matlab微分方程代码-pyHH:Hodgkin-Huxley尖峰神经元模型的简单Python实现

# pyHH **pyHH is a simple Python implementation of the Hodgkin-Huxley spiking neuron model.** pyHH simulates conductances and calculates membrane voltage at discrete time points without requiring a differential equation solver. [HHSharp](https://github.com/swharden/HHSharp) is a similar project written in C#.  ### Minimal Code Example A full Hodgkin-Huxley spiking neuron model and simulation was created in fewer than 100 lines of Python ([dev/concept4.py](dev/concept4.py)). Unlike other code examples on the internet, this implementation is object-oriented and Pythonic. When run, it produces the image above. ## Python Package The `pyhh` package includes Hodgkin-Huxley models and additional tools to organize simulation data. ### Simulation Steps 1. Create a model cell and customize its properties if desired 2. Create a stimulus waveform (a numpy array) 3. Create a simulation by giving it model the waveform you created 4. Plot various properties of the stimulation ### Example Usage ```python # customize a neuron model if desired model = pyhh.HHModel() model.gNa = 100 # typically 120 model.gK = 5 # typically 36 model.EK = -35 # typically -12 # customize a stimulus waveform stim = np.zeros(20000) stim[7000:13000] = 50 # add a square pulse # simulate the model cell using the custom waveform sim = pyhh.Simulation(model) sim.Run(stimulusWaveform=stim, stepSizeMs=0.01) ``` ```python # plot the results with MatPlotLib plt.figure(figsize=(10, 8)) ax1 = plt.subplot(411) ax1.plot(sim.times, sim.Vm - 70, color='b') ax1.set_ylabel("Potential (mV)") ax1.set_title("Hodgkin-Huxley Spiking Neuron Model", fontSize=16) ax2 = plt.subplot(412) ax2.plot(sim.times, stim, color='r') ax2.set_ylabel("Stimulation (µA/cm²)") ax3 = plt.subplot(413, sharex=ax1) ax3.plot(sim.times, sim.StateH, label='h') ax3.plot(sim.times, sim.StateM, label='m') ax3.plot(sim.times, sim.StateN, label='n') ax3.set_ylabel("Activation (frac)") ax3.legend() ax4 = plt.subplot(414, sharex=ax1) ax4.plot(sim.times, sim.INa, label='VGSC') ax4.plot(sim.times, sim.IK, label='VGKC') ax4.plot(sim.times, sim.IKleak, label='KLeak') ax4.set_ylabel("Current (µA/cm²)") ax4.set_xlabel("Simulation Time (milliseconds)") ax4.legend() plt.tight_layout() plt.savefig("tests/demo.png") plt.show() ```  ## Theory Visit https://github.com/swharden/HHSharp for code concepts and simulation notes. Although the language is different, the biology and implementation is the same.  ### Additional Resources * [Hodgkin and Huxley, 1952](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1392413/pdf/jphysiol01442-0106.pdf) (the original manuscript) * [The Hodgkin-Huxley Mode](http://www.genesis-sim.org/GENESIS/iBoG/iBoGpdf/chapt4.pdf) (The GENESIS Simulator, Chapter 4) * Wikipedia: [Hodgkin–Huxley model](https://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model) * [Hodgkin-Huxley spiking neuron model in Python](https://www.bonaccorso.eu/2017/08/19/hodgkin-huxley-spiking-neuron-model-python/) by Giuseppe Bonaccorso - a HH model which uses the [`scipy.integrate.odeint` ordinary differential equation solver](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.odeint.html) * [Introduction to Computational Modeling: Hodgkin-Huxley Model](http://andysbrainblog.blogspot.com/2013/10/introduction-to-computational-modeling.html) by Andrew Jahn - a commentary of the HH model with matlab code which discretely simulates conductances * [NeuroML Hodgkin Huxley Tutorials](https://github.com/swharden/hodgkin_huxley_tutorial) * [Summary of the Hodgkin-Huxley model](http://ecee.colorado.edu/~ecen4831/HHsumWWW/HHsum.html) by Dave Beeman