When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’tincludes below detection limits and/or zero values, and since most of the geological dataresponds to lognormal distributions, these “zero data” represent a mathematicalchallenge for the interpretation.We need to start by recognizing that there are zero values in geology. For example theamount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-existswith nepheline. Another common essential zero is a North azimuth, however we canalways change that zero for the value of 360°. These are known as “Essential zeros”, butwhat can we do with “Rounded zeros” that are the result of below the detection limit ofthe equipment?Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimeswe need to differentiate between a sodic and a potassic alteration. Pre-classification intogroups requires a good knowledge of the distribution of the data and the geochemicalcharacteristics of the groups which is not always available. Considering the zero valuesequal to the limit of detection of the used equipment will generate spuriousdistributions, especially in ternary diagrams. Same situation will occur if we replace thezero values by a small amount using non-parametric or parametric techniques(imputation).The method that we are proposing takes into consideration the well known relationshipsbetween some elements. For example, in copper porphyry deposits, there is always agood direct correlation between the copper values and the molybdenum ones, but whilecopper will always be above the limit of detection, many of the molybdenum values willbe “rounded zeros”. So, we will take the lower quartile of the real molybdenum valuesand establish a regression equation with copper, and then we will estimate the“rounded” zero values of molybdenum by their corresponding copper values.The method could be applied to any type of data, provided we establish first theircorrelation dependency.One of the main advantages of this method is that we do not obtain a fixed value for the“rounded zeros”, but one that depends on the value of the other variable.Key words: compositional data analysis, treatment of zeros, essential zeros, roundedzeros, correlation dependency

1st radiometric dating of a paleontologically dated Bathonian level from Georgia (USSR) - Use of the cathodoluminescence for selection of suitable plagioclases

Jurassic volcanic formations interlayered with (ammonite-bearing) sediments are common in the Caucasus area; this situation is of interest for the numerical calibration of the poorly documented Jurassic portion of the time scale. However, following petrographic study on thin sections no whole-rocks can be considered reliable geochronometers due to subsequent alteration; from about 20 samples, two were selected for plagioclase dating; one (V134) is probably early Kimmeridgian in age; the other (V136) is probably located in the Lower Bathonian stage according to diagnostic ammonites. Cathodoluminescence (CTL) study has shown that sample V136 was similar to usual volcanic feldspars (blue to green colour); however, the lack of CTL of the V134 plagioclase is a character common to diagenetic feldspars; consequently, in spite of a good optical preservation, this geo-chronometer cannot give an age representative of the time of emplacement of the lava flow. We have combined CTL observation with microprobe analysis in order to document the poorly known CTL behaviour of volcanic feldspars; cations Ti4+ and Fe2+ play a major role in the CTL colour of plagioclases and are able to document the growing history of these feldspars ; phenocrysts are initially rich in Fe2+ (core of the crystals, green in colour), then richer in Ti toward the exterior; microcrysts are even richer in Ti (blue to bright blue). We have also observed that natural CTL colour was modified resulting from acid ``cleaning'' of the separated feldspars : the initial blue or green colour tends to change to yellow or violet, respectively, after acid treatment probably due to oxydation of Fe2+ toward Fe3+. X-ray and microprobe analyses both indicated that plagioclases from sample V134 was near the sodic end member (albite) suggesting a diagenetic origin in this andesitic basalt; In contrast, sample V136 contains a calcic plagioclase of common composition for a doleritic basalt. The K-Ar conventional technique was applied as a preliminary tool for radiometric analysis. The Kimmeridgian Na-plagioclase sample gave a ``rejuvenated'' (85 Ma) apparent age which confirms a late genesis for the separated plagioclase phase; this interpretation is based on CTL observation, X-ray analysis, and microprobe analysis ; these techniques are able to distinguish samples which have been submitted to diagenetic alteration from those which have not. An age consistent with the stratigraphic location has been obtained from sample V136. This age of 161 +/- 3 (2-sigma) Ma, is the first one available from a sample palaeontologically located with reasonable precision within the mid Jurassic time.

Chemical changes in argisols under irrigated grape production in the central São Francisco river valley, Brazil

This study compares the chemical composition of the solution and exchange complex of soil in a 3-year-old irrigated vineyard (Vitis vinifera L., Red Globe cultivar) with that of adjacent clearing in the native hyperxerophyllic 'caatinga' vegetation. The soils are classified as Plinthic Eutrophic Red-Yellow Argisol; according to Soil Taxonomy they are isohyperthermic Plinthustalfs. Detailed physiographic characterization revealed an impermeable gravel and cobble covering the crystalline rocks; the relief of this layer was more undulating than the level surface. Significant higher concentrations of extractable Na, K, Mg and Ca were observed within the vineyard. Lower soil acidity, higher Ca/Mg ratios, as well as lower sodium adsorption and Na/K ratios reflected additions of dolomitic lime, superphosphate and K-bearing fertilizers. As the water of the São Francisco River is of good quality for irrigation (C1S1), the increases in Na were primarily attributed to capillary rise from the saline groundwater table. None of the soil in the study area was found to be sodic. About 62% of the vineyard had an Ap horizon with salinity levels above 1.5dSm-1 (considered detrimental for grape production); according to average values for this horizon, a potential 13% reduction in grape production was predicted. Differences in chemical composition in function of distance to the collector canals were observed in the clearing, but not in the vineyard. The influence of differences in the elevations of the surface and impermeable layers, as well as pediment thickness, was generally weaker under irrigation. Under irrigation, soil moisture was greater in points of convergent surface waterflow; the effect of surface curvature on chemical properties, though less consistent, was also stronger in the vineyard.

Irrigation with domestic wastewater: a multivariate analysis of main soil changes

Irrigation with treated domestic sewage wastewater (TSE) is an agricultural practice to reduce water requirements of agroecossystems and the nutrient load impact on freshwaters, but adverse effects on soil chemical (salinization, sodification, etc.) and soil physical properties (alteration in soil porosity and hydraulic conductivity, etc.) have been reported. This study aimed to define some relationships among these changes in an Oxisol using multivariate analysis. Corn (Zea mays L.) and sunflower (Helianthus annuus L.) were grown for two years, irrigated with TSE. The following soil properties were determined: Ca2+; Mg2+; Na+; K+ and H + Al contents, cationic exchangeable capacity (CEC), sum of bases (SB), base saturation (V), texture (sand, silt and clay), macro-, micro-, and cryptoporosity (V MA, V MI and V CRI), water content at soil saturation (θS) and at field capacity (θFC), residual water content (θR), soil bulk density (d s), water dispersed clay (WDC) and saturated hydraulic conductivity (K SAT). Factor analysis revealed the following six principal factors: Fine Porosity (composed of Na+; K+; WDC, θR, θRFC, and V CRI); Large Porosity (θS, d s, V MA, Vs); Soil CEC (Ca2+; Mg2+; CEC, SB, V); Soil Acidity (H + Al); and Soil Texture (factors 5 and 6). A dual pore structure appears clearly to the factors 1 and 2, with an apparent relationship between fine porosity and the monovalent cations Na+ and K+. The irrigation (with potable sodic tap water or sewage wastewater) only had a significant effect on Fine Porosity and Large Porosity factors, while factors 3 and 4 (Soil CEC and Soil Acidity) were correlated with soil depth. The main conclusion was a shift in pore distribution (large to fine pores) during irrigation with TSE, which induces an increase of water storage and reduces the capacity of drainage of salts.

Alkali-calcic and alkaline post-orogenic (PO) granite magmatism: petrologic constraints and geodynamic settings

The end of an orogenic Wilson cycle corresponds to amalgamation of terranes into a Pangaea and is marked by widespread magmatism dominated by granitoids. The post-collision event starts with magmatic processes still influenced by subducted crustal materials. The dominantly calc-alkaline suites show a shift from normal to high-K to very high-K associations. Source regions are composed of depleted and later enriched orogenic subcontinental lithospheric mantle, affected by dehydration melting and generating more and more K- and LILE-rich magmas. In the vicinity of intra-crustal magma chambers, anatexis by incongruent melting of hydrous minerals may generate peraluminous granitoids bearing mafic enclaves. The post-collision event ends with emplacement of bimodal post-orogenic (PO) suites along transcurrent fault zones. Two suites are defined, (i) the alkali-calcic monzonite-monzogranite-syenogranite-alkali feldspar granite association characterised by [biotite + plagioclase] fractionation and moderate [LILE + HFSE] enrichments and (ii) the alkaline monzonite-syenite-alkali feldspar granite association characterised by [amphibole + alkali feldspar] fractionation and displaying two evolutionary trends, one peralkaline with sodic mafic mineralogy and higher enrichments in HFSE than in LILE, and the other aluminous biotite-bearing marked by HFSE depletion relative to LILE due to accessory mineral precipitation. Alkali-calcic and alkaline suites differ essentially in the amounts of water present within intra-crustal magma chambers, promoting crystallisation of various mineral assemblages. The ultimate enriched and not depleted mantle source is identical for the two PO suites. The more primitive LILE and HFSE-rich source rapidly replaces the older orogenic mantle source during lithosphere delamination and becomes progressively the thermal boundary layer of the new lithosphere. Present rock compositions are a mixture of major mantle contribution and various crustal components carried by F-rich aqueous fluids circulating within convective cells created around magma chambers. In favourable areas, PO suites pre-date a new orogenic Wilson cycle. (C) 1998 Elsevier Science B.V. All rights reserved.

Igneous layering, fractional crystallization and growth of granitic plutons: The Dolbel batholith in SW Niger

This study reassesses the development of compositional layering during the growth of granitic plutons, with emphasis on fractional crystallization and its interaction with both injection and inflation-related deformation. The Dolbel batholith (SW Niger) consists of 14, kilometre-sized plutons emplaced by pulsed magma inputs. Each pluton has a coarse-grained core and a peripheral layered series. Rocks consist of albite (An(<= 11)), K-feldspar (Or(96 99), Ab(1) (4)), quartz, edenite (X(Mg)=0337-0.55), augite (X(Mg)=0.65-0.72) and accessories (apatite, titanite and Fe-Ti-oxides). Whole-rock compositions are metaluminous, sodic (K(2)O/Na(2)O=0.49-0.62) and iron-rich [FeO(tot)/(FeO(tot)+MgO)=0.65-0.82]. The layering is present as size-graded and modally graded, sub-vertical, rhythmic units. Each unit is composed of three layers, which are, towards the interior: edenite +/- plagioclase (C(a/p)), edenite+plagioclase+augite+quartz (C(q)), and edenite+plagioclase+augite+quartz+K-feldspar (C(k)). All phases except quartz show zoned microstructures consisting of external intercumulus overgrowths, a central section showing oscillatory zoning and, in the case of amphibole and titanite, complexly zoned cores. Ba and Sr contents of feldspars decrease towards the rims. Plagioclase crystal size distributions are similar in all units, suggesting that each unit experienced a similar thermal history. Edenite, characteristic of the basal C(a/p) layer, is the earliest phase to crystallize. Microtextures and phase diagrams suggest that edenite cores may have been brought up with magma batches at the site of emplacement and mechanically segregated along the crystallized wall, whereas outer zones of the same crystals formed in situ. The subsequent C(q) layers correspond to cotectic compositions in the Qz-Ab-Or phase diagram at P(H2O)=5 kbar. Each rhythmic unit may therefore correspond to a magma batch and their repetition to crystallization of recurrent magma recharges. Microtextures and chemical variations in major phases allow four main crystallization stages to be distinguished: (1) open-system crystallization in a stirred magma during magma emplacement, involving dissolution and overgrowth (core of edenite and titanite crystals); (2) in situ fractional crystallization in boundary layers (C(a/p) and C(q) layers); (3) equilibrium `en masse' eutectic crystallization (C(k) layers); (4) compaction and crystallization of the interstitial liquid in a highly crystallized mush (e. g. feldspar intercumulus overgrowths). It is concluded that the formation of the layered series in the Dolbel plutons corresponds principally to in situ differentiation of successive magma batches. The variable thickness of the Ck layers and the microtextures show that crystallization of a rhythmic unit stops and it is compacted when a new magma batch is injected into the chamber. Therefore, assembly of pulsed magma injections and fractional crystallization are independent, but complementary, processes during pluton construction.

Cartografia detallada de sòls en àrees de regadiu de Catalunya

La superfície regada a Catalunya és d'unes 260.00 ha. aproximadament, la qual constitueix el 26 % de l'àrea conreada i el 8 % de l'àrea total; tot i així, en l'àrea regada es produeix, aproximadament, el 68 % del producte final agrari. El pes econòmic de l'àrea regada, la facilitat més gran per introduir noves tecnologies amb una rendibilitat superior i la necessitat que tenen les mateixes tecnologies de disposar d'una informació de base van fer aconsellable iniciar les tasques de cartografia de sòls del Departament d'Agricultura, Ramaderia i Pesca (DARP) en les àrees indicades. La naturalesa del problema plantejat, consistent bàsicament en l'aplicació de tecnologia agrícola (programació de regs, utilització de l'aigua de reg sota condicions de salinitat-sodicitat, plans de fertilització, reg de sòls guixencs, i selecció de sòls segons l'aptitud per als cultius, etc.), i també la grandària de les explotacions i parcel·les, obliguen a disposar d'una acurada informació quantitativa i a plantejar una cartografia de sòls detallada. En aquest treball s'exposen els estudis realitzats fins ara sobre cartografia de sòls i les aplicacions que s'han efectuat o que es preveu que s'efectuaran en un termini curt. Es comenta la problemàtica sorgida en el transcurs de la realització d'aquests treballs cartogràfics, es revisen les aplicacions dutes a terme i les dificultats que s'han trobat en la transmissió i la transferència de la informació generada al sector agrari en general i als tècnics de l'Administració.

Variabilidad espacial del arroz como cultivo indicador de salinidad en regadíos del valle del Ebro a partir de series temporales en imágenes Landsat TM

El presente trabajo pretende la caracterización de la distribución espacial típica del cultivo de arroz en regadíos del valle del Ebro, donde la presencia del cultivo está ligada a la existencia de suelos salino-sódicos. Esta caracterización ha de permitir identificar las áreas donde es típica la presencia del cultivo año tras año y las áreas donde es frecuente su fluctuación debido tanto a condiciones variables de salinidad del suelo como a variabilidad en las condiciones de mercado. Para ello se ha recurrido al análisis de una serie temporal de mapas de cultivos (7 años) derivados de la clasificación supervisada de imágenes Landsat TM. La determinación de las áreas típicas y de fluctuación del cultivo de arroz se hace entonces a partir del análisis estadístico de clases, y mediante superposición espacial de coberturas en un entorno SIG-Raster.

Osteoclastic tartrate-resistant acid phosphatase 5b. Diagnostic use and biological significance in bone physiology

The skeleton undergoes continuous turnover throughout life. In women, an increase in bone turnover is pronounced during childhood and puberty and after menopause. Bone turnover can be monitored by measuring biochemical markers of bone resorption and bone formation. Tartrate-resistant acid phosphatase (TRACP) is an enzyme secreted by osteoclasts, macrophages and dendritic cells. The secreted enzyme can be detected from the blood circulation by recently developed immunoassays. In blood circulation, the enzyme exists as two isoforms, TRACP 5a with an intact polypeptide chain and TRACP 5b in which the polypeptide chain consists of two subunits. The 5b form is predominantly secreted by osteoclasts and is thus associated with bone turnover. The secretion of TRACP 5b is not directly related to bone resorption; instead, the levels are shown to be proportional to the number of osteoclasts. Therefore, the combination of TRACP 5b and a marker reflecting bone degradation, such as C-terminal cross-linked telopeptides of type I collagen (CTX), enables a more profound analysis of the changes in bone turnover. In this study, recombinant TRACP 5a-like protein was proteolytically processed into TRACP 5b-like two subunit form. The 5b-like form was more active both as an acid phosphatase and in producing reactive oxygen species, suggesting a possible function for TRACP 5b in osteoclastic bone resorption. Even though both TRACP 5a and 5b were detected in osteoclasts, serum TRACP 5a levels demonstrated no change in response to alendronate treatment of postmenopausal women. However, TRACP 5b levels decreased substantially, demonstrating that alendronate decreases the number of osteoclasts. This was confirmed in human osteoclast cultures, showing that alendronate decreased the number of osteoclats by inducing osteoclast apoptosis, and TRACP 5b was not secreted as an active enzyme from the apoptotic osteoclasts. In peripubertal girls, the highest levels of TRACP 5b and other bone turnover markers were observed at the time of menarche, whereas at the same time the ratio of CTX to TRACP 5b was lowest, indicating the presence of a high number of osteoclasts with decreased resorptive activity. These results support the earlier findings that TRACP 5b is the predominant form of TRACP secreted by osteoclasts. The major source of circulating TRACP 5a remains to be established, but is most likely other cells of the macrophage-monocyte system. The results also suggest that bone turnover can be differentially affected by both osteoclast number and their resorptive activity, and provide further support for the possible clinical use of TRACP 5b as a marker of osteoclast number.

Alendronato de sódio: metodologias para análise quantitativa

This paper presents a review of some published proposals for the analysis of sodium alendronate. The drug is an aminobisphosphonate compound used to inhibit the osteoclastic resorption of bone, and different methods were developed for its quantitative determination. These methodologies employed reversed-phase or ion-exchange HPLC analysis, both associated with different detectors: UV and fluorescence detection after derivatization of the drug, conductivity and refractive index detectors, as well as the indirect UV detection. Titrimetry and spectrophotometry (with previous complexation of the drug), which are simpler procedures, were also described, but they showed poor specificity when compared to liquid chromatography.

Orthotopic PC-3 Tumor Xenografts in Studies on Prostate Cancer Growth and Metastasis

Prostate cancer is generally a slowly developing disease. However, some cancers develop into an aggressive, metastasic and consequently life-threatening state. The mechanisms of prostate cancer spread are still mainly unidentified but hormones and growth factors are known to been involved. The forming of new blood vessels i.e. angiogenesis is crucial for tumor growth. Blood vessels and lymphatic vessels are also prominent routes for metastasis. Both angiogenic and lymphangiogenic factors are overexpressed in prostate cancer. We established an in vivo model to study the factors effecting human prostate cancer growth and metastasis. Tumors were produced by the orthotopic inoculation of PC-3 prostate cancer cells into the prostates of immunodeficient mice. Like human prostate tumors, these tumors metastasized to prostate-draining lymph nodes. Treatment of the mice with the bisphosphonate alendronate known to decrease prostate cancer cell invasion in vitro inhibited metastasis and decreased tumor growth. Decreased tumor growth was associated with decreased angiogenesis and increased apoptosis of tumor cells. To elucidate the role of angiogenesis in prostate cancer progression, we studied the growth of orthotopic PC-3 tumors overexpressing fibroblast growth factor b (FGF8b) known to be expressed in human prostate cancer. FGF8b increased tumor growth and angiogenesis, which were both associated with a characteristic gene expression pattern. To study the role of lymphangiogenesis, we produced orthotopic PC-3 tumors overexpressing vascular endothelial growth factor C (VEGF-C). Blocking of VEGF-C receptor (VEGFR3) completely inhibited lymph node metastasis whereas overexpression of VEGF-C increased tumor growth and angiogenesis. VEGF-C also increased lung metastases but, surprisingly, decreased spread to lymph nodes. This suggests that the expanded vascular network was primarily used as a route for tumor spreading. Finally, the functionality of the capillary network in subcutaneous FGF8b-overexpressing PC-3 tumors was compared to that of tumors overexpressing VEGF. Both tumors showed angiogenic morphology and grew faster than control tumors. However, FGF8b tumors were hypoxic and their perfusion and oxygenation was poor compared with VEGF tumors. This suggests that the growth advantage of FGF8b tumors is more likely due to stimulated proliferation than effective angiogenesis. In conclusion, these results show that orthotopic prostate tumors provide a useful model to explore the mechanisms of prostate cancer growth and metastasis.

Inhibitors of human collagenase, MMP1

Different common drugs (Meloxicam, Tenoxicam and Piroxicam, and sodium alendronate) were tested both experimental and theoretically as inhibitors of interstitial human collagenase, also known as matrix metalloproteinase 1 (MMP-1). The in vitro collagenase activity, alone and in the presence of inhibitors, was quantified by the reaction with a fluorescent synthetic substrate and measuring the change of emission. Collagenase-inhibitor interaction was studied theoretically by computational calculations. Three among the four tested substances showed moderate inhibiting activity against the human collagenase.

Bisphosphonate Inhibition of Prostate Cancer Cell Invasion, Migration and Cytoskeletal Organization

Metastatic bone lesions are commonly associated with prostate cancer affecting approximately 60-80% of the patients. The progression of prostate cancer into an advanced stage is a complex process and its molecular mechanisms are poorly understood. So far, no curative treatment is available for advanced stages of prostate cancer. Bisphosphonates (BPs) are synthetic pyrophosphate analogues, which are used as therapeutics for various metabolic bone diseases because of their ability to inhibit osteoclastic bone resorption. Nitrogen-containing bisphosphonates block the function of osteoclasts by disturbing the vesicular traffic and the mevalonate pathway -related enzymes, for example farnesyl diphosphate synthase, which is involved in post-translational isoprenylation of small GTPases. In addition, the anti-proliferative, anti-invasive and pro-apoptotic effects of nitrogen-containing bisphosphonates on various cancer cell lines have been reported. The aim of this thesis work was to clarify the effects of bisphosphonates on prostate cancer cells, focusing on the mechanisms of adhesion, invasion and migration. Furthermore, the role of the mevalonate pathway and prenylation reactions in invasion and regulation of the cytoskeleton of prostate cancer cells were examined. Finally, the effects of alendronate on cytoskeleton- and actin-related proteins in prostate cancer cells were studied in vitro and in vivo. The results showed that the nitrogen-containing bisphosphonate alendronate inhibited the adhesion of prostate cancer cells to various extracellular matrix proteins and migration and invasion in vitro. Inhibition of invasion and migration was reversed by mevalonate pathway intermediates. The blockage of the prenylation transferases GGTase I and FTase inhibited the invasion, migration and actin organization of prostate cancer cells. The marked decrease of cofilin was observed by the prenylation inhibitors used. Inhibition of GGTase I also disrupted the regulation of focal adhesion kinase and paxillin. In addition, alendronate disrupted the cytoskeletal organization and decreased the level of cofilin in vitro and in vivo. The decrease of the cofilin level by alendronate could be one of the key mechanisms behind the observed inhibition of migration and invasion. Based on the effects of nitrogen-containing bisphosphonates on tumor cell invasion and cytoskeletal organization, they can be suggested to be developed as therapeutics for inhibiting prostate cancer metastasis.

Bone Health, Osteoporosis and Fracture Risk in Neurofibromatosis 1 - An Emphasis on Osteoclasts

Neurofibromatosis 1 (NF1) is an autosomal dominant hereditary syndrome, affecting skin, neural tissues and skeleton. Hallmarks of NF1 include benign cutaneous neurofibroma tumors, pigmentation lesions on the skin and in the iris, learning disabilities and predisposition to selected malignancies. Low bone mineral density (BMD) and osteopenia/osteoporosis are common in NF1. Osteoporosis is a systemic disorder characterized by low bone mineral density and increased fracture risk. Treatment of osteoporosis aims to prevent falls and decrease fracture risk. Osteoporosis is diagnosed in adults by measuring BMD and evaluating clinical risk factors of the patient. Bone turnover is a process of old bone resorbed by osteoclasts and new bone formed by osteoblasts. Multinuclear osteoclasts are derived from osteoclast progenitors, which can be isolated from peripheral blood. Osteoclast progenitors were isolated from 17 NF1 patients and healthy controls, and cultured in vitro to osteoclasts. NF1 osteoclasts are hyperactive, displaying increased differentiation and resorption capacity, abnormal morphology and tolerance to serum deprivation compared to control osteoclasts. These findings expanded the study to evaluate the effects of bisphosphonates, drugs designed to treat osteoporosis, in osteoclasts derived from blood samples of 20 NF1 and control persons. The number of control osteoclasts was expectedly reduced after bisphosphonate treatment. However, NF1 osteoclasts tolerated the apoptotic effect of alendronate, zoledronic acid and clodronate in vitro compared to controls. NF1-related osteoporosis was found in ~20 % of the patients, and selected laboratory parameters were measured. Patients with NF1 have increased levels of serum CTX and PINP, reflecting increased bone turnover in vivo. BMD decreases progressively in NF1 as evaluated in 19 NF1 patients 12 years after their initial BMD measurement. Patients with NF1-related osteopenia often progress to osteoporosis. This was found in patients aged 37-76.

Évaluation de l'utilisation des agents prévenant la résorption osseuse en situation réelle et impact de la non-adhésion au traitement sur la survenue de fractures ostéoporotiques : l'utilisation et les coûts directs des soins de santé

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.