{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# AxCaliber with time-dependent zeppelin\n", "\n", "In this example, we use the AxCaliber method *(Assaf et al. 2008)* presented in a previous example while including the diffusion time-dependency of the extra-axonal space *(Novikov et al. 2014, Burcaw et al. 2015)*. \n", "\n", "\n", "The signal representation is \n", "\n", "\n", "\\begin{equation}\n", "E_{\\textrm{AxCaliber}}^{\\textrm{Temporal}}= \\underbrace{(1-f_r)\\overbrace{E_h(b,\\textbf{n},\\lambda_\\parallel,D_{\\infty},A)}^{\\textrm{GPA-Zeppelin}}}_{\\textrm{Extra-Axonal}} + \\underbrace{f_r \\overbrace{\\Gamma(\\alpha,\\beta)}^{\\textrm{Gamma Distribution}}*_{\\mathbb{R}}\\overbrace{E_r(\\cdot|D_\\perp)}^{\\textrm{Cylinder}}}_{\\textrm{Intra-Axonal}}\n", "\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where the cylinder was initially represented using the Callaghan model, but was later replaced with the more general Van Gelderen model *(Huang et al. 2015, De Santis et al. 2016)*. The initial Ball, which accounted for the extra-axonal signal, is replaced by the time-dependent Zeppelin *(De Santis et al, 2016)*. The formulation of the time-dependent Zeppelin is as follows:\n", "\n", "\\begin{equation}\n", " E_h(b,\\textbf{n},\\lambda_\\parallel,D_{\\infty},A)=\\exp(-b\\textbf{n}^T(\\textbf{R}\\textbf{D}^h_{\\textrm{diag}}\\textbf{R}^T)\\textbf{n})\\quad\\textrm{with}\\quad\n", " \\textbf{D}^h_{\\textrm{diag}}=\n", "\\begin{pmatrix}\n", " \\lambda_\\parallel & 0 & 0 \\\\\n", " 0 & D_{\\infty}+A\\frac{\\ln(\\Delta/\\delta)+3/2}{\\Delta-\\delta/3} & 0 \\\\\n", " 0 & 0 & D_{\\infty}+A\\frac{\\ln(\\Delta/\\delta)+3/2}{\\Delta-\\delta/3}\n", " \\end{pmatrix}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "here the perpendicular diffusivity is now dependent on $\\Delta$ and $\\delta$, with $D_{\\infty}$ the bulk diffusion constant and $A$ a characteristic coefficient for extra-axonal hindrence.\n", "\n", "Our goal here is to reproduce the Monte Carlo simulations presented in *(De Santis et al, 2016)*, where they investigated the impact of including extra-axonal hindrence through the temporal zeppelin on axonal density and diameter estimation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# AxCaliber model with time-dependent zeppelin" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using Dmipy, we can construct the time-dependent version of AxCaliber by calling `G3TemporalZeppelin` instead of the previously used `G1Ball`. \n", "As before, the Gamma-distributed Gaussian-Phase cylinders are instantiated by first calling the cylinder model, and then using it as input for the GammaDistributed model." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from dmipy.signal_models import cylinder_models, gaussian_models\n", "from dmipy.distributions import distribute_models\n", "\n", "temporal_zeppelin = gaussian_models.G3TemporalZeppelin()\n", "cylinder = cylinder_models.C4CylinderGaussianPhaseApproximation()\n", "gamma_cylinder = distribute_models.DD1GammaDistributed(models=[cylinder])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then put the models together in a MultiCompartmentModel and display the parameters. Note that this model has a lot of parameters." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "OrderedDict([('G3TemporalZeppelin_1_mu', 2),\n", " ('DD1GammaDistributed_1_DD1Gamma_1_beta', 1),\n", " ('G3TemporalZeppelin_1_lambda_inf', 1),\n", " ('DD1GammaDistributed_1_C4CylinderGaussianPhaseApproximation_1_lambda_par',\n", " 1),\n", " ('DD1GammaDistributed_1_C4CylinderGaussianPhaseApproximation_1_mu',\n", " 2),\n", " ('G3TemporalZeppelin_1_A', 1),\n", " ('DD1GammaDistributed_1_DD1Gamma_1_alpha', 1),\n", " ('G3TemporalZeppelin_1_lambda_par', 1),\n", " ('partial_volume_0', 1),\n", " ('partial_volume_1', 1)])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from dmipy.core import modeling_framework\n", "temporal_AxCaliber = modeling_framework.MultiCompartmentModel(models=[temporal_zeppelin, gamma_cylinder])\n", "temporal_AxCaliber.parameter_cardinality" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize the model:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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v3jyUl5dj8+bNKCwsRE1NDerr65+5TFP2a3R0NJycnBAXF9fkv6MpyzTm0dfX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\n", "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "temporal_AxCaliber.visualize_model_setup(view=False, cleanup=False, with_parameters=True)\n", "Image('Model Setup.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data we will fit is measured only along 2 gradients perpendicular to the fiber axis (along x and y axis). This means there is no data that provides information to fit parallel diffusivity \"lambda_par\" or the axon orientation \"mu\". \n", "\n", "So first, we make sure that the intra- and extra-axonal orientations are aligned and that their parallel diffusivities are equal by using the set_equal_parameter() :" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "temporal_AxCaliber.set_equal_parameter(\n", " 'G3TemporalZeppelin_1_mu',\n", " 'DD1GammaDistributed_1_C4CylinderGaussianPhaseApproximation_1_mu');\n", "temporal_AxCaliber.set_equal_parameter(\n", " 'G3TemporalZeppelin_1_lambda_par',\n", " 'DD1GammaDistributed_1_C4CylinderGaussianPhaseApproximation_1_lambda_par');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then to not fit these superfluous parameters, we fix the orientation mu along the z-axis and give lambda_par an arbitrary value (it will not affect the results). " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "temporal_AxCaliber.set_fixed_parameter(\n", " 'G3TemporalZeppelin_1_lambda_par', 1.5e-9)\n", "temporal_AxCaliber.set_fixed_parameter(\n", " 'G3TemporalZeppelin_1_mu', [0, 0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that we are now only fitting the volume fractions, the Gamma distribution parameters $\\alpha$ and $\\beta$, the bulk diffusivity $\\lambda_\\infty$ and the coefficient for extra-axonal hindrance $A$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['DD1GammaDistributed_1_DD1Gamma_1_beta',\n", " 'G3TemporalZeppelin_1_lambda_inf',\n", " 'G3TemporalZeppelin_1_A',\n", " 'DD1GammaDistributed_1_DD1Gamma_1_alpha',\n", " 'partial_volume_0',\n", " 'partial_volume_1']" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "temporal_AxCaliber.parameter_names" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Load Monte Carlo simulated data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using Camino, we previously generated a substrate of Gamma-distributed cylinders and simulated the perpendicular acquisition scheme that was used by *(De Santis et al. 2016)*." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from dmipy.data import saved_data\n", "acquisition_scheme, signal = saved_data.de_santis_camino_data()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unlike De Santis et al who simulated STEAM acquistion scheme, we simulate a PGSE scheme considering their parameters: $\\delta = 17$ ms, $\\Delta = 48,60,80,100,120,140,160,180,195$ ms, 4 b-values $(500, 1000, 2000$ and $4000$ $s/mm^2$) and 2 unweighted images for each $\\Delta$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Acquisition scheme summary\n", "\n", "total number of measurements: 54\n", "number of b0 measurements: 18\n", "number of DWI shells: 36\n", "\n", "shell_index |# of DWIs |bvalue [s/mm^2] |gradient strength [mT/m] |delta [ms] |Delta[ms] |TE[ms]\n", "0 |2 |0 |0 |17.0 |48.0 |83.0 \n", "1 |1 |500 |23 |17.0 |48.0 |83.0 \n", "2 |1 |999 |33 |17.0 |48.0 |83.0 \n", "3 |1 |2000 |47 |17.0 |48.0 |83.0 \n", "4 |1 |3999 |67 |17.0 |48.0 |83.0 \n", "5 |2 |0 |0 |17.0 |60.0 |95.0 \n", "6 |1 |500 |21 |17.0 |60.0 |95.0 \n", "7 |1 |1000 |29 |17.0 |60.0 |95.0 \n", "8 |1 |2000 |42 |17.0 |60.0 |95.0 \n", "9 |1 |4000 |59 |17.0 |60.0 |95.0 \n", "10 |2 |0 |0 |17.0 |80.0 |115.0\n", "11 |1 |500 |18 |17.0 |80.0 |115.0\n", "12 |1 |1000 |25 |17.0 |80.0 |115.0\n", "13 |1 |2000 |36 |17.0 |80.0 |115.0\n", "14 |1 |4000 |51 |17.0 |80.0 |115.0\n", "15 |2 |0 |0 |17.0 |100.0 |135.0\n", "16 |1 |499 |16 |17.0 |100.0 |135.0\n", "17 |1 |1000 |22 |17.0 |100.0 |135.0\n", "18 |1 |1999 |32 |17.0 |100.0 |135.0\n", "19 |1 |4000 |45 |17.0 |100.0 |135.0\n", "20 |2 |0 |0 |17.0 |120.0 |155.0\n", "21 |1 |499 |14 |17.0 |120.0 |155.0\n", "22 |1 |1000 |20 |17.0 |120.0 |155.0\n", "23 |1 |1999 |29 |17.0 |120.0 |155.0\n", "24 |1 |4000 |41 |17.0 |120.0 |155.0\n", "25 |2 |0 |0 |17.0 |140.0 |175.0\n", "26 |1 |500 |13 |17.0 |140.0 |175.0\n", "27 |1 |999 |18 |17.0 |140.0 |175.0\n", "28 |1 |2000 |26 |17.0 |140.0 |175.0\n", "29 |1 |3999 |37 |17.0 |140.0 |175.0\n", "30 |2 |0 |0 |17.0 |160.0 |195.0\n", "31 |1 |500 |12 |17.0 |160.0 |195.0\n", "32 |1 |1000 |17 |17.0 |160.0 |195.0\n", "33 |1 |2000 |25 |17.0 |160.0 |195.0\n", "34 |1 |4000 |35 |17.0 |160.0 |195.0\n", "35 |2 |0 |0 |17.0 |180.0 |215.0\n", "36 |1 |500 |11 |17.0 |180.0 |215.0\n", "37 |1 |1000 |16 |17.0 |180.0 |215.0\n", "38 |1 |2000 |23 |17.0 |180.0 |215.0\n", "39 |1 |4000 |33 |17.0 |180.0 |215.0\n", "40 |2 |0 |0 |17.0 |195.0 |230.0\n", "41 |1 |500 |11 |17.0 |195.0 |230.0\n", "42 |1 |1000 |15 |17.0 |195.0 |230.0\n", "43 |1 |2000 |22 |17.0 |195.0 |230.0\n", "44 |1 |4000 |31 |17.0 |195.0 |230.0\n" ] } ], "source": [ "acquisition_scheme.print_acquisition_info" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To estimate the robustness of the model's parameter estimates, we simulate 20 Rician noise instances on the data at SNR=30." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Fit time-dependent AxCaliber model to simulated data" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using parallel processing with 8 workers.\n", "Setup MIX optimizer in 6.103515625e-05 seconds\n", "Fitting of 50 voxels complete in 551.341907024 seconds.\n", "Average of 11.0268381405 seconds per voxel.\n" ] } ], "source": [ "temporal_AxCaliber_fit = temporal_AxCaliber.fit(\n", " acquisition_scheme, signal, solver='mix', \n", " maxiter=100)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "A_s = temporal_AxCaliber_fit.fitted_parameters['G3TemporalZeppelin_1_A']\n", "fr_s = temporal_AxCaliber_fit.fitted_parameters['partial_volume_0']\n", "D_inf_s = temporal_AxCaliber_fit.fitted_parameters['G3TemporalZeppelin_1_lambda_inf']\n", "alpha_s = temporal_AxCaliber_fit.fitted_parameters['DD1GammaDistributed_1_DD1Gamma_1_alpha']\n", "beta_s = temporal_AxCaliber_fit.fitted_parameters['DD1GammaDistributed_1_DD1Gamma_1_beta']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Visualize fitted parameters" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from scipy import stats\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "A_kernel = stats.gaussian_kde(A_s)\n", "D_inf_kernel = stats.gaussian_kde(D_inf_s)\n", "AD_s = 2 * alpha_s * beta_s\n", "AD_kernel = stats.gaussian_kde(AD_s)\n", "fr_kernel = stats.gaussian_kde(fr_s)\n", "\n", "ind_A = np.linspace(A_s.min(), A_s.max(), 50)\n", "ind_D_inf = np.linspace(D_inf_s.min(), D_inf_s.max(), 50)\n", "ind_AD = np.linspace(AD_s.min(), AD_s.max(), 50)\n", "ind_fr = np.linspace(fr_s.min(), fr_s.max(), 50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the gaussian_kde function to show the distribution of the fitted parameters. For each figure, the red vertical line is the ground truth while the green vertical one represents the mean value of the estimated parameter." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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syJEjR3jhhRfw9vbmj3/840XH3ph9uuEoLUL8uKZ7xXeW9c1NfaN4fPFOPvox\nwZJDBSpMDiJyM3BzsaK/ikhqqd0CgKsAG4Jaw+6//342bdrElClTSEtL45FHHjk/1qE8vXr14p13\n3uFvf/sbn332GcOHD+edd95h8ODBJfZ79dVX6dq1K2+++SYzZ84kNDSUHj168Itf/KKWr8jR5rB8\n+XIeeOABxo4dS9OmTXnwwQfLXFdBQUG5U2rMmzePESNG0LJly3KPX1RUxNNPP018fDxhYWGMGzeO\nJ598kpCQkNq4nEYhMyefb/ak8NNB7fD19szmxOoI8fdhTO/WLNyaxF/H9iDElhEtQyqqcxORe4Gp\nzpcDgN3AmVK75TnLH1fVOp20JDY2VuPi4srdtmvXLi655JK6DMcYl9Wnv8/PNh7loY+38Okvr2BA\ne9fm3xz23jAAVkxeUTNBDHMcjxU1dDynjUfSuOW1H3hy/KX89LJ2NXpsTyYiG1Q19kL7VZguVfVN\n4E3nwb4F7lfVXTUXojHG0y3ckkR000D6tW14VS/92jalW2QT5q0/0qiSg6tcuk9U1WssMRjTuKSd\nyeO7fScY07s1Xl71d2xDRUSEiYPasvVoOjuS0t0djseprM3hfuA/qprqfF4ZVdXXazY0Y4w7Ldlx\njIIiZWyfijtC1Hfj+0Xz9692M+/HBP42zvVpaBqDylphXgHigFTn88ooYMnBmAZk4ZYkOrQIpmdU\n+bPlNgRNg/y4rmcrFmxJ4q9jetSLle3qSoW/CVX1OjdvkvN5ZQ+Pm5vABrcYT1Rf/i5TMnJYc/Ak\nY3u3rtfTZbhifP9o0rPzWbHH1pgurkGmSV9fX7Kzs90dhjFlZGdn4+vr+dNdf7ktGVUadJXSOVd1\nbkF4sB9fbE50dygexdU1pK9yjns497qFiMwRkc0i8pyIeNRfe0REBImJiZw9e7befFMzDZuqcvbs\nWRITEyudpsRTLNyaTPdWTerVUqDV5ePtxdg+USzblUJGTr67w/EYro78eAbHEqHzna9fAkYAn+NY\n1yEX+FNNB1dd50bbJiUlkZ9v/9jGM/j6+hIZGVnhinee4mjaWTbEp/Hw6MazEvDNfaN474fDLNl2\njNvr8XoVNcnV5NANeBTOL/YzHpiiqvNEZD2OxHDB5CAibXHMwdQKKAJmq+pLItIc+AjHtOCHgdtV\n1fUJ/ssRGhrq8f8JjfFEi7cmA9TLpUCrq2/bprQPD+KLzYmWHJxcbXPwA87NAjcYR1JZ7Hy9F3D1\nr6gA+L2qXgJcDvxKRHrgWCBouap2wbEmxB9cPJ4xpoYt3JpEnzZhtA8PdncodUZEGNc3mjUHT3Is\n3fUJLxsyV5PDbuA65/OfAWvVpIoWAAAgAElEQVRU9dwUnVGAS8tsqWqyqm50Ps8EdgHROOZwOreQ\n8fvAOBfjMsbUoIOpWWxPzGgUDdGljesXjSos2GIN0+B6cngMeNA58d5PKbna23XApqqeWERigH7A\nOiBSVZPBkUCAclvsRGSqiMSJSFxqauk5AI0xF2uRs0rpxkZUpXROhxbB9GnblM83Jbk7FI/g6vQZ\nC4BLgGlAL1X9qtjmNcATVTmpiITgWF3ud6rq8nTfqjpbVWNVNbaimTmNMdWjqizYksSgmOa0Dgt0\ndzhuMa5vFLuSM9hzrPK1SxoDl8c5qOpBVf209FKhzg/sta4ex9nt9VPgQ1X9zFl8XERaO7e3Bmw0\nijF1bM/xTPanZDG2T+O7azhnTO8ovL3Exjzgem8lRCQAuBpog2Mdh+JcmltJHEMt3wZ2qerzxTYt\nAO7CUV11F//rMmuMqSMLtyThJXD9pY03ObRs4s+Qzi1YsDmJh6/t1iAnHHSVS8lBRIYAnwEVrQPp\n6txKg4E7gG0istlZ9iccSeFjEfkFcAT4iStxGWNqhqqyaGsyV3ZqQYsQf3eH41bj+0Xzu482s/7w\nKS7rGO7ucNzG1TuHl4EDwChgp6pWa2SZqq6m4iVHR1TnmMaYi7cjKYP4k2f55dBO7g7F7Ub1iCTQ\n15svNic16uTgaptDN2CWqm6pbmIwxniuRVuT8fYSRvds5e5Q3C7Y34fRPSNZvDWJ3IKyy9U2Fq4m\nh604RjUbYxoYVeXLbckM7tyCZsF+7g7HI9zcL5qMnAJW7Gm8XeZdTQ6/xDHOYWhtBmOMqXvbEzM4\ncuosYxpxQ3Rp52dq3dR4ey252uawFAgCvhGRfKDM2ARV9fypJo0xZSzaloSPl3Btz0h3h+Ixzs3U\nOufHI2Tk5BMa4FETT9cJV5PDqzh6JBljGhBVZfFWR5VS0yCrUipubB/HTK1Ldxzn1gFt3B1OnXMp\nOajqrFqOwxjjBtsS0zmals1vRnRxdygep3+7pkQ3DWTR1qRGmRyqtBKciDRzLvzzUxFp5iwLEJEG\nuaKcMQ3d4q3J+HoLo3tYf5PSRIQxvVvz3b4TpJ3Jc3c4dc7VleB8ROQZ4CiwEvgX0MG5+VPgkdoJ\nzxhTW84NfBvcuQVhQY2vTt0VY/tEUVCkfL3jmLtDqXOufuN/ArgXeADoSMmBbPOBsTUclzGmlm09\nmk7i6WxutF5KFeoZFUpMeBALtza+mVpdTQ53An9Q1XeBhFLbDuBIGMaYemTxNkeV0rVWpVQhEWFs\nnyjWHDhJamauu8OpU64mh6Y4kkB5/ADvmgnHGFMXzvVSuqpLS6tSuoAxvaMoUvhqe7K7Q6lTriaH\n7ThWayvP9cDGmgnHGFMXtjirlG6wKqUL6taqCV0jQ1i0pXElB1fHOTwOfCoigcB/cIx56Csi44H7\ngJtqKT5jTC1YvDUJX29hVA8b+OaKMb2jeH7pXpLTsxvNQkiurgQ3H8fyoCOBr3A0SL8FTAbuUNWv\naytAY0zNcsyldIyru7QkLNCqlFwxxrls6uKtjefuoSorwX2sqjFAd2AI0ANop6of11JsxphasDnh\ntKOXUiNcJ7q6OrYMoWdUKAstOVRMVfeq6g+qultVbUoNY+qZxVuT8fP2YqRVKVXJ2D5RbEk4TcKp\ns+4OpU5U2OYgIjOrciBVfeziwzHG1KaiIsf03Fd3bdEoJ5O7GDde2pqnvtrNwq1J3D+ss7vDqXWV\nNUj/utTrQBwzswJkASHO52edD0sOxni4jUfSSErP4eHrurk7lHqnbfMg+rVryqItyY0iOVRYraSq\nLc89cPRGSgF+DgSpaiiORHGHs7yibq7GGA8yf3MSAb5eNvCtmsb0jmJncgYHUrPcHUqtc7XN4WXg\nSVWdo6o5AKqao6ofAk/hmNLbGOPB8guLWLwtmZGXRBLs72ovdlPcjZe2RoRGMebB1eTQC6hocpFE\n4JKaCccYU1tW7z/BqTN53Nw32t2h1FutwgIYGNOchVuTaOj9cVxNDnuBh0TEv3ihiAQADwF7ajow\nY0zNWrA5ibBAX4Z2benuUOq1sX2i2J+Sxe5jme4OpVa5mhx+DVwOHBWROSLyoojMwTEJ3+XAb2or\nQGPMxcvOK+TrHce44dJW+PnY8isX4/perfASWNTAZ2p1dYT0KqAL8C7QGhjt/Pku0MW53RjjoZbt\nOs7ZvEJu6mNVSherRYg/gzu3YNHW5AZdteRyq5SqJgPTazEWY0wtmb85iVahAQzq0NzdoTQIY3tH\nMf3TrWxLTKd3m6buDqdW2P2lMQ3c6bN5rNybwtg+rfH2kgu/wVzQ6J6t8PUWFjXg6TQsORjTwC3Z\nfoz8QrVeSjUoLMiXq7u0ZNGWJIqKGmbVUp0mBxF5R0RSRGR7sbJZIpIoIpudjxvqMiZjGrr5m5Po\n2CKYnlGh7g6lQRnTpzVJ6TlsPJLm7lBqRV3fObwHXFdO+Quq2tf5+LKOYzKmwTqWnsPaQye5qW8U\nIlalVJNGXhKJv49Xg61acik5iEiNLAPq7NV0qiaOZYy5sEVbk1CFm/pEuTuUBqdJgC/Du0ewaGsy\nhQ2wasnVO4dEEXlGRGprJPQDIrLVWe3UrJbOYUyjM39zEr3bhNGxZciFdzZVNqZ3FCeycll38KS7\nQ6lxriaHfwK3AdtFZJ2ITBWRmqrAfB3oBPQFkoHnKtrRed44EYlLTU2todMb0zAdSM1iW2K63TXU\nouHdIwjy826QiwC5OgjuEVXtCIzCMVXG80CyiHwoIiMvJgBVPa6qhapaBLwJDKpk39mqGquqsS1b\n2hQAxlRmweYkRBzTPZjaEejnzchLIvlqezL5hUXuDqdGValBWlW/UdU7gVY4ptToBnwtIoedvY6q\n/FcoIsXXKhwPbK9oX2OMa1SVBVuSuKJjOJGhAe4Op0Eb2yeK02fzWb3/hLtDqVHV7a0UC1yNYz3p\nNOA74B5gv4j8vKI3ichcYA3QTUSOisgvgGdEZJuIbAWuAR6sZkzGGKetR9M5dOKMVSnVgau7tqBJ\ngE+Dm8bb5ekzRKQ9MBm4E4gBlgFTgC9UNc/Zo+n/gGeBf5d3DFWdVE7x21UL2RhzIfPWJxDg68UN\nvVtfeGdzUfx9vBndsxVfbz9GTn4vAnxrpHOn27nalfUb4ABwN/AvoKOqjlbVj1U1D0BVC4E5gK1a\nbowbncktYMHmRG68NMrWia4jY/tEkZlbwKq9DaejjKvVSieAG4AOqjpLVeMr2G8z0KFGIjPGVMvi\nrcmcyStk0qC27g6l0biyUzjNgnwbVK8lV5PDK8APWs78tCISIiJXA6hqfiWJwxhTB+auP0LniBAG\ntLchQ3XF19uL6y9tzbKdxzmbV+DucGqEq8nhW6BHBdu6ObcbY9xsz7FMNh05zcSBbW26jDo2pndr\nsvMLWb4rxd2h1AhXk0Nlf2UhwNkaiMUYc5HmrT+Cr7dwS/827g6l0bmsQziRof7M39wwVoirsLeS\ns6poWLGie0Sk9KR5AcCNwLaaD80YUxU5+YV8vimRa3u2onmwn7vDaXS8vYSb+kTx7veHSTuTR7N6\n/m9QWVfWy3AMdANQ4CdA6cq0PGA38HDNh2aMqYqvdxzj9Nl8Jg1s5+5QGq2b+0bz5neHWLwtmZ9f\n3t7d4VyUCquVVPVZVW2pqi2BI8A1514Xe0Sr6ghV3Vh3IRtjyjPvxwTaNg/kyk7h7g6l0eoZFUqX\niBC+2JTo7lAumqtzK3VQ1c21HYwxpnoOnzjDmoMnmRDbFi9bCtRtRIRx/aKJi08j4VT9boqtrM3h\nBmC1qma4sjqbLdJjjPt8FJeAl8BPYm1sg7vd1CeKZ7/ew4ItSfzqms7uDqfaKmtzWARcDvzofK5U\n3GtJgYYxZtyYeia/sIj/xB1lePcIm2TPA7RtHsTAmGZ8vimR+4d1qrddiitLDh1wrK9w7rkxxgN9\nszuFE1m5TLSGaI8xrl80f/58OzuSMugVHebucKqlsgbp+GLzJsVf6FF3IRtjipv34xEiQ/0Z1s3W\nOPEUN17aGl9vqdcN0xUmBxEJqsqjLoM2xjgknc5m5d5UfjKgLT7e1Z2B39S0pkF+DO0awYItSfV2\nfenK/pqygMwqPIwxdWzOuiMoMGGgNUR7mvH9oknJzGXNgfq5vnRlbQ5TcDQ0G2M8UFZuAR+sOcy1\nPSJp29xu3j3NiEsiCPH34YvNiQzp0sLd4VRZhclBVd+rwziMMVU078cjZOQUMG1oJ3eHYsoR4OvN\n9b1a8dX2Yzw+rv4tAmSVlMbUQ7kFhbz53UGu6BhOv3Y2NbenGtcvmqzcApbtOu7uUKqsskFwPwKT\nVXWniKznAlVMqjqopoMzxpRv/qYkjmfk8sxtfdwdiqnE5R0dM7V+sSmJMb3r13relbU57ACyiz23\n9gdjPEBRkfLGqgP0aB3K1fWwLrsxqc8ztVbW5nB3seeT6yQaY8wF/XfncQ6mnuEfk/rV29G3jcm4\nfvVzptYqtzmIQ0uxv0pj6pyq8vrKA7RrHsT1vVq5Oxzjgh6tQ+kaGcKnG4+6O5QqcTk5iMgNIvID\nkAMcA3JE5AcRubHWojPGlLD24Cm2JJxm6tUdbdBbPSEi3B7blk1HTrP3eP0ZEubSX5eI3AcsxDEw\n7rc4Fv75rfP1Aud2Y0wte33lAVqE+HPbAFsGtD4Z3y8aX2/ho/UJ7g7FZa5+9fgTMFtVr1XVN1T1\nM+fPa4E3gT/XXojGGIDtiems2pvKlCEx9a7PfGMXHuLPyEsi+XxTInkFRe4OxyWuJodw4LMKtn0K\nNK+ZcIwxFXlj5QFC/H342WX1p1HT/M/tA9ty6kxevRnz4Gpy+BYYWsG2ocCqmgnHGFOe+JNn+HJb\nMj+7vB1hgb7uDsdUw9VdWtI6LKDeVC1VNgiuR7GXLwNviUg48AWQAkQA44HrgXtcOZmIvAOMAVJU\ntZezrDnwERADHAZuV9W0ql6IMQ3Z6ysO4OPlxS8G29Iq9ZW3l3DbgDa88u1+kk5nE9U00N0hVaqy\nO4ftwDbnYwnQFrgP+AqIc/6c6ixf4uL53gOuK1X2B2C5qnYBljtfG2Octiem81FcAj+7vB0RttJb\nvfaTAW1RhU82eH631spGSF9T0ydT1VUiElOq+GZgmPP5+8AKYEZNn9uY+khVmbVgB82D/PjdyK7u\nDsdcpHbhQQzuHM7HcQk8cE1nvLw8d7hYZSOkV9ZRDJGqmuw8Z7KIRNTReY3xeAu2JBEXn8bTt15q\nbQ0NxO2xbfntvM2sOXiSwZ09d/qT6oyQ9nLXSnAiMlVE4kQkLjU1tS5OaYzbnMkt4Mkvd9G7TRg/\nGWCL+TQUo3u2IizQl3ke3jDt6iA4EZEZIrIfyKdmV4I7LiKtnedpjaOxu1yqOltVY1U1tmVLWy/X\nNGyvfruf4xm5PDK2p0dXP5iqCfD1ZlzfKL7ecYzTZ/PcHU6FXL1z+A2OhuK3AQGeAB4D9uLoYTT1\nImJYANzlfH4XMP8ijmVMg3D4xBne+u4Qt/SLZkB7W6+hobl9YFvyCor4YlOiu0OpkKvJ4V7gEeAZ\n5+svVPVRoCewG+jiykFEZC6wBugmIkdF5BfAU8AoEdkHjHK+NqZRe3zxTny9hRnXd3d3KKYW9IwK\no1d0KB/FHUXVM1dDcDU5dAA2q2ohjmqlpgCqWgS8xv+++VdKVSepamtV9VXVNqr6tqqeVNURqtrF\n+fNUdS7EmIbi2z0pLNuVwq9HdCHSuq42WBNi27IrOYPtiRnuDqVcriaHk0CI8/kRoF+xbc0Azx7N\nYUw9kVdQxN8W7qRDi2DuHhzj7nBMLbqpbzT+Pl58FHfE3aGUy9Xk8D0w0Pl8DjBLRJ4QkUeA53EM\nXjPGXKT3fjjEwRNnmDmmB/4+NrleQxYW6MuNl7bmi01JZObkuzucMlxNDrOA75zPnwTeASbjmLb7\nW+CXNR2YMY3NnmOZPL90L8O7R3BNdxvu0xjceWUMWbkF/CfO80ZMu5QcVHWPqn7jfJ6rqr9V1WhV\nba6qE1S1wu6nxpgLy8ot4Jf/3kCTAF+euvVSd4dj6kjftk0Z0L4Z7685TGGRZzVMV2cQXBsRGSgi\n0bURkDGNjaoy45OtxJ86yyuT+hHRxBqhG5MpgzsQf/Is3+z2rO/YVVkm9JcikgDEA+uAI87uqPfX\nWnTGNALv/XCYxduSeXh0Ny7rGO7ucEwdG90zkqiwAN5ZfcjdoZTg6gjpmcArOGZivRGIdf78CnjZ\nud0YU0Ub4tN4YvEuRl4SyX1Xd3R3OMYNfLy9uPPKGNYcPMmuZM/p1urqncOvgCdVdaqqLlHVjc6f\n9+IYtPar2gvRmIbpZFYuD8zZSOumATx3ex9EbIqMxmriwLYE+nrz7veec/fganIIpOLV3lYCVklq\nTBUUFim/+2gzJ8/k8frPBtiMq41c0yA/bukfzRebkziRlevucADXk8MXwC0VbLsVWFQz4RjTOLy8\nfB/f7TvBozf1pFd0mLvDMR7g7sEx5BUUMWedZwyKq2yZ0BuKvfwKeMa5UE/pZUJ7AtNrL0RjGpYP\n18Xz0vJ93Nq/DRMH2lTcxqFzRBOGdm3Jv9bGM21oJ/x8qtyZtEZVthLcIkBxzMJ6TjQwupx9/w3M\nrcG4jGmQ3ll9iMcW7WR49wieGN/L2hlMCXcPjmHyu+tZvC2J8f3auDWWypKDrWRuTA16fcUBnl6y\nm+t6tuLlSf3c/s3QeJ6ru7SkU8tg3l59iHF9o9365aGyZULj6zIQYxoqVeWl5ft4cdk+buoTxfO3\n98HH2xKDKcvLS7h7cAf+8sV24uLTGBjT3H2xuLqjiPiIyAQR+YeIfOj8ebuIVHb3YUyjpqo8+/Ue\nXly2j9sGtOGFCX0tMZhK3dI/mrBAX7d3a3V1EFwEEIejXeFGoKPz5zxgvYjYmp3GlKKqPL54F6+t\nOMBPL2vHM7f2xtuW+zQXEOTnw8RBbVmy/RiHTpxxWxyufoV5HggHLlPVjqp6hap2BC5zlj9fWwEa\nUx+dyMplynvreXv1Ie4eHMMT43rZOtDGZb8Y0gE/Hy/+sXyf22JwNTncAMxQ1fXFC52v/4jjLsIY\nA6zYk8J1L37H9wdOMmtsD2aO6WG9kkyVRDQJ4I7L2/PF5kT2p2S5JQZXk4M/kFnBtkzAr2bCMab+\nyi0o5LGFO5n87nqaB/uy4IHBTB7cwRKDqZZpQzsR4OvNy266e3A1OawFZohIcPFC5+sZzu3GNFr7\njmcy7tUfeOf7Q9x1RXsWPDCE7q1C3R2WqcfCQ/y568oYFm5NYu/xir6b1x5Xk8PvcYyEThCReSLy\nkojMBRKAHs7txjQ6OfmFvL7iAGNfWc3xjBzeviuWR2/uRYCvLfFpLt7UqzoS5OvNi8v21vm5XeqG\nqqqbRaQL8P9wrCXdG0gG3gCeV9UTtReiMZ6nqEj5fFMiz/13D0npOYy8JIInx19KRKjNQWlqTrNg\nP6YM6cA/vtnPzqQMekTV3d3oBZODiPgCg4BDqvqH2g/JGM+2et8JnvxyFzuTM+gVHcr/3d6HKzu1\ncHdYpoG6Z0hH3vvhMC8u28vsO2Pr7Lyu3DkUAt/g6LGUVLvhGOO5tiem88zXe1i1N5XopoG8NLEv\nY3tHWRdVU6vCgny5Z0hHXli2l21H07m0Td3M4nvB5KCqRSKyD4isg3iM8ShFRcrKvam8+d1Bfjhw\nkrBAX/5y4yXccUV7/H2sXcHUjbuHxPDO94d4cdle3p48sE7O6erUF38GnhaRbaq6rTYDMsYT5OQX\n8sWmRN5afYj9KVm0Cg3gD9d3Z9KgdrYwj6lzoQG+TL26I89+vYfNCafp27ZprZ/T1eTwFxwjoTeL\nSCJwHMd03uep6qAajs2YOncsPYd564/w77XxnMjKo0frUF6Y0IcbL42yWVSNW911ZQxvrz7E80v3\n8sGU2v+4dTU57AC212YgxrhLUZHy3f4TfLg2nuW7UygsUoZ1a8m9V3Xkyk7hNojNeIQQfx/uu7oj\nf/9qN3GHTxFbyzO2utqVdXKtRgGIyGEco60LgQJVrbtmedMopWbm8p8NCcz98QgJp7IJD/bjnqs6\nMGlgO2JaBF/4AMbUsTuuaE/8qbNENKn9LtOVJgcRCcTRSykGx7iG5ap6vBbjucbGTJjaVFSk/HDg\nJHN/PMJ/dx4jv1C5vGNzHh7dndE9I62R2Xi0ID8fnhx/aZ2cq7I1pDsCy3AkhnMyROR2Vf1vbQdm\nTE1Kyczhkw1HmfdjAkdOnaVpkC93XhHDpEHt6BwR4u7wjPE4ld05PAMUAVcBG3AsG/oa8E9qZwlR\nBf4rIgr8U1Vnl95BRKYCUwHatWtXCyGYhkRVWXPgJP9aG8/SnccpKFIu69Cc31/bldE9W9kUF8ZU\norLkcAXwe1X93vl6l4jc5/zZWlWTaziWwaqa5FxYaKmI7FbVVcV3cCaM2QCxsbFa3kGMOZNbwGcb\nj/L+mnj2p2TRLMiXuwfHMHFQOzq1tLsEY1xRWXJoDRwsVXYAEKAVjjaIGqOqSc6fKSLyOY4pO1ZV\n/i5j/udgahYfrInn0w1Hycwt4NLoMP7vJ30Y07u13SUYU0UX6q1UJ9/OnVN/e6lqpvP5tcBjdXFu\nU/+tP3yK11cc4JvdKfh6C2N6R3HnFe3p27apdUM1ppoulBy+FpGCcsqXly5X1YiLiCMS+Nz5H9kH\nmKOqSy7ieKaBKypSvtmdwusrD7AhPo3wYD8eHNmVn17WjpZN/N0dnjH1XmXJ4dG6CkJVDwJ96up8\npv7KLyxiweYk3lh5gH0pWbRpFshjN/fkJwPaEuhnVUfG1JQKk4Oq1llyMOZCCp3rJ7y4bC9H07Lp\n3qoJL03sy42XtsbH26a1MKamuTp9hjFuUVSkLNlxjOeX7mV/ShaXRofx2M09uaZbhLUnGFOLLDkY\nj6SqrNibynP/3cP2xAw6R4Twxs/7M7pnK0sKxtQBSw7G42w9eprHF+3ix8OnaNs8kOd+0odx/aLx\ntkV1jKkzlhyMx0jJzOHZJXv4ZONRmgf58bebezJhYDubKtsYN7DkYNwuJ7+Qd74/xKvf7CevsIip\nV3XkV8M7Expgi+oY4y6WHIzbqCpf7zjGE1/uIuFUNqN6RPLnGy6x6bKN8QCWHIxbHEzN4pEFO/hu\n3wm6Robw719cxpAuLdwdljHGyZKDqVM5+YW89u1+3lh5EH8fL2aN7cHPL29vYxWM8TCWHEydWb7r\nOLMW7iDhVDbj+kbxpxsvqZMVrYwxVWfJwdS6o2lneWzhTv678zidI0KYc+9lXNnJqpCM8WSWHEyt\nySso4u3Vh3h5+T4AZlzXnV8M6WBdU42pByw5mFqx9uBJ/vrFdvalZHFtj0hmju1Bm2ZB7g7LGOMi\nSw6mRp3IyuXJL3fx2cZE2jQL5O27YhlxSaS7wzLGVJElB1MjCgqLmPPjEf7v6z1k5xfywDWd+dU1\nnW0abWPqKUsO5qJ9v/8Ejy7cwd7jWVzZKZzHbu5F5whbq9mY+sySg6m2+JNneGLxLv678zhtmwfy\nxs8HMLpnpM2aakwDYMnBVFlWbgGvfLOfd1YfwsdbeHh0N34xpAMBvlaFZExDYcnBuCw7r5B/r43n\njZUHOHkmj1v6RzPjuu5EhtpANmMaGksO5oJy8guZs+4Ir604wImsXIZ0bsH/G92Nvm2bujs0Y0wt\nseRgKpRbUMjH6xN45dv9HM/I5fKOzXntZ/0Z1KG5u0MzxtQySw6mjNTMXD5af4QP1x0hOT2HgTHN\neGFCX5vywphGpNElhx8OnGDf8SwCfL0I8PXG38f7/PNgPx9aNPGjRYg/vo1sllBVJS4+jQ/WxLNk\nezL5hcqQzi14+tbeXNWlhfVAMqaRaXTJYdHWZOasO1LpPiIQHuxHRJMAIkL9iWwSQLvwIGLCg4lp\nEUSHFsEE+TWMX93JrFy+3H6MD9fGs/tYJk0CfLjj8hh+dnk7OrW0sQrGNFYN4xOuCmaO6cHvR3Ul\np6CInPxC56OI3PxCsnILSM3KJSUjl5TMXFIyckjJzGV7YgYnsnJLHCcy1J+Y8GA6RYTQJSKELhFN\n6BoZQssm/h7/LftgahZLdx5n2a7jbIhPo0ihR+tQnrrlUm7qG9VgEp8xpvoa3adAgK93tfrjn8kt\n4PDJMxw+cZZDJ7I45Py5aEsSGTkF5/cLDfChS2QTOrcMoVNEMJ1ahtCpZQhtmgW6bUGblMwctiem\ns+7QKZbtPM6B1DOAIyH8engXRvWIpGdUqMcnNWNM3Wl0yaG6gv196BkVRs+osBLlqkpqVi77j2ex\nLyWLfSmZ7D2exfLdx/koLu/8fn7eXuerpNo0CyK6aSDRzQKJbhpI22ZBhAb6XPSH89m8AlIycjl4\nIottRzPYlniabYnpHM9w3PX4eAmXdwznjsvbM7JHpM2SaoypkMckBxG5DngJ8AbeUtWn3BySS0TE\n0TbRJIArO5fszXP6bB4HUs9wIDXL8Ug5w4HUM6zae4Ls/MIS+wb5edMsyI/QQF/CAn0IDfAlLNCX\n0EBfvL2EoiKlSKFIFVWlUJX07AJSMnJIzXRUg2XlFhSLCzq0COaKjuH0ig7j0ugwekaHEeLvMf/k\nxhgP5hGfFCLiDbwKjAKOAutFZIGq7nRvZBenaZAfA9r7MaB9sxLlqsqpM3kkns4mMS2bo2nZJKfn\ncDo7j4zsfDKyC4g/eZb07HwycvJRBS8BLxG8vAQvcSSlJgE+RDTx55KoUIY28XcmKX/aNg+iR1So\nJQJjTLV5yqfHIGC/qh4EEJF5wM1AvU4OFRERwkP8CQ/xp3cbG2VsjPE8ntKZPxpIKPb6qLPMGGOM\nG3hKciivJVbL7CQyVUTiRCQuNTW1DsIyxpjGyVOSw1GgbbHXbYCk0jup6mxVjVXV2JYtW9ZZcMYY\n09h4SnJYD3QRkQ4i4gdMBBa4OSZjjGm0PKJBWlULROQB4GscXVnfUdUdbg7LGGMaLY9IDgCq+iXw\npbvjMMYY4znVSsYYY9vhLyMAAAWOSURBVDyIJQdjjDFliGqZHqP1goikAvFuDKEFcMKN53cnu/bG\np7FeNzS8a2+vqhfs7llvk4O7iUicqsa6Ow53sGtvfNfeWK8bGu+1W7WSMcaYMiw5GGOMKcOSQ/XN\ndncAbmTX3vg01uuGRnrt1uZgjDGmDLtzMMYYU4YlB2OMMWVYciiHiFwnIntEZL+I/KGc7S+IyGbn\nY6+InHaW9xWRNSKyQ0S2isiEuo+++qp73cW2h4pIooi8UndR14yLuXYRaSci/xWRXSKyU0Ri6jL2\ni3WR1/6M8+99l4i8LBe7EHodc+Ha24nItyKyyfl/+oZi2/7ofN8eERldt5HXAXWuSWwPxwPHxH8H\ngI6AH7AF6FHJ/r/GMVEgQFegi/N5FJAMNHX3NdX2dRcrewmYA7zi7uupy2sHVgCjnM9DgCB3X1Nd\nXDtwJfC98xjewBpgmLuvqSavHUdj9C+dz3sAh4s93wL4Ax2cx/F29zXV5MPuHMo6v2SpquYB55Ys\nrcgkYC6Aqu5V1X3O50lAClBfFp6o9nUDiMgAIBL4b61GWTuqfe0i0gPwUdWlAKqapapnazvgGnQx\n/+4KBOD4YPUHfIHjtRhrTXPl2hUIdT4P43/rzNz8/9u7m9c6qjCO49/HxqJ7FSWCG7GWQhsERRGz\ncCEiKIigLYhExI0vIFh3LsSV+PIHFBcK3UgpIohvYHUjWLuptcQW0Vqw4lIRXdRaHxdnIjeZFG7u\nmcl06vcDgWRyc/M89yb3N2fOnTnAO5l5NjN/BL5v7u+SYTi0Tb1kaUTcQNlr+Gyd791G+af5oYca\n+zBz3xFxGfAG8ELPNfal5jm/CfgtIt5tDj28FhFbeq22WzP3nplfAp9TRsi/AJ9k5oleq+3WNL2/\nBDwaEWcoV41+dgM/O2qGQ9tUS5Y2dgMHM/P8qjuIuA7YDzyemf90XF9favp+CvgwM3+6wO0vdjW9\nzwF3AXuBWymHKJa6LrBHM/ceETcC2ykrN84Dd0fEYi9V9mOa3vcAb2fm9cB9wP5mZ2gjj9soGQ5t\nUy1Z2tjNxKEVKJOywAfAi5l5uJcK+1HT9x3AMxFxGngdeCwiXumjyJ7U9H4GONocmvgbeA+4pZcq\n+1HT+4PA4eZQ2h/AR8DtvVTZj2l6fwI4AP+NlK6gXIhvI4/bOA096XGxfVD2BE9Rhs8rk1Q71rnd\nNuA0zYmEzbatwCHguaH72My+13x/ifFNSNc851ua21/dfP0W8PTQPW1S748Anzb3cXnzt3//0D11\n2Tsl8Jaaz7dTAiCAHayekD6FE9KXtix7fytLlp4ADmTmckS8HBEPTNx0D2VCanIo+TCwCCxNvPVv\nYdOKr1DZ96jV9J7lEMte4FBEHKe8cLy5edXXqXzeD1Lm1I5TXiiPZeb7m1R6tSl7fx54MiKOUUZN\nS1ksU0YU3wIfU3YIzrd/y3h5+QxJUosjB0lSi+EgSWoxHCRJLYaDJKnFcJAktRgOkqQWw0HqSEQs\nRsSRiPgzIjIirhq6JmlWnucgdSAitgI/U06o2geczcwjw1Ylzc5wkDoQEfdQguHazBzTZauldRkO\nUqWI+AK4c83m+SxrekijZDhIlZrrZ70KXElZ0yIz86thq5LqzA1dgDR2mfl1RFxDWexmTJdply7I\ndytJlSJijnI552+GrkXqiuEg1buZsh7AuuEwsmVDJcDDSlIXdgLngJMrGyJiH/AXJTh+Bx4apjRp\nNoaDVG8XcDIzz01sWwCWgXsvtUVg9P9gOEj1djJxSKlZgH4bBoNGzDkHqd6qcKAEw3eZ+etA9UjV\nHDlIlTJzfs2mBeDoELVIXXHkIHVvF4aDRs4zpCVJLY4cJEkthoMkqcVwkCS1GA6SpBbDQZLUYjhI\nkloMB0lSi+EgSWoxHCRJLf8CO9llkgPOF7cAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('Axonal density', fontsize=15)\n", "plt.plot(ind_fr, fr_kernel(ind_fr))\n", "plt.axvline(fr_s.mean(), c='g', label='mean $f_r$ = '+str(np.round(fr_s.mean(), 2)))\n", "plt.axvline(0.79, c='r', label='true = 0.79')\n", "plt.ylabel('Probability density', fontsize=15)\n", "plt.xlabel('$f_r$', fontsize=15)\n", "plt.legend(fontsize=15, loc=2)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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2cxTu/gHwQYr1d6U1IhERySqxE4WZNQdOBPII5qFIpLGeREQaqFiJwsx6A48C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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('Mean Axon Diameter', fontsize=15)\n", "plt.hist(1e6 * AD_s, normed=True, bins=20)\n", "plt.axvline(1e6 * AD_s.mean(), c='g', label='mean diameter = '+str(np.round(1e6 * AD_s.mean(), 2)))\n", "plt.axvline(0.79, c='r', label='true = 1.7')\n", "plt.ylabel('Probability density', fontsize=15)\n", "plt.xlabel('$f_r$', fontsize=15)\n", "plt.legend(fontsize=15, loc=1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the estimated mean axon diameter either defaults to \"Stick-like\" behavior or finds axon diameter much too large. The mean is therefore mostly outlier driven." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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BoKrPAMOBq0SkGNgHjNBaNl5rfEwkT/3xKM54ciZ/nfgDr/3Z6iuMqS2++OILpk2bBsCS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\nMXWer5XZiEgUTsV1P6ARsB3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nSmJEMGM0xhhzsKB3Cqiqk4HJ5Zbd5fG4ADg3iCGND+Jz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\nryxRGGOM8coShTHGGK/+H40abqYc+wSlAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ind_A*1e12, A_kernel(ind_A)*1e12)\n", "plt.axvline(A_s.mean()*1e12, c='g', label='mean $A$ = '+str(np.round(A_s.mean()*1e12, 2)))\n", "plt.ylabel('Probability density', fontsize=15)\n", "plt.xlabel('A [$mm^2$]', fontsize=15)\n", "plt.title('Characteristic coefficient A', fontsize=15)\n", "plt.legend(fontsize=15)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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NZFjgTSV+Kq5OaskrP6Twyg8b6Nv6hGndTBXg7VxPQy1JGHPyPl60DQFuOCPw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\ncU1ufiGjZ6zi/o9+pX3T2nz5wAAGtrU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('Bulk diffusion constant', fontsize=15)\n", "plt.plot(ind_D_inf*1e9, D_inf_kernel(ind_D_inf)*1e9)\n", "plt.axvline(D_inf_s.mean()*1e9, c='g', label='mean $D_{\\infty}$ = '+str(np.round(D_inf_s.mean()*1e9, 2)))\n", "plt.ylabel('Probability density', fontsize=15)\n", "plt.xlabel('$D_{\\infty}$ [$mm^2/s$]', fontsize=15)\n", "plt.legend(fontsize=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Except for the axon diameter estimation, our results are comparable to De Santis et al results (of the 3rd simulation presented in table 1). Indeed,\n", "the mean of the estmated axonal density $f_r$ is close to the ground truth, however, with this scheme, the axonal diameter is badly estimated.\n", "\n", "As for the characteristic coefficient A, the estimated value is very close to De Santis et al, while its variance is a bit larger. And the mean of the estimated bulk diffision constant $D_{\\infty}$ is 3 times bigger. Further study is needed to explain the differences between De Santis et al's findings and ours." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## References\n", "- Assaf, Yaniv, et al. \"AxCaliber: a method for measuring axon diameter distribution from diffusion MRI.\" Magnetic resonance in medicine 59.6 (2008): 1347-1354.\n", "- Novikov, Dmitry S., et al. \"Revealing mesoscopic structural universality with diffusion.\" Proceedings of the National Academy of Sciences 111.14 (2014): 5088-5093.\n", "- Huang, Susie Y., et al. \"The impact of gradient strength on in vivo diffusion MRI estimates of axon diameter.\" NeuroImage 106 (2015): 464-472.\n", "- Burcaw, Lauren M., Els Fieremans, and Dmitry S. Novikov. \"Mesoscopic structure of neuronal tracts from time-dependent diffusion.\" NeuroImage 114 (2015): 18-37.\n", "- De Santis, Silvia, Derek K. Jones, and Alard Roebroeck. \"Including diffusion time dependence in the extra-axonal space improves in vivo estimates of axonal diameter and density in human white matter.\" NeuroImage 130 (2016): 91-103.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 2 }