Electrolytes / glucose · LIVE

Adrogué–Madias ΔNa from infusate

Adrogué–Madias ΔNa

Estimate the change in serum sodium after 1 L of a given infusate from Adrogué–Madias TBW fractions and infusate sodium plus potassium.

LIVE $0.005 USDC GET /api/calc/adrogue_madias

Markdown: /docs/adrogue-madias.md · Canonical: https://magentlab.com/docs/adrogue-madias

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

What it computes

Estimate the change in serum sodium after 1 L of a given infusate from Adrogué–Madias TBW fractions and infusate sodium plus potassium.

When to use

When an agent needs the published ΔNa-per-liter infusate arithmetic and must not invent a correction rate, infusion protocol, or TBW fraction.

When not to use

• Not a treatment order, infusion protocol, or correction-rate target. The result is the estimated change in serum Na after 1 L of the given infusate.
• Does not model ongoing urinary losses, SIADH, or the safe rate of correction.
• TBW fractions follow Adrogué and Madias 2000: children 0.6; adult male 0.6; adult female 0.5; elderly male 0.5; elderly female 0.45. The papers say elderly without an age cutoff; magent treats age ≥65 as elderly (implementation clamp). pediatric=true/false is required and is not inferred from age.

Formula

delta_na_mmol_l = (infusate_na_mmol_l + infusate_k_mmol_l - sodium_mmol_l) / (tbw_l + 1); tbw_l = tbw_fraction * weight_kg

Citation

Title

Hyponatremia

Authors

Adrogué HJ, Madias NE

Source

N Engl J Med. 2000;342(21):1581-1589

DOI

10.1056/NEJM200005253422107

Worked example

Also searched as

• Adrogue Madias
• delta Na infusate
• change in serum sodium
• hyponatremia infusate formula
• hypernatremia infusate formula
• sodium correction per liter

Try

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

/api/calc/adrogue_madias?sodium_mmol_l=110&infusate_na_mmol_l=513&sex=female&age=40&weight_kg=70&pediatric=false

Full URL: https://api.magentlab.com/api/calc/adrogue_madias?sodium_mmol_l=110&infusate_na_mmol_l=513&sex=female&age=40&weight_kg=70&pediatric=false

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/adrogue_madias?sodium_mmol_l=110&infusate_na_mmol_l=513&sex=female&age=40&weight_kg=70&pediatric=false"

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/adrogue_madias 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": [
    {
      "age": "40",
      "infusate_na_mmol_l": "513",
      "pediatric": "false",
      "sex": "female",
      "sodium_mmol_l": "110",
      "weight_kg": "70"
    },
    {
      "age": "40",
      "infusate_na_mmol_l": "513",
      "pediatric": "false",
      "sex": "female",
      "sodium_mmol_l": "110",
      "weight_kg": "70"
    }
  ]
}

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/adrogue_madias",
  "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": "Adrogué HJ, Madias NE",
        "doi": "10.1056/NEJM200005253422107",
        "id": "adrogue-madias-2000",
        "source": "N Engl J Med. 2000;342(21):1581-1589",
        "title": "Hyponatremia"
      },
      "formula": "adrogue_madias",
      "formula_expression": "delta_na_mmol_l = (infusate_na_mmol_l + infusate_k_mmol_l - sodium_mmol_l) / (tbw_l + 1); tbw_l = tbw_fraction * weight_kg",
      "age_years": 40,
      "sodium_mmol_l": 110.0,
      "sex": "female",
      "weight_kg": 70.0,
      "delta_na_mmol_l": 11.2,
      "infusate_k_mmol_l": 0.0,
      "infusate_na_mmol_l": 513.0,
      "pediatric": false,
      "tbw_fraction": 0.5,
      "tbw_l": 35.0
    },
    {
      "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": "Adrogué HJ, Madias NE",
        "doi": "10.1056/NEJM200005253422107",
        "id": "adrogue-madias-2000",
        "source": "N Engl J Med. 2000;342(21):1581-1589",
        "title": "Hyponatremia"
      },
      "formula": "adrogue_madias",
      "formula_expression": "delta_na_mmol_l = (infusate_na_mmol_l + infusate_k_mmol_l - sodium_mmol_l) / (tbw_l + 1); tbw_l = tbw_fraction * weight_kg",
      "age_years": 40,
      "sodium_mmol_l": 110.0,
      "sex": "female",
      "weight_kg": 70.0,
      "delta_na_mmol_l": 11.2,
      "infusate_k_mmol_l": 0.0,
      "infusate_na_mmol_l": 513.0,
      "pediatric": false,
      "tbw_fraction": 0.5,
      "tbw_l": 35.0
    }
  ]
}

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": "Adrogué HJ, Madias NE",
    "doi": "10.1056/NEJM200005253422107",
    "id": "adrogue-madias-2000",
    "source": "N Engl J Med. 2000;342(21):1581-1589",
    "title": "Hyponatremia"
  },
  "formula": "adrogue_madias",
  "formula_expression": "delta_na_mmol_l = (infusate_na_mmol_l + infusate_k_mmol_l - sodium_mmol_l) / (tbw_l + 1); tbw_l = tbw_fraction * weight_kg",
  "age_years": 40,
  "sodium_mmol_l": 110.0,
  "sex": "female",
  "weight_kg": 70.0,
  "delta_na_mmol_l": 11.2,
  "infusate_k_mmol_l": 0.0,
  "infusate_na_mmol_l": 513.0,
  "pediatric": false,
  "tbw_fraction": 0.5,
  "tbw_l": 35.0
}

Client errors (HTTP 400)

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

Related tools

• Sodium deficit — Estimate sodium (cation) deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.
• Free water deficit — Estimate free water deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.
• Corrected sodium — Compute expected sodium in hyperglycemia using Katz 1.6 or Hillier 2.4. The formula argument is required.

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.
• 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.