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PubMed1989

Stochastic models of soil denitrification.

Soil denitrification is a highly variable process that appears to be lognormally distributed. This variability is manifested by large sample coefficients of variation for replicate estimates of soil core denitrification rates. Deterministic models for soil denitrification have been proposed in the past, but none of these models predicts the approximate lognormality exhibited by natural denitrification rate estimates. In this study, probabilistic (stochastic) models were developed to understand how positively skewed distributions for field denitrification rate estimates result from the combined influences of variables known to affect denitrification. Three stochastic models were developed to describe the distribution of measured soil core denitrification rates. The driving variables used for all the models were denitrification enzyme activity and CO(2) production rates. The three models were distinguished by the functional relationships combining these driving variables. The functional relationships used were (i) a second-order model (model 1), (ii) a second-order model with a threshold (model 2), and (iii) a second-order saturation model (model 3). The parameters of the models were estimated by using 12 separate data sets (24 replicates per set), and their abilities to predict denitrification rate distributions were evaluated by using three additional independent data sets of 180 replicates each. Model 2 was the best because it produced distributions of denitrification rate which were not significantly different (P > 0.1) from distributions of measured denitrification rates. The generality of this model is unknown, but it accurately predicted the mean denitrification rates and accounted for the stochastic nature of this variable at the site studied. The approach used in this study may be applicable to other areas of ecological research in which accounting for the high spatial variability of microbiological processes is of interest.

Journal Article↗
PubMed2006

Relation between blood glucose and coronary mortality over 33 years in the Whitehall Study.

OBJECTIVE: Glucose intolerance is a risk factor for coronary disease, but there is uncertainty about the shape of the dose-response relationship between glucose level and risk of coronary mortality. We examined the prospective relation of 2-h postload blood glucose (2hBG) with coronary and other major causes of mortality over 33 years. RESEARCH DESIGN AND METHODS: A 50-g oral glucose tolerance test (OGTT) was performed at baseline (1967-1969) in 17,869 male civil servants aged 40-64 years. RESULTS: There were 3,561 coronary deaths during 451,787 person-years of observation. All-cause, cardiovascular, and respiratory mortality were elevated among participants with glucose intolerance. The hazard of coronary mortality rose from 2hBG = 4.6 mmol/l (83 mg/dl [95% CI 4.2-5.3]). The dose-response relation was best fitted by a single slope above this level, with no evidence of nonlinearity, compared with Cox models using other threshold levels, and those containing log 2hBG terms. There was no evidence for a dose-response relationship below 2hBG = 4.6 mmol/l. Between this level and 11.1 mmol/l (200 mg/dl), the age-adjusted hazard ratio was 3.62 (95% CI 2.3-5.6). The graded relationship was attenuated by 45% after adjustment for baseline coronary heart disease (CHD), BMI, systolic blood pressure, blood cholesterol, smoking, physical activity, lung function, and employment grade. CONCLUSIONS: A threshold model with linear slope best described the dose-response relationship between postload blood glucose and CHD mortality risk.

Adult↗
PubMed2004

Genetics of osteochondral disease and its relationship with meat quality and quantity, growth, and feed conversion traits in pigs.

The main objective of this research was to estimate heritabilities of seven osteochondrosis (OC) lesions in station-tested pigs and their genetic and phenotypic correlations with four meat quality (MQ) traits, the percentage of premium cuts (PPC), daily weight gain (DWG), and feed conversion ratio (FCR). Observed OC lesions were on the head of humerus (HK), condylus medialis humeri (CMH), condylus lateralis humeri (CLH), radius and ulna proximal (RUP), distal epiphyseal cartilage of ulna (DEU), head of femur (FK), and condylus medialis femoris (CMF). Meat quality traits were i.m. fat (IMF), muscle pH at 1 h after slaughter (pH1), muscle pH at 30 h after slaughter (pH30), and light reflectance on muscle (H30). The data set comprised 2,710 animals, of which 1,291 animals had OC records. All traits were analyzed by multiple-trait linear mixed model, with the animal's genetic and common litter effects as random. Fixed effects in the model varied between traits. Each OC lesion was further analyzed by a univariate generalized linear mixed model or, equivalently, "threshold models," assuming logistic, probit (normal), and Poisson distributions of the underlying "liability" to the disease. For OC lesions, estimates of heritability were low on the original "incidence" scale (0.06 for HK to 0.16 for CLH) and moderate to high on the liability scale (0.08 to 0.42). Genetic correlations (r(g)) between OC lesions and most MQ traits and PPC were generally unfavorable. Significant r(g) were -0.44 for DWG-CMH, 0.31 for DWG-CMF, 0.40 for FCR-HK, 0.21 for PPC-CLH, 0.32 for PPC-RUP, 0.30 for PPC-CMF, -0.54 for pH1-CLH, 0.47 for pH1-DEU, -0.34 for pH30-CMH, 0.58 for pH30-DEU, -0.50 for H30-HK, -0.31 for H30-DEU, and 0.31 for H30-CMF. Genetic susceptibilities to some OC lesions within the front leg were positively related to each other (r(g) range = 0.57 to 0.69), but r(g) between front and hind leg OC lesions were mostly negative (range = -0.21 to -0.40). Estimated h2 was 0.60 for PPC, and ranged from 0.12 to 0.66 for MQ traits, 0.28 for DWG, and 0.42 for FCR. Genetic correlations among meat quality and quantity traits ranged from -0.66 to 0.37. This is the first study to report genetic and phenotypic correlations between OC lesions and several meat quality and quantity traits in pigs. These findings will be useful to pig industry, especially in designing breeding programs for robust pigs.

Aging↗
PubMed1995

Evaluating the spectrum concept of schizophrenia in the Roscommon Family Study.

OBJECTIVE: The authors sought to evaluate whether the pattern of schizophrenia and related disorders in probands and their relatives can be explained by a single underlying continuum of liability to the "schizophrenia spectrum." METHOD: In the epidemiologically based Roscommon Family Study, the authors separately examined--in siblings, parents, and relatives of index and comparison probands--the familial aggregation and coaggregation of five hierarchically defined disorders: schizophrenia, schizoaffective disorder, schizotypal/paranoid personality disorder, other nonaffective psychoses, and psychotic affective illness. A multiple threshold model was fitted to these contingency tables by maximum likelihood. RESULTS: The multiple threshold model that constrained resemblance to be the same in siblings and parents fit the data well and estimated the correlation in liability to schizophrenia spectrum disorders between probands and first-degree relatives at 0.36. Parents, however, required higher levels of liability to manifest schizophrenia spectrum disorders than siblings. While schizophrenia and psychotic affective illness could be clearly assigned to the two extremes of the schizophrenia spectrum, the proper ordering of schizoaffective disorder, schizotypal/paranoid personality disorder, and other nonaffective psychoses could not be unambiguously determined. CONCLUSIONS: These results are consistent with the existence of a schizophrenia spectrum in which these five disorders are manifestations, of varying severity, of the same underlying vulnerability. This vulnerability is strongly transmitted within families.

Adult↗
PubMedDate not supplied

Segmented regression with errors in predictors: semi-parametric and parametric methods.

We consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors, with a focus on linear and logistic regression. In epidemiologic studies segmented regression models often occur as threshold models, where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold. Furthermore, in occupational and environmental studies the exposure typically cannot be measured exactly. Ignoring this measurement error leads to asymptotically biased estimators of the threshold. It is shown that this asymptotic bias is different from that observed for estimating standard generalized linear model parameters in the presence of measurement error, being both larger and in different directions than expected. In most cases considered the threshold is asymptotically underestimated. Two standard general methods for correcting for this bias are considered; regression calibration and simulation extrapolation (simex). In ordinary logistic and linear regression these procedures behave similarly, but in the threshold segmented regression model they operate quite differently. The regression calibration estimator usually has more bias but less variance than the simex estimator. Regression calibration and simex are typically thought of as functional methods, also known as semi-parametric methods, because they make no assumptions about the distribution of the unobservable covariate X. The contrasting structural, parametric maximum likelihood estimate assumes a parametric distributional form for X. In ordinary linear regression there is typically little difference between structural and functional methods. One of the major, surprising findings of our study is that in threshold regression, the functional and structural methods differ substantially in their performance. In one of our simulations, approximately consistent functional estimates can be as much as 25 times more variable than the maximum likelihood estimate for a properly specified parametric model. Structural (parametric) modelling ought not be a neglected tool in measurement error models. An example involving dust concentration and bronchitis in a mechanical engineering plant in Munich is used to illustrate the results.

Bias↗
PubMed2006

Attempts to predict the long-term decrease in lung function due to radiotherapy of non-small cell lung cancer.

PURPOSE: To obtain a model which can predict long-term decrease in lung function due to radiation damage from dose-volume data for patients with non-small cell lung cancer. PATIENTS AND METHODS: 27 patients were included, all long-term survivors after radical radiation therapy. For each patient a regression analysis was performed on a post-RT succession of measurements of FEV1 in order to estimate the decrease after 2 years and a standard error (SE) on this regression estimate. The modelling was based on dose-volume histograms (DVH) exported from the treatment planning system, and involved fits of threshold models, a mean lung dose model as well as more complex models based on the relative damaged volume (rdV). RESULTS: Decreases after 2 years of up to 28% in FEV1 was measured (median 10%), with significant day-to-day variation in FEV1 for the individual patient. The threshold models predicted the long-term decrease in FEV1 well when the SE was interpreted as the uncertainty of the measured decrease. The best threshold value, marginally, was 30 Gy with an R(2) of 0.46. The mean lung dose model did not perform so well. A complex model based on rdV performed better than any of the other models (R(2)=0.52). CONCLUSION: The long-term decrease in FEV1 could be predicted from a simple dose-volume model when the SE was interpreted as the uncertainty of the measured decrease.

Carcinoma, Non-Small-Cell Lung↗
PubMed1994

Ionizing radiation and genetic risks. V. Multifactorial diseases: a review of epidemiological and genetic aspects of congenital abnormalities in man and of models on maintenance of quantitative traits in populations.

This paper discusses (a) data on the epidemiological and etiological aspects of human congenital abnormalities, (b) the multifactorial threshold model and other models which have been proposed to explain their inheritance patterns and recurrence risks in families and (c) current concepts on mechanisms on the prevalence of heritable variation for quantitative traits in populations. Congenital abnormalities, which afflict an estimated 6% of all live births, are etiologically heterogeneous. The majority of these do not follow Mendelian transmission patterns, but do 'run' in families. The multifactorial threshold model is an extension of genetic principles developed for quantitative traits to all-or-none traits; in its simplest formulation, it assumes the existence in the population of an underlying normally distributed 'liability' (which is due to numerous genetic and environmental factors acting additively, each contributing a small amount of liability) and of a 'threshold' beyond which the individual is affected. For most congenital abnormalities, the nature of these factors remains unknown. Other models assume fewer causal factors although, again, these remain to be identified. The question of how considerable heritable variation for most quantitative/polygenic traits has come to exist is a long-standing one in evolutionary population genetics. Models postulating that its existence is consistent with a balance between recurrent mutation and stabilizing selection or suggesting the possible operation of other mechanisms have been published in the literature. In the absence of knowledge on mechanisms responsible for the stable prevalences of congenital abnormalities or other multifactorial conditions in the population (but which is required to predict the consequences of an increase in mutation rate on their prevalences) it is necessary (a) to adapt and use concepts derived from quantitative and evolutionary population genetics and (b) to examine how sensitive the predictions are to the assumptions used, and how consistent they are with biological realities.

Abnormalities, Radiation-Induced↗
PubMed1994

A nonlinear model of step responses in the cockroach tactile spine neuron.

Rapid sensory adaptation in the cockroach tactile spine neuron has previously been associated with a labile threshold for action potentials, which changes with the membrane potential by a process involving two time constants. A feed-forward, variable-threshold model has previously been used to account for the frequency response function of the neuron when stimulated with small-signal, white-noise currents. Here, we used a range of accurately controlled steps of extracellular current to stimulate the neuron. The same model was able to predict the individual step responses and could also fit the entire set of step responses from a single neuron if an initial, saturating, static nonlinearity was included. These results indicate that the two-time-constant, variable-threshold model can account for most of the rapidly adapting behavior of the tactile spine neuron.

Animals↗
PubMed1994

Genetic prediction for calving ease in the United States: data, models, and use by the dairy industry.

Dystocia of Holsteins has a major economic impact on the dairy cattle industry. Genetic evaluation of AI sires for calving ease is sponsored by the National Association of Animal Breeders. The AI organizations and dairy records processing centers collect data from herds that have progeny of AI bulls. Genetic predictions of merit for calving ease have been available for Holstein AI bulls in the US since 1978. A threshold model was implemented during 1988. The threshold model adjusts for the effects of herd-year, season, sex of calf, parity, and birth-year group of sire to predict the genetic merit of each sire for calving ease. Pedigree information from sires, sons, and grandsons is also included in the analysis to improve the reliability of genetic predictions for bulls that have pedigree data available. Each sire's genetic prediction for calving ease is reported as the expected percentage of difficult births of primiparous cows. National in scope, genetic predictions for calving ease are used internationally by breeders of dairy cattle to minimize the risk of difficult births of primiparous cows and to increase the use of AI for young cows.

Animals↗
PubMed2002

Hypertension-related hypoalgesia, autonomic function and spontaneous baroreflex sensitivity.

OBJECTIVE: The mechanisms involved in the relationship between pain perception and hypertension are poorly understood. This study has sought to investigate whether the spontaneous baroreflex sensitivity and the autonomic nervous system balance are related to hypertension-associated hypoalgesia. METHODS: In the morning, 73 untreated male subjects (45 hypertensives, 28 normotensives) were submitted to a simultaneous recording of electrocardiographic and blood pressure signals in resting condition. The tracings were analysed off-line to evaluate the spectral components of the low frequency (LF) and high frequency (HF) powers (autoregressive algorithm; LF/HF ratio used in subsequent analysis as an index of sympathovagal balance), and the alphaLF (alphaLF), an index of baroreflex sensitivity. After the rest period, the subjects underwent dental pain perception evaluation (pulpar tester: test current increasing from 0 to 0.03 mA, expressed in relative Units) to determine the dental pain threshold and tolerance. Afterwards, a 24-h ambulatory blood pressure monitoring was performed. RESULTS: A significant relationship was observed between alphaLF and pain threshold (r = -0.34; p = 0.003). When a multivariate analysis was computed to control for age, 24-h systolic pressure and LF/HF ratio, alphaLF was a predictive independent factor associated with pain threshold (model p = 0.019; r = -0.31; p = 0.025). Moreover, the 24-h systolic pressure was independently associated with pain threshold (model p = 0.019; r = 0.30, p = 0.031). The relationship between alphaLF and relative tolerance was not statistically significant. When the association between the LF/HF ratio and pain sensitivity was assessed as a secondary endpoint, no significant relationship was observed. Since no significant interaction was found, the effect of alphaLF and LF/HF ratio on pain perception was assumed to be similar in normotensive and hypertensive subjects. CONCLUSIONS: The relationship found between unstimulated baroreflex sensitivity and pain threshold suggests a modulation of pain perception by baroreflex pathways in hypertension-associated hypoalgesia. In a baseline condition, the autonomic nervous system balance does not seem to influence pain sensitivity.

Adult↗
PubMed2006

A resource-depletion model of forest insect outbreaks.

Detailed analyses of thresholded ecological interactions can improve our understanding of the transition from aperiodic to periodic dynamics. We develop a threshold model of the population dynamics of outbreaking bark beetle populations that alternate between non-epidemic and epidemic behavior. The model involves accumulation of resources during low-density periods and depletion during outbreaks. The transition between the two regimes is caused by disturbance events in the form of major tree felling by wind. The model is analyzed with particular reference to the population dynamics of the spruce bark beetle (Ips typographus) in Scandinavia for which a comprehensive literature allows full parameterization. The fairly constant outbreak lengths and the highly variable waiting time between outbreaks that are seen in the historical records of this species agree well with the predictions of the model. The thresholded resource-depletion dynamics result in substantial variation in the degree of periodicity between stochastic realizations. The completely aperiodic tree colonizations are partly predictable when the timing of the irregular windfall events are known. However, the predictability of inter-outbreak periods is low due to the large variation of cases falling most frequently in the middle between the extremes of purely nonperiodic (erratic) and periodic (cyclic) fluctuations.

Animals↗
PubMed1998

Factors shaping the response latencies of neurons in the cat's auditory cortex.

This article addresses two issues. Firstly, the hypothesis that response latency might be a neural code for tone frequency was examined in single-neuron data from the primary auditory cortex of anesthetized cats. Minimal response latencies for characteristic frequency (CF) tones were independent of neural CF. Mean response latencies for a constant amplitude CF tone were also independent of CF. These data, and the fact that cortical neurons do not have an obvious independent referent for stimulus onset time, do not support the view that latency is a code for frequency. Secondly, to investigate a simple threshold model of spike initiation time, we describe the prolongations of response latency with increases in stimulus rise time and their dependence on the peak amplitude of the stimulus. These data show that in cortical neurons, it is not the peak stimulus intensity which determines first-spike latency, and second, that the response latencies are systematically not those expected on the basis of simple threshold model.

Acoustic Stimulation↗
PubMed2000

Effect of maturation on nerve excitability in an experimental model of threshold electrotonus.

Threshold electrotonus (TE) is a new tool for investigating axonal function noninvasively in vivo. To increase its potential clinical value, we developed a rat model of TE, and examined the effects of maturation and pharmacological intervention. We recorded TE in 92 male rats (body weight 90-650 g) by stimulating the motor nerve in the tail, and applying 100-ms conditioning currents. Motor conduction velocities increased up to a body weight of 330 g, and remained constant thereafter. TE in mature rats was similar to that in humans, and two parameters were analyzed: TEd(10-20) or the mean threshold reduction 10-20 ms after the onset of the depolarizing conditioning current at 40% of threshold intensity; and TEh(10-20) or the corresponding threshold decrease on hyperpolarization. Like latency, the absolute value of TEh(10-20) decreased up to 330 g, and then stabilized thereafter, probably reflecting the progressive increase in the axonal diameter and relative reduction in internodal impedance. In contrast, TEd(10-20) gradually decreased up to 330 g, and then jumped to a higher level, which was maintained for animals of >400 g. 4-Aminopyridine, a blocker of fast potassium channels, selectively increased TEd(10-20) only in the immature or young (<330 g) rats. This suggests that, in the mature animals, fast potassium channels become sequestrated from the nodal membrane and not activated in response to nodal depolarization. These findings indicate that mature rats (>400 g) may provide a useful experimental model for interpreting abnormal TE responses in humans, and provide evidence for nonlinear maturation of potassium channel function in myelinated axons.

4-Aminopyridine↗
PubMed2000

Hand eczema in twins: a questionnaire investigation.

Hand eczema in a population-based twin cohort of 6666 persons aged 20-44 years was investigated by means of a questionnaire regarding skin symptoms on the hands and self- or physician-diagnosed hand eczema. Genetic influence was observed by significant differences between identical and fraternal twins regarding casewise concordance rate and correlations in liability under the threshold model. The casewise concordance rates were almost twice as high in identical compared with fraternal twins in both sexes. By extension of the threshold model a joint analysis could be performed, resulting in a heritability estimate of 0.65. Tendencies towards stronger genetic influence for men and for younger individuals were present, but neither was statistically significant. No particular symptom pattern expressed especially strong or weak genetic influence. Hereditary factors for hand eczema were observed despite a presumably substantial individual-specific environmental variation. The hypothesis that hereditary risk factors may play a significant part in the development of hand eczema in the general population, when no extreme environmental exposure exists, seems justifiable. The relevance of known individual risk factors such as atopic dermatitis or contact allergy in relation to heredity remains to be analysed. The possible importance of age and temporal change also needs further consideration.

Adult↗
PubMed1994

Dynamic synaptic modification threshold: computational model of experience-dependent plasticity in adult rat barrel cortex.

Previous electrophysiological experiments have documented the response of neurons in the adult rat somatic sensory ("barrel") cortex to whisker movement after normal experience and after periods of experience with all but two whiskers trimmed close to the face (whisker "pairing"). To better understand how the barrel cortex adapts to changes in the flow of sensory activity, we have developed a computational model of a single representative barrel cell based on the Bienenstock, Cooper, and Munro (BCM) theory of synaptic plasticity. The hallmark of the BCM theory is the dynamic synaptic modification threshold, theta M, which dictates whether a neuron's activity at any given instant will lead to strengthening or weakening of the synapses impinging on it. The threshold theta M is proportional to the neuron's activity averaged over some recent past. Whisker pairing was simulated by setting input activities of the cell to the noise level, except for two inputs that represented untrimmed whiskers. Initially low levels of cell activity, resulting from whisker trimming, led to low values for theta M. As certain synaptic weights potentiated, due to the activity of the paired inputs, the values of theta M increased and after some time their mean reached an asymptotic value. This saturation of theta M led to the depression of some inputs that were originally potentiated. The changes in cell response generated by the model replicated those observed in in vivo experiments. Previously, the BCM theory has explained salient features of developmental experience-dependent plasticity in kitten visual cortex. Our results suggest that the idea of a dynamic synaptic modification threshold, theta M, is general enough to explain plasticity in different species, in different sensory systems, and at different stages of brain maturity.

Animals↗
PubMed1979

Intracranial self-stimulation thresholds: a model for the hedonic effects of drugs of abuse.

We present the thesis that many drugs of abuse are used for their hedonic effects and that a relevant animal model for the study of these effects is the action of these drugs on the pathways that support rewarding intracranial self-stimulation. A relationship between abuse potential of a drug and its ability to lower the threshold for rewarding brain stimulation in the rat was found. Of all the compounds we have studied, morphine and cocaine were the drugs that caused the maximum lowering of the rewarding threshold. Phencyclidine hydrochloride and the mixed agonist-antagonist pentazocine also lowered the threshold to a lesser degree, while the mixed agonist-antagonists cyclazocine and nalorphine hydrochloride had inconsistent effects. Naloxone hydrochloride, at the doses tested, had no effect on the threshold. Further, there is no evidence that tolerance develops to the threshold-lowering effect of morphine, suggesting that continued use of narcotics by the physically dependent individual is not simply due to an effort to avoid the pain of withdrawal.

Animals↗