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PubMed1994

Determining appropriate models for joint control using surface electrical stimulation of soleus in spinal cord injury.

The mechanical impedance of the ankle joint during electrical stimulation of the soleus is studied by applying constant-velocity 10 degrees angular perturbations to the ankle and measuring the resultant torque. Both neurologically intact subjects and spinal cord injured subjects are tested. Lumped, piecewise linear models are developed to predict the torque from the measured displacement and acceleration signals. The commonly used second-order mass-spring-dashpot model fails to predict the changes in torque that occur following imposed movements. A five-element, directionally-dependent piecewise linear model is much better at predicting the measured responses for velocities up to 50 degrees s-1. Numerical least squared error identification techniques are used to estimate the model parameters for three neurologically intact and three spinal cord injured subjects. The average error between the model's response and the measured response across all subjects is 10.9%. There is some evidence that a velocity-dependent non-linear model could produce better results than the directionally-dependent piecewise linear model.

Ankle Joint↗

PubMed2005

Temperature and treatment time influence high hydrostatic pressure inactivation of feline calicivirus, a norovirus surrogate.

Interest in high hydrostatic pressure processing as a nonthermal pasteurization process for foods continues to increase. Feline calicivirus (FCV), a propagable virus that is genetically related to the nonpropagable human noroviruses, was used for detailed evaluation of the high pressure processing parameters necessary for virus inactivation. Pressure inactivation curves of FCV strain KCD in Dulbecco's modified Eagle medium with 10% fetal bovine serum were obtained at 200 and 250 MPa as a function of time at room temperature. Pressure inactivation curves at 200 and 250 MPa also were determined as a function of temperature ranging from --10 to 50 degrees C at treatment times of 4 and 2 min, respectively. Tailing was observed for inactivation as a function of treatment time, indicating that the linear model was not adequate for describing these curves. The two nonlinear models, the log logistic and Weibull functions, consistently produced better fit to inactivation curves than did the linear model. The mean square errors were 0.381 for the log logistic model, 0.425 for the Weibull model, and 1.546 for the linear model. For inactivation as a function of temperature, FCV was most resistant to pressure at 20 degrees C. Temperatures above and below 20 degrees C significantly increased pressure inactivation of FCV. A 4-min treatment of 200 MPa at --10 and 50 degrees C reduced the titer of FCV by 5.0 and 4.0 log units, respectively; whereas at 20 degrees C the same treatment only reduced the titer by 0.3 log units. These novel results point to the potential for using temperatures above and particularly below room temperature to lower the pressure needed to cause the desired level of virus inactivation.

Animals↗

PubMed2005

Mixture model equations for marker-assisted genetic evaluation.

Marker-assisted genetic evaluation needs to infer genotypes at quantitative trait loci (QTL) based on the information of linked markers. As the inference usually provides the probability distribution of QTL genotypes rather than a specific genotype, marker-assisted genetic evaluation is characterized by the mixture model because of the uncertainty of QTL genotypes. It is, therefore, necessary to develop a statistical procedure useful for mixture model analyses. In this study, a set of mixture model equations was derived based on the normal mixture model and the EM algorithm for evaluating linear models with uncertain independent variables. The derived equations can be seen as an extension of Henderson's mixed model equations to mixture models and provide a general framework to deal with the issues of uncertain incidence matrices in linear models. The mixture model equations were applied to marker-assisted genetic evaluation with different parameterizations of QTL effects. A sire-QTL-effect model and a founder-QTL-effect model were used to illustrate the application of the mixture model equations. The potential advantages of the mixture model equations for marker-assisted genetic evaluation were discussed. The mixed-effect mixture model equations are flexible in modelling QTL effects and show desirable properties in estimating QTL effects, compared with Henderson's mixed model equations.

Animals↗

PubMed2006

In silico prediction of drug solubility in water-ethanol mixtures using Jouyban-Acree model.

PURPOSE: A predictive method was proposed to predict solubility of drugs in water-ethanol mixtures at various temperatures based on the Jouyban-Acree model. The model requires the experimental solubility data of the drug in mono-solvent systems. METHODS: The accuracy of the proposed prediction method was evaluated using collected experimental solubility data from the literature. The proposed method is: log Xm,T = fc log Xc,T + fw log Xw,T + fcfw[724.21/T + 485.17(fc-fw)/T + 194.41(fc-fw)2/T] Where Xm,T, Xc,T and Xw,T are the solute solubility at temperature (T) in mixed solvent and neat cosolvent and water, respectively, fc and fw denote the solute free fraction of cosolvent (ethanol) and water. The average absolute error (AAE) of the experimental and the predicted solubilities was computed as an accuracy criterion and compared with that of a well-established log-linear model. RESULTS: The AAE (+/-SD) of the Jouyban-Acree and log-linear models were 0.19 (+/-0.13) and 0.48 (+/-0.28), respectively. The mean difference of AAEs was statistically significant (p < 0.0005) revealing that the Jouyban-Acree model was provided more accurate predictions. Although the log-linear model was used to predict solubility at a fixed temperature (25 or 23 degrees C), the results also showed that the model could be employed to predict the solubility in solvent mixtures at various temperatures. CONCLUSION: More accurate predictions were provided using the Jouyban-Acree model in comparison with a previously established log-linear model of Yalkowsky. The prediction methods were successfully extended to predict the solubility in water-ethanol mixtures at various temperatures.

Ethanol↗

PubMed1999

Medium-dose-rate brachytherapy of cancer of the cervix: preliminary results of a prospectively designed schedule based on the linear-quadratic model.

PURPOSE: To compare results and complications of our previous low-dose-rate (LDR) brachytherapy schedule for early-stage cancer of the cervix, with a prospectively designed medium-dose-rate (MDR) schedule, based on the linear-quadratic model (LQ). METHODS AND MATERIALS: A combination of brachytherapy, external beam pelvic and parametrial irradiation was used in 102 consecutive Stage Ib-IIb LDR treated patients (1986-1990) and 42 equally staged MDR treated patients (1994-1996). The planned MDR schedule consisted of three insertions on three treatment days with six 8-Gy brachytherapy fractions to Point A, two on each treatment day with an interfraction interval of 6 hours, plus 18 Gy external whole pelvic dose, and followed by additional parametrial irradiation. The calculated biologically effective dose (BED) for tumor was 90 Gy10 and for rectum below 125 Gy3. RESULTS: In practice the MDR brachytherapy schedule achieved a tumor BED of 86 Gy10 and a rectal BED of 101 Gy3. The latter was better than originally planned due to a reduction from 85% to 77% in the percentage of the mean dose to the rectum in relation to Point A. The mean overall treatment time was 10 days shorter for MDR in comparison with LDR. The 3-year actuarial central control for LDR and MDR was 97% and 98% (p = NS), respectively. The Grades 2 and 3 late complications (scale 0 to 3) were 1% and 2.4%, respectively for LDR (3-year) and MDR (2-year). CONCLUSIONS: LQ is a reliable tool for designing new schedules with altered fractionation and dose rates. The MDR schedule has proven to be an equivalent treatment schedule compared with LDR, with an additional advantage of having a shorter overall treatment time. The mean rectal BED Gy3 was lower than expected.

Adult↗

PubMed1987

Elongation and surface extension of individual cells of Escherichia coli B/r: comparison of theoretical and experimental size distributions.

The way individual cells grow and divide uniquely determines the (time-invariant) cell size distribution of populations in steady-state exponential growth. In the preceding article, theoretical distributions were derived for two exponential and six linear models containing a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. The linear models differ from each other with respect to the timing of the presumptive doubling in their growth rate, the exponential models--according to whether there is or is not a part of the cell that does not contribute to the growth rate. Here we compared the size distributions predicted by each of these models with those of cell length and surface area measured by electron microscopy; the quality of the fit, as determined by the mean-square successive-differences test and the chi 2 goodness-of-fit test, was taken as a measure of the adequacy of the model. The actual data came from two slow-growing E. coli B/r cultures, an A strain (pi = 125 min) and a K strain (pi = 106 min), and a correction was introduced in each to account for the distortion caused by the finite size of the picture frame. The parameter estimates produced by the various models are quite reliable (cv less than 0.1%); we discuss them briefly and compare their values in the two strains. All the length extension models were rejected outright whereas most of the surface growth versions were not. When the same models were tested on A-strain data from a faster growing culture (tau = 21 min), those models that provided an adequate fit to the cell surface area data proved equally satisfactory in the case of cell length. These findings are evaluated and shown to be consistent with cell surface area rather than cell length being the dimension under active control. Three surface area models, all linear, are rejected--those in which doubling of the growth rate occurs with a constant probability from cell birth, at a particular cell age, and precisely at cell division. The evidence in the literature that appears to contradict this last result, rejection of the simple linear surface growth model, is shown to be faulty. The 16 original models are here reduced to five, two involving exponential surface growth and three linear, and possible reasons are presented for our inability to discriminate further at this stage.

Cell Division↗

PubMed1991

Simulation study on covariance component estimation for two binary traits in an underlying continuous scale.

The usefulness of the variance and covariance component estimation methods based on a threshold model was studied in a multiple-trait situation with two binary traits. Estimation equations that yield marginal maximum likelihood estimates of variance components on the underlying continuous variable scale and point estimates of location parameters with empirical Bayesian properties are described. Methods were tested on simulated data sets that were generated to exhibit three different incidences, 25, 15, and 5%. Results were compared with analyses of the same data sets with a REML method based on normal distribution and a linear model. Heritabilities and residual correlations calculated from discrete observations were transformed to underlying parameters. In estimation of heritabilities, all methods performed equally well at all incidence levels and with no detectable bias. As suggested by threshold theory, the genetic correlation was accurately estimated directly from the observations without any need of correction for incidence. Marginal maximum likelihood estimates of genetic correlations were similar to linear model estimates; discrepancies from the true parameters were consistent with both methods. In estimation of residual correlations, the method with the linear model approach yielded satisfactory estimates only at the highest incidence level, 25%. For 5% incidence, the uncorrected estimate of residual correlation was 50% less than the true value, and after correction for incidence, the parameter was overestimated by 90%. The estimates of residual correlation from the threshold model were regarded fair, except at the lowest level of incidence, where the estimate was 27% higher than the true value. Results indicated that when an accurate estimate of residual correlation is needed, the marginal maximum likelihood estimates are superior to the estimates calculated with the linear model. Using correction for the incidence level for residual correlation did not work well except at the highest incidence level.

Analysis of Variance↗

PubMed2006

Transmission disequilibrium test for quantitative trait loci detection in livestock populations.

The performance of several transmission disequilibrium tests (TDT) for detection of quantitative trait loci (QTL) in data structures typical of outbred livestock populations were investigated. Factorial mating designs were simulated with 10 sires mated to either 50 or 200 dams, each family having five or eight full sibs. A single marker and QTL, both bi-allelic, were simulated using a disequilibrium coefficient based on complete initial disequilibrium and 50 generations of recombination [i.e. D = D(0)(1 - theta)50], where theta is the recombination fraction between marker and QTL. The QTL explained either 10% (small QTL) or 30% (large QTL) of the genetic variance for a trait with heritability of 0.3. Methods were: TDT for QTL (Q-TDT; both parents known), 1-TDT (only one parent known) and sibling-based TDT (S-TDT; neither parent known, but sibs available). All were found to be effective tests for association and linkage between the QTL and a tightly linked marker (theta < 0.02) in these designs. For a large QTL, theta = 0.01, and five full sibs per family, the empirical power for Q-TDT, 1-TDT and S-TDT was 0.966, 0.602 and 0.974, respectively, in a large population, versus 0.700, 0.414 and 0.654, respectively, in a small population. For a small QTL effect, theta = 0.01, large population the empirical power of these tests were 0.709, 0.287 and 0.634. The power of Q-TDT, 1-TDT and S-TDT was satisfactory for large populations, for QTL with large effects and for five full sibs per family. The 1-TDT based on a linear model was more powerful than the normal 1-TDT. The empirical power for Q-TDT and 1-TDT with a linear model was 0.978 and 0.995 respectively. TDT based on analogous linear models, incorporating the polygenic covariance structure, provided only small increases in power compared with the usual TDT for QTL.

Algorithms↗

PubMed1989

Analysis of simple reaction time to a sinusoidal grating by means of a linear filter model of the detection process.

Simple reaction time (RT) to a sinusoidal grating was analyzed in terms of a linear filter model of the detection process. First, RT contrast functions were determined over a wide range of spatial frequencies and retinal illuminances. Second, calculating the time course of the linear filter's response, theoretical visual latency contrast functions were derived for the same conditions of spatial frequency and retinal illuminance as those in the RT measurements. Comparison of the two functions showed that the contrast dependence of the RT functions was much larger than that of the visual latency functions. The discrepancy between the two functions was satisfactorily described as a power function of the slope of the filter's response at threshold level. On the basis of these results, we propose a model of the RT process. According to the model, the RT process is mediated by a cascade that consists of a level detector, which includes a linear filter followed by a threshold device, and a differentiator of the filter's response.

Attention↗

PubMed1999

Analysis of time-dependent covariates in failure time data.

In failure time analyses, time-dependent covariates are only rarely used. In some clinical studies, however, consideration of available covariate information over time could be relevant to understanding complex disease processes. We propose the time-dependent Cox model and the linear model of Aalen as two possible approaches for such time-dependent survival analyses. The approaches are illustrated with the data of the Stanford Heart Transplantation Study and a study of malignant glioma. Differences between these models and the baseline analysis are discussed.

Adult↗

PubMed1993

Linear quadratic model--estimation of alpha/beta ratio for mucosal reaction.

In radiotherapy to ensure that appropriate tumor lethal dose is delivered without exceeding normal tissue tolerance, concepts like NSD and its derivatives were used in the past. Due to their short coming these concepts are now replaced by a linear quadratic model. As this model is based on the recent radiobiological data, it is claimed to be able to predict the biological responses of tumors as well as normal tissues more accurately. However, the accuracy of prediction depends on the precise values of various parameters such as alpha/beta, repair constant mu and repopulation factor that are involved in the linear quadratic model. For most of the tumors and normal tissues, values of the parameters are not yet accurately known. We have estimated alpha/beta value for mucosal reactions, i.e. normal tissue early reactions in head neck cases treated with twice daily fractionation schedules and observed it to be 7.90 Gy for slight mucositis whereas it is 7.68 and 8.11 Gy for patchy and confluent mucositis, respectively.

Carcinoma, Squamous Cell↗

PubMed2005

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Adult↗

PubMed2001

Potential accuracy of genetic evaluation for calving difficulty with incomplete data on calving difficulty and/or birth weight using a bivariate threshold-linear animal model.

The purpose of this study was to evaluate the potential loss of accuracy in direct and maternal predicted breeding values (PBV) for calving difficulty (CD) with different levels of missing records of CD and/or birth weight (BW), using a bivariate threshold-linear animal model. Data obtained from the American Gelbvieh Association included 84,420 first-parity records with both CD and BW available. The final pedigree file included 178,858 animals. The model included fixed calf-sex-dam-age, random herd-year-season, and animal direct and maternal effects. Different levels of missing observations for CD and BW were obtained by randomly deleting 0, 25, 50, 75, and 100% of records for both traits in various combinations. Correlation estimates between PBV for CD obtained with complete and incomplete data were used to measure the changes in PBV for different levels of missing records. Reported correlations are means of three replicates. The results suggest that the information on direct and maternal PBV provided by CD records is more reliable than the information provided by BW records. The difference was especially large when a high proportion of CD records were missing. Correlations above 0.96 and 0.95 for direct and maternal PBV, respectively, when missing 25% or 0% of the CD or BW records suggest that small changes would be predicted with a low proportion incomplete data. For genetic prediction of popular sires (with > 100 pogeny), a higher proportion of missing records could be tolerated. The results suggest that the bivariate threshold-linear animal model is useful for routine genetic evaluation of CD with incomplete field data.

Journal Article↗

PubMed2000

Neural coding: higher-order temporal patterns in the neurostatistics of cell assemblies.

Recent advances in the technology of multiunit recordings make it possible to test Hebb's hypothesis that neurons do not function in isolation but are organized in assemblies. This has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data. We mention three possible measures for the presence of higher-order patterns of neural activation--coefficients of log-linear models, connected cumulants, and redundancies--and present arguments in favor of the coefficients of log-linear models. We present test statistics for detecting the presence of higher-order interactions in spike train data by parameterizing these interactions in terms of coefficients of log-linear models. We also present a Bayesian approach for inferring the existence or absence of interactions and estimating their strength. The two methods, the frequentist and the Bayesian one, are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other. A heuristic for the analysis of temporal patterns is also proposed. Finally, a Bayesian test is presented that establishes stochastic differences between recorded segments of data. The methods are applied to experimental data and synthetic data drawn from our statistical models. Our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys, the somatosensory cortex of anesthetized rats, and multiunit recordings in the visual cortex of behaving monkeys.

Action Potentials↗

PubMed2004

Daily mortality and air pollution in Atlanta: two years of data from ARIES.

Associations between daily mortality and air pollution were investigated in Fulton and DeKalb Counties, Georgia, for the 2-yr period beginning in August 1998, as part of the Aerosol Research and Inhalation Epidemiological Study (ARIES). Mortality data were obtained directly from county offices of vital records. Air quality data were obtained from a dedicated research site in central Atlanta; 15 separate air quality indicators (AQIs) were selected from the 70 particulate and gaseous air quality parameters archived in the ARIES ambient air quality database. Daily meteorological parameters, comprising 24-h average temperatures and dewpoints, were obtained from Atlanta's Hartsfield International Airport. Effects were estimated using Poisson regression with daily deaths as the response variable and time, meteorology, AQI, and days of the week as predictor variables. AQI variables entered the model in a linear fashion, while all other continuous predictor variables were smoothed via natural cubic splines using the generalized linear model (GLM) framework in S-PLUS. Knots were spaced either quarterly, monthly, or biweekly for temporal smoothing. A default model using monthly knots and AQIs averaged for lags 0 and 1 was postulated, with other models considered in sensitivity analyses. Lags up to 5 days were considered, and multipollutant models were evaluated, taking care to avoid overlapping (and thus collinear) AQIs. For this reason, PM(2.5) was partitioned into its three major constituents: SO(2-)(4), carbon (EC + 1.4 OC), and the remainder; sulfate was assumed to be (NH(4))(2)SO(4) for this purpose. Initial AQI screening was based on all-cause (ICD-9 codes <800) mortality for those aged 65 and over. For the (apparently) most important pollutants--PM(2.5) and its 3 major constituents, coarse PM mass [CM], 1-h maximum CO, 8-h maximum O(3)--we investigated 15 mortality categories in detail. (The 15 categories result from three age groups [all ages, <65, 65+] and five cause-of-death groups [all disease causes, cardiovascular, respiratory, cancer, and other "remainder" disease causes]). The GLM model outputs that were considered included mean AQI effects and their standard errors, and two indicators of relative model performance (deviance and deviance adjusted for the number of observations and model parameters). The latter indicator was considered to account for variations in the number of observations created by varying amounts of missing AQI data, which were not imputed. The single-AQI screening regressions on all-cause 65+ mortality show that CO, NO(2), PM(2.5), CM, SO(2), and O(3), followed by EC and OC, consistently have the best model fits, after adjusting for the number of observations. Their relative rankings, however, vary according to the smoothing knots used, and there is no correspondence between mean AQI effect and overall model fit.(Other regression runs often show that the best model fits are obtained with no AQI in the model.) There is no correspondence between mean AQI effect and statistical significance or between mean effect and serial correlation. There is a highly significant (.001 level) relationship between overall model fit and serial correlation; the best fitting models have the most frequent knot spacing and the most negative serial correlation. The regression analyses by cause of death find elderly circulatory deaths to be consistently associated with CO for all models.

Adult↗

PubMed1981

A linear programming model for determining efficient combinations of 8-, 10-, and 12-hour shifts.

I have formulated a linear programming model to determine changes in efficiency and productivity that would result from scheduling personnel to work combinations of 8-, 10-, and 12-hour shifts in a section of our pulmonary medicine department. My objective was to minimize the number of staff hours worked each day, subject to the constraints imposed by the levels of staffing required during each hour of the day. I found that a combination of 8-, 10- and 12-hour shifts could increase productivity 8.1% and reduce personnel requirements by one full-time equivalent. Salary expenses would decrease 7.5% if overtime were not paid for the extended hours of the 10- and 12-hour shifts. Two considerations in implementing the proposed schedule are the willingness of staff to work extended hours and the necessity of developing a format for communication between therapists who work discontinuous shifts.

Hospital Bed Capacity, 100 to 299↗

PubMed1990

Algorithm for optimal linear model-based control with application to pharmacokinetic model-driven drug delivery.

Computerized pharmacokinetic model-driven administration of intravenous anesthetic agents has been implemented using a variety of algorithms to control the drug infusion regimen. All such algorithms are similar to the extent that they use a linear pharmacokinetic model of the drug being administered to determine drug infusion rates to theoretically achieve and maintain plasma drug concentrations (setpoints) specified by the physician. Since the behavior of the pharmacokinetic model can be computed for any input, it should be possible to achieve regulation of the drug infusion rates that is flexible (i.e., the physician can interactively adjust the setpoint), practical, and analytically optimized; these objectives are realized by the algorithm described in this communication.

Algorithms↗

PubMed1998

Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior.

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics.

Animals↗