Mathematical modelling of the neural control of blood pressure

Prof Champneys (University of Bristol)

Thursday 24th November, 2016 14:00-15:00 Maths 522


This talk is based on work carried out by PhD student Linford Briant
in collaboration woth Dr Tony Pickering and Prof Julian Paton in
Bristol University's Department of
Physiology and Pharmacology.   The starting point for the work is
experimental recordings of pre-ganglionic sympathetic nerves that
innervate vasoconstrictor muscles in
rats. It is found that compared with wild type rats, mutants that are
spontaneously hypertensive (develop high blood pressure as they
mature) are found to produce more bursts
during the active part of the respiratory cycle. This increased
excitability is studied through mathematical modelling using the
software neuron, and found to be consistent with an increase in the
A-current channel in the neuron.

Next, a mathematical model is constructed of the pathway from action
potential generation in a sympathetic postganglionic neurone to
contraction of an arterial smooth muscle cell. The differential
equation model is a synthesis of models of the individual
physiological processes, and is shown to be consistent with
physiological data.
The model is found to be unresponsive to tonic (regular) stimulation
at typical frequencies recorded in sympathetic efferents. However,
when stimulated at the same average frequency, but with repetitive
respiratory-modulated burst patterns, it produces marked contractions.
Moreover, the contractile force produced is found to be highly
dependent on the number of spikes in each burst. In particular, when
the model is driven by preganglionic spike trains recorded from
wild-type and spontaneously hypertensive rats the contractile force
was found to be 10-fold greater in the hypertensive case. An
explanation is provided in terms of the summative increased release of

The findings of the model have led to some new in vivo tests using
wild type rats whose sympathetic nerves are stimulated with both
bursty and tonic firing patterns. The bursting signal is shown to
increase vascular resistance and therefore lead to a possible
explanation for the onset of hypertension, being due to abnormal
sympathetic coupling between the respiratory cycle and vascular

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