{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:29.500399Z",
     "start_time": "2025-10-13T09:24:29.498313Z"
    }
   },
   "source": [
    ""
   ],
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "# 不同积分方法对 HH 模型神经元动态的影响\n",
    "\n",
    "本实例将通过实现经典的 Hodgkin-Huxley 模型，对比指数欧拉法 ``exp_euler`` 和独立指数欧拉法 ``ind_exp_euler`` 对神经元膜电位动态的影响。\n",
    "你将学习如何在 `braincell` 中配置不同的积分器，以及它们在模拟神经元电活动时的差异。\n",
    "\n",
    "## 准备工作\n",
    "\n",
    "首先确保已安装必要的库（`braincell`、`brainstate`、`brainunit`、`matplotlib`），并导入所需模块："
   ],
   "id": "429af1236fbf9cc9"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:30.089467Z",
     "start_time": "2025-10-13T09:24:30.087001Z"
    }
   },
   "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": 7
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## 代码详解\n",
    "\n",
    "### 定义 HH 模型神经元\n",
    "\n",
    "使用 `SingleCompartment` 构建基于 HH 模型的单神经元，包含钠通道 `INa` 、钾通道 `IK` 和漏电流 `IL` ，这些通道共同决定神经元的放电特性："
   ],
   "id": "c341e894ad361a38"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:30.684505Z",
     "start_time": "2025-10-13T09:24:30.681243Z"
    }
   },
   "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": 8
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 初始化神经元与配置积分方法\n",
    "\n",
    "创建两个 HH 神经元实例，分别使用标准指数欧拉法 ``exp_euler``和独立指数欧拉法 ``ind_exp_euler``，并初始化神经元状态："
   ],
   "id": "732ddc0d5f2ae215"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:31.282863Z",
     "start_time": "2025-10-13T09:24:31.273301Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 创建使用标准指数欧拉法的 HH 神经元\n",
    "hh_exp = HH(1, solver='exp_euler')\n",
    "\n",
    "# 创建使用独立指数欧拉法的 HH 神经元\n",
    "hh_ind_exp = HH(1, solver='ind_exp_euler')\n",
    "\n",
    "# 初始化神经元状态（如膜电位、门控变量等）至静息状态\n",
    "hh_exp.init_state()\n",
    "hh_ind_exp.init_state()"
   ],
   "id": "816b85f68e47b926",
   "outputs": [],
   "execution_count": 9
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 定义模拟步骤函数\n",
    "\n",
    "编写函数描述神经元在每个时间步的更新规则，包括接收输入电流并返回膜电位："
   ],
   "id": "a2738d2e50756e5b"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:31.853907Z",
     "start_time": "2025-10-13T09:24:31.851610Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def step_fun(t, neuron):\n",
    "    # 在当前时间 t 下更新神经元状态\n",
    "    with brainstate.environ.context(t=t):\n",
    "        # 向神经元注入持续电流以触发动作电位\n",
    "        neuron.update(10 * u.nA / u.cm** 2)\n",
    "    # 返回当前膜电位值\n",
    "    return neuron.V.value"
   ],
   "id": "59a9c6475282c560",
   "outputs": [],
   "execution_count": 10
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 运行模拟并记录结果\n",
    "\n",
    "配置模拟参数，分别运行两种积分方法的模拟，记录膜电位随时间的变化："
   ],
   "id": "cb0d0d48311b7ecd"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:32.858797Z",
     "start_time": "2025-10-13T09:24:32.445671Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 设置模拟时间步长\n",
    "with brainstate.environ.context(dt=0.1 * u.ms):\n",
    "    # 生成模拟时间序列\n",
    "    times = u.math.arange(0. * u.ms, 100 * u.ms, brainstate.environ.get_dt())\n",
    "\n",
    "    # 用标准指数欧拉法模拟，记录膜电位\n",
    "    vs_exp = brainstate.transform.for_loop(\n",
    "        lambda t: step_fun(t, hh_exp),\n",
    "        times\n",
    "    )\n",
    "\n",
    "    # 用独立指数欧拉法模拟，记录膜电位\n",
    "    vs_ind_exp = brainstate.transform.for_loop(\n",
    "        lambda t: step_fun(t, hh_ind_exp),\n",
    "        times\n",
    "    )"
   ],
   "id": "c36a6a765b641fae",
   "outputs": [],
   "execution_count": 11
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 可视化膜电位动态\n",
    "\n",
    "绘制两种积分方法下的膜电位变化曲线，对比动作电位波形差异："
   ],
   "id": "985b61fb082a8a5b"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:33.514722Z",
     "start_time": "2025-10-13T09:24:33.443389Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 绘制标准指数欧拉法的结果\n",
    "plt.plot(times, u.math.squeeze(vs_exp), label='exp_euler', linewidth=1.5)\n",
    "\n",
    "# 绘制独立指数欧拉法的结果\n",
    "plt.plot(times, u.math.squeeze(vs_ind_exp), label='ind_exp_euler', linestyle='--', linewidth=1.5)\n",
    "\n",
    "# 添加标签和图例\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()"
   ],
   "id": "8334597c7452dd7",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 12
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## 结果解读\n",
    "\n",
    "运行代码后，你将看到膜电位随时间变化的曲线。\n",
    "\n",
    "核心结论如下：\n",
    "动作电位基本特征：两种方法均能模拟出动作电位的产生，但波形细节存在差异。\n",
    "积分方法差异：\n",
    "   - `exp_euler` 曲线更平滑，对强耦合的门控变量与膜电位关系拟合更精确，动作电位峰值和时程更接近理论值。\n",
    "   - `ind_exp_euler` 由于独立更新状态变量，可能在快速变化阶段出现微小偏差，但计算速度更快，尤其在大规模模拟时。\n",
    "适用性场景：\n",
    "   - 对精度要求高的单细胞模拟，如复现特定电生理实验，优先选择 `exp_euler` 。\n",
    "   - 大规模网络模拟，如包含数千神经元，`ind_exp_euler` 能在保证足够精度的同时显著提升效率。\n",
    "\n",
    "## 扩展练习\n",
    "\n",
    "- 尝试使用四阶龙格-库塔法 `solver='rk4'` ，对比其与指数欧拉法的精度和计算效率。\n",
    "- 调整输入电流强度，观察不同积分方法对神经元发放频率的影响。\n",
    "- 增加模拟时长，分析长期模拟中积分误差的累积效应。\n",
    "\n",
    "通过这些实践，你将深入理解数值方法在神经模拟中的关键作用，为复杂模型设计提供依据。\n",
    "\n",
    "## 更多\n",
    "\n",
    "若想了解更多的数值积分方法，我们在[数值积分方法库](https://braincell.readthedocs.io/latest/apis/integration.html) 中提供了丰富的积分器与相关资料。"
   ],
   "id": "c616776761e9f65e"
  }
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