Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Hyperbolic reaction-diffusion equations for a forest fire model

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Proximal tibia volumetric bone mineral density is correlated to the magnitude of local acceleration in male long distance runners.

Introduction: The beneficial effect of physical exercise on bone mineral density (BMD) is at least partly explained by the forces exerted directly on the bones. Male runners present generally higher BMD than sedentary individuals. We postulated that the proximal tibia BMD is related to the running distance as well as to the magnitude of the shocks (while running) in male runners. Methods: A prospective study (three yearly measurements) included 81 healthy male subjects: 16 sedentary lean subjects and three groups of runners (5-30 km/week, n=19; 30-50 km/week, n=29; 50-100 km/week, n=17). Several measurements were performed at the proximal tibia level: volumetric BMD (vBMD), cortical index (CI) i.e. an index of cortical bone thickness and peak accelerations (an index of shocks during heel strike) while running (measured by a 3-D accelerometer). A general linear model assessed the prediction of vBMD or CI by a) simple effects (running distance, peak accelerations, time) and b) interactions (for instance if vBMD prediction by peak acceleration depends on running distance). Results: CI and vBMD a) increase with running distance to reach a plateau over 30 km/wk, b) are positively associated with peak accelerations over 30 km/week. Discussion: Running may be associated with high peak accelerations in order to have beneficial effects on BMD. More important strains are needed to be associated with the same increase in BMD during running sessions of short duration than those of long duration. Conclusion: CI and vBMD are associated with the magnitude of the shocks during heel strike in runners. Key words: Bone mineral density, strains, physical exercise, running distance.

Assessment of volumetric bone mineral density of the femoral neck in postmenopausal women with and without vertebral fractures using quantitative multi-slice CT.

OBJECTIVE: To demonstrate the validity and reliability of volumetric quantitative computed tomography (vQCT) with multi-slice computed tomography (MSCT) and dual energy X-ray absorptiometry (DXA) for hip bone mineral density (BMD) measurements, and to compare the differences between the two techniques in discriminating postmenopausal women with osteoporosis-related vertebral fractures from those without. METHODS: Ninety subjects were enrolled and divided into three groups based on the BMD values of the lumbar spine and/or the femoral neck by DXA. Groups 1 and 2 consisted of postmenopausal women with BMD changes <-2SD, with and without radiographically confirmed vertebral fracture (n=11 and 33, respectively). Group 3 comprised normal controls with BMD changes > or =-1SD (n=46). Post-MSCT (GE, LightSpeed16) scan reconstructed images of the abdominal-pelvic region, 1.25 mm thick per slice, were processed by OsteoCAD software to calculate the following parameters: volumetric BMD values of trabecular bone (TRAB), cortical bone (CORT), and integral bone (INTGL) of the left femoral neck, femoral neck axis length (NAL), and minimum cross-section area (mCSA). DXA BMD measurements of the lumbar spine (AP-SPINE) and the left femoral neck (NECK) also were performed for each subject. RESULTS: The values of all seven parameters were significantly lower in subjects of Groups 1 and 2 than in normal postmenopausal women (P<0.05, respectively). Comparing Groups 1 and 2, 3D-TRAB and 3D-INTGL were significantly lower in postmenopausal women with vertebral fracture(s) [(109.8+/-9.61) and (243.3+/-33.0) mg/cm3, respectively] than in those without [(148.9+/-7.47) and (285.4+/-17.8) mg/cm(3), respectively] (P<0.05, respectively), but no significant differences were evident in AP-SPINE or NECK BMD. CONCLUSION: the femoral neck-derived volumetric BMD parameters using vQCT appeared better than the DXA-derived ones in discriminating osteoporotic postmenopausal women with vertebral fractures from those without. vQCT might be useful to evaluate the effect of osteoporotic vertebral fracture status on changes in bone mass in the femoral neck.

Spirometry reference equations for central European populations from school age to old age.

BACKGROUND: Spirometry reference values are important for the interpretation of spirometry results. Reference values should be updated regularly, derived from a population as similar to the population for which they are to be used and span across all ages. Such spirometry reference equations are currently lacking for central European populations. OBJECTIVE: To develop spirometry reference equations for central European populations between 8 and 90 years of age. MATERIALS: We used data collected between January 1993 and December 2010 from a central European population. The data was modelled using "Generalized Additive Models for Location, Scale and Shape" (GAMLSS). RESULTS: The spirometry reference equations were derived from 118'891 individuals consisting of 60'624 (51%) females and 58'267 (49%) males. Altogether, there were 18'211 (15.3%) children under the age of 18 years. CONCLUSION: We developed spirometry reference equations for a central European population between 8 and 90 years of age that can be implemented in a wide range of clinical settings.

Trabecular bone score is associated with volumetric bone density and microarchitecture as assessed by central QCT and HRpQCT in Chinese American and white women.

Although high-resolution peripheral quantitative computed tomography (HRpQCT) and central quantitative computed tomography (QCT) studies have shown bone structural differences between Chinese American (CH) and white (WH) women, these techniques are not readily available in the clinical setting. The trabecular bone score (TBS) estimates trabecular microarchitecture from dual-energy X-ray absorptiometry spine images. We assessed TBS in CH and WH women and investigated whether TBS is associated with QCT and HRpQCT indices. Areal bone mineral density (aBMD) by dual-energy X-ray absorptiometry, lumbar spine (LS) TBS, QCT of the LS and hip, and HRpQCT of the radius and tibia were performed in 71 pre- (37 WH and 34 CH) and 44 postmenopausal (21 WH and 23 CH) women. TBS did not differ by race in either pre- or postmenopausal women. In the entire cohort, TBS positively correlated with LS trabecular volumetric bone mineral density (vBMD) (r = 0.664), femoral neck integral (r = 0.651), trabecular (r = 0.641) and cortical vBMD (r = 0.346), and cortical thickness (C/I; r = 0.540) by QCT (p < 0.001 for all). TBS also correlated with integral (r = 0.643), trabecular (r = 0.574) and cortical vBMD (r = 0.491), and C/I (r = 0.541) at the total hip (p < 0.001 for all). The combination of TBS and LS aBMD predicted more of the variance in QCT measures than aBMD alone. TBS was associated with all HRpQCT indices (r = 0.20-0.52) except radial cortical thickness and tibial trabecular thickness. Significant associations between TBS and measures of HRpQCT and QCT in WH and CH pre- and postmenopausal women demonstrated here suggest that TBS may be a useful adjunct to aBMD for assessing bone quality.

Personality traits, cognition and volumetric MRI changes in elderly patients with early-onset depression: A 2-year follow-up study.

Previous studies revealed personality changes in elderly patients with early-onset depression (EOD) that persist in euthymic stages. However, depression in older patients is a complex disorder that may affect not only personality, but also cognition and brain structure. To address this issue, a cross-sectional comparison and 2-year follow-up of 28 EOD elderly patients and 48 healthy controls included detailed neurocognitive assessment, estimates of brain volumes in limbic areas and white matter hyperintensities, as well as evaluation of the Five Factor Model of personality, in a remitted mood state. Results revealed that cognitive performances as well as brain volumes were preserved in EOD patients both at baseline and at follow-up. The increased Neuroticism factor and Anxiety facet scores as well as the decreased Warmth and Positive Emotions facet scores found at baseline reached the level of healthy controls after 2years. Only the Depression facet scores remained significantly higher in EOD patients compared to controls upon follow-up. Results were independent of depressive relapse since baseline (25% of patients). These findings suggest that both cognitive performances and brain volumes show long-term preservation in older EOD patients. In contrast, the depression-related personality facet might be a trait like marker that persists in the long-term evolution of this disorder.

High order hydrodynamical equations

Hydrodynamical equations act as a link between the local observed magnitudes of galactic motion and the general ones accounting for the behaviour of the Galaxy as a whole. Constraints are set usually in order to use them even in the lower order hierarchy. The authors present in this paper the complete expressions up to their fourth order. These equations will be used in the next future in their general form taking into account both the expected increase of kinematic data that the astrometric mission Hipparcos will provide, and some recent results indicating the possibility to obtain estimates for the momenta gradients.

Brain volumetric correlates of autism spectrum disorder symptoms in attention deficit/hyperactivity disorder.

Autism spectrum disorder (ASD) symptoms frequently occur in subjects with attention deficit/hyperactivity disorder (ADHD). While there is evidence that both ADHD and ASD have differential structural correlates, no study to date has investigated these structural correlates within a framework that robustly accounts for the phenotypic overlap between the two disorders. The presence of ASD symptoms was measured by the parent-reported Children's Social and Behavioural Questionnaire (CSBQ) in ADHD subjects (n = 180), their unaffected siblings (n = 118) and healthy controls (n = 146). ADHD symptoms were assessed by a structured interview (K-SADS-PL) and the Conners' ADHD questionnaires. Whole brain T1-weighted MPRAGE images were acquired and the structural MRI correlates of ASD symptom scores were analysed by modelling ASD symptom scores against white matter (WM) and grey matter (GM) volumes using mixed effects models which controlled for ADHD symptom levels. ASD symptoms were significantly elevated in ADHD subjects relative to both controls and unaffected siblings. ASD scores were predicted by the interaction between WM and GM volumes. Increasing ASD score was associated with greater GM volume. Equivocal results from previous structural studies in ADHD and ASD may be due to the fact that comorbidity has not been taken into account in studies to date. The current findings stress the need to account for issues of ASD comorbidity in ADHD.

Dielectric constant obtained from TDR and volumetric moisture of soils in southern Brazil

Soil moisture is the property which most greatly influences the soil dielectric constant, which is also influenced by soil mineralogy. The aim of this study was to determine mathematical models for soil moisture and the dielectric constant (Ka) for a Hapludalf, two clayey Hapludox and a very clayey Hapludox and test the reliability of universal models, such as those proposed by Topp and Ledieu and their co-workers in the 80's, and specific models to estimate soil moisture with a TDR. Soil samples were collected from the 0 to 0.30 m layer, sieved through a mesh of 0.002 m diameter and packed in PVC cylinders with a 0.1 m diameter and 0.3 m height. Seven samples of each soil class were saturated by capillarity and a probe composed of two rods was inserted in each one of them. Moisture readings began with the saturated soil and concluded when the soil was near permanent wilting point. In each step, the samples were weighed on a precision scale to calculate volumetric moisture. Linear and polynomial models were adjusted for each soil class and for all soils together between soil moisture and the dielectric constant. Accuracy of the models was evaluated by the coefficient of determination, the standard error of estimate and the 1:1 line. The models proposed by Topp and Ledieu and their co-workers were not adequate for estimating the moisture in the soil classes studied. The adjusted linear and polynomial models for the entire set of data of the four soil classes did not have sufficient accuracy for estimating soil moisture. The greater the soil clay and Fe oxide content, the greater the dielectric constant of the medium for a given volumetric moisture. The specific models, θ = 0.40283 - 0.04231 Ka + 0.00194 Ka² - 0.000022 Ka³ (Hapludox) θ = 0.01971 + 0.02902 Ka - 0.00086 Ka² + 0.000012 Ka³ (Hapludox -PF), θ = 0.01692 - 0.00507 Ka (Hapludalf) and θ = 0.08471 + 0.01145 Ka (Hapludox-CA), show greater accuracy and reliability for estimating soil moisture in the soil classes studied.

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Fluctuations in domain growth: Ginzburg-Landau equations with multiplicative noise

Ginzburg-Landau equations with multiplicative noise are considered, to study the effects of fluctuations in domain growth. The equations are derived from a coarse-grained methodology and expressions for the resulting concentration-dependent diffusion coefficients are proposed. The multiplicative noise gives contributions to the Cahn-Hilliard linear-stability analysis. In particular, it introduces a delay in the domain-growth dynamics.

Numerical algorithm for Ginzburg-Landau equations with multiplicative noise: Application to domain growth

We consider stochastic partial differential equations with multiplicative noise. We derive an algorithm for the computer simulation of these equations. The algorithm is applied to study domain growth of a model with a conserved order parameter. The numerical results corroborate previous analytical predictions obtained by linear analysis.