{
 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "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:"
   ],
   "id": "429af1236fbf9cc9"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:41.359012Z",
     "start_time": "2025-10-13T09:24:41.356141Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import brainstate\n",
    "import brainunit as u\n",
    "import matplotlib.pyplot as plt\n",
    "import braincell"
   ],
   "id": "5b7ca4b7210454f8",
   "outputs": [],
   "execution_count": 13
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "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"
   ],
   "id": "c341e894ad361a38"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:41.940636Z",
     "start_time": "2025-10-13T09:24:41.937349Z"
    }
   },
   "cell_type": "code",
   "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.INa_HH1952(size))\n",
    "\n",
    "        self.k = braincell.ion.PotassiumFixed(size, E=-77. * u.mV)\n",
    "        self.k.add(IK=braincell.channel.IK_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",
    "        )"
   ],
   "id": "e17a1fa000960a94",
   "outputs": [],
   "execution_count": 14
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "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"
   ],
   "id": "732ddc0d5f2ae215"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:42.623482Z",
     "start_time": "2025-10-13T09:24:42.615408Z"
    }
   },
   "cell_type": "code",
   "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"
   ],
   "id": "816b85f68e47b926",
   "outputs": [],
   "execution_count": 15
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "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"
   ],
   "id": "a2738d2e50756e5b"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:43.220884Z",
     "start_time": "2025-10-13T09:24:43.217560Z"
    }
   },
   "cell_type": "code",
   "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"
   ],
   "id": "59a9c6475282c560",
   "outputs": [],
   "execution_count": 16
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "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"
   ],
   "id": "cb0d0d48311b7ecd"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:44.225933Z",
     "start_time": "2025-10-13T09:24:43.806004Z"
    }
   },
   "cell_type": "code",
   "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"
   ],
   "id": "c36a6a765b641fae",
   "outputs": [],
   "execution_count": 17
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "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"
   ],
   "id": "985b61fb082a8a5b"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:44.864181Z",
     "start_time": "2025-10-13T09:24:44.797187Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# Plot the results using standard exponential Euler\n",
    "plt.plot(times, u.math.squeeze(vs_exp), label='exp_euler', linewidth=1.5)\n",
    "\n",
    "# Plot the results using independent exponential Euler\n",
    "plt.plot(times, u.math.squeeze(vs_ind_exp), 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"
   ],
   "id": "8334597c7452dd7",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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    "## 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://braincell.readthedocs.io/latest/apis/integration.html).\n"
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