Respiratory · LIVE

Oxygenation index (OI)

Oxygenation index

Compute the oxygenation index from inspired oxygen fraction, mean airway pressure in cm H2O, and arterial PO2.

LIVE $0.005 USDC GET /api/calc/oxygenation_index

Markdown: /docs/oxygenation-index.md · Canonical: https://magentlab.com/docs/oxygenation-index

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

What it computes

Compute the oxygenation index from inspired oxygen fraction, mean airway pressure in cm H2O, and arterial PO2.

When to use

When an agent needs FiO2 × mean airway pressure × 100 / PaO2 and must not invent an OI or an ECMO-initiation threshold.

When not to use

• Not a diagnosis. This is FiO2 × mean airway pressure × 100 / PaO2; it is not an ECMO-initiation protocol.
• Mean airway pressure is ventilator cm H2O, not blood-pressure MAP.
• FiO2 is a fraction (0.21–1.0), not a percent.

Formula

oxygenation_index = fio2 * mean_airway_pressure_cm_h2o * 100 / pao2_mm_hg

Citation

Title

Extracorporeal membrane oxygenation in pediatric respiratory failure

Authors

Ortiz RM, Cilley RE, Bartlett RH

Source

Pediatr Clin North Am. 1987;34(1):39-46

DOI

10.1016/S0031-3955(16)36180-7

Worked example

Also searched as

• OI
• oxygenation index
• oxygenation index OI
• ventilator OI
• FiO2 mean airway pressure PaO2
• mean airway pressure oxygenation

Try

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

/api/calc/oxygenation_index?fio2=0.5&mean_airway_pressure_cm_h2o=12&pao2_mm_hg=80

Full URL: https://api.magentlab.com/api/calc/oxygenation_index?fio2=0.5&mean_airway_pressure_cm_h2o=12&pao2_mm_hg=80

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/oxygenation_index?fio2=0.5&mean_airway_pressure_cm_h2o=12&pao2_mm_hg=80"

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/oxygenation_index 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": [
    {
      "fio2": "0.5",
      "mean_airway_pressure_cm_h2o": "12",
      "pao2_mm_hg": "80"
    },
    {
      "fio2": "0.5",
      "mean_airway_pressure_cm_h2o": "12",
      "pao2_mm_hg": "80"
    }
  ]
}

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/oxygenation_index",
  "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": "Ortiz RM, Cilley RE, Bartlett RH",
        "doi": "10.1016/S0031-3955(16)36180-7",
        "id": "ortiz-bartlett-1987",
        "source": "Pediatr Clin North Am. 1987;34(1):39-46",
        "title": "Extracorporeal membrane oxygenation in pediatric respiratory failure"
      },
      "formula": "oxygenation_index",
      "formula_expression": "oxygenation_index = fio2 * mean_airway_pressure_cm_h2o * 100 / pao2_mm_hg",
      "fio2": 0.5,
      "pao2_mm_hg": 80.0,
      "mean_airway_pressure_cm_h2o": 12.0,
      "oxygenation_index": 7.5
    },
    {
      "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": "Ortiz RM, Cilley RE, Bartlett RH",
        "doi": "10.1016/S0031-3955(16)36180-7",
        "id": "ortiz-bartlett-1987",
        "source": "Pediatr Clin North Am. 1987;34(1):39-46",
        "title": "Extracorporeal membrane oxygenation in pediatric respiratory failure"
      },
      "formula": "oxygenation_index",
      "formula_expression": "oxygenation_index = fio2 * mean_airway_pressure_cm_h2o * 100 / pao2_mm_hg",
      "fio2": 0.5,
      "pao2_mm_hg": 80.0,
      "mean_airway_pressure_cm_h2o": 12.0,
      "oxygenation_index": 7.5
    }
  ]
}

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": "Ortiz RM, Cilley RE, Bartlett RH",
    "doi": "10.1016/S0031-3955(16)36180-7",
    "id": "ortiz-bartlett-1987",
    "source": "Pediatr Clin North Am. 1987;34(1):39-46",
    "title": "Extracorporeal membrane oxygenation in pediatric respiratory failure"
  },
  "formula": "oxygenation_index",
  "formula_expression": "oxygenation_index = fio2 * mean_airway_pressure_cm_h2o * 100 / pao2_mm_hg",
  "fio2": 0.5,
  "pao2_mm_hg": 80.0,
  "mean_airway_pressure_cm_h2o": 12.0,
  "oxygenation_index": 7.5
}

Client errors (HTTP 400)

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

Related tools

• A-a O2 gradient — Compute the alveolar–arterial oxygen gradient from arterial blood-gas values using the simplified ideal alveolar-gas equation.

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.