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PubMed1995

Limitations of the standard linear solid model of intervertebral discs subject to prolonged loading and low-frequency vibration in axial compression.

The purpose of this study was to answer the following questions: (1) Can the standard linear solid model for viscoelastic material simulate the influence of disc level and degeneration on the ability of a disc to withstand prolonged loading and low-frequency vibration? (2) How well does the SLS model explain the relationship between the ability of a disc to resist prolonged loading and its ability to resist dynamic loads and dissipate energy when subjected to low-frequency vibration? Responses of human thoracic and lumbar discs were measured in axial compression under a constant load, and for cyclic deformations at three frequencies. Parameters of the SLS model for each disc were determined by a least-squares fit to the experimental creep response. The model was subsequently used to predict the disc's response to cyclic deformations. The SLS model was able to qualitatively simulate the effects of disc level and degeneration on the ability of an intervertebral disc to resist both prolonged loading and low-frequency vibration. However, the model underestimated the stress relaxation, dynamic modulus and hysteresis of thoracic and lumbar discs subjected to low-frequency vibration. The SLS model was unable to explain the relationship between the ability of a disc to resist prolonged loading and its ability to resist dynamic loads and dissipate energy when subjected to low-frequency vibration. Although in the lumbar discs the steady-state predictions of the SLS model were significantly correlated to the experimental response, the strength of model predictions decreased with increasing frequency, particularly for hysteresis.

Adult↗
PubMed2000

Generalized linear mixture models for handling nonignorable dropouts in longitudinal studies.

This paper presents a method for analysing longitudinal data when there are dropouts. In particular, we develop a simple method based on generalized linear mixture models for handling nonignorable dropouts for a variety of discrete and continuous outcomes. Statistical inference for the model parameters is based on a generalized estimating equations (GEE) approach (Liang and Zeger, 1986). The proposed method yields estimates of the model parameters that are valid when nonresponse is nonignorable under a variety of assumptions concerning the dropout process. Furthermore, the proposed method can be implemented using widely available statistical software. Finally, an example using data from a clinical trial of contracepting women is used to illustrate the methodology.

Journal Article↗
PubMed1982

A molecular model for linear and lateral growth of type I collagen fibrils.

A model is proposed for Type I collagen fibrillogenesis in which linear and lateral growth are directed by attractive charged pair interactions. It is suggested that linear growth decreases the rate of rotational motion resulting in an increased rate of lateral collisions. The mechanism of linear aggregation involves interactions between sets of unusual charged pairs located at positions 53, 54 and 56 and positions 990 and 992 as well as in the non-helical ends. These charged pairs attract each other electrostatically as well as form a hydrophobic pocket between the molecules. Lateral growth occurs by attractions between D-staggered, charged pairs which alternate between intra- and interchain states. Interchain interactions lead to lateral association of neighboring molecules and formation of a D-staggered unit containing five trimers. Rotational motion of the triple-helical backbone as well as the ability of charged pairs in their interchain state to interact by several different possible combinations between alpha-chains suggest that lateral packing of collagen molecules into fibrils at least in vitro may not need to be specific.

Amino Acid Sequence↗
PubMed1994

A non-linear estimation model for adaptive minimization of EOG artefacts from EEG signals.

In this paper, we propose an adaptive noise cancellation scheme in a novel way for the minimization of electrooculogram (EOG) artefacts from corrupted EEG signals. This method is based on the fact that the transfer function of the biological neuron can be modeled as a sigmoid non-linearity. Comparison of the time plots and the smoothed linear prediction spectra show that the proposed method effectively minimizes the EOG artefacts from corrupted EEG signals. We have also studied the performance of the above scheme for different values of filter order (P) and the convergence factor (mu). Normalised Mean Squared Error (NMSE) has been used as the measure for comparison. The study shows that the NMSE decreases with increase in P and mu (but saturates after certain values of the parameters), thereby implying a better EOG minimization from EEG signals. It is also observed that the EOG minimization scheme with two EOG reference inputs works better than that with one reference input.

Algorithms↗
PubMedDate not supplied

Optimizing a linear algorithm for real-time robotic control using chronic cortical ensemble recordings in monkeys.

Previous work in our laboratory has demonstrated that a simple linear model can be used to translate cortical neuronal activity into real-time motor control commands that allow a robot arm to mimic the intended hand movements of trained primates. Here, we describe the results of a comprehensive analysis of the contribution of single cortical neurons to this linear model. Key to the operation of this model was the observation that a large percentage of cortical neurons located in both frontal and parietal cortical areas are tuned for hand position. In most neurons, hand position tuning was time-dependent, varying continuously during a 1-sec period before hand movement onset. The relevance of this physiological finding was demonstrated by showing that maximum contribution of individual neurons to the linear model was only achieved when optimal parameters for the impulse response functions describing time-varying neuronal position tuning were selected. Optimal parameters included impulse response functions with 1.0- to 1.4-sec time length and 50- to 100-msec bins. Although reliable generalization and long-term predictions (60-90 min) could be achieved after 10-min training sessions, we noticed that the model performance degraded over long periods. Part of this degradation was accounted by the observation that neuronal position tuning varied significantly throughout the duration (60-90 min) of a recording session. Altogether, these results indicate that the experimental paradigm described here may be useful not only to investigate aspects of neural population coding, but it may also provide a test bed for the development of clinically useful cortical prosthetic devices aimed at restoring motor functions in severely paralyzed patients.

Action Potentials↗
PubMed2000

A linear regression model to predict the pH of neonatal parenteral nutrition solution.

INTRODUCTION: Providing the high calcium intake necessary for normal bone mineralization in rapidly growing very low birth weight infants is difficult because calcium and phosphorus solubility is limited in the range of parenteral nutrition pH. A major determinant of calcium and phosphorus solubility in vitro is solution pH. The objective of this study was to develop and assess the accuracy of a method to predict the final parenteral solution pH as a linear function of the individual parenteral component concentrations. METHODS: pH values were measured for 205 neonatal parenteral nutrition solutions prepared during a 5-week period. Concentrations of the 13 components used to synthesize parenteral nutrition were determined for each solution. Data from 135 samples were used to develop a linear regression coefficient model with pH as the dependent variable. From the regression model the pH was predicted for the remaining 70 samples using the seven significant solution component concentrations, and the predicted and measured solution pH values were compared. RESULTS: The mean measured parenteral nutrition pH for all solutions was 5.364 +/- 0.110 (mean +/- SD, range 5.03-5.73). The absolute mean pH difference between the predicted and measured value for the 70 test samples was 0.04 +/- 0.04. pH estimated with the model correlated highly with measured pH (r2 = 0.77). The seven components in the regression model accounted for 81% of the pH variance. CONCLUSION: The pH of neonatal parenteral nutrition solutions can be predicted accurately as a linear function of the solution concentrations of the following seven components: sodium acetate, sodium phosphate, potassium phosphate, potassium acetate, magnesium sulphate, amino acid solution and dextrose. The absolute mean difference between measured pH and predicted pH was 0.04. Applying this method to estimate pH with the interactive properties of computer-based ordering systems could enhance calcium and phosphorus administration to very low birth weight infants.

Calcification, Physiologic↗
PubMed2006

Population analysis of the pharmacokinetics and the haematological toxicity of the fluorouracil-epirubicin-cyclophosphamide regimen in breast cancer patients.

PURPOSE: The aims of the study were (a) to characterise the pharmacokinetics (PK), including inter-individual variability (IIV) and inter-occasion variability (IOV) as well as covariate relationships and (b) to characterise the relationship between the PK and the haematological toxicity of the component drugs of the fluorouracil (5-FU)-epirubicin (EPI)-cyclophosphamide (CP) regimen in breast cancer patients. PATIENTS AND METHODS: Data from 140 breast cancer patients, either within one of different studies or in routine clinical management, were included in the analyses. The patients were all treated with the fluorouracil-epirubicin-cyclophosphamide (FEC) regimen every third week for 3-12 courses, either in standard doses, i.e. 600/60/600 mg/m(2) of 5-FU, EPI and CP, respectively, or according to a dose escalation/reduction protocol (tailored dosing). PK data were available from 84 of the patients, whereas time-courses of haematological toxicity were available from 87 patients. The data analysis was carried out using mixed effects models within the NONMEM program. RESULTS: The PK of 5-FU, EPI and 4-hydroxy-cyclophosphamide (4-OHCP), the active metabolite of CP, were described with a one-compartment model with saturable elimination, a three-compartment linear model and a two-compartment linear model, respectively. No clinical significant correlation was found between PK across drugs. The unexplained variability in clearance was found to be less within patients, between courses (inter-occasion variability, IOV) than between patients (inter-individual variability, IIV) for EPI and 5-FU. For 4-OHCP, however, the IIV diminished by approximately 45% when significant covariates were included and the final population model predicts an IIV that is equal to IOV. Significant covariates for elimination capacity parameters were serum albumin (5-FU, EPI and 4-OHCP), creatinine clearance (5-FU), bilirubin (EPI) and body surface area (BSA) (4-OHCP). Elimination capacity of 5-FU and EPI was not related to BSA and for none of the studied drugs did body weight explain the PK variability. The time-course of haematological toxicity after treatment was well described by a semi-physiological model that assumes additive haematological toxicity between CP and EPI with negligible contribution from 5-FU. The influence of G-CSF could be incorporated into the model in a mechanistic manner as shortening the maturation time to 43% of the normal duration and increasing the mitotic activity to 269% of normal activity. CONCLUSIONS: The models presented describe the dose-concentration-toxicity relationships for the FEC therapy and may provide a basis for implementation and comparison of different individualisation strategies based on covariates, therapeutic drug monitoring and/or pharmacodynamic (PD) feedback. The PD model extends on previous semi-mechanistic models in that it also takes G-CSF administration into account.

Antineoplastic Combined Chemotherapy Protocols↗
PubMed1990

Application of the root locus technique to the closed-loop SO2 pacemaker-cardiovascular system.

A previously developed nonlinear model of the pacemaker-cardiovascular system contained a term of the form 1/CO in the forward loop. CO, the cardiac output, is a linear function of heart rate and exercise level. To evaluate the dynamic behavior of the system over a range of pacemaker controller gains, a piecewise linear model was developed. The model was linearized by taking the first two terms of the Taylor's series expansion of 1/CO about the steady state heart rate. A root locus algorithm, with the unique feature of a time delay element in the forward loop, was used to calculate the linear model closed-loop poles as a function of pacemaker controller gain for exercise levels of 25, 50, and 100 W. Step response simulation of the complete nonlinear model showed dynamics close to that predicted from the pole location in the root locus plot. Thus, the root locus technique can be used to quantify systematically the dynamics of the pacemaker-cardiovascular system for different exercise levels and over a wide range of controller gain values.

Cardiac Output↗
PubMed1991

Risk factors associated with caprine arthritis-encephalitis virus infection in goats on California dairies.

Log-linear methodology was used to examine relations among caprine arthritis-encephalitis virus (CAEV) seroreactivity and host/management factors in a cross-sectional study of 2,826 goats on 13 California dairies. The CAEV serologic status was associated with age and feeding method (pasteurized/unpasteurized milk), but not with breed. Data from a prevalence survey of 321 goats from 2 additional dairies demonstrated very good fit of the selected log-linear model (P = 1.00), indicating that the model was very appropriate to describe the relations. Odds of seropositivity and odds ratios were generated by use of a logit model derived from the log-linear model. Goats raised by the unpasteurized feeding method were estimated to have been 3.3 times more likely to be CAEV-seropositive than goats fed by the pasteurized method, when adjusted for the effects of age. Goats aged 2, 3, 4, and 5 or greater years were estimated to have been 1.7, 2.6, 4.5, and 5.7 times, respectively, more likely to be CAEV-seropositive than were yearling goats when ratios were adjusted for pasteurization status. Breed, gender, and herd of origin were not associated with CAEV seroreactivity when the effects of other factors were considered. Estimated odds of CAEV seroreactivity and the associated odds ratios for combinations of factor levels are reported. In this study, the magnitude and direction of the associations among CAEV serologic status, age, and pasteurized feeding methods were demonstrated.

Age Factors↗
PubMed1990

Fluoride pharmacokinetics in the ewe: a linear pharmacokinetics model.

The kinetics of fluoride was studied in a group of 3 adult ewes given sodium fluoride solutions at 3 dose levels (0.15, 0.375 and 0.75 mg/kg bw). Data were analysed using both compartmental and noncompartmental approaches. A 3-compartment open model was selected to describe the data. Comparison of the different parameters indicated an absence of change with dose level, suggesting that fluoride behaved linearly at the doses under study. The half-life of elimination was 2.57 +/- 1.28 h, the steady-state volume of distribution was 0.26 +/- 0.5 L/kg and the body clearance was 0.105 +/- 0.26 L/kg/h. It was concluded that a single intravascular fluoride administration (bolus) may be used to evaluate oral bioavailability of fluoride in sheep in toxicity studies.

Administration, Oral↗
PubMed2006

Modeling and inverse controller design for an unmanned aerial vehicle based on the self-organizing map.

The next generation of aircraft will have dynamics that vary considerably over the operating regime. A single controller will have difficulty to meet the design specifications. In this paper, a self-organizing map (SOM)-based local linear modeling scheme of an unmanned aerial vehicle (UAV) is developed to design a set of inverse controllers. The SOM selects the operating regime depending only on the embedded output space information and avoids normalization of the input data. Each local linear model is associated with a linear controller, which is easy to design. Switching of the controllers is done synchronously with the active local linear model that tracks the different operating conditions. The proposed multiple modeling and control strategy has been successfully tested in a simulator that models the LoFLYTE UAV.

Aircraft↗
PubMed1988

A non-linear elastic model of contraction of ischaemic segments.

Previous studies have characterised the motion of the myocardium using a linear time varying elastance model, ie, they have sought to characterise the relationship between left ventricular volume and internal pressure as linear, but with time varying slopes over the cardiac cycle. However, the motion of myocardium during regional ischaemia has not been characterized by such models. Studies of totally ischaemic tissue and of myocardium in diastole have characterised the relationship between tension or stress and segment length as exponential. It is the purpose of this study to present a new model in which myocardial contraction is expressed as an exponential, but time varying elastic relationship. In this model tension, T, is related to segment length according to the formula T = e alpha(t)L + beta, where alpha(t) rises with systole and falls in diastole. This model was applied to the motion of hypokinetic segments noted in a series of conscious dogs studied for other purposes. Hypokinetic segments display early systolic bulging, decreased systolic shortening, and early diastolic recoil. These particular types of segment motion are naturally predicted by this model. Furthermore, the motion of myocardial segments as they become increasingly ischaemic may be predicted, including a gradual shift to the right and narrowing of the tension-length loop. alpha was noted to be independent of loading change, and thus may be viewed as an index of contractility. This model thus predicts the pattern of motion of hypokinetic segments and provides new insight into myocardial contractility.

Animals↗
PubMed2002

Non-linear hierarchical models for monitoring compliance.

As biomarkers transformable by specific drug agents increasingly become available, so their usefulness also increases for monitoring compliance in clinical and prevention trials, and for subsequent monitoring in the general population if a treatment is found successful. Marker levels measured over the course of a treatment yield a longitudinal trajectory that is typically non-linear, with varying velocities during the phase-in and steady-state periods of treatment, followed by decays back to normal in the presence of non-compliance. There is often considerable between-individual variability both in the mean parameters of the trajectory and the variability over time. An example is the biomarker mean corpuscular volume (MCV), which increases by 20 per cent from the drug zidovudine (AZT), and has been used to monitor compliance to AZT. Using MCV data from a previous AIDS clinical trial as an example, we describe a non-linear hierarchical growth model suitable for biomarkers that exhibit sigmoidal and/or asymptotic growth behaviour and show how such models can be supplemented with a change-point to identify potential times of non-compliance. We perform a fully Bayesian analysis to obtain a variety of posterior summaries for the behaviour of the longitudinal trajectory and the times of non-compliance, and describe how to obtain predictions of non-compliance for new individuals.

Acquired Immunodeficiency Syndrome↗
PubMed1999

Simple model for linear and nonlinear mixing at unstable fluid interfaces in spherical geometry.

A simple model was recently described for predicting linear and nonlinear mixing at an unstable planar fluid interface subjected to an arbitrary time-dependent variable acceleration history [J. D. Ramshaw, Phys. Rev. E 58, 5834 (1998)]. Here we present an analogous model for describing the mixing of two adjacent spherical fluid shells of different density resulting from an arbitrary time-dependent mean interface radius R(t). As in the planar case, the model is based on a heuristic expression for the kinetic energy of the system. This expression is based on that for the kinetic energy of a linearly perturbed interface, but with a dynamically renormalized effective wavelength which becomes proportional to the half-width a(t) of the mixing layer in the nonlinear regime. An equation of motion for s=R(2)a is then derived from Lagrange's equations. This evolution equation properly reduces to Plesset's equation for small perturbations, and to the previous planar model in the limit of very large R. The conservation properties of the model are established, and a suitable numerical scheme which preserves these properties is proposed.

Journal Article↗
PubMed2005

Monitoring of gallbladder and gastric coordination by EPI.

PURPOSE: To assess for the first time the potential of echo-planar magnetic resonance imaging (EPI) for measuring simultaneously both gallbladder and gastric emptying. MATERIALS AND METHODS: Eight healthy subjects ingested 500 mL of an acid-stable liquid test meal containing 15% olive oil and flavoring. Every 20 minutes for three hours thereafter, a rapid EPI multislice set was acquired across the whole abdomen, using a dedicated whole-body 0.5-T EPI scanner. RESULTS: The bile in the gallbladder and the test meal in the stomach appeared bright in the EPI images, aiding localization and region of interest analysis. We measured the gallbladder emptying curve and fitted the data to a simple analytical model. The mean fasted gallbladder volume was 25 +/- 4 mL, comparable to previously published MRI and ultrasound values. Gastric emptying data fitted well to a linear model linear (R2 = 0.99), and we observed an exponential (R2 = 0.98) relationship between gallbladder and gastric volumes for the first 90 minutes. CONCLUSION: This study shows the potential of EPI to monitor simultaneously and noninvasively the emptying of the gallbladder and of the gastric lumen. No contrast enhancing agents are needed. This method could overcome the limitations of previous gamma scintigraphy and ultrasound techniques.

Echo-Planar Imaging↗
PubMed2004

Towards a standard analysis for functional near-infrared imaging.

Functional near-infrared spectroscopy (fNIRS) allows the ability to monitor brain activation by measuring changes in the concentration of oxy- and deoxy-hemoglobin. Until now no standardized approach for fNIRS data analysis has been established, although this has to be regarded as a precondition for future application. Hence, we applied the well-established general linear model to optical imaging data. Further, fNIRS data were analyzed in the frequency domain. Two visual tasks were investigated with optical imaging: a checkerboard paradigm supposed to activate the primary and secondary visual cortex, and a paradigm consisting of moving colored stimuli (rotating 'L's) additionally involving the motion area V5. Analysis with the general linear model detected the activation focus in the primary and secondary visual cortex during the first paradigm. For the second paradigm, a second laterally localized activated brain region was found, most likely representing V5. Spatially resolved spectral analysis confirmed the results by showing maxima of power spectral density and coherence in the same respective brain regions. Moreover, it demonstrated a delay of the hemodynamic response in the motion area. In summary, the present study suggests that the general linear model and spatially resolved spectral analysis can be used as standard statistical approaches for optical imaging data, particularly because they are almost independent of the assumed differential path length factors.

Adult↗
PubMed1994

Linear quadratic model compared with TDF and TSD concepts for malignancy of cervix uteri treated with twice daily fractionated schedules.

PURPOSE: Various types of fractionation schemes have been tried in recent year with the objective of improving tumor control rate because conventional fractionation schedules do not always produce optimum results. To compare the radiobiological effectiveness and the gain in the therapeutic ratio due to various fractionation schemes, empirical formulae such as NSD, TDF, CRE and TSD were introduced and used despite of many short comings. Recent linear quadratic (LQ) model is claimed to be able to predict the radiobiological responses of tumor as well as normal tissues more accurately. In the present study various empirical models are compared. PATIENTS AND METHOD: We treated malignancy of cervix uteri by twice daily fractionation schedules of 1.2 Gy/fraction, 1.4 Gy/fraction and 1.6 Gy/fraction with interfraction interval of four to six hours. The percentage tumor regression was estimated from weekly clinical observations and the TDFt, TSD and ERDt concepts were applied to the data and the predictions are compared. RESULTS: It was observed that TDFt and TSD concepts predicts equally well (within +/- 3%) the probable tumor regression as predicted by LQ concept. CONCLUSIONS: Till precise values of various parameters of LQ model are known, the TDF and TSD models can be used to predict probable tumor control rates within reasonable accuracy.

Carcinoma, Squamous Cell↗