Semiparametric models and inference for biomedical time series with extra-variation

Biomedical trials often give rise to data having the form of time series of a common process on separate individuals. One model which has been proposed to explain variations in such series across individuals is a random effects model based on sample periodograms. The use of spectral coefficients enables models for individual series to be constructed on the basis of standard asymptotic theory, whilst variations between individuals are handled by permitting a random effect perturbation of model coefficients. This paper extends such methodology in two ways: first, by enabling a nonparametric specification of underlying spectral behaviour; second, by addressing some of the tricky computational issues which are encountered when working with this class of random effect models. This leads to a model in which a population spectrum is specified nonparametrically through a dynamic system, and the processes measured on individuals within the population are assumed to have a spectrum which has a random effect perturbation from the population norm. Simulation studies show that standard MCMC algorithms give effective inferences for this model, and applications to biomedical data suggest that the model itself is capable of revealing scientifically important structure in temporal characteristics both within and between individual processes.     

Quantitative predictions of a noncarrier model for glucose transport across the human red cell membrane

There is an increasing amount of experimental data on transport across biological membranes which cannot be readily accommodated by classical mobile carrier models. We propose models for membrane transport based upon current concepts in molecular enzymology, in which the membrane component involved in transport is an oligomeric protein which undergoes substrate-induced conformational changes. A number of paradoxical observations on glucose transport in the human erythrocyte are explained if the protein involved is a tetramer possessing two classes of binding sites with different affinities for glucose. We develop in detail a particular model of this type, the internal transfer model, in which transport occurs by transfer of substrate from one subunit to another of the protein. The fit of the predictions of the internal transfer model with most of the experimental data is very good. Those data which cannot be fitted by the model cannot be accounted for by any presently available model. We extend our model qualitatively to include the sodium-activated cotransport systems for sugars and amino acids.     

A network model for the control of the movement of a redundant manipulator

In an earlier investigation (Cruse and Brüwer 1987) an algorithmic model was proposed which describes targeting movements of a human arm when restricted to a horizontal plane. As three joints at shoulder, elbow and wrist are allowed to move, the system is redundant. Two models are discussed here which replace this algorithmic model by a network model. Both networks solve the static problem, i.e. they provide the joint angles which the arm has to adopt in order to reach a given point in the workspace. In the first model the position of this point is given in the form ofx —y coordinates, the second model obtains this information by means of a retina-like input layer. The second model is expanded by a simple procedure to describe movements from a start to an end point. The results qualitatively correspond to those obtained from human subjects. The advantages of the network models in comparison to the algorithmic model are discussed.     

SWAT模型对景观格局变化的敏感性分析——以丹江口库区老灌河流域为例

景观的空间配置与类型组成能够对流域的产流、产沙及非点源污染产生影响。在以往SWAT模型研究中,往往默认水文模型考虑了该影响。为分析SWAT模型对不同景观格局变化的敏感性,根据老灌河流域2000年土地利用在各子流域的组成,模拟研究区更为破碎、复杂的景观空间配置,通过设置多套试验参数,利用SWAT模型生成基于不同景观格局的模拟结果。结果表明,SWAT模型不能反映除坡度和面积变化之外的景观水平下各斑块之间因景观空间格局改变对流域产流、产沙以及非点源污染的影响;模型通过其他参数的调整,弥补了模型分析数据的不足,使实测数据与模型部分结果高度吻合。这表明,一个能够反映流域部分水文特征的SWAT模型,未必是对研究区真实情形的模拟,而是各个参数间平衡的结果。因此,在利用SWAT模型分析模拟景观变化时,不应默认模型能够模拟景观空间格局改变对流域水文过程的影响,同时研究者可以通过划分坡度带,提高模型对不同坡度土地利用的敏感性。     

On the molecular dynamics of the chemo-mechanical conversion in muscle contraction

The molecular dynamics of energy conversion by the actomyosin system in muscle contraction is studied by comparing two different types of model on the motion of crossbridge on thin filament. The motion is associated with a transition between two stable states in Huxley and Simmons' model while in Shimizu et al.'s model with a transition from an unstable to a stable state. The rate of the transition, which is proportional to the velocity of shortening of muscle in steady state, is calculated by representing the motion of crossbridge by that of a Brownian particle moving on a one-dimensional linear potential. In the case of the Huxley-Simmons model the energy conversion process is essentially a thermal one and the velocity of shortening depends sharply on the number of crossbridges on muscular filament, which is proportional to the overlapping length between thin and thick filaments. On the other hand, in the case of the Shimizu model the energy conversion process is a deterministic one which means that muscle is able to shorten smoothly and that the velocity of shortening is almost independent of the overlapping length. Experimental observations by Gordon et al. are consistent with the latter model.     

A discrete method for the identification of parameters of a deterministic epidemic model

We study a problem of identification of the parameters for a deterministic epidemic model of the Kermack-McKendrick type. Particular emphasis is put on the analysis of the conditions of numerical stability of the method of integration used to calculate the solutions of the system of differential equations which describe the model. The numerical method can be regarded as a discrete model which reproduces the basic qualitative properties of the continuous model, which are positivity of the solutions, points of equilibrium, and the “threshold theorem.” This allows us to identify the parameters with good reliability, by means of an iterative procedure to minimize the functional which is the measure of discrepancy between the data observed and the data obtained from the discrete model. The initial estimate of the parameters is obtained by a direct method applied to the discretized system of equations.     

A generalized mover-stayer model for panel data

A generalized mover-stayer model is described for conditionally Markov processes under panel observation. Marginally the model represents a mixture of nested continuous-time Markov processes in which sub-models are defined by constraining some transition intensities to zero between two or more states of a full model. A Fisher scoring algorithm is described which facilitates maximum likelihood estimation based only on the first derivatives of the transition probability matrices. The model is fit to data from a smoking prevention study and is shown to provide a significant improvement in fit over a time-homogeneous Markov model. Extensions are developed which facilitate examination of covariate effects on both the transition intensities and the mover-stayer probabilities.     

The assembly of ionic currents in a thalamic neuron. I. The three-dimensional model

We have previously discussed qualitative models for bursting and thalamic neurons that were obtained by modifying a simple two-dimensional model for repetitive firing. In this paper we report the results of making a similar sequence of modifications to a more elaborate six-dimensional model of repetitive firing which is based on the Hodgkin-Huxley equations. To do this we first reduce the six-dimensional model to a two-dimensional model that resembles our original two-dimensional qualitative model. This is achieved by defining a new variable, which we call q. We then add a subthreshold inward current and a subthreshold outward current having a variable, z, that changes slowly. This gives a three-dimensional (v,q,z) model of the Hodgkin-Huxley type, which we refer to as the z-model. Depending on the choice of parameter values this model resembles our previous models of bursting and thalamic neurons. At each stage in the development of these models we return to the corresponding seven-dimensional model to confirm that we can obtain similar solutions by using the complete system of equations. The analysis of the three-dimensional model involves a state diagram and a stability diagram. The state diagram shows the projection of the phase path from v,q,z space into the v,z plane, together with the projections of the curves z = 0 and v = q = 0. The stability of the points on the curve v = q = 0, which we call the v, q nullcurve, is determined by the stability diagram. Taken together the state and stability diagrams show how to assemble the ionic currents to produce a given firing pattern.     

A vector-magnitude model of contrast detection

A model of contrast detection is proposed in which the visibility of a low-contrast stimulus is determined by a non-Euclidean magnitude of the vector composed of the responses of a large number of independent channels. Although the vector-magnitude model is quite different from the probability-summation model which has been suggested previously, the contrast thresholds and psychometric functions predicted by the two models can be in agreement within 10% for up to 10⁵ channels in the system. Presently available experimental evidence is insufficient to establish the correctness of either model, but the computational simplicity of the vector-magnitude model makes it interesting, if only as a useful approximation to the probability-summation model.     

A framework for models of biological behaviour

Modelling is most clearly understood as a adjunct in the process of deriving predictions from hypotheses. By representing a hypothesised mechanism in a model we hope by manipulating the model to understand the hypotheses' consequences. Eight dimensions on which models of biological behaviour can vary are described: the degree of realism with which they apply to biology; the level of biology they represent; the generality or range of systems the model is supposed to cover; the abstraction or amount of biological detail represented; the accuracy of representation of the mechanisms; the medium in which the model is built; the match of the model behaviour to biological behaviour; and the utility of the model in providing biological understanding and/or technical insight. It is hoped this framework will help to clarify debates over different approaches to modelling, particularly by pointing out how the above dimensions are relatively independent and should not be conflated.     

Simplifying a physiologically structured population model to a stage-structured biomass model

We formulate and analyze an archetypal consumer-resource model in terms of ordinary differential equations that consistently translates individual life history processes, in particular food-dependent growth in body size and stage-specific differences between juveniles and adults in resource use and mortality, to the population level. This stage-structured model is derived as an approximation to a physiologically structured population model, which accounts for a complete size-distribution of the consumer population and which is based on assumptions about the energy budget and size-dependent life history of individual consumers. The approximation ensures that under equilibrium conditions predictions of both models are completely identical. In addition we find that under non-equilibrium conditions the stage-structured model gives rise to dynamics that closely approximate the dynamics exhibited by the size-structured model, as long as adult consumers are superior foragers than juveniles with a higher mass-specific ingestion rate. When the mass-specific intake rate of juvenile consumers is higher, the size-structured model exhibits single-generation cycles, in which a single cohort of consumers dominates population dynamics throughout its life time and the population composition varies over time between a dominance by juveniles and adults, respectively. The stage-structured model does not capture these dynamics because it incorporates a distributed time delay between the birth and maturation of an individual organism in contrast to the size-structured model, in which maturation is a discrete event in individual life history. We investigate model dynamics with both semi-chemostat and logistic resource growth.     

Self-assembly and differentiation as models of computability

An idealization of chemical combination is formulated as a model of computability, and it is shown that this model has universal computational power just in case assembly has at least two-dimensional space in which to occur. It is also shown that this model, under reinterpretation, corresponds to a cellular automaton in which growth occurs by differentiation only (i.e., the state into which any cell is born is thereadfter fixed). Hence this latter model of growth is also computationally universal.     

A transient excited state model for sodium permeability changes in excitable membranes.

In this paper we explore the properties of a mathematical model for the passive sodium permeability system of excitable membranes. This model is distinguished by the explicit inclusion of a rate constant which depends not on instantaneous voltage, but on rate of voltage change. Actually, the model is a rather modest modification of the Hodgkin-Huxley model, but displays some behaviors which the H-H model does not. Among these behaviors are a pronounced inactivation shift (for certain parameter values), a difference between inactivation time constant as measured by turning off a sodium current under sustained depolarization and as measured by double pulse experiments, skip runs under sustained current stimulation, and accommodation to slowing rising currents.     

Pattern recognition and associative memory as dynamical processes in a synergetic system

We consider a model for associative memory and pattern recognition which was devised by Haken (1987b). This model treats the activity of the neurons as continuous variables and exploits an analogy with pattern formation in synergetic systems. The capability of such a system to act as associative memory is demonstrated by the reconstruction of faces which are partially offered to the system, and which are restored by the corresponding dynamical process. We demonstrate how this model can be cast into a form which is translation invariant and how partially hidden faces in scenes can be recognized by means of the control of attention parameters of specific patterns.     

Computation of a Stabilizing Set of Feedback Matrices bf a Large-scale Nonlinear Musculoskeletal Dynamic Model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/ output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Bayesian predictive inference for time series count data

Correlated count data arise often in practice, especially in repeated measures situations or instances in which observations are collected over time. In this paper, we consider a parametric model for a time series of counts by constructing a likelihood-based version of a model similar to that of Zeger (1988, Biometrika 75, 621-629). The model has the advantage of incorporating both overdispersion and autocorrelation. We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for prediction. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified into a prior distribution for the current study. We derive the Bayesian predictive distribution and use a Bayesian criterion, called the predictive L measure, for assessing the predictions for a given time series model. The distribution of the predictive L measure is also derived, which will enable us to compare the predictive ability for each model under consideration. Our methodology is motivated by a real data set involving yearly pollen counts, which is examined in some detail.     

Deformation of the diastolic left ventricle—II. Nonlinear geometric effects

A finite element model for the rat left ventricle has been developed which is based on finite deformation elasticity theory: i.e. the model is not limited by assumptions relating to the magnitudes of extensions, shears and angles of rotation which are inherent in the classical theory of elasticity. This model represents the ventricle as a heterogeneous, nonlinearly elastic, isotropic thick-wall solid of revolution. For the representation of myocardial elasticity used in this study, the model predicts overall ventricular stiffnesses at physiological pressures which are 20–30 per cent lower than those obtained with a model based on the classical theory. However, extentions predicted by the two theories differ by as much as 100 per cent in certain portions of the ventricular wall.