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Length of stay-based patient flow models: recent developments and future directions.

Modelling patient flow in health care systems is vital in understanding the system activity and may therefore prove to be useful in improving their functionality. An extensively used measure is the average length of stay which, although easy to calculate and quantify, is not considered appropriate when the distribution is very long-tailed. In fact, simple deterministic models are generally considered inadequate because of the necessity for models to reflect the complex, variable, dynamic and multidimensional nature of the systems. This paper focuses on modelling length of stay and flow of patients. An overview of such modelling techniques is provided, with particular attention to their impact and suitability in managing a hospital service.

Bed Occupancy↗

Probabilistic automata as a model for epigenesis of cellular networks.

Probabilistic automata are compared with deterministic ones in simulations of growing networks made of dividing interconnected cells. On examples of chains, wheels and tree-like structures made of large numbers of cells it is shown that the number of necessary states in the initial generating cell automaton is reduced drastically when the automaton is probabilistic rather than deterministic. Since the price being paid is a decrease in the accuracy of the generated network, conditions under which reasonable compromises can be achieved are studied. They depend on the degree of redundancy of the final network (defined from the complexity of a deterministic automaton capable of generating it with maximum accuracy), on the "entropy" of the generating probabilistic automaton, and on the effects of different inputs on its transition probabilities (as measured by its "'capacity" in the sense of Shannon's information theory). The results are used to discuss and make more precise the notion of biological specificity. It is suggested that the weak metaphor of a genetic program, classically used to account for the role of DNA in specific genetic determinations, is replaced by that of inputs to biochemical probabilistic automata.

Biological Evolution↗

On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis.

The question whether the human cardiac system is chaotic or not has been an open one. Recent results in chaos theory have shown that the usual methods, such as saturation of correlation dimension D(2) or the existence of positive Lyapunov exponent, alone do not provide sufficient evidence to confirm the presence of deterministic chaos in an experimental system. The results of surrogate data analysis together with the short-term prediction analysis can be used to check whether a given time series is consistent with the hypothesis of deterministic chaos. In this work nonlinear dynamical tools such as surrogate data analysis, short-term prediction, saturation of D(2) and positive Lyapunov exponent have been applied to measured ECG data for several normal and pathological cases. The pathology presently studied are PVC (Premature Ventricular Contraction), VTA (Ventricular Tachy Arrhythmia), AV (Atrio-Ventricular) block and VF (Ventricular Fibrillation). While these results do not prove that ECG time series is definitely chaotic, they are found to be consistent with the hypothesis of chaotic dynamics. (c) 1998 American Institute of Physics.

Journal Article↗

Stem cell renewal and determination during clonal expansion in normal and leukaemic haemopoiesis.

Normal haemopoiesis is a cellular hierarchy headed by pluripotent stem cells capable of both self renewal and, after determination, the generation of differentiating lineages that end in terminal functional cells. The role of stem cells is crucial because only these have the capacity to generate clonal populations during development or after injury. During clonal expansion the cells are affected by many sets of receptors and ligands. These belong to at least two classes: one consists of growth factors that bind cell surface receptors and initiate signalling events; the other class contains receptors which act as ligand-dependent transcription factors such as the intracellular steroid superfamily. In spite of this elaborate regulatory apparatus, control during clonal expansion is lax, perhaps stochastic, as evident from the great heterogeneity disclosed by examining the cellular compositions of haemopoietic clones. It may be that the large number of signals impinging on binary possible outcomes (for example self-renewal or determination) serve to set probabilities rather than to determine outcomes. In leukaemia, many of the features of normal haemopoiesis are retained. The disease begins as transformations in normal stem cells; after additional leukaemogenic events clonal expansion yields malignant populations which are clonal in each affected individual. These dominant clonal populations retain the hierarchical organization found in the normal, the major difference is that post-deterministic divisions in leukaemia yield descendants that retain primitive (blast) morphology although proliferative capacity is lost. In acute myeloblastic leukaemia (AML) cell culture methods are available that permit the measurement of clonogenic blast stem cells. These methods have shown that regulatory mechanisms active in normal haemopoiesis are retained in AML, including lax regulation during clonal expansion. The biological features of blast stems cells displayed by the culture technique reflect in part, events in vivo, as associations have been found between results in cell culture and clinical outcome. Thus, study of leukaemic populations provides a challenge for basic science and an opportunity for successful application in control of disease.

Bone Marrow↗

Possible detection of turbulent blood flow using multiparametric encoding gradients in MRI.

Magnetic resonance imaging (MRI) has significant potential as a highly accurate noninvasive flow measurement technique. Presented here is an approach to the imaging of turbulence in the velocity profiles. Recent publications have presented multiparametric encoding gradient methods, which are based on a deterministic rather than a statistical approach to spin motion. Following these methods of building up a general gradient from a basic set of gradients, the effects of turbulence and undetermined moments of motion on the image are discussed. Image blurring due to the nondeterministic behavior of spins (e.g., diffusion, turbulence) is not removed by these techniques, and this fact may be useful in identifying regions of turbulent flow, which are of importance in the clinical observation of cardiac and vascular haemodynamics. Due to its random nature, the elimination of turbulent effects by the use of a deterministic method is bound to fail. On the other hand, regions of turbulent flow may be identified due to signal decrease from those regions, provided one is careful to remove all the causes of nonturbulent signal reduction present due to nonturbulent flow moments. In the multiparametric phase encoding method, gradient amplitude tends to increase with higher moments of motion. The temporal behavior of these gradients is discussed, and it is suggested that the increase in their duration will enhance the encoding of higher motion terms at the expense of imaging time.

Blood Flow Velocity↗

Effect of reducing temporal intensity modulations on sentence intelligibility.

Modulations in the temporal intensity envelope of 24 1/4-octave bands were reduced by proportionally raising the troughs and lowering the peaks relative to the mean intensity in each band. The effect on intelligibility of various degrees of modulation reduction was investigated by measuring the speech-reception threshold (SRT) in noise. For conditions of severe modulation reduction, the number of correctly received sentences in quiet was scored. The effect of this deterministic modulation reduction was compared to the effect of stochastic modulation reduction obtained with addition of noise. Results for 12 normal-hearing subjects show that in the case of deterministic modulation reduction, intelligibility is reduced to 50% when the modulation-transfer factor equals 0.10, whereas in the case of modulation reduction by addition of noise, this intelligibility is reached already at a modulation-transfer factor of 0.27. This confirms that the effect of additive noise on intelligibility cannot be understood completely as a result of only modulation reduction. As suggested by Drullman [J. Acoust. Soc. Am. 97, 585-592 (1995)] two other factors associated with the addition of noise have to be taken into account: (1) the introduction of nonrelevant modulations, and (2) the corruption of the fine structure.

Adult↗

EEG analysis with nonlinear deterministic and stochastic methods: a combined strategy.

We describe nonlinear deterministic versus stochastic methodology, their applications to EEG research and the neurophysiological background underlying both approaches. Nonlinear methods are based on the concept of attractors in phase space. This concept on the one hand incorporates the idea of an autonomous (stationary) system, on the other hand implicates the investigation of a long time evolution. It is an unresolved problem in nonlinear EEG research that nonlinear methods per se give no feedback about the stationarity aspect. Hence, we introduce a combined strategy utilizing both stochastic and nonlinear deterministic methods. We propose, in a first step to segment the EEG time series into piecewise quasi-stationary epochs by means of nonparametric change point analysis. Subsequently, nonlinear measures can be estimated with higher confidence for the segmented epochs fulfilling the stationarity condition.

Algorithms↗

Use of artificial neural networks within deterministic logic for the computer ECG diagnosis of inferior myocardial infarction.

An investigation into the use of software-based artificial neural networks for the electrocardiographic (ECG) detection of inferior myocardial infarction was made. A total of 592 clinically validated subjects, including 208 with inferior myocardial infarction, 300 normal subjects, and 84 left ventricular hypertrophy cases, were used in this study. A total of 200 ECGs (100 from patients with inferior myocardial infarction and 100 from normal subjects) were fed to 66 supervised feedforward neural networks for training using a back-propagation algorithm. QRS and ST-T wave measurements were used as the input parameters for the neural networks. The best performing network using QRS measurements only and the best using QRS and ST-T data were selected by assessing a test set of 292 ECGs (108 from patients with inferior myocardial infarction, 84 from patients with left ventricular hypertrophy, and 100 from normal subjects). These two networks were then implanted separately into the deterministic Glasgow program for further study. After the implementation, it was found necessary to include a small inferior Q criterion to improve the specificity of reporting inferior myocardial infarction, thereby producing a small loss of sensitivity as compared with use of the network alone. The use of an artificial neural network within the deterministic logic performed better than either alone in the diagnosis of inferior myocardial infarction, producing a 20% gain in sensitivity with 2% loss in overall specificity compared with the original deterministic logic.

Diagnosis, Computer-Assisted↗

Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series.

An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.

Animals↗

Adaptive realtime compensatory feedback to open the light-pupil reflex loop.

Integrity of the visual pathway is often clinically determined from response of the pupil to light. The need for more quantitative measurement of pupillary response has led engineers to investigate the light-pupil reflex with systems analysis techniques. The results have made the light-pupil reflex a model of the application of the principles of control theory to physiologic mechanisms. This analysis required that the system be rendered open loop by focusing the stimulus at the center of the pupil. Patients may not be able to restrict their head and eye movement well enough to permit the feedback loop to be rendered open loop optically. Thus, clinical applications of the technique have been limited. A means of opening the feedback loop by using a realtime deterministic autoregressive moving average prediction algorithm integrated into a computer based television pupillometer has been developed. It employs a model reference adaptive scheme to identify the physiologic system, then predicts future values of pupil area to compensate for delays in the measuring apparatus. A computer driven liquid crystal display shutter controls retinal illuminance to render the light-pupil reflex open loop. This technique reduced the mean square error of retinal illuminance by about 75% compared to uncompensated pupil responses.

Algorithms↗

Predicting stochastic gene expression dynamics in single cells.

Fluctuations in protein numbers (noise) due to inherent stochastic effects in single cells can have large effects on the dynamic behavior of gene regulatory networks. Although deterministic models can predict the average network behavior, they fail to incorporate the stochasticity characteristic of gene expression, thereby limiting their relevance when single cell behaviors deviate from the population average. Recently, stochastic models have been used to predict distributions of steady-state protein levels within a population but not to predict the dynamic, presteady-state distributions. In the present work, we experimentally examine a system whose dynamics are heavily influenced by stochastic effects. We measure population distributions of protein numbers as a function of time in the Escherichia coli lactose uptake network (lac operon). We then introduce a dynamic stochastic model and show that prediction of dynamic distributions requires only a few noise parameters in addition to the rates that characterize a deterministic model. Whereas the deterministic model cannot fully capture the observed behavior, our stochastic model correctly predicts the experimental dynamics without any fit parameters. Our results provide a proof of principle for the possibility of faithfully predicting dynamic population distributions from deterministic models supplemented by a stochastic component that captures the major noise sources.

Escherichia coli↗

Radiation doses in interventional radiology procedures: the RAD-IR study: part II: skin dose.

PURPOSE: To determine peak skin dose (PSD), a measure of the likelihood of radiation-induced skin effects, for a variety of common interventional radiology and interventional neuroradiology procedures, and to identify procedures associated with a PSD greater than 2 Gy. MATERIALS AND METHODS: An observational study was conducted at seven academic medical centers in the United States. Sites prospectively contributed demographic and radiation dose data for subjects undergoing 21 specific procedures in a fluoroscopic suite equipped with built-in dosimetry capability. Comprehensive physics evaluations and periodic consistency checks were performed on each unit to verify the stability and consistency of the dosimeter. Seven of 12 fluoroscopic suites in the study were equipped with skin dose mapping software. RESULTS: Over a 3-year period, skin dose data were recorded for 800 instances of 21 interventional radiology procedures. Wide variation in PSD was observed for different instances of the same procedure. Some instances of each procedure we studied resulted in a PSD greater than 2 Gy, except for nephrostomy, pulmonary angiography, and inferior vena cava filter placement. Some instances of transjugular intrahepatic portosystemic shunt (TIPS) creation, renal/visceral angioplasty, and angiographic diagnosis and therapy of gastrointestinal hemorrhage produced PSDs greater than 3 Gy. Some instances of hepatic chemoembolization, other tumor embolization, and neuroembolization procedures in the head and spine produced PSDs greater than 5 Gy. In a subset of 709 instances of higher-dose procedures, there was good overall correlation between PSD and cumulative dose (r = 0.86; P <.000001) and between PSD and dose-area-product (r = 0.85, P <.000001), but there was wide variation in these relationships for individual instances. CONCLUSIONS: There are substantial variations in PSD among instances of the same procedure and among different procedure types. Most of the procedures observed may produce a PSD sufficient to cause deterministic effects in skin. It is suggested that dose data be recorded routinely for TIPS creation, angioplasty in the abdomen or pelvis, all embolization procedures, and especially for head and spine embolization procedures. Measurement or estimation of PSD is the best method for determining the likelihood of radiation-induced skin effects. Skin dose mapping is preferable to a single-point measurement of PSD.

Fluoroscopy↗

Nonlinear analysis of sleep EEG in depression: calculation of the largest lyapunov exponent.

Conventional sleep analysis according to Rechtschaffen and Kales (1968) has provided meaningful contributions to the understanding of disturbed sleep architecture in depression. However, there is no characteristic alteration of the sleep cycle, which could serve as a highly specific feature for depressive illness. Therefore, we started to investigate nonlinear properties of sleep electroencephalographic (EEG) data in order to elucidate functional alterations other than those obtained from classical sleep analysis. The application of methods from nonlinear dynamical system theory to EEG data has led to the assumption that the EEG can be treated as a deterministic chaotic process. Chaotic systems are characterized by a so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's Lyapunov exponents, which measure the exponential separation of nearby initial states in phase space. For 15 depressive inpatients (major depressive episodes according to DSM-III-R criteria) and 13 healthy controls, matched in gender, age, and education, we computed the principal Lyapunov exponents L1 of EEG segments corresponding to sleep stages, I, II, III, IV, and rapid eye movement (REM), according to Rechtschaffen and Kales, for the lead positions CZ and PZ. We found statistically significant decreased values of L1 during sleep stage IV in depressives compared with a healthy control group.

Adult↗

Identifying nonlinear difference equation and functional expansion representations: the fast orthogonal algorithm.

A method is presented for identifying functional expansion and difference equation representations for nonlinear systems. The method relies on an orthogonal approach which does not require explicit creation of orthogonal functions. This greatly reduces computing time, so that 15-fold increases in speed of estimating kernels or difference equation coefficients are readily obtainable, compared with a previous orthogonal technique. In addition, storage requirements are considerably diminished. A wide variety of input excitation, both random and deterministic, can be used, and the method is not limited to inputs which are Gaussian, white or lengthy. A model of the peripheral auditory system is simulated to show kernel measurement is free of artifacts using the present method, in contrast to the crosscorrelation approach.

Algorithms↗

Estimating statistics of neuronal dynamics via Markov chains.

We present an efficient computational method for estimating the mean and variance of interspike intervals defined by the timing of spikes in typical orbits of one-dimensional neuronal maps. This is equivalent to finding the mean and variance of return times of orbits to particular regions of phase space. Rather than computing estimates directly from time series, the system is modelled as a finite state Markov chain to extract stationary behaviour in the form of invariant measures and average absorption times. Ergodic-theoretic formulae are then applied to produce the estimates without the need to generate orbits directly. The approach may be applied to both deterministic and randomly forced systems.

Action Potentials↗

Dimensional analysis of the human EEG and intelligence.

The purpose of this study was the determination of the relationship between the dimensional complexity of the electroencephalogam (EEG) and the level of intelligence in humans. In two experiments 34 male subjects were divided into two groups, with high and low levels of intelligence (as measured by the intelligence quotient (IQ)). During a resting phase and various mental imagery conditions the EEG was recorded from several scalp sites. Nonlinear analysis, based on the theory of deterministic chaos, revealed that subjects with high IQs demonstrate higher dimensional complexity of the EEG attractors than subjects with low IQs only during resting conditions. During performance of the imagery tasks the less intelligent subjects increase the complexity of electrical brain dynamics such that IQ-dependency vanishes. The gross (mass) neuronal manifestation of general intelligence seems to depend on task conditions and may be related to the individual brain dynamics only when no specific task is present.

Adult↗

Approximating Markov chains.

A common framework of finite state approximating Markov chains is developed for discrete time deterministic and stochastic processes. Two types of approximating chains are introduced: (i) those based on stationary conditional probabilities (time averaging) and (ii) transient, based on the percentage of the Lebesgue measure of the image of cells intersecting any given cell. For general dynamical systems, stationary measures for both approximating chains converge weakly to stationary measures for the true process as partition width converges to 0. From governing equations, transient chains and resultant approximations of all n-time unit probabilities can be computed analytically, despite typically singular true-process stationary measures (no density function). Transition probabilities between cells account explicitly for correlation between successive time increments. For dynamical systems defined by uniformly convergent maps on a compact set (e.g., logistic, Henon maps), there also is weak continuity with a control parameter. Thus all moments are continuous with parameter change, across bifurcations and chaotic regimes. Approximate entropy is seen as the information-theoretic rate of entropy for approximating Markov chains and is suggested as a parameter for turbulence; a discontinuity in the Kolmogorov-Sinai entropy implies that in the physical world, some measure of coarse graining in a mixing parameter is required.

Journal Article↗

Influence of spatiotemporally correlated noise on structure formation in excitable media.

We discuss the influence of additive, spatiotemporally correlated (i.e., colored) noise on pattern formation in a two-dimensional network of excitable systems. The signature of spatiotemporal stochastic resonance (STSR) is analyzed using cross-correlation and information theoretic measures. It is found that the STSR behavior is affected by both the spatial and temporal correlations of the noise due to an interplay with the length scales of the deterministic network. Increasing the spatiotemporal noise correlation shifts the occurrence of STSR to smaller values of the noise variance. Additionally, if the spatial correlation of the noise exceeds that of the network, the excitation patterns disappear in favor of cloudy structures, directly rendering the underlying spatial noise field.

Journal Article↗