Prehospital HMG Co-A reductase inhibitor use and reduced mortality in hemorrhagic shock due to trauma.

INTRODUCTION: 3-Hydroxy-3-methyl-glutaryl Co-A reductase inhibitors (HMG Co-A reductase inhibitors, statins) are commonly used medications for the control of serum cholesterol. Recent data suggests that these medications also modify the inflammatory pathways in sepsis, septic shock, and hemorrhagic shock due to ruptured abdominal aortic aneurysms. Statin use in hemorrhagic shock due to trauma, however, has conflicting data, with one study showing improvement, but only in certain subsets of patients. STUDY DESIGN: We retrospectively reviewed the medical records of patients from our institution's trauma registry database from January 2000 to December 2008. We included patients with an age greater than 45 years and an Injury Severity Score (ISS) greater than 15 with evidence of shock as follows: hypotension, elevated serum lactate, base deficit, metabolic acidosis, or objective evidence of end-organ malperfusion. We excluded patients with devastating head injury, patients with pre-existing advance directives directing against life-sustaining measures, patients for whom family or health care proxies withdrew support in 24 h or less, and patients who succumbed to their injuries in the first 24 h in the hospital. We compared age, gender, mortality, statin use, aspirin use, and Sequential Organ Failure Assessment (SOFA) scores. RESULTS: Mortality in the group without prehospital statin use was 38.1% (95% confidence interval [CI]: 28.4-48.8%) and mortality in the group with prehospital statin use was 8.3% (95% CI: 2.13-22.5%, P = 0.0009). The absolute risk reduction was 29.8% and the relative risk reduction was 78.1%. Survivors were statistically significantly younger than nonsurvivors in the group without prehospital statin use, but not in the group with documented prehospital statin use. There was no similar benefit to aspirin use. There were no significant differences in the SOFA scores, hospital length of stay (HLOS), or intensive care unit length of stay (ICU LOS) between statin users and nonusers. CONCLUSIONS: Prehospital HMG Co-A reductase use was associated with improved survival in a population with severe trauma and evidence of ongoing hemorrhagic shock.

Egg size evolution and energetic constraints on population dynamics.

We use population models that are based on dynamic energy budget models for individuals in order to study the evolution of offspring size and its relationship to the evolution of population dynamics. We show the existence of alternative evolutionarily stable strategies for offspring investment strategy resulting from a trade off between offspring number and time-to-maturity. The model predicts egg energy in Daphnia magna well, and suggests that the observed egg energy in D. magna is the result of selection for minimal egg investment constrained by minimum viable egg energy, combined with selection for a juvenile energy reserve. The selection for minimal egg size pushes populations toward chaotic dynamics. However, the minimum viable egg size combined with low efficiency of conversion of energy to new biomass is sufficient to keep population dynamics out of chaos.

End-tidal carbon dioxide measurements as a prognostic indicator of outcome in cardiac arrest.

PURPOSE: To evaluate the use of end-tidal carbon dioxide values in predicting survival in cardiopulmonary arrest. BACKGROUND: The decision about when to terminate resuscitative efforts for patients with cardiopulmonary arrest is often subjective. End-tidal carbon dioxide values have been suggested as potential objective criteriafor making this decision. METHODS: This study was a cooperative effort of the St Louis chapter of the American Association of Critical-Care Nurses and its members and involved 6 hospitals and an air evacuation service. All adult patients who had a cardiopulmonary arrest were eligiblefor the study. Once a patient with cardiac arrest was intubated, end-tidal carbon dioxide and cardiac rhythms were measured and recorded every 5 minutes for 20 minutes or until resuscitation efforts were terminated. Patients' survival at the time of the arrest, survival 24 hours after the arrest, and discharge status were followed up. RESULTS: A total of 127 patients were enrolled in the study. All but 1 patient with end-tidal carbon dioxide values less than 10 mm Hg died before discharge. End-tidal carbon dioxide values greater than 10 mm Hg were associated with various degrees of survival. Overall survival to discharge was less than 14%, regardless of the end-tidal carbon dioxide value. CONCLUSION: Measurements of end-tidal carbon dioxide can be used to accurately predict nonsurvival of patients with cardiopulmonary arrest. End-tidal carbon dioxide levels should be monitored during cardiopulmonary arrest and should be considered a useful prognostic value for determining the outcome of resuscitative efforts.

Habitat structure and population persistence in an experimental community.

Understanding spatial population dynamics is fundamental for many questions in ecology and conservation. Many theoretical mechanisms have been proposed whereby spatial structure can promote population persistence, in particular for exploiter-victim systems (host-parasite/pathogen, predator-prey) whose interactions are inherently oscillatory and therefore prone to extinction of local populations. Experiments have confirmed that spatial structure can extend persistence, but it has rarely been possible to identify the specific mechanisms involved. Here we use a model-based approach to identify the effects of spatial population processes in experimental systems of bean plants (Phaseolus lunatus), herbivorous mites (Tetranychus urticae) and predatory mites (Phytoseiulus persimilis). On isolated plants, and in a spatially undivided experimental system of 90 plants, prey and predator populations collapsed; however, introducing habitat structure allowed long-term persistence. Using mechanistic models, we determine that spatial population structure did not contribute to persistence, and spatially explicit models are not needed. Rather, habitat structure reduced the success of predators at locating prey outbreaks, allowing between-plant asynchrony of local population cycles due to random colonization events.

Pair approximation for lattice models with multiple interaction scales.

Pair approximation has frequently proved effective for deriving qualitative information about lattice-based stochastic spatial models for population, epidemic and evolutionary dynamics. Pair approximation is a moment closure method in which the mean-field description is supplemented by approximate equations for the frequencies of neighbor-site pairs of each possible type. A limitation of pair approximation relative to moment closure for continuous space models is that all modes of interaction between individuals (e.g., dispersal of offspring, competition, or disease transmission) are assumed to operate over a single spatial scale determined by the size of the interaction neighborhood. In this paper I present a multiscale pair approximation which allows different sized neighborhoods for each type of interaction. To illustrate and test the approximation I consider a spatial single-species logistic model in which offspring are dispersed across a birth neighborhood and established individuals have a death rate depending on the population density in a competition neighborhood, with one of these neighborhoods nested inside the other. Analysis of the steady-state equations yields several qualitative predictions that are confirmed by simulations of the model, and numerical solutions of the dynamic equations provide a close approximation to the transient behavior of the stochastic model on a large lattice. The multiscale pair approximation thus provides a useful intermediate between the standard pair approximation for a single interaction neighborhood, and a complete set of moment equations for more spatially detailed models.

A multicenter 12-month evaluation of single-tooth implants restored 3 weeks after 1-stage surgery.

The time-intensive, multi-step process of dental implant therapy limits patient acceptance. This 3-year prospective multicenter study sought to determine the safety of an expedited therapy that consisted of loading unsplinted maxillary anterior single-tooth implants 3 weeks after 1-stage surgical placement, and determination of the peri-implant cortical bone and mucosal responses to the expedited procedure. Fifty-two patients missing 1 or 2 maxilliary anterior teeth were enrolled in a study approved by the Institutional Committee on Human Subjects Research and based on strict inclusion and exclusion criteria. Astra Tech ST implants placed in a 1-stage procedure were restored 3 weeks later with ST abutments and a provisional crown (baseline); 7 to 9 weeks later, a porcelain-fused-to-metal or all-ceramic crown was cemented. Radiographic and clinical examinations were made at baseline and at 6 and 12 months. Implant survival was recorded. Cortical bone responses and peri-implant mucosal responses were evaluated. Fifty-eight implants were placed. During the 3-week period after implant placement, 4 patients were dismissed because of smoking cigarettes (a protocol deviation), and 1 patient was excluded because of deviation in loading time. Of the remaining 53 implants, 2 failed before definitive crown cementation. The resultant 96.2% survival rate was independent of implant length, tooth position, and bone quality/quantity. The mean change in marginal bone level was 0.4 mm at 12 months. The number of surfaces with plaque decreased from 3.4% at baseline to 0.5% at 12 months. The surfaces with inflammation also decreased. A mean gain in papilla length of 0.61 mm occurred, and a gain in buccal gingiva (x = 0.34 mm) was observed. A high success rate with positive tissue responses was achieved for maxillary anterior unsplinted single-tooth implants placed in a 1-stage surgery and restored at 3 weeks. This 2-component system is suited to a single-stage, rapid loading protocol for esthetic single-tooth replacement.

Crossing the hopf bifurcation in a live predator-prey system.

Population biologists have long been interested in the oscillations in population size displayed by many organisms in the field and laboratory. A wide range of deterministic mathematical models predict that these fluctuations can be generated internally by nonlinear interactions among species and, if correct, would provide important insights for understanding and predicting the dynamics of interacting populations. We studied the dynamical behavior of a two-species aquatic laboratory community encompassing the interactions between a demographically structured herbivore population, a primary producer, and a mineral resource, yet still amenable to description and parameterization using a mathematical model. The qualitative dynamical behavior of our experimental system, that is, cycles, equilibria, and extinction, is highly predictable by a simple nonlinear model.

Cholera dynamics and El Niño-Southern Oscillation.

Analysis of a monthly 18-year cholera time series from Bangladesh shows that the temporal variability of cholera exhibits an interannual component at the dominant frequency of El Niño-Southern Oscillation (ENSO). Results from nonlinear time series analysis support a role for both ENSO and previous disease levels in the dynamics of cholera. Cholera patterns are linked to the previously described changes in the atmospheric circulation of south Asia and, consistent with these changes, to regional temperature anomalies.

Testing for predator dependence in predator-prey dynamics: a non-parametric approach.

The functional response is a key element in all predator-prey interactions. Although functional responses are traditionally modelled as being a function of prey density only, evidence is accumulating that predator density also has an important effect. However, much of the evidence comes from artificial experimental arenas under conditions not necessarily representative of the natural system, and neglecting the temporal dynamics of the organism (in particular the effects of prey depletion on the estimated functional response). Here we present a method that removes these limitations by reconstructing the functional response non-parametrically from predator-prey time-series data. This method is applied to data on a protozoan predator-prey interaction, and we obtain significant evidence of predator dependence in the functional response. A crucial element in this analysis is to include time-lags in the prey and predator reproduction rates, and we show that these delays improve the fit of the model significantly. Finally, we compare the non-parametrically reconstructed functional response to parametric forms, and suggest that a modified version of the Hassell-Varley predator interference model provides a simple and flexible function for theoretical investigation and applied modelling.

Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling.

We present and evaluate an approach to analyzing population dynamics data using semimechanistic models. These models incorporate reliable information on population structure and underlying dynamic mechanisms but use nonparametric surface-fitting methods to avoid unsupported assumptions about the precise form of rate equations. Using historical data on measles epidemics as a case study, we show how this approach can lead to better forecasts, better characterizations of the dynamics, and a better understanding of the factors causing complex population dynamics relative to either mechanistic models or purely descriptive statistical time-series models. The semimechanistic models are found to have better forecasting accuracy than either of the model types used in previous analyses when tested on data not used to fit the models. The dynamics are characterized as being both nonlinear and noisy, and the global dynamics are clustered very tightly near the border of stability (dominant Lyapunov exponent lambda approximately 0). However, locally in state space the dynamics oscillate between strong short-term stability and strong short-term chaos (i.e., between negative and positive local Lyapunov exponents). There is statistically significant evidence for short-term chaos in all data sets examined. Thus the nonlinearity in these systems is characterized by the variance over state space in local measures of chaos versus stability rather than a single summary measure of the overall dynamics as either chaotic or nonchaotic.

Patterns of genetic polymorphism maintained by fluctuating selection with overlapping generations.

We study the form of polymorphisms that can be maintained by the joint effects of generation overlap and randomly fluctuating selection, acting on a quantitative trait affecting offspring viability. The genetic system can be single locus or multilocus, haploid or diploid. Selection is assumed to be stabilizing with a randomly fluctuating optimum, and we assume additive allelic effects without epistasis. For fluctuations above a certain threshold, nonzero genetic variance is maintained in an evolutionarily stable population. Our model allows a continuum of alleles with arbitrary effects at each locus. Nonetheless, the genotype distribution in an evolutionarily stable population is discrete--a polymorphism of a few alleles with distinctly different effects--and often involves only a pair of alleles at each locus. The form of the genotype distribution depends on the number of loci affecting the trait, and on the kurtosis of the distribution of the phenotypic optimum theta. If the trait is affected by several loci, the number of polymorphic loci increases with increased variance of fluctuations in selection. For distributions of theta with negative kurtosis (i.e., lower kurtosis than a Gaussian) the number of polymorphic loci increases gradually (0-->1-->2--> ...M), and the genetic variability is in the form of a few diallelic or triallelic loci with alleles of large effect. For distributions with positive kurtosis, the increase is abrupt (0 -> many) and involves many diallelic loci. These results do not fit the conventional multivariate Gaussian or near-Gaussian models for quantitative traits, but may partially explain recent findings that heritable variation in natural populations is often due to genes of large effect.

Environmental fluctuations and the maintenance of genetic diversity in age or stage-structured populations.

The ability of random fluctuations in selection to maintain genetic diversity is greatly increased when generations overlap. This result has been derived previously using genetic models with very special assumptions about the population age structure. Here we explore its robustness in more realistic population models, with very general age structure or physiological structure. For a range of genetic models (haploid, diploid, single and multi-locus) we find that the condition for maintaining genetic diversity generalizes almost without change. Genetic diversity is maintained by selection if a product of the form (generation overlap) x (selection intensity) x (variability in the selection regime) is sufficiently large, where the generation overlap is measured in units of Fisher's reproductive value. This conclusion is based on a local evolutionary stability analysis, which differs from the standard "protected polymorphism" criterion for the maintenance of genetic diversity. Simulation results match the predictions from the local stability analysis, but not those from the protected polymorphism criterion. The condition obtained here for maintaining genetic diversity requires fitness fluctuations that are substantial but well within the range observed in many studies of natural populations.

A mathematical model for estimation of broiler egg weight loss from physical dimensions and air cell size during incubation.

A formula was derived that will enable hatcheries to estimate percentage weight loss using the width, length, and air cell diameter of the egg. The formula was derived by fitting an equation to the shape of the egg and using this shape equation to obtain estimates of air cell volume and egg volume. These estimates were coupled with the principle that weight = density x volume to give the final formula as a function of air cell diameter divided by egg width. The formula was tested by comparing its estimated values with measured values from eggs set at two different incubation conditions chosen to cover the range of conditions found in commercial hatcheries. As the day of transfer approached, embryo size and distortion of the air cell caused inaccuracies to develop in the results of this equation. However, data suggest that the equation can be used to calculate percentage weight loss until approximately the 16th day of incubation.

Convergence to stationary distributions in two-species stochastic competition models.

Two sets of sufficient conditions are given for convergence to stationary distributions, for some general models of two species competing in a randomly varying environment. The models are nonlinear stochastic difference equations which define Markov chains. One set of sufficient conditions involves strong continuity and phi-irreducibility of the transition probability for the chain. The second set has a much weaker irreducibility condition, but is only applicable to monotonic models. The results are applied to a stochastic two-species Ricker model, and to Chesson's "lottery model with vacant space", to illustrate how the assumptions can be checked in specific models.

Effects of noise on some dynamical models in ecology.

We investigate effects of random perturbations on the dynamics of one-dimensional maps (single species difference equations) and of finite dimensional flows (differential equations for n species). In particular, we study the effects of noise on the invariant measure, on the "correlation" dimension of the attractor, and on the possibility of detecting the nonlinear deterministic component by applying reconstruction techniques to the time series of population abundances. We conclude that adding noise to maps with a stable fixed-point obscures the underlying determinism. This turns out not to be the case for systems exhibiting complex periodic or chaotic motion, whose essential properties are more robust. In some cases, adding noise reveals deterministic structure which otherwise could not be observed. Simulations suggest that similar results hold for flows whose attractor is almost two-dimensional.

ESS germination strategies in randomly varying environments. I. Logistic-type models.

ESS germination strategies are studied in a model of annual plant population dynamics in a randomly varying environment. The possible strategies are different values of the annual germination fraction G, either constant over time or varying in response to a "cue" correlated with upcoming environmental conditions. The model generalizes D. Cohen's model (1966, J. Theor. Biol. 12, 119-129; 1968, J. Ecol. 56, 219-228) by allowing density-dependent per capita seed yields. ESSs are characterized in terms of the resulting harmonic mean growth rate of population density. The ESS criterion cannot be solved analytically, but qualitative relationships between the value of the ESS and other population parameters are obtained, and environments in which 100% germination is an ESS are identified. Some explicit predictions of the theory are summarized and compared with ideas of M. Westoby (1981, Amer. Nat. 118, 882-885). The results of this study are compared with those of Cohen (op. cit.) in a companion paper.

ESS germination strategies in randomly varying environments. II. Reciprocal Yield-Law models.

The study of ESS germination fractions in S. Ellner (1985, Theor. Pop. Biol. 27, 000-000) is applied and extended in the case of annuals obeying the Reciprocal Yield Law. The effects of parameter changes on the value of the ESS germination fraction are determined in some limiting cases by analyses of approximations. Numerical solutions of the ESS criterion are used to check the robustness of the conclusions and the accuracy of the approximations. In general, the ESS germination fraction decreases with an increased survivorship of buried seeds and with increased "variability" of seed yields. However, different measures of "variability" are appropriate in different circumstances. To avoid the possibility of conflicting predictions depending on the measure of variability, it is suggested that tests of the theory be limited to co-occurring species, and to variability due to climatic fluctuations. The ESS theory based on the Reciprocal Yield Law is compared with D. Cohen's (1966, J. Theor. Biol. 12, 119-129; 1968, J. Ecol. 56, 219-228) density-independent theory of "optimal" germination. The theories differ qualitatively and quantitatively regarding the influence of mean yield, seed survivorship, and the frequency of favorable years on the predicted germination fraction.