The Becker-Döring equations with monomer input, competition and inhibition

We investigate the Becker-Döring model of nucleation with three generalisations; an input of monomer, an input of inhibitor and finally, we allow the monomers to form two morphologies of cluster. We assume size-independent aggregation and fragmentation rates. Initially we consider the problem of constant monomer input and determine the steady-state solution approached in the large-time limit, and the manner in which it is approached. Secondly, in addition to a constant input of monomer we allow a constant input of inhibitor, which prevents clusters growing any larger and this removes them from the kinetics of the process; the inhibitor is consumed in the action of poisoning a cluster. We determine a critical ratio of poison to monomer input below which the cluster concentrations tend to a non-zero steady-state solution and the poison concentration tends to a finite value. Above the critical input ratio, the concentrations of all cluster sizes tend to zero and the poison concentration grows without limit. In both cases the solution in the large-time limit is determined. Finally we consider a model where monomers form two morphologies, but the inhibitor only acts on one morphology. Four cases are identified, depending on the relative poison to monomer input rates and the relative thermodynamic stability. In each case we determine the final cluster distribution and poison concentration. We find that poisoning the less stable cluster type can have a significant impact on the structure of the more stable cluster distribution; a counter-intuitive result. All results are shown to agree with numerical simulation.

Effect of maternal cold exposure and nutrient restriction on insulin-like growth factor sensitivity in adipose tissue of newborn sheep

Adipose tissue mass in the newborn is determined in part by insulin-like growth factor (IGF)s, which are dependent on the maternal nutritional and metabolic environment during late gestation. The present study was designed to determine whether maternal cold exposure (CE) commencing in mid gestation could modulate some of the adaptive effects of nutrient restriction in late gestation on adipose tissue endocrine sensitivity in the resulting offspring. Twenty eight pregnant sheep were entered into the study and were either shorn, i.e. cold exposed, from 70 days gestation (term = 147 days), or remained unshorn, and were fed either their total calculated metabolisable energy (ME) requirements for body weight and pregnancy from 110 days gestation or 50% of this amount (n=7 per group). Adipose tissue was sampled from the offspring at one day of age and the mRNA abundance for IGF-I, II their receptors (R) and GH secretagogue receptor-1a (GHSR-1a) were determined. CE mothers produced larger offspring with more perirenal adipose tissue, an adaptation prevented by maternal nutrient restriction. Nutrient restriction in unshorn mothers increased IGF-I and IIR mRNA abundance. The mRNA abundances for IGF-I, II and IIR in adipose tissue were reduced by CE, adaptations independent of maternal food intake, whereas CE plus nutrient restriction increased GHSR-1a mRNA. In conclusion, maternal nutrient restriction with or without CE has very different effects on IGF sensitivity of adipose tissue and may act to ensure adequate fat stores are present in the newborn in the face of very different maternal endocrine and metabolic environments.

Ontogeny and nutritional programming of the hepatic growth hormone-insulin-like growth factor-prolactin axis in the sheep

The liver is an important metabolic and endocrine organ in the fetus but the extent to which its hormone receptor (R) sensitivity is developmentally regulated in early life is not fully established. We, therefore, examined developmental changes in mRNA abundance for the growth hormone (GH) and prolactin (PRL) receptors (R) plus insulin-like growth factor (IGF)-I and –II and their receptors. Fetal and postnatal sheep were sampled at either 80, or 140 days gestation, 1, 30 days or six months of age. The effect of maternal nutrient restriction between early to mid (i.e. 28 to 80 days gestation, the time of early liver growth) gestation on gene expression was also examined in the fetus and juvenile offspring. Gene expression for the GHR, PRLR and IGF-IR increased through gestation peaking at birth, whereas IGF-I was maximal near to term. In contrast, IGF-II mRNA decreased between mid and late gestation to increase after birth whereas IGF-IIR remained unchanged. A substantial decline in mRNA abundance for GHR, PRLR and IGF-IR then occurred up to six months. Maternal nutrient restriction reduced GHR and IGF-IIR mRNA abundance in the fetus, but caused a precocious increase in the PRLR. Gene expression for IGF-I and –II were increased in juvenile offspring born to nutrient restricted mothers. In conclusion, there are marked differences in the developmental ontogeny and nutritional programming of specific hormones and their receptors involved in hepatic growth and development in the fetus. These could contribute to changes in liver function during adult life.

Ontogeny and nutritional programming of mitochondrial proteins in the ovine kidney, liver and lung

This study investigated the developmental and nutritional programming of two important mitochondrial proteins, namely voltage dependent anion channel (VDAC) and cytochrome c in the sheep kidney, liver and lung. The effect of maternal nutrient restriction between early to mid gestation (i.e. 28 to 80 days gestation, the period of maximal placental growth) on the abundance of these proteins was also examined in fetal and juvenile offspring. Fetuses were sampled at 80 and 140 days gestation (term ~147 days), and postnatal animals at 1 and 30 days and 6 months of age. The abundance of VDAC peaked at 140 days gestation in the lung, compared with 1 day after birth in the kidney and liver, whereas cytochrome c abundance was greatest at 140 days gestation in the liver, 1 day after birth in the kidney and 6 months of age in lungs. This differential ontogeny in mitochondrial protein abundance between tissues was accompanied with very different tissue specific responses to changes in maternal food intake. In the liver, maternal nutrient restriction only increased mitochondrial protein abundance at 80 days gestation, compared with no effect in the kidney. In contrast, in the lung mitochondrial protein abundance was raised near to term, whereas VDAC abundance was decreased by 6 months of age. These findings demonstrate the tissue specific nature of mitochondrial protein development that reflects differences in functional adaptation after birth. The divergence in mitochondrial response between tissues to maternal nutrient restriction early in pregnancy further reflects these differential ontogeny’s.

Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to eigenvalue/stability problems. The underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution. In this way, errors stemming from both the numerical approximation of the original nonlinear flow problem, as well as the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

Can we improve the statistical analysis of stroke trials? Statistical re-analysis of functional outcomes in stroke trials

Background: Most large acute stroke trials have been neutral. Functional outcome is usually analysed using a yes or no answer, e.g. death or dependency vs. independence. We assessed which statistical approaches are most efficient in analysing outcomes from stroke trials. Methods: Individual patient data from acute, rehabilitation and stroke unit trials studying the effects of interventions which alter functional outcome were assessed. Outcomes included modified Rankin Scale, Barthel Index, and ‘3 questions’. Data were analysed using a variety of approaches which compare two treatment groups. The results for each statistical test for each trial were then compared. Results: Data from 55 datasets were obtained (47 trials, 54,173 patients). The test results differed substantially so that approaches which use the ordered nature of functional outcome data (ordinal logistic regression, t-test, robust ranks test, bootstrapping the difference in mean rank) were more efficient statistically than those which collapse the data into 2 groups (chi square) (ANOVA p<0.001). The findings were consistent across different types and sizes of trial and for the different measures of functional outcome. Conclusions: When analysing functional outcome from stroke trials, statistical tests which use the original ordered data are more efficient and more likely to yield reliable results. Suitable approaches included ordinal logistic regression, t-test, and robust ranks test.

A randomised controlled trial of triple antiplatelet therapy (Aspirin, Clopidogrel and Dipyridamole) in the secondary prevention of stroke: safety, tolerability and feasibility

Background: Aspirin, dipyridamole and clopidogrel are effective in secondary vascular prevention. Combination therapy with three antiplatelet agents might maximise the benefit of antiplatelet treatment in the secondary prevention of ischaemic stroke. Methodology/Principal Findings: A randomised, parallel group, observer-blinded phase II trial compared the combination of aspirin, clopidogrel and dipyridamole with aspirin alone. Adult patients with ischaemic stroke or transient ischaemic attack (TIA) within 5 years were included. The primary outcome was tolerability to treatment assessed as the number of patients completing randomised treatment. Recruitment was halted prematurely after publication of the ESPRIT trial (which confirmed that combined aspirin and dipyridamole is more effective than aspirin alone). 17 patients were enrolled: male 12 (71%), mean age 62 (SD 13) years, lacunar stroke syndrome 12 (71%), median stroke/TIA onset to randomisation 8 months. Treatment was discontinued in 4 of 9 (44%) patients receiving triple therapy vs. none of 8 taking aspirin (p = 0.08). One recurrent stroke occurred in a patient in the triple group who was noncompliant of all antiplatelet medications. The number of patients with adverse events and bleeding complications, and their severity, were significantly greater in the triple therapy group (p,0.01). Conclusions/Significance: Long term triple antiplatelet therapy was asociated with a significant increase in adverse events and bleeding rates, and their severity, and a trend to increased discontinuations. However, the patients had a low risk of recurrence and future trials should focus on short term therapy in high risk patients characterised by a very recent event or failure of dual antiplatelet therapy.

Telmisartan to prevent recurrent stroke and cardiovascular events

Background Prolonged lowering of blood pressure after a stroke reduces the risk of recurrent stroke. In addition, inhibition of the renin–angiotensin system in high-risk patients reduces the rate of subsequent cardiovascular events, including stroke. However, the effect of lowering of blood pressure with a renin–angiotensin system inhibitor soon after a stroke has not been clearly established. We evaluated the effects of therapy with an angiotensin-receptor blocker, telmisartan, initiated early after a stroke. Methods In a multicenter trial involving 20,332 patients who recently had an ischemic stroke, we randomly assigned 10,146 to receive telmisartan (80 mg daily) and 10,186 to receive placebo. The primary outcome was recurrent stroke. Secondary outcomes were major cardiovascular events (death from cardiovascular causes, recurrent stroke, myocardial infarction, or new or worsening heart failure) and new-onset diabetes. Results The median interval from stroke to randomization was 15 days. During a mean followup of 2.5 years, the mean blood pressure was 3.8/2.0 mm Hg lower in the telmisartan group than in the placebo group. A total of 880 patients (8.7%) in the telmisartan group and 934 patients (9.2%) in the placebo group had a subsequent stroke (hazard ratio in the telmisartan group, 0.95; 95% confidence interval [CI], 0.86 to 1.04; P = 0.23). Major cardiovascular events occurred in 1367 patients (13.5%) in the telmisartan group and 1463 patients (14.4%) in the placebo group (hazard ratio, 0.94; 95% CI, 0.87 to 1.01; P = 0.11). New-onset diabetes occurred in 1.7% of the telmisartan group and 2.1% of the placebo group (hazard ratio, 0.82; 95% CI, 0.65 to 1.04; P = 0.10). Conclusions Therapy with telmisartan initiated soon after an ischemic stroke and continued for 2.5 years did not significantly lower the rate of recurrent stroke, major cardiovascular events, or diabetes. (ClinicalTrials.gov number, NCT00153062.)

Aspirin and extended-release dipyridamole versus clopidogrel for recurrent stroke

Background Recurrent stroke is a frequent, disabling event after ischemic stroke. This study compared the efficacy and safety of two antiplatelet regimens — aspirin plus extendedrelease dipyridamole (ASA–ERDP) versus clopidogrel. Methods In this double-blind, 2-by-2 factorial trial, we randomly assigned patients to receive 25 mg of aspirin plus 200 mg of extended-release dipyridamole twice daily or to receive 75 mg of clopidogrel daily. The primary outcome was first recurrence of stroke. The secondary outcome was a composite of stroke, myocardial infarction, or death from vascular causes. Sequential statistical testing of noninferiority (margin of 1.075), followed by superiority testing, was planned. Results A total of 20,332 patients were followed for a mean of 2.5 years. Recurrent stroke occurred in 916 patients (9.0%) receiving ASA–ERDP and in 898 patients (8.8%) receiving clopidogrel (hazard ratio, 1.01; 95% confidence interval [CI], 0.92 to 1.11). The secondary outcome occurred in 1333 patients (13.1%) in each group (hazard ratio for ASA–ERDP, 0.99; 95% CI, 0.92 to 1.07). There were more major hemorrhagic events among ASA–ERDP recipients (419 [4.1%]) than among clopidogrel recipients (365 [3.6%]) (hazard ratio, 1.15; 95% CI, 1.00 to 1.32), including intracranial hemorrhage (hazard ratio, 1.42; 95% CI, 1.11 to 1.83). The net risk of recurrent stroke or major hemorrhagic event was similar in the two groups (1194 ASA–ERDP recipients [11.7%], vs. 1156 clopidogrel recipients [11.4%]; hazard ratio, 1.03; 95% CI, 0.95 to 1.11). Conclusions The trial did not meet the predefined criteria for noninferiority but showed similar rates of recurrent stroke with ASA–ERDP and with clopidogrel. There is no evidence that either of the two treatments was superior to the other in the prevention of recurrent stroke. (ClinicalTrials.gov number, NCT00153062.)