# Static respiratory-system compliance (Cstat)

Static respiratory-system compliance

Status: LIVE
Price: $0.005 USDC
`GET /api/calc/cstat`
HTML: https://magentlab.com/docs/cstat
Markdown: https://magentlab.com/docs/cstat.md

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

[Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome](https://doi.org/10.1056/NEJM200005043421801)
Acute Respiratory Distress Syndrome Network; Brower RG, Matthay MA, Morris A, Schoenfeld D, Thompson BT, Wheeler A
N Engl J Med. 2000;342(18):1301-1308
DOI: [10.1056/NEJM200005043421801](https://doi.org/10.1056/NEJM200005043421801)

## Worked example

### VT 500 mL, Pplat 20, PEEP 5

Given: `peep_cm_h2o=5, pplat_cm_h2o=20, tidal_volume_ml=500`

1. driving_pressure = 20 − 5 = 15 cm H2O
2. cstat_ml_cm_h2o = 500 / 15 = 33.333… → 33.3


## 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

## Parameters

- `tidal_volume_ml` (number, required): Expired tidal volume in mL (50-2000, magent clamp). Caller supplies the measured term. magent does not read the ventilator.
- `pplat_cm_h2o` (number, required): End-inspiratory plateau pressure in cm H2O (5-80, magent clamp). Must be greater than PEEP. magent does not read the ventilator.
- `peep_cm_h2o` (number, required): Positive end-expiratory pressure in cm H2O (0-40, magent clamp). Must be less than plateau pressure. magent does not read the ventilator.

## 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.

Method: `POST /api/calc/cstat`
Max items: 25
Price: unit_amount + extra_item_amount * (n - 1) (unit 5000 atomic, extra 2000 atomic)
Status: 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:

```json
{
  "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"
    }
  ]
}
```

Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/cstat

Example 200:

```json
{
  "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 fields

- `formula` (string): cstat
- `formula_expression` (string): Exact expression used
- `tidal_volume_ml` (number): Tidal volume used, mL
- `pplat_cm_h2o` (number): Plateau pressure used, cm H2O
- `peep_cm_h2o` (number): PEEP used, cm H2O
- `driving_pressure_cm_h2o` (number): Pplat minus PEEP in cm H2O, 1 decimal
- `cstat_ml_cm_h2o` (number): Static respiratory-system compliance in mL/cm H2O, 1 decimal
- `citation` (object): ARDS Network 2000 NEJM citation
- `disclaimer` (string): Not-a-device notice

## Example JSON

Frozen fixture. Not a live lookup.

```json
{
  "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
}
```

## Errors

- HTTP 400 `invalid_cstat`: Static compliance needs tidal_volume_ml, pplat_cm_h2o greater than peep_cm_h2o, as used in the ARDS Network 2000 methods. Returned before settlement; you are not charged.
- HTTP 400 `invalid_items`: POST body must be a JSON object with only an items array Returned before settlement; you are not charged.
- HTTP 400 `invalid_item_count`: items must be an array of 1 to 25 objects Returned before settlement; you are not charged.
- HTTP 400 `invalid_item`: each items entry must be a JSON object Returned before settlement; you are not charged.

Shared HTTP 402 and 503: https://magentlab.com/docs/payments

## Related tools

- [Murray lung injury score](https://magentlab.com/docs/murray) — 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](https://magentlab.com/docs/pf-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.

- GET the tool with Accept: application/json (do not send Accept: text/html unless you want the human paywall).
- HTTP 402 means you have not paid. Decode the base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote.
- Sign accepts[0] (exact, EIP-3009) with validBefore = now + maxTimeoutSeconds (600 seconds), or accepts[1] (batch-settlement deposit/voucher) on product GET. Ping and POST {items} stay exact. Magent retries transient facilitator 429/5xx before answering.
- Retry the same URL with PAYMENT-SIGNATURE (base64 JSON of accepted and payload). Magent attaches canonical extensions.bazaar on CDP verify/settle; echoing 402 bazaar is optional.
- Success is HTTP 200 JSON plus PAYMENT-RESPONSE. exact settles before the tool. batch-settlement verifies (and deposit-settles) before the tool and commits the charge after HTTP 2xx. HTTP 503: retry the same PAYMENT-SIGNATURE. Mint a new exact nonce only after a new HTTP 402.

- offered `exact` on eip155:8453: Fixed-price USDC on Base. The buyer authorizes the advertised amount (EIP-3009). magent settles before the tool runs (paymentFlow upfront). extra.assetTransferMethod=eip3009 extra.paymentFlow=upfront.
- offered `batch-settlement` on eip155:8453: Payment-channel vouchers claimed later in batches. Exact stays accepts[0]. Same-path POST {items} is still exact. extra.assetTransferMethod=eip3009 extra.paymentFlow=authorization.

- not offered `upto`: Not offered. Usage-based: buyer authorizes a ceiling, seller settles the actual amount after work. Reserved for a future metered tool. Not for current calculators or code search.

Same-path POST {items} is still scheme exact: one EIP-3009 authorization for GET unit plus $0.002 per extra item. That is not x402 batch-settlement (payment channels / vouchers).

Shared HTTP 402 and 503 table: https://magentlab.com/docs/payments

Stdio MCP (one process per host): https://magentlab.com/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.