Exponential increase in mortality with age is a generic property of a simple model system of damage accumulation and death

The risk of dying increases exponentially with age, in humans as well as in many other species. This increase is often attributed to the "accumulation of damage" known to occur in many biological structures and systems. The aim of this paper is to describe a generic model of damage accumulation and death in which mortality increases exponentially with age. The damage-accumulation process is modeled by a stochastic process know as a queue, and risk of dying is a function of the accumulated damage, i.e. length of the queue. The model has four parameters and the main characteristics of the model are: (i) damage occurs at random times with a constant high rate; (ii) the damage is repaired at a limited rate, and consequently damage can accumulate; (iii) the efficiency of the repair mechanism decays linearly with age; (iv) the risk of dying is a function of the accumulated damage. Using standard results from the mathematical theory of queues it is shown that there is an exponential dependence between risk of dying and age in these models, and that this dependency holds irrespective of how the damage-accumulation process is modeled. Furthermore, the ways in which this exponential dependence is shaped by the model parameters are also independent of the details of the damage accumulation process. These generic features suggest that the model could be useful when interpreting changes in the relation between age and mortality in real data. To examplify, historical mortality data from Sweden are interpreted in the light of the model. The decrease in mortality seen between cohorts born in 1905, compared to those born in 1885, can be accounted for by higher threshold to damage. This fits well with the many advances made in public health during the 20th century

Locomotion-Related Oscillatory Body Movements at 6–12 Hz Modulate the Hippocampal Theta Rhythm

The hippocampal theta rhythm is required for accurate navigation and spatial memory but its relation to the dynamics of locomotion is poorly understood. We used miniature accelerometers to quantify with high temporal and spatial resolution the oscillatory movements associated with running in rats. Simultaneously, we recorded local field potentials in the CA1 area of the hippocampus. We report that when rats run their heads display prominent vertical oscillations with frequencies in the same range as the hippocampal theta rhythm (i.e., 6–12 Hz). In our behavioral set-up, rats run mainly with speeds between 50 and 100 cm/s. In this range of speeds, both the amplitude and frequency of the “theta” head oscillations were increasing functions of running speed, demonstrating that the head oscillations are part of the locomotion dynamics. We found evidence that these rhythmical locomotor dynamics interact with the neuronal activity in the hippocampus. The amplitude of the hippocampal theta rhythm depended on the relative phase shift with the head oscillations, being maximal when the two signals were in phase. Despite similarity in frequency, the head movements and LFP oscillations only displayed weak phase and frequency locking. Our results are consistent with that neurons in the CA1 region receive inputs that are phase locked to the head acceleration signal and that these inputs are integrated with the ongoing theta rhythm

Estimating the size of hidden populations from register data

BACKGROUND: Prevalence estimates of drug use, or of its consequences, are considered important in many contexts and may have substantial influence over public policy. However, it is rarely possible to simply count the relevant individuals, in particular when the defining characteristics might be illegal, as in the drug use case. Consequently methods are needed to estimate the size of such partly ‘hidden’ populations, and many such methods have been developed and used within epidemiology including studies of alcohol and drug use. Here we introduce a method appropriate for estimating the size of human populations given a single source of data, for example entries in a health-care registry. METHODS: The setup is the following: during a fixed time-period, e.g. a year, individuals belonging to the target population have a non-zero probability of being “registered”. Each individual might be registered multiple times and the time-points of the registrations are recorded. Assuming that the population is closed and that the probability of being registered at least once is constant, we derive a family of maximum likelihood (ML) estimators of total population size. We study the ML estimator using Monte Carlo simulations and delimit the range of cases where it is useful. In particular we investigate the effect of making the population heterogeneous with respect to probability of being registered. RESULTS: The new estimator is asymptotically unbiased and we show that high precision estimates can be obtained for samples covering as little as 25% of the total population size. However, if the total population size is small (say in the order of 500) a larger fraction needs to be sampled to achieve reliable estimates. Further we show that the estimator give reliable estimates even when individuals differ in the probability of being registered. We also compare the ML estimator to an estimator known as Chao’s estimator and show that the latter can have a substantial bias when applied to epidemiological data. CONCLUSIONS: The population size estimator suggested herein complements existing methods and is less sensitive to certain types of dependencies typical in epidemiological data

A 4D approach to the analysis of functional brain images: Application to FMRI data

This paper presents a new approach to functional magnetic resonance imaging (FMRI) data analysis. The main difference lies in the view of what comprises an observation. Here we treat the data from one scanning session (comprising t volumes, say) as one observation. This is contrary to the conventional way of looking at the data where each session is treated as t different observations. Thus instead of viewing the v voxels comprising the 3D volume of the brain as the variables, we suggest the usage of the vt hypervoxels comprising the 4D volume of the brain-over-session as the variables. A linear model is fitted to the 4D volumes originating from different sessions. Parameter estimation and hypothesis testing in this model can be performed with standard techniques. The hypothesis testing generates 4D statistical images (SIs) to which any relevant test statistic can be applied. In this paper we describe two test statistics, one voxel based and one cluster based, that can be used to test a range of hypotheses. There are several benefits in treating the data from each session as one observation, two of which are: (i) the temporal characteristics of the signal can be investigated without an explicit model for the blood oxygenation level dependent (BOLD) contrast response function, and (ii) the observations (sessions) can be assumed to be independent and hence inference on the 4D SI can be made by nonparametric or Monte Carlo methods. The suggested 4D approach is applied to FMRI data and is shown to accurately detect the expected signa

Effective Reduced Diffusion-Models: A Data Driven Approach to the Analysis of Neuronal Dynamics

We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality of the data is first reduced to the first principal component, and then fitted by the stationary solution of a mean-field-like one-dimensional Langevin equation, which describes the motion of a Brownian particle in a potential. The advantage of such description is that the stationary probability density of the dynamical variable can be easily derived. We applied this method to the analysis of cortical network dynamics during up and down states in an anesthetized animal. During deep anesthesia, intracellularly recorded up and down states transitions occurred with high regularity and could not be adequately described by a one-dimensional diffusion equation. Under lighter anesthesia, however, the distributions of the times spent in the up and down states were better fitted by such a model, suggesting a role for noise in determining the time spent in a particular state

Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation

The response behaviors in many two-alternative choice tasks are well described by so-called sequential sampling models. In these models, the evidence for each one of the two alternatives accumulates over time until it reaches a threshold, at which point a response is made. At the neurophysiological level, single neuron data recorded while monkeys are engaged in two-alternative choice tasks are well described by winner-take-all network models in which the two choices are represented in the firing rates of separate populations of neurons. Here, we show that such nonlinear network models can generally be reduced to a one-dimensional nonlinear diffusion equation, which bears functional resemblance to standard sequential sampling models of behavior. This reduction gives the functional dependence of performance and reaction-times on external inputs in the original system, irrespective of the system details. What is more, the nonlinear diffusion equation can provide excellent fits to behavioral data from two-choice decision making tasks by varying these external inputs. This suggests that changes in behavior under various experimental conditions, e.g. changes in stimulus coherence or response deadline, are driven by internal modulation of afferent inputs to putative decision making circuits in the brain. For certain model systems one can analytically derive the nonlinear diffusion equation, thereby mapping the original system parameters onto the diffusion equation coefficients. Here, we illustrate this with three model systems including coupled rate equations and a network of spiking neurons

When Two Become One: The Limits of Causality Analysis of Brain Dynamics

Biological systems often consist of multiple interacting subsystems, the brain being a prominent example. To understand the functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of these interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such interacting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural causal effect. This new concept takes into account that when studying interactions in biological systems, one is often not interested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections participate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal connections that determine the existence of natural causal effects. In particular, we show that the influence of the causal connections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem on another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We note that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be quantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be characterized when they exist. Our work also has important consequences for the interpretation of other approaches commonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest