# eFeature descriptions¶

A pdf document describing the eFeatures is available here.

Time, voltage and current (if given) are interpolated using interp_step setting (default interp_step = 0.1 ms) before efeatures are extracted from them. Since, they are technically features in eFEL, you can retrieve the interpolated time, voltage and current (if given), like any other feature.

## Implemented eFeatures¶

### Spike event features¶

#### peak_time¶

SpikeEvent : The times of the maxima of the peaks

**Required features**: peak_indices**Units**: ms**Pseudocode**:peak_time = time[peak_indices]

#### time_to_first_spike¶

SpikeEvent : Time from the start of the stimulus to the maximum of the first peak

**Required features**: peak_time**Units**: ms**Pseudocode**:time_to_first_spike = peaktime[0] - stimstart

#### time_to_last_spike¶

SpikeEvent : Time from stimulus start to last spike

**Required features**: peak_time (ms), stimstart (ms)**Units**: ms**Pseudocode**:if len(peak_time) > 0: time_to_last_spike = peak_time[-1] - stimstart else: time_to_last_spike = 0

#### time_to_second_spike¶

SpikeEvent : Time from the start of the stimulus to the maximum of the second peak

**Required features**: peak_time**Units**: ms**Pseudocode**:time_to_second_spike = peaktime[1] - stimstart

#### inv_time_to_first_spike¶

SpikeEvent : 1.0 over time to first spike (times 1000 to convert it to Hz); returns 0 when no spike

**Required features**: time_to_first_spike**Units**: Hz**Pseudocode**:if len(time_to_first_spike) > 0: inv_time_to_first_spike = 1000.0 / time_to_first_spike[0] else: inv_time_to_first_spike = 0

#### ISI_values¶

ISI Python efeature : The interspike intervals (i.e. time intervals) between adjacent peaks.

**Required features**: peak_time (ms)**Units**: ms**Pseudocode**:isi_values = numpy.diff(peak_time)[1:]

#### all_ISI_values¶

SpikeEvent : The interspike intervals, i.e., the time intervals between adjacent peaks.

**Required features**: peak_time (ms)**Units**: ms**Pseudocode**:all_isi_values_vec = numpy.diff(peak_time)

#### inv_ISI_values¶

ISI Python efeature : Computes all inverse spike interval values.

**Required features**: peak_time (ms)**Units**: Hz**Pseudocode**:all_isi_values_vec = numpy.diff(peak_time) inv_isi_values = 1000.0 / all_isi_values_vec

#### inv_first_ISI, inv_second_ISI, inv_third_ISI, inv_fourth_ISI, inv_fifth_ISI, inv_last_ISI¶

ISI Python efeature : 1.0 over first/second/third/fourth/fith/last ISI; returns 0 when no ISI

**Required features**: peak_time (ms)**Units**: Hz**Pseudocode**:all_isi_values_vec = numpy.diff(peak_time) if len(all_isi_values_vec) > 0: inv_first_ISI = 1000.0 / all_isi_values_vec[0] else: inv_first_ISI = 0 if len(all_isi_values_vec) > 1: inv_second_ISI = 1000.0 / all_isi_values_vec[1] else: inv_second_ISI = 0 if len(all_isi_values_vec) > 2: inv_third_ISI = 1000.0 / all_isi_values_vec[2] else: inv_third_ISI = 0 if len(all_isi_values_vec) > 3: inv_fourth_ISI = 1000.0 / all_isi_values_vec[3] else: inv_fourth_ISI = 0 if len(all_isi_values_vec) > 4: inv_fifth_ISI = 1000.0 / all_isi_values_vec[4] else: inv_fifth_ISI = 0 if len(all_isi_values_vec) > 0: inv_last_ISI = 1000.0 / all_isi_values_vec[-1] else: inv_last_ISI = 0

#### doublet_ISI¶

SpikeEvent : The time interval between the first two peaks

**Required features**: peak_time (ms)**Units**: ms**Pseudocode**:doublet_ISI = peak_time[1] - peak_time[0]

#### ISI_semilog_slope¶

ISI Python efeature : The slope of a linear fit to a semilog plot of the ISI values.

Attention: the 1st ISI is not taken into account unless ignore_first_ISI is set to 0. See Python efeature: ISIs feature for more details.

**Required features**: t, V, stim_start, stim_end, ISI_values**Units**: ms**Pseudocode**:x = range(1, len(ISI_values)+1) log_ISI_values = numpy.log(ISI_values) slope, _ = numpy.polyfit(x, log_ISI_values, 1) ISI_semilog_slope = slope

#### ISI_log_slope¶

ISI Python efeature : The slope of a linear fit to a loglog plot of the ISI values.

Attention: the 1st ISI is not taken into account unless ignore_first_ISI is set to 0. See Python efeature: ISIs feature for more details.

**Required features**: t, V, stim_start, stim_end, ISI_values**Units**: ms**Pseudocode**:log_x = numpy.log(range(1, len(ISI_values)+1)) log_ISI_values = numpy.log(ISI_values) slope, _ = numpy.polyfit(log_x, log_ISI_values, 1) ISI_log_slope = slope

#### ISI_log_slope_skip¶

ISI Python efeature : The slope of a linear fit to a loglog plot of the ISI values, but not taking into account the first ISI values.

The proportion of ISI values to be skipped is given by spike_skipf (between 0 and 1). However, if this number of ISI values to skip is higher than max_spike_skip, then max_spike_skip is taken instead.

**Required features**: t, V, stim_start, stim_end, ISI_values**Parameters**: spike_skipf (default=0.1), max_spike_skip (default=2)**Units**: ms**Pseudocode**:start_idx = min([max_spike_skip, round((len(ISI_values) + 1) * spike_skipf)]) ISI_values = ISI_values[start_idx:] log_x = numpy.log(range(1, len(ISI_values)+1)) log_ISI_values = numpy.log(ISI_values) slope, _ = numpy.polyfit(log_x, log_ISI_values, 1) ISI_log_slope = slope

#### ISI_CV¶

ISI Python efeature : The coefficient of variation of the ISIs.

Attention: the 1st ISI is not taken into account unless ignore_first_ISI is set to 0. See Python efeature: ISIs feature for more details.

**Required features**: ISIs**Units**: constant**Pseudocode**:ISI_mean = numpy.mean(ISI_values) ISI_CV = np.std(isi_values, ddof=1) / ISI_mean

#### irregularity_index¶

ISI Python efeature : Mean of the absolute difference of all ISIs, except the first one (see Python efeature: ISIs feature for more details.)

The first ISI can be taken into account if ignore_first_ISI is set to 0.

**Required features**: ISI_values**Units**: ms**Pseudocode**:irregularity_index = numpy.mean(numpy.absolute(ISI_values[1:] - ISI_values[:-1]))

#### adaptation_index¶

SpikeEvent : Normalized average difference of two consecutive ISIs, skipping the first ISIs

The proportion of ISI values to be skipped is given by spike_skipf (between 0 and 1). However, if this number of ISI values to skip is higher than max_spike_skip, then max_spike_skip is taken instead.

The adaptation index is zero for a constant firing rate and bigger than zero for a decreasing firing rate

**Required features**: stim_start, stim_end, peak_time**Parameters**: offset (default=0), spike_skipf (default=0.1), max_spike_skip (default=2)**Units**: constant**Pseudocode**:# skip the first ISIs peak_selection = [peak_time >= stim_start - offset, peak_time <= stim_end - offset] spike_time = peak_time[numpy.all(peak_selection, axis=0)] start_idx = min([max_spike_skip, round(len(spike_time) * spike_skipf)]) spike_time = spike_time[start_idx:] # compute the adaptation index ISI_values = spike_time[1:] - spike_time[:-1] ISI_sum = ISI_values[1:] + ISI_values[:-1] ISI_sub = ISI_values[1:] - ISI_values[:-1] adaptation_index = numpy.mean(ISI_sum / ISI_sub)

#### adaptation_index_2¶

SpikeEvent : Normalized average difference of two consecutive ISIs, starting at the second ISI

The adaptation index is zero for a constant firing rate and bigger than zero for a decreasing firing rate

**Required features**: stim_start, stim_end, peak_time**Parameters**: offset (default=0)**Units**: constant**Pseudocode**:# skip the first ISI peak_selection = [peak_time >= stim_start - offset, peak_time <= stim_end - offset] spike_time = peak_time[numpy.all(peak_selection, axis=0)] spike_time = spike_time[1:] # compute the adaptation index ISI_values = spike_time[1:] - spike_time[:-1] ISI_sum = ISI_values[1:] + ISI_values[:-1] ISI_sub = ISI_values[1:] - ISI_values[:-1] adaptation_index = numpy.mean(ISI_sum / ISI_sub)

#### spike_count¶

Python efeature : Number of spikes in the trace, including outside of stimulus interval

**Required features**: peak_indices**Units**: constant**Pseudocode**:spike_count = len(peak_indices)

**Note**: “spike_count” is the new name for the feature “Spikecount”.
“Spikecount”, while still available, will be removed in the future.

#### spike_count_stimint¶

Python efeature : Number of spikes inside the stimulus interval

**Required features**: peak_time**Units**: constant**Pseudocode**:peaktimes_stimint = numpy.where((peak_time >= stim_start) & (peak_time <= stim_end)) spike_count_stimint = len(peaktimes_stimint)

**Note**: “spike_count_stimint” is the new name for the feature “Spikecount_stimint”.
“Spikecount_stimint”, while still available, will be removed in the future.

#### number_initial_spikes¶

SpikeEvent : Number of spikes at the beginning of the stimulus

**Required features**: peak_time**Required parameters**: initial_perc (default=0.1)**Units**: constant**Pseudocode**:initial_length = (stimend - stimstart) * initial_perc number_initial_spikes = len(numpy.where( \ (peak_time >= stimstart) & \ (peak_time <= stimstart + initial_length)))

#### mean_frequency¶

SpikeEvent : The mean frequency of the firing rate

**Required features**: stim_start, stim_end, peak_time**Units**: Hz**Pseudocode**:condition = np.all((stim_start < peak_time, peak_time < stim_end), axis=0) spikecount = len(peak_time[condition]) last_spike_time = peak_time[peak_time < stim_end][-1] mean_frequency = 1000 * spikecount / (last_spike_time - stim_start)

#### strict_burst_mean_freq¶

SpikeEvent : The mean frequency during a burst for each burst

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

The burst detection can be fine-tuned by changing the setting strict_burst_factor. Default value is 2.0.

**Required features**: burst_begin_indices, burst_end_indices, peak_time**Units**: Hz**Pseudocode**:if burst_begin_indices is None or burst_end_indices is None: strict_burst_mean_freq = None else: strict_burstmean_freq = ( (burst_end_indices - burst_begin_indices + 1) * 1000 / ( peak_time[burst_end_indices] - peak_time[burst_begin_indices] ) )

#### burst_mean_freq¶

ISI Python efeature : The mean frequency during a burst for each burst

If burst_ISI_indices did not detect any burst beginning, then the spikes are not considered to be part of any burst

**Required features**: burst_ISI_indices, peak_time**Units**: Hz**Pseudocode**:if burst_ISI_indices is None: return None elif len(burst_ISI_indices) == 0: return [] burst_mean_freq = [] burst_index = numpy.insert( burst_index_tmp, burst_index_tmp.size, len(peak_time) - 1 ) # 1st burst span = peak_time[burst_index[0]] - peak_time[0] N_peaks = burst_index[0] + 1 burst_mean_freq.append(N_peaks * 1000 / span) for i, burst_idx in enumerate(burst_index[:-1]): if burst_index[i + 1] - burst_idx != 1: span = peak_time[burst_index[i + 1]] - peak_time[burst_idx + 1] N_peaks = burst_index[i + 1] - burst_idx burst_mean_freq.append(N_peaks * 1000 / span) return burst_mean_freq

#### strict_burst_number¶

ISI Python efeature : The number of bursts

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

The burst detection can be fine-tuned by changing the setting strict_burst_factor. Default value is 2.0.

**Required features**: strict_burst_mean_freq**Units**: constant**Pseudocode**:burst_number = len(strict_burst_mean_freq)

#### burst_number¶

Python efeature : The number of bursts

**Required features**: burst_mean_freq**Units**: constant**Pseudocode**:burst_number = len(burst_mean_freq)

#### single_burst_ratio¶

ISI Python efeature : Length of the second isi over the median of the rest of the isis. The first isi is not taken into account, because it could bias the feature. See ISI_values feature for more details.

If ignore_first_ISI is set to 0, then signle burst ratio becomes the length of the first isi over the median of the rest of the isis.

**Required features**: ISI_values**Units**: constant**Pseudocode**:single_burst_ratio = ISI_values[0] / numpy.mean(ISI_values)

#### spikes_per_burst¶

Python efeature : Number of spikes in each burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

The burst detection can be fine-tuned by changing the setting strict_burst_factor. Defalt value is 2.0.

**Required features**: burst_begin_indices, burst_end_indices**Units**: constant**Pseudocode**:spike_per_bursts = [] for idx_begin, idx_end in zip(burst_begin_indices, burst_end_indices): spike_per_bursts.append(idx_end - idx_begin + 1)

#### spikes_per_burst_diff¶

Python efeature : Difference of number of spikes between each burst and the next one.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

The burst detection can be fine-tuned by changing the setting strict_burst_factor. Defalt value is 2.0.

**Required features**: spikes_per_burst**Units**: constant**Pseudocode**:spikes_per_burst[:-1] - spikes_per_burst[1:]

#### spikes_in_burst1_burst2_diff¶

Python efeature : Difference of number of spikes between the first burst and the second one.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

The burst detection can be fine-tuned by changing the setting strict_burst_factor. Defalt value is 2.0.

**Required features**: spikes_per_burst_diff**Units**: constant**Pseudocode**:numpy.array([spikes_per_burst_diff[0]])

#### spikes_in_burst1_burstlast_diff¶

Python efeature : Difference of number of spikes between the first burst and the last one.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: spikes_per_burst**Units**: constant**Pseudocode**:numpy.array([spikes_per_burst[0] - spikes_per_burst[-1]])

#### strict_interburst_voltage¶

SpikeEvent : The voltage average in between two bursts

Iterating over the burst indices determine the first peak of each burst. Starting 5 ms after the previous peak, take the voltage average until 5 ms before the peak.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

The burst detection can be fine-tuned by changing the setting strict_burst_factor. Default value is 2.0.

**Required features**: burst_begin_indices, peak_indices**Units**: mV**Pseudocode**:interburst_voltage = [] for idx in burst_begin_idxs[1:]: ts_idx = peak_idxs[idx - 1] t_start = t[ts_idx] + 5 start_idx = numpy.argwhere(t < t_start)[-1][0] te_idx = peak_idxs[idx] t_end = t[te_idx] - 5 end_idx = numpy.argwhere(t > t_end)[0][0] interburst_voltage.append(numpy.mean(v[start_idx:end_idx + 1]))

#### interburst_voltage¶

ISI Python efeature : The voltage average in between two bursts

Iterating over the burst ISI indices determine the last peak before the burst. Starting 5 ms after that peak take the voltage average until 5 ms before the first peak of the subsequent burst.

**Required features**: burst_ISI_indices, peak_indices**Units**: mV**Pseudocode**:interburst_voltage = [] for idx in burst_ISI_idxs: ts_idx = peak_idxs[idx] t_start = time[ts_idx] + 5 start_idx = numpy.argwhere(time < t_start)[-1][0] te_idx = peak_idxs[idx + 1] t_end = time[te_idx] - 5 end_idx = numpy.argwhere(time > t_end)[0][0] interburst_voltage.append(numpy.mean(voltage[start_idx:end_idx + 1]))

#### interburst_min_values¶

SpikeEvent : The minimum voltage between the end of a burst and the next spike.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: peak_indices, burst_end_indices**Units**: mV**Pseudocode**:interburst_min = [ numpy.min( v[peak_indices[i]:peak_indices[i + 1]] ) for i in burst_end_indices if i + 1 < len(peak_indices) ]

#### interburst_duration¶

SpikeEvent : Duration between the last spike of each burst and the next spike.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: burst_end_indices, peak_time**Units**: ms**Pseudocode**:interburst_duration = [ peak_time[idx + 1] - peak_time[idx] for idx in burst_end_indices if idx + 1 < len(peak_time) ]

#### interburst_15percent_values, interburst_20percent_values, interburst_25percent_values, interburst_30percent_values, interburst_40percent_values, interburst_60percent_values¶

SpikeEvent : Voltage value after a given percentage (15%, 20%, 25%, 30%, 40% or 60%) of the interburst duration after the fast AHP.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: postburst_fast_ahp_indices, burst_end_indices, peak_indices**Units**: mV**Pseudocode**:interburst_XXpercent_values = [] for i, postburst_fahp_i in enumerate(postburst_fahpi): if i < len(burst_endi) and burst_endi[i] + 1 < len(peaki): time_interval = t[peaki[burst_endi[i] + 1]] - t[postburst_fahp_i] time_at_XXpercent = t[postburst_fahp_i] + time_interval * percentage / 100. index_at_XXpercent = numpy.argwhere(t >= time_at_XXpercent)[0][0] interburst_XXpercent_values.append(v[index_at_XXpercent])

#### time_to_interburst_min¶

SpikeEvent : The time between the last spike of a burst and the minimum between that spike and the next.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: peak_indices, burst_end_indices, peak_time**Units**: ms**Pseudocode**:time_to_interburst_min = [ t[peak_indices[i] + numpy.argmin( v[peak_indices[i]:peak_indices[i + 1]] )] - peak_time[i] for i in burst_end_indices if i + 1 < len(peak_indices) ]

#### time_to_postburst_slow_ahp¶

SpikeEvent : The time between the last spike of a burst and the slow ahp afterwards.

The number of ms to skip after the spike to skip fast AHP and look for slow AHP can be set with sahp_start. Default is 5.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: postburst_slow_ahp_indices, burst_end_indices, peak_time**Units**: ms**Pseudocode**:time_to_postburst_slow_ahp_py = t[postburst_slow_ahp_indices] - peak_time[burst_end_indices]

#### postburst_min_values¶

SpikeEvent : The minimum voltage after the end of a burst.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: peak_indices, burst_end_indices**Units**: mV**Pseudocode**:postburst_min = [ numpy.min( v[peak_indices[i]:peak_indices[i + 1]] ) for i in burst_end_indices if i + 1 < len(peak_indices) ] if len(postburst_min) < len(burst_end_indices): if t[burst_end_indices[-1]] < stim_end: end_idx = numpy.where(t >= stim_end)[0][0] postburst_min.append(numpy.min( v[peak_indices[burst_end_indices[-1]]:end_idx] )) else: postburst_min.append(numpy.min( v[peak_indices[burst_end_indices[-1]]:] ))

#### postburst_slow_ahp_values¶

SpikeEvent : The slow AHP voltage after the end of a burst.

The number of ms to skip after the spike to skip fast AHP and look for slow AHP can be set with sahp_start. Default is 5.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: peak_indices, burst_end_indices**Units**: mV**Pseudocode**:postburst_slow_ahp = [] for i in burst_end_indices: i_start = numpy.where(t >= t[peak_indices[i]] + sahp_start)[0][0] if i + 1 < len(peak_indices): postburst_slow_ahp.append(numpy.min(v[i_start:peak_indices[i + 1]])) else: if t[burst_end_indices[-1]] < stim_end: end_idx = numpy.where(t >= stim_end)[0][0] postburst_slow_ahp.append(numpy.min(v[i_start:end_idx])) else: postburst_slow_ahp.append(numpy.min(v[i_start:]))

#### postburst_fast_ahp_values¶

SpikeEvent : The fast AHP voltage after the end of a burst.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: peak_indices, burst_end_indices**Units**: mV**Pseudocode**:postburst_fahp = [] for i in burst_end_indices: if i + 1 < len(peak_indices): stop_i = peak_indices[i + 1] elif i + 1 < stim_end_index: stop_i = stim_end_index else: stop_i = len(v) - 1 v_crop = v[peak_indices[i]:stop_i] # get where the voltage is going up crop_args = numpy.argwhere(numpy.diff(v_crop) >= 0)[:,0] # the voltage should go up for at least two consecutive points crop_arg_arg = numpy.argwhere(numpy.diff(crop_args) == 1)[0][0] crop_arg = crop_args[crop_arg_arg] end_i = peak_indices[i] + crop_arg + 1 # the fast ahp is between last peak of burst and the point where voltage is going back up postburst_fahp.append(numpy.min(v[peak_indices[i]:end_i])) return postburst_fahp

#### postburst_adp_peak_values¶

SpikeEvent : The small ADP peak after the fast AHP after the end of a burst.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: postburst_fast_ahp_indices, postburst_slow_ahp_indices**Units**: mV**Pseudocode**:adp_peak_values = [] for i, sahpi in enumerate(postburst_sahpi): if sahpi < postburst_fahpi[i]: continue adppeaki = numpy.argmax(v[postburst_fahpi[i]:sahpi]) + postburst_fahpi[i] if adppeaki != sahpi - 1: adp_peak_values.append(v[adppeaki]) if len(adp_peak_values) == 0: return None return adp_peak_values

#### time_to_postburst_fast_ahp¶

SpikeEvent : Time to the fast AHP after the end of a burst.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: postburst_fast_ahp_indices, burst_end_indices, peak_time**Units**: ms**Pseudocode**:[t[fahpi] - peak_time[burst_endi[i]] for i, fahpi in enumerate(postburst_fahpi)]

#### time_to_postburst_adp_peak¶

SpikeEvent : Time to the small ADP peak after the fast AHP after the end of a burst.

This implementation does not assume that every spike belongs to a burst.

The first spike is ignored by default. This can be changed by setting ignore_first_ISI to 0.

**Required features**: postburst_adp_peak_indices, burst_end_indices, peak_time**Units**: ms**Pseudocode**:time_to_postburst_adp_peaks = [] n_peaks = len(peak_time) for i, adppeaki in enumerate(postburst_adppeaki): # there are not always an adp peak after each burst # so make sure that the burst and adp peak indices are consistent k = 0 while ( burst_endi[i] + k + 1 < n_peaks and peak_time[burst_endi[i] + k + 1] < t[adppeaki] ): k += 1 time_to_postburst_adp_peaks.append(t[adppeaki] - peak_time[burst_endi[i] + k]) return time_to_postburst_adp_peaks

### Spike shape features¶

#### peak_voltage¶

SpikeShape : The voltages at the maxima of the peaks

**Required features**: peak_indices**Units**: mV**Pseudocode**:peak_voltage = voltage[peak_indices]

#### AP_height¶

SpikeShape : Same as peak_voltage: The voltages at the maxima of the peaks

**Required features**: peak_voltage**Units**: mV**Pseudocode**:AP_height = peak_voltage

#### AP_amplitude, AP1_amp, AP2_amp, APlast_amp¶

SpikeShape : The relative height of the action potential from spike onset

**Required features**: AP_begin_indices, peak_voltage (mV)**Units**: mV**Pseudocode**:AP_amplitude = peak_voltage - voltage[AP_begin_indices] AP1_amp = AP_amplitude[0] AP2_amp = AP_amplitude[1] APlast_amp = AP_amplitude[-1]

#### mean_AP_amplitude¶

SpikeShape : The mean of all of the action potential amplitudes

**Required features**: AP_amplitude (mV)**Units**: mV**Pseudocode**:mean_AP_amplitude = numpy.mean(AP_amplitude)

#### AP_Amplitude_change¶

SpikeShape : Difference of the amplitudes of the second and the first action potential divided by the amplitude of the first action potential

**Required features**: AP_amplitude**Units**: constant**Pseudocode**:AP_amplitude_change = (AP_amplitude[1:] - AP_amplitude[0]) / AP_amplitude[0]

#### AP_amplitude_from_voltagebase¶

SpikeShape : The relative height of the action potential from voltage base

**Required features**: voltage_base, peak_voltage (mV)**Units**: mV**Pseudocode**:AP_amplitude_from_voltagebase = peak_voltage - voltage_base

#### AP1_peak, AP2_peak¶

SpikeShape : The peak voltage of the first and second action potentials

**Required features**: peak_voltage (mV)**Units**: mV**Pseudocode**:AP1_peak = peak_voltage[0] AP2_peak = peak_voltage[1]

#### AP2_AP1_diff¶

SpikeShape : Difference amplitude of the second to first spike

**Required features**: AP_amplitude (mV)**Units**: mV**Pseudocode**:AP2_AP1_diff = AP_amplitude[1] - AP_amplitude[0]

#### AP2_AP1_peak_diff¶

SpikeShape : Difference peak voltage of the second to first spike

**Required features**: peak_voltage (mV)**Units**: mV**Pseudocode**:AP2_AP1_diff = peak_voltage[1] - peak_voltage[0]

#### amp_drop_first_second¶

SpikeShape : Difference of the amplitude of the first and the second peak

**Required features**: peak_voltage (mV)**Units**: mV**Pseudocode**:amp_drop_first_second = peak_voltage[0] - peak_voltage[1]

#### amp_drop_first_last¶

SpikeShape : Difference of the amplitude of the first and the last peak

**Required features**: peak_voltage (mV)**Units**: mV**Pseudocode**:amp_drop_first_last = peak_voltage[0] - peak_voltage[-1]

#### amp_drop_second_last¶

SpikeShape : Difference of the amplitude of the second and the last peak

**Required features**: peak_voltage (mV)**Units**: mV**Pseudocode**:amp_drop_second_last = peak_voltage[1] - peak_voltage[-1]

#### max_amp_difference¶

SpikeShape : Maximum difference of the height of two subsequent peaks

**Required features**: peak_voltage (mV)**Units**: mV**Pseudocode**:max_amp_difference = numpy.max(peak_voltage[:-1] - peak_voltage[1:])

#### AP_amplitude_diff¶

SpikeShape : Difference of the amplitude of two subsequent peaks

**Required features**: AP_amplitude (mV)**Units**: mV**Pseudocode**:AP_amplitude_diff = AP_amplitude[1:] - AP_amplitude[:-1]

#### min_AHP_values¶

SpikeShape : Absolute voltage values at the first after-hyperpolarization.

**Required features**: min_AHP_indices**Units**: mV

#### AHP_depth¶

SpikeShape : Relative voltage values at the first after-hyperpolarization

**Required features**: voltage_base (mV), min_AHP_values (mV)**Units**: mV**Pseudocode**:min_AHP_values = first_min_element(voltage, peak_indices) AHP_depth = min_AHP_values[:] - voltage_base

#### AHP_depth_abs¶

SpikeShape : Absolute voltage values at the first after-hyperpolarization. Is the same as min_AHP_values

**Required features**: min_AHP_values (mV)**Units**: mV

#### AHP_depth_diff¶

SpikeShape : Difference of subsequent relative voltage values at the first after-hyperpolarization

**Required features**: AHP_depth (mV)**Units**: mV**Pseudocode**:AHP_depth_diff = AHP_depth[1:] - AHP_depth[:-1]

#### AHP_depth_from_peak, AHP1_depth_from_peak, AHP2_depth_from_peak¶

SpikeShape : Voltage difference between AP peaks and first AHP depths

**Required features**: peak_indices, min_AHP_indices**Units**: mV**Pseudocode**:AHP_depth_from_peak = v[peak_indices] - v[min_AHP_indices] AHP1_depth_from_peak = AHP_depth_from_peak[0] AHP2_depth_from_peak = AHP_depth_from_peak[1]

#### AHP_time_from_peak¶

SpikeShape : Time between AP peaks and first AHP depths

**Required features**: peak_indices, min_AHP_values (mV)**Units**: ms**Pseudocode**:min_AHP_indices = first_min_element(voltage, peak_indices) AHP_time_from_peak = t[min_AHP_indices[:]] - t[peak_indices[i]]

#### fast_AHP¶

SpikeShape : Voltage value of the action potential onset relative to the subsequent AHP

Ignores the last spike

**Required features**: AP_begin_indices, min_AHP_values**Units**: mV**Pseudocode**:fast_AHP = voltage[AP_begin_indices[:-1]] - voltage[min_AHP_indices[:-1]]

#### fast_AHP_change¶

SpikeShape : Difference of the fast AHP of the second and the first action potential divided by the fast AHP of the first action potential

**Required features**: fast_AHP**Units**: constant**Pseudocode**:fast_AHP_change = (fast_AHP[1:] - fast_AHP[0]) / fast_AHP[0]

#### AHP_depth_abs_slow¶

SpikeShape : Absolute voltage values at the first after-hyperpolarization starting a given number of ms (default: 5) after the peak

**Required features**: peak_indices**Units**: mV

#### AHP_depth_slow¶

SpikeShape : Relative voltage values at the first after-hyperpolarization starting a given number of ms (default: 5) after the peak

**Required features**: voltage_base (mV), AHP_depth_abs_slow (mV)**Units**: mV**Pseudocode**:AHP_depth_slow = AHP_depth_abs_slow[:] - voltage_base

#### AHP_slow_time¶

SpikeShape : Time difference between slow AHP (see AHP_depth_abs_slow) and peak, divided by interspike interval

**Required features**: AHP_depth_abs_slow**Units**: constant

#### ADP_peak_values¶

SpikeShape : Absolute voltage values of the small afterdepolarization peak

strict_stiminterval should be set to True for this feature to behave as expected.

**Required features**: min_AHP_indices, min_between_peaks_indices**Units**: mV**Pseudocode**:adp_peak_values = numpy.array( [numpy.max(v[i:j + 1]) for (i, j) in zip(min_AHP_indices, min_v_indices)] )

#### ADP_peak_amplitude¶

SpikeShape : Amplitude of the small afterdepolarization peak with respect to the fast AHP voltage

strict_stiminterval should be set to True for this feature to behave as expected.

**Required features**: min_AHP_values, ADP_peak_values**Units**: mV**Pseudocode**:adp_peak_amplitude = adp_peak_values - min_AHP_values

#### depolarized_base¶

SpikeShape : Mean voltage between consecutive spikes (from the end of one spike to the beginning of the next one)

**Required features**: AP_end_indices, AP_begin_indices**Units**: mV**Pseudocode**:depolarized_base = [] for (start_idx, end_idx) in zip( AP_end_indices[:-1], AP_begin_indices[1:]) ): depolarized_base.append(numpy.mean(voltage[start_idx:end_idx]))

#### min_voltage_between_spikes¶

SpikeShape : Minimal voltage between consecutive spikes

**Required features**: peak_indices**Units**: mV**Pseudocode**:min_voltage_between_spikes = [] for peak1, peak2 in zip(peak_indices[:-1], peak_indices[1:]): min_voltage_between_spikes.append(numpy.min(voltage[peak1:peak2]))

#### min_between_peaks_values¶

SpikeShape : Minimal voltage between consecutive spikes

The last value of min_between_peaks_values is the minimum between last spike and stimulus end if strict stiminterval is True, and minimum between last spike and last voltage value if strict stiminterval is False

**Required features**: min_between_peaks_indices**Units**: mV**Pseudocode**:min_between_peaks_values = v[min_between_peaks_indices]

#### AP_duration_half_width¶

SpikeShape : Width of spike at half spike amplitude, with spike onset as described in AP_begin_time

**Required features**: AP_rise_indices, AP_fall_indices**Units**: ms**Pseudocode**:AP_rise_indices = index_before_peak((v(peak_indices) - v(AP_begin_indices)) / 2) AP_fall_indices = index_after_peak((v(peak_indices) - v(AP_begin_indices)) / 2) AP_duration_half_width = t(AP_fall_indices) - t(AP_rise_indices)

#### AP_duration_half_width_change¶

SpikeShape : Difference of the FWHM of the second and the first action potential divided by the FWHM of the first action potential

**Required features**: AP_duration_half_width**Units**: constant**Pseudocode**:AP_duration_half_width_change = ( AP_duration_half_width[1:] - AP_duration_half_width[0] ) / AP_duration_half_width[0]

#### AP_width¶

SpikeShape : Width of spike at threshold, bounded by minimum AHP

Can use strict_stiminterval compute only for data in stimulus interval.

**Required features**: peak_indices, min_AHP_indices, threshold**Units**: ms**Pseudocode**:min_AHP_indices = numpy.concatenate([[stim_start], min_AHP_indices]) for i in range(len(min_AHP_indices)-1): onset_index = numpy.where(v[min_AHP_indices[i]:min_AHP_indices[i+1]] > threshold)[0] onset_time[i] = t[onset_index] offset_time[i] = t[numpy.where(v[onset_index:min_AHP_indices[i+1]] < threshold)[0]] AP_width[i] = t(offset_time[i]) - t(onset_time[i])

#### AP_duration¶

SpikeShape : Duration of an action potential from onset to offset

**Required features**: AP_begin_indices, AP_end_indices**Units**: ms**Pseudocode**:AP_duration = time[AP_end_indices] - time[AP_begin_indices]

#### AP_duration_change¶

SpikeShape : Difference of the durations of the second and the first action potential divided by the duration of the first action potential

**Required features**: AP_duration**Units**: constant**Pseudocode**:AP_duration_change = (AP_duration[1:] - AP_duration[0]) / AP_duration[0]

#### AP_width_between_threshold¶

SpikeShape : Width of spike at threshold, bounded by minimum between peaks

Can use strict_stiminterval to not use minimum after stimulus end.

**Required features**: peak_indices, min_between_peaks_indices, threshold**Units**: ms**Pseudocode**:min_between_peaks_indices = numpy.concatenate([[stim_start], min_between_peaks_indices]) for i in range(len(min_between_peaks_indices)-1): onset_index = numpy.where(v[min_between_peaks_indices[i]:min_between_peaks_indices[i+1]] > threshold)[0] onset_time[i] = t[onset_index] offset_time[i] = t[numpy.where(v[onset_index:min_between_peaks_indices[i+1]] < threshold)[0]] AP_width[i] = t(offset_time[i]) - t(onset_time[i])

#### spike_half_width, AP1_width, AP2_width, APlast_width¶

SpikeShape : Width of spike at half spike amplitude, with the spike amplitude taken as the difference between the minimum between two peaks and the next peak

**Required features**: peak_indices, min_AHP_indices**Units**: ms**Pseudocode**:min_AHP_indices = numpy.concatenate([[stim_start], min_AHP_indices]) for i in range(1, len(min_AHP_indices)): v_half_width = (v[peak_indices[i-1]] + v[min_AHP_indices[i]]) / 2. rise_idx = numpy.where(v[min_AHP_indices[i-1]:peak_indices[i-1]] > v_half_width)[0] v_dev = v_half_width - v[rise_idx] delta_v = v[rise_idx] - v[rise_idx - 1] delta_t = t[rise_idx] - t[rise_idx - 1] t_dev_rise = delta_t * v_dev / delta_v fall_idx = numpy.where(v[peak_indices[i-1]:min_AHP_indices[i]] < v_half_width)[0] v_dev = v_half_width - v[fall_idx] delta_v = v[fall_idx] - v[fall_idx - 1] delta_t = t[fall_idx] - t[fall_idx - 1] t_dev_fall = delta_t * v_dev / delta_v spike_half_width[i] = t[fall_idx] + t_dev_fall - t[rise_idx] - t_dev_rise AP1_width = spike_half_width[0] AP2_width = spike_half_width[1] APlast_width = spike_half_width[-1]

#### spike_width2¶

SpikeShape : Width of spike at half spike amplitude, with the spike onset taken as the maximum of the second derivative of the voltage in the range between the minimum between two peaks and the next peak

**Required features**: peak_indices, min_AHP_indices**Units**: ms**Pseudocode**:for i in range(len(min_AHP_indices)): dv2 = CentralDiffDerivative(CentralDiffDerivative(v[min_AHP_indices[i]:peak_indices[i + 1]])) peak_onset_idx = numpy.argmax(dv2) + min_AHP_indices[i] v_half_width = (v[peak_indices[i + 1]] + v[peak_onset_idx]) / 2. rise_idx = numpy.where(v[peak_onset_idx:peak_indices[i + 1]] > v_half_width)[0] v_dev = v_half_width - v[rise_idx] delta_v = v[rise_idx] - v[rise_idx - 1] delta_t = t[rise_idx] - t[rise_idx - 1] t_dev_rise = delta_t * v_dev / delta_v fall_idx = numpy.where(v[peak_indices[i + 1]:] < v_half_width)[0] v_dev = v_half_width - v[fall_idx] delta_v = v[fall_idx] - v[fall_idx - 1] delta_t = t[fall_idx] - t[fall_idx - 1] t_dev_fall = delta_t * v_dev / delta_v spike_width2[i] = t[fall_idx] + t_dev_fall - t[rise_idx] - t_dev_rise

#### AP_begin_width, AP1_begin_width, AP2_begin_width¶

SpikeShape : Width of spike at spike start

**Required features**: min_AHP_indices, AP_begin_indices**Units**: ms**Pseudocode**:for i in range(len(min_AHP_indices)): rise_idx = AP_begin_indices[i] fall_idx = numpy.where(v[rise_idx + 1:min_AHP_indices[i]] < v[rise_idx])[0] AP_begin_width[i] = t[fall_idx] - t[rise_idx] AP1_begin_width = AP_begin_width[0] AP2_begin_width = AP_begin_width[1]

#### AP2_AP1_begin_width_diff¶

SpikeShape : Difference width of the second to first spike

**Required features**: AP_begin_width**Units**: ms**Pseudocode**:AP2_AP1_begin_width_diff = AP_begin_width[1] - AP_begin_width[0]

#### AP_begin_voltage, AP1_begin_voltage, AP2_begin_voltage¶

SpikeShape : Voltage at spike start

**Required features**: AP_begin_indices**Units**: mV**Pseudocode**:AP_begin_voltage = v[AP_begin_indices] AP1_begin_voltage = AP_begin_voltage[0] AP2_begin_voltage = AP_begin_voltage[1]

#### AP_begin_time¶

SpikeShape : Time at spike start. Spike start is defined as where the first derivative of the voltage trace is higher than 10 V/s , for at least 5 points

**Required features**: AP_begin_indices**Units**: ms**Pseudocode**:AP_begin_time = t[AP_begin_indices]

#### AP_peak_upstroke¶

SpikeShape : Maximum of rise rate of spike

**Required features**: AP_begin_indices, peak_indices**Units**: V/s**Pseudocode**:ap_peak_upstroke = [] for apbi, pi in zip(ap_begin_indices, peak_indices): ap_peak_upstroke.append(numpy.max(dvdt[apbi:pi]))

#### AP_peak_downstroke¶

SpikeShape : Minimum of fall rate from spike

**Required features**: min_AHP_indices, peak_indices**Units**: V/s**Pseudocode**:ap_peak_downstroke = [] for ahpi, pi in zip(min_ahp_indices, peak_indices): ap_peak_downstroke.append(numpy.min(dvdt[pi:ahpi]))

#### AP_rise_time¶

SpikeShape : Time between the AP threshold and the peak, given a window (default: from 0% to 100% of the AP amplitude)

**Required features**: AP_begin_indices, peak_indices, AP_amplitude**Units**: ms**Pseudocode**:rise_times = [] begin_voltages = AP_amps * rise_start_perc + voltage[AP_begin_indices] end_voltages = AP_amps * rise_end_perc + voltage[AP_begin_indices] for AP_begin_indice, peak_indice, begin_v, end_v in zip( AP_begin_indices, peak_indices, begin_voltages, end_voltages ): voltage_window = voltage[AP_begin_indice:peak_indice] new_begin_indice = AP_begin_indice + numpy.min( numpy.where(voltage_window >= begin_v)[0] ) new_end_indice = AP_begin_indice + numpy.max( numpy.where(voltage_window <= end_v)[0] ) rise_times.append(time[new_end_indice] - time[new_begin_indice])

#### AP_fall_time¶

SpikeShape : Time from action potential maximum to the offset

**Required features**: AP_end_indices, peak_indices**Units**: ms**Pseudocode**:AP_fall_time = time[AP_end_indices] - time[peak_indices]

#### AP_rise_rate¶

SpikeShape : Voltage change rate during the rising phase of the action potential

**Required features**: AP_begin_indices, peak_indices**Units**: V/s**Pseudocode**:AP_rise_rate = (voltage[peak_indices] - voltage[AP_begin_indices]) / ( time[peak_indices] - time[AP_begin_indices] )

#### AP_fall_rate¶

SpikeShape : Voltage change rate during the falling phase of the action potential

**Required features**: AP_end_indices, peak_indices**Units**: V/s**Pseudocode**:AP_fall_rate = (voltage[AP_end_indices] - voltage[peak_indices]) / ( time[AP_end_indices] - time[peak_indices] )

#### AP_rise_rate_change¶

SpikeShape : Difference of the rise rates of the second and the first action potential divided by the rise rate of the first action potential

**Required features**: AP_rise_rate_change**Units**: constant**Pseudocode**:AP_rise_rate_change = (AP_rise_rate[1:] - AP_rise_rate[0]) / AP_rise_rate[0]

#### AP_fall_rate_change¶

SpikeShape : Difference of the fall rates of the second and the first action potential divided by the fall rate of the first action potential

**Required features**: AP_fall_rate_change**Units**: constant**Pseudocode**:AP_fall_rate_change = (AP_fall_rate[1:] - AP_fall_rate[0]) / AP_fall_rate[0]

#### AP_phaseslope¶

SpikeShape : Slope of the V, dVdt phasespace plot at the beginning of every spike

(at the point where the derivative crosses the DerivativeThreshold)

**Required features**: AP_begin_indices**Parameters**: AP_phaseslope_range**Units**: 1/(ms)**Pseudocode**:range_max_idxs = AP_begin_indices + AP_phseslope_range range_min_idxs = AP_begin_indices - AP_phseslope_range AP_phaseslope = (dvdt[range_max_idxs] - dvdt[range_min_idxs]) / (v[range_max_idxs] - v[range_min_idxs])

#### phaseslope_max¶

Python efeature : Computes the maximum of the phase slope. Attention, this feature is sensitive to interpolation timestep.

**Required features**: time, voltage**Units**: V/s**Pseudocode**:phaseslope = numpy.diff(voltage) / numpy.diff(time) phaseslope_max = numpy.array([numpy.max(phaseslope)])

#### initburst_sahp¶

Python efeature : Slow AHP voltage after initial burst

The end of the initial burst is detected when the ISIs frequency gets lower than initburst_freq_threshold, in Hz. Then the sahp is searched for the interval between initburst_sahp_start (in ms) after the last spike of the burst, and initburst_sahp_end (in ms) after the last spike of the burst.

**Required features**: peak_time**Parameters**: initburst_freq_threshold (default=50), initburst_sahp_start (default=5), initburst_sahp_end (default=100)**Units**: mV

#### initburst_sahp_ssse¶

Python efeature : Slow AHP voltage from steady_state_voltage_stimend after initial burst

**Required features**: steady_state_voltage_stimend, initburst_sahp**Units**: mV**Pseudocode**:numpy.array([initburst_sahp_value[0] - ssse[0]])

#### initburst_sahp_vb¶

Python efeature : Slow AHP voltage from voltage base after initial burst

**Required features**: voltage_base, initburst_sahp**Units**: mV**Pseudocode**:numpy.array([initburst_sahp_value[0] - voltage_base[0]])

### Subthreshold features¶

#### steady_state_voltage_stimend¶

Subthreshold : The average voltage during the last 10% of the stimulus duration.

**Required features**: t, V, stim_start, stim_end**Units**: mV**Pseudocode**:stim_duration = stim_end - stim_start begin_time = stim_end - 0.1 * stim_duration end_time = stim_end steady_state_voltage_stimend = numpy.mean(voltage[numpy.where((t < end_time) & (t >= begin_time))])

#### steady_state_hyper¶

Subthreshold : Steady state voltage during hyperpolarization for 30 data points (after interpolation)

**Required features**: t, V, stim_start, stim_end**Units**: mV**Pseudocode**:stim_end_idx = numpy.argwhere(time >= stim_end)[0][0] steady_state_hyper = numpy.mean(voltage[stim_end_idx - 35:stim_end_idx - 5])

#### steady_state_voltage¶

Subthreshold : The average voltage after the stimulus

**Required features**: t, V, stim_end**Units**: mV**Pseudocode**:steady_state_voltage = numpy.mean(voltage[numpy.where((t <= max(t)) & (t > stim_end))])

#### voltage_base¶

Subthreshold : The average voltage during the last 10% of time before the stimulus.

**Required features**: t, V, stim_start, stim_end**Parameters**: voltage_base_start_perc (default = 0.9), voltage_base_end_perc (default = 1.0)**Units**: mV**Pseudocode**:voltage_base = numpy.mean(voltage[numpy.where( (t >= voltage_base_start_perc * stim_start) & (t <= voltage_base_end_perc * stim_start))])

#### current_base¶

Subthreshold : The average current during the last 10% of time before the stimulus.

**Required features**: t, I, stim_start, stim_end**Parameters**: current_base_start_perc (default = 0.9), current_base_end_perc (default = 1.0), precision_threshold (default = 1e-10), current_base_mode (can be “mean” or “median”, default=”mean”)**Units**: nA**Pseudocode**:current_slice = I[numpy.where( (t >= current_base_start_perc * stim_start) & (t <= current_base_end_perc * stim_start))] if current_base_mode == "mean": current_base = numpy.mean(current_slice) elif current_base_mode == "median": current_base = numpy.median(current_slice)

#### time_constant¶

Subthreshold : The membrane time constant

The extraction of the time constant requires a voltage trace of a cell in a hyper- polarized state. Starting at stim start find the beginning of the exponential decay where the first derivative of V(t) is smaller than -0.005 V/s in 5 subsequent points. The flat subsequent to the exponential decay is defined as the point where the first derivative of the voltage trace is bigger than -0.005 and the mean of the follwowing 70 points as well. If the voltage trace between the beginning of the decay and the flat includes more than 9 points, fit an exponential decay. Yield the time constant of that decay.

**Required features**: t, V, stim_start, stim_end**Units**: ms**Pseudocode**:min_derivative = 5e-3 decay_start_min_length = 5 # number of indices min_length = 10 # number of indices t_length = 70 # in ms # get start and middle indices stim_start_idx = numpy.where(time >= stim_start)[0][0] # increment stimstartindex to skip a possible transient stim_start_idx += 10 stim_middle_idx = numpy.where(time >= (stim_start + stim_end) / 2.)[0][0] # get derivative t_interval = time[stim_start_idx:stim_middle_idx] dv = five_point_stencil_derivative(voltage[stim_start_idx:stim_middle_idx]) dt = five_point_stencil_derivative(t_interval) dvdt = dv / dt # find start and end of decay # has to be over deriv threshold for at least a given number of indices pass_threshold_idxs = numpy.append( -1, numpy.argwhere(dvdt > -min_derivative).flatten() ) length_idx = numpy.argwhere( numpy.diff(pass_threshold_idxs) > decay_start_min_length )[0][0] i_start = pass_threshold_idxs[length_idx] + 1 # find flat (end of decay) flat_idxs = numpy.argwhere(dvdt[i_start:] > -min_derivative).flatten() # for loop is not optimised # but we expect the 1st few values to be the ones we are looking for for i in flat_idxs: i_flat = i + i_start i_flat_stop = numpy.argwhere( t_interval >= t_interval[i_flat] + t_length )[0][0] if numpy.mean(dvdt[i_flat:i_flat_stop]) > -min_derivative: break dvdt_decay = dvdt[i_start:i_flat] t_decay = time[stim_start_idx + i_start:stim_start_idx + i_flat] v_decay_tmp = voltage[stim_start_idx + i_start:stim_start_idx + i_flat] v_decay = abs(v_decay_tmp - voltage[stim_start_idx + i_flat]) if len(dvdt_decay) < min_length: return None # -- golden search algorithm -- # from scipy.optimize import minimize_scalar def numpy_fit(x, t_decay, v_decay): new_v_decay = v_decay + x log_v_decay = numpy.log(new_v_decay) (slope, _), res, _, _, _ = numpy.polyfit( t_decay, log_v_decay, 1, full=True ) range = numpy.max(log_v_decay) - numpy.min(log_v_decay) return res / (range * range) max_bound = min_derivative * 1000. golden_bracket = [0, max_bound] result = minimize_scalar( numpy_fit, args=(t_decay, v_decay), bracket=golden_bracket, method='golden', ) # -- fit -- # log_v_decay = numpy.log(v_decay + result.x) slope, _ = numpy.polyfit(t_decay, log_v_decay, 1) time_constant = -1. / slope

#### decay_time_constant_after_stim¶

Subthreshold : The decay time constant of the voltage right after the stimulus

**Required features**: t, V, stim_start, stim_end**Parameters**: decay_start_after_stim (default = 1.0 ms), decay_end_after_stim (default = 10.0 ms)**Units**: ms**Pseudocode**:time_interval = t[numpy.where(t => decay_start_after_stim & t < decay_end_after_stim)] - t[numpy.where(t == stim_end)] voltage_interval = abs(voltages[numpy.where(t => decay_start_after_stim & t < decay_end_after_stim)] - voltages[numpy.where(t == decay_start_after_stim)]) log_voltage_interval = numpy.log(voltage_interval) slope, _ = numpy.polyfit(time_interval, log_voltage_interval, 1) decay_time_constant_after_stim = -1. / slope

#### multiple_decay_time_constant_after_stim¶

Subthreshold : When multiple stimuli are applied, this function returns a list of decay time constants each computed on the voltage right after each stimulus.

The settings multi_stim_start and multi_stim_end are mandatory for this feature to work. Each is a list containing the start and end times of each stimulus present in the current protocol respectively.

**Required features**: t, V, stim_start, stim_end**Required settings**: multi_stim_start, multi_stim_end**Parameters**: decay_start_after_stim (default = 1.0 ms), decay_end_after_stim (default = 10.0 ms)**Units**: ms**Pseudocode**:multiple_decay_time_constant_after_stim = [] for i in range(len(number_stimuli): stim_start = multi_stim_start[i] stim_end = multi_stim_end[i] multiple_decay_time_constant_after_stim.append( decay_time_constant_after_stim(stim_start, stim_end) )

#### sag_time_constant¶

Subthreshold : The decay time constant of the exponential voltage decay from the bottom of the sag to the steady-state.

The start of the decay is taken at the minimum voltage (the bottom of the sag). The end of the decay is taken when the voltage crosses the steady state voltage minus 10% of the sag amplitude. The time constant is the slope of the linear fit to the log of the voltage. The golden search algorithm is not used, since the data is expected to be noisy and adding a parameter in the log ( log(voltage + x) ) is likely to increase errors on the fit.

**Required features**: t, V, stim_start, stim_end, minimum_voltage, steady_state_voltage_stimend, sag_amplitude**Units**: ms**Pseudocode**:# get start decay start_decay = numpy.argmin(vinterval) # get end decay v90 = steady_state_v - 0.1 * sag_ampl end_decay = numpy.where((tinterval > tinterval[start_decay]) & (vinterval >= v90))[0][0] v_reference = vinterval[end_decay] # select t, v in decay interval interval_indices = numpy.arange(start_decay, end_decay) interval_time = tinterval[interval_indices] interval_voltage = abs(vinterval[interval_indices] - v_reference) # get tau log_interval_voltage = numpy.log(interval_voltage) slope, _ = numpy.polyfit(interval_time, log_interval_voltage, 1) tau = abs(1. / slope)

#### sag_amplitude¶

Subthreshold : The difference between the minimal voltage and the steady state at stimend

**Required features**: t, V, stim_start, stim_end, steady_state_voltage_stimend, minimum_voltage, voltage_deflection_stim_ssse**Parameters**:**Units**: mV**Pseudocode**:if (voltage_deflection_stim_ssse <= 0): sag_amplitude = steady_state_voltage_stimend - minimum_voltage else: sag_amplitude = None

#### sag_ratio1¶

Subthreshold : The ratio between the sag amplitude and the maximal sag extend from voltage base

**Required features**: t, V, stim_start, stim_end, sag_amplitude, voltage_base, minimum_voltage**Parameters**:**Units**: constant**Pseudocode**:if voltage_base != minimum_voltage: sag_ratio1 = sag_amplitude / (voltage_base - minimum_voltage) else: sag_ratio1 = None

#### sag_ratio2¶

Subthreshold : The ratio between the maximal extends of sag from steady state and voltage base

**Required features**: t, V, stim_start, stim_end, steady_state_voltage_stimend, voltage_base, minimum_voltage**Parameters**:**Units**: constant**Pseudocode**:if voltage_base != minimum_voltage: sag_ratio2 = (voltage_base - steady_state_voltage_stimend) / (voltage_base - minimum_voltage) else: sag_ratio2 = None

#### ohmic_input_resistance¶

Subthreshold : The ratio between the voltage deflection and stimulus current

**Required features**: t, V, stim_start, stim_end, voltage_deflection**Parameters**: stimulus_current**Units**: MΩ**Pseudocode**:ohmic_input_resistance = voltage_deflection / stimulus_current

#### ohmic_input_resistance_vb_ssse¶

Subthreshold : The ratio between the voltage deflection (between voltage base and steady-state voltage at stimend) and stimulus current

**Required features**: t, V, stim_start, stim_end, voltage_deflection_vb_ssse**Parameters**: stimulus_current**Units**: MΩ**Pseudocode**:ohmic_input_resistance_vb_ssse = voltage_deflection_vb_ssse / stimulus_current

#### voltage_deflection_vb_ssse¶

Subthreshold : The voltage deflection between voltage base and steady-state voltage at stimend

The voltage base used is the average voltage during the last 10% of time before the stimulus and the steady state voltage at stimend used is the average voltage during the last 10% of the stimulus duration.

**Required features**: t, V, stim_start, stim_end, voltage_base, steady_state_voltage_stimend**Units**: mV**Pseudocode**:voltage_deflection_vb_ssse = steady_state_voltage_stimend - voltage_base

#### voltage_deflection¶

Subthreshold : The voltage deflection between voltage base and steady-state voltage at stimend

The voltage base used is the average voltage during all of the time before the stimulus and the steady state voltage at stimend used is the average voltage of the five values before the last five values before the end of the stimulus duration.

**Required features**: t, V, stim_start, stim_end**Units**: mV**Pseudocode**:voltage_base = numpy.mean(V[t < stim_start]) stim_end_idx = numpy.where(t >= stim_end)[0][0] steady_state_voltage_stimend = numpy.mean(V[stim_end_idx-10:stim_end_idx-5]) voltage_deflection = steady_state_voltage_stimend - voltage_base

#### voltage_deflection_begin¶

Subthreshold : The voltage deflection between voltage base and steady-state voltage soon after stimulation start

The voltage base used is the average voltage during all of the time before the stimulus and the steady state voltage used is the average voltage taken from 5% to 15% of the stimulus duration.

**Required features**: t, V, stim_start, stim_end**Units**: mV**Pseudocode**:voltage_base = numpy.mean(V[t < stim_start]) tstart = stim_start + 0.05 * (stim_end - stim_start) tend = stim_start + 0.15 * (stim_end - stim_start) condition = numpy.all((tstart < t, t < tend), axis=0) steady_state_voltage_stimend = numpy.mean(V[condition]) voltage_deflection = steady_state_voltage_stimend - voltage_base

#### voltage_after_stim¶

Subthreshold : The mean voltage after the stimulus in (stim_end + 25%*end_period, stim_end + 75%*end_period)

**Required features**: t, V, stim_end**Units**: mV**Pseudocode**:tstart = stim_end + (t[-1] - stimEnd) * 0.25 tend = stim_end + (t[-1] - stimEnd) * 0.75 condition = numpy.all((tstart < t, t < tend), axis=0) voltage_after_stim = numpy.mean(V[condition])

#### minimum_voltage¶

Subthreshold : The minimum of the voltage during the stimulus

**Required features**: t, V, stim_start, stim_end**Units**: mV**Pseudocode**:minimum_voltage = min(voltage[numpy.where((t >= stim_start) & (t <= stim_end))])

#### maximum_voltage¶

Subthreshold : The maximum of the voltage during the stimulus

**Required features**: t, V, stim_start, stim_end**Units**: mV**Pseudocode**:maximum_voltage = max(voltage[numpy.where((t >= stim_start) & (t <= stim_end))])

#### maximum_voltage_from_voltagebase¶

Subthreshold : Difference between maximum voltage during stimulus and voltage base

**Required features**: maximum_voltage, voltage_base**Units**: mV**Pseudocode**:maximum_voltage_from_voltagebase = maximum_voltage - voltage_base

#### depol_block_bool¶

Python efeature : Check for a depolarization block. Returns 1 if there is a depolarization block or a hyperpolarization block, and returns 0 otherwise.

A depolarization block is detected when the voltage stays higher than the mean of AP_begin_voltage for longer than 50 ms.

A hyperpolarization block is detected when, after stimulus start, the voltage stays below -75 mV for longer than 50 ms.

**Required features**: AP_begin_voltage**Units**: constant

#### impedance¶

Python efeature : Computes the impedance given a ZAP current input and its voltage response. It will return the frequency at which the impedance is maximal, in the range (0, impedance_max_freq] Hz, with impedance_max_freq being a setting with 50.0 as a default value.

**Required features**: current, spike_count, voltage_base, current_base**Units**: Hz**Pseudocode**:normalized_voltage = voltage_trace - voltage_base normalized_current = current_trace - current_base if spike_count < 1: # if there is no spikes in ZAP fft_volt = numpy.fft.fft(normalized_voltage) fft_cur = numpy.fft.fft(normalized_current) if any(fft_cur) == 0: return None # convert dt from ms to s to have freq in Hz freq = numpy.fft.fftfreq(len(normalized_voltage), d=dt / 1000.) Z = fft_volt / fft_cur norm_Z = abs(Z) / max(abs(Z)) select_idxs = numpy.swapaxes(numpy.argwhere((freq > 0) & (freq <= impedance_max_freq)), 0, 1)[0] smooth_Z = gaussian_filter1d(norm_Z[select_idxs], 10) ind_max = numpy.argmax(smooth_Z) return freq[ind_max] else: return None