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PubMed1996

Myocardial material property determination in the in vivo heart using magnetic resonance imaging.

OBJECTIVES: To determine nonlinear material properties of passive, diastolic myocardium using magnetic resonance imaging (MRI) tissue-tagging, finite element analysis (FEA) and nonlinear optimization. BACKGROUND: Alterations in the diastolic material properties of myocardium may pre-date the onset of or exist exclusive of systolic ventricular dysfunction in disease states such as hypertrophy and heart failure. Accordingly, significant effort has been expended recently to characterize the material properties of myocardium in diastole. The present study defines a new technique for determining material properties of passive myocardium using finite element (FE) models of the heart, MRI tissue-tagging and nonlinear optimization. This material parameter estimation algorithm is employed to estimate nonlinear material parameter sin the in vivo canine heart and provides the necessary framework to study the full complexities of myocardial material behavior in health and disease. METHODS AND RESULTS: Material parameters for a proposed exponential strain energy function were determined by minimizing the least squares difference between FE model-predicted and MRI-measured diastolic strains. Six mongrel dogs underwent MRI imaging with radiofrequency (RF) tissue-tagging. Two-dimensional diastolic strains were measured from the deformations of the MRI tag lines. Finite element models were constructed from early diastolic images and were loaded with the mean early to late left ventricular and right ventricular diastolic change in pressure measured at the time of imaging. A nonlinear optimization algorithm was employed to solve the least squares objective function for hte material parameters. Average material parameters for the six dogs were E = 28,722 +/- 15984 dynes/cm2 and c = 0.00182 +/- 0.00232 cm2/dyne. CONCLUSION: This parameter estimation algorithm provides the necessary framework for estimating the nonlinear, anisotropic and non-homogeneous material properties of passive myocardium in health and disease in the in vivo beating heart.

Algorithms↗

PubMed2002

Economic evaluation of bone morphogenetic protein versus autogenous iliac crest bone graft in single-level anterior lumbar fusion: an evidence-based modeling approach.

STUDY DESIGN: Economic evaluation provides a framework to explicitly measure and compare the value of alternative medical interventions in terms of their clinical, health-related quality-of-life, and economic outcomes. Computerized economic models can help inform the design of future prospective studies by identifying the cost-drivers, the most uncertain parameter estimates, and the parameters with the greatest impact on the results and inferences. OBJECTIVE: An economic analysis of bone morphogenetic protein versus autogenous iliac crest bone graft for single-level anterior lumbar fusion poses several methodologic challenges. This article describes how such an economic evaluation may be framed and designed, while enumerating challenges, offering some solutions, and suggesting an agenda for future research. SUMMARY OF BACKGROUND DATA: An evidence-based modeling approach can incorporate epidemiologic, clinical, and economic data from several sources including randomized clinical trials, peer-reviewed literature, and expert opinion. Sensitivity analyses can be conducted by varying key parameter estimates within a reasonable range to assess the impact on the results and inferences. RESULTS: Preliminary results suggest that from a payer perspective, the upfront price of bone morphogenetic protein is likely to be entirely offset by reductions in the use of other medical resources. That is, bone morphogenetic protein appears to be cost neutral. The cost offsets were attributable largely to prevention of pain and complications associated with autogenous iliac crest bone graft, as well as reduction of the costs associated with fusion failures. CONCLUSIONS: Future research should focus on quantifying the health-related quality-of-life impact of bone morphogenetic protein relative to autogenous iliac crest bone graft, as well as the impact on lost productivity.

Activities of Daily Living↗

PubMed2006

Bringing metabolic networks to life: convenience rate law and thermodynamic constraints.

BACKGROUND: Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. RESULTS: We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. CONCLUSION: Convenience kinetics can be used to translate a biochemical network--manually or automatically--into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases.

Energy Metabolism↗

PubMed1976

Morphometrical method to estimate the parameters of distribution functions assumed for spherical bodies from measurements on a random section.

The general equations to correlate the distribution of the radius r of spheres randomly dispersed in the three-dimensional space with measurements on a random test plane are (see article) and (see article) for the diameter delta of circular sections of spheres; and (see article) and (see article) for the length lambda of chords delivered by intersection of a random test line. In the above expressions Nvo, Nao and Nlambdao are the numbers of spheres in a unit volume, of circles on a unit surface area and of chords per unit length of a test line, respectively; n is O or a positive integer; r the arithmetical mean of r; (deltan) and (lambdan) the means of the n-th powers of delta and lambda, respectively; and Qn a quotient defined by Qn = (rn)/rn. The ratio of measured (delta2/delta2 or (lambda2/lambda2 is used for calculating one of the parameters of assumed theoretical distribution functions. A second parameter is then estimated from delta or lambda. The method was applied to the normal pancreatic islets, and the use of chord length lambda was preferred to that of diameter delta, because the error due to the failure in identifying very small islet sections was minimized in the former.

Biometry↗

PubMed2004

Endogeneity bias in the absence of unobserved heterogeneity.

PURPOSE: To demonstrate that endogeneity bias can still arise even when no unobserved heterogeneity exists. METHODS: A formal mathematical proof and a Monte Carlo simulation are used to demonstrate that ordinary estimation techniques will generate biased parameter estimates. RESULTS: The Monte Carlo results support the formal proof. Even in the absence of unobserved heterogeneity, ordinary least squares estimation that does not account for the endogenous nature of an explanatory variable resulted in a parameter estimate for the endogenous variable that was significantly biased (by a factor of 1.42 for the simple model and 1.98 for the saturated model). Alternatively, controlling for endogeneity using the instrumental variables approach led to an unbiased parameter estimate. CONCLUSIONS: Endogeneity bias can still occur even when unobserved heterogeneity is not present.

Algorithms↗

PubMed1984

Continuous perineural infusions of bupivacaine for prolonged analgesia--a rapid two-point method for estimating individual pharmacokinetic parameters.

Results of previous studies have shown a 5-10 fold range in the clearance total and half-life of bupivacaine. Since bupivacaine has a narrow therapeutic range and highly variable pharmacokinetic parameters, rapid estimation of the parameters allows early dosage regimen adjustments, and hence, better pain management. The pharmacokinetic parameters in 17 patients were estimated based on two samples drawn within 18 h after initiation of therapy. Based on the estimated parameters, a later sample's concentration was predicted. Results of this study confirm the previously reported large variation in pharmacokinetic parameters. An excellent agreement between actual and predicted concentration was found. The use of this method allows early readjustment in the dosage regimen, resulting in effective pain management without compromising patient safety.

Aged↗

PubMed1997

Nonlinear genetic relationships between traits and their implications on the estimation of genetic parameters.

To estimate nonlinear genetic relationships between traits, formulas based on the paternal halfsib analysis theory were derived. To illustrate the usefulness of the formulas, a series of data sets with halfsib structure for some preselected parameters and sample size situations were generated by means of Monte Carlo techniques. When a nonlinear relationship in the form of a polynomial relationship of degree two is present, the linear and quadratic regression coefficients can be estimated from a paternal halfsib analysis without bias. Some of the traditional linear genetic parameters need correction; however, their value is limited if the relationship between two traits is nonlinear. Although regression coefficients may be estimated appropriately in many situations, the application of the described method is restricted to situations in which the causal flow between the traits involved is clear and the heritability of the determining trait is larger than approximately .10. Further work should be directed to investigation of possibilities for including such parameters in selection decisions in a formalized way.

Analysis of Variance↗

PubMed1995

Three new residual error models for population PK/PD analyses.

Residual error models, traditionally used in population pharmacokinetic analyses, have been developed as if all sources of error have properties similar to those of assay error. Since assay error often is only a minor part of the difference between predicted and observed concentrations, other sources, with potentially other properties, should be considered. We have simulated three complex error structures. The first model acknowledges two separate sources of residual error, replication error plus pure residual (assay) error. Simulation results for this case suggest that ignoring these separate sources of error does not adversely affect parameter estimates. The second model allows serially correlated errors, as may occur with structural model misspecification. Ignoring this error structure leads to biased random-effect parameter estimates. A simple autocorrelation model, where the correlation between two errors is assumed to decrease exponentially with the time between them, provides more accurate estimates of the variability parameters in this case. The third model allows time-dependent error magnitude. This may be caused, for example, by inaccurate sample timing. A time-constant error model fit to time-varying error data can lead to bias in all population parameter estimates. A simple two-step time-dependent error model is sufficient to improve parameter estimates, even when the true time dependence is more complex. Using a real data set, we also illustrate the use of the different error models to facilitate the model building process, to provide information about error sources, and to provide more accurate parameter estimates.

Models, Theoretical↗

PubMed1990

Single-channel data and missed events: analysis of a two-state Markov model.

Patch-clamp recording permits investigation of the gating kinetics of single ion channels. Careful statistical analysis of kinetic data can yield clues as to the molecular events underlying channel gating. However, it is important that such analysis should take full account of the limitations that arise from the finite time resolution of patch-clamp recording techniques. Single-ion-channel data are generally interpreted in terms of Markov process models of channel gating mechanisms. Experimental channel records suffer from time interval omission, i.e. failure to detect brief channel openings and closings. This leads to an identifiability problem when analysing single-channel data, i.e. different gating mechanisms provide equally convincing descriptions of the same experimental data. We consider a two-state Markov model of receptor-channel gating in which the channel opening rate is proportional to the agonist concentration, C in equilibrium with OA. By using computer-simulated data, the approximate likelihood of the data is maximized to yield parameter estimates for the model. At a single agonist concentration there is an identifiability problem in that two pairs of parameter estimates are obtained. The 'true' parameter estimates cannot be distinguished from the 'false' ones. By considering data corresponding to a range of agonist concentrations one may identify the 'true' parameter estimates as those that do not change as the agonist concentration is increased. Alternatively, one may identify the 'true' parameter estimates directly by maximizing a global likelihood, the latter being obtained by simultaneous consideration of data obtained at several different agonist concentrations.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed1998

Increased efficiency of analyses: cumulative logistic regression vs ordinary logistic regression.

The common practice of collapsing inherently continuous or ordinal variables into two categories causes information loss that may potentially weaken power to detect effects of explanatory variables and result in Type II errors in statistical inference. The purpose of this investigation was to illustrate, using a substantive example, the potential increase in power gained from an ordinal instead of a dichotomous specification for an inherently continuous response. Ordinary (OLR) and cumulative logistic regression (CLR) modeling were used to test the hypothesis that the risk of alveolar bone loss over 2 years is greater for subjects with poorer control of non-insulin-dependent diabetes mellitus (NIDDM) than for those who do not have diabetes or have better controlled NIDDM. There were 359 subjects; 21 of whom had NIDDM. Analysis of main effects using OLR for the dichotomous outcome (no change in radiographic bone loss vs any change) produced parameter estimates for better control and poorer control that were not statistically significant. CLR analysis of main effects using a 4-category ordinal specification for radiographic bone loss also produced a parameter estimate for better control that was not statistically significant, but which estimated poorer control to have a significant effect. The fit of this CLR model was significantly better at P < 0.05 than that for the OLR. While an OLR model testing the interaction between age and control status did not converge after 100 iterations, the CLR interaction model converged without difficulty and estimated a significant effect for interaction between age and poorer control. Results from the CLR analysis, in contrast to the OLR model, would lead one to conclude that the risk for more severe bone loss progression after 2 years is greater in subjects with poorer controlled NIDDM and that subjects with better controlled NIDDM may not have greater risk of bone loss progression than those without diabetes. The use of an ordinal instead of a dichotomous specification for an inherently continuous response provided increased power, more precise parameter estimates, and a significantly better fitting model. In estimating parameter estimates for odds ratios or risks, it is important to consider using ordinal logistic regression where the response is inherently continuous or ordinal.

Adolescent↗

PubMed1997

Estimation of parameters in a two-pool urea kinetic model for hemodialysis.

A two-pool, variable volume urea kinetic model for estimation of solute removal in hemodialysis is solved analytically, and closed form expressions are presented for urea concentration in both compartments, both during dialysis and between dialyses. This approach also includes an estimation of the extent of the post dialysis rebound phenomenon of urea concentration. A method is presented to estimate values for the urea generation rate G, the distribution volume V and its partition in two compartments with volumes alpha 1V and alpha 2V (alpha 1-alpha 2-1), the total clearance K, and intercompartmental transfer coefficient X. To apply this analysis, several measurements are needed as input; the urea concentration at the end of a dialysis, the evolution of this concentration during the next dialysis, with at least four measurements including the initial and the final concentration, the volume of the dialysate, and its urea concentration. The main results are: the magnitude of the rebound is approximately proportional to alpha 2(2) K/X; the accuracy of the parameter estimation does not improve much further by taking more than six measurements during dialysis.

Humans↗

PubMed1993

An algorithm for robust non-linear analysis of radioimmunoassays and other bioassays.

The four-parameter logistic function is an appropriate model for many types of bioassays that have continuous response variables, such as radioimmunoassays. By modelling the variance of replicates in an assay, one can modify the usual parameter estimation techniques (for example, Gauss-Newton or Marquardt-Levenberg) to produce parameter estimates for the standard curve that are robust against outlying observations. This article describes the computation of robust (M-) estimates for the parameters of the four-parameter logistic function. It describes techniques for modelling the variance structure of the replicates, modifications to the usual iterative algorithms for parameter estimation in non-linear models, and a formula for inverse confidence intervals. To demonstrate the algorithm, the article presents examples where the robustly estimated four-parameter logistic model is compared with the logit-log and four-parameter logistic models with least-squares estimates.

Algorithms↗

PubMed1993

bpshape wk4: a computer program that implements a physiological model for analyzing the shape of blood pressure waveforms.

We describe the theory and computer implementation of a newly-derived mathematical model for analyzing the shape of blood pressure waveforms. Input to the program consists of an ECG signal, plus a single continuous channel of peripheral blood pressure, which is often obtained invasively from an indwelling catheter during intensive-care monitoring or non-invasively from a tonometer. Output from the program includes a set of parameter estimates, made for every heart beat. Parameters of the model can be interpreted in terms of the capacitance of large arteries, the capacitance of peripheral arteries, the inertance of blood flow, the peripheral resistance, and arterial pressure due to basal vascular tone. Aortic flow due to contraction of the left ventricle is represented by a forcing function in the form of a descending ramp, the area under which represents the stroke volume. Differential equations describing the model are solved by the method of Laplace transforms, permitting rapid parameter estimation by the Levenberg-Marquardt algorithm. Parameter estimates and their confidence intervals are given in six examples, which are chosen to represent a variety of pressure waveforms that are observed during intensive-care monitoring. The examples demonstrate that some of the parameters may fluctuate markedly from beat to beat. Our program will find application in projects that are intended to correlate the details of the blood pressure waveform with other physiological variables, pathological conditions, and the effects of interventions.

Animals↗

PubMed1998

A New Method for Estimating Model Parameters for Multinomial Data.

A new procedure for estimating the parameters of a scientific model is described, and the method is applied and illustrated for the class of experiments with multinominal data structure. The procedure is referred to as the method of population-parameter mapping, and it has a number of novel and advantageous features. The method is a variation of a standard Bayesian analysis. However, instead of directly developing a posterior distribution for the model parameters, this procedure first characterizes the population proportions for the multinomial cells. Random samples are then drawn from the posterior distribution for these proportions, and these samples are mapped to the parameters of the scientific model. This method leads naturally to a definition of model identifiability, and leads to a direct probability estimate of the coherence of the scientific model. Moreover, the new procedure can circumvent the problem of dealing with computationally difficult integrals that frequently occur with Bayesian analyses of complex multinomial models. The method is illustrated by means of several memory measurement models as well as a signal-detection model. Copyright 1998 Academic Press.

Journal Article↗

PubMed1989

Correction of ocular artifacts in EEGs using an autoregressive model to describe the EEG; a pilot study.

The basic idea in eye movement (EM) artifact corrections is that the actual recording is the summation of brain potentials (true EEG) and artifact. Often a regression analysis is performed, using simultaneous EEG and EOG data, to find the parameters describing the relationship between artifact and EOG derivations (EOGs). Our method uses a maximum likelihood parameter estimation and considers data from preceding sample moments as well, since there may be a delay in the artifact transferring over the scalp. For the error term (true EEG) an autoregressive function is used. Results from estimations on data from one volunteer indicate that a delay need not be considered and that 3 autoregressive parameters are sufficient. For F3 4 EOGs give only somewhat better results than 2 EOGs. For C3 and C4 2 EOGs are sufficient. For practical reasons for each of these 3 EEG recordings, 2 EOGs were used to perform corrections. Corrections were performed using either the parameters estimated for EMs and blinks together, or the parameters estimated for EMs only (used for EMs), or the parameters estimated for blinks only (used for blinks). For EMs the differences between these corrections are very small. For blinks the differences are much larger. Parameters estimated for one trial may be used to correct other trials, recorded within a period of about 15 min preceding or following that trial.

Blinking↗

PubMed1995

Sequential, single-dose pharmacokinetic evaluation of meropenem in hospitalized infants and children.

Meropenem is a new carbapenem antibiotic which possesses a broad spectrum of antibacterial activity against many of the pathogens responsible for pediatric bacterial infections. In order to define meropenem dosing guidelines for children, an escalating, single-dose, pharmacokinetic study at 10, 20, and 40 mg/kg of body weight was performed. A total of 73 infants and children in four age groups were enrolled in the study: 2 to 5 months, 6 to 23 months, 2 to 5 years, and 6 to 12 years. The first patients enrolled were those in the oldest age group, who received the lowest dose. Subsequent enrollment was determined by decreasing age and increasing dose. Complete studies were performed on 63 patients. No age- or dose-dependent effects on pharmacokinetic parameter estimates were noted. Mean pharmacokinetic parameter estimates were as follows: half-life, 1.13 +/- 0.15 h; volume of distribution at steady state, 0.43 +/- 0.06 liters/kg; mean residence time, 1.57 +/- 0.11 h; clearance, 5.63 +/- 0.75 ml/min/kg; and renal clearance, 2.53 +/- 0.50 ml/min/liters kg. Approximately 55% of the administered dose was recovered as unchanged drug in the urine during the 12 h after dosing. No significant side effects were reported in any patients. By using the derived pharmacokinetic parameter estimates, a dose of 20 mg/kg given every 8 h will maintain plasma meropenem concentrations above the MIC that inhibits 90% of strains tested for virtually all potentially susceptible bacterial pathogens.

Aging↗

PubMed2003

Identifiability and retrievability of unique parameters describing intrinsic Andrews kinetics.

A key factor contributing to the variability in the microbial kinetic parameters reported from batch assays is parameter identifiability, i.e., the ability of the mathematical routine used for parameter estimation to provide unique estimates of the individual parameter values. This work encompassed a three-part evaluation of the parameter identifiability of intrinsic kinetic parameters describing the Andrews growth model that are obtained from batch assays. First, a parameter identifiability analysis was conducted by visually inspecting the sensitivity equations for the Andrews growth model. Second, the practical retrievability of the parameters in the presence of experimental error was evaluated for the parameter estimation routine used. Third, the results of these analyses were tested using an example data set from the literature for a self-inhibitory substrate. The general trends from these analyses were consistent and indicated that it is very difficult, if not impossible, to simultaneously obtain a unique set of estimates of intrinsic kinetic parameters for the Andrews growth model using data from a single batch experiment.

Bacteria↗

PubMed2004

[Construction of a stress reaction scale based on an item response model and examination of the developmental process of psychological stress reactions by using test characteristic curves].

In this study, a stress reaction scale was constructed based on an Item Response Model, and the developmental process of psychological stress reactions was investigated by using test characteristic curves. Subjects consisted of 286 private college students and 234 national college students. The Job Stress Scale (JSS) was revised for college students, and used to assess psychological stress reaction. Graded response model of Item Response Theory (IRT) was used to estimate parameters. After estimating item and subject parameters, we assessed the precision of measurement and the fit of the model, and found both precision and fit to be satisfactory. Then we examined the test characteristic curves of each subscale to investigate the developmental process of psychological stress reactions of college students in comparison with company employees.

Adult↗