A Simple Soft Limiter Describing Function for Biomedical Applications

Abstract

Abstract-This paper suggests an arctangent function as a suitable parameterisation for the soft-limiting gain characteristic frequently encountered in models of biomedical systems. This function is shown, as an example, to fit the neural arc component of the baroreflex with the main contribution of the paper being the development of a simple describing function (DF) characteristic for the arctangent. The simple form of the DF allows transparency of the physiological parameters in, for example, stability analysis. For illustration, the derived DF is used to examine low-frequency limit cycles in blood pressure, sometimes termed Mayer waves.

Age-Related Normative Changes in Phasic Orthostatic Blood Pressure in a Large Population Study

“…Analytical approaches to date have used simple magnitude-and timing-based measures to capture the range of transient responses to standing, 35 with more advanced clustering methods used by Finucane et al, 40 Romero-Ortuno et al, 18 and Cooke et al 15 The use of these approaches and more advanced methods may enable us to capture the full range of responses while also providing a transparent mechanistic link between the underlying physiology and observed patterns. 41 …”

The effect of pulsatile blood flow on blood pressure regulatory mechanisms

“…In [12], a simple describing function is developed for the arctan function, allowing some transparency between the nature/presence of potential low frequency baroreflex oscillations and the parameters of the system, including the baroreflex curve. Unfortunately, the calculation of the equivalent nonlinearity, to include the effect of pulsatility, introduces some mathematical complexity to the description of the effective nonlinearity (via (13)) which impairs the development of any simple relationships between nature/presence of potential low frequency baroreflex oscillations and the parameters of the system.…”

“…The describing function for the arctan function is given [12] as: where M is the amplitude of the input sinusoid, while that for a saturation characteristic [17] is:…”

“…Note that the parameterisation of the static baroreflex characteristic by an arctan function allows for a relatively simple describing function to be calculated, facilitating straightforward stability analysis [12]. A set of parameters for the arctan function for a rabbit in the normoxia case [12] is specified in Table I, with a typical fit to experimental data shown in Fig.2.…”

“…A set of parameters for the arctan function for a rabbit in the normoxia case [12] is specified in Table I, with a typical fit to experimental data shown in Fig.2. The dynamic components of the model in Fig.1 are: …”