{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "header",
   "metadata": {},
   "source": [
    "# Getting Started with BrainMass\n",
    "\n",
    "Welcome to BrainMass, a Python library for whole-brain computational modeling using differentiable neural mass models built on JAX."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "learning-objectives",
   "metadata": {},
   "source": [
    "## Learning Objectives\n",
    "\n",
    "By the end of this tutorial, you will be able to:\n",
    "\n",
    "- Understand what BrainMass is and its place in the BrainX ecosystem\n",
    "- Install and configure BrainMass for your hardware (CPU/GPU/TPU)\n",
    "- Run your first neural mass simulation\n",
    "- Understand the basic workflow: model creation, initialization, simulation, visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "prerequisites",
   "metadata": {},
   "source": [
    "## Prerequisites\n",
    "\n",
    "- Basic Python programming knowledge\n",
    "- Familiarity with NumPy arrays\n",
    "- No prior knowledge of computational neuroscience required"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "background",
   "metadata": {},
   "source": [
    "## Background\n",
    "\n",
    "### What is BrainMass?\n",
    "\n",
    "**BrainMass** is a library for simulating brain dynamics using **neural mass models**. These models describe the collective activity of neuronal populations rather than individual neurons, making them computationally efficient for whole-brain simulations.\n",
    "\n",
    "Key capabilities:\n",
    "- **Brain dynamics simulation**: Model complex neural activity across brain regions\n",
    "- **Neural signal fitting**: Fit model parameters to empirical data (MEG, EEG, fMRI)\n",
    "- **Cognitive task training**: Train neural models to perform cognitive tasks\n",
    "- **Differentiable optimization**: Leverage JAX for gradient-based parameter fitting\n",
    "\n",
    "### The BrainX Ecosystem\n",
    "\n",
    "BrainMass is part of the **BrainX ecosystem** for computational neuroscience:\n",
    "\n",
    "| Library | Purpose |\n",
    "|---------|--------|\n",
    "| `brainstate` | State management and neural dynamics framework |\n",
    "| `brainunit` | Physical units for neuroscience (ms, mV, Hz) |\n",
    "| `braintools` | Visualization, metrics, and initialization utilities |\n",
    "| `brainmass` | Neural mass models for whole-brain modeling |\n",
    "\n",
    "### Neural Mass Models\n",
    "\n",
    "Neural mass models represent the average activity of large neuronal populations. Instead of simulating millions of individual neurons, we model the *mean-field* dynamics of populations. This abstraction enables:\n",
    "\n",
    "- Simulation of whole-brain dynamics with ~100 regions\n",
    "- Direct comparison with macroscopic brain signals (EEG, MEG, fMRI)\n",
    "- Efficient parameter optimization using gradient descent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "installation",
   "metadata": {},
   "source": [
    "## Installation\n",
    "\n",
    "Install BrainMass using pip. Choose the appropriate variant for your hardware:\n",
    "\n",
    "```bash\n",
    "# CPU-only\n",
    "pip install -U brainmass[cpu]\n",
    "\n",
    "# NVIDIA GPU (CUDA 12)\n",
    "pip install -U brainmass[cuda12]\n",
    "\n",
    "# NVIDIA GPU (CUDA 13)\n",
    "pip install -U brainmass[cuda13]\n",
    "\n",
    "# Google TPU\n",
    "pip install -U brainmass[tpu]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "implementation-header",
   "metadata": {},
   "source": [
    "## Implementation\n",
    "\n",
    "Let's walk through a complete simulation workflow step by step."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "step1-header",
   "metadata": {},
   "source": [
    "### Step 1: Setup and Imports\n",
    "\n",
    "First, import the required libraries:"
   ]
  },
  {
   "cell_type": "code",
   "id": "imports",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:09.465808800Z",
     "start_time": "2026-03-21T13:51:05.013735700Z"
    }
   },
   "source": [
    "import brainstate  # State management and compilation\n",
    "import braintools  # initialization and visualization\n",
    "import brainmass  # Neural mass models\n",
    "import brainunit as u  # Physical units\n",
    "import numpy as np  # Numerical operations\n",
    "import matplotlib.pyplot as plt  # Plotting\n",
    "\n",
    "# Check versions\n",
    "print(f\"BrainMass version: {brainmass.__version__}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BrainMass version: 0.0.6\n"
     ]
    }
   ],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "id": "step2-header",
   "metadata": {},
   "source": [
    "### Step 2: Configure the Simulation Environment\n",
    "\n",
    "Set the simulation time step. BrainMass uses physical units from `brainunit`:"
   ]
  },
  {
   "cell_type": "code",
   "id": "config",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:09.541783Z",
     "start_time": "2026-03-21T13:51:09.507525100Z"
    }
   },
   "source": [
    "# Set time step to 0.1 milliseconds\n",
    "dt = 0.1 * u.ms\n",
    "brainstate.environ.set(dt=dt)\n",
    "\n",
    "print(f\"Time step: {dt}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time step: 0.1 ms\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "id": "step3-header",
   "metadata": {},
   "source": [
    "### Step 3: Create a Neural Mass Model\n",
    "\n",
    "We'll use the **Hopf oscillator**, a simple model that captures oscillatory brain dynamics. The Hopf model describes how a neural population transitions between quiescent and oscillatory states.\n",
    "\n",
    "Key parameters:\n",
    "- `a`: Bifurcation parameter (a > 0 = oscillation, a < 0 = silent)\n",
    "- `w`: Angular frequency of oscillation\n",
    "- `beta`: Amplitude saturation"
   ]
  },
  {
   "cell_type": "code",
   "id": "create-model",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:09.692765500Z",
     "start_time": "2026-03-21T13:51:09.566119800Z"
    }
   },
   "source": [
    "# Create a single Hopf oscillator node\n",
    "node = brainmass.HopfStep(\n",
    "    1,  # Number of nodes (brain regions)\n",
    "    a=0.5,  # Bifurcation parameter (positive = oscillating)\n",
    "    w=0.2,  # Angular frequency\n",
    "    beta=1.0,  # Amplitude saturation\n",
    "    init_x=braintools.init.Constant(0.5),\n",
    "    init_y=braintools.init.Constant(0.5),\n",
    ")\n",
    "\n",
    "node"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "HopfStep(\n",
       "  in_size=(1,),\n",
       "  out_size=(1,),\n",
       "  init_x=Constant(value=0.5),\n",
       "  init_y=Constant(value=0.5),\n",
       "  noise_x=None,\n",
       "  noise_y=None,\n",
       "  method=exp_euler,\n",
       "  a=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.5, dtype=float32)\n",
       "  ),\n",
       "  w=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.2, dtype=float32)\n",
       "  ),\n",
       "  beta=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1., dtype=float32)\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "id": "step4-header",
   "metadata": {},
   "source": [
    "### Step 4: Initialize Model States\n",
    "\n",
    "Neural mass models have internal states (e.g., membrane potentials) that must be initialized before simulation:"
   ]
  },
  {
   "cell_type": "code",
   "id": "init-states",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:09.770129800Z",
     "start_time": "2026-03-21T13:51:09.712767400Z"
    }
   },
   "source": [
    "# Initialize all state variables\n",
    "node.init_all_states()\n",
    "\n",
    "print(f\"Initial x: {node.x.value}\")\n",
    "print(f\"Initial y: {node.y.value}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial x: [0.5]\n",
      "Initial y: [0.5]\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "id": "step5-header",
   "metadata": {},
   "source": [
    "### Step 5: Run the Simulation\n",
    "\n",
    "Define a step function and run the simulation using BrainState's efficient `for_loop`:"
   ]
  },
  {
   "cell_type": "code",
   "id": "simulation",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:10.023785100Z",
     "start_time": "2026-03-21T13:51:09.773123200Z"
    }
   },
   "source": [
    "# Define the simulation step\n",
    "def step_run(i):\n",
    "    \"\"\"Single simulation step.\"\"\"\n",
    "    node.update()  # Update model dynamics\n",
    "    return node.x.value, node.y.value  # Return state values\n",
    "\n",
    "\n",
    "# Simulate for 1000 ms (10,000 steps at dt=0.1ms)\n",
    "n_steps = 10000\n",
    "indices = np.arange(n_steps)\n",
    "\n",
    "# Run simulation (compiled with JAX JIT for speed)\n",
    "x_trace, y_trace = brainstate.transform.for_loop(step_run, indices)\n",
    "\n",
    "print(f\"Simulation complete!\")\n",
    "print(f\"Output shape: {x_trace.shape} (time steps, nodes)\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulation complete!\n",
      "Output shape: (10000, 1) (time steps, nodes)\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "id": "step6-header",
   "metadata": {},
   "source": [
    "### Step 6: Visualize Results\n",
    "\n",
    "Plot the simulated neural activity:"
   ]
  },
  {
   "cell_type": "code",
   "id": "visualization",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:10.430061900Z",
     "start_time": "2026-03-21T13:51:10.046778Z"
    }
   },
   "source": [
    "# Create time axis in milliseconds\n",
    "t_ms = indices * brainstate.environ.get_dt()\n",
    "\n",
    "# Plot time series\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "# Time series plot\n",
    "axes[0].plot(t_ms, x_trace[:, 0], 'b-', label='x(t)', linewidth=0.8)\n",
    "axes[0].plot(t_ms, y_trace[:, 0], 'r-', label='y(t)', linewidth=0.8, alpha=0.7)\n",
    "axes[0].set_xlabel('Time (ms)')\n",
    "axes[0].set_ylabel('Activity')\n",
    "axes[0].set_title('Neural Activity Over Time')\n",
    "axes[0].legend()\n",
    "axes[0].set_xlim([0, 500])  # Show first 500 ms\n",
    "\n",
    "# Phase portrait (x vs y)\n",
    "axes[1].plot(x_trace[:, 0], y_trace[:, 0], 'k-', linewidth=0.5, alpha=0.5)\n",
    "axes[1].set_xlabel('x')\n",
    "axes[1].set_ylabel('y')\n",
    "axes[1].set_title('Phase Portrait')\n",
    "axes[1].set_aspect('equal')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "id": "exploration-header",
   "metadata": {},
   "source": [
    "## Exploring Model Behavior\n",
    "\n",
    "The Hopf oscillator exhibits different behaviors depending on the bifurcation parameter `a`:\n",
    "\n",
    "- **a < 0**: Stable fixed point (no oscillation)\n",
    "- **a = 0**: Bifurcation point\n",
    "- **a > 0**: Limit cycle oscillation\n",
    "\n",
    "Let's visualize this:"
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:10.470682Z",
     "start_time": "2026-03-21T13:51:10.431058700Z"
    }
   },
   "cell_type": "code",
   "source": [
    "@brainstate.transform.jit\n",
    "def simulate_hope_model(a):\n",
    "    model = brainmass.HopfStep(1, a=a, w=0.2, beta=1.0)\n",
    "    model.init_all_states()\n",
    "\n",
    "    # Set non-zero initial condition\n",
    "    model.x.value = np.array([0.5])\n",
    "    model.y.value = np.array([0.5])\n",
    "\n",
    "    # Run simulation\n",
    "    def step(i):\n",
    "        model.update()\n",
    "        return model.x.value\n",
    "\n",
    "    return brainstate.transform.for_loop(step, indices)"
   ],
   "id": "4633a8bce67f2251",
   "outputs": [],
   "execution_count": 7
  },
  {
   "cell_type": "code",
   "id": "exploration",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:51:10.851865500Z",
     "start_time": "2026-03-21T13:51:10.473682400Z"
    }
   },
   "source": [
    "# Compare different values of 'a'\n",
    "a_values = [-0.5, 0.0, 0.5]\n",
    "colors = ['blue', 'orange', 'green']\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3))\n",
    "\n",
    "for idx, a_val in enumerate(a_values):\n",
    "    x_trace = simulate_hope_model(a_val)\n",
    "\n",
    "    # Plot\n",
    "    axes[idx].plot(t_ms[:3000], x_trace[:3000, 0], color=colors[idx], linewidth=0.8)\n",
    "    axes[idx].set_xlabel('Time (ms)')\n",
    "    axes[idx].set_ylabel('x')\n",
    "    axes[idx].set_title(f'a = {a_val}')\n",
    "    axes[idx].set_ylim([-1.5, 1.5])\n",
    "\n",
    "plt.suptitle('Effect of Bifurcation Parameter on Dynamics', y=1.02)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x300 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "id": "available-models",
   "metadata": {},
   "source": [
    "## Available Neural Mass Models\n",
    "\n",
    "BrainMass provides a variety of neural mass models:\n",
    "\n",
    "| Model | Description | Use Case |\n",
    "|-------|-------------|----------|\n",
    "| `HopfStep` | Hopf oscillator | Oscillatory dynamics, bifurcation studies |\n",
    "| `FitzHughNagumoStep` | FitzHugh-Nagumo | Excitable systems, spiking dynamics |\n",
    "| `WilsonCowanStep` | Wilson-Cowan | E/I balance, population dynamics |\n",
    "| `JansenRitStep` | Jansen-Rit | EEG generation, alpha rhythms |\n",
    "| `WongWangStep` | Wong-Wang | Decision making, working memory |\n",
    "| `QIFStep` | Quadratic I&F | Mean-field spiking models |\n",
    "| `KuramotoNetwork` | Kuramoto | Phase synchronization |\n",
    "| `StuartLandauStep` | Stuart-Landau | Oscillations near bifurcation |\n",
    "| `VanDerPolStep` | Van der Pol | Relaxation oscillations |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "exercises-header",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "### Exercise 1: Modify Parameters\n",
    "\n",
    "Try changing the Hopf model parameters:\n",
    "1. What happens when you increase `w` (frequency)?\n",
    "2. What happens when you increase `beta` (saturation)?\n",
    "\n",
    "### Exercise 2: Use a Different Model\n",
    "\n",
    "Replace `HopfStep` with `FitzHughNagumoStep` and observe the different dynamics.\n",
    "\n",
    "*Hint*: The FitzHugh-Nagumo model has parameters `a`, `b`, `tau`, and `I_ext`.\n",
    "\n",
    "### Exercise 3: Add Noise\n",
    "\n",
    "Neural systems are inherently noisy. Add Ornstein-Uhlenbeck noise to the model:\n",
    "\n",
    "```python\n",
    "node = brainmass.HopfStep(\n",
    "    1,\n",
    "    a=0.5,\n",
    "    w=0.2,\n",
    "    beta=1.0,\n",
    "    noise_x=brainmass.OUProcess(1, sigma=0.05, tau=5.0 * u.ms),\n",
    "    noise_y=brainmass.OUProcess(1, sigma=0.05, tau=5.0 * u.ms),\n",
    ")\n",
    "```\n",
    "\n",
    "How does noise affect the regularity of oscillations?"
   ]
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   "source": [
    "## References\n",
    "\n",
    "- Deco, G., et al. (2017). \"The dynamics of resting fluctuations in the brain.\" *Nature Reviews Neuroscience*.\n",
    "- BrainMass Documentation: https://brainmass.readthedocs.io/\n",
    "- BrainX Ecosystem: https://brainmodeling.readthedocs.io/"
   ]
  }
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