{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE30338](https://jckantor.github.io/CBE30338)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE30338.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Controller Tuning Rules in Frequency Domain](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/05.04-Controller-Tuning-Rules-in-Frequency-Domain.ipynb) | [Contents](toc.ipynb) | [Optimization](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/06.00-Optimization.ipynb) >
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Baroreflex as a Linear Control System\n",
"\n",
"The [baroreflex](https://en.wikipedia.org/wiki/Baroreceptor) is one of several mechanisms in the body for maintaining arterial blood pressure (AP) at near constant levels. Specialized neurons, known as [baroreceptors](https://en.wikipedia.org/wiki/Baroreceptor), sense pressure through the stretching of the walls in key blood vessels. The signals are processed in the brainstem which, in turn, produces a compensating change in sympathetic and parasympathetic nervous system causing a response by the heart. (Figure from Victor, 2015).\n",
"\n",
"![baroreflex system](figures/nrcardio.2015.96-f2.jpg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook presents a linear control analysis of the closed-loop system consisting of a 'peripheral arc' from the sympathetic efferents connected to the heart tissue that cause the blood pressure to increase, and a corresponding 'neural arc' from the carotid baroreceptors sensing blood pressure to the sympathetic nervous response. Together these arcs comprise a closed-loop for the short-term control of blood pressure in the body (McLoone, 2014). \n",
"\n",
"This is diagrammed below in the form a closed loop control system\n",
"\n",
"![baroreflex control diagram](figures/baroreflex.png)\n",
"\n",
"where $AP$ refers to arterial blood pressure, and $SNA$ is the activity of the sympathetic nervous system correlated with response of the heart, $G_p$ represents the transfer function of the peripheral arc, and $G_c$ represents the transfer function of the neural (or control) arc. The signal $p$ is placeholder for the influence of exogenous influences on blood pressure, such as a change in body body position. "
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"import control.matlab as control\n",
"\n",
"sns.set_context('talk')\n",
"\n",
"# needed to avoid a deprecation warning in the control library \n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\", category=UserWarning) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Peripheral Arc\n",
"\n",
"Transfer function models for the 'peripheral arc', denoted $G_p(s)$ in the closed-loop diagram, have been measured for various animal models. For anesthesized rats, for example, Chapius et al., 2004, found\n",
"\n",
"$$G_p(jf) = \\left(\\frac{K}{1 + 2\\lambda(f/f_n) + (j(f/f_n))^2}\\right)\\exp\\left(-2\\pi Tjf\\right)$$\n",
"\n",
"where $j$ is the imaginary operator $\\sqrt{-1}$, and $f$ is frequency in units of Hertz. Reported values for the parameters are given in the following table.\n",
"\n",
"| Parameter | Description | $\\qquad\\qquad$ Value $\\qquad\\qquad$ | Conversion |\n",
"| :--: | :- | :-: | :-: |\n",
"| $K$ | static gain | $1.16 \\pm 0.21$ mmHg/% SNA | $K_p \\approx 1.16$ mmHg/% SNA|\n",
"| $f_n$ | natural frequency | $0.089\\pm 0.007$ Hz | $\\tau \\approx 1.79$ sec |\n",
"| $\\lambda$ | damping coefficient | $1.23\\pm 0.14$ | $\\zeta \\approx 1.23$\n",
"| $T$ | fixed time delay | $0.476\\pm 0.020$ sec | $t_d \\approx 0.476$ |\n",
"\n",
"Using the indicated conversions of values and parameters, the literature model is recast into standard transfer function notation\n",
"\n",
"$$G_p(s) = \\left(\\frac{K_p}{\\tau^2 s^2 + 2\\zeta\\tau s + 1}\\right)\\exp\\left(-t_d s\\right)$$\n",
"\n",
"The following cell implements this transfer function using the [Python Control Systems Library](https://pypi.python.org/pypi/control/0.7.0)."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Without Time Delay -->\n",
" \n",
" 1.16\n",
"-----------------------\n",
"3.198 s^2 + 4.399 s + 1\n",
"\n",
"\n",
"With a 3rd order Pade approximation for Time Delay -->\n",
" \n",
" -1.16 s^3 + 29.24 s^2 - 307.2 s + 1291\n",
"------------------------------------------------------------\n",
"3.198 s^5 + 85.02 s^4 + 958.7 s^3 + 4748 s^2 + 5160 s + 1113\n",
"\n"
]
}
],
"source": [
"Kp = 1.16 # mmHg/%SNA\n",
"tau = 1.0/(2*0.089*np.pi) # sec\n",
"zeta = 1.23\n",
"td = 0.476\n",
"\n",
"Gp_ = control.tf([Kp],[tau**2,2*zeta*tau,1])\n",
"print('\\nWithout Time Delay -->\\n', Gp_)\n",
"\n",
"num,den = control.pade(td,3)\n",
"Gp = Gp_ * control.tf(num,den)\n",
"print('\\nWith a 3rd order Pade approximation for Time Delay -->\\n', Gp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following cell demonstrates the step response of the peripheral arc to a 1% change in $SNA$."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
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0+cmLE87HJ1Rhv2Rew9d6bE2K4118v9Mz23jeccBS59w/kvo/JbYP+/l5NfCSc+5J59zs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\n2bad7PymN9Ou4UXERLJp6YeL/+9rNPDvZP8CnEV2CGhxcbq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"text/plain": [
" "
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}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}