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@jimfleming
Last active February 20, 2024 22:35
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2017-08-07T15:42:34.469956Z",
"start_time": "2017-08-07T15:42:33.478139"
},
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"from IPython.display import Image\n",
"\n",
"import numpy as np\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"\n",
"sns.set_style('whitegrid')\n",
"sns.set_context('notebook', font_scale=2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"# Hill-type muscle model"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"## Elements"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"The model consists of three elements:\n",
"\n",
"- A contractile element (CE) that represents the muscle fibers that contract based on the muscle activation state.\n",
"- A serial elastic element (SEE) that represents the tendons that connect the muscle to the bones.\n",
"- A parallel elastic element (PEE) that represents the passive elastic material surrounding muscle fibers."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2017-08-07T15:42:35.983213Z",
"start_time": "2017-08-07T15:42:35.974028"
},
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
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J8rfUQ+mjMo6yPLKf5Ork4xTUSRCpUzFHyVKZQXlIpUTVVY1LbQTJAjcNNo1hzRNartrC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\nNrgvai5deOGF0qNHD3PeUpM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4z549O3PPYIQMAbE1ClLWq2BSGCP+csmBKsHB6kgW/kK8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\nAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='images/muscle_model.png')"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"## Forces"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
" - $F_{max}$: maximum isometrical force. optimized constant.\n",
" - $F_{CE}$: contractile element force. calculated. $\\eqref{1}$\n",
" - $F_{SEE}$: parallel element force. calculated. $\\eqref{2}$\n",
" - $F_{PEE}$: parallel element force. $\\eqref{3}$\n",
" - $F_M$: total muscle force. calculated. $\\eqref{4}$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"### Force relationships"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$ \\begin{align}\n",
" \\tag{4}\n",
" \\label{4}\n",
" F_M &= F_{CE} + F_{PEE} = F_{SEE}\n",
"\\end{align} $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"### Contractile element"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"From Wang et al. 2012 and confirmed by author:"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$ L_{CE}^{norm} = \\frac{L_{CE}}{L_{CE}^{opt}} $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$ V_{CE}^{norm} = \\frac{V_{CE}}{L_{CE}^{opt}} $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"#### Force-length relationship [Geyer et al. 2003]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2017-08-07T15:42:42.230428Z",
"start_time": "2017-08-07T15:42:42.222609"
},
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"image/png": 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J8rfUQ+mjMo6yPLKf5Ork4xTUSRCpUzFHyVKZQXlIpUTVVY1LbQTJAjcNNo1hzRNartrC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\nuUOKAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='images/force_length.png')"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$ \\begin{equation}\n",
"f_L(L_{CE}^{norm}) =\n",
" \\exp \\left[ c \\left|\\frac{L_{CE}^{norm} - L_{CE}^{opt}}{L_{CE}^{opt} w}\\right|^3 \\right]\n",
"\\end{equation} $$\n",
"\n",
"- $L_{CE}^{opt}$: optimum CE length (for maximum force production).\n",
"- $w$: width of the bell-shaped $f_L(L_{CE}^{norm})$ curve.\n",
"- $c$: $ln(0.05)$ fulfilling $f_L\\left(L_{CE}^{opt}\\left(1 \\pm w\\right)\\right)$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2017-08-07T16:03:09.840050Z",
"start_time": "2017-08-07T16:03:09.423486"
},
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x109b66b50>]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GI9dxprgOre0GzJg0vKubjgYnJTEUbgoZjpyuwJJbE8Quh8juRA8HRmPnzGMqlfXnsC3b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\n51cfmQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1093d8e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"c = np.log(0.05)\n",
"L_CE_opt = 1.0\n",
"w = 0.5\n",
"\n",
"def f_L(L_CE_norm):\n",
" return np.exp(c * np.power(np.absolute((L_CE_norm - L_CE_opt) / (L_CE_opt * w)), 3.0))\n",
"f_L = np.vectorize(f_L)\n",
"\n",
"L_CE_norm = np.linspace(0, 2, 100)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"ax.set_xlabel('Length')\n",
"ax.set_ylabel('Force')\n",
"ax.plot(L_CE_norm, f_L(L_CE_norm))"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"#### Force-velocity relationship [Geyer et al. 2003]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2017-08-07T15:42:48.892024Z",
"start_time": "2017-08-07T15:42:48.885530"
},
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"image/png": 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J8rfUQ+mjMo6yPLKf5Ork4xTUSRCpUzFHyVKZQXlIpUTVVY1LbQTJAjcNNo1hzRNartrC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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='images/force_velocity.png')"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$ f_V\\left(V_{CE}^{norm}\\right) = \\begin{cases}\n",
" \\frac{V_{max} - V_{CE}^{norm}}{V_{max} + K V_{CE}^{norm}} & \\text{if $V_{CE}^{norm} < 0$} \\\\\n",
" N + (N - 1) \\frac{V_{max} + V_{CE}^{norm}}{7.56 K V_{CE}^{norm} - V_{max}} & \\text{if $V_{CE}^{norm} \\geq 0$}\n",
"\\end{cases} $$\n",
"\n",
"- $V_{CE} < 0$ follows the Hill equation (Hill 1938) for muscle shortening where $V_{max} < 0$ is the maximum contraction velocity.\n",
"- $V_{CE} \\geq 0$ muscle lengthing is characterized by an equation based on Aubert (1956).\n",
"\n",
"- $V_{max} = -12 l_{opt}s^{-1}$: maximum shortening velocity\n",
"- $K$: curvature constant.\n",
"- $N$: dimensionless amount of force $\\frac{F_M}{F_{max}}$ reached at a lengthening velocity $V_{CE} = -V_{max}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"Relationship (cannot compute directly for $V_{CE}$ because its recursive):\n",
"\n",
"$$ \\begin{equation}\n",
"f_V\\left(V_{CE}^{norm}\\right) = \\frac{F_{SEE} - F_{PEE}}{a F_{max} f_L(L_{CE}^{norm})}\n",
"\\end{equation} $$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2017-08-07T16:03:05.757706Z",
"start_time": "2017-08-07T16:03:05.446049"
},
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1099f2d50>]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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4HOTl5TFmzJgWtxORC8swDLbuKSE02MrFca2/VVhEvFO7g8SNN97It99+y8qV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\nIYQQQjqMEglCCCGEdNj/AA1joRhmFEjCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1093f9f90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"V_max = -10.0\n",
"K = 5.0\n",
"N = 1.5\n",
"\n",
"def f_V(V_CE_norm): \n",
" if V_CE_norm < 0:\n",
" return (V_max - V_CE_norm) / (V_max + (K * V_CE_norm))\n",
" else:\n",
" return N + (N - 1) * ((V_max + V_CE_norm) / ((7.56 * K * V_CE_norm) - V_max))\n",
"f_V = np.vectorize(f_V)\n",
"\n",
"V_CE_norm = np.linspace(-10, 10, 100)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"ax.set_xlabel('Velocity')\n",
"ax.set_ylabel('Force')\n",
"ax.plot(V_CE_norm, f_V(V_CE_norm))"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"#### Force-velocity inverse"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$ f_V^{-1} \\left(y\\right) = \\begin{cases}\n",
" \\frac{V_{max} \\left(1 - y\\right)}{1 + y K} & \\text{if $y < 1$} \\\\\n",
" \\frac{V_{max} \\left(y - 1\\right)}{7.56 K \\left(y - N\\right) - N + 1} & \\text{if $y \\geq 1$}\n",
"\\end{cases} $$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2017-08-07T15:43:34.242397Z",
"start_time": "2017-08-07T15:43:33.998202"
},
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x109939b90>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GjBiB6dOnd0hhRERE1kih1OLVj08gK68Sk4d3xZwHG57ryByZPOTyq6++as86iIiIrF61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\nABHRAABERAMAEHldRiyEKfofnAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1094c5050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def f_V_inv(y):\n",
" if y < 1:\n",
" return (V_max * (1 - y)) / (1 + (y * K))\n",
" else:\n",
" return (V_max * (y - 1)) / ((7.56 * K * (y - N)) - N + 1)\n",
"f_V_inv = np.vectorize(f_V_inv)\n",
"\n",
"y = np.linspace(0, 1.5, 100)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"ax.set_xlabel('Force')\n",
"ax.set_ylabel('Velocity')\n",
"ax.plot(y, f_V_inv(y))"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"#### Contractile-element velocity"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$V_{CE}$ is the result of equation $\\eqref{6}$ and derived from Equations $\\eqref{1}$ and $\\eqref{4}$, by inverting the force-velocity relation $f_V$:"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$\\begin{align}\n",
" \\label{6}\n",
" \\tag{6}\n",
" V_{CE} &= f_v^{-1} \\left[\\frac{F_{SEE} - F_{PEE}}{a F_{max} f_L(L_{CE}^{norm})}\\right] \\\\\n",
" &= f_v^{-1} \\left[\\frac{F_{CE}}{\\frac{F_{CE}}{f_V(V_{CE}^{norm})}}\\right] \\\\\n",
" &= f_v^{-1} \\left[f_V(V_{CE}^{norm})\\right]\n",
"\\end{align}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"Because the following relationship is true:\n",
"\n",
"$$ \\frac{x}{\\frac{x}{y}} = y $$\n",
"\n",
"Thus:\n",
"\n",
"$$ \\frac{F_{CE}}{\\frac{F_{CE}}{f_V(V_{CE})}} = f_V(V_{CE}) $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"As well as this inverse function relationship (http://en.wikipedia.org/wiki/Inverse_function):\n",
"\n",
"$$ x = f^{-1}(f(x)) = f(f^{-1}(x)) $$\n",
"\n",
"Thus:\n",
"\n",
"$$ V_{CE} = f_V^{-1}(f_V(V_{CE})) = f_V(f_V^{-1}(V_{CE})) $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"#### Contractile-element force"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$\\begin{align}\n",
" \\label{1}\n",
" \\tag{1}\n",
" F_{CE}& = a F_{max} f_L(L_{CE}^{norm}) f_V(V_{CE}^{norm}) \\\\\n",
" \\frac{F_{CE}}{f_V(V_{CE}^{norm})}& = a F_{max} f_L(L_{CE}^{norm})\n",
"\\end{align}$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10e13c050>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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dR5mYmdzur7VhwjDk5MmTfOs3fxPx2FN80bB5LvJwKjr36xl0Q6MoAnRNQ0qW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iSxZ88eZs2aRX19PfPmzaOqqnhtRYkTmlKRUOLLw+/3s3DhQr744gtmz56dNStdyONdkiT+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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10dd53610>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
"from matplotlib import cm\n",
"\n",
"F_max = 22.0\n",
"a = 1.0\n",
"\n",
"def f_CE(L_CE_norm, V_CE_norm): \n",
" return a * F_max * f_L(L_CE_norm) * f_V(V_CE_norm)\n",
"\n",
"L_CE_norm = np.linspace(0, 2, 100)\n",
"V_CE_norm = np.linspace(-10, 10, 100)\n",
"L_CE_norm, V_CE_norm = np.meshgrid(L_CE_norm, V_CE_norm)\n",
"\n",
"f_CE = np.vectorize(f_CE)\n",
"F_CE = f_CE(L_CE_norm, V_CE_norm)\n",
"\n",
"fig = plt.figure(figsize=(20, 8))\n",
"ax = fig.add_subplot(1, 2, 1, projection='3d')\n",
"ax.plot_surface(L_CE_norm, V_CE_norm, F_CE, rstride=4, cstride=4, alpha=0.8, linewidth=0.25, cmap=cm.coolwarm)\n",
"\n",
"cset = ax.contour(L_CE_norm, V_CE_norm, F_CE, zdir='x', offset=0, cmap=cm.coolwarm)\n",
"\n",
"ax.view_init(35, -45)\n",
"\n",
"ax.set_xlabel('L_CE_norm')\n",
"ax.set_ylabel('V_CE_norm')\n",
"ax.set_zlabel('F_CE')"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"### Serial element"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"The passive forces produced by the elastic elements, $F_{PEE}$ and $F_{SEE}$ are modeled as non-linear springs based on their lengths:"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"\\begin{align}\n",
" \\label{2}\n",
" \\tag{2}\n",
" F_{SEE} & = f_{SEE}(L_M - L_{CE}) \\\\\n",
" & = f_{SEE}(L_{SEE})\n",
"\\end{align}"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$f_{SEE}$ is described in Geyer et al. 2003:\n",
"\n",
"$$ f_{SEE} = \\begin{cases}\n",
" \\left(\\frac{\\epsilon}{\\epsilon_{ref}}\\right)^2 & \\text{if $\\epsilon > 0$} \\\\\n",
" 0 & \\text{if $\\epsilon \\leq 0$}\n",
"\\end{cases} $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"- $\\epsilon$: tendon strain. $\\epsilon = \\frac{L_{SEE} - L_{SEE}^{rest}}{L_{SEE}^{rest}}$\n",
"- $L_{SEE}^{rest}$: tendon's resting length\n",
"- $\\epsilon_{ref}$: tendon reference strain with $f_{SEE}\\left(\\epsilon_{ref}\\right) = 1$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10e1f3710>]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ErJLUMy3vBcwuqbcyLVsLrCgpX5GWm9kmeu45OOkkePZZmDMHdtst74is3tXK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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10df79650>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"L_SEE_rest = 0.4\n",
"epsilon_ref = 0.04 * L_SEE_rest\n",
"\n",
"def f_SEE(L_SEE):\n",
" epsilon = (L_SEE - L_SEE_rest) / L_SEE_rest\n",
" if epsilon > 0.0:\n",
" return (epsilon / epsilon_ref)**2.0\n",
" else:\n",
" return 0.0\n",
"\n",
"L_SEE = np.linspace(0, 1, 100)\n",
"\n",
"f_SEE = np.vectorize(f_SEE)\n",
"F_SEE = f_SEE(L_SEE)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"ax.set_xlabel('L_SEE')\n",
"ax.set_ylabel('F_SEE')\n",
"ax.plot(L_SEE, F_SEE)"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"### Parallel element"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"\\begin{equation}\n",
" \\label{3}\n",
" \\tag{3}\n",
" F_{PEE} = f_{PEE}(L_{CE}^{norm})\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$f_{PEE}$ isn't described in Geyer et al. 2003 but is described in Geyer et al. 2010:"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"\\begin{equation}\n",
" f_{PEE} = F_{max} \\left(\\frac{L_{CE}^{norm} - L_{CE}^{opt}}{L_{CE}^{opt}\\epsilon_{PE}}\\right)^2 f_V\\left(V_{CE}^{norm}\\right)\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$\\epsilon_{PE}$ = $w$ according to Geyer et al. 2010"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10e251ad0>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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kW79B+vq50+kUfoNpMMSUsZ4tzIilS6ZSvbEMYYQzZZqoWAwUw/yJ1GUbY38Fg8EpPo90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\nS4IEIYQQQlTr/wGPYgm5br1koQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10eaeca90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
"from matplotlib import cm\n",
"\n",
"w = 0.6\n",
"V_max = -12.0\n",
"K = 5.0\n",
"N = 1.5\n",
"\n",
"def f_PEE(L_CE_norm, V_CE_norm): \n",
" return F_max * ((L_CE_norm - L_CE_opt) / (L_CE_opt * w)) * f_V(V_CE_norm)\n",
"\n",
"L_CE_norm = np.linspace(0, 2, 100)\n",
"V_CE_norm = np.linspace(-10, 10, 100)\n",
"L_CE_norm, V_CE_norm = np.meshgrid(L_CE_norm, V_CE_norm)\n",
"\n",
"f_PEE = np.vectorize(f_PEE)\n",
"F_PEE = f_PEE(L_CE_norm, V_CE_norm)\n",
"\n",
"fig = plt.figure(figsize=(20, 8))\n",
"ax = fig.add_subplot(1, 2, 1, projection='3d')\n",
"ax.plot_surface(L_CE_norm, V_CE_norm, F_PEE, rstride=8, cstride=8, alpha=0.8, linewidth=0.25, cmap=cm.coolwarm)\n",
"\n",
"ax.view_init(35, 135)\n",
"\n",
"ax.set_xlabel('L_CE_norm')\n",
"ax.set_ylabel('V_CE_norm')\n",
"ax.set_zlabel('F_PEE')"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"## Lengths"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"- $L_M$: total muscle length $\\eqref{8}$\n",
"- $L_{CE}$: contractile element length. initialized to $L_{CE}^{opt}$ then integrated from $V_{CE}$.\n",
"- $L_{SEE}$: serialize element length. derived from relationship.\n",
"- $L_{PEE}$: parallel element length. unused.\n",
"- $L_M^{rest}$: muscle rest length. derived from relationship.\n",
"- $L_{SEE}^{slack}$: tendon slack length. optimized param.\n",
"- $L_{CE}^{opt}$: optimal contractile element length. optimized param."
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$ \\begin{equation}\n",
" L_M = L_{SEE} + L_{CE}\n",
"\\end{equation} $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"\\begin{equation}\n",
" \\label{5}\n",
" \\tag{5}\n",
" L_M^{rest} = L_{SEE}^{slack} + L_{CE}^{opt}\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"$$\\begin{equation}\n",
" \\label{8}\n",
" \\tag{8}\n",
" L_M = \\sum_{i=1}^{n-1} ||s_i||\n",
"\\end{equation}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"Muscle segment length:\n",
"\n",
"$$ s_i = P_{i+1}^W - P_i^W $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"#### Contractile element length"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"The muscle state parameter $L_{CE}$ is then updated (each time step) through integration of the contraction velocity $V_{CE}$.\n",
"\n",
"Be sure to use the velocity, then update it for Euler integration."
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"\\begin{equation}\n",
" \\tag{6}\n",
" L_{CE} = \\int V_{CE} dt\n",
"\\end{equation}\n",
"\n",
"\\begin{equation} L_{CE} = L_{CE} + V_{CE} dt \\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"## Activation"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"- $a$: muscle activation\n",
"- $u$: neural activation signal:\n",
"- $c_a$: constant activation and deactivation rate. Default: $c_a = 100s^{-1}$ or 0.01."
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"\\begin{equation}\n",
" \\label{7}\n",
" \\tag{7}\n",
" \\frac{\\partial a}{\\partial t} = c_a (u - a)\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10ec8e710>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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1kwLAWGKMjdMQJ45UTKaUwXBsGOFQGABfHStXzjVThZwRSVOcGKJGg5PbmC4XlrdEOSqE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\noaGhoSGF/x+78eA/bThPCQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e2cc110>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"c_a = 0.01\n",
"\n",
"def da(u, a): \n",
" return c_a * (u - a)\n",
"\n",
"t_series = np.linspace(0, 100, 1000)\n",
"u_series = np.sin(t_series - (np.pi / 2)) * 100\n",
"\n",
"a_series = []\n",
"a = 0.0\n",
"\n",
"prev_t = 0\n",
"for (t, u) in zip(t_series, u_series):\n",
" dt = t - prev_t\n",
" a += da(u, a) * dt\n",
" prev_t = t\n",
" a_series.append(a)\n",
"\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"ax.plot(t_series, a_series, \"g\") # activation\n",
"# ax.plot(t_series, u_series, \"b\") # neural input\n",
"ax.set_xlabel('t')\n",
"ax.set_ylabel('a / u')"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"## Force application"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"image/png": 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J8rfUQ+mjMo6yPLKf5Ork4xTUSRCpUzFHyVKZQXlIpUTVVY1LbQTJAjcNNo1hzRNartrC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\nVLv5ipILS7oeSbENlsEXRxxxhOPbxLPEYGuqIOlR8GxAflf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"Image(filename='images/force_application.png')"
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"The total muscle length $L_M$ with activation state $a$ to compute the scalar muscle contraction force $F_M$.\n",
"\n",
"- $k$: a joint spanned by the muscle.\n",
"- $\\tau_k$: the torque generated in the direction of the moment arm $r_k$.\n",
"- $r_k$: moment arm corresponding to the cross-product between the direction of the segment that crosses the joint $s_c$ and a vector from the joint center $j_k$ to any point on the segment $s_c$, such as $P_c^W$.\n",
"- $s_c$: muscle segment\n",
"- $j_k$: joint center"
]
},
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"$$\\begin{equation}\n",
" \\label{9}\n",
" \\tag{9}\n",
" \\tau_{k} = F_M ||r_k|| \\\\\n",
" r_k = (P_{i+1}^W - P_i^W) \\times \\frac{s_c}{||s_c||}\n",
"\\end{equation}$$"
]
},
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"### Force relationships"
]
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"- Torque (http://en.wikipedia.org/wiki/Torque): $ T = \\frac{\\partial L}{\\partial t} $\n",
"- Net torque: $ T_{net} = I \\cdot a $\n",
"- Moment of inertia (http://en.wikipedia.org/wiki/Moment_of_inertia): $ I = \\frac{L}{w} $\n",
"- Angular momentum: $ L = I \\cdot w $\n",
"- Force (http://en.wikipedia.org/wiki/Force): $ F = m \\cdot a $\n",
"- Angular acceleration (http://en.wikipedia.org/wiki/Angular_acceleration): $ a = \\frac{T}{I} $"
]
},
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@Fox671
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Fox671 commented Nov 4, 2023

Forces chapter. "$F_{SEE}$: parallel element force. calculated"
Isn't it serial element force?

@jimfleming
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Yup, that’s correct. Just a typo.

@SPOREIII
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Thank you for writing this code, which greatly helped me to learn Hill model.
It seems that there is a problem with the cell 9:

def f_PEE(L_CE_norm, V_CE_norm): 
    return F_max * ((L_CE_norm - L_CE_opt) / (L_CE_opt * w)) * f_V(V_CE_norm)

should be

def f_PEE(L_CE_norm, V_CE_norm): 
    return F_max * np.power((L_CE_norm - L_CE_opt) / (L_CE_opt * w), 2) * f_V(V_CE_norm)

Refer to equation 7

@jimfleming
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Hmm. That's possibly a typo or I may have removed it on purpose. It's been so long I don't remember.

@haoction
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Thank you for writing this code, which greatly helped me to learn Hill model. It seems that there is a problem with the cell 9:

def f_PEE(L_CE_norm, V_CE_norm): 
    return F_max * ((L_CE_norm - L_CE_opt) / (L_CE_opt * w)) * f_V(V_CE_norm)

should be

def f_PEE(L_CE_norm, V_CE_norm): 
    return F_max * np.power((L_CE_norm - L_CE_opt) / (L_CE_opt * w), 2) * f_V(V_CE_norm)

Refer to equation 7

The power is calculated in the following if

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