major update

README.md

@@ -15,25 +15,25 @@ Created 28 September 2020
 - Fit signal enhancement using pharmacokinetic model
 - Pharmacokinetic models: steady-state, Patlak, extended Tofts, Tofts, 2CXM, 2CUM
 - AIFs: patient-specific (measured), Parker, bi-exponential Parker
-- Fitting an AIF time delay
+- Fitting free AIF time delay parameter
 - Relaxivity models: linear
 - Signal models: spoiled gradient echo
 - Water exchange models: FXL, NXL, NXL_be
 - T1 fitting using variable flip angle method, IR-SPGR and DESPOT1-HIFI
 
 ### Not yet implemented/limitations:
 - Generally untested. Not optimised for speed or robustness.
-- Additional pharmacokinetic models (add by inheriting from pk_model class)
-- Additional relaxivity models (add by inheriting from c_to_r_model class)
-- Additional AIF functions (add by inheriting from aif class)
-- Additional water exchange models, e.g. 3S2X, 2S1X (add by inheriting from water_ex_model class)
-- Additional signal models (add by inheriting from signal_model class)
+- Additional pharmacokinetic models (add by inheriting from PkModel class)
+- Additional relaxivity models (add by inheriting from CRModel class)
+- Additional water exchange models, e.g. 3S2X, 2S1X (add by inheriting from WaterExModel class)
+- Additional signal models (add by inheriting from SignalModel class)
 - R2/R2* effects not included in fitting of enhancement curves (but is included for enhancement-to-concentration conversion)
 - Compartment-specific relaxivity parameters/models
 - Fitting free water exchange parameters
 - Special model implementations, e.g. linear and graphical versions of Patlak model
 
-TODO:
-- Convert fitting functions to OO methods. Add image processing functions.
-- Parallel
-- Calculate IRF integrals exactly.
+### TODO:
+- linear Patlak model
+- option to truly constrain k in HIFI fit 
+- fast C calculation for SPGR with r2=0
+- inversion recovery T1 measurement

demo/demo_relaxivity_module.ipynb

@@ -0,0 +1,116 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "fifty-passport",
+   "metadata": {},
+   "source": [
+    "## Relaxivity module demo"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "internal-arbor",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The autoreload extension is already loaded. To reload it, use:\n",
+      "  %reload_ext autoreload\n"
+     ]
+    }
+   ],
+   "source": [
+    "import sys\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "sys.path.append('../src')\n",
+    "import relaxivity\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "arabic-latvia",
+   "metadata": {},
+   "source": [
+    "### The CRModel class\n",
+    "This is an abstract base class. Subclasses represent specific relaxivity models.  \n",
+    "The main function of these objects is to return relaxation rates as a function of contrast agent concentration.  \n",
+    "At the moment, only the linear model is implemented:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "4080ceab-24f8-4b2e-b57d-816474887489",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cr_model = relaxivity.CRLinear(r1=5.0, r2=7.1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "52762d06-81e5-4153-88f5-5d0e827d7f82",
+   "metadata": {},
+   "source": [
+    "Now we can use the R1 and R2 methods to calculate the relaxation rates for a given concentration and pre-contrast relaxation rate values:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "a3c01c12-fb5e-4aed-b9fb-b882270ba27f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[ 1.  6. 11. 16. 21. 26.]\n"
+     ]
+    }
+   ],
+   "source": [
+    "C_t = np.array([0, 1, 2, 3, 4, 5])\n",
+    "R10 = 1\n",
+    "R1_post = cr_model.R1(R10, C_t)\n",
+    "print(R1_post)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4a7c1681-7e9d-49b2-9474-56f86a8f25ef",
+   "metadata": {},
+   "source": [
+    "Additional subclasses could be implemented to represent other concentration-relaxation relationships, e.g. quadratic."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.7.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

demo/demo_signal_models.ipynb

@@ -0,0 +1,108 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "eb332c7d-4589-47da-81d0-e2697ee70254",
+   "metadata": {},
+   "source": [
+    "## Signal models demo"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "42671502-6096-4107-8c21-3f876b950a66",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import sys\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "sys.path.append('../src')\n",
+    "import signal_models\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "33acaa3b-10e0-454f-b62b-6a2cb5b1d0f4",
+   "metadata": {},
+   "source": [
+    "### The SignalModel Class\n",
+    "This abstract base class represents different signal models i.e. conversion between relaxation parameters and signal intensity for a given pulse sequence. The model is defined by specifying the sequence parameters. At present, only the SPGR signal model is implemented:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "c2e14ed8-c6f6-4e79-9fe0-fbc9b323d156",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sm = signal_models.SPGR(tr=5e-3, fa=15, te=1.5e-3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "25cb9206-ef8d-4d4f-bf82-779d9463530a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0, 0.5, 'signal')"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "R1_range = np.linspace(0.5, 50, 100)\n",
+    "s = sm.R_to_s(s0=100, R1=R1_range, R2s=0, k_fa=1)\n",
+    "\n",
+    "plt.plot(R1_range, s)\n",
+    "plt.xlabel('R1 (/s)')\n",
+    "plt.ylabel('signal')"
+   ]
+  }
+ ],
+ "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": "3.8.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}