{
  "id": 613240,
  "title": "Einthoven’s Law ",
  "url": "/competitions/physionet-ecg-image-digitization/discussion/613240",
  "author_name": "",
  "post_date": "2025-10-25T08:17:58.629448700Z",
  "votes": 11,
  "comment_count": 2,
  "views": 0,
  "content": "<p>I have verified the following relationships between the limb leads:</p>\n<p>Einthoven’s law: I + III = II<br>\naVR = −(I + II)/2<br>\naVL = I − II/2<br>\naVF = II − I/2<br>\nHowever, I couldn't find any established mathematical relationship between the precordial leads (V1–V6) and the other leads.</p>\n<p>Given this, can we assume that the precordial leads are periodic and replicate their values for other timesteps?</p>",
  "messages": [
    {
      "id": "3306774",
      "postDate": "10/25/2025 08:17:58",
      "content": "<p>I have verified the following relationships between the limb leads:</p>\n<p>Einthoven’s law: I + III = II<br>\naVR = −(I + II)/2<br>\naVL = I − II/2<br>\naVF = II − I/2<br>\nHowever, I couldn't find any established mathematical relationship between the precordial leads (V1–V6) and the other leads.</p>\n<p>Given this, can we assume that the precordial leads are periodic and replicate their values for other timesteps?</p>",
      "rawMarkdown": "I have verified the following relationships between the limb leads:\n\nEinthoven’s law: I + III = II\naVR = −(I + II)/2\naVL = I − II/2\naVF = II − I/2\nHowever, I couldn't find any established mathematical relationship between the precordial leads (V1–V6) and the other leads.\n\nGiven this, can we assume that the precordial leads are periodic and replicate their values for other timesteps?",
      "votes": null
    },
    {
      "id": "3306854",
      "postDate": "10/25/2025 12:15:21",
      "content": "<p>Check out Chapter 15 <a href=\"https://www.bem.fi/book/\" target=\"_blank\">[here]</a> on the 12-lead ECG system.</p>",
      "rawMarkdown": "Check out Chapter 15 [[here]](https://www.bem.fi/book/) on the 12-lead ECG system.",
      "votes": null
    },
    {
      "id": "3306937",
      "postDate": "10/25/2025 16:33:29",
      "content": "<p>Adding to the great link Reza provided, it could be useful to note that there's some redundancy between the leads. You might be able to use this redundancy to help deal with potential artifacts. You might think that all you need are three (orthogonal) leads, since the heart is three-dimensional and you can model the electrical activity of the heart as a point source. But that's just an approximation. The heart has near-field electrical activity - it's a large and complex structure, with parts of itself much closer to some groups of electrodes than other groups. So some leads are more sensitive to issues that are localized to certain regions of the heart. You should also note that the heart is not static. It twists, rotates and translates throughout the cardiac and respiratory cycles. If you look at the rhythm strip at the bottom, you might see the amplitude of the peaks going up and down as the heart is periodically displaced by the air entering the lungs. So the leads don't always look at exactly the same part of the heart with every beat. That means that the matrix to map one set of leads to another is constantly changing. Still, a simple least squares fit using the 3-4 simultaneously recorded leads (in each 2.5-second block) should give you some clues about which lead's morphology is inconsistent with the other leads. </p>",
      "rawMarkdown": "Adding to the great link Reza provided, it could be useful to note that there's some redundancy between the leads. You might be able to use this redundancy to help deal with potential artifacts. You might think that all you need are three (orthogonal) leads, since the heart is three-dimensional and you can model the electrical activity of the heart as a point source. But that's just an approximation. The heart has near-field electrical activity - it's a large and complex structure, with parts of itself much closer to some groups of electrodes than other groups. So some leads are more sensitive to issues that are localized to certain regions of the heart. You should also note that the heart is not static. It twists, rotates and translates throughout the cardiac and respiratory cycles. If you look at the rhythm strip at the bottom, you might see the amplitude of the peaks going up and down as the heart is periodically displaced by the air entering the lungs. So the leads don't always look at exactly the same part of the heart with every beat. That means that the matrix to map one set of leads to another is constantly changing. Still, a simple least squares fit using the 3-4 simultaneously recorded leads (in each 2.5-second block) should give you some clues about which lead's morphology is inconsistent with the other leads.",
      "votes": null
    }
  ],
  "comments": [
    {
      "id": 3306854,
      "author_name": "r2241272",
      "author_url": "",
      "post_date": "10/25/2025 12:15:21",
      "content": "<p>Check out Chapter 15 <a href=\"https://www.bem.fi/book/\" target=\"_blank\">[here]</a> on the 12-lead ECG system.</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 3306937,
      "author_name": "gdclifford",
      "author_url": "",
      "post_date": "10/25/2025 16:33:29",
      "content": "<p>Adding to the great link Reza provided, it could be useful to note that there's some redundancy between the leads. You might be able to use this redundancy to help deal with potential artifacts. You might think that all you need are three (orthogonal) leads, since the heart is three-dimensional and you can model the electrical activity of the heart as a point source. But that's just an approximation. The heart has near-field electrical activity - it's a large and complex structure, with parts of itself much closer to some groups of electrodes than other groups. So some leads are more sensitive to issues that are localized to certain regions of the heart. You should also note that the heart is not static. It twists, rotates and translates throughout the cardiac and respiratory cycles. If you look at the rhythm strip at the bottom, you might see the amplitude of the peaks going up and down as the heart is periodically displaced by the air entering the lungs. So the leads don't always look at exactly the same part of the heart with every beat. That means that the matrix to map one set of leads to another is constantly changing. Still, a simple least squares fit using the 3-4 simultaneously recorded leads (in each 2.5-second block) should give you some clues about which lead's morphology is inconsistent with the other leads. </p>",
      "votes": null,
      "replies": []
    }
  ],
  "raw_markdown_by_id": {
    "3306774": "I have verified the following relationships between the limb leads:\n\nEinthoven’s law: I + III = II\naVR = −(I + II)/2\naVL = I − II/2\naVF = II − I/2\nHowever, I couldn't find any established mathematical relationship between the precordial leads (V1–V6) and the other leads.\n\nGiven this, can we assume that the precordial leads are periodic and replicate their values for other timesteps?",
    "3306854": "Check out Chapter 15 [[here]](https://www.bem.fi/book/) on the 12-lead ECG system.",
    "3306937": "Adding to the great link Reza provided, it could be useful to note that there's some redundancy between the leads. You might be able to use this redundancy to help deal with potential artifacts. You might think that all you need are three (orthogonal) leads, since the heart is three-dimensional and you can model the electrical activity of the heart as a point source. But that's just an approximation. The heart has near-field electrical activity - it's a large and complex structure, with parts of itself much closer to some groups of electrodes than other groups. So some leads are more sensitive to issues that are localized to certain regions of the heart. You should also note that the heart is not static. It twists, rotates and translates throughout the cardiac and respiratory cycles. If you look at the rhythm strip at the bottom, you might see the amplitude of the peaks going up and down as the heart is periodically displaced by the air entering the lungs. So the leads don't always look at exactly the same part of the heart with every beat. That means that the matrix to map one set of leads to another is constantly changing. Still, a simple least squares fit using the 3-4 simultaneously recorded leads (in each 2.5-second block) should give you some clues about which lead's morphology is inconsistent with the other leads."
  },
  "source": "meta"
}