammatory processes in left-sided UC, pancolitis, and UC-associated dysplasia at the transcriptional level to identify potential biomarkers and transcripts of importance for the carcinogenic behavior of chronic inflammation. METHODS: The Affymetrix GeneChip Human Genome U133 Plus 2.0 was applied on colonic biopsies from UC patients with left-sided UC, pancolitis, dysplasia, and controls. Reverse transcription polymerase chain reaction and immunohistochemistry were performed for validating selected transcripts in the initial cohort and in 2 independent cohorts of patients with UC. Microarray data were analyzed by principal component analysis, and reverse transcription polymerase chain reaction and immunohistochemistry data by the Wilcoxon's rank-sum test. RESULTS: The principal component analysis results revealed separate clusters for left-sided UC, pancolitis, dysplasia, and controls. Close clustering of dysplastic and pancolitic samples indicated similarities in gene expression. Indeed, 101 and 656 parallel upregulated and downregulated transcripts, respectively, were identified in specimens from dysplasia and pancolitis. Validation of selected transcripts hereof identified insulin receptor alpha (INSRA) and MAP kinase interacting serine/threonine kinase 2 (MKNK2) with an enhanced expression in dysplasia compared with left-sided UC and controls, whereas laminin γ2 (LAMC2) was found with a lower expression in dysplasia compared with the remaining 3 groups. CONCLUSIONS: This study demonstrates pancolitis and left-sided UC as distinct inflammatory processes at the transcriptional level, and identifies INSRA, MKNK2, and LAMC2 as potential critical transcripts in the inflammation-driven preneoplastic process of UC.

Proteomic analysis of peach fruit mesocarp softening and chilling injury using difference gel electrophoresis (DIGE)

Background: Peach fruit undergoes a rapid softening process that involves a number of metabolic changes. Storing fruit at low temperatures has been widely used to extend its postharvest life. However, this leads to undesired changes, such as mealiness and browning, which affect the quality of the fruit. In this study, a 2-D DIGE approach was designed to screen for differentially accumulated proteins in peach fruit during normal softening as well as under conditions that led to fruit chilling injury. Results:The analysis allowed us to identify 43 spots -representing about 18% of the total number analyzed- that show statistically significant changes. Thirty-nine of the proteins could be identified by mass spectrometry. Some of the proteins that changed during postharvest had been related to peach fruit ripening and cold stress in the past. However, we identified other proteins that had not been linked to these processes. A graphical display of the relationship between the differentially accumulated proteins was obtained using pairwise average-linkage cluster analysis and principal component analysis. Proteins such as endopolygalacturonase, catalase, NADP-dependent isocitrate dehydrogenase, pectin methylesterase and dehydrins were found to be very important for distinguishing between healthy and chill injured fruit. A categorization of the differentially accumulated proteins was performed using Gene Ontology annotation. The results showed that the 'response to stress', 'cellular homeostasis', 'metabolism of carbohydrates' and 'amino acid metabolism' biological processes were affected the most during the postharvest. Conclusions: Using a comparative proteomic approach with 2-D DIGE allowed us to identify proteins that showed stage-specific changes in their accumulation pattern. Several proteins that are related to response to stress, cellular homeostasis, cellular component organization and carbohydrate metabolism were detected as being differentially accumulated. Finally, a significant proportion of the proteins identified had not been associated with softening, cold storage or chilling injury-altered fruit before; thus, comparative proteomics has proven to be a valuable tool for understanding fruit softening and postharvest.

Characterization of olive oil by carbon isotope analysis of individual fatty acids: Implications for authentication

The fatty acids of olive oils of distinct quality grade from the most important European Union (EU) producer countries were chemically and isotopically characterized. The analytical approach utilized combined capillary column gas chromatography-mass spectrometry (GC/MS) and the novel technique of compound-specific isotope analysis (CSIA) through gas chromatography coupled to a stable isotope ratio mass spectrometer (IRMS) via a combustion (C) interface (GC/C/IRMS). This approach provides further insights into the control of the purity and geographical origin of oils sold as cold-pressed extra virgin olive oil with certified origin appellation. The results indicate that substantial enrichment in heavy carbon isotope (C-13) of the bulk oil and of individual fatty acids are related to (1) a thermally induced degradation due to deodorization or steam washing of the olive oils and (2) the potential blend with refined olive oil or other vegetable oils. The interpretation of the data is based on principal component analysis of the fatty acids concentrations and isotopic data (delta(13)C(oil), delta(13)C(16:0), delta(13)C(18:1)) and on the delta(13)C(16:0) vs delta(13)C(18:1) covariations. The differences in the delta(13)C values of palmitic and oleic acids are discussed in terms of biosynthesis of these acids in the plant tissue and admixture of distinct oils.

Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.