{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Ball and Stick" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*(Behrens et al. 2003)* proposed to represent the intra-axonal diffusion as a Stick - a cylinder with zero radius - and the extra-axonal diffusion as a Ball - an isotropic Gaussian compartment.\n", "\n", "\\begin{equation}\n", " E^{\\textrm{Ball and}}_{\\textrm{Sticks}}=\\underbrace{f_h\\overbrace{E_{iso}(\\lambda_{\\textrm{iso}})}^{\\textrm{Ball}}}_{\\textrm{Extra-Axonal}}+ \\sum_{i=1}^{N}\\underbrace{f_{i,r}\\overbrace{E_r(\\boldsymbol{\\mu}_i|\\lambda_\\parallel)}^{\\textrm{Stick}}}_{\\textrm{Intra-Axonal}}\n", "\\end{equation}\n", "\n", "For this first example, we will restrict ourselves to the case where $N$=2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Human Connectome Project Example" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This data slice originates from Subject 100307 of the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.\n" ] } ], "source": [ "from dmipy.data import saved_data\n", "scheme_hcp, data_hcp = saved_data.wu_minn_hcp_coronal_slice()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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3fLqMzz3uJPD69/fQPxv1j/jrM18lXPPGRwEAD964D9f+AV40SNWHhISEDpKn\ncBm0fQ2PvnGIG25xtegbls7i06uep/Cxfej7qUTZjDorZLvSVmMVXNBsGkmb14x6JCtnoNkq0R3s\nrZtolabQ+ZdFQ19NEWfRxfuw1HXbY0p1WI1rlqnTcWY+l3p+HNqwBuolv1MGys+4tuLBXNzsrSsJ\nuZNBRO8CsPCTZFUTTaxi7nSGtiGPKRE8CFNEnotl6JYrUcd6jUDVl8RtSBDmwPSgO/7pFQizKoqL\nCoPj/kI8uIRHd7lk5IMrVwBjdxBvfsn9GGaOwnzfI4cweNgRQoqNSBgmg4Qk1y/w89f+DgDgu+tv\nx9Y3uwngy3edg3ngYbyQkYzCJdAry6iPOEXUxW7G0bNOhfnExhKUf+Dm+yzIP23EKkxD1pXc0KoR\nHYFmINJmKpdmHlNQeKhUDSy08vth9M+5u68fGw6KGpmKS8p40ev44UG0SbsfU1JoNorDCpOLoVEG\nQcpttpcw3+N2mq8r5L4nSFeMYqM9R3IPKIDJIcLSo0JSinMKASRNStkcIUdgc6k4MEW5iag3gUxk\n1JhQr7YHHeV5phqjx9yFHh+z0Asb9j/1jWQTVqg8Oe3P7rgFg2Pu9epZUcQCu1ZqwP1ea69yFuL1\nNz6M/3jOxZalbnDqpdpfk1WMZ864vFAHz6TwISEhoYPkKXionqOv8pGDuHCzc4+LNYI+7ZY/ZQDt\nk2fDJQkZmj5Frcei/IMoU12NKUwryqYcVnsAyKfy2dDXUERy7CykI7WQ5FzcHSgai+472+MxuYis\ntCsl4FbLIIgSCZ84afaWiBWt5DPG0sPu+AenKCwlqpbKBWtg60q//yvnqMfueu76HKC99+TakyVU\nCUlT7S/YJcevo/CHDICW7k0y7arYBKa5O7ebrj6JB0/uAwD0Pldg5eHGX3MbzrHpqYi4BeQX3Qo/\nOEnon5Vr1JKUmiGFORrNAOg97i723z50M4wXgG2GFsqPsTt/c4ZyzVU08ukU5vwFvNCQjIIHLbug\nuVodBHdaNZDx6pGLPjjJkQyZ7IMVBfKPK5u5D/TPMyrvWttI/kxXkZYBcxjWEj+oJpdx8XrBnWOj\n8MBHkmfRyDZWYlzCMQEAR6rHINieHJs8tI50BbgHUtSNYjZhFKrUwPhR93q+1cf8gDux9es1Ro/5\nDwx10FmImYKXisrGaI0XscT2YA7XJ99iZKfdg/rIcBXqqKsQjY/ZbimxtaHkHm7ADYnJN2NCl1zD\n1nCrSo4pmyLkTVTDQf9iYRXqJXcC9TKwdp27oHtPrAAvQKOQwoeEhIQOkqcAhCnQgFuhqyVxp9sp\nTmS6akUthTaWIWdFYTJSZza2ba4YAAAgAElEQVRBNCg1tsJMCHLsrRoQcEmmvUGHky9TkgBE05Au\nuyqy7KezMkeiJtVYKNXEQhDKphxeP2n1Lttjlv6IfGJdJQbOc+md99TmXLwtMggJxXwaC5xQR3Al\nnlgVC7fqePK0v5B6wdjjxzWY+0bSaaoR7ZNEbzInzPf6xOfYQC/cwZkewcza4xTOCLH0m3AWta6X\ncszZFKhcVz2aAxXWlPNclh7bhSzqwXihIBkFuLZXGjvDsNidh5tGTylk112LsXvtDEFMUpLX7cPW\n9JWMQgM6aketilHvYpxHEBc6m3E0W4FDizRrKU/aPBJTHQujUVcM65/ibCEutImrFUAYlMJaDJ/N\notbvGh1WYuvGZ1Hrcbx9PrXhfFlnoW8im0n1IZ9xyG2YUnUsZBsOxNeZLEBKzr2JJNjipqy4qSv8\nFhS/Jsx3uS/bOkxoxi5JoLd0aIHPpozGh1H1SKFYb0MzBsq23As0Y389SlGRVhWgK18ibQjNHvdj\nXLyhwN4/xwsOKXxISEjoIHkKACjL0OxzicbZKiFfb5NPUqNmJe6iKQGbe07BojsxKUiqR1LrTpI8\nCkn86mpyERSxmVQKnOCKvB/PhpBeBtl/viUuPatYa5CAyEOJJyy1FQsmeb/YZJQbUa+EFle5nXDV\nWzPB+5js0+F7iw0G+WPrn2uQzeSL23NRUaKUI/6FqrmTEJUpTzHvQxKcTIhHYAS47kmhV7fekF5I\nKJdvAsW6u+31nEMVJ/6uZiB09WzSFdRtPTLWCFUJZYDyfBvK5ah2uws0PUhQL3cS8vYzn3vyAW9T\nJKMAgHolmpFXYR6Jm21zcfs1X6KYfJmbMgxbQTebzZmwCWOCEKtI40BfopsQwpN4dBp3wpb2C5wL\nLccR2rqNPJAmpygDTxIyRIamd9Gi8PJqNiPXbAQXXrQDabItE0KAaqxC6Y6ivvH+uQa9c5U/L4pG\nvBGagQ7HH5cGW7ACOMqnMIkRjKXZQp7FRufbdAfhyDRqQm/N7XR4uhsGtoZjsZuCodQVkHvjWGwx\n2DdKNSWhHgs5LdbUCL9FTjCejdoMGPNDLt4oPoMXDFL4kJCQ0EHyFABQUQTxz3iwKll0dBM5aApG\nlYVc3E5dS7acqDv+rIWuuoNYY7c/cAGs6CaS4cBTUKY7cDUQe5iDK8uRQIibtnQZb4KA0islqZqF\nWxENvLVah05H1iK4YnOFesnrVjZAueZDmIlFsV7LNiO5tVoPyhYqUJgd1dq/zqXvw63A4ulcKlxz\nKUyB4BJoFu9MV4BMgpLtOeoKZSXEs2wLUJ7rkU8Zg/NtOUemTpFFSEDaHMFrsLqrtcleL1PPCdlW\nxFR7gSAZBQA87IdSIiyQtb9jNIDESa2513pOkVSZkIjmq+J46YWLswGXmc/D6DRhQ9qoSSl2j1nJ\n+zbvknyC22zEuJCRG58YnTxFKMtFYQKIglZCNhfxVbfvtqxow4Naj7IgD7d1RYbpfrfN4BSjf8Eb\nl4bF74xCq3qkgnF0ylHtRZdjLuYWsbxai6Yn8yx0JcaRWQhg4K4mRXDpKxvmVnbUqCJ5OLIcKgj5\n1HZKtjYSdG0rL6qRBrBqiQKjsVph2EIsvV1xN5A6E1FNX0BI4UNCQkIHO9pTUAPPd82zsBroCh1X\nvCXeqFoy9pqcvh/gPIj5IV/33tTonfWuZiTyaXoqaBzGg15dFUDq6mGq0oxFrIWi/gIlrc2mFI8j\nW8gq2luPNd27Cbmg0WicKw8AdUTsATOU8VOnKFJDqjlMo8qnHEbgles2eBxkOLQVOy9AqNwdIZn2\n2kYkK4o6KVkTFstKjiHqKI1VrZqIQMWhtyLqlbCRZxQlaB0JTcbMUTvDYhFpNOYUKOdNj8JovPb3\nAVxVqlr21ZYb17DUc52RmbK4eZdTYfqTv771KadvbWfsaKPQgosMC68sVI27nP8AQhgcYjMxENWS\nhRq4O50nukNACvuP3Omm3212akt98aAU05PwwQ1lEXZdyFNEoqdgecCaaEiMrrtlPBVJiQViT0nh\ngadoHgTnIhKrFzb0HTAhqEItljVWHpFQxfQjQlFUUo0f5pYd2PRUqBqoGuGBbEoVzY+QXIk7bn8M\nnTFzYjhiPYjOAJtMBtvomQFnLQWVAyvU5lJ1MrkQonQd7ycqkdYyPm/z9Aib7FlNDGxc4WKMYu8U\na9e7ppddH8MLBil8SEhI6GBHewpcu2XIjsqQQIqnG7uOQ/faZgiJJbKSYbbLDfQp9+HBSYV8sw0B\nJIuuK/a1bD+l2bvlJoeEADNJkXc6EXPuuNkmrsNHnIWYKKUbed0eQzVS4bzKDUDbJyc4m4FGM3Qb\nqYqRzdzyutgl4dXmEQV+leN+b54YIp96IZPH61ChcAk5cddbLsD6DcDo1vPh+Dc+5cRsVh6yUBNJ\nyrZJXzLd6kxQbYrCEygCRXTsFnpuRUUqi+fSiQfEGTqhXKCTR9yQlkfi9kNoeu21peA99R/PRQXL\nANVjbhxYddMc517tfteVB28FffyuJx3ndsSONgpq5PodmlyFKca45P4SAgywuM6lqrPcgP0fDu3e\nwKl118Mft9myAsxl+iPimQLKCNlGmchVpm6WXOJnMVhxcxRYsuXaSnzuYmP3/tpLgF03uQfy9NoQ\n5edcUmT350zU/szSKq79vEq///Yh6Z9l2D9rZyswii0vKpsRVKvZoAhk3PfOVjNc+Cp33b7/5R/F\n9eVpdzxmgJ964O1Puj7ZzAZDxkpCm06buY3Fb/0oOLSNZE82EDGRrOlH4QlHzU6FAuVtyMChPFyN\nJSTUlbA89SJiN2boEqvaismpEs2yO+jJFT2MnnRk2xMpfEhISOhgR3sKWHWjoM/f0sPG9c6il+d0\nmO9AhqEXwofnqbtcNWlQ6ZaPk6dXwgDSmPgU1+qZIgrtQiY+O0KUe9/khDxSR2pX+5ie3Nm+kPd1\nxUCQQucOx6GtSmRXbeFdNzuh0VPNMv7r4dcCAO5evQZLDzkCxvIjdZjsZAsVOP/KMEpP2hmeMoHs\nxCTeRL4lWdm6r3HuZe5aXfnmx/GdB53b3KMac3bf9e/ufgtW75Ssfvu9HE+atoy6L95KG8LYnDor\nc+v2m5IkwRtpQKqGgdAnYiNeg0K7LppS6OfVSJK18XWOR+/pSngrNpfOV1NImJNvEci7Im1V54WA\nHW0U7LIrSdoCUFUUq7esOxLiUL4J9P/G/cCmjARXDUK+QC8ulVrrSqABzjUNo98gZTM9s10tgEgA\nNpCI+qqT74hzFjYeMFO1Lq7oAuSfHuNHl78BAPD2K+7C1+1zD+rXfPXdeM+JVwMAHr7nCiw/4O70\n8fEGpe9fqJdy6SmIypyAhEKbV5bYOuzeH77+LL7m4EMAgG9c+TQeqNx4tZeUJ/HvT3wVAKD8+Bjt\nk5dPDJq2zyJqXqKIpFRHQ3E4Gt9WblhhZBqC8UbE/b0tbSLkcWwWEZN6CMYultJrCU2Aqw7p+ZMf\naNNT4Zhqog6RLLTJs1SwFksKSwfcdWhOnX7S/rYTUviQkJDQwY72FKpVl2ybXGmDW64XwrcvInHU\nWN0onzAKr9XH1BUjCeBLxFfaLskiVmoCQnfdWCP3nYjUMAhtDZ9Qjb2ak5Ewwc10iDj8VlzooGto\nxZXd/dkG5/RBAMCj3/gEbhvLTMjvuOITAIDT+5fxiVdeCwC458RB0MMuEbtyP9A/73bkwhGhAE8O\nevGSaxvcdJOTNP+2Q59Ej5zLNFYVet59erA6gLv+8CYAwJ6HmhBiVSMtPRFRgrXYtMFFz6c2VDEo\n4mXYjDDdm4X3Wy+gHqLjtXW1Lf1bBkFQVy8Y2VT4IPE1tLvd0p8tRPyGKaJak3iXs31R3GhdCAEA\ngzM1uG6luyj0ZWxH7GijMN3nTn9w3To2z7sHwF4sAjPvUvLS5dxC3UjIECYn+21aJR8nKxZVGaKb\nMow8L4HKNxH1LoqKkRvZ3lYuur0S2jPzTE5hpgKxhCe6YmTzVkiWMXrCffZDj9+IA9e7suL1vVOI\nGfpfu/duAMA/3HcXzr7UVRn+0+1fidU73LFtHtEdEhHf5hIwN+26iIdOORXjHzv5dTAbbq/lGY1s\n4o6n2GDsfbxlgEmFhSwHQVeOSob1QCFr5zVkhHLTt2yPuo1VQZfBcAi1srnkHZo+hJhURMSwOEdT\nyjyOZiBEplgUt7LdxqfAwiTJZfTPsPs83KAa094zhJDXoCwH160K7fbDjjYKCX83nBjtwj0/8wPd\nN3/mi/+9Jwe7vvhfkhCwY42CGo9RbLZTgxpM+849pqYIakvNQFprWUVc/Uhe3WgKHgFZ4cebgkKt\nW89kRbKZUHRtLC6qJWyZ7ZFeiZhv39EizGU4ra44ElbhkFRreuTUlwDYnJH7mn//D5bwa1e/2W1/\n8yaU5z9P1/tQuQ9hFLBnl4uRsg13PP/obT+CtRtUCEkGpxhnb3P/uOmG43jwr68CAIyPAuMn3H6K\ntSqMwOOMoD0hyhYyf6EZqNBnYSLatY2Uqdxv0HIZpNfDTakyYT9tm3PTk+ucTz1RDEAzBBZLUikI\n+9ZANpWQIfNU98VuRD0RHKjNXEtvi2oiAd5KfmsyAPvvqIca0C+MFN6OMwqUu19Jre4KsfrWrMR1\n+88BAB4+eSX6p0VbIYwkh2Tate3eUNLwE21r0Cklxm6/6C9EugwZofEzJg0hhDD1kMJYumwhoQEZ\nlrg3IkTFbDxlgNwrKbnSnTcKZy12fc4/eB/OgxrSfEVj67A7Mb0Ami0/v2DNivrzzVMYX5pdeVDj\n4J+7zx594mqUngDWv2DFRc+UGLN4jJ2m0JikahGkbf8GeJ2C1hAshOmoFyIb1/QJTV+qDLF2QtvI\nBMh1VhVDtYSx2o0GBIB6JHMcVOWOCQDKC8DWEck1tEpQWhGakf/svhr6orsm/dMKtRcHr1YN9FbL\nzmRQ3+WwaFFt6/DhhWG6EhISnjPsOE9BDZ21bg6sYPOws4nzk0M8Uvkk3zWb2Fpy/AW9lqFYl+Rh\nS4WORTuYKCSikIt3oKNat6MJS79DSBxy17tok1XT/YSZY05jcDLyFKZWFKLQDSfaWn3TV4E/pSvh\nPuiFgZ64JB8x0AzdQZtCpOh7F0ykp4gw/6Ja0jLzAoDquYOuxrkoF00hIc/CikJUROjSsybqMpRR\nbtnEdFZ7GyXn2nOphip0qapG5lnohXAWbDS8Vxlg7idlL3YRijW5zkH2vudWcwDQ4xrNxFcxFgr1\nit//VKG84K9J4UIIAGhGDOOFVXbt2cQ/ee1HAQB/dv4m3H3iEAAgB1ANnOe1ebjA0n3uvqLNTWxn\n7DijAO0JSL0stEhnD2uo+90PtnmNxVUvc/3wzWGFixNnRFZH07CLUxeWYE+494sLkqkGRS4rSWtt\nuS6MwDhOZk3B1ZzvJjQDX4Y0Et8CUqHQpYqk2SSvAZLRcqwQKQURdNRoZQbOEOh5A1W5h8GUKsT5\neS1sxXqsMT2Q+eMExn70W/7BPgZn3fb901uYHnLXYb6ayfTtuQ15DTCgFj6PUOpg1LKpCdWTZpgh\n32rnQchAHWLJ/IMlL0AmyqdEDE5TRuxP+BkVAKaHLCqfqxycUJJfGDPIhwlmM8dgr7shbthzDkeG\nbtzbWt3HX953o/vsgwWoVeUmWRgunhvjXVtvAQDs372B5ZH74rWNAW651olP3GuuxMGP+tBVxxLb\n2w8pfEhISOhgx3kK5NWWpvuLy4qglucUHnvE+e79PVOM+i5meOnuk1jxon8PDffiU5NrAAD6VBG0\nAN0XuP8tdgHVLrdszfcgjIVz8wLc6133M0rv1q7fwDBjvwIfyztCL/EQ27aCoGr23P1WUCSqRLR6\nkErmU6iaoRq/Mg/yDpW4/Wxd5rL9grH8iF+9C0I+ca/Xrteolto5cP3glYyOm1CVaNWY3PkS2B+n\nzWQAL1iqJCDC3BOE4kpK06Mwl6HpiYeVTW2gRceUcLCEYLZGNJBWYfMlLvaY3FJBn3bZ43ydMDiu\nw/WZXOHijbuu6GP1ZvcD5GRBE7eNfdUmrtnjOk03Fj00vh1yUWc4uOR4HyvFDK/f5SjeNWvcvelG\ncd9rCM3YeQp5VQfVLzuNb57tgR1nFHjJ+evZ3KLYaNlvkhdQDdB/ws8XPDvGmnYEng81e8I+VEVY\n9k1TxSaHGzGeO9g7j8D24y9fw8LPLOTHhtB1m12PWpLPEMzFlrko77MWF7ozgKTmEN8yUSD5XCr6\nGiTJgMCiU7UVdWYguPSqlrFuzVCHgF41HGZATK6rUa64hMnFbIzeeZ+PWDPIfFNUa1gA3+DUqhhF\nDV8gAvkmoXy9Amv3wFRj3TGCocJipMQYi9PG27hZntF183d3NmXs/bj7x3y3aB/km8JQzBaM4Rn3\nvv2Mxqc/83IAwOYrFhhe6XIAt11xFKveWv/un7we9oi7Dl/zJfeE9//i9I34mbvf6va5pkNkOT5D\noMYLug4H4OkM2xUpfEhISOhgx3kKOOMSSNnBEZrDwplvJyaZEmGoLDUyyo2F8o+OEkvEw9eVBbUD\nYyOFpMnjS+ifcvZ3eFKESchIYrK8ILs0PZFCJ4vgQsdaj1ZTaBmOB96CcfnJ1znB5nK+7Yi3mL/A\nRMGDoEYo0i6R6Y//kRw2d65L/ywHjckn8TJaXcloRScjUu621EGUpRkV4Xj0goNwK1nhBYDQSZrG\nVZvWg8gWDOtf10NJAFfLBN8Bj+EJRjERr6q9zrEorq4YoxNtwrXE1jXuwx964BXon/bh0owxepWL\n/X7u0KfwgydfBQB47NG9KM45d7HYoFCF0guZnYE8B3mPBhsb2G7YcUbBHnH5glOvKzG72lmC4YMF\ncv/bFOscDARf4kcFppqFNNgYmYPYROXCuPFp/KjC0N9kxaaMXTOFctRBuLCl9gai6UdDUC4pW7Z5\nhPgByybysHCnP4IvibdbIlP0vpWcAlkGQ163ZUhbUDAQo2NiyFTUBq4XVvQLLAfylc2V9B305XZz\nn8vlez3brzPnQkXXuebg11ItJUnTE2FbbRjcXs/ajwAEUI85zHe0RYbhca8BMZX9IBrww0oUq8qL\nCEaQLIWydDMgnDjn6pa/t7WEvzc6CgB439ZrQhOUqiMyFbvQBQCKUR+4kMhLCQkJLxDsOE9BTZ2F\nHj/GsJlLbrESUVYn7CkuazydqV05dc0yCZpk+7hPgZW4r6oSohErGbLqhEBbHr6oM9kC4bPxLAOb\nU+jXyCYmqB6ZngpZfV0JKQgRvVpVVnQiC+l0jKdL64UNbrwtVXeVbslChfRrZIuuJmLT02GfnWse\nhRAtP4J1hnrsw5mGQ8dkLEKbzRGSo06dyX1WLQxMT27dQAzrUVBAanqSPG76DOQSCoUwkBFdB3lf\nNdJtCaZAYMsmjOGZNvQA9MxxNH74kW/D1bcdc9dtqYF6wv2Q2ZQjr0o8z2ZlgOxcxKbaZthxRgGN\nb57pI4r3hK0Yi6aanlQT9ALI/fRhE7m4uhZ1I1VxaJ9u+tJmS1YUmW0hrilZeWCspsC9d6Po3Paq\nFk2ETla+rzpVg6CGxAg3dzz4RBkLti2pKWYukjyQWouKkRXDF8PNbnSv8y0jjWGFCn4nK6EiBoKV\nv7bGG45guABXXowqHe0JqJpR+zZkR/ryF7SvQx7ElKozabrYkh6TkI7YD4z3uOrA7ELeSQm1xxdP\nDLcZySCf0hkDAOhfiGdtEvrnvSFeEB5vjrjvj9S3TSGKzzaX/o7eIENebt+Rcil8SEhI6GDHeQrk\nPQW9QGiRjhWKshlL5t9Edf54BWYgn7U1f6ntuzFwbcJMyDPZDN3kmUdcHWj63bkSbR9BNufIne7K\nt8fiorFQrEi227Ciko0SdZZB05Z6nIURck2kg5hPmuhcpNPR5BSum+uJiFbmSJo9lmkn21YoGM1Q\nbrkwhWkh1ZB6pDrTt8PKH43bc0SsmFIt4q4trBaxluICYXrAXVw7tCGp6QRs/DVUJJqaLL+dJpkY\nhmi6tyIEV8T0FJqh/422CDpM644mZRGhGba9JBl62falOu84o8A9d0c3fcCU7Q1H4NbNyyIZNS2Z\nebDkDMhKWOEmOz95PkKxwWJoFtwpJ4ZQIidUo/ZGocDJz7dEULTYtNHxEFhdprIQNR25bfxrpUTt\nx6JTbqRcWnpbw5FFD1UdPby6sqhHOlyTNm63WqN3UeYytOerGgZ59qRihNecqfBaNxyMSDPQIc+S\nzTka00YdA9EeZ0zIIu7mMIIhmER5jBqge138v9htUS27bfJJdz+hn2Iu07SdapbbpthoQshmc4WF\n3898D2D6noi1qSNFKUSt7nJtiRm8NcF2RQofEhISOthxnoL1nsL6DQy77Je2s7nw8CHJIdbCTYgF\nP4FuGNBWEADZprduQ1jhWnqlytC+dt6Kz2zPxe0vNqM6fEmBCGVKQla021sJSbQkylRnMjJ1OAh6\nIcKwYfJVpjrkq7aFGSSUaqslOTrfQ5jtd188fEJBn4lXZKl0hOtECNeWWKZXk7GhfZsVCb16oML5\nZguOKjgW2SSaNhsN5CXbzm5Q4JYSTkJIYw2Z5WEVGk8cqgcyWZssg/z3NiUCwQyRh9UMNOYrzo1Z\n7CIsfOflYp+Iqei5XIemHyWkKw73VXm+RhJu3UYw7Y2YM2jmm3CmFJqa8k2JY+NxZk6d2b20GZC1\nvf1G3ncj25/s3sdqSGQQblyQGBFbxHoNYmiyuagGZ9FMhPb7AEBPug9hIC8ZCg+kzX04AUBbC1X7\n0mDk3ttScgSspD2ZMhmCYnPAlu33qWDgiGUwjClVmJWgDEu79MyEvgg7zML+bSbqSTYTBqeqJZQA\nEPIRpq9lErcRpmA8j8JmktdQjeRB9ByY73HHtnWY0D8j1zk0UBHC/Mksmu5d9xVmez0haiS/1/Ax\nDe1bGfQiOmZCaI1XNaF/3reon9mETeFDQkLCCwU7zlNoXejhYzqsHtkEUUJLRE1sjsAdYEKYC6Ci\nKUAmEnTV0YBTW3T7EVp+vppbtLaYFYHLdlWMxVcgJKWZuNDxTARwdAylUH1tTuBGVtom0h1sOQim\nL8uvWjRAFk9Skq9oQxuTi6Q6LKAW0faXQTyclqYGKiRWhRBFhkHt9Ymmb6ta+kZYye+iDCPbcEuz\nneVoonOolt3BLZZIqjYLDr9j3DHJCjBL7sfYfdMaLnzWdb8OnyBk/kCzqVyHpifJzmwhre66kt8r\n5pLkU9sZb8ej9hiB5Ud96DRfgLzQynYMInacUVBrzm3rnxu5eQDwrnL7QxYi1nrp+PN24AcaSLZf\nUcjwO5fbv38J8SfOkIfxZAuIe59Jr0E+lUy+U3MS3YRW1yCbGDEWpUxSzjeNuNPx2PqMRAcBCMds\n+mXH7W7LkOiEIRyM2sZ1CtjjHs7s4T56F5tw7iFPoaVEyhmBWrblvAmVmnqci9EpVGf0ezBehZIc\nB7Jo3JsW49JEcyhJhWoOWSnxmkJi+6YPZCOvrTAvRGaOJRwwBcLvohdxvsaGbXhNpN+yGYe+kmag\nRTnKuHGD7f7D72E5KIBtR6TwISEhoYMd5ymgcEv54EyDjSN+ivQoap2O+g5UJauHXnB4rRpx6RlR\nz0PkC6qGuyt12yuRRZTahXyWVSw6Kvt3JCUh+bR6iqxc5QBwBB6KstlUtdtz4BvUQyWCIhMDPff7\nyVToLLS59FA4Ulb7XRQ8iH13ANX9bgkuNxrkG9LtF4vBBhp1TjCl74loJLyixsL6iVgml8pLfB11\ntDKDYhUpG143A9WpsBQ+f2cz6YmwOYJXCADZA678oLaA0ZaEJ4EQFc1uyOYckqZk5drGVRXWwGKX\nF3FZVpjvbT0gIT71z1j0zrZsNg3axjMgdpxRsIVvwjEy3qtaZuSbkkUPD38NefjjwS3R7Ia4r8G1\n+raGoHszhaamQpiIqolGyHEksFqqMDfRFMDwjM9ab0ho4I7PP8CV9CDYnpbGp1xHZU4b3HXOFKpd\nOhxzW8ZUDSOb+bgl6gUgI2QnvbAYtjMvDcOWbQWnQX7BNZOoYY56yRkIS1E+AgD5qofKhbnYXiN3\nTtwJDUJZt5BKh6o5VE/IKNiQ+yAxfDOGakSXoX3KWQH5OX+tIsNBi7iNOqr4zKwQ2EgqKaboCsy2\nRme6n7DY541pz2DhK1yLFQVVO2M6NsvQm1vYrti+5iohIeF5wY7zFFozuNiVydSgWhJjagFJIlK3\nZ6Gdg8BEIfHmplT7FSxaXVVNoHa6FIsYaYezEHkQTgGpzX6LgEqsOMRKugtZC48gm1JHLFWOQdzs\nmMjExCg26nAuYZYEkSggrUeDKzIVQol6XKAei9ipioRYKYQ5BqZpwxZEycIcxdqTeRBWE/JFW22R\n83D8hbbVVPbTDKP+CMPQcwnfwspvEGTjyRDIX2gb5ff0PEoiRoQuglSUqrEWD0tFvRKFVKaavmwP\nAtSsbWk3uO3V9wMAlvI5/nj/y9x3/bc+lo5u30TjjjMKzdg9qSYn1E6TFYvDFWjqfqTeKR3mBagG\nnQe4LUGZUh7suCc/LhmaAh2jE+unhhuaJKvPkMpFNrMo1p0bbwsV+gJU5E4zR+FDzaHM6HQfhHwV\nz6QQubE4gBeYHoEa/11zHbQnwCzzIJU8eKwg7dKZikInAbEQtFgjhBuXtlS3BqIe6WgqNEnVxiKo\nP5kiapfOqNMrIQ1aEg7kW9F1jgxrLABrMynBMiG0bDclRQpOgOm3bEUxgkyA3eWMbG9UwU786L3C\n4FPHXEt1c2KAwisyVSOABlGSY5shhQ8JCQkd7DhPoZ1WtHmEsO+1JwEApy6OQccdHzUWXHE0Z/ea\nrAh7qgrRlGeRYG96BNNyH7Sbygy4DPZs1YcYTbxyqkAf1gsrFYeMoCPXIp6A1FYTXA8Fwj7bVdR1\nGco+gyir0oFnYQolLdVgyd43XW5C4F9EVRQVVRBcb0gUUs0qv70On80mkXZjw9BT7wGVOhKwkVWX\nDETfsaTQa1APKVDIe6RU5kwAABjdSURBVBdlLB3r7rGFEI6FG6IMR+GAJD5jKX1lAJqLh1INW06E\neHC6Eo/GVabktTrjPdCyRO6l913o57bpbTn9TwAYnG1gx+5Gya68As0Tx7GdsOOMQttI0z/LmPu4\n90sPH8Mn1q8H4PQFson82HmUJA43RC1EI71gzPa4O6taRof3LhOrKbimqhJXFlE4EOcXAGCx2x3b\nZJ9G5ecaml5kKKqo2WYBDE4LaScWQQ1SaBQTqmQ/rZYC0FZYJGeB0s+qyHUofzYD3VF8Eo0D44wB\ngGaldHMjAD+voXXRCTyWsmV7/G4+RXuY0bFlFPI47rvd682RzLYs12ReZqf3QYvYLEXhiSkoVBZc\nb4V7f7GkgpEqN2wobZKV8NBmFJrEiKWKFBOl4nAyvtSqEiHZea3RO+m/rImavLYJUviQkJDQwY7z\nFKoVt1KpGljfci7czYdPInu5W74fXt+D9akfmjrPYR70k4ItYAtZxUICspEOy7ijT8/ilmpGedF9\nNp/aUEtXtdS940RXNYqEUrRoSWYTCm2/zYhRj31oMDTYvD5STVp3r3ffrVCut8k5yfbXAw3jM/n5\nRhP4FLbQWKx474B64sUYGxKNpidDblESQH7lL3WoUICdIEkLqYCoqOKAkJishhRUn3TFWOxqk46M\n/mm5pm1fQ1d4RqTx65EMmO2dtyFhbCMaNdmon6LmEBoUWyJ4qyJty2KDA3nM9FWYfxF30DrylXiX\nZISo1n7v5EpG438vda+C9XL3+jLJ2ecbO84otA8AAGR3um6V3/jsV6AeeRe3YHDbGpxZ8FjKWu2s\nRz2uMRhKyW52v/Pv+2coYsK5GxMAyg0T4uSYgadm1jGh4G646V53B833MHrn3DbFhsTDgIQzzRZB\n+4rJ7IhFtuzi+eyBQZhhMbmCQmijFzLPoo3NAddHUGw6X7y8GLVgx6rTRR7Gxpm8O6gmVFxYJNvy\ntQXUtI2vCPUuZ2StJug2H9FTaH3rfCrSeE2PsPAzOG3OYTBPMbFB+LQaKzkHRhhRXytg/UZnjLYm\nCrvvyfz+pT+iXJPJ2qxJwsCZiUhKUvVQlYWe+zzIXEMN5JFp51naJdUx4rFwbotsSmhl41hRUKPe\njgKuKXxISEjoYMd5Cu1KPj1AmF7lVoDxA1lwU02p3MwDeNGNNlFkgMZb93qcYVb2wj7bLDQT0Lvg\nXdwtRr7plopsZoTg1IigKEfqQfNlhdn+NksfTU/OIRLsJCGKaoDVz/ql6D6FrYMurtAVi1JTHxFN\nW9SNsjl3eiVqv/oVG3VY4TlXYOXnYmQiGDtbVZhc6Vf4TcLIjTtAsWlCH4Sa1iHpyFG7dFfYVkIk\nk5PoIG4y+JRP/u0mzPa695u+kmRtzYFiHM9xUAtg/0e9jPqa6fSeBFCswSnt7aRVSMSq2obqCRAR\nohrphgRBllSWe6DpdQVd2gRkPZLEpI04LNsRO84otL33zZAxesS97p8TBed8wiE7TYY7zU7V2P2S\nixWpJoDdjRw+22a841FvPR3YeLqyIYRhRSG2r0fismYTcdFNNEJO1ZGbTcB0n1c0mspMClsg5B04\nA7hVrO7JjUtWXG4igIPuQAHyPQvZzHSIQy0mhxk3v+4RAMD9Z/ZhYhwDLJ8qqJHP1/SzaECL6vQL\ntCXPYtMgX3cHUe0qsHXIlx4LYYuWF6NrWIrh4Eyuj55Lo1o862G2Owu/XT6xHeJWW5ZuRnm4nmgo\n5BHIMHRLDFsYWG/gYsUnm8lD7qTx/EJigKaJGJDUsk6lspNvcqiCcT+UqLYNtrG9SkhIeD6w4zyF\n3nm3Oo0fK8NE4/mqjGzrn2GwX0VjAoye27DKlWvyfiw6qmorybk8qv9HXiwrCmxgXdngjjptxZYz\nj0CCAkv1ARAdQVXLfk0pYUU1lj6ObAr0z7ljGx1boFp2K/l8l5YwpI5W11Vx9fVCo1w34dxne33o\ntGRwYe5ckWqRIffzDua7FbK57xqcW9FrLESI1WohhhVrdeivsIUO05/ijso4Iapq8b6aAaB8tj+b\nRZ5U060IBCn6XKF3oR1XR1JJKaUlXEMmaBEDlfeY5is9uSYVo9iUieFhzkXEj9AVh2pI3CZvQCB/\nX5mSUC15Wn3z5J6V5xs7zijkF1z9sH8+x2y3tCe3wzwmh0g4/Azoqu078M1SAMp1G0p9xKKbQEwd\nhl0sbRbPKggyaiT6BcWmCXHmdK8OIQABHUWmuL03fA1LHkHVwrAEIp6/saHK0AyisiJxaMQqjOy/\nWG9CibHp6zByft9fadR/uR8AcHjdAOzyMk4t2l+TRhq69NyGkA2QPMJiV4HmCj+gJRMDoBfdeRbx\n3AdRnabQqmwLhPCmM8MyGpDT9AizPT5vsiXhmxurJ01obZgzW9ZhbBwgxCebU5j1oOrod5nZjlp3\nG7bUuZCd8k0Zw1ctA8Mzfudrm9huSOFDQkJCBzvOU1AbzlMYPqbByvEUpgc0qhWfmd9SHZpqGOXG\ngGqrDDrahmQ1LjdNaHNWjUxztmW34tCGKlVEtsm3ZFBtuWFDBcSUkkTUFUeUW3GnswWj8KPZ8qno\nFJq+JC+r5QJbV7qfe7aX0D8t3yXUXQ6t027QrgirWH9evTqa/lxJa3ac1SetO5RjCa8i2jWArUOe\nQLXJGJ0QslPrPTV96deIB9LGY/7YiPy8rmTKMysJH8qLHF1zBR3mSkhfRtNXXS8vQpD2z4GqPcco\nrGsG0f1ggd76k7s8qyXCYo97PT4KLN193n94+9Gcd5xR4Jn7JfU5hrnRZc6rm2YunQ+ANsvQxAJI\nll7PRc253JChJqyBppT4uYWqGZfKswHOlW3bck1J4aYnI/MpszkHQ0BGstz1QPodshkHl15VNjyo\nea5AfrBExZLxJsshvwBWGPgZBI7V513iKHcRj2xz27Ut2/Lw1ONMiFixtgKkjGdLGX5TrjVBBs70\ndEd5ORynkXFycSmXchUIVNVIyn7ZVK6tqhl23O3lcB+G5FnmIruWb0jIZnMV9ukazLyrH+VoVIVQ\nGbG5k/Fzr4XVms1ERTqfimpTPSKw/yHHTzSguYtFm4tRiWWbIIUPCQkJHew4T8GcPhNejw/tBgBM\n/3qIyeFWOp1QXhD6bTuJON80IshRCJGmKSVjbxXALfFJC2dBLbiToW5XsGYAIRdFqj6sKAxuNVvC\niSAj2oH5xHT4A0LRleQZWUmMmTwPk5f65y1U6wUoIPMj0pThDjfBXkbuHcZIiNHXLUvbzVPw5+7o\nw/66bdjAxbC5ChWTajkL5xhPglK1eArUWJCJ+B2V52XMZS1zXaH+GDJE4quEcq31IKQKQJZDNyQr\nBD5C29XpPiskJV1J9SROPiLqajV9Rr3kPzuLSEoZhdBm9ITF8lF//Y9PAHN5oZvtgB1nFGJkF1x/\n7PKjJUy/bQSSEp3JgWbVZ6R3qzBK3JWj3DaqkRmB7t/+BQFctX4nAgOvGlKQ8bIFQtOOriRu1rWI\nvmaMIEwKlu+N2Xp6jlAKZRUThCxK3zvQlKJQlE+MqCdBHhgmCq3LnIl+RDyvoelrUNzEw5K9DwrO\nsQISc6ffJI7b58tun+WGDdetWtJhm2xmwgPW9HUITwaPT4KP2yyVWPgmt2qs0EQ5oEB2UhIaxXG+\n6WlUK/IIhDmgF6rA8swnFj2fE9FVFvIL1VhmhcRkM1sytpzYEvpnCf2H3E77T0ygz/pJMk0D3saz\nJFP4kJCQ0MGO9hRaqmk2MWgvxfRIA5v7mvZ61zUN1NoFoP3KpirI5CiGmx4FR9RpOwhZAXPfDrzY\nRYEToWpCz8uN99aMyL1bSYaZQkVCHRzccred/z9zqAKYUsINvZBk5/SwDqvx4JQoFLElND0v017Z\nEJKYaGW2pYbNRC5dedfXkpK2hlgSXket30pCBl1Jtl8vovkIpcbSsUbO18OUOuynPDcXMZVBjsXu\nIlzz0BPRMHTV9iAIjwCQ3y4eGDvbo4Nnkc3dbwAAVFlY/3upSsKZ3sVGxF05k4lSZSziSljsbsMf\noDznNtJnLoIrd0Dm7FlsZ+xso+DZZLZQoXUauSj5dIg00ukb/ga4kfMtEagai+uez2wgqzR9cTUB\nEf9kLZoLdV+FakLcN0HMsLp9IKNx7EqGrLQPtdupqBg3A4Uzr/Zx/nVbyO4ehc2CHJtl1OM8fLad\np5Bv2CCyakrh/IP+//bOrUeOowzDb1Uf57C73l3vIes4tlEOCmBfABeJxI/gCn4GglsuEAJuIyEu\n4CdAfkgSxSBQgnBi4sRxEtvZ48zOsXu6q7io6qquOCYbh8S78ftIkcaT2Z7unpm3vu+r79AqEKq1\nizu0OzgFKI143mxh+u5Msayd+A6uVRBWfZc/rFq1IYCyDWmnT3ddVF9ouMzCaOYzTRc96YQ4KkIB\naLIzk3HlXIOy34oHtW7hfDPzHaKBYG5ls13au1c6IZ5uxphlvsZh6Y752+UPpoj3jP9WfXL38+/P\nKYTuAyEk4Mm2FFyQrMbWdWveLyeYm00JzDZ9E4501N4Ph4uc5/ul6+ZUrESuqUk1FsgHtrHHUDnL\nosolkrE19Tve9Vj0/coP3Y6i+0pNlUrMnjL2rhZ+2KzKWum04wrTLWNaH3xfuO5M6c2ea1iiUukn\nL7VqNCCAqmuupT2Wrp1/UOe+6austRtjZ+6LtbwS38exHdWHEM6iELVGZ1e714wuw34WvrpxfEFi\numPPs1dj/bq5WavvzJDeNUE7nSUot5fsuQk3rdu0tG+OWSM9smb8pITeNE1645nv9SgUXBOXqGxd\nSypQ2DkXsw3vFnX2Wp9LLNzOjlyYxqwAEB9MAHn21t0nWxRs15vkcIpoan4M+X6Ezr55fPjdBKPv\nma2F2TjCyjt+JqL/AsW+hHYGV/8PIdC18YJ0sEDsfH6J1IpClQvnPtSZj0Go2BfZLHqmAxEAZAOB\n3r2mTZhqdRb2sYPhlQwHP7A7F+dnwJ7v++DmIyTCzYmoU19/AQ3fZ0EL11NAaO3KjYWKgh0El7xU\n1L4HgfSilg4rd8y6E/nJ1Kl0Qta5LzB+xpzD3o9rxD3zS+12C0Q3TFerc+/G2HjTJPqIO/egN9bN\nPVzruWnastRAq5FRdmSOE00rP3tyOXfuT2d/4a5Lpb5FnSx8odqiH6PeMPdq8rSCst23ivUYnU/t\nd2Cukdpks2zoy7ShNXA4wFnj7MkYIeRr5cm2FApjBQghEBVm2dKdFNKuoslYI79jlp7OfY3uvl0l\nliXma2a1mZ9PXPoz4KPciyWN2PZQ1FGry5JGUIrr5kcM4ZJkIHwzUpUIzHds2e9zcxS3jOm7/bpP\nnilWInf82aZANLUr2Ds9XPnNawCA2799GfP1JvIfoW9GXkCW3gUQtfLt4Tsy2OnQzcTnsnaP2+hI\nQOXW9RDC9TWs89jtXJi+jzbvY1Vift6e85ZyE5YAQL5vSiD7b+W48E+bbNZeceMYSJrEAO0a2JSb\nApmtO+jslojGNoFEAfHR2F1j3ARuJzN/zCiCzlP3GjdReuccVGSuSyhAFPbezvwcCll6K+/4mRjZ\nsLEgliBu3nrgXp12nmxROLBfNCkgEvvBFxkS23Zt5QOBjb+ZL45Y1KiWjSkeTxPEc/ODn5+TwWwC\nN4thJjA1FcYoV2LEk5ZwJE1hlW/flh/6TkftmQjpQCN525xPsdp3LkCxIrH0oZ3yvEgw3bRdpPY0\n0qF5zcafX3PvmR8KTJ42Bx1dEk6wurvetJbSi5ebL+lOutmdkUEj2cYdqM5FzoeP5rVLBpOVQh03\nvRK8T75YFphdNfc2TmrIf5udka3rC/TeNj3e9GhkBAAwTU+VFa80hV7Ykm0dZig2cSIVC9R9+yMv\nFYSyblRZQRyZ4IpeLCD6RmRRK4i5FZE0cQKxWEpQ2qxQUQGduzbh6lA7AdLS7yIlE+3iGnK6aG9Y\nnRnoPhBCAp5oS6G2FWrRxgaQ27Ffq0sQNvKcv3/ggpHVSh6MP2snDjW9D/NDhe6uWcGiokZlV8uq\nKzG1uxKzzVZl5ALOTJUL6aPZkWlpDphqPVmZxxv/mCPeNaucmJfQC2Nyp1IivWLMksmFHPO1B7W+\neHmEemyuUUwi1/knHftAoxa+E5GpEfB5AWg1mRVN/8JW6bSogcTmUFTdKKjLcLMtEoHRBfO+xy8u\n0MnN+Rcf9bH1rvmDzt2JLydOUqCwGUJSQHRsZ5VODt011yKnJVb/ZZOCuimUzdkY76QoVs37Ln1U\nof+esarErHApxmJlObxJjcsQSVQr5r1GF2M36at7XzjLTgtvHWjpdzo6hzU690zJpLxzD6evr9IX\n80SLQkO9twc0SWa3W8+3XiNeuoaq12zX+dz+/NAPPsnvTyHvmgPp4THS8yZCrs4toX/Lbnlu9TC8\nYo4zugLMXzBf+uNpjP4t83EsfaSQHZpjJkdzoMkmLCuIsfnCqckUoqlHGAwh7t0HAPTtf5/l0k/f\nxu3fvwwAKM9XmFxshCNCNrCmeKWg+k3Of+W3IpVGbRN+dOS7S7UbmWZHpXMl8t2F217ViXSvKdYj\nlCv2bTUw/9SY7svvSyz9xbg6CoGehAyMXxQ/tQ0xmrinRWqTr9aXUaybH3rVFS7Wk4zrVmm2ckKj\nG8EBoGsF2bgSWYrxpY69XmDllt3xGauWeyVc3CeeeZchmVSQA3NuejJ92JWcaug+EEICaCmckPje\nEaIm4p0myNMm+q0gbfWbOhqgtvnt0Ao4Ms/LqoLum6aL+cc10iNjj3YOuti/agJgxc7CNe2ABpJh\n0wxmCD22q2Ikgcy6AGmC+uDwS13D5V+9DgC4/ddrSDfNMYfLfQhrH0el9sk5hwKptSDSQQFpLReV\n+8YqdR65/Agt7L9h+zVOzH2YXei5FO9iVaBcU/4PbGObrT/6gOhJ0JOpvw955lwbeThCz7p+nU9S\nREO7Yg+P3aqtAJ9QJISrRxB5Bm3T3qu1HibbtivUWCM79q3f45m9D4lEagPG6WABObfHWdTAru2q\nlCTAvNW55oxAUTghau8AIva3y3nYUkA3ST55Bhk1oXANuWwy7fTqsvNRRa2MCQugs1di67rd9dAA\nYJNtZsp9cdXaEqRuJcNYvqwgtLn8s7fw4atXAQDZ2gyDq+bcsr0I6dBcWW/XF03VncS9d1TUUNbA\nTAeF64xs/l9TcxEjsfekd/MARz8yGV2jywo6bSLzEs/+8o1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib.patches as patches\n", "%matplotlib inline\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.imshow(data_hcp[:, 0, :, 0].T, origin=True)\n", "rect = patches.Rectangle((70,70),20,20,linewidth=1,edgecolor='r',facecolor='none')\n", "ax.add_patch(rect)\n", "ax.set_axis_off()\n", "ax.set_title('HCP coronal slice B0 with ROI');" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data_hcp_small = data_hcp[70:90, :, 70:90]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate Ball and Stick model" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from dmipy.signal_models import cylinder_models, gaussian_models\n", "from dmipy.core.modeling_framework import MultiCompartmentModel\n", "ball = gaussian_models.G1Ball()\n", "stick1 = cylinder_models.C1Stick()\n", "stick2 = cylinder_models.C1Stick()\n", "BAS_mod = MultiCompartmentModel(models=[ball, stick1, stick2])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "OrderedDict([('C1Stick_2_mu', 2),\n", " ('G1Ball_1_lambda_iso', 1),\n", " ('C1Stick_1_mu', 2),\n", " ('C1Stick_1_lambda_par', 1),\n", " ('C1Stick_2_lambda_par', 1),\n", " ('partial_volume_0', 1),\n", " ('partial_volume_1', 1),\n", " ('partial_volume_2', 1)])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BAS_mod.parameter_cardinality" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "BAS_mod.set_fixed_parameter('G1Ball_1_lambda_iso', 3e-9)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "OrderedDict([('C1Stick_2_mu', 2),\n", " ('C1Stick_1_mu', 2),\n", " ('C1Stick_1_lambda_par', 1),\n", " ('C1Stick_2_lambda_par', 1),\n", " ('partial_volume_0', 1),\n", " ('partial_volume_1', 1),\n", " ('partial_volume_2', 1)])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BAS_mod.parameter_cardinality" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit Ball and Sticks model to HCP data" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using parallel processing with 8 workers.\n", "Setup brute2fine optimizer in 80.1930429935 seconds\n", "Fitting of 400 voxels complete in 80.4078359604 seconds.\n", "Average of 0.201019589901 seconds per voxel.\n" ] } ], "source": [ "BAS_fit_hcp = BAS_mod.fit(scheme_hcp, data_hcp_small)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from dipy.viz import fvtk\n", "from dipy.viz.actor import slicer\n", "import numpy as np\n", "affine = np.eye(4)\n", "affine[0,3] = -10\n", "affine[1,3] = -10\n", "\n", "volume1 = BAS_fit_hcp.fitted_parameters['partial_volume_1']\n", "volume2 = BAS_fit_hcp.fitted_parameters['partial_volume_2']\n", "volume_im = slicer(1. - BAS_fit_hcp.fitted_parameters['partial_volume_0'][:, 0, :, None],\n", " interpolation='nearest', affine=affine, opacity=0.7)\n", "\n", "peak_intensities = np.concatenate([volume1[..., None], volume2[..., None]], axis=-1)\n", "\n", "ren = fvtk.ren()\n", "peaks = BAS_fit_hcp.peaks_cartesian()\n", "peaks_fvtk = fvtk.peaks(peaks, peak_intensities, scale=1.)\n", "peaks_fvtk.RotateX(90)\n", "peaks_fvtk.RotateZ(180)\n", "peaks_fvtk.RotateY(180)\n", "fvtk.add(ren, peaks_fvtk)\n", "fvtk.add(ren, volume_im)\n", "fvtk.record(ren=ren, size=[700, 700], out_path='dipy.png')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EAd+orsZtH30EANg+xrYRY5UvCLi+pQX30w5K2ZrcTSTG6BGvFwezs5nHeTQqQfgRp74i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\nsGpCQ+nKzydFUS/CopgYiq6+mtTeXjaUl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.image as mpimg\n", "img = mpimg.imread('dipy.png')\n", "plt.figure(figsize=[10, 10])\n", "plt.imshow(img[100:-97, 100:-85])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Seems like two sticks overparameterize the problem in the corpus callosum, but on the right we can see consistent crossings. Possibly MIX can do a slighly better job, but it looks like we need somethings that enforces sparsity in the volume fractions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "- Behrens, Timothy EJ, et al. \"Characterization and propagation of uncertainty in diffusion‐weighted MR imaging.\" Magnetic resonance in medicine 50.5 (2003): 1077-1088" ] } ], "metadata": { "cite2c": { "citations": { "1647435/VAXS7CUI": { "author": [ { "family": "Behrens", "given": "TEJ" }, { "family": "Woolrich", "given": "MW" }, { "family": "Jenkinson", "given": "M" }, { "family": "Johansen-Berg", "given": "H" }, { "family": "Nunes", "given": "RG" }, { "family": "Clare", "given": "S" }, { "family": "Matthews", "given": "PM" }, { "family": "Brady", "given": "JM" }, { "family": "Smith", "given": "SM" } ], "container-title": "Magnetic resonance in medicine", "id": "1647435/VAXS7CUI", "issue": "5", "issued": { "year": 2003 }, "page": "1077–1088", "page-first": "1077", "title": "Characterization and propagation of uncertainty in diffusion-weighted MR imaging", "type": "article-journal", "volume": "50" } } }, "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": 1 }