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PubMed1997

Temporal stability of node-based internal bone adaptation simulations.

Jacobs et al. (1995, J. Biomechanics 28, 449-459) introduced a new implementation of the remodeling theory developed by Beaupre et al. (1990, J. Orthop. Res. 8, 651-661) that eliminates certain spurious spatial instabilities of previous implementations. Due to the highly nonlinear, coupled nature of multi-dimensional adaptation simulations, direct stability analyses of this method are not practical. In this manuscript, a linearized stability analysis was used to derive an expression for the critical time step for the stability of a simple model problem. In addition to accurately predicting the temporal response of the single degree-of-freedom problem, the analysis provided a conservative estimate of the critical time step for a more realistic, multiple degree-of-freedom adaptation simulation.

Adaptation, Physiological↗

PubMed1994

Reaction of phthalate dioxygenase reductase with NADH and NAD: kinetic and spectral characterization of intermediates.

Phthalate dioxygenase reductase (PDR) is an electron transferase that contains FMN, which accepts a hydride from NADH, and a [2Fe-2S] center, which transfers electrons to phthalate dioxygenase. The reduction of PDR by NADH has been studied by stopped-flow spectroscopy. Data from studies using both portio- and deuterio-NADH were analyzed by nonlinear curve fitting and numerical simulation techniques. The results of these analyses indicate that the reductive half-reaction of PDR consists of five distinct kinetic phases: (a) NADH binds to form a primary Michaelis complex (MC-1) (Kd = 50 microM). (b) The enzyme undergoes a structural change (116 +/- 5 s-1) resulting in a charge-transfer complex (CT-1). (c) The next phase in the reaction shows a deuterium isotope effect of 7.0 when (4R)-[2H]NADH (NADD) is substituted for NADH, identifying this step as the one involving hydride transfer. The rate of hydride transfer from NADH to FMN is 70 s-1, and this process results in a charge-transfer intermediate between the flavin hydroquinone anion and NAD (CT). (d) Internal electron transfer from the flavin to the iron-sulfur center, which is only 35 +/- 4 s-1, then results in an intermediate consisting of a reduced [2Fe-2S] center and a neutral flavin semiquinone (SQ). It is surprising that this rate is so slow, since the shortest interatomic distance between these centers is only 4.7 A [Correll, C. C., et al. (1992) Science 258, 1604-1610]. The 2-electron-reduced form of PDR (SQ in Figure 1) binds weakly to the reaction product, NAD (Kd = 3.7 mM), but forms a tight complex with NADH (Kd = 10 microM). (e) Two molecules of the reduced iron-sulfur flavin semiquinone (SQ) form of PDR then undergo a relatively slow second-order disproportionation reaction, resulting in one molecule of 3-electron-reduced PDR and one molecule of 1-electron-reduced PDR. The latter reacts rapidly with excess NADH to form a 3-electron-reduced PDR.

Burkholderia cepacia↗

PubMed1988

Clustering individuals as a way of dealing with multiple predictors in occupational stress research.

As the number and type of variables thought to affect the amount of stress experienced by an individual in the workplace increase, and as these effects are often found to be nonlinear and to interact with each other, the forms of statistical analyses employed present different costs and benefits. The use of cluster analysis as a preliminary means of categorizing individuals is described as the least artificial and empirically most accurate means of deriving groups that can lead to hypotheses and hypothesis testing using the more conventional means of analysis of variance. Such a methodology is described as it was applied to an investigation of the effects of demands, attitudes to demands, supports-constraints, and trait neuroticism upon job satisfaction and scores on the General Health Questionnaire for a sample of psychiatric nurses.

Affective Symptoms↗

PubMed2004

Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour.

In this paper a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. In particular, attention is focused upon the attack of tumour cells by so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. At this stage the immune cells and the tumour cells are considered to be in a state of dynamic equilibrium--cancer dormancy--a phenomenon which has been observed in primary tumours, micrometastases and residual disease after ablation of the primary tumour. Nonetheless, the precise biochemical and cellular mechanisms by which TICLs control cancer dormancy are still poorly understood from a biological and immunological point of view. Therefore we focus on the analysis of the spatio-temporal dynamics of tumour cells, immune cells and chemokines in an immunogenic tumour. The lymphocytes are assumed to migrate into the growing solid tumour and interact with the tumour cells in such a way that lymphocyte-tumour cell complexes are formed. These complexes result in either the death of the tumour cells (the normal situation) or the inactivation (sometimes even the death) of the lymphocytes. The migration of the TICLs is determined by a combination of random motility and chemotaxis in response to the presence of chemokines. The resulting system of four nonlinear partial differential equations (TICLs, tumour cells, complexes and chemokines) is analysed and numerical simulations are presented. We consider two different tumour geometries--multi-layered cell growth and multi-cellular spheroid growth. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time and heterogeneous in space. A linear stability analysis of the underlying (spatially homogeneous) ordinary differential equation (ODE) kinetics coupled with a numerical investigation of the ODE system reveals the existence of a stable limit cycle. This is verified further when a subsequent bifurcation analysis is undertaken using a numerical continuation package. These results then explain the complex heterogeneous spatio-temporal dynamics observed in the partial differential equation (PDE) system. Our approach may lead to a deeper understanding of the phenomenon of cancer dormancy and may be helpful in the future development of more effective anti-cancer vaccines.

Cell Division↗

PubMed2005

Some models of viscous-inviscid interaction.

Some hydrodynamical problems in which viscous-inviscid interaction is important are analysed. These problems are: disturbances propagation in channels, three-dimensional nonlinearly disturbed flows and the blow-off phenomenon.

Journal Article↗

PubMed2004

Long-wavelength thermocapillary instability with the Soret effect.

We study the onset of Marangoni instability of the quiescent equilibrium in a binary liquid layer with a nondeformable interface in the presence of the Soret effect. Linear stability analysis shows that both monotonic and oscillatory long-wavelength instabilities are possible depending on the value of the Soret number chi. Sets of long-wavelength nonlinear evolution equations are derived for both types of instability. Bifurcation analyses reveal that in the regime of monotonic instability square patterns bifurcate supercritically and they are preferred in competition with roll patterns. Hexagonal patterns bifurcate transcritically and the condition for the emergence of steady stable hexagonal patterns is derived. In the case of oscillatory instability, traveling and standing waves are found to bifurcate supercritically in the narrow range of the Soret parameter and traveling waves are found to become the selected type of flow.

Journal Article↗

PubMed1993

Nonlinear statistical models for the joint action of toxins.

A general approach using nonlinear regression models is presented for evaluating additivity, synergism, and antagonism of mixtures of toxins for proportions and ratio-scale response measures. This approach provides several advantages over the analysis methods typically used, which involve linear regression with logits or probits. A single model fit is performed, rather than a multistep procedure. Nonadditive alternative models can be easily constructed and tested against the appropriate additive models. The approach avoids the use of data "adjustments" for nonzero background response rates. The analyses are performed in the natural response metric, making interpretation straightforward. Also, the nonlinear regression model can be reparameterized to provide more meaningful primary parameters.

Animals↗

PubMed1995

Simple modelling of linear and nonlinear mechanical responses to sinusoidal oscillations during muscle contraction.

The mechanical responses of muscle to sinusoidal oscillations were analysed using a contraction model based on Huxley's 1957 model. To reproduce the three well-documented exponential processes resolved in the course of sinusoidal analysis, a few modifications had to be made on the original Huxley's model: (1) Each myosin cross-bridge should support substantial force at its position where the rate of detachment (g) abruptly changes. (2) Each cross-bridge should have the capability of stress-relaxation while attached to actin. This stress-relaxation should occur with a rate constant greater than the overall turnover rate of cross-bridges. After these modifications, the model reproduces not only the three exponential processes, but also the nonlinearity in the mechanical response, which is derived from the asymmetrical dependence of the rate constants on the cross-bridge strain. The present study provides a simplest model which reproduces the linear and nonlinear responses to sinusoidal oscillations, and help relate the exponential processes to the underlying attachment/detachment steps in the cross-bridge cycle.

Animals↗

PubMed1992

Analysis of machine-dependent and object-induced geometric distortion in 2DFT MR imaging.

Geometric distortion in MR imaging predominantly arises from the inhomogeneity of the static field and the nonlinearity of the gradients. It is the purpose of this paper to analyse the object and machine related contributions to geometric distortion in order to determine which corrections are necessary for attaining a specified precision. System related imperfections were measured by systematic variation of the strength, direction, and polarity of the read-out gradient in imaging experiments on a grid of cylindrical sample tubes. For the 1.5-T system used in this study, static field related errors up to 7 mm and gradient related errors up to 4 mm were observed (midcoronal plane, FOV 400-mm, G-read between 0.5 and 3.0 mT/m). Field related errors were shown to be inversely proportional to gradient strength, whereas gradient related errors turned out to be virtually independent of gradient strength. It therefore seems recommendable to always apply the strongest available selection and read-out gradients when geometric fidelity is given preference to signal-to-noise considerations. Correction of system related geometric distortions in MR images can readily be performed by table lookup. Object-induced distortions of the gradient fields were studied by experiments on a grid of sample tubes immersed into a cylindrical water bath of variable saline concentration. These experiments revealed a negligible influence of the object on the gradient error distribution, and lead to the conclusion that correction for the nonlinearity of the gradients only requires the application of system dependent correction factors. Object-related distortions of B0 were studied by conventional SE and fat-suppressed IR experiments on phantoms and human subjects. In these experiments the polarity of the read-out gradient was reversed. Subtraction images showed significant object-induced inhomogeneities of the static field at tissue-air interfaces and in the immediate vicinity of the object being imaged. A first attempt to correct for object related B0 inhomogeneities was made by contour analysis of the source images. At present this correction still has to be done manually.

Fourier Analysis↗

PubMed1999

Invasion thresholds for fungicide resistance: deterministic and stochastic analyses

Fungicide resistance is an important practical problem, but one that is poorly understood at the population level. Here we introduce a simple nonlinear model for fungicide resistance in botanical epidemics which includes the dynamics of the chemical control agent and the host population, while also allowing for demographic stochasticity in the host-parasite dynamics. This provides a mathematical framework for analysing the risk of fungicide resistance developing by including the parameters for the amount applied, longevity and application frequency of the fungicide. The model demonstrates the existence of thresholds for the invasion of the resistant strain in the parasite population which depend on two quantities: the relative fitness of the resistant strain and the effectiveness of control. This threshold marks a change from definite elimination of the resistant strain below the threshold to a finite probability of invasion which increases above the threshold. The fungicide decay rate, the amount of fungicide applied and the period between applications affect the effectiveness of control and, consequently, they influence whether or not resistance develops and the time taken to achieve a critical frequency of resistance. All three parameters are amenable to control by the grower or by coordinating the activity of a population of growers. Providing crude estimates of the effectiveness of control and relative fitness are available, the results can be used to predict the consequences of changing these parameters for the risk of invasion and the proportion of sites at which this might be expected to occur. Although motivated for fungicide resistance, the model has broader application to herbicide, antibiotic and antiviral resistance. The modelling approach and results are discussed in the context of resistance to chemical control in general.

Journal Article↗

PubMed1982

Comparative tumor-initiating activity of complex mixtures from environmental particulate emissions on SENCAR mouse skin.

The value of the SENCAR mouse for testing tumorigenic properties of complex mixtures on mouse skin was studied. Seven complex mixtures were obtained as dichloromethane extracts of collected particulate emissions from three diesel-fueled automobiles, a heavy-duty diesel engine, a nonleaded gasoline-fueled automobile, a coke oven battery, and a roofing tar pot. These emissions were applied topically at multiple doses to both male and female SENCAR mice that were subsequently promoted with 12-O-tetradecanoylphorbol 13-acetate. Two statistical analyses were applied to the data to rank the samples and to provide 95% confidence intervals. One analysis used tumor multiplicity data, applied them to a nonlinear Poisson model, and the second analysis used tumor incidence data and applied them to a log-probit model. Both analyses ranked the complex mixtures in similar order. Benzo[a]pyrene content alone could not account for all the tumorigenic activity in each complex mixture, indicating that other components also contribute to the overall tumorigenic activity.

Administration, Topical↗

PubMed2006

Fractal rigidity by enhanced sympatho-vagal antagonism in heartbeat interval dynamics elicited by central application of corticotropin-releasing factor in mice.

The dynamics of heartbeat interval fluctuations were studied in awake unrestrained mice following intracerebroventricular application of the neuropeptide corticotropin-releasing factor (CRF). The cardiac time series derived from telemetric ECG monitoring were analyzed by non-parametric techniques of nonlinear signal processing: delay-vector variance (DVV) analysis, higher-order variability (HOV) analysis, empirical mode decomposition (EMD), multiscale embedding-space decomposition (MESD), multiexponent multifractal (MEMF) analysis. The analyses support the conjecture that cardiac dynamics of normal control mice has both deterministic and stochastic elements, is nonstationary, nonlinear, and exerts multifractal properties. Central application of CRF results in bradycardia and increased variability of the beat-to-beat fluctuations. The altered dynamical properties elicited by CRF reflect a significant loss of intrinsic structural complexity of cardiac control which is due to central neuroautonomic hyperexcitation, i.e., enhanced sympatho-vagal antagonism. The change in dynamical complexity is characterized by an effect referred to as fractal rigidity, leading to a significant impairment of adaptability to extrinsic challenges in a fluctuating environment. The impact of dynamical neurocardiopathy as a major precipiting factor for the propensity of cardiac arrhythmias or sudden cardiac death by unchecked central CRF release in significant acute life events in man is critically discussed.

Animals↗

PubMed1999

Linear and nonlinear analysis of blood flow in healthy subjects and in subjects with Raynaud's phenomenon.

The paper presents analyses of the dynamics contained in the blood flow signals measured on healthy subjects and on subjects with primary Raynaud's phenomenon. Different signal processing methods are presented and discussed. The dynamics was evaluated in the time and frequency domains and in phase space. Additionally, changes in the basal value during temperature provocation were studied using multiresolution analysis. The analyses demonstrate differences between the blood flow dynamics in healthy subjects and subjects with Raynaud's phenomenon. Moreover, the observed decrease in the amplitude of oscillation in regions approximately 0.04 Hz and approximately 0.1 Hz suggests an impairment in the neurogenic and the myogenic regulation of the blood flow. The administration of nifedipine in subjects with Raynaud's phenomenon results in an increase in the basal value and in the amplitude of the blood flow component oscillating with the heart rate. However, it does not restore the dynamics to that found in healthy subjects.

Adolescent↗

PubMed2006

Prostate-specific antigen changes as a result of chlormadinone acetate administration to patients with benign prostatic hyperplasia: a retrospective multi-institutional study.

BACKGROUND: Antiandrogens used to treat benign prostatic hyperplasia (BPH) may affect the diagnosis of prostate cancer by decreasing serum prostate-specific antigen (PSA) values. We conducted a retrospective survey of BPH patients treated with chlormadinone acetate (CMA) and analysed the effect of CMA on their PSA values. METHODS: A chart-based, retrospective, multi-institutional survey of clinically diagnosed patients with BPH who had been treated with CMA (Prostal; 50 mg/day) was conducted. The patients were divided into three groups according to their baseline PSA values: <4 ng/mL, Group I; >or=4 ng/mL and <10 ng/mL, Group II; and >or=10 ng/mL, Group III. The changes in the PSA values from baseline after 16, 26, and 52 weeks of CMA therapy were predicted using a nonlinear regression model analysis. RESULTS: Data from 192 of the 303 enrolled patients were analysed. The predicted percent changes from baseline among all patients after 16, 26, and 52 weeks of treatment were -49.6%, -49.8%, and -49.9%, respectively. The corresponding values were -42.4%, -43.7% and -43.8% in Group I; -57.4%, -58.4% and -58.5% in Group II; and -50.6%, -50.6% and -50.6% in Group III, respectively. CONCLUSION: The PSA values reached a nadir, approximately -50% of the baseline, after 16 weeks of CMA administration and remained at the same level thereafter. When CMA is used to treat BPH patients, the possibility of abnormal increases in PSA associated with prostate cancer must be considered; if prostate cancer is suspected, prompt testing, including a biopsy, should be performed.

Aged↗

PubMed1999

A method for assessing the accuracy of intersubject registration of the human brain using anatomic landmarks.

Several groups have developed methods for registering an individual's 3D MRI by deforming a standard template. This achievement leads to many possibilities for segmentation and morphology that will impact nuclear medical research in areas such as activation and receptor studies. Accordingly, there is a need for methods that can assess the accuracy of intersubject registration. We have developed a method based on a set of 128 anatomic landmarks per hemisphere, both cortical and subcortical, that allows assessment of both global and local transformation accuracy. We applied our method to compare the accuracy of two standard methods of intersubject registration, AIR 3.0 with fifth-order polynomial warping and the Talairach stereotaxic transformation (Talairach and Tournoux, 1988). SPGR MRI's (256 x 256 x 160) of six normal subjects (age 18-24 years) were derformed to match a standard template volume. To assess registration accuracy the landmarks were located on both the template volume and the transformed volumes by an experienced neuroanatomist. The resulting list of coordinates was analyzed graphically and by ANOVA to compare the accuracy of the two methods and the results of the manual analysis. ANOVA performed over all 128 landmarks showed that the Woods method was more accurate than Talairach (left hemisphere F = 2.8, P < 0.001 and right hemisphere F =2.4, P < 0.006). The Woods method provided a better brain surface transformation than did Talairach (F = 18.0, P < 0.0001), but as expected there was a smaller difference for subcortical structures and both had an accuracy <1 mm for the majority of subcortical landmarks. Overall, both the Woods and Talairach method located about 70% of landmarks with an error of 3 mm or less. More striking differences were noted for landmark accuracy </=1 mm, where the Woods method located about 40% and Talairach about 23%. These results demonstrate that this anatomically based assessment method can help evaluate new methods of intersubject registration and should be a helpful tool in appreciating regional differences in accuracy. Consistent with expectation, we confirmed that the Woods nonlinear registration method was more accurate than Talairach. Landmark-based anatomic analyses of intersubject registration accuracy offer opportunities to explore the relationship among structure, function and architectonic boundaries in the human brain.

Adolescent↗

PubMed1985

On the nature of the 'nothing dehydrogenase' reaction.

The biochemical mechanism underlying the 'nothing dehydrogenase' reaction during the histochemical demonstration of dehydrogenases using tetranitro BT as the final electron acceptor has been investigated in unfixed, frozen rat liver sections. The reaction is stronger with NAD+ than either with NADP+ or in the absence of coenzyme. As much as 50% of the reaction is due to lactate dehydrogenase converting endogenous lactate and is largely inhibited by pyruvate. No NAD+-dependent alcohol dehydrogenase activity was detected at pH 7.45, the pH used for the incubations. The coenzyme-independent activity may be caused by SH-groups present in proteins and compounds like glutathione and cysteine and can be inhibited by N-ethylmaleimide and p-chloromercuribenzoic acid. It was also found that the 'nothing dehydrogenase' reaction mainly occurs during the first few minutes of incubation, levelling off quickly to a slow rate. When studying the kinetics of dehydrogenase reactions with tetrazolium salts, it should be realized that the 'nothing dehydrogenase' reaction, which as a whole is nonlinear with time, can interfere seriously with the dehydrogenase reaction to be analysed and may yield initial reaction rates that are too high. The findings of the present study reveal the nature of the reactions used for detection of necrosis in tissues with tetrazolium salts.

Alcohol Dehydrogenase↗

PubMed1991

Purification and properties of NADP-linked glucose-6-phosphate dehydrogenase from Acetobacter hansenii (Acetobacter xylinum).

The NADP-linked glucose-6-phosphate dehydrogenase from Acetobacter hansenii (formerly known as Acetobacter xylinum) has been purified to apparent homogeneity. The sequence of the 10 N-terminal amino acids was determined. The subunit molecular weight of the enzyme is 53,000 as determined by sodium dodecyl sulfate-polyacrylamide gel electrophoresis; gel filtration studies under nondenaturing conditions revealed that the molecular weight of the enzyme is 200,000 to 220,000 at pH 6.5 and 9.5, suggesting that the native enzyme is a tetramer. Specificity studies at both pH 6.5 and 9.5 demonstrated that the enzyme is a typical NADP-preferring glucose-6-phosphate dehydrogenase. The enzyme's catalytic activity increases with increasing pH, kcat being approximately 4 times greater at pH 9.5 than at pH 6.7 and the Km for NADP+ being 3 times lower at the higher pH; but the Km for glucose 6-phosphate is nearly 20 times higher at pH 9.5 than at pH 6.7, suggesting that the enzyme is catalytically more efficient at the lower pH. At pH 6.7, initial velocity measurements, product inhibition by NADPH, and inhibition by glucosamine 6-phosphate yielded results that were consistent with a steady-state random mechanism. At pH 9.5, steady-state kinetic analyses suggested that the mechanism is ordered, with coenzyme binding first, but nonlinear double-reciprocal plots were observed in the presence of NADPH when glucose 6-phosphate was varied and a complete kinetic analysis was not undertaken. Among several nucleotides and potential inhibitory ligands examined, only 2',5'-ADP inhibited the enzyme significantly.

Amino Acid Sequence↗

PubMed1995

Population pharmacokinetics of the active metabolite of nabumetone in renal dysfunction.

We determined the pharmacokinetics of 6-methoxy-2-naphythylacetic acid (6-MNA), the active metabolite of nabumetone, in normal subjects and in subjects with impaired renal function, including subjects requiring hemodialysis. Subjects received a 1000 mg oral dose of nabumetone either as a single dose or daily for 15 days. We used a noncompartmental pharmacokinetic analysis and compared those results to a population pharmacokinetic analysis performed with nonlinear mixed-effects modeling (NONMEM). The results of the two different analyses were similar. The elimination half-life increased with decreased renal function and ranged from 22 to 44 hours. The area under the curve decreased significantly at steady state, regardless of renal function. The apparent clearance determined by NONMEM analysis increased from 0.68 L/hr after a single dose to 1.13 L/hr at steady state. The apparent volume of distribution was directly proportional to the nonalbumin protein concentration and ranged from 23 to 60 L. We conclude that the pharmacokinetics of 6-MNA in this population are complicated by possible protein binding changes. However, the increased half-life in patients with renal failure is offset by changes in the apparent volume of distribution that prevent the accumulation of 6-MNA in the serum of patients with impaired renal function. Therefore dosage adjustments may not be necessary in patients with decreased renal function.

Administration, Oral↗