Modelling heart rate changes in the mouse as a system of delayed, weakly coupled oscillators

A problem presented at the UK MMSG NC3Rs Study Group 2013.

Presented by:
Dr Mark Christie (Pharmaceutical Sciences, King's College London)
Dr Manasi Nandi (Institute of Pharmaceutical Science, King's College London)
PJ Aston, S Bayram, Y Borg, V Carapella, B Chakrabarti, MI Christie, GR Mirams, M Nandi, JH Siggers, RD Simitev

Problem Description

The measurement of cardiovascular variables such as heart rate (HR) and blood pressure (BP) in conscious experimental animals is complicated by the complexity of the signals involved. In anaesthetised (or over short time periods in conscious) animals the BP can be simply described as a sinusoidal wave with peak and trough defined as systolic and diastolic BP, respectively, whilst the HR is the reciprocal of the beat to beat interval. However, the influence of other oscillating systems such as the respiratory cycle, neuronal (sympathetic and parasympathetic) and endocrine hormone outflow on the cardiovascular system alters the HR and BP signals such that they become considerably more complex. Conventional methods tend to under-analyse this complexity.

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Study Group Report

We used a standard experimental data set for the purposes of analysis and modelling. Arterial blood pressure waveform data was collected from conscious mice instrumented with radiotelemetry devices over 24 hours, at a 100Hz and 1kHz time base. During a 24 hour period, these mice display diurnal variation leading to changes in the cardiovascular waveform. We undertook preliminary analysis of our data using Fourier transforms and subsequently applied a series of both linear and nonlinear mathematical approaches in parallel.

We provide a minimalistic linear and nonlinear coupled oscillator model and employed spectral and Hilbert analysis as well as a phase plane analysis. This provides a route to a three way synergistic investigation of the original blood pressure data by a combination of physiological experiments, data analysis viz. Fourier and Hilbert transforms and attractor reconstructions, and numerical solutions of linear and nonlinear coupled oscillator models. We believe that a minimal model of coupled oscillator models that quantitatively describes the complex physiological data could be developed via such a method.

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Follow-Up Activities

The following funding for further work has been obtained to investigate aspects of this problem:

Reconstruction of Attractors in ECG signals
PJ Aston & G Chaffey
University of Surrey, EPSRC Impact Acceleration Account funding, April 2014.

The following student projects have been inspired by this problem:

Reconstruction of Attractors for Blood Pressure Data as a Diagnostic Tool
Undergraduate summer research studentship, University of Surry, July to September 2013.
Supervised by PJ Aston.