{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Solving a multitraces formulation problem coupled with ordinary differential equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Code considerations:\n", "- We try to use numpy arrays for faster computations whenever it is possible (lists are very slow)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Import of the numpy library:" ] }, { "cell_type": "code", "execution_count": 190, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we solve an example based in the problem solved in `e2.mtf_time_coupled_Kavian.ipynb` but the with FitzHugh-Nagumo and different parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## One sphere" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume that the center of the sphere is in the origin." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameters set up." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we set up the parameters of the problem:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Geometry and physical parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Radius of the sphere. It has to be a float number:" ] }, { "cell_type": "code", "execution_count": 191, "metadata": {}, "outputs": [], "source": [ "radius = 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The variable `sigmas` is a numpy array with the medium conductivities in the order $\\sigma_0$, $\\sigma_1$. The numbers have to be floats:" ] }, { "cell_type": "code", "execution_count": 192, "metadata": {}, "outputs": [], "source": [ "sigma_e = 15. # extracellular conductivity\n", "sigma_i = 1.5 # intracellular conductivity\n", "sigmas = np.asarray([sigma_e, sigma_i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Capacitance of the membrane (needs to be a float):" ] }, { "cell_type": "code", "execution_count": 193, "metadata": {}, "outputs": [], "source": [ "c_m = 1. # capacitance " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Discretization parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maximum degree of the spherical harmonics to be used for discretize ($L$). It has to be an integer:" ] }, { "cell_type": "code", "execution_count": 194, "metadata": {}, "outputs": [], "source": [ "big_l = 17" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maximum degree of the spherical harmonics to be used for quadratures ($L_c$). It has to be an integer:" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [], "source": [ "big_l_c = big_l * 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parameters for the time scheme used:" ] }, { "cell_type": "code", "execution_count": 196, "metadata": {}, "outputs": [], "source": [ "initial_time = 0.\n", "final_time = 10.\n", "number_steps = 2**7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Initial conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up of initial conditions, for this model we need two arrays of length `(big_l + 1)**2`. Each array has the coefficients of the spherical harmonic expansion of each initial condition.\n", "In the following we give a couple of examples for building one of the arrays:" ] }, { "cell_type": "code", "execution_count": 197, "metadata": {}, "outputs": [], "source": [ "# Initial condition equal to zero\n", "v_0_zero = np.zeros(((big_l+1)**2))\n", "# Intial condition equal to a cte value\n", "cte = 4.\n", "v_0_cte_value = np.zeros(((big_l+1)**2))\n", "v_0_cte_value[0] = cte * 2* np.sqrt(np.pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example we use initial conditions equal to zero. We need to set up both arrays in one:" ] }, { "cell_type": "code", "execution_count": 198, "metadata": {}, "outputs": [], "source": [ "initial_conditions = np.zeros((2, (big_l+1)**2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Set up of the external excitation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up the contributions to the right hand side made by $\\phi_e$. For this, we set up a function only dependent on time, to account for changes in time. In the module `biosspheres.formulations.mtf.timecouplings.righthands` there are implementations on how to do this. We show some of the predetermined, and how to make a new one:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pre-defined:" ] }, { "cell_type": "code", "execution_count": 199, "metadata": {}, "outputs": [], "source": [ "# Import of the module where pre-defined right hand sides are.\n", "import biosspheres.formulations.mtf.timecouplings.righthands as righthands\n", "# phi_e cte in time and space\n", "cte=5.\n", "phi_cte_space_time = righthands.phi_part_of_b_cte_space_and_time(\n", "\tbig_l, n=1, radii=np.asarray([radius]), cte=cte\n", ")\n", "# phi_e point source in space, cte in time\n", "phi_point_source_space_cte_time = righthands.phi_part_of_b_point_source_space_and_cte_time(\n", " big_l, n=1, radii=np.asarray([radius]), center_positions=[np.zeros((3))], p0 = 25.*np.ones((3)),\n", " sigma_e = sigmas[0], pii = np.asarray([sigmas[1]/sigmas[0]]), amplitude = 1.\n", ")\n", "# phi_e = cte * z_coordinate\n", "phi_point_source_linear = righthands.phi_part_of_b_linear_space_z_cte_time(\n", " big_l, n=1, radii=np.asarray([radius]), center_positions=[np.zeros((3))],cte=cte, pii = np.asarray([sigmas[1]/sigmas[0]]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Custom made:" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [], "source": [ "# Space part, cte * z_coordinate\n", "import biosspheres.formulations.mtf.mtf as mtf\n", "import biosspheres.formulations.mtf.righthands as mtfrighthand\n", "\n", "# Parameters for the function\n", "n=1\n", "radii=np.asarray([radius])\n", "cte = 5.\n", "ps =[np.zeros((3))]\n", "pii = np.asarray([sigmas[1]/sigmas[0]])\n", "x_dia, x_dia_inv = mtf.x_diagonal_with_its_inv(\n", " n, big_l, radii, pii, azimuthal=False\n", " )\n", "# Pre-defined space part\n", "space_phi = mtfrighthand.b_vector_n_spheres_mtf_linear_function_z(\n", " big_l, n, ps, cte, radii, x_dia)\n", "\n", "# Time part, step function, custom made\n", "def time_function_step(time):\n", " if time >= 5. or time < 0:\n", " return 0.\n", " else:\n", " return 1.\n", "\n", "# Time part, sine function, custom made\n", "parameter_1 = 1.\n", "parameter_2 = 0.\n", "def time_function_sine(time):\n", " return np.sin(time*parameter_1 + parameter_2)\n", "\n", "custom_phi_step = righthands.phi_part_of_b_separable_in_space_time(space_phi, time_function_step)\n", "\n", "custom_phi_sine = righthands.phi_part_of_b_separable_in_space_time(space_phi, time_function_sine)\n", "\n", "\n", "# Which we are using:\n", "b_phi_part_time_function = custom_phi_sine" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Parameters for the coupled currents and ordinary differential equations:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a non-linear current following FitzHugh-Nagumo dynamics:" ] }, { "cell_type": "code", "execution_count": 201, "metadata": {}, "outputs": [], "source": [ "parameter_theta = 0.8 # must be a float, adimensional parameter\n", "parameter_b = 0.7 # must be a float, adimensional parameter\n", "parameter_a = 0.3 # must be a float, adimensional parameter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set up of internals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up of the time steps:" ] }, { "cell_type": "code", "execution_count": 202, "metadata": {}, "outputs": [], "source": [ "import biosspheres.formulations.mtf.timecouplings.solvertemplates as solve\n", "tau, times, medium_times = solve.tau_times_medium(\n", "\tinitial_time, final_time, number_steps\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set up of the coupled problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up of the non linear current. Different models for the current can be used, there are models ready to use in the module `biosspheres.miscella.forcouplings.currents`. See the internals of the module for making custom made currents." ] }, { "cell_type": "code", "execution_count": 203, "metadata": {}, "outputs": [], "source": [ "import biosspheres.miscella.forcouplings.currents as currents" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FitzHugh-Nagumo current:" ] }, { "cell_type": "code", "execution_count": 204, "metadata": {}, "outputs": [], "source": [ "i_current_fitzhughnagumo = currents.i_fitzhughnagumo_one_sphere_function_creation(\n", "\tbig_l,\n", " big_l_c,\n", " radius\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up of the semi-implicit scheme for the \"gating\" variables (or similar)" ] }, { "cell_type": "code", "execution_count": 205, "metadata": {}, "outputs": [], "source": [ "import biosspheres.miscella.forcouplings.oderesolutions as oderesolutions\n", "ode_next_sol_fitzhugh = (\n", "\toderesolutions.semi_implicit_fitzhughnagumo_one_sphere_next_step(\n", "\t\ttau, parameter_theta, parameter_b, parameter_a\n", "\t)\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Model to be used:" ] }, { "cell_type": "code", "execution_count": 206, "metadata": {}, "outputs": [], "source": [ "i_current = i_current_fitzhughnagumo\n", "ode_next_sol = ode_next_sol_fitzhugh" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we set up internal parameters used for requirements of numpy for threading:" ] }, { "cell_type": "code", "execution_count": 207, "metadata": {}, "outputs": [], "source": [ "import os\n", "number = \"7\" # Maximum of threads\n", "os.environ[\"OMP_NUM_THREADS\"] = number\n", "os.environ[\"OPENBLAS_NUM_THREADS\"] = number\n", "os.environ[\"MKL_NUM_THREADS\"] = number\n", "os.environ[\"VECLIB_MAXIMUM_THREADS\"] = number\n", "os.environ[\"NUMEXPR_NUM_THREADS\"] = number" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We implemented a direct solver (LU decomposition) that takes as parameters what we previously defined, including the current and the coupled ODE system. The complete list can be seen in the following:" ] }, { "cell_type": "code", "execution_count": 208, "metadata": {}, "outputs": [], "source": [ "solutions = solve.mtf_time_coupling_one_sphere(\n", "\tbig_l,\n", "\tradius,\n", "\tsigmas,\n", "\tc_m,\n", "\tinitial_time,\n", "\tfinal_time,\n", "\tnumber_steps,\n", "\tinitial_conditions,\n", "\tb_phi_part_time_function,\n", "\ti_current,\n", "\tode_next_sol,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the functions is defined in the module `biosspheres.formulations.mtf.timecouplings.solvertemplates` shortened in `solve`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Saving the results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following saves all solutions, i.e. traces, transmembrane potential, and recovery variables, in numpy format. We have commented the line for the saving." ] }, { "cell_type": "code", "execution_count": 209, "metadata": {}, "outputs": [], "source": [ "filename=\"example.npy\"\n", "directory=\"\"\n", "# np.save(directory+filename, solutions)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To load the solutions:" ] }, { "cell_type": "code", "execution_count": 210, "metadata": {}, "outputs": [], "source": [ "# solutions = np.load(directory+filename)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To save in `txt` format:" ] }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "outputs": [], "source": [ "filename=\"example.txt\"\n", "directory=\"\"\n", "# np.savetxt(directory+filename, solutions)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To load the solutions:" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [], "source": [ "# solutions = np.loadtxt(directory+filename)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For plotting the evolution of time of the solutions evaluated in the north pole of the sphere:" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'v')" ] }, "execution_count": 213, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "# Auxiliary arrays for plotting\n", "import biosspheres.utils.auxindexes as auxindexes\n", "num = (big_l + 1)**2\n", "eles, l_square_plus_l, el_square_plus_el_divided_by_two = (\n", " auxindexes.eles_combination(big_l)\n", " )\n", "little_partial_spherical = np.sqrt((2 * eles + 1))\n", "plt.figure()\n", "plt.plot(\n", "\ttimes,\n", "\tnp.sum(\n", "\t\tsolutions[:, (4 * num + l_square_plus_l[0 : big_l + 1])]\n", "\t\t* little_partial_spherical[0 : big_l + 1],\n", "\t\taxis=1,\n", "\t)\n", "\t/ (2.0 * np.sqrt(np.pi)),\n", "\tlabel=\"Numerical solution\",\n", "\tmarker=\".\",\n", ")\n", "plt.title(\"v\")" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Additional variable')" ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(\n", "\ttimes,\n", "\tnp.sum(\n", "\t\tsolutions[:, (5 * num + l_square_plus_l[0 : big_l + 1])]\n", "\t\t* little_partial_spherical[0 : big_l + 1],\n", "\t\taxis=1,\n", "\t)\n", "\t/ (2.0 * np.sqrt(np.pi)),\n", "\tlabel=\"Numerical solution\",\n", "\tmarker=\".\",\n", ")\n", "plt.title(\"Additional variable\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking the value of a specific coefficient:" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Coeficiente l = 10, m = 0')" ] }, "execution_count": 215, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num = (big_l + 1)**2\n", "eles, l_square_plus_l, el_square_plus_el_divided_by_two = (\n", " auxindexes.eles_combination(big_l)\n", " )\n", "plt.figure()\n", "l = 10 # Coefficient\n", "plt.plot(\n", "\ttimes,solutions[:, (4 * num + l_square_plus_l[l])],\n", "\tlabel=\"Numerical solution\",\n", "\tmarker=\".\",\n", ")\n", "plt.title(\"Coeficiente l = \"+ str(l) + \", m = 0\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For plotting the transmembrane potential on the surface of the sphere at a given time:" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [], "source": [ "# Auxiliary arrays\n", "import biosspheres.quadratures.sphere as quadratures\n", "(\n", "\tquantity_theta_points,\n", "\tquantity_phi_points,\n", "\tweights,\n", "\tpre_vector,\n", "\tspherical_harmonics,\n", ") = quadratures.gauss_legendre_trapezoidal_real_sh_mapping_2d(\n", "\tbig_l, big_l_c\n", ")" ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "time_index = number_steps // 2 # half of the simulation \n", "vector = pre_vector * radius\n", "surface_v = np.zeros((quantity_theta_points, quantity_phi_points))\n", "surface_v[:, :] = np.sum(\n", "\tsolutions[time_index, 4 * num:5*num, np.newaxis, np.newaxis]\n", "\t* spherical_harmonics, axis=0)\n", "surface_v_max = np.max(np.abs(surface_v))\n", "surface_v = (surface_v + surface_v_max) / (2. * surface_v_max)\n", "\n", "from matplotlib import cm, colors\n", "fig = plt.figure()\n", "ax_1 = fig.add_subplot(111, projection='3d')\n", "ax_1.plot_surface(\n", "\tvector[0, :, :],\n", "\tvector[1, :, :],\n", "\tvector[2, :, :],\n", "\trstride=1, cstride=1, \n", "\tfacecolors=cm.coolwarm(surface_v[:, :]))\n", "ax_1.set_xlabel('$x$')\n", "ax_1.set_ylabel('$y$')\n", "ax_1.set_zlabel('$z$')\n", "ax_1.set_aspect('equal')\n", "fig.colorbar(cm.ScalarMappable(\n", " norm=colors.CenteredNorm(halfrange=surface_v_max), cmap=cm.coolwarm),\n", " ax=ax_1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That can be made a video too." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For plotting a plane cut without $\\phi_e$:" ] }, { "cell_type": "code", "execution_count": 218, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 218, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import biosspheres.laplace.drawing as draw\n", "from matplotlib import cm, colors\n", "cut = 1\n", "# Size of the window to be plotted\n", "horizontal = 5.\n", "vertical = 5.\n", "# For the resolution of the plot\n", "inter_horizontal = 100\n", "inter_vertical = 100\n", "# For plotting without the external function we make the following function\n", "def zero(x: np.ndarray) -> float:\n", " return 0.\n", "\n", "x1, y1, data = draw.draw_cut_representation_formula_one_sphere_azimuthal_symmetry(\n", " cut, np.zeros((3)), horizontal, vertical, inter_horizontal, inter_vertical, solutions[time_index, 0 : 4 * num], radius, big_l, zero)\n", "plt.figure()\n", "plt.imshow(data, origin='lower',\n", " extent=[-horizontal / 2, horizontal / 2,\n", " -vertical / 2, vertical / 2],\n", " norm=colors.CenteredNorm()\n", " )\n", "plt.xlabel('$y$')\n", "plt.ylabel('$z$')\n", "plt.title('$x = 0.$')\n", "plt.colorbar()" ] } ], "metadata": { "kernelspec": { "display_name": "biosspheres", "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": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 2 }