Shoulder Kinematics Is Not Influenced by External Load During Elevation in the Scapular Plane

The current study aimed to compare the shoulder kinematics (3D scapular orientation, scapular angular displacement and scapulohumeral rhythm) of asymptomatic participants under unloaded and loaded conditions during unilateral shoulder elevation in the scapular plane. We used a repeated-measures design with a convenience sample. Eleven male participants with an age range of 21–28 years with no recent history of shoulder injury participated in the study. The participants performed isometric shoulder elevation from a neutral position to approximately 150 degrees of elevation in the scapular plane in intervals of approximately 30 degrees during unloaded and loaded conditions. Shoulder kinematic data were obtained with videogrammetry. During shoulder elevation, the scapula rotated upwardly and externally, and tilted posteriorly. The addition of an external load did not affect 3D scapular orientation, scapular angular displacement, or scapulohumeral rhythm throughout shoulder elevation (P > .05). In clinical practice, clinicians should expect to observe upward and external rotation and posterior tilt of the scapula during their assessments of shoulder elevation. Such behavior was not influenced by an external load normalized to 5% of body weight when performed in an asymptomatic population.

A efectividade de um programa de exercícios terapêuticos na doença osteo-articular no idoso

RESUMO: O presente estudo teve como objectivo avaliar a efectividade de um programa de intervenção de fisioterapia comparativamente ao tratamento conservador (calor húmido, ultra-som e massagem), relativamente à dor e capacidade funcional, no utente idoso com doença osteoarticular do joelho. A amostra foi aleatória, tendo sido seleccionados 20 utentes que respeitaram os critérios de inclusão, e que foram distribuídos aleatoriamente pelos dois grupos de tratamento, 9 no grupo A (experimental) e 11 no grupo B (controle). Todos os utentes deram o seu consentimento informado. Trata-se de um estudo experimental, controlado aleatorizado (RCT). A intervenção em estudo consistiu em 15 sessões de tratamento individuais, efectuadas 3 vezes por semana. O programa terapêutico efectuado pelo grupo A incluiu o tratamento conservador (20 minutos calor húmido, 5 minutos ultra-som (contínuo; 1,5W/cm2) e aproximadamente 10 minutos de massagem local) e o protocolo de exercícios terapêuticos em estudo. Este protocolo de exercícios foi progredindo semanalmente em termos da sua intensidade. Os utentes do Grupo B efectuaram apenas o tratamento conservador (tal como no grupo A). Para avaliar a dor e a capacidade funcional foi utilizado o Questionário knee Injury and Osteoarthritis Outcome Score. A análise dos resultados foi realizada através dos testes Mann-Whitney e Kruskal-Wallis para a comparação entre grupos. Os resultados sugerem não haver diferenças estatisticamente significativos entre os grupos, embora o grupo de controle tenha obtido melhores resultados. O grupo B apresentou uma diminuição da dor de 17,33, comparativamente aos valores de -3,00 no grupo A (p=0,101), e melhoria da capacidade funcional de 13,00, mantendo-se a capacidade funcional igual, no grupo A (0,00) p=0,080). Estes resultados parecem sugerir que não há diferenças significativas entre as duas modalidades de intervenção, realçando a necessidade de continuar a investigar este protocolo de exercícios e a sua efectividade.-----------------ABSTRACT: The aims of this study was to evaluate the effectiveness of a treatment program compared with conventional treatment (post hoots, ultrasound and massage), for the outcomes pain and functional ability in elderly with knee osteoarthritis. The sample was non-probability, and 20 patients have been selected that fulfilled the criteria for inclusion and who were randomly assigned to the two treatment groups, in group A and 11 in group B. All of the patients gave their informed consent. This is an experimental, randomized controlled trial (RCT) with blinded assessment, of comparative design. This study protocol program was carry out in 15 individual treatment sessions, 3x per week. The therapeutic program made by group A consisted of the performance of conservative treatment: 20 minutes of hot packs, 5 minutes of ultrasound (continuous, 1.5 W/cm2) and 10 minutes of massage plus the exercise protocol therapy consisted of: isometric exercises of quadriceps contractions, muscle strengthening for knee and aerobic training. This exercise protocol was progressing every week in terms of its intensity. The users in Group B, only made the conservative treatment (such as in group A). In this study there were evaluated the pain and functional capacity, assessed by questionnaire knee Injury Osteoarthritis Outcome Score. For comparison between groups were used Mann-Whitney and Kruskal-Wallis tests. The results revealed that in group B was that it obtained better results, although they are not statistical significance. The group B show a decrease in pain of 17.33 compared to -3.00 in group A (p = 0.101), and improved capacity functional of 13.00, keeping in group A (0.00) (p = 0.080). However, the differences are not statistically significant. These results show that there are not statistically significant in both treatments, but more studies are needed.

Effects of protein-calorie restriction on mechanical function of hypertrophied cardiac muscle

OBJECTIVE: To assess the effect of food restriction (FR) on hypertrophied cardiac muscle in spontaneously hypertensive rats (SHR). METHODS: Isolated papillary muscle preparations of the left ventricle (LV) of 60-day-old SHR and of normotensive Wistar-Kyoto (WKY) rats were studied. The rats were fed either an unrestricted diet or FR diet (50% of the intake of the control diet) for 30 days. The mechanical function of the muscles was evaluated through monitoring isometric and isotonic contractions. RESULTS: FR caused: 1) reduction in the body weight and LV weight of SHR and WKY rats; 2) increase in the time to peak shortening and the time to peak developed tension (DT) in the hypertrophied myocardium of the SHR; 3) diverging changes in the mechanical function of the normal cardiac muscles of WKY rats with reduction in maximum velocity of isotonic shortening and of the time for DT to decrease 50% of its maximum value, and increase of the resting tension and of the rate of tension decline. CONCLUSION: Short-term FR causes prolongation of the contraction time of hypertrophied muscles and paradoxal changes in mechanical performance of normal cardiac fibers, with worsening of the shortening indices and of the resting tension, and improvement of the isometric relaxation.

Effect of arginine vasopressin on the canine epicardial coronary artery: experiments on V1-receptor-mediated production of nitric oxide

OBJECTIVE: To determine whether arginine vasopressin releases endothelium-derived nitric oxide (EDNO) from the epicardial coronary artery. METHODS: We studied segments of canine left circumflex coronary arteries suspended in organ chambers to measure isometric force. The coronary artery segments were contracted with prostaglandin F2alpha (2 x 10-6M) and exposed to a unique, strong arginine vasopressin concentration (10-6M) or titrated concentrations (10-9 a 10-5 M). RESULTS: The unique dose of arginine vasopressin concentration (10-6M) induced transient, but significant (p<0.05), relaxation in arterial segments with endothelium, and an increase, not significant, in tension in arteries without endothelium. Endothelium-dependent relaxation to arginine vasopressin was inhibited by Ng-monomethyl-L-arginine (L-NMMA, 10-5M) or N G-nitro-L-arginine (L-NOARG) (10-4M), 2 inhibitors of nitric oxide synthesis from L-arginine. Exogenous L-arginine (10-4M), but not D-arginine (10-4M), reversed the inhibitory effect of L-NMMA on vasopressin-mediated vasorelaxation. Endothelium dependent relaxation to vasopressin was also reversibly inhibited by the vasopressin V1-receptor blocker d(CH2)5Try(Me) arginine vasopressin (10-6M) (n=6, P<0.05). CONCLUSION: Vasopressin acts through V1 endothelial receptors to stimulate nitric oxide release from L-arginine.

Behavior of cardiac variables in animals exposed to cigarette smoke

OBJECTIVE: To assess the behavior of cardiac variables in animals exposed to cigarette smoke. METHODS: Two groups of Wistar rats were studied as follows: control group (C), comprising 28 animals; and smoking group (S), comprising 23 animals exposed to cigarette smoke for 30 days. Left ventricular cardiac function was assessed in vivo with transthoracic echocardiography, and myocardial performance was analyzed in vitro in preparations of isolated left ventricular papillary muscle. The cardiac muscle was assessed in isometric contractions with an extracellular calcium concentration of 2.5 mmol/L. RESULTS: No statistical difference was observed in the values of the body variables of the rats and in the mechanical data obtained from the papillary muscle between the control and smoking groups. The values of left ventricular systolic diameter were significantly greater in the smoking animals than in the control animals (C= 3.39 ± 0.4 mm and S= 3.71 ± 0.51 mm, P=0.02). A significant reduction was observed in systolic shortening fraction (C= 56.7 ± 4.2% and S= 53.5 ± 5.3%, P=0.02) and in ejection fraction (C= 0.92 ± 0.02 and S= 0.89 ± 0.04, P=0.01). CONCLUSION: The rats exposed to cigarette smoke had a reduction in left ventricular systolic function, although their myocardial function was preserved.

Loss of connexin40 is associated with decreased endothelium-dependent relaxations and eNOS levels in the mouse aorta.

Upon agonist stimulation, endothelial cells trigger smooth muscle relaxation through the release of relaxing factors such as nitric oxide (NO). Endothelial cells of mouse aorta are interconnected by gap junctions made of connexin40 (Cx40) and connexin37 (Cx37), allowing the exchange of signaling molecules to coordinate their activity. Wild-type (Cx40(+/+)) and hypertensive Cx40-deficient mice (Cx40(-/-)), which also exhibit a marked decrease of Cx37 in the endothelium, were used to investigate the link between the expression of endothelial connexins (Cx40 and Cx37) and endothelial nitric oxide synthase (eNOS) expression and function in the mouse aorta. With the use of isometric tension measurements in aortic rings precontracted with U-46619, a stable thromboxane A(2) mimetic, we first demonstrate that ACh- and ATP-induced endothelium-dependent relaxations solely depend on NO release in both Cx40(+/+) and Cx40(-/-) mice, but are markedly weaker in Cx40(-/-) mice. Consistently, both basal and ACh- or ATP-induced NO production were decreased in the aorta of Cx40(-/-) mice. Altered relaxations and NO release from aorta of Cx40(-/-) mice were associated with lower expression levels of eNOS in the aortic endothelium of Cx40(-/-) mice. Using immunoprecipitation and in situ ligation assay, we further demonstrate that eNOS, Cx40, and Cx37 tightly interact with each other at intercellular junctions in the aortic endothelium of Cx40(+/+) mice, suggesting that the absence of Cx40 in association with altered Cx37 levels in endothelial cells from Cx40(-/-) mice participate to the decreased levels of eNOS. Altogether, our data suggest that the endothelial connexins may participate in the control of eNOS expression levels and function.

Development and growth of the early juveniles of the spider crab Maja squinado (Brachyura: Majoidea) in an individual culture system

The spider crab Maja squinado is an endangered Mediterranean species; therefore, culturing it successfully is essential for developing restocking programs. The survival, growth and development of post-larval stages (juvenile crabs, C1-C8) were studied using larvae obtained from adult individuals collected in the Catalan Sea. The juvenile crab stages were cultured individually from a megalopal stage using a semi-open recirculation system to obtain the precise growth data of each juvenile crab stage until C8. Development up to C8 at 20ºC lasted 154±10 days. Survival from C1 to C8 was 5.8 %. Moult increment values in cephothoracic length were similar in all the crab stages (21-35 %). Intermoult duration (9±1 in C1-C2 to 51±8 days in C7-C8) increased sharply from juvenile stage 5. Males and females can be distinguished from C4 based on sexual dimorphism in the pleopods and the presence of gonopores. The allometric growth of the pleon is sex-dependent from C4, with females showing positive allometry and males isometric growth. The juvenile growth rate was lower compared with that of the previously studied Atlantic species Maja brachydactyla.

Hypoxic contraction of small pulmonary arteries from normal and endotoxemic rats: fundamental role of NO.

The present study was aimed at examining the role of nitric oxide (NO) in the hypoxic contraction of isolated small pulmonary arteries (SPA) in the rat. Animals were treated with either saline (sham experiments) or Escherichia coli lipolysaccharide [LPS, to obtain expression of the inducible NO synthase (iNOS) in the lung] and killed 4 h later. SPA (300- to 600-micrometer outer diameter) were mounted as rings in organ chambers for the recording of isometric tension, precontracted with PGF2alpha, and exposed to either severe (bath PO2 8 +/- 3 mmHg) or milder (21 +/- 3 mmHg) hypoxia. In SPA from sham-treated rats, contractions elicited by severe hypoxia were completely suppressed by either endothelium removal or preincubation with an NOS inhibitor [NG-nitro-L-arginine methyl ester (L-NAME), 10(-3) M]. In SPA from LPS-treated rats, contractions elicited by severe hypoxia occurred irrespective of the presence or absence of endothelium and were largely suppressed by L-NAME. The milder hypoxia elicited no increase in vascular tone. These results indicate an essential role of NO in the hypoxic contractions of precontracted rat SPA. The endothelium independence of HPV in arteries from LPS-treated animals appears related to the extraendothelial expression of iNOS. The severe degree of hypoxia required to elicit any contraction is consistent with a mechanism of reduced NO production caused by a limited availability of O2 as a substrate for NOS.

Influence of inter-electrode distance, contraction type, and muscle on the relationship between the sEMG power spectrum and contraction force.

INTRODUCTION: Spectral frequencies of the surface electromyogram (sEMG) increase with contraction force, but debate still exists on whether this increase is affected by various methodological and anatomical factors. This study aimed to investigate the influence of inter-electrode distance (IED) and contraction modality (step-wise vs. ramp) on the changes in spectral frequencies with increasing contraction strength for the vastus lateralis (VL) and vastus medialis (VM) muscles. METHODS: Twenty healthy male volunteers were assessed for isometric sEMG activity of the VM and VL, with the knee at 90° flexion. Subjects performed isometric ramp contractions in knee extension (6-s duration) with the force gradually increasing from 0 to 80 % MVC. Also, subjects performed 4-s step-wise isometric contractions at 10, 20, 30, 40, 50, 60, 70, and 80 % MVC. Interference sEMG signals were recorded simultaneously at different IEDs: 10, 20, 30, and 50 mm. The mean (F mean) and median (F median) frequencies and root mean square (RMS) of sEMG signals were calculated. RESULTS: For all IEDs, contraction modalities, and muscles tested, spectral frequencies increased significantly with increasing level of force up to 50-60 % MVC force. Spectral indexes increased systematically as IED was decreased. The sensitivity of spectral frequencies to changes in contraction force was independent of IED. The behaviour of spectral indexes with increasing contraction force was similar for step-wise and ramp contractions. CONCLUSIONS: In the VL and VM muscles, it is highly unlikely that a particular inter-electrode distance or contraction modality could have prevented the observation of the full extent of the increase in spectral frequencies with increasing force level.

Geometric morphometric differences between Panstrongylus geniculatus from field and laboratory

The finding of Panstrongylus geniculatus nymphs inside a house in northeastern Antioquia, Colombia, and the reports related to their increasing presence in homes suggest the need for surveillance methods for monitoring the invasion processes. We analyzed the morphological differences between a wild population and its laboratory descendants, using the techniques of geometric morphometry, with the idea that such differences might parallel those between sylvatic and synanthropic populations. The analyses over five generations showed differences in size but not in shape. Head size and wing size were both reduced from sylvatic to laboratory populations, but the decrease in head size occurred only up to the second generation while the decrease in wing size proceeded up to the fifth generation. In contrast, although a decrease in sexual size dimorphism has been proposed as a marker of colonization in human dwellings, we did not detect any significant loss of dimorphism between sexes of P. geniculatus over the five generations studied. We conclude that size changes may have a physiological origin in response to a change of ecotopes, but more than five generations may be required for the expression of permanent morphological markers of human dwellings colonization.

Rôle de l'exercice dans l'approche multidisciplinaire de la lombalgie chronique

RÉSUMÉ L'exercice est utilisé dans le traitement de la lombalgie depuis plus de cent ans. La recherche dans ce domaine a commencé au milieu du XXème siècle puis s'est développée exponentiellement jusqu'à nos jours. La première étude de cette thèse a eu pour but de passer en revue cette abondante littérature scientifique. Il en est ressorti que l'exercice est un moyen efficace de prévention primaire et secondaire de la lombalgie. En tant que modalité de traitement, l'exercice permet de diminuer l'incapacité et la douleur et d'améliorer la condition physique et le statut professionnel des patients lombalgiques subaigus et chroniques. Parmi les caractéristiques de l'exercice, la supervision est essentielle. Des investigations ultérieures sont nécessaires afin d'identifier des sous-groupes de patients répondant favorablement à d'autres caractéristiques de l'exercice. L'exercice est souvent utilisé dans l'optique de maintenir les résultats obtenus à la suite d'un traitement, bien que peu d'études s'y soient penchées. La deuxième partie de cette thèse a eu pour objectifs d'évaluer l'efficacité d'un programme d'exercice (PE) suivi par des patients lombalgiques chroniques ayant complété une restauration fonctionnelle multidisciplinaire (RFM), en comparaison avec le suivi classique (SC) consistant simplement à encourager les patients à adopter un quotidien aussi actif que possible par la suite. Les résultats ont montré que les améliorations obtenues au terme de RFM étaient maintenues par les deux groupes à un an de suivi. Bien qu'aucune différence n'ait été obtenue entre les deux groupes, seul le groupe PE améliorait significativement l'incapacité et l'endurance isométrique des muscles du tronc. Une analyse économique a ensuite été réalisée afin d'évaluer la rentabilité de PE. L'évaluation de la qualité de vie des patients au terme de RFM et à un an de suivi permettait d'estimer les années de vie ajustées par leur qualité (QALYs) gagnées par chaque groupe. Les coûts directs (visites chez le médecin, spécialiste, physio, autres) et indirects (jours d'absence au travail) étaient estimés avant RFM et à un an de suivi à l'aide d'un agenda. Aucune différence significative n'était obtenue entre les groupes. Une mince différence de QALYs en faveur de PE ne se traduisait néanmoins pas en bénéfices mesurables. La recherche future devrait s'attacher à identifier un ou des sous-groupe(s) de patients pour lesquels SC ne permet pas de maintenir à long terme les améliorations obtenues au terme de RFM, et pour lesquels l'efficacité thérapeutique et la rentabilité économique de PE pourraient être accrues. ABSTRACT Exercise is used to treat low back pain for over a hundred years. Research in this area began in the mid-twentieth century and then grew exponentially until nowadays. The first study of this thesis was aimed to review this abundant scientific literature. It showed that exercise is effective in the primary and secondary prevention of low back pain. As a modality of treatment, exercise can reduce disability and pain and improve physical fitness and professional status of patients with subacute and chronic low back pain. Among different exercise characteristics, supervision is essential. Further investigations are needed to identify subgroups of patients responding positively to other characteristics of exercise. Exercise is often used as a post-treatment modality in order to maintain results over time, although only a few studies addressed this issue directly. The purpose of the second part of this thesis was to evaluate the effectiveness of an exercise program (EP) for patients with chronic low back pain who completed a functional multidisciplinary rehabilitation (FMR), compared to the routine follow-up (RF) which simply consisted of encouraging patients to adopt an active daily life thereafter. The results showed that improvements obtained at the end of FMR were maintained by both groups at one year follow-up. Although no difference was obtained between both groups, only the EP group significantly improved disability and isometric endurance of trunk muscles. An economic analysis was then carried out to assess the cost-effectiveness of EP. Based on the evaluation of patients' quality of life after FMR and at one year follow-up, an estimation of adjusted life years for their quality (QALYs) gained by each group was done. Direct costs (physician, specialist, physiotherapist, other therapists visits) and indirect costs (days off work) were measured before FMR and at one year follow-up using a cost diary. No significant difference was obtained between both groups. A slight difference in QALYs in favour of EP did yet not translate into measurable benefits. Future research should focus on identifying subgroups of patients for which RF is insufficient to reach long-term improvements after FMR, and for which the therapeutic effectiveness and cost-effectiveness of EP could be increased.

Vibration training elicits a mixed aerobic and resistance-type exercise in sedentary subjects.

Objective. Vibration training (VT) is a new exercise method, with good acceptance among sedentary subjects, due to its passive principle: the machine moves the subject, not the opposite. We hypothesize that untrained subjects can benefit from a greater cardiovascular and metabolic stimulation than trained athletes, resembling classical aerobic-type activity, in addition of eliciting strength gains shown in diverse studies. Methods. 3 group of male subjects, inactive (SED), endurance trained athletes (END) and strength trained athletes (STR) underwent fitness (VO2max) and lower-body strength tests (isokinetic). Subjects were submitted to a session of oscillating VT, composed of 3 exercises (isometric half-squat, dynamic squat, dynamic squat with added load), each of 3 minutes duration, and repeated at 3 frequencies. VO2, heart rate and Borg scale were monitored. Results. 27 healthy subjects (10 SED, 9 END and 8 STR), mean age 24.5 (SED), 25.0 (STR) and 29.8 (END) were included. VO2max was significantly different as expected (47.9 vs. 52.9 vs. 63.9 ml/kg/min, resp. for SED, STR and END). Isokinetic dominant leg extensors strength was higher in STR (3.32 Nm/kg vs. 2.60 and 2.74 in SED and END). During VT, peak oxygen consumption (% of VO2max) attained was 59.3 in SED, 50.8 in STR and 48.0 in END (P<0.001 between SED and other subjects). Peak heart rate (% of heart rate max) was 82.7 in SED, 80.4 in STR and 72.4 in END. In SED, dynamic exercises without extra load elicited 51.0% of VO2max and 72.1% of heart rate max, and perceived effort reached 15.1/20. Conclusions. VT is an unconventional type of exercise, which has been shown to enhance strength, bone density, balance and flexibility. Users are attracted by the relative passivity. In SED, we show that VT elicits sufficient cardiovascular response to benefit overall fitness in addition to the known strength effects. VT's higher acceptance as an exercise in sedentary people, compared to jogging or cycling for example, can lead to better adherence to physical activity. Although long-term effects of VT on health are not avalaible, we believe this type of combination of aerobic and resistance-type exercise can be beneficial on multiple health parameters, especially cardiovascular health.

Mechanical properties of rat cardiac skinned fibers are altered by chronic growth hormone hypersecretion.

Chronic growth hormone (GH) hypersecretion in rats leads to increased isometric force without affecting the unloaded shortening velocity of isolated cardiac papillary muscles, despite a marked isomyosin shift toward V3. To determine if alterations occurred at the level of the contractile proteins in rats bearing a GH-secreting tumor (GH rats), we examined the mechanical properties of skinned fibers to eliminate the early steps of the excitation-contraction coupling mechanism. We found that maximal active tension and stiffness at saturating calcium concentrations (pCa 4.5) were markedly higher in GH rats than in control rats (tension, 52.9 +/- 5.2 versus 38.1 +/- 4.6 mN.mm-2, p < 0.05; stiffness, 1,105 +/- 120 versus 685 +/- 88 mN.mm-2.microns-1, p < 0.01), whereas values at low calcium concentrations (pCa 9) were unchanged. In addition, the calcium sensitivity of the contractile proteins was slightly but significantly higher in GH rats than in control rats (delta pCa 0.04, p < 0.001). The crossbridge cycling rate, reflected by the response to quick length changes, was lower in GH rats than in control rats (62.0 +/- 2.6 versus 77.4 +/- 6.6 sec-1, p < 0.05), in good agreement with a decrease in the proportion of alpha-myosin heavy chains in the corresponding papillary muscles (45.5 +/- 2.0% versus 94.6 +/- 2.4%, p < 0.001). The changes in myosin heavy chain protein phenotype were paralleled by similar changes of the corresponding mRNAs, indicating that the latter occurred mainly at a pretranslational level. These results demonstrate that during chronic GH hypersecretion in rats, alterations at the myofibrillar level contribute to the increase in myocardial contractility observed in intact muscle.

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr)transformation to obtain the random vector y of dimension D. The factor model istheny = Λf + e (1)with the factors f of dimension k & D, the error term e, and the loadings matrix Λ.Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon a full-rank data matrix Y which is not the case for clr transformed data (see,e.g., Aitchison, 1986).The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation