Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram
Abstract
:1. Introduction
2. ECG Diagnostic Procedures
- Beat-to-beat variations of selected heartbeat parameters such as RR interval, beat types (arrhythmia), ST-segment, T-wave alternans etc., also known as sequence analysis.
- Details of the conduction path functionality, expressed in parameters of most typical heartbeat or group representative, also known as contour analysis.
- a heartbeat detector,
- a heartbeat classifier, and
- a wave border delineator.
3. Non-Uniform Sampling
- Uniform signals with occasionally missing samples, e.g., being results of data transmission or storage errors, where outliers are usually interpolated from the neighbor values.
- Partially decimated signals, where local sampling interval is a multiple of given basic interval, being usually a result of compressed sensing or time-domain reconstruction from incomplete dyadic wavelet representation; in these signals we assume the sampling interval to be given by a discrete-time function with discrete values.
- Signals with random sampling intervals; in these signals we assume the sampling interval to be given by a continuous time domain discrete value function.
- (1)
- Given a generator φ, one need to find conditions on X, in the form of a density, such that for cp and Cp being positive constants independent of f the norm equivalence holds:
- (2)
- One needs to design reconstruction procedures which are useful in practical applications to recover f from its samples , when the norm equivalence (above) is satisfied. The numerical algorithm has to be efficient and fast, therefore first approaches useful for arbitrary sampling used adaptive weights to compensate for the local variations of the sampling density.
4. Proposed Methodology of Non-Uniform ECG Interpretation
4.1. QRS Detection in Non-Uniform Ecg Signal
- (1)
- We build two pairs: (1) a long time (ΔtL = 61 ms) and (2) a short time (ΔtM = 20 ms) of triangle legs with ends wL−, wL+:
- (2)
- We determine the slope coefficients mL−(t) and mL+(t) (and respectively mM−(t) and mM+(t)) of segments y = m·t best fitted to the selected samples as:
- (3)
- We calculate the angle L(t) of best fitted triangle legs wL− and wL+ adjacent to the time point t (Equation (8)) as in [26]:
- (4)
- Since the heartbeat peak is characterized by significant turn of activity represented in small values of angles between long time triangle legs and concurrently between short time triangle legs, we simply take the inverse of product of these values:
4.2. QRS/Beat Classification for Non-Uniform Patterns
- In the first step, for each node in GA corresponding node(s) in GB are found so as they have most similar time attribute; similar correspondence is reciprocally built for GB nodes.
- The GA node at the detection point is aligned to its counterpart at the GB detection point.
- For each other node the node of minimum absolute time is selected and the value of its counterpart node (i.e., with the same time attribute) is interpolated in the other graph.
- Similarity score is then calculated as cumulative sum of absolute differences of values at subsequent nodes modulated by a time-dependent weighting factor.
- Dividing of the similarity score by the average amplitude ends calculation of the distance.
- In a multilead record common wave border values are used to determine arbitrary sampling grid at signal source, therefore time attributes of graph signal representation in particular leads are the same.
- In arbitrary sampling shorter sampling interval was applied to more informative parts of the ECG (e.g., within the confines of QRS), consequently the information on sampling interval may be used as modulator of the similarity score.
- In threshold-based decision making the beat-to-kernel comparison can be stopped immediately when the cumulative dissimilarity exceeds the threshold value; doing so helps to avoid unnecessary calculations.
- While in uniform case updating of the kernel may be done by averaging of respective samples, arbitrarily sampled beats may update the kernel either by updating the values existing near to respective time coordinates, or by contributing with new data falling between the existing samples. Therefore, for class kernel representations we adopt a beat-independent arbitrary quantization pattern (Figure 4). It increases local sampling density (i.e., decreases the sampling interval) near the fiducial point to a value 8-times higher than maximum signal sampling density and decreases it respectively with the distance from the fiducial point. Consequently, amplitude values next to the fiducial point (i.e., in central part of the pattern) contribute more significantly to the likelihood assessment than the peripheral part of the beat or kernel. This significantly limits the count of required interpolations and saves much of the computation burden at the price of classification accuracy.
4.3. Delineation of QRS Waves in Non-Uniform Representation
- Discrete regularly sampled analyzing wavelets are located in a time-scale decomposition grid accordingly to their values of scale a and shift b corresponding to the position of the atom in a pyramid decomposition scheme.
- The correlation coefficient c between the non-uniform signal and the analyzing wavelet is calculated and attributed to the atom at a given position (a, b) in the grid:
5. Test Procedure, Signals, and Conditions
5.1. Test Procedure
- reference (i.e., uniform) interpretation of uniform signal oECG,
- uniform interpretation of uniformized signal uECG,
- non-uniform interpretation of non-uniform signal nECG, and
- non-uniform interpretation of pseudo-non-uniform signal pECG.
5.2. Error Metrics
5.3. Test Signals
5.4. Perceptual Information Distribution as Arbitrary Sampling Model of the ECG
- local bandwidth of ECG waves [113],
- susceptibility of diagnostic result to signal distortion caused by a local data loss, and
5.5. Processing of Test Signals Accordingly to the Arbitrary Sampling Model
6. Test Results
6.1. Results of QRS Detection Test
6.2. Results of QRS/Beat Classification Test
6.3. Results of QRS Waves Delineator Test
- Average position of the fiducial point, being an approximate of the ground truth.
- Standard deviation of the results, being an approximate of difficulty level in getting a consistent result; it is noteworthy that due to various medical content and recording conditions, particular records pose different challenges to the interpretive software making the results more or less reliable; consequently, absolute values of position difference cannot be directly collected from all files.
- Rank of the delineator under test given accordingly to ascending absolute difference of calculated or provided and ground truth result; the rank R displayed in Table 6 for four proposed testing scenarios was calculated among 19 reference interpretive software from CSE database.
- Original signal (oECG) results, in which the delineation accuracy was affected by limited precision of reference interpretive software,
- Uniformized signal (uECG) results, in which the delineation accuracy was affected by limited precision of reference interpretive software and non-uniform representation of the signal (however the use of reference software required transforming the nECG back to the uniform sampling space),
- Non-uniform signal (nECG) results, in which the delineation accuracy was affected by limited precision of proposed delineator under test and non-uniform representation of the signal.
- Pseudo-non-uniform signal (pECG) results, in which the delineation accuracy was affected only by limited precision of proposed delineator under test.
7. Discussion
Funding
Acknowledgments
Conflicts of Interest
References
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AAMI Type | AAMI Label | MITDB Type and Label | Total |
---|---|---|---|
Normal | N | Normal (NOR)—N Left Bundle Branch Block (LBBB)—L Right Bundle Branch Block (RBBB)—R | 89,838 |
Supraventricular ectopic | S | Atrial Premature Contraction (APC)—A Nodal (Junctional Escape Beat)—j Blocked Atrial Premature Beat (BAP)—x Aberrant Atrial Premature Beat (AP)—a Nodal (Junctional) Premature Beat (NP)—J Atrial Escape Beat (AE)—e | 3217 |
Ventricular ectopic | V | Premature Ventricular Contraction (PVC)—V Ventricular Flutter (VF)—! Ventricular Escape Beat (VE)—E | 7480 |
Fusion | F | Fusion of Ventricular and Normal Beat (VFN)—F | 802 |
Unknown | Q | Unclassificable Beat (UN)—Q | 15 |
MITDB File ID | Results | ||||||
---|---|---|---|---|---|---|---|
Beats | TP | FP | FN | Se [%] | PPV [%] | Fd [%] | |
100 | 2273 | 2272 | 0 | 1 | 99.96 | 100.00 | 0.04 |
101 | 1865 | 1864 | 3 | 1 | 99.95 | 99.84 | 0.21 |
103 | 2084 | 2083 | 0 | 1 | 99.95 | 100.00 | 0.05 |
105 | 2572 | 2568 | 13 | 4 | 99.84 | 99.50 | 0.66 |
106 | 2027 | 2026 | 0 | 1 | 99.95 | 100.00 | 0.05 |
108 | 1774 | 1773 | 28 | 1 | 99.94 | 98.45 | 1.61 |
109 | 2532 | 2532 | 0 | 0 | 100.00 | 100.00 | 0.00 |
111 | 2124 | 2124 | 1 | 0 | 100.00 | 99.95 | 0.05 |
112 | 2539 | 2539 | 0 | 0 | 100.00 | 100.00 | 0.00 |
113 | 1795 | 1795 | 0 | 0 | 100.00 | 100.00 | 0.00 |
114 | 1873 | 1871 | 9 | 2 | 99.89 | 99.52 | 0.58 |
115 | 1953 | 1953 | 0 | 0 | 100.00 | 100.00 | 0.00 |
116 | 2412 | 2396 | 1 | 16 | 99.34 | 99.96 | 0.70 |
117 | 1535 | 1535 | 0 | 0 | 100.00 | 100.00 | 0.00 |
118 | 2288 | 2288 | 1 | 0 | 100.00 | 99.96 | 0.04 |
119 | 1987 | 1987 | 1 | 0 | 100.00 | 99.95 | 0.05 |
121 | 1863 | 1862 | 0 | 1 | 99.95 | 100.00 | 0.05 |
122 | 2476 | 2476 | 0 | 0 | 100.00 | 100.00 | 0.00 |
123 | 1518 | 1518 | 0 | 0 | 100.00 | 100.00 | 0.00 |
124 | 1619 | 1619 | 0 | 0 | 100.00 | 100.00 | 0.00 |
200 | 2601 | 2600 | 1 | 1 | 99.96 | 99.96 | 0.08 |
201 | 2000 | 1998 | 0 | 2 | 99.90 | 100.00 | 0.10 |
202 | 2136 | 2136 | 1 | 0 | 100.00 | 99.95 | 0.05 |
203 | 2980 | 2969 | 16 | 11 | 99.63 | 99.46 | 0.90 |
205 | 2656 | 2655 | 0 | 1 | 99.96 | 100.00 | 0.04 |
207 | 2332 | 2332 | 3 | 0 | 100.00 | 99.87 | 0.13 |
208 | 2955 | 2946 | 1 | 9 | 99.70 | 99.97 | 0.34 |
209 | 3005 | 3005 | 1 | 0 | 100.00 | 99.97 | 0.03 |
210 | 2650 | 2633 | 3 | 17 | 99.36 | 99.89 | 0.75 |
212 | 1825 | 1825 | 1 | 0 | 100.00 | 99.95 | 0.05 |
213 | 3251 | 3250 | 0 | 1 | 99.97 | 100.00 | 0.03 |
214 | 2262 | 2261 | 0 | 1 | 99.96 | 100.00 | 0.04 |
215 | 3363 | 3360 | 0 | 3 | 99.91 | 100.00 | 0.09 |
219 | 2287 | 2287 | 0 | 0 | 100.00 | 100.00 | 0.00 |
220 | 2048 | 2048 | 0 | 0 | 100.00 | 100.00 | 0.00 |
221 | 2427 | 2426 | 0 | 1 | 99.96 | 100.00 | 0.04 |
222 | 2483 | 2483 | 3 | 0 | 100.00 | 99.88 | 0.12 |
223 | 2605 | 2604 | 0 | 1 | 99.96 | 100.00 | 0.04 |
228 | 2053 | 2452 | 13 | 1 | 99.96 | 99.47 | 0.57 |
230 | 2256 | 2256 | 0 | 0 | 100.00 | 100.00 | 0.00 |
231 | 1573 | 1573 | 0 | 0 | 100.00 | 100.00 | 0.00 |
232 | 1780 | 1780 | 3 | 0 | 100.00 | 99.83 | 0.17 |
233 | 3079 | 3078 | 0 | 1 | 99.97 | 100.00 | 0.03 |
234 | 2753 | 2753 | 1 | 0 | 100.00 | 99.96 | 0.04 |
Sum: | 100,469 | 100,791 | 104 | 78 | |||
Average: | 99.9309 | 99.8928 | 0.1761 |
Algorithm | Results | ||||||
---|---|---|---|---|---|---|---|
Total | TP | FN | FP | Se [%] | PPV [%] | Fd [%] | |
Pan and Tompkins (1985) [21] | 109,809 | 109,532 | 277 | 507 | 99.75 | 99.54 | 0.71 |
Martínez et al. (2004) [81] | 109,428 | 109,208 | 220 | 153 | 99.80 | 99.86 | 0.34 |
Yeh and Wang (2008) [118] | 109,809 | 109,643 | 166 | 58 | 99,85 | 99,95 | 0.20 |
Martínez et al. (2010) [24] | 109,428 | 109,111 | 317 | 35 | 99.71 | 99.97 | 0.32 |
Zidelmal et al. (2012) [119] | 109,494 | 109,101 | 393 | 193 | 99,64 | 99,82 | 0,54 |
Song et al. (2015) [26] | 109,494 | 109,398 | 96 | 103 | 99.91 | 99.91 | 0.18 |
proposed algorithm * | 100,469 | 100,791 | 104 | 78 | 99.93 | 99.89 | 0.18 |
Ref. Class | Determined Class | Total * | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N | L | R | A | j | x | a | J | e | V | ! | E | F | Q | ||
N | 73,980 | 32 | 0 | 253 | 37 | 7 | 35 | 0 | 13 | 73 | 27 | 0 | 47 | 7 | 74,511 |
L | 12 | 8053 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 7 | 0 | 0 | 0 | 0 | 8072 |
R | 27 | 0 | 7197 | 15 | 0 | 0 | 9 | 3 | 4 | 0 | 0 | 0 | 0 | 7255 | |
A | 5 | 5 | 0 | 2518 | 0 | 0 | 0 | 0 | 0 | 5 | 3 | 0 | 10 | 0 | 2546 |
j | 4 | 0 | 0 | 5 | 217 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 229 |
x | 7 | 0 | 0 | 2 | 1 | 180 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 193 |
a | 4 | 0 | 1 | 1 | 0 | 0 | 144 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 150 |
J | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 79 | 0 | 0 | 0 | 0 | 0 | 0 | 83 |
e | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 16 |
V | 11 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 6878 | 7 | 0 | 1 | 0 | 6902 |
! | 0 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 11 | 453 | 0 | 0 | 0 | 472 |
E | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 101 | 0 | 0 | 106 |
F | 7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 1 | 792 | 0 | 802 |
Q | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 1 | 0 | 8 | 15 |
Total | 74,069 | 8105 | 7198 | 2796 | 255 | 187 | 188 | 85 | 25 | 6983 | 493 | 103 | 850 | 15 | 101,352 |
Reference | Determined Beat Type | Total | ||||
---|---|---|---|---|---|---|
N | S | V | F | Q | ||
N | 89,301 | 372 | 111 | 47 | 7 | 89,838 |
S | 32 | 3164 | 11 | 10 | 0 | 3217 |
V | 29 | 0 | 7450 | 1 | 0 | 7480 |
F | 7 | 0 | 3 | 792 | 0 | 802 |
Q | 3 | 0 | 4 | 0 | 8 | 15 |
Total | 89,372 | 3536 | 7579 | 850 | 15 | 101,352 |
CSE NR | Fiducial Point | CSE-Reference | oECG | uECG | nECG | pECG | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Mean | std. | ∆T | R | ∆T | R | ∆T | R | ∆T | R | ||
001 | P-ons | 51.26 | 13.99 | 4.26 | 3 | 5.26 | 4 | 5.71 | 5 | 4.51 | 3 |
P-end | 170.6 | 19.98 | −3.63 | 3 | -3.63 | 3 | −2.28 | 2 | −2.61 | 2 | |
QRS-ons | 277.6 | 5.57 | 1.58 | 2 | 2.58 | 5 | 2.77 | 6 | 1.91 | 3 | |
QRS-end | 407.6 | 4.48 | 1.58 | 3 | 2.58 | 6 | 2.80 | 6 | 1.88 | 4 | |
T-end | 723.5 | 12.50 | 3.47 | 3 | 4.47 | 5 | 5.11 | 6 | 3.85 | 3 | |
002 | P-ons | 20.89 | 9.34 | 3.89 | 4 | 3.89 | 4 | 4.41 | 5 | 4.06 | 4 |
P-end | 135.8 | 7.51 | −2.78 | 3 | −2.78 | 3 | −4.11 | 5 | −3.50 | 4 | |
QRS-ons | 178.2 | 2.82 | 0.21 | 1 | 1.21 | 6 | 1.57 | 8 | 0.59 | 2 | |
QRS-end | 264.1 | 5.33 | −1.11 | 2 | −1.11 | 2 | −1.93 | 5 | −1.31 | 2 | |
T-end | 523.1 | 54.70 | 7.11 | 4 | 8.11 | 4 | 8.51 | 4 | 7.91 | 4 | |
…120 files… | |||||||||||
125 | P-ons | 96.63 | 6.62 | 2.62 | 4 | 2.62 | 4 | 2.97 | 5 | 2.91 | 5 |
P-end | 186.0 | 4.86 | 2.0 | 3 | 2.0 | 3 | 2.57 | 5 | 2.13 | 3 | |
QRS-ons | 206.8 | 2.31 | 0.84 | 2 | 0.84 | 2 | 1.12 | 3 | 0.99 | 3 | |
QRS-end | 314,2 | 4.53 | −1.21 | 3 | −1.21 | 3 | −1.85 | 5 | −1.02 | 2 | |
T-end | 612.6 | 6.56 | 1.63 | 3 | 2.63 | 5 | 2.90 | 5 | 2.83 | 5 | |
Average rank (out of 19 packages): | 2.87 | 3.93 | 5.0 | 3.37 |
ECG Section | oECG | uECG | nECG | pECG | IEC Allowed Tolerance | |||||
---|---|---|---|---|---|---|---|---|---|---|
Mean | std. | Mean | std. | Mean | std. | Mean | std. | Mean | std. | |
P | ±4.3 | 3.5 | ±7.7 | 6.8 | ±9.7 | 8.1 | ±5.7 | 4.1 | ±10 | 15 |
QRS | ±2.1 | 1.8 | ±2.8 | 3.7 | ±3.4 | 5.1 | ±2.8 | 3.2 | ±10 | 10 |
P-Q | ±3.7 | 4.5 | ±5.4 | 6.7 | ±6.7 | 8.4 | ±4.1 | 4.9 | ±10 | 10 |
Q-T | ±11.1 | 7.1 | ±12.8 | 8.8 | ±17.7 | 10.9 | ±11.7 | 8.1 | ±25 | 30 |
CSE-NR | uECG—oECG | WDD | |||||||
---|---|---|---|---|---|---|---|---|---|
PRD | PRD P | PRD QRS | PRD T | oECG- uECG | pECG- nECG | uECG- nECG | oECG- pECG | nECG- oECG | |
Column | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
001 | 3.18 | 0.11 | 0.34 | 0.46 | 0.27 | 0.25 | 0.41 | 0.27 | 0.51 |
002 | 2.67 | 0.18 | 0.19 | 0.26 | 0.19 | 0.17 | 0.24 | 0.20 | 0.36 |
…120 files… | |||||||||
125 | 3.46 | 0.21 | 0.31 | 0.34 | 0.27 | 0.28 | 0.44 | 0.33 | 0.60 |
Mean | 3.11 | 0.16 | 0.22 | 0.37 | 0.21 | 0.23 | 0.33 | 0.27 | 0.47 |
Std. | 0.327 | 0.042 | 0.065 | 0.082 | 0.038 | 0.046 | 0.088 | 0.053 | 0.099 |
Diagnostic Outcome | oECG | uECG | nECG | pECG |
---|---|---|---|---|
correct | 121 | 117 | 115 | 117 |
incorrect statement | 1 | 2 | 3 | 3 |
incorrect modifier | 1 | 4 | 5 | 3 |
total | 123 | 123 | 123 | 123 |
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Augustyniak, P. Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram. Sensors 2021, 21, 2969. https://doi.org/10.3390/s21092969
Augustyniak P. Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram. Sensors. 2021; 21(9):2969. https://doi.org/10.3390/s21092969
Chicago/Turabian StyleAugustyniak, Piotr. 2021. "Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram" Sensors 21, no. 9: 2969. https://doi.org/10.3390/s21092969
APA StyleAugustyniak, P. (2021). Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram. Sensors, 21(9), 2969. https://doi.org/10.3390/s21092969