{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "429af1236fbf9cc9",
   "metadata": {},
   "source": [
    "# Effects of Different Integration Methods on HH Neuron Dynamics\n",
    "\n",
    "This example implements the classic Hodgkin-Huxley model to compare the effects of the exponential Euler method `exp_euler` and the independent exponential Euler method `ind_exp_euler` on the neuron's membrane potential dynamics. You will learn how to configure different integrators in `braincell` and understand their differences when simulating neuronal electrical activity.\n",
    "\n",
    "## Preparation\n",
    "\n",
    "First, make sure the necessary libraries (`braincell`, `brainstate`, `brainunit`, `matplotlib`) are installed, and import the required modules:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5b7ca4b7210454f8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:41.359012Z",
     "start_time": "2025-10-13T09:24:41.356141Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:57:24.701895Z",
     "iopub.status.busy": "2026-05-25T09:57:24.701635Z",
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     "shell.execute_reply": "2026-05-25T09:57:28.032567Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
     ]
    }
   ],
   "source": [
    "import brainstate\n",
    "import brainunit as u\n",
    "import matplotlib.pyplot as plt\n",
    "import braincell"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c341e894ad361a38",
   "metadata": {},
   "source": [
    "## Code Explanation\n",
    "\n",
    "### Define HH Model Neuron\n",
    "\n",
    "Use `SingleCompartment` to construct a single neuron based on the HH model, including sodium channel `INa`, potassium channel `IK`, and leak current `IL`. These channels collectively determine the neuron's firing characteristics:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e17a1fa000960a94",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:41.940636Z",
     "start_time": "2025-10-13T09:24:41.937349Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:57:28.035771Z",
     "iopub.status.busy": "2026-05-25T09:57:28.035354Z",
     "iopub.status.idle": "2026-05-25T09:57:28.039666Z",
     "shell.execute_reply": "2026-05-25T09:57:28.038804Z"
    }
   },
   "outputs": [],
   "source": [
    "class HH(braincell.SingleCompartment):\n",
    "    def __init__(self, size, solver='rk4'):\n",
    "        super().__init__(size, solver=solver)\n",
    "\n",
    "        self.na = braincell.ion.SodiumFixed(size, E=50. * u.mV)\n",
    "        self.na.add(INa=braincell.channel.Na_HH1952(size))\n",
    "\n",
    "        self.k = braincell.ion.PotassiumFixed(size, E=-77. * u.mV)\n",
    "        self.k.add(IK=braincell.channel.K_HH1952(size))\n",
    "\n",
    "        self.IL = braincell.channel.IL(\n",
    "            size,\n",
    "            E=-54.387 * u.mV,\n",
    "            g_max=0.03 * (u.mS / u.cm **2)\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "732ddc0d5f2ae215",
   "metadata": {},
   "source": [
    "### Initialize Neurons and Configure Integration Methods\n",
    "\n",
    "Create two HH neuron instances, using the standard exponential Euler method `exp_euler` and the independent exponential Euler method `ind_exp_euler`, respectively, and initialize the neuron states:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "816b85f68e47b926",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:42.623482Z",
     "start_time": "2025-10-13T09:24:42.615408Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:57:28.041894Z",
     "iopub.status.busy": "2026-05-25T09:57:28.041673Z",
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     "shell.execute_reply": "2026-05-25T09:57:30.913111Z"
    }
   },
   "outputs": [],
   "source": [
    "# Create an HH neuron using the standard exponential Euler method\n",
    "hh_exp = HH(1, solver='exp_euler')\n",
    "\n",
    "# Create an HH neuron using the independent exponential Euler method\n",
    "hh_ind_exp = HH(1, solver='ind_exp_euler')\n",
    "\n",
    "# Initialize neuron states (such as membrane potential, gating variables, etc.) to resting state\n",
    "hh_exp.init_state()\n",
    "hh_ind_exp.init_state()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2738d2e50756e5b",
   "metadata": {},
   "source": [
    "### Define the simulation step function\n",
    "\n",
    "Write a function that describes the update rules of the neuron at each time step, including receiving input current and returning the membrane potential:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "59a9c6475282c560",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:43.220884Z",
     "start_time": "2025-10-13T09:24:43.217560Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:57:30.916542Z",
     "iopub.status.busy": "2026-05-25T09:57:30.916177Z",
     "iopub.status.idle": "2026-05-25T09:57:30.919835Z",
     "shell.execute_reply": "2026-05-25T09:57:30.919276Z"
    }
   },
   "outputs": [],
   "source": [
    "def step_fun(t, neuron):\n",
    "    # Update the neuron's state at the current time t\n",
    "    with brainstate.environ.context(t=t):\n",
    "        # Inject a constant current to the neuron to evoke action potentials\n",
    "        neuron.update(10 * u.nA / u.cm**2)\n",
    "    # Return the current membrane potential value\n",
    "    return neuron.V.value\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb0d0d48311b7ecd",
   "metadata": {},
   "source": [
    "### Run simulation and record results\n",
    "\n",
    "Set up the simulation parameters and run the simulations for the two integration methods, recording the membrane potential changes over time:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c36a6a765b641fae",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:44.225933Z",
     "start_time": "2025-10-13T09:24:43.806004Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:57:30.921947Z",
     "iopub.status.busy": "2026-05-25T09:57:30.921645Z",
     "iopub.status.idle": "2026-05-25T09:57:31.772735Z",
     "shell.execute_reply": "2026-05-25T09:57:31.771304Z"
    }
   },
   "outputs": [],
   "source": [
    "# Set simulation time step\n",
    "with brainstate.environ.context(dt=0.1 * u.ms):\n",
    "    # Generate simulation time series\n",
    "    times = u.math.arange(0. * u.ms, 100 * u.ms, brainstate.environ.get_dt())\n",
    "\n",
    "    # Simulate using standard exponential Euler method and record membrane potential\n",
    "    vs_exp = brainstate.transform.for_loop(\n",
    "        lambda t: step_fun(t, hh_exp),\n",
    "        times\n",
    "    )\n",
    "\n",
    "    # Simulate using independent exponential Euler method and record membrane potential\n",
    "    vs_ind_exp = brainstate.transform.for_loop(\n",
    "        lambda t: step_fun(t, hh_ind_exp),\n",
    "        times\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "985b61fb082a8a5b",
   "metadata": {},
   "source": [
    "### Visualize Membrane Potential Dynamics\n",
    "\n",
    "Plot the membrane potential traces under the two integration methods to compare the differences in action potential waveforms:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8334597c7452dd7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:44.864181Z",
     "start_time": "2025-10-13T09:24:44.797187Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:57:31.775847Z",
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     "shell.execute_reply": "2026-05-25T09:57:31.949165Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results using standard exponential Euler\n",
    "plt.plot(times / u.ms, u.math.squeeze(vs_exp) / u.mV, label='exp_euler', linewidth=1.5)\n",
    "\n",
    "# Plot the results using independent exponential Euler\n",
    "plt.plot(times / u.ms, u.math.squeeze(vs_ind_exp) / u.mV, label='ind_exp_euler', linestyle='--', linewidth=1.5)\n",
    "\n",
    "# Add labels and legend\n",
    "plt.xlabel('Time (ms)')\n",
    "plt.ylabel('Membrane Potential (mV)')\n",
    "plt.legend()\n",
    "plt.title('HH Model Dynamics with Different Integrators')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c616776761e9f65e",
   "metadata": {},
   "source": [
    "## Result Interpretation\n",
    "\n",
    "After running the code, you will see the membrane potential over time.\n",
    "\n",
    "Key conclusions:\n",
    "Action potential characteristics: Both methods can simulate the generation of action potentials, but the waveform details differ.\n",
    "Integrator differences:\n",
    "   - `exp_euler` produces smoother curves, fitting the relationship between tightly coupled gating variables and membrane potential more accurately, with action potential peaks and time courses closer to theoretical values.\n",
    "   - `ind_exp_euler` updates state variables independently, which may introduce slight deviations during rapid changes, but it is faster, especially for large-scale simulations.\n",
    "Applicable scenarios:\n",
    "   - For high-precision single-cell simulations, such as reproducing specific electrophysiological experiments, prefer `exp_euler`.\n",
    "   - For large-scale network simulations involving thousands of neurons, `ind_exp_euler` can significantly improve efficiency while maintaining sufficient accuracy.\n",
    "\n",
    "## Extended Exercises\n",
    "\n",
    "- Try using the fourth-order Runge-Kutta method `solver='rk4'` and compare its accuracy and computational efficiency with exponential Euler methods.\n",
    "- Adjust the input current intensity to observe how different integrators affect neuronal firing frequency.\n",
    "- Extend the simulation duration to analyze the cumulative effect of integration errors over long-term simulations.\n",
    "\n",
    "Through these exercises, you will gain a deeper understanding of the critical role of numerical methods in neural simulations and provide guidance for complex model design.\n",
    "\n",
    "## More\n",
    "\n",
    "For more numerical integration methods, we provide a rich set of integrators and related resources in the [Numerical Integration Methods Library](https://brainx.chaobrain.com/braincell/apis/integration.html).\n"
   ]
  }
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