Mathematical modelling

The development of a new process model of cement grinding in two-stage mills is discussed. The new model has been used to simulate cement grinding and predicting mill performance in open and closed circuit configuration. The new model considered the two-compartment mill as perfectly mixed slices in series. The breakage rate function uses the back calculation technique to determine offline using drop weight and abrasion tests.

Green turtle somatic growth dynamics in a spatially disjunct Great Barrier Reef metapopulation

The growth dynamics of green sea turtles resident in four separate foraging grounds of the southern Great Barrier Reef genetic stock were assessed using a nonparametric regression modeling approach. Juveniles recruit to these grounds at the same size, but grow at foraging-ground-dependent rates that result in significant differences in expected size- or age-at-maturity. Mean age-at-maturity was estimated to vary from 25-50 years depending on the ground. This stock comprises mainly the same mtDNA haplotype, so geographic variability might be due to local environmental conditions rather than genetic factors, although the variability was not a function of latitudinal variation in environmental conditions or whether the food stock was seagrass or algae. Temporal variability in growth rates was evident in response to local environmental stochasticity, so geographic variability might be due to local food stock dynamics. Despite such variability, the expected size-specific growth rate function at all grounds displayed a similar nonmonotonic growth pattern with a juvenile growth spurt at 60-70 cm curved carapace length, (CCL) or 15-20 years of age. Sex-specific growth differences were also evident with females tending to grow faster than similar-sized males after the Juvenile growth spurt. It is clear that slow sex-specific growth displaying both spatial and temporal variability and a juvenile growth spurt are distinct growth behaviors of green turtles from this stock.

Age and growth in olive ridley seaturtles (Lepidochelys olivacea) from the north-central Pacific: a skeletochronological analysis

The olive ridley is the most abundant seaturtle species in the world but little is known of the demography of this species. We used skeletochronological data on humerus diameter growth changes to estimate the age of North Pacific olive ridley seaturtles caught incidentally by pelagic longline fisheries operating near Hawaii and from dead turtles washed ashore on the main Hawaiian Islands. Two age estimation methods [ranking, correction factor (CF)] were used and yielded age estimates ranging from 5 to 38 and 7 to 24 years, respectively. Rank age-estimates are highly correlated (r = 0.93) with straight carapace length (SCL), CF age estimates are not (r = 0.62). We consider the CF age-estimates as biologically more plausible because of the disassociation of age and size. Using the CF age-estimates, we then estimate the median age at sexual maturity to be around 13 years old (mean carapace size c. 60 cm SCL) and found that somatic growth was negligible by 15 years of age. The expected age-specific growth rate function derived using numerical differentiation suggests at least one juvenile growth spurt at about 10–12 years of age when maximum age-specific growth rates, c. 5 cm SCL year−1, are apparent.

The importance of different timings of excitatory and inhibitory pathways in neural field models

In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.

Influence of aging, tidal volume, and respiratory rate on Doppler echocardiographic indices of diastolic function in normal male subjects: A quantitative evaluation

Background: Although the influence of respiration on ventricular filling, as evaluated by Doppler technique, and the evaluation of diastolic velocities of mitral valve annulus (MVA), as measured by Doppler tissue imaging (DTI), can provide valuable information for the study of left ventricular (LV) diastolic function, the concomitant effects of aging, tidal volume (TV), and respiratory rate (RR) on these velocities have not been quantitatively investigated. Methods: We evaluated 12 normal male volunteers (Group I) aged 20-26 years (mean: 22.8) and 8 normal subjects aged 41 to 54 years old (mean: 45.9) (Group II). Using DTI we measured peak early (E-a) and late (A(a)) velocities of longitudinal axis expansion at lateral and medial MVA. Doppler mitral and tricuspid flow velocities were measured: peak early (E) and late (A) inflow velocity, early (E-i) and late (A(i)) flow integral, and deceleration time of peak early mitral flow velocity (DT). Respiratory cycles were simultaneously recorded at RR of 9, 12, 15, and 18 cycles/min and TV of 600 and 900 mL during respiration (RESP). Results and conclusions: (1) E, A, and A(i) in MV had negligible change during respiration, but E-i was significantly reduced during inspiration; (2) DT reduced slightly with inspiration, but the change was significant only with TV of 900 mL; (3) an important increase of E in right ventricular flow was observed during inspiration; (4) variations of RR and TV did not significantly influence right and left ventricular inflow in normal subjects, in the conditions of this investigation; (5) a significant increase of E-a at medial MVA was documented during inspiration only in young subjects; (6) a significant decrease of A(a) at medial MVA was observed during inspiration in both groups of volunteers; (7) RR and TV did not influence MVA velocities in young and adult subjects; (8) a consistent reduction in E-a and a significant increase in A(a) were observed with increasing age; (9) these changes were more conspicuous and consistent than those documented in ventricular filling when young and middle-age men are compared, suggesting that the DTI is more sensitive to detect changes in diastolic function; and (10) in addition, these data suggest that, for evaluation of diastolic function, in clinical context, it is not necessary to control rigorously RR or TV.

Estimation of glomerular filtration rate in hospitalised patients: are we overestimating renal function?

QUESTIONS UNDER STUDY AND PRINCIPLES: Estimating glomerular filtration rate (GFR) in hospitalised patients with chronic kidney disease (CKD) is important for drug prescription but it remains a difficult task. The purpose of this study was to investigate the reliability of selected algorithms based on serum creatinine, cystatin C and beta-trace protein to estimate GFR and the potential added advantage of measuring muscle mass by bioimpedance. In a prospective unselected group of patients hospitalised in a general internal medicine ward with CKD, GFR was evaluated using inulin clearance as the gold standard and the algorithms of Cockcroft, MDRD, Larsson (cystatin C), White (beta-trace) and MacDonald (creatinine and muscle mass by bioimpedance). 69 patients were included in the study. Median age (interquartile range) was 80 years (73-83); weight 74.7 kg (67.0-85.6), appendicular lean mass 19.1 kg (14.9-22.3), serum creatinine 126 μmol/l (100-149), cystatin C 1.45 mg/l (1.19-1.90), beta-trace protein 1.17 mg/l (0.99-1.53) and GFR measured by inulin 30.9 ml/min (22.0-43.3). The errors in the estimation of GFR and the area under the ROC curves (95% confidence interval) relative to inulin were respectively: Cockcroft 14.3 ml/min (5.55-23.2) and 0.68 (0.55-0.81), MDRD 16.3 ml/min (6.4-27.5) and 0.76 (0.64-0.87), Larsson 12.8 ml/min (4.50-25.3) and 0.82 (0.72-0.92), White 17.6 ml/min (11.5-31.5) and 0.75 (0.63-0.87), MacDonald 32.2 ml/min (13.9-45.4) and 0.65 (0.52-0.78). Currently used algorithms overestimate GFR in hospitalised patients with CKD. As a consequence eGFR targeted prescriptions of renal-cleared drugs, might expose patients to overdosing. The best results were obtained with the Larsson algorithm. The determination of muscle mass by bioimpedance did not provide significant contributions.

The rate of recovery in renal function when patients with HIV infection discontinue treatment with tenofovir.

OBJECTIVES: Tenofovir is associated with reduced renal function. It is not clear whether patients can be expected to fully recover their renal function if tenofovir is discontinued. METHODS: We calculated the estimated glomerular filtration rate (eGFR) for patients in the Swiss HIV Cohort Study remaining on tenofovir for at least 1 year after starting a first antiretroviral therapy regimen with tenofovir and either efavirenz or the ritonavir-boosted protease inhibitor lopinavir, atazanavir or darunavir. We estimated the difference in eGFR slope between those who discontinued tenofovir after 1 year and those who remained on tenofovir. RESULTS: A total of 1049 patients on tenofovir for at least 1 year were then followed for a median of 26 months, during which time 259 patients (25%) discontinued tenofovir. After 1 year on tenofovir, the difference in eGFR between those starting with efavirenz and those starting with lopinavir, atazanavir and darunavir was - 0.7 [95% confidence interval (CI) -2.3 to 0.8], -1.4 (95% CI -3.2 to 0.3) and 0.0 (95% CI -1.7 to 1.7) mL/min/1.73 m(2) , respectively. The estimated linear rate of decline in eGFR on tenofovir was -1.1 (95% CI -1.5 to -0.8) mL/min/1.73 m(2) per year and its recovery after discontinuing tenofovir was 2.1 (95% CI 1.3 to 2.9) mL/min/1.73 m(2) per year. Patients starting tenofovir with either lopinavir or atazanavir appeared to have the same rates of decline and recovery as those starting tenofovir with efavirenz. CONCLUSIONS: If patients discontinue tenofovir, clinicians can expect renal function to recover more rapidly than it declined.

Estimation of glomerular filtration rate in hospitalized patients : are we overestimating renal function?

Estimer la filtration glomérulaire chez les personnes âgées, tout en tenant compte de la difficulté supplémentaire d'évaluer leur masse musculaire, est difficile et particulièrement important pour la prescription de médicaments. Le taux plasmatique de la creatinine dépend à la fois de la fraction d'élimination rénale et extra-rénale et de la masse musculaire. Actuellement, pour estimer là filtration glomérulaire différentes formules sont utilisées, qui se fondent principalement sur la valeur de la créatinine. Néanmoins, en raison de la fraction éliminée par les voies tubulaires et intestinales la clairance de la créatinine surestime généralement le taux de filtration glomérulaire (GFR). Le but de cette étude est de vérifier la fiabilité de certains marqueurs et algorithmes de la fonction rénale actuellement utilisés et d'évaluer l'avantage additionnel de prendre en considération la masse musculaire mesurée par la bio-impédance dans une population âgée (> 70 ans) et avec une fonction rénale chronique compromise basée sur MDRD eGFR (CKD stades lll-IV). Dans cette étude, nous comparons 5 équations développées pour estimer la fonction rénale et basées respectivement sur la créatinine sérique (Cockcroft et MDRD), la cystatine C (Larsson), la créatinine combinée à la bêta-trace protéine (White), et la créatinine ajustée à la masse musculaire obtenue par analyse de la bio-impédance (MacDonald). La bio-impédance est une méthode couramment utilisée pour estimer la composition corporelle basée sur l'étude des propriétés électriques passives et de la géométrie des tissus biologiques. Cela permet d'estimer les volumes relatifs des différents tissus ou des fluides dans le corps, comme par exemple l'eau corporelle totale, la masse musculaire (=masse maigre) et la masse grasse corporelle. Nous avons évalué, dans une population âgée d'un service interne, et en utilisant la clairance de l'inuline (single shot) comme le « gold standard », les algorithmes de Cockcroft (GFR CKC), MDRD, Larsson (cystatine C, GFR CYS), White (beta trace protein, GFR BTP) et Macdonald (GFR = ALM, la masse musculaire par bio-impédance. Les résultats ont montré que le GFR (mean ± SD) mesurée avec l'inuline et calculée avec les algorithmes étaient respectivement de : 34.9±20 ml/min pour l'inuline, 46.7±18.5 ml/min pour CKC, 47.2±23 ml/min pour CYS, 54.4±18.2ml/min pour BTP, 49±15.9 ml/min pour MDRD et 32.9±27.2ml/min pour ALM. Les courbes ROC comparant la sensibilité et la spécificité, l'aire sous la courbe (AUC) et l'intervalle de confiance 95% étaient respectivement de : CKC 0 68 (055-0 81) MDRD 0.76 (0.64-0.87), Cystatin C 0.82 (0.72-0.92), BTP 0.75 (0.63-0.87), ALM 0.65 (0.52-0.78). ' En conclusion, les algorithmes comparés dans cette étude surestiment la GFR dans la population agee et hospitalisée, avec des polymorbidités et une classe CKD lll-IV. L'utilisation de l'impédance bioelectrique pour réduire l'erreur de l'estimation du GFR basé sur la créatinine n'a fourni aucune contribution significative, au contraire, elle a montré de moins bons résultats en comparaison aux autres equations. En fait dans cette étude 75% des patients ont changé leur classification CKD avec MacDonald (créatinine et masse musculaire), contre 49% avec CYS (cystatine C), 56% avec MDRD,52% avec Cockcroft et 65% avec BTP. Les meilleurs résultats ont été obtenus avec Larsson (CYS C) et la formule de Cockcroft.

Correlation between heart rate variability and pulmonary function adjusted by confounding factors in healthy adults

The autonomic nervous system maintains homeostasis, which is the state of balance in the body. That balance can be determined simply and noninvasively by evaluating heart rate variability (HRV). However, independently of autonomic control of the heart, HRV can be influenced by other factors, such as respiratory parameters. Little is known about the relationship between HRV and spirometric indices. In this study, our objective was to determine whether HRV correlates with spirometric indices in adults without cardiopulmonary disease, considering the main confounders (e.g., smoking and physical inactivity). In a sample of 119 asymptomatic adults (age 20-80 years), we evaluated forced vital capacity (FVC) and forced expiratory volume in 1 s (FEV1). We evaluated resting HRV indices within a 5-min window in the middle of a 10-min recording period, thereafter analyzing time and frequency domains. To evaluate daily physical activity, we instructed participants to use a triaxial accelerometer for 7 days. Physical inactivity was defined as <150 min/week of moderate to intense physical activity. We found that FVC and FEV1, respectively, correlated significantly with the following aspects of the RR interval: standard deviation of the RR intervals (r =0.31 and 0.35), low-frequency component (r =0.38 and 0.40), and Poincaré plot SD2 (r =0.34 and 0.36). Multivariate regression analysis, adjusted for age, sex, smoking, physical inactivity, and cardiovascular risk, identified the SD2 and dyslipidemia as independent predictors of FVC and FEV1 (R2=0.125 and 0.180, respectively, for both). We conclude that pulmonary function is influenced by autonomic control of cardiovascular function, independently of the main confounders.

Aggregate vs disaggregate data analysis: a paradox in the estimation of money demand function of Japan under the low interest rate policy

We investigate the issue of whether there was a stable money demand function for Japan in 1990's using both aggregate and disaggregate time series data. The aggregate data appears to support the contention that there was no stable money demand function. The disaggregate data shows that there was a stable money demand function. Neither was there any indication of the presence of liquidity trapo Possible sources of discrepancy are explored and the diametrically opposite results between the aggregate and disaggregate analysis are attributed to the neglected heterogeneity among micro units. We also conduct simulation analysis to show that when heterogeneity among micro units is present. The prediction of aggregate outcomes, using aggregate data is less accurate than the prediction based on micro equations. Moreover. policy evaluation based on aggregate data can be grossly misleading.

Pitch detection algorithms based on zero-cross rate and autocorrelation function for musical notes

This paper discusses two pitch detection algorithms (PDA) for simple audio signals which are based on zero-cross rate (ZCR) and autocorrelation function (ACF). As it is well known, pitch detection methods based on ZCR and ACF are widely used in signal processing. This work shows some features and problems in using these methods, as well as some improvements developed to increase their performance. © 2008 IEEE.

Age and gender influence the cardiorespiratory function and metabolic rate of broiler chicks during normocapnia and hypercapnia

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation of Cardiovascular Function During S(+)-Ketamine Constant Rate Infusion in Dorsally Recumbent Halothane-Anesthetized Horses

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A comparison of measured and estimated glomerular filtration rate in successfully treated HIV-patients with preserved renal function

Monitoring of renal function becomes increasingly important in the aging population of HIV-1 infected patients. We compared Cockroft & Gault (C&G), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI), Modification of Diet in Renal Disease (MDRD), Cystatin C- and 24 h urine-based estimated GFR (eGFR) with the gold standard, measured GFR (mGFR) using [125I]-iothalamate.