A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability

2005 ◽  
Vol 288 (1) ◽  
pp. H424-H435 ◽  
Author(s):  
Riccardo Barbieri ◽  
Eric C. Matten ◽  
AbdulRasheed A. Alabi ◽  
Emery N. Brown
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Gaussian Model ◽  
Quantitative Measure ◽  
Local Maximum ◽  
Inverse Gaussian ◽  
Design Of Algorithms

Heart rate is a vital sign, whereas heart rate variability is an important quantitative measure of cardiovascular regulation by the autonomic nervous system. Although the design of algorithms to compute heart rate and assess heart rate variability is an active area of research, none of the approaches considers the natural point-process structure of human heartbeats, and none gives instantaneous estimates of heart rate variability. We model the stochastic structure of heartbeat intervals as a history-dependent inverse Gaussian process and derive from it an explicit probability density that gives new definitions of heart rate and heart rate variability: instantaneous R-R interval and heart rate standard deviations. We estimate the time-varying parameters of the inverse Gaussian model by local maximum likelihood and assess model goodness-of-fit by Kolmogorov-Smirnov tests based on the time-rescaling theorem. We illustrate our new definitions in an analysis of human heartbeat intervals from 10 healthy subjects undergoing a tilt-table experiment. Although several studies have identified deterministic, nonlinear dynamical features in human heartbeat intervals, our analysis shows that a highly accurate description of these series at rest and in extreme physiological conditions may be given by an elementary, physiologically based, stochastic model.

scholarly journals An Efficient Time-Varying Filter for Detrending and Bandwidth Limiting the Heart Rate Variability Tachogram without Resampling: MATLAB Open-Source Code and Internet Web-Based Implementation

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
A. Eleuteri ◽  
A. C. Fisher ◽  
D. Groves ◽  
C. J. Dewhurst
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Open Source ◽  
Process Model ◽  
Engineering Practice ◽  
Time Varying ◽  
Time Axis ◽  
Web Based ◽  
Regular Time ◽  
Require Data

The heart rate variability (HRV) signal derived from the ECG is a beat-to-beat record of RR intervals and is, as a time series, irregularly sampled. It is common engineering practice to resample this record, typically at 4 Hz, onto a regular time axis for analysis in advance of time domain filtering and spectral analysis based on the DFT. However, it is recognised that resampling introduces noise and frequency bias. The present work describes the implementation of a time-varying filter using a smoothing priors approach based on a Gaussian process model, which does not require data to be regular in time. Its output is directly compatible with the Lomb-Scargle algorithm for power density estimation. A web-based demonstration is available over the Internet for exemplar data. The MATLAB (MathWorks Inc.) code can be downloaded as open source.

scholarly journals Thinning spatial point processes into Poisson processes

2010 ◽  
Vol 42 (02) ◽  
pp. 347-358 ◽  
Author(s):  
Jesper Møller ◽  
Frederic Paik Schoenberg
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Point Processes ◽  
Death Process ◽  
Cox Process ◽  
Birth And Death Process ◽  
Conditional Intensity ◽  
Spatial Point Processes ◽  
Spatial Point

In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.

An Adjustment to the Time-Rescaling Method for Application to Short-Trial Spike Train Data

2003 ◽  
Vol 15 (11) ◽  
pp. 2565-2576 ◽  
Author(s):  
Matthew C. Wiener
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Simulated Data ◽  
Interval Censoring ◽  
Trial Data ◽  
Observation Window ◽  
Neural Data ◽  
Conditional Intensity Function ◽  
Spike Train Data

It is important to validate models of neural data using appropriate goodness-of-fit measures. Models summarizing some response features—for example, spike count distributions or peristimulus time histograms—can be assessed using standard statistical tools. Measuring the fit of a full point-process model of spike trains is more difficult. Recently, Barbieri, Quirk, Frank, Wilson, and Brown (2001) and Brown, Barbieri, Ventura, Kass, and Frank (2002) presented a method for rescaling time so that if an underlying description correctly describes the conditional intensity function of a point process, the rescaling will convert the process into a homogeneous Poisson process. The corresponding interevent intervals are exponential with mean 1 and can be transformed to be uniform; tests of the uniformity of the transformed intervals are thus tests of how well the model fits the data. When the lengths of interevent intervals are comparable to the length of the observation window, as can happen in common neurophysiology paradigms using short trials, the fact that long intervals cannot be observed (are censored) can cause the tests based on time rescaling to reject a correct model inappropriately. This article presents a simple adjustment to the time-rescaling method to account for interval censoring, avoiding inappropriate rejection of acceptable models for short-trial data. We illustrate the adjustment's effect using both simulated data and short-trial data from monkey primary visual cortex.

scholarly journals Point Process Models for the Spread of Coccidioidomycosis in California

2021 ◽  
Vol 13 (2) ◽  
pp. 558-570
Author(s):  
Jiajia Wang ◽  
Ryan J. Harrigan ◽  
Frederic P. Schoenberg
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
United States ◽  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Process Models ◽  
Squared Error ◽  
Point Process Models

Coccidioidomycosis is an infectious disease of humans and other mammals that has seen a recent increase in occurrence in the southwestern United States, particularly in California. A rise in cases and risk to public health can serve as the impetus to apply newly developed methods that can quickly and accurately predict future caseloads. The recursive and Hawkes point process models with various triggering functions were fit to the data and their goodness of fit evaluated and compared. Although the point process models were largely similar in their fit to the data, the recursive point process model offered a slightly superior fit. We explored forecasting the spread of coccidioidomycosis in California from December 2002 to December 2017 using this recursive model, and we separated the training and testing portions of the data and achieved a root mean squared error of just 3.62 cases/week.

scholarly journals Thinning spatial point processes into Poisson processes

2010 ◽  
Vol 42 (2) ◽  
pp. 347-358 ◽  
Author(s):  
Jesper Møller ◽  
Frederic Paik Schoenberg
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Point Processes ◽  
Death Process ◽  
Cox Process ◽  
Birth And Death Process ◽  
Conditional Intensity ◽  
Spatial Point Processes ◽  
Spatial Point

In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.

Heart-Rate Variability as a Quantitative Measure of Hypnotic Depth

2007 ◽  
Vol 56 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Solomon Gilbert Diamond ◽  
Orin C. Davis ◽  
Robert D. Howe
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Quantitative Measure

Nonlinear Modeling of Neural Interaction for Spike Prediction Using the Staged Point-Process Model

2018 ◽  
Vol 30 (12) ◽  
pp. 3189-3226 ◽  
Author(s):  
Cunle Qian ◽  
Xuyun Sun ◽  
Shaomin Zhang ◽  
Dong Xing ◽  
Hongbao Li ◽  
...  
Keyword(s):  
Linear Combination ◽  
Point Process ◽  
Nonlinear Interaction ◽  
Process Model ◽  
Goodness Of Fit ◽  
Primary Motor Cortex ◽  
Premotor Cortex ◽  
Nonlinear Function ◽  
Point Process Model ◽  
Log Likelihood

Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than quadratic models, and the modified L-M algorithm also demonstrates fast convergence.

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