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Nonlinear stochastic compartmental models.

Compartmental models have been widely applied to biological systems where material is transferred between compartments. The simple assumption of linear transfer functions results in a mathematically tractable system, but can underestimate the variation. Processes with some particular forms of nonlinear transfer functions are analysed, and numerical results suggest that concave transfer functions increase variability, whereas convex transfer functions decrease variability.

Biometry↗

Simultaneous high-resolution measurement of adenosine triphosphate levels and blood flow in the hamster amelanotic melanoma A-Mel-3.

BACKGROUND: Some studies suggest that nutritional blood flow and intratumor levels of high-energy phosphates such as adenosine triphosphate (ATP) affect tumor response to treatment. Reports of intratumor variabilities have shown that distribution of high-energy phosphates within experimental and human tumors is not uniform, and this variability may be related to differences in blood flow in different regions of the tumor. However, previous studies provide no insight into the intratumor relationship of these parameters. PURPOSE: To study the intratumor relationship between blood flow and ATP concentration, we have developed a method that allows simultaneous quantitation of the two variables almost at a cellular level at adjacent sites. In addition, this technique, which uses digital image processing and analysis, facilitates regional high-resolution measurements of blood flow and ATP concentrations in relation to histology. METHODS: We examined tissue samples cut in consecutive order from one representative hamster A-Mel-3 amelanotic melanoma. Specimens from the same tumor were analyzed for histological features, blood flow (measured autoradiographically by the use of [4-N-methyl-14C]iodoantipyrine), and ATP content (measured by a quantitative substrate-induced bioluminescence reaction, using single-photon imaging). The data on the three parameters were stored as digitized images, which were later transformed to reach geometric congruency. The relationship between blood flow and ATP was examined by nonlinear regression and correlation analyses. RESULTS: Regional distribution of blood flow was highly correlated with distribution of ATP within the A-Mel-3 tumor. For images of the tumor using measuring fields of approximately 20 tumor cells, the coefficient of correlation was .92 (P < .001). The relationship between the two parameters was described by a second-order function. At low blood flow values, small differences in blood flow were associated with large changes in levels of ATP, whereas at high blood flow values, differences in blood flow were associated with much smaller changes in ATP levels. CONCLUSION: This high-resolution technique may have applications in future studies investigating the relationship between tumor cell metabolism and regional blood flow and in studies aimed at identifying the locoregional target of various cancer therapies.

Adenosine Triphosphate↗

Physiologic data acquisition system and database for the study of disease dynamics in the intensive care unit.

OBJECTIVE: To describe a real-time, continuous physiologic data acquisition system for the study of disease dynamics in the intensive care unit. DESIGN: Descriptive report. SETTING: A 16-bed pediatric intensive care unit in a tertiary care children's hospital. PATIENTS: A total of 170 critically ill or injured pediatric patients. INTERVENTIONS: None. MAIN OUTCOME MEASURES: None. RESULTS: We describe a computerized data acquisition and analysis system for the study of critical illness and injury from the perspective of complex dynamic systems. Both parametric (1 Hz) and waveform (125-500 Hz) signals are recorded and analyzed. Waveform data include electrocardiogram, respiration, systemic arterial pressure (invasive and noninvasive), central venous pressure, pulmonary arterial pressure, left and right atrial pressures, intracranial pressure, body temperature, and oxygen saturation. Details of the system components are explained and examples are given from the resultant physiologic database of signal processing algorithms and signal analyses using linear and nonlinear metrics. CONCLUSIONS: We have successfully developed a real-time, continuous physiologic data acquisition system that can capture, store, and archive data from pediatric intensive care unit patients for subsequent time series analysis of dynamic changes in physiologic state. The physiologic signal database generated from this system is available for analysis of dynamic changes caused by critical illness and injury.

Algorithms↗

Application of mathematical model to experimental chemotherapy of fatal murine pneumonia.

Two beta-lactam antibiotics, cefazolin and cefmenoxime, were administered in an experimental model of murine pneumonia caused by Klebsiella pneumoniae in a way which enabled us to approximate the serum antibiotic concentration time course in humans. Bacterial counts during the experiments were subjected to nonlinear least-squares analyses by using a mathematical model that explained the bacterial killing by the antibiotic concentration time course and other factors associated with antimicrobial potency and bacterial growth. Cefazolin gave a killing curve that changed synchronously with the drug levels in serum; in contrast, cefmenoxime gave a curve that was prolonged as compared with the change in the drug levels in serum. Multiple correlation coefficients were about 0.9, and the model worked well for bacterial count data. Parameters relating to antimicrobial potency of the drugs, bacterial growth rate, and drug distribution into the tissue were estimated numerically.

Animals↗

Biodegradation of N-nitrosodimethylamine in aqueous and soil systems.

N-Nitrosodimethylamine (NDMA) was mineralized by microorganisms in aqueous and soil systems. Initial rates of mineralization (micrograms per milliliter per day) were calculated for a wide range of initial concentrations of NDMA (micrograms per milliliter to picograms per milliliter). Log-log plots of the data were fitted with both linear and nonlinear least-squares analyses; however, linear models provided better fits for the kinetic data in all cases. The slopes of the linear fits were not significantly different than 1.0 (P < 0.05); thus, first-order reaction kinetics were in effect over the range of concentrations tested, and saturation kinetics were not achieved. Rate constants (day) and total percent mineralized increased with decreasing initial concentrations of NDMA. Rates of mineralization were reduced in aqueous systems when supplemental carbon was available, whereas in soils, percentages of organic matter and supplemental carbon had little effect on rates of mineralization. Implications of these results for predictions of rates and threshold limits of mineralization activity in natural systems are discussed. A laboratory scale simulated trickling filter containing an activated charcoal bed provided a suitable environment for mineralization of NDMA at concentrations of 50 and 100 mug/ml on a continuous basis. NDMA was not toxic to natural populations of microorganisms at concentrations up to 10 mg/ml. Using high-pressure liquid chromatography coupled with radioactivity detection, we identified formaldehyde and methylamine as intermediates produced during the biodegradation of NDMA.

Journal Article↗

EEG markers for cognitive decline in elderly subjects with subjective memory complaints.

New treatments for Alzheimer's disease require early detection of cognitive decline. Most studies seeking to identify markers of early cognitive decline have focused on a limited number of measures. We sought to establish the profile of brain function measures which best define early neuropsychological decline. We compared subjects with subjective memory complaints to normative controls on a wide range of EEG derived measures, including a new measure of event-related spatio-temporal waves and biophysical modeling, which derives anatomical and physiological parameters based on subject's EEG measurements. Measures that distinguished the groups were then related to cognitive performance on a variety of learning and executive function tasks. The EEG measures include standard power measures, peak alpha frequency, EEG desynchronization to eyes-opening, and global phase synchrony. The most prominent differences in subjective memory complaint subjects were elevated alpha power and an increased number of spatio-temporal wave events. Higher alpha power and changes in wave activity related most strongly to a decline in verbal memory performance in subjects with subjective memory complaints, and also declines in maze performance and working memory reaction time. Interestingly, higher alpha power and wave activity were correlated with improved performance in reverse digit span in the subjective memory complaint group. The modeling results suggest that differences in the subjective memory complaint subjects were due to a decrease in cortical and thalamic inhibitory gains and slowed dendritic time-constants. The complementary profile that emerges from the variety of measures and analyses points to a nonlinear progression in electrophysiological changes from early neuropsychological decline to late-stage dementia, and electrophysiological changes in subjective memory complaint that vary in their relationships to a range of memory-related tasks.

Aged↗

Reliability of longitudinal ultrasonographic measurements of carotid intimal-medial thicknesses. Asymptomatic Carotid Artery Progression Study Research Group.

BACKGROUND AND PURPOSE: Serial ultrasonic B-mode measurements of intimal-medial thickness (IMT) of the carotid artery are commonly used as surrogates for describing atherosclerosis progression. This report describes the longitudinal reliability of IMT measurement during a multicenter clinical trial, quantifies the error attributable to differences among readers, and discusses how studies can be efficiently designed. METHODS: Serial B-mode measurements of carotid IMT from the 3-year Asymptomatic Carotid Artery Progression Study (ACAPS; formerly Asymptomatic Carotid Artery Plaque Study) were used to estimate the contributions to longitudinal measurement error of systematic reader effects, nonvisualization, and nonsystematic error and to describe the distribution of "true" progression rates that underlie the observed data. Variance components were estimated from random-effects models fitted to outcome measures formed by averaging IMTs from different sets of carotid artery walls. These were used to contrast the relative efficiency of study designs. RESULTS: Of the total variance of measured IMT, 11% was attributable to systematic differences among readers. Nonvisualization contributed less than 7%. Thus, the predominant source of error was unaccounted for (ie, random error or "noise," which in our analyses included any drift, nonlinearity, and sonographer differences). For studies with measurement protocols similar to ACAPS, follow-up times of 2 years or more are desirable for describing the mean progression rates of cohorts, and of 6 years or more for categorizing progression within individuals. In 3-year studies, sample sizes as low as 237 provide 90% statistical power for detecting risk factors that have correlations with IMT progression of .50 or greater. CONCLUSIONS: The ACAPS measurement protocol provided highly reliable serial IMT data. Moderate-sized multicenter studies using B-mode outcomes are feasible.

Adult↗

Significance of multiple forms of brain monoamine oxidase in situ as probed by electron spin resonance.

Spin-labeled hydroxyamphetamine, a competitive reversible inhibitor of brain monoamine oxidase, has been shown to be useful as an electron spin resonance (ESR) probe of the microenvironment of the active sites of the possible monoamine oxidase multiple forms. The ESR spectrum of spin-labeled hydroxyamphetamine was strongly quenched upon binding to the enzyme. The conformation of the active site of rat brain monoamine oxidase existing in various physical states, i.e. monoamine oxidase in situ (intact brain mitochondria), crude solubilized monoamine oxidase (MAOS) and isolated monoamine oxidase fractions (MAOa and MAOb) were critically and systematically examined. Nonlinear least squares regression analyses have been used to fit the binding data (obtained at room temperature with varying spin-labeled hydroxyamphetamine concentrations) to three groups of independent noninteracting ligand-binding models. A Gibbs-Helmholtz relationship was applied to the interpretation of the measured apparent association constant K as a function of temperature ranging from 4-50 degrees with increments of 2 degreesmfrom the extracted intensive parameters, k (intrinsic association constant) and deltaF (intrinsic free energy), as well as the apparent heat, deltaH, it was clear that the microenvironment of the binding sites existing in the more purified enzyme fractions MAOa and MAOb were similar to those found in the crude solubilized enzyme. More importantly, they correlated well with the conformation of the sites characterized in situ. The data suggested that the microenvironment of this multienzyme system was unperturbed in spite of the treatment due to the isolation process. In terms of the composition of binding sites, MAOa appeared to be heterogeneous while MAOb appeared to be more homogeneous. Since the isolated fractions MAOa and MAOb possessed marked different substrate specificities, these observations directly implied that monoamine oxidase multiple forms do exist in situ. The extracted extensive parameters, n (specific binding activity, nanomoles/mg of protein), as well as the measured characteristic transition temperatures, indicated that the relative abundance of the sites which directly affected substrate specificities was indeed altered. The consistency of the characteristic transition temperatures of 21 degrees and 38 degrees for the case of intact membrane preparations was particularly significant. A tenable hypothesis is that the manipulation in the composition of the monoamine oxidase binding forms through intimate lipid-protein interactions, which has been amply demonstrated in many biomembrane systems to be functionally important might be the underlying regulatory mechanism in vivo.

Animals↗

Interaction of thrombospondin with resting and stimulated human platelets.

The interaction of isolated and radioiodinated thrombospondin with washed human platelets has been characterized. The ligand bound to nonstimulated and thrombin-stimulated platelets in a time-dependent manner, and apparent steady state was reached within 25 min. Binding was not due to iodination of the ligand and was inhibited by nonlabeled thrombospondin but not by unrelated proteins, and bound ligand was identical with thrombospondin in terms of subunit structure. Nonlinear curve-fitting analyses of binding to resting platelets suggested the presence of a single class of sites which bound 3,100 +/- 1,000 molecules/platelet with an apparent Kd of 50 +/- 20 nM. This interaction was not attributable to contaminating cells or inadvertant platelet activation. Binding to thrombin-stimulated platelets had a lower apparent affinity (Kd = 250 +/- 100 nM) and higher apparent capacity (35,600 +/- 9,600 molecules/platelet). Thrombin-enhanced binding was dependent upon agonist dose and platelet stimulation. Fibrinogen, a monoclonal antibody to GPIIb-IIIa, temperature, and divalent ions had differential effects upon thrombospondin binding to resting and stimulated platelets, suggesting the presence of two distinct mechanisms of thrombospondin binding to platelets. While thrombospondin binding to thrombin-stimulated platelets occurs with characteristics similar to those observed for fibrinogen, fibronectin, and von Willebrand Factor, its high affinity interaction with resting platelets is unique to this adhesive glycoprotein.

Binding, Competitive↗

Circadian-infradian intermodulation of corneal epithelial mitoses in adult female rats.

An infradian modulation with a 5-day period characterizes corneal mitoses in adult female inbred Lewis rats. The animals had been standardized, two per cage, with Purina Chow and deionized water freely available at 24 +/- 1 degree C and approximately 50% relative humidity, on six different sequences of light (L) alternating every 12 hr with darkness (D). The LD 12:12 regimen was staggered by approximately 4hr in the six environments to approximate, by sampling within 1 hr, sampling over a 24-hr LD span. Bedding was changed 3 days before each day of killing. During each of 8 consecutive days, one rat from each environment was anesthetized with ether and the eyeballs were removed. Mitotic indices, computed separately for each eye, were analyzed by linear and nonlinear least-squares analyses. For a prominent circadian component of mitotic activity, the 95% confidence interval (CI) extended from 23.84 to 24.85 hr, with a point estimate of 24.32 hr; for a second component of 117 hr, the Cl extended from 90 to 163 hr. Whether the approximate 5-day infradian rhythm is of ovarian or other origin is a problem for further study.

Animals↗

Circatrigintan rectal temperature and endocrine rhythms of clinically healthy, menstrually cycling women.

Rectal temperatures were measured automatically every 10 min for part or most of two menstrual cycles in ten clinically healthy young women, 20-30 years of age, with a wearable instrument, the Polychronor. Occasional malfunction of the instrumentation resulted in corresponding gaps in the series. Data were examined by chronograms, plexograms, and chronobiologic serial sections computed with the fit of a 24-hr period, population-mean cosinor, and linear-nonlinear least-squares analyses. Single cosinor-derived circadian parameters were next fitted with a cosine curve of a period equal to the number of days of the corresponding intermenstruum. Second-order infradian inferential statistics were calculated next; the first day of menstruation was used as acrophase reference. A population-mean cosinor at the intermenstrual period yields a temperature acrophase of -279 degrees, with the 95% confidence interval extending from -254 degrees to -312 degrees. Since the intermenstruum differs in different subjects and/or in different menstrual cycles of a given woman, this acrophase corresponds to different time intervals from the first day of menstruation in different cases. This acrophase thus indicates the relative timing within the menstrual cycle of overall high rectal temperatures. On four subjects in four stages of their menstrual cycle, plasma was also obtained at 2-hr intervals around the clock. Ten hormones were determined. The sparse endocrine sampling along the menstrual cycle notwithstanding, a circatrigintan rhythm in all hormones investigated was demonstrated for a woman 26 years of age. At the period corresponding to the intermenstrual interval, the acrophases for T3, cortisol, FSH, testosterone, DHEA-S, T4, and LH occurred before the circatrigintan rectal temperature acrophase, whereas the acrophases for prolactin, estradiol, and progesterone occurred near or shortly after the rectal temperature acrophase. Whereas earlier circatrigintan mapping of adult women had been summarized on a group basis, this study allows individualized circatrigintan rhythm assessment. Circatrigintan, like circadian and circannual, acrophase and amplitude relations do not necessarily imply causal relations, yet they are an indispensable quantitative reference standard for the study of basic mechanisms and for diagnosis and intervention, including endeavors in planned parenthood that might take into account the organism's dynamics with multiple frequencies.

Adult↗

Stress-strain analysis and the lung.

Stress is the magnitude and direction of forces acting on a body, and strain is the magnitude and direction of deformations. Constitutive equations define the relationship between stress and strain for any material. If the material can be considered homogeneous, isotropic, and elastic--that is, if the mechanical properties are uniform and independent of direction and the deformations are reversible--the constitutive equations are greatly simplified and problems of physiological interest become more tractable. Material properties may be expressed as linear elastic constants or a strain energy function. Strain energy is most suitable for large-deformation nonlinear elasticity, but such analyses are extremely complex. Theoretically, linear elasticity is limited to very small deformations, but its applicability can be expanded by considering perturbations from an initial prestressed state, but using material properties that are functions of the initial conditions. Two independent elastic constants, the bulk modulus for volume change and the shear modulus for shape change, are required to define the material properties. For problems in which the geometry of the body and the applied forces are too complex to allow an analytic solution, the body may be broken up into many small, simple elements, and the resulting matrix of equations may be simultaneously solved by a computer. The disadvantage of this finite-element analysis, in addition to its inherent complexity, is that solutions are in terms of numbers rather than equations, and determining the effect of parameters requires that a number of sample problems be solved. Nevertheless, because of its immense power, this technique has an important place in lung mechanics.

Animals↗

Differences in beta adrenergic receptor agonist affinity between cardiac myocytes and coronary arterioles in canine heart.

Beta adrenergic receptors (beta AR) are localized in several tissue compartments of the heart, including cardiac myocytes, coronary arteries and coronary arterioles, but it is unclear whether there are differences between tissues in beta AR coupling to G protein. The goal of these studies was to use receptor autoradiography to analyze beta receptor agonist binding characteristics in different tissue compartments of dog heart, including ventricular myocytes (predominantly beta-1) and coronary arterioles (predominantly beta-2). Frozen sections were incubated in [125I]-pindolol with the beta agonist isoproterenol in the absence and presence of 0.1 mM sodium 5'-guanylylimidodiphosphate (GppNHp, a nonhydrolyzable GTP analog) and analyzed by gamma counting or autoradiography. Nonlinear curve-fitting analyses of ventricular section radioactivity indicated that in the absence of GppNHp, the data were consistent with a two-site fit, with 88% of the receptors in the high-affinity state. In autoradiographic analyses, GppNHp displaced the agonist binding curve to a greater extent in arterioles (approximately 100-fold) than in myocytes (approximately 10-fold). This suggests that beta receptors on arterioles are more tightly coupled to G protein than are beta receptors on myocytes. Thus these studies suggest that 1) beta AR on arterioles are coupled more tightly to G protein than are beta AR on myocytes, possibly because of differences in beta receptor subtype, and 2) more beta AR are in the high-affinity state than has been reported previously in more traditional analyses on membrane preparations.

Adrenergic beta-Agonists↗

Nonlinear aspects of infrasonic pressure transfer into the perilymph.

The perilymphatic pressure was studied in response to various low frequency pressure changes in the ear canal. The pressure transfer was analysed and found to be nonlinear in many aspects. The pressure response was found to contain two time constants representing the inner ear pressure regulating mechanisms. The time constants showed an asymmetry in response to positive and negative going inputs--the effects to some extent proportional to input levels. Further nonlinearities were found when infrasonic sine waves were applied to the ear. Harmonic distortion and modulation appeared. When short bursts of infrasound were introduced a clear d.c. shift was observed as a consequence of an asymmetry in the response to positive and negative going pressure inputs. A temporary change in mean perilymphatic pressure was thus achieved and continued throughout the duration of the signal. At very low frequencies a distinct phase shift was detected in the sine waves. This appeared as a phase lead, breaking the continuity of the output sine wave.

Acoustic Stimulation↗

High-intensity rocket noise: nonlinear propagation, atmospheric absorption, and characterization.

Analyses of rocket noise data measured at far-field locations during the launch of a large rocket and a smaller rocket are presented. Weak shocks are present in all of the data sets. In order to characterize these shocks, those segments of the waveforms where the acoustic pressure is increasing are isolated and the rate of increase in pressure plotted versus magnitude of pressure rise. The plots follow a trend consistent with random noise at low values of pressure rise, then transition to the pressure-squared dependence expected for weak shocks at higher pressure rise values. Power spectral densities of the noise during the period of maximum overall sound-pressure levels display high- and low-frequency spectral slopes that are close to those predicted for shock-dominated noise. It is concluded that shocks must be included in propagation models if high frequency levels are to be estimated as a function of distance from the source. Initial shock thicknesses will have to be characterized experimentally and will require instrumentation with a bandwidth well in excess of 20 kHz. Reflection-free data are essential if meaningful assessments of the statistical properties of the noise are to be made.

Journal Article↗

Stabilization of telomeres in nonlinear models of proliferating cell lines.

We analyse an age-structured model of telomere loss in a proliferating cell population. The cell population is divided into telomere classes, which shorten each round of division. The model consists of a nonlinear system of partial differential equations for the telomere classes. We prove that if the highest telomere class is exempted from mortality, then all the classes stabilize to a nontrivial equilibrium dependent on the initial state of cells in the highest telomere class.

Animals↗

A quantitative model-based approach to examining aging effects on information-integration category learning.

Information-integration category learning was examined in older and younger adults. Accuracy results indicated that older participants learned less well than younger participants in both linear and nonlinear conditions. Model-based analyses indicated that both groups in the linear condition tended to use information integration but that later in training younger participants were more likely to do so. In contrast, the 2 groups in the nonlinear condition were equally likely to use information integration. Further analysis indicated that younger adults were more accurate than older adults when an information-integration approach was adopted, whereas fewer age-related differences were observed when a rule-based approach was used, suggesting that age can have a negative impact on information-integration category learning processes but less impact on rule-based learning.

Adult↗

Bayesian analysis of structural equation models with multinomial variables and an application to type 2 diabetic nephropathy.

There is now increasing evidence proving that many complex diseases can be significantly influenced by correlated phenotype and genotype variables, as well as their interactions. Effective and rigorous assessment of such influence is difficult, because the number of phenotype and genotype variables of interest may not be small, and a genotype variable is an unordered categorical variable that follows a multinomial distribution. To address the problem, we establish a novel nonlinear structural equation model for analysing mixed continuous and multinomial data that can be missing at random. A confirmatory factor analysis model with Kronecker product is proposed for grouping the manifest continuous and multinomial variables into latent variables according to their functions; and a nonlinear structural equation is formulated to assess the linear and interaction effects of the independent latent variables to the dependent latent variables. Bayesian methods for estimation and model comparison are developed through Markov chain Monte Carlo techniques and path sampling. The newly developed methodologies are applied to a case-control cohort of type 2 diabetic patients with nephropathy.

Bayes Theorem↗