When I first encountered correction methods based on Einthoven’s law, they appeared to be an intuitive and eye-opening approach.\nI wondered whether similar principle-based corrections could be applied in some way.\nSince precordial leads do not have relationships that can be expressed by simple equations, I focused on single limb leads.
\nTaking aVL as an example: aVL represents the difference between the potential at the left arm and a virtual zero potential (the Wilson central terminal, defined as the average of the L, R, and F electrode potentials).\nIn practice, this difference is amplified by a factor of 1.5 before being output.
\nIf the electrode potentials are denoted as VR, VL, and VF, then:
aVL = 1.5 × (VL − (VL + VR + VF)/3)
That is,
aVL = 1.5 × (2VL/3 − VR/3 − VF/3),
which simplifies to:
aVL = VL − VR/2 − VF/2.
First, consider the sum of the following expressions:
\n aVR = VR − 0.5VL − 0.5VF,
\n aVF = VF − 0.5VL − 0.5VR,
\n aVL = VL − 0.5VR − 0.5VF.
\nTheir sum is:
\n (VR − 0.5VL − 0.5VF) + (aVF − 0.5VL − 0.5VR) + (aVL − 0.5VR − 0.5VF) = 0 … (1)
\nNext,
\n −aVL − 2aVR
\n = −(VL − 0.5VR − 0.5VF) − 2(VR − 0.5VL − 0.5VF) = 1.5VF − 1.5VR
\n = 1.5(VF − VR)
\n = 1.5 × II … (2)
I attempted to correct aVL, aVR, and aVF using these two equations, but the resulting in a lower score.\nI am not entirely sure why. One possible explanation for why correction using equation (2) did not work is that multiplying signals by factors such as 2 or 1.5 may have amplified noise and errors.
\nI also considered whether corrections could be made based on other principles of ECGs or ECG recording devices.\nECG machines are often equipped with filters to remove noise, and I wondered whether these could be exploited.\nAccording to standards used in Japan (though they may differ internationally), frequencies below 0.05 Hz and above 500 Hz are filtered out.\nIn addition, since the power-line frequency differs by region in Japan, either 50 Hz or 60 Hz is also filtered.\nIf components that should have been removed by these filters remain only in specific leads, it might be acceptable for me to apply filtering myself.\nHowever, this approach also resulted in a lower score.
\nPerhaps this kind of approach could work if implemented more carefully.\nIf anyone has tried something similar, I would appreciate hearing about it, even after the submission deadline.
", "messages": [ { "id": "3393920", "postDate": "01/20/2026 06:22:35", "content": "When I first encountered correction methods based on Einthoven’s law, they appeared to be an intuitive and eye-opening approach.\nI wondered whether similar principle-based corrections could be applied in some way.\nSince precordial leads do not have relationships that can be expressed by simple equations, I focused on single limb leads.
\nTaking aVL as an example: aVL represents the difference between the potential at the left arm and a virtual zero potential (the Wilson central terminal, defined as the average of the L, R, and F electrode potentials).\nIn practice, this difference is amplified by a factor of 1.5 before being output.
\nIf the electrode potentials are denoted as VR, VL, and VF, then:
aVL = 1.5 × (VL − (VL + VR + VF)/3)
That is,
aVL = 1.5 × (2VL/3 − VR/3 − VF/3),
which simplifies to:
aVL = VL − VR/2 − VF/2.
First, consider the sum of the following expressions:
\n aVR = VR − 0.5VL − 0.5VF,
\n aVF = VF − 0.5VL − 0.5VR,
\n aVL = VL − 0.5VR − 0.5VF.
\nTheir sum is:
\n (VR − 0.5VL − 0.5VF) + (aVF − 0.5VL − 0.5VR) + (aVL − 0.5VR − 0.5VF) = 0 … (1)
\nNext,
\n −aVL − 2aVR
\n = −(VL − 0.5VR − 0.5VF) − 2(VR − 0.5VL − 0.5VF) = 1.5VF − 1.5VR
\n = 1.5(VF − VR)
\n = 1.5 × II … (2)
I attempted to correct aVL, aVR, and aVF using these two equations, but the resulting in a lower score.\nI am not entirely sure why. One possible explanation for why correction using equation (2) did not work is that multiplying signals by factors such as 2 or 1.5 may have amplified noise and errors.
\nI also considered whether corrections could be made based on other principles of ECGs or ECG recording devices.\nECG machines are often equipped with filters to remove noise, and I wondered whether these could be exploited.\nAccording to standards used in Japan (though they may differ internationally), frequencies below 0.05 Hz and above 500 Hz are filtered out.\nIn addition, since the power-line frequency differs by region in Japan, either 50 Hz or 60 Hz is also filtered.\nIf components that should have been removed by these filters remain only in specific leads, it might be acceptable for me to apply filtering myself.\nHowever, this approach also resulted in a lower score.
\nPerhaps this kind of approach could work if implemented more carefully.\nIf anyone has tried something similar, I would appreciate hearing about it, even after the submission deadline.
", "rawMarkdown": "When I first encountered correction methods based on Einthoven’s law, they appeared to be an intuitive and eye-opening approach.\nI wondered whether similar principle-based corrections could be applied in some way.\nSince precordial leads do not have relationships that can be expressed by simple equations, I focused on single limb leads.\n\nTaking aVL as an example: aVL represents the difference between the potential at the left arm and a virtual zero potential (the Wilson central terminal, defined as the average of the L, R, and F electrode potentials).\nIn practice, this difference is amplified by a factor of 1.5 before being output.\n\nIf the electrode potentials are denoted as VR, VL, and VF, then:We apply I-II+III=0 and aVR+aVL+aVF=0 if they are close enough. For example: if np.abs(aVR+aVL+aVF).mean()<0.01, and gain 0.06 on LB.
We apply I-II+III=0 and aVR+aVL+aVF=0 if they are close enough. For example: if np.abs(aVR+aVL+aVF).mean()<0.01, and gain 0.06 on LB.