Respiratory · LIVE

Static respiratory-system compliance (Cstat)

Static respiratory-system compliance

Compute static respiratory-system compliance in mL/cm H2O as tidal volume divided by plateau pressure minus PEEP, as used in the ARDS Network 2000 methods.

LIVE $0.005 USDC GET /api/calc/cstat

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

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

What it computes

Compute static respiratory-system compliance in mL/cm H2O as tidal volume divided by plateau pressure minus PEEP, as used in the ARDS Network 2000 methods.

When to use

When an agent already has measured tidal volume, plateau pressure, and PEEP and must not read a ventilator, invent ARDS severity bands from Cstat, or copy Murray 1988 0–4 compliance points onto this identity.

When not to use

• Not a medical device. Not a ventilator order or ARDS diagnosis. magent does not read the ventilator.
• Does not invent ARDS severity bands from Cstat. Murray 1988 compliance 0–4 points are a different tool (murray).
• Rejects plateau pressure less than or equal to PEEP (nonpositive driving pressure).
• Caller supplies measured VT, Pplat, and PEEP. Does not infer volumes or pressures from mode, flow, or set tidal volume.

Formula

cstat_ml_cm_h2o = tidal_volume_ml / (pplat_cm_h2o - peep_cm_h2o)

Citation

Title

Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome

Authors

Acute Respiratory Distress Syndrome Network; Brower RG, Matthay MA, Morris A, Schoenfeld D, Thompson BT, Wheeler A

Source

N Engl J Med. 2000;342(18):1301-1308

DOI

10.1056/NEJM200005043421801

Worked example

Also searched as

• Cstat
• static compliance
• static respiratory-system compliance
• Crs
• tidal volume over driving pressure
• Pplat minus PEEP compliance
• ARDS Network compliance
• respiratory system compliance

Try

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

/api/calc/cstat?tidal_volume_ml=500&pplat_cm_h2o=20&peep_cm_h2o=5

Full URL: https://api.magentlab.com/api/calc/cstat?tidal_volume_ml=500&pplat_cm_h2o=20&peep_cm_h2o=5

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/cstat?tidal_volume_ml=500&pplat_cm_h2o=20&peep_cm_h2o=5"

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/cstat 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": [
    {
      "peep_cm_h2o": "5",
      "pplat_cm_h2o": "20",
      "tidal_volume_ml": "500"
    },
    {
      "peep_cm_h2o": "5",
      "pplat_cm_h2o": "20",
      "tidal_volume_ml": "500"
    }
  ]
}

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/cstat",
  "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": "Acute Respiratory Distress Syndrome Network; Brower RG, Matthay MA, Morris A, Schoenfeld D, Thompson BT, Wheeler A",
        "doi": "10.1056/NEJM200005043421801",
        "id": "ardsnet-2000",
        "pmid": "10793162",
        "source": "N Engl J Med. 2000;342(18):1301-1308",
        "title": "Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome"
      },
      "formula": "cstat",
      "formula_expression": "cstat_ml_cm_h2o = tidal_volume_ml / (pplat_cm_h2o - peep_cm_h2o)",
      "cstat_ml_cm_h2o": 33.3,
      "driving_pressure_cm_h2o": 15.0,
      "peep_cm_h2o": 5.0,
      "pplat_cm_h2o": 20.0,
      "tidal_volume_ml": 500.0
    },
    {
      "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": "Acute Respiratory Distress Syndrome Network; Brower RG, Matthay MA, Morris A, Schoenfeld D, Thompson BT, Wheeler A",
        "doi": "10.1056/NEJM200005043421801",
        "id": "ardsnet-2000",
        "pmid": "10793162",
        "source": "N Engl J Med. 2000;342(18):1301-1308",
        "title": "Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome"
      },
      "formula": "cstat",
      "formula_expression": "cstat_ml_cm_h2o = tidal_volume_ml / (pplat_cm_h2o - peep_cm_h2o)",
      "cstat_ml_cm_h2o": 33.3,
      "driving_pressure_cm_h2o": 15.0,
      "peep_cm_h2o": 5.0,
      "pplat_cm_h2o": 20.0,
      "tidal_volume_ml": 500.0
    }
  ]
}

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": "Acute Respiratory Distress Syndrome Network; Brower RG, Matthay MA, Morris A, Schoenfeld D, Thompson BT, Wheeler A",
    "doi": "10.1056/NEJM200005043421801",
    "id": "ardsnet-2000",
    "pmid": "10793162",
    "source": "N Engl J Med. 2000;342(18):1301-1308",
    "title": "Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome"
  },
  "formula": "cstat",
  "formula_expression": "cstat_ml_cm_h2o = tidal_volume_ml / (pplat_cm_h2o - peep_cm_h2o)",
  "cstat_ml_cm_h2o": 33.3,
  "driving_pressure_cm_h2o": 15.0,
  "peep_cm_h2o": 5.0,
  "pplat_cm_h2o": 20.0,
  "tidal_volume_ml": 500.0
}

Client errors (HTTP 400)

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

Related tools

• Murray lung injury score — Mean the four Murray 1988 lung injury score components (chest radiograph quadrants, PaO2/FiO2, PEEP, and compliance), each 0–4, and return LIS and injury_band.
• PaO2/FiO2 ratio — Compute the PaO2/FiO2 ratio as arterial PO2 in mm Hg divided by inspired oxygen fraction.

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.