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.

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:

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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

Source

eFeatures.rst