# Fick cardiac output

Fick cardiac output

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

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

[Ueber die Messung des Blutquantums in den Herzventrikeln](https://vlp-new.ur.de/records/lit26189)
Fick A
Sitzungsberichte der Physikalisch-Medizinischen Gesellschaft zu Würzburg. 1870;XVI-XVII
DOI: none

## Worked example

### VO2 250, CaO2 200 ml/L, CvO2 150 ml/L

Given: `cao2_ml_l=200, cvo2_ml_l=150, vo2_ml_min=250`

1. avo2_difference = 200 − 150 = 50 ml/L
2. cardiac_output_l_min = 250 / 50 = 5.0


### VO2 250, CaO2 20 ml/dL, CvO2 15 ml/dL

Given: `cao2_ml_dl=20, cvo2_ml_dl=15, vo2_ml_min=250`

1. cao2_ml_l = 20 × 10 = 200
2. cvo2_ml_l = 15 × 10 = 150
3. cardiac_output_l_min = 250 / (200 − 150) = 5.0


## 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

## Parameters

- `vo2_ml_min` (number, required): Measured oxygen consumption in ml/min (50-2000, magent clamp; Fick 1870 does not publish an input band). Caller supplies the measured term. magent does not estimate VO2 from BSA or assume 125 ml/min/m².
- `cao2_ml_l` (number, optional): Arterial oxygen content in ml/L (50-400, magent clamp). Provide this or cao2_ml_dl, not both. magent does not compute content from hemoglobin or Hüfner factors.
- `cvo2_ml_l` (number, optional): Mixed-venous oxygen content in ml/L (20-350, magent clamp). Provide this or cvo2_ml_dl, not both. Must be less than CaO2. magent does not sample mixed-venous blood.
- `cao2_ml_dl` (number, optional): Arterial oxygen content in ml/dL (5-40, magent clamp). Converted as ml/L = ml/dL × 10. Provide this or cao2_ml_l, not both.
- `cvo2_ml_dl` (number, optional): Mixed-venous oxygen content in ml/dL (2-35, magent clamp). Converted as ml/L = ml/dL × 10. Provide this or cvo2_ml_l, not both. Must be less than CaO2 after conversion.

## 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/fick`
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": [
    {
      "cao2_ml_l": "200",
      "cvo2_ml_l": "150",
      "vo2_ml_min": "250"
    },
    {
      "cao2_ml_l": "200",
      "cvo2_ml_l": "150",
      "vo2_ml_min": "250"
    }
  ]
}
```

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

Example 200:

```json
{
  "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 fields

- `formula` (string): fick
- `formula_expression` (string): Exact expression used
- `vo2_ml_min` (number): Measured oxygen consumption used, ml/min
- `cao2_ml_l` (number): Arterial oxygen content used, ml/L (ml/dL inputs converted ×10)
- `cvo2_ml_l` (number): Mixed-venous oxygen content used, ml/L (ml/dL inputs converted ×10)
- `avo2_difference_ml_l` (number): CaO2 minus CvO2 in ml/L, 1 decimal
- `cardiac_output_l_min` (number): Fick cardiac output in L/min, 1 decimal
- `citation` (object): Fick 1870 Würzburg 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": "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
}
```

## Errors

- HTTP 400 `invalid_fick`: Fick cardiac output inputs must be numeric oxygen consumption and arterial and mixed-venous oxygen contents from that principle. 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

- [CPO](https://magentlab.com/docs/cpo) — Compute Fincke 2004 cardiac power output in watts from mean arterial pressure and cardiac output.
- [MAP](https://magentlab.com/docs/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.

- 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.