Hemodynamics · LIVE

Fick cardiac output

Compute Fick 1870 cardiac output in L/min from measured oxygen consumption and arterial and mixed-venous oxygen contents.

LIVE $0.005 USDC GET /api/calc/fick

Markdown: /docs/fick.md · Canonical: https://magentlab.com/docs/fick

Not a medical device. Not a diagnosis, dose, or listing recommendation.

What it computes

Compute Fick 1870 cardiac output in L/min from measured oxygen consumption and arterial and mixed-venous oxygen contents.

When to use

When an agent already has measured VO2, CaO2, and CvO2 and must not estimate VO2 from BSA, invent Hüfner oxygen-content factors, or treat the result as a shock diagnosis or catheter order.

When not to use

• Not a medical device. Not a shock diagnosis or catheter order. magent does not sample blood.
• Does not estimate VO2 from body-surface area and does not assume 125 ml/min/m².
• Does not compute oxygen content from hemoglobin, saturation, or Hüfner 1.34/1.36 factors. Caller supplies measured CaO2 and CvO2.
• Oxygen contents may be ml/L or ml/dL (×10). Do not send both unit paths for the same content. Rejects when CaO2 ≤ CvO2.

Formula

cardiac_output_l_min = vo2_ml_min / (cao2_ml_l - cvo2_ml_l)

Citation

Title

Ueber die Messung des Blutquantums in den Herzventrikeln

Authors

Fick A

Source

Sitzungsberichte der Physikalisch-Medizinischen Gesellschaft zu Würzburg. 1870;XVI-XVII

DOI

none

Worked example

Also searched as

• Fick cardiac output
• Fick principle
• Fick formula
• VO2 CaO2 CvO2
• measured Fick CO
• arteriovenous oxygen difference cardiac output
• Fick VO2 cardiac output

Try

Opens the live endpoint. Unpaid browser requests show the paywall; agents should send Accept: application/json.

/api/calc/fick?vo2_ml_min=250&cao2_ml_l=200&cvo2_ml_l=150

Full URL: https://api.magentlab.com/api/calc/fick?vo2_ml_min=250&cao2_ml_l=200&cvo2_ml_l=150

Call

Expect HTTP 402 until you retry with PAYMENT-SIGNATURE. Incomplete query params return HTTP 400 before any quote or charge.

curl -i -H "Accept: application/json" "https://api.magentlab.com/api/calc/fick?vo2_ml_min=250&cao2_ml_l=200&cvo2_ml_l=150"

Parameters

Bulk (POST)

POST the same path with a JSON items array. The first item is the GET unit; each additional item is $0.002. Invalid items return HTTP 400 before settlement.

POST /api/calc/fick Max 25 unit_amount + extra_item_amount * (n - 1) extra $0.002 PREVIEW

• 1 to 25 items. Each item uses the same keys as the GET query parameters.
• POST of 1 item costs the same as GET. Lists longer than 25: chunk into multiple POSTs. Extra items still execute; do not pad dummy rows.
• The first invalid item fails the whole request (index in the 400 JSON). You are not charged.
• HTTP 200 is {count, path, items}. Each items[i] is the GET 200 body for that row.
• Catalog misses (empty matches, found=false) stay paid 200s inside that slot.
• x402 resource URL is this path plus n and body_sha256. Browsers that prefer text/html get the same paywall as GET; Pay retries POST with the same items.

Example request (fixture)

{
  "items": [
    {
      "cao2_ml_l": "200",
      "cvo2_ml_l": "150",
      "vo2_ml_min": "250"
    },
    {
      "cao2_ml_l": "200",
      "cvo2_ml_l": "150",
      "vo2_ml_min": "250"
    }
  ]
}

Open bulk paywall →

Opens a two-item fixture on the API host. Unpaid browsers get the same MetaMask paywall as GET; Pay retries POST with those items.

Example 200 (fixture)

{
  "count": 2,
  "path": "/api/calc/fick",
  "items": [
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Fick A",
        "id": "fick-1870",
        "source": "Sitzungsberichte der Physikalisch-Medizinischen Gesellschaft zu Würzburg. 1870;XVI-XVII",
        "title": "Ueber die Messung des Blutquantums in den Herzventrikeln"
      },
      "formula": "fick",
      "formula_expression": "cardiac_output_l_min = vo2_ml_min / (cao2_ml_l - cvo2_ml_l)",
      "cardiac_output_l_min": 5.0,
      "avo2_difference_ml_l": 50.0,
      "cao2_ml_l": 200.0,
      "cvo2_ml_l": 150.0,
      "vo2_ml_min": 250.0
    },
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Fick A",
        "id": "fick-1870",
        "source": "Sitzungsberichte der Physikalisch-Medizinischen Gesellschaft zu Würzburg. 1870;XVI-XVII",
        "title": "Ueber die Messung des Blutquantums in den Herzventrikeln"
      },
      "formula": "fick",
      "formula_expression": "cardiac_output_l_min = vo2_ml_min / (cao2_ml_l - cvo2_ml_l)",
      "cardiac_output_l_min": 5.0,
      "avo2_difference_ml_l": 50.0,
      "cao2_ml_l": 200.0,
      "cvo2_ml_l": 150.0,
      "vo2_ml_min": 250.0
    }
  ]
}

Response

Example JSON

Machine form of the same example. Frozen fixture. Not a live lookup.

{
  "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
  "citation": {
    "authors": "Fick A",
    "id": "fick-1870",
    "source": "Sitzungsberichte der Physikalisch-Medizinischen Gesellschaft zu Würzburg. 1870;XVI-XVII",
    "title": "Ueber die Messung des Blutquantums in den Herzventrikeln"
  },
  "formula": "fick",
  "formula_expression": "cardiac_output_l_min = vo2_ml_min / (cao2_ml_l - cvo2_ml_l)",
  "cardiac_output_l_min": 5.0,
  "avo2_difference_ml_l": 50.0,
  "cao2_ml_l": 200.0,
  "cvo2_ml_l": 150.0,
  "vo2_ml_min": 250.0
}

Client errors (HTTP 400)

Invalid params return 400 without charge. Shared HTTP 402 and 503 meanings: Payments.

Related tools

• CPO — Compute Fincke 2004 cardiac power output in watts from mean arterial pressure and cardiac output.
• MAP — Compute conventional estimated mean arterial pressure from cuff systolic and diastolic pressures.

Payment

Unpaid requests return HTTP 402 even if query parameters or POST items are missing or invalid, so CDP and agents can index the path. After a PAYMENT-SIGNATURE, invalid params return HTTP 400 JSON before settlement. magent does not charge. Fix the params, then request a new 402 quote for that complete URL. Catalog misses (empty matches, found=false) are valid paid 200s. Unpaid valid requests return HTTP 402 with a base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote: retry the same PAYMENT-SIGNATURE. Full handshake and shared payment errors: Payments. Stdio MCP: /docs/mcp.

Guarantees

• HTTP 402 is unpaid, including a missing query. After PAYMENT-SIGNATURE, invalid parameters return HTTP 400 before settlement. You are not charged. HTTP 402 never includes the tool JSON.
• exact: settlement finishes before the tool (paymentFlow upfront). batch-settlement: verify/deposit before the tool; chargedCumulativeAmount commits after HTTP 2xx. Uncertain or failed settlement fails closed (HTTP 503). Retry the same PAYMENT-SIGNATURE.
• HTTP 402 is unpaid only. Do not sign a second authorization because of a 503.
• Execution is timeout-bounded and concurrency-capped.
• Calculator inputs are stored encrypted for allowlisted operators (Magent Console). They are not in public logs, SSH lookups, catalog, or rollups. Request logs store path without query.