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PubMed1993

A microcomputer program to determine the precision of elimination rate constant and half-life estimates when sampling time is short.

First-order elimination of drugs is often assumed in pharmacokinetics and elimination rate constant is then frequently determined by log-linear regression analysis from plasma concentration measurements. When the time which elapses between the first and the last plasma sample is short compared to the decay half-life, the elimination rate constant may not be determined with satisfactory precision, in particular because of analytical error. Application of basic principles of linear regression analysis allowed us to quantify the theoretical effect of analytical error on the determination of the drug elimination rate constant in that situation. It was highlighted that the precision of that determination could be efficiently improved by measuring samples in replicate, which should be recommended in practice. A user-friendly program was developed which can be used prospectively to optimize sampling strategy, and retrospectively to estimate the precision of parameter estimates. The program works on IBM PC and compatible microcomputers and is available on request.

Drug Monitoring↗
PubMed1983

Right- and left-hand skill II: Estimating the parameters of the distribution of L-R differences in males and females.

The distribution of differences between the hands (L-R) in skill, as measured by a peg-moving task, was examined for several samples in which volunteer bias was absent or minimal. After comparing the main samples for hand preference and L-R times, they were combined to give 617 males and 863 females, aged 12-63 years. There was also a smaller sample of 122 males and 156 females, aged 6-15 years. The L-R distributions were negatively skewed and leptokurtotic. They were not compatible with the sum of two normal distributions, one of right-handers and one of left-handers. They were compatible with the sum of two or three normal distributions when one was unbiased to either side and the others were shifted to the right, as expected for the dominant or additive versions of the single gene interpretation of the right shift theory of handedness (Annett, 1978b, 1979). Sex differences in L-R scores confirmed that females tend to be more dextral than males. This was true of right-handers but not of left-handers, as expected if the sex difference is due to stronger expression of the rs+ gene in females than males and if this gene is absent in the majority of left-handers. There were trends suggesting that L-R asymmetry differs with educational status, undergraduates being less shifted toward dextrality than the general population.

Adolescent↗
PubMed2002

Modeling pulmonary and CNS O(2) toxicity and estimation of parameters for humans.

The power expression for cumulative oxygen toxicity and the exponential recovery were successfully applied to various features of oxygen toxicity. From the basic equation, we derived expressions for a protocol in which PO(2) changes with time. The parameters of the power equation were solved by using nonlinear regression for the reduction in vital capacity (DeltaVC) in humans: %DeltaVC = 0.0082 x t(2)(PO(2)/101.3)(4.57), where t is the time in hours and PO(2) is expressed in kPa. The recovery of lung volume is DeltaVC(t) = DeltaVC(e) x e(-(-0.42 + 0.00379PO(2))t), where DeltaVC(t) is the value at time t of the recovery, DeltaVC(e) is the value at the end of the hyperoxic exposure, and PO(2) is the prerecovery oxygen pressure. Data from different experiments on central nervous system (CNS) oxygen toxicity in humans in the hyperbaric chamber (n = 661) were analyzed along with data from actual closed-circuit oxygen diving (n = 2,039) by using a maximum likelihood method. The parameters of the model were solved for the combined data, yielding the power equation for active diving: K = t(2) (PO(2)/101.3)(6.8), where t is in minutes. It is suggested that the risk of CNS oxygen toxicity in diving can be derived from the calculated parameter of the normal distribution: Z = [ln(t) - 9.63 +3.38 x ln(PO(2)/101.3)]/2.02. The recovery time constant for CNS oxygen toxicity was calculated from the value obtained for the rat, taking into account the effect of body mass, and yielded the recovery equation: K(t) = K(e) x e(-0.079t), where K(t) and K(e) are the values of K at time t of the recovery process and at the end of the hyperbaric oxygen exposure, respectively, and t is in minutes.

Algorithms↗
PubMed1977

Estimating the parameters of the incompletely penetrant single locus model using multiple populations.

A method involving the comparison of two or more populations is suggested as a means of obtaining a unique solution to the parameters of the incompletely penetrant single locus model. The proposed method allows a test of the assumptions of the model when three or more populations are compared. Equations that allow the inclusion of data on twin concordance rates and/or the proportion of affected children given neither, one or both parents affected are also given. Finally, some implications of fitting the model are discussed in terms of genetic counseling, residual environmental variance and the concept of heritability as applied to dichotomous traits.

Female↗
PubMed2005

Iterative approach to model identification of biological networks.

BACKGROUND: Recent advances in molecular biology techniques provide an opportunity for developing detailed mathematical models of biological processes. An iterative scheme is introduced for model identification using available system knowledge and experimental measurements. RESULTS: The scheme includes a state regulator algorithm that provides estimates of all system unknowns (concentrations of the system components and the reaction rates of their inter-conversion). The full system information is used for estimation of the model parameters. An optimal experiment design using the parameter identifiability and D-optimality criteria is formulated to provide "rich" experimental data for maximizing the accuracy of the parameter estimates in subsequent iterations. The importance of model identifiability tests for optimal measurement selection is also considered. The iterative scheme is tested on a model for the caspase function in apoptosis where it is demonstrated that model accuracy improves with each iteration. Optimal experiment design was determined to be critical for model identification. CONCLUSION: The proposed algorithm has general application to modeling a wide range of cellular processes, which include gene regulation networks, signal transduction and metabolic networks.

Algorithms↗
PubMed2002

Estimation of covariate-dependent Markov transition probabilities from nested case-control data.

Multi-state models are used to describe situations where individuals may move among a finite number of states defined by specific conditions of health, including death. The transition intensities of the models are described by proportional hazards models, and it is reviewed how estimation of the regression parameters and the baseline transition intensities may be performed when only nested case-control data are available for all or some of the transitions. The regression parameter estimates and the estimates of baseline transition intensities are combined to give estimates of the integrated transition intensities for specified covariate histories, and from these estimates covariate-dependent Markov transition probabilities are derived.

Analysis of Variance↗
PubMed2000

Robust transformation with applications to structural equation modelling.

Data sets in social and behavioural sciences are seldom normal. Influential cases or outliers can lead to inappropriate solutions and problematic conclusions in structural equation modelling. By giving a proper weight to each case, the influence of outliers on a robust procedure can be minimized. We propose using a robust procedure as a transformation technique, generating a new data matrix that can be analysed by a variety of multivariate methods. Mardia's multivariate skewness and kurtosis statistics are used to measure the effect of the transformation in achieving approximate normality. Since the transformation makes the data approximately normal, applying a classical normal theory based procedure to the transformed data gives more efficient parameter estimates. Three procedures for parameter evaluation and model testing are discussed. Six examples illustrate the various aspects with the robust transformation.

Humans↗
PubMedDate not supplied

The 'double' Michaelis-Menten equation: estimation of parameters.

When the concentration dependence of an enzymic reaction or a transport process can be described by the sum of two Michaelis-Menten terms, reliable data that relate reaction rate and substrate concentration can be obtained even when as much as 70 per cent of substrate was consumed during the assay. Each data pair consists of the average reaction rate during an assay and the concentration where the instantaneous reaction rate was equal to the average rate. Although that concentration cannot be computed exactly (as it depends on the four kinetic parameters), it may be computed in a good approximation as if the reaction followed the simple Michaelis-Menten relationship. The relative error in the approximated concentration for 1 less than or equal to K2/K1 less than or equal to 10(5) and 10(-2) less than or equal to V2/V1 less than or equal to 10(2) did not exceed 5 per cent up to 50 per cent of substrate consumption, and did not exceed 10 per cent up to 70 per cent of substrate consumption.

Biological Transport↗
PubMed2005

Growth of the tambaqui Colossoma macropomum (Cuvier) (Characiformes: Characidae): which is the best model?

In order to decide which is the best growth model for the tambaqui Colossoma macropomum Cuvier, 1818, we utilized 249 and 256 length-at-age ring readings in otholiths and scales respectively, for the same sample of individuals. The Schnute model was utilized and it is concluded that the Von Bertalanffy model is the most adequate for these data, because it proved highly stable for the data set, and only slightly sensitive to the initial values of the estimated parameters. The phi values estimated from five different data sources presented a CV = 4.78%. The numerical discrepancies between these values are of not much concern due to the high negative correlation between k and Linfinity viz, so that when one of them increases, the other decreases and the final result in phi remains nearly unchanged.

Age Factors↗
PubMedDate not supplied

Control uncertain continuous-time chaotic dynamical system.

The new chaos control method presented in this paper is useful for taking advantage of chaos. Based on sliding mode control theory, this paper provides a switching manifold controlling strategy of chaotic system, and also gives a kind of adaptive parameters estimated method to estimate the unknown systems' parameters by which chaotic dynamical system can be synchronized. Taking the Lorenz system as example, and with the help of this controlling strategy, we can synchronize chaotic systems with unknown parameters and different initial conditions.

Computer Simulation↗
PubMed1999

Using current on-line carcass evaluation parameters to estimate boneless and bone-in pork carcass yield as influenced by trim level.

The objective of this study was to develop prediction equations for estimating proportional carcass yield to a variety of external trim levels and bone-in and boneless pork primal cuts. Two hundred pork carcasses were selected from six U.S. pork processing plants and represented USDA carcass grades (25% USDA #1, 36% USDA #2, 25% USDA #3, and 14% USDA #4). Carcasses were measured (prerigor and after a 24 h chill) for fat and muscle depth at the last rib (LR) and between the third and fourth from last rib (TH) with a Hennessy optical grading probe (OGP). Carcasses were shipped to Texas A&M University, where one was randomly assigned for fabrication. Selected sides were fabricated to four lean cuts (ham, loin, Boston butt, and picnic shoulder) then fabricated progressively into bone-in (BI) and boneless (BL) four lean cuts (FLC) trimmed to .64, .32, and 0 cm of s.c. fat, and BL 0 cm trim, seam fat removed, four lean cuts (BLS-OFLC). Total dissected carcass lean was used to calculate the percentage of total carcass lean (PLEAN). Lean tissue subsamples were collected for chemical fat-free analysis and percentage carcass fat-free lean (FFLEAN) was determined. Longissimus muscle area and fat depth also were collected at the 10th and 11th rib interface during fabrication. Regression equations were developed from linear carcass and OGP measurements predicting FLC of each fabrication point. Loin muscle and fat depths from the OPG obtained on warm, prerigor carcasses at the TH interface were more accurate predictors of fabrication end points than warm carcass probe depth obtained at the last rib or either of the chilled carcass probe sites (probed at TH or LR). Fat and loin muscle depth obtained via OGP explained 46.7, 52.6, and 57.1% (residual mean square error [RMSE] = 3.30, 3.19, and 3.04%) of the variation in the percentage of BI-FLC trimmed to .64, .32, and 0 cm of s.c. fat, respectively, and 49.0, 53.9, and 60.7% (RMSE = 2.91, 2.81, and 2.69%) of the variation in the percentage of BL-FLC trimmed to .64, .32, and 0 cm of s.c. fat, respectively. Fat and loin muscle depth from warm carcass OGP probes at the TH interface accounted for 62.4 and 63.5% (RMSE = 3.38 and 3.27%) of the variation in PLEAN and FFLEAN, respectively. These equations provide an opportunity to estimate pork carcass yield for a variety of procurement end point equations using existing on-line techniques.

Animals↗
PubMed2004

Partitioning variances of growth in ultrasound longissimus muscle area measures in Angus bulls and heifers.

The objective of the study was to estimate variance components, heritability, and repeatability of ultrasound longissimus muscle area (ULMA) measures. Data included 4,653 serial ULMA measures from 882 purebred Angus bulls and heifers. Animals were born over a 4-yr period from 1998 to 2001. Each year, bulls and heifers were ultrasonically scanned four to eight times, with a 4- to 6-wk interval between scans. Initially, data were subdivided by scan session across years and were analyzed in a multitrait model (MTM). Data pooled across years and scan session were then analyzed using random regression models (RRM) to estimate trends in genetic parameter estimates. Additive direct genetic variance increased with advancing scan session ranging from 8.67 cm4 at the first scan (mean age = 35 wk) to a maximum of 19.48 cm4 at the sixth scan (mean age = 56 wk). Heritability of ULMA increased from 0.35 at first scan to a maximum of 0.48 at the fourth scan (mean age = 50 wk). Additive direct genetic variance and heritability values at about 1 yr of age (fifth scan) were 18.24 cm4 and 0.45, respectively. Estimates from RRM also showed an increase in sigma(a)2 and h2 with age. Trends in sigma(pe)2 estimates, although tending to fluctuate, also increased with age. Additive direct genetic variance at 1 yr of age ranged from 15.8 cm4 to 17.0 cm4 for the different models. Heritability of yearling ULMA measures ranged from 0.40 to 0.42 and repeatabilities ranged from 0.80 to 0.84. For the range of ages used in the current study, both MTM and RRM showed close to maximum heritability values at around 1 yr of age. Therefore, phenotypic differences in yearling ULMA between Angus cattle are better indicators of genetic differences than earlier measurements. Angus breeders could, therefore, use ULMA measures made at around 1 yr of age to select next generation parents.

Animals↗
PubMed2000

Estimation of parameters describing lipid metabolism in lactation: challenge of existing knowledge described in a model of metabolism.

We have been conducting research to improve quantitative descriptions of metabolism in lactating dairy cows depicted in an existing mechanistic, computer-assisted model. The model is dynamic and deterministic and is based on biochemical equations describing ruminal fermentation and chemical interactions in body tissues. The objective was to challenge this model with data collected in in vivo and in vitro experiments on high producing dairy cattle fed a range of energy. Cows that varied in genetic propensity for milk production (7045 to 12,909 kg of milk/305 d), lactation number (1 to 4), stage of lactation (-30 to 345 d in milk), and rate of intake (14 to 29 kg/d of dry matter) and that were fed various energy-yielding feedstuffs were used. Dietary inputs, milk component outputs, body fat, nutrient concentrations in blood, and maximal velocity and substrate sensitivity of adipose tissue metabolic reactions were observed. Model simulations were conducted; simulated yields of milk components for a 305-d lactation were within 5% of observed means. Simulated lipid metabolism and accumulation of body fat were adequate in many situations; however, the model response to changes in energy intake was too sensitive. This inadequacy was especially noticeable in later lactation because of inadequate representation of dynamic responses over periods more than a few weeks long. The model behaves consistently with biochemical principles, behavior was in the correct direction, and precision was adequate for many variables. Lack of precision in long-term dynamic changes indicates that the parameters describing energy-utilizing reactions are inadequate. This severe challenge of the model supports its functionality. Further experiments must be designed to determine how nutrients in viscera, muscle, and adipose tissue are used; these experiments must encompass sufficient range in genetic ability, nutrient input, and time to adequately describe the dynamic and integrated nature of metabolic reactions.

Adipose Tissue↗