It was once claimed

Alpha rhythms have nonzero power only at an alpha-band frequency and its higher harmonics

However, this assumes the alpha rhythm is stationary, which is often not true in neural signals in which the oscillations are bursting and have variable amplitudes, periods, and shapes.

This notebook shows how changes in the rhythms affect the power spectra.



In [1]:

    
import numpy as np
import neurodsp

%matplotlib inline
import matplotlib.pyplot as plt



In [2]:

    
np.random.seed(0)

1. Effect of bursting changes on PSD

More bursting: more broadband power
Bursting to any extent will significantly increase non-harmonic power



In [3]:

    
freq = 10
T = 100
Fs = 1000



In [4]:

    
cycle_features_use = {'amp_mean': 1, 'amp_burst_std': 0, 'amp_std': 0,
                      'period_mean': 100,
                      'period_burst_std': 0,
                      'period_std': 0,
                      'rdsym_mean': .3, 'rdsym_burst_std': 0, 'rdsym_std': 0}
prob_leave_burst = .2

loop_prob_enter_burst = [.1, .5, 1]



In [5]:

    
loop_oscs = []
for p_enter in loop_prob_enter_burst:
    if p_enter == 1:
        p_leave = 0
    else:
        p_leave = prob_leave_burst
    osc = neurodsp.sim_bursty_oscillator(freq, T, Fs,
                                         cycle_features = cycle_features_use,
                                         prob_enter_burst=p_enter,
                                         prob_leave_burst=p_leave)
    loop_oscs.append(osc)









    



---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-5-839c220cbdee> in <module>()
      5     else:
      6         p_leave = prob_leave_burst
----> 7     osc = neurodsp.sim_bursty_oscillator(freq, T, Fs,
      8                                          cycle_features = cycle_features_use,
      9                                          prob_enter_burst=p_enter,

AttributeError: module 'neurodsp' has no attribute 'sim_bursty_oscillator'



In [ ]:

    
t = np.arange(0,T,1/Fs)
tidx = t <= 2
plt.figure(figsize=(12,3))
for i in range(len(loop_oscs)):
    plt.plot(t[tidx], loop_oscs[i][tidx] + i*2)
plt.xlim((0,2))
plt.xlabel('Time (s)')
plt.ylabel('Voltage')



In [ ]:

    
fs, psds = [], []
for i in range(len(loop_oscs)):
    f, psd = neurodsp.spectral.psd(loop_oscs[i], Fs)
    fs.append(f)
    psds.append(psd)

plt.figure(figsize=(10,5))
for i in range(len(loop_oscs)):
    fidx = fs[i] <= 100
    plt.semilogy(fs[i][fidx], psds[i][fidx],
                 label=loop_prob_enter_burst[i])
plt.legend(title='burst prevalence')

2. Effect of period changes on PSD



In [ ]:

    
freq = 10
T = 100
Fs = 1000



In [ ]:

    
cycle_features_use = {'amp_mean': 1, 'amp_burst_std': 0, 'amp_std': 0,
                      'period_mean': 100,
                      'period_burst_std': 0,
                      'period_std': None,
                      'rdsym_mean': .3, 'rdsym_burst_std': 0, 'rdsym_std': 0}
prob_enter_burst = 1
prob_leave_burst = 0

loop_period_stds = [0, 3, 15]



In [ ]:

    
loop_oscs = []
for per_std in loop_period_stds:
    cycle_features_use['period_std'] = per_std
    osc = neurodsp.sim_bursty_oscillator(freq, T, Fs,
                                         cycle_features = cycle_features_use,
                                         prob_enter_burst=prob_enter_burst,
                                         prob_leave_burst=prob_leave_burst)
    loop_oscs.append(osc)



In [ ]:

    
t = np.arange(0,T,1/Fs)
tidx = t <= 2
plt.figure(figsize=(12,3))
for i in range(len(loop_oscs)):
    plt.plot(t[tidx], loop_oscs[i][tidx] + i*2)
plt.xlim((0,2))
plt.xlabel('Time (s)')
plt.ylabel('Voltage')



In [ ]:

    
fs, psds = [], []
for i in range(len(loop_oscs)):
    f, psd = neurodsp.spectral.psd(loop_oscs[i], Fs)
    fs.append(f)
    psds.append(psd)

plt.figure(figsize=(10,5))
for i in range(len(loop_oscs)):
    fidx = fs[i] <= 100
    plt.semilogy(fs[i][fidx], psds[i][fidx],
                 label=loop_period_stds[i])
plt.legend(title='period st. dev.')

3. Effect of symmetry changes on PSD



In [ ]:

    
cycle_features_use = {'amp_mean': 1, 'amp_burst_std': 0, 'amp_std': 0,
                      'period_mean': 100,
                      'period_burst_std': 0,
                      'period_std': 0,
                      'rdsym_mean': .3, 'rdsym_burst_std': 0, 'rdsym_std': None}
prob_enter_burst = 1
prob_leave_burst = 0

loop_rdsym_stds = [0, .01, .07]



In [ ]:

    
loop_oscs = []
for rdsym_std in loop_rdsym_stds:
    cycle_features_use['rdsym_std'] = rdsym_std
    osc = neurodsp.sim_bursty_oscillator(freq, T, Fs,
                                         cycle_features = cycle_features_use,
                                         prob_enter_burst=prob_enter_burst,
                                         prob_leave_burst=prob_leave_burst)
    loop_oscs.append(osc)



In [ ]:

    
t = np.arange(0,T,1/Fs)
tidx = t <= 2
plt.figure(figsize=(12,3))
for i in range(len(loop_oscs)):
    plt.plot(t[tidx], loop_oscs[i][tidx] + i*2)
plt.xlim((0,2))
plt.xlabel('Time (s)')
plt.ylabel('Voltage')



In [ ]:

    
fs, psds = [], []
for i in range(len(loop_oscs)):
    f, psd = neurodsp.spectral.psd(loop_oscs[i], Fs)
    fs.append(f)
    psds.append(psd)

plt.figure(figsize=(10,5))
for i in range(len(loop_oscs)):
    fidx = fs[i] <= 100
    plt.semilogy(fs[i][fidx], psds[i][fidx],
                 label=loop_rdsym_stds[i])
plt.legend(title='rdsym st. dev.')