def _find_peak(siginfo):
"""
Obtains an estimation of the peak situation of a QRS complex, from the
energy interval that forms the base evidence, a fragment of signal evidence,
a reference time point, and the interval of valid points for the peak.
"""
dist = lambda p : 1.0 + 2.0 * abs(p - C.QRS_BANN_DMAX)/ms2sp(150)
dist = np.vectorize(dist)
peak = None
#For each lead, the peak will be the maximum deviation point wrt the
#baseline, and applying the distance function just defined. We give more
#importance to the first leads, as they supposedly have more quality.
for _, sig, points, baseline, _ in siginfo:
if len(points) < 3:
continue
peaks = points[sig_meas.get_peaks(sig[points])]
if len(peaks) == 0:
continue
peakscore = abs(sig[peaks]-baseline)/dist(peaks)
lpeak = peaks[peakscore.argmax()]
if peak is None:
peak = lpeak
elif abs(peak-lpeak) <= C.TMARGIN:
peak = lpeak if lpeak < peak else peak
return peak
def delineate_qrs(siginfo):
"""
Performs the multi-lead delineation of a QRS complex enclosed in a
specific time interval, returning an instance of the QRS class.
Parameters
----------
siginfo:
List-like structure containing all the necessary information of the
ECG signal in the searching time interval. Each entry in this list
is assumed to be a tuple of the **LeadInfo** class, and the list is
assumed to be ordered by the quality of the signal in each lead.
Returns
-------
out:
QRS object with all the attributes properly set. If the delineation
cannot be performed, an InconsistencyError is raised.
"""
verify(siginfo)
qrs = QRS()
#Peak point estimation.
peak = _find_peak(siginfo)
verify(peak is not None)
#QRS start and end estimation
#For each lead, we first check if it is a paced beat, whose delineation
#process is different. In case of failure, we perform common delineation.
limits = OrderedDict()
for lead, sig, points, baseline, _ in siginfo:
endpoints = _paced_qrs_delineation(sig, points, peak, baseline)
if endpoints is None:
endpoints = _qrs_delineation(sig, points, peak)
if endpoints is None:
continue
limits[lead] = (False, endpoints)
else:
limits[lead] = (True, endpoints)
#Now we combine the limits in all leads.
start, end = _combine_limits(limits, siginfo, peak)
verify(start is not None and end > start)
#QRS waveform extraction for each lead.
for lead, sig, points, baseline, _ in siginfo:
#We constrain the area delineated so far.
sig = sig[start:end+1]
points = points[np.logical_and(points >= start,
points <= end)] - start
if len(points) == 0:
continue
if points[0] != 0:
points = np.insert(points, 0, 0)
if points[-1] != len(sig) - 1:
points = np.append(points, len(sig) - 1)
if len(points) < 3:
continue
#We define a distance function to evaluate the peaks
dist = (lambda p : 1.0 + 2.0 * abs(start + p - C.QRS_BANN_DMAX)
/ms2sp(150))
dist = np.vectorize(dist)
#We get the peak for this lead
pks = points[sig_meas.get_peaks(sig[points])]
if len(pks) == 0:
continue
peakscore = abs(sig[pks]-baseline)/dist(pks)
peak = pks[peakscore.argmax()]
#Now we get the shape of the QRS complex in this lead.
shape = None
#If there is a pace detection in this lead
if lead in limits and limits[lead][0]:
endpoints = limits[lead][1]
shape = _get_paced_qrs_shape(sig, points,
endpoints.start - start,
min(endpoints.end-start,len(sig)))
if shape is None:
limits[lead] = (False, endpoints)
if shape is None:
shape = _get_qrs_shape(sig, points, peak, baseline)
if shape is None:
continue
qrs.shape[lead] = shape
#There must be a recognizable QRS waveform in at least one lead.
verify(qrs.shape)
#The detected shapes may constrain the delineation area.
llim = min(qrs.shape[lead].waves[0].l for lead in qrs.shape)
if llim > 0:
start = start + llim
for lead in qrs.shape:
qrs.shape[lead].move(-llim)
ulim = max(qrs.shape[lead].waves[-1].r for lead in qrs.shape)
if ulim < end-start:
end = start + ulim
#The definitive peak is assigned to the first relevant wave
#(each QRS shapeform has a specific peak point.)
peak = start + min(s.waves[_reference_wave(s)].m
for s in qrs.shape.itervalues())
#Segmentation points set
qrs.paced = any(v[0] for v in limits.itervalues())
qrs.start, qrs.peak, qrs.end = start, peak, end
###################################################################
#Amplitude conditions (between 0.5mV and 6.5 mV in at least one
#lead or an identified pattern in most leads).
###################################################################
verify(len(qrs.shape) > len(siginfo)/2.0 or
C.QRS_MIN_AMP <= max(s.amplitude for s in qrs.shape.itervalues())
<= C.QRS_MAX_AMP)
return qrs
def _find_spike(signal, points):
"""
Looks for a pacemaker spike in a signal fragment, applying fixed thresholds
on wave duration, angles and amplitude. These thresholds are the following:
- The duration of the spike must be shorter than 30ms.
- The ascent and descent angles of the spike must be higher than 75º in
common ECG scale.
- The amplitude of the spike must be at least 0.2 mV (2mm) in the edge with
lower amplitude.
- The falling edge must be of lower amplitude than the rising edge.
Parameters
----------
signal:
Numpy array containing the signal information referenced by the wave
object.
points:
Relevant points detected on the signal.
Returns
-------
out:
Tuple with three integer values, which are the begin, peak, and
end of the detected spike. If no spikes were detected, returns None.
"""
#Angle between two points
angle = lambda a, b : math.atan(dg2mm(abs(signal[b]-signal[a])/sp2mm(b-a)))
#First we search for the left edge of the spike.
spike = []
for i in xrange(1, len(points)-3):
for j in xrange(i+1, len(points)-2):
pts = points[i:j+1]
llim = pts[-1]
#There can be no peaks inside the left edge.
if (llim-pts[0] > C.SPIKE_DUR or
(len(pts) >= 3 and len(get_peaks(signal[pts])) > 0)):
break
#The end of the left edge must be a peak.
if len(get_peaks(signal[llim-1:llim+2])) < 1:
continue
#Left edge candidate
ledge = abs(signal[pts[0]] - signal[llim])
if (ledge >= C.SPIKE_EDGE_AMP and
angle(pts[0], llim) >= math.radians(85)):
#Right edge delineation.
ulim = min(int(pts[0]+C.SPIKE_DUR), points[-1])
rsig = signal[llim:ulim+1]
if len(rsig) < 3:
break
rpks = get_peaks(rsig)
if np.any(rpks):
ulim = llim + rpks[0]
ulim = ulim-1 if ulim-1 in points else ulim
ulim = ulim+1 if ulim+1 in points else ulim
while ulim > llim:
redge = abs(signal[ulim] - signal[llim])
if redge < C.SPIKE_EDGE_AMP:
break
if (redge-ledge < C.SPIKE_ECGE_DIFF and
angle(llim, ulim) >= math.radians(75)):
#Spike candidate detected
spike.append((pts[0], llim, ulim))
break
ulim -= 1
if not spike or max(sp[0] for sp in spike) >= min(sp[-1] for sp in spike):
return None
#We get the spike with highest energy.
return max(spike, key = lambda spk:
np.sum(np.diff(signal[spk[0]:spk[-1]+1])**2))
def _paced_qrs_delineation(signal, points, peak, baseline):
"""
Checks if a sequence of waves is a paced heartbeat. The main criteria is
the presence of a spike at the beginning of the beat, followed by at least
one significant wave.
"""
try:
#Gets the slope between two points.
slope = lambda a, b : abs(dg2mm((signal[b]-signal[a])/sp2mm(b-a)))
#First we search for the spike.
spike = _find_spike(signal, points)
verify(spike)
if not spike[-1] in points:
points = np.insert(points, bisect.bisect(points, spike[-1]),
spike[-1])
#Now we get relevant points, checking some related constraints.
bpts = points[points <= spike[0]]
apts = points[points >= spike[-1]]
verify(len(apts) >= 2)
#Before and after the spike there must be a significant slope change.
verify(slope(spike[0], spike[1]) > 2.0 * slope(bpts[-2], bpts[-1]))
verify(slope(spike[1], spike[-1]) > 2.0 * slope(apts[0], apts[1]))
#Now we look for the end of the QRS complex, by applying the same
#clustering strategy than regular QRS, but only for the end.
slopes = (signal[apts][1:]-signal[apts][:-1])/(apts[1:]-apts[:-1])
features = []
for i in xrange(len(slopes)):
#The features are the slope in logarithmic scale and the distance to
#the peak.
features.append([math.log(abs(slopes[i])+1.0),
abs(apts[i+1] - peak)])
features = whiten(features)
#We initialize the centroids in the extremes (considering what is
#interesting of each feature for us)
fmin = np.min(features, 0)
fmax = np.max(features, 0)
valid = np.where(kmeans2(features, np.array([[fmin[0], fmax[1]],
[fmax[0], fmin[1]]]), minit = 'matrix')[1])[0]
verify(np.any(valid))
end = apts[valid[-1]+1]
#The duration of the QRS complex after the spike must be more than 2
#times the duration of the spike.
verify((end-apts[0]) > 2.0 * (spike[-1]-spike[0]))
#The amplitude of the qrs complex must higher than 0.5 the amplitude
#of the spike.
sgspike = signal[spike[0]:spike[-1]+1]
sgqrs = signal[apts[0]:end+1]
verify(np.ptp(sgqrs) > ph2dg(0.5))
verify(np.ptp(sgqrs) > 0.5 * np.ptp(sgspike))
#There must be at least one peak in the QRS fragment.
qrspt = signal[apts[apts <= end]]
verify(len(qrspt) >= 3)
verify(abs(signal[end] - signal[spike[0]]) <= ph2dg(0.3)
or len(get_peaks(qrspt)) > 0)
#The area of the rest of the QRS complex must be higher than the spike.
verify(np.sum(np.abs(sgspike-sgspike[0])) <
np.sum(np.abs(sgqrs-sgspike[0])))
#The distance between the beginning of the spike and the baseline
#cannot be more than the 30% of the amplitude of the complex.
verify(abs(signal[spike[0]]-baseline) <
0.3 * np.ptp(signal[spike[0]:end+1]))
#At last, we have found the paced QRS limits.
return Iv(spike[0], end)
except InconsistencyError:
return None
def _qrs_delineation(signal, points, peak):
"""
Returns the interval points of a possible QRS complex in a signal fragment.
Parameters
----------
signal:
Array containing a signal fragment with a possible QRS inside its limits
points:
Representative points candidates to be the limits..
peak:
Point of the determined QRS peak.
Returns
-------
out:
The interval of the QRS.
"""
try:
verify(len(points) >= 3)
#We get the slope of each segment determined by the relevant points
slopes = ((signal[points][1:]-signal[points][:-1])/
(points[1:]-points[:-1]))
#We also get the peaks determined by the signal simplification.
pks = points[sig_meas.get_peaks(signal[points])]
verify(len(pks) > 0)
#Now we perform a clustering operation over each slope, with a certain
#set of features.
features = []
for i in xrange(len(slopes)):
#We obtain the midpoint of the segment, and its difference with
#respect to the peak, applying a temporal margin.
#We get as representative point of the segment the starting point
#if the segment is prior to the peak, and the ending point
#otherwise.
point = points[i] if points[i] < peak else points[i+1]
#The features are the slope in logarithmic scale and the distance to
#the peak.
dist = abs(point - peak)
features.append([math.log(abs(slopes[i])+1.0), dist])
#We perform a clustering operation on the extracted features
features = whiten(features)
#We initialize the centroids in the extremes (considering what is
#interesting of each feature for us)
fmin = np.min(features, 0)
fmax = np.max(features, 0)
tags = kmeans2(features, np.array([[fmin[0], fmax[1]],
[fmax[0], fmin[1]]]),
minit = 'matrix')[1]
valid = np.where(tags)[0]
verify(np.any(valid))
start = points[valid[0]]
end = points[valid[-1]+1]
#If the relation between not valid and valid exceeds 0.5, we take the
#highest valid interval containing the peak.
if _invalidtime_rate(points, valid) > 0.5:
#We get the last valid segment before the peak, and the first valid
#segment after the peak. We expand them with consecutive valid
#segments.
try:
start = max(v for v in valid if points[v] <= peak)
while start-1 in valid:
start -= 1
end = min(v for v in valid if points[v+1] >= peak)
while end+1 in valid:
end += 1
start, end = points[start], points[end+1]
except ValueError:
return None
#We ensure there is a peak between the limits.
verify(np.any(np.logical_and(pks > start, pks < end)))
#If there are no peaks, we don't accept the delineation
return Iv(start, end)
except InconsistencyError:
return None