# Adrogué–Madias ΔNa from infusate Adrogué–Madias ΔNa Status: LIVE Price: $0.005 USDC `GET /api/calc/adrogue_madias` HTML: https://magentlab.com/docs/adrogue-madias Markdown: https://magentlab.com/docs/adrogue-madias.md 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 [Hyponatremia](https://doi.org/10.1056/NEJM200005253422107) Adrogué HJ, Madias NE N Engl J Med. 2000;342(21):1581-1589 DOI: [10.1056/NEJM200005253422107](https://doi.org/10.1056/NEJM200005253422107) ## Worked example ### 70 kg adult woman, Na 110, 1 L 3% saline (513 mmol/L) Given: `age=40, infusate_na_mmol_l=513, pediatric=false, sex=female, sodium_mmol_l=110, weight_kg=70` 1. TBW = 0.5 × 70 = 35 L (adult female fraction) 2. ΔNa = (513 + 0 − 110) / (35 + 1) = 403 / 36 = 11.2 mmol/L ### 70 kg adult man, Na 160, 1 L 5% dextrose (0 mmol/L) Given: `age=40, infusate_na_mmol_l=0, pediatric=false, sex=male, sodium_mmol_l=160, weight_kg=70` 1. TBW = 0.6 × 70 = 42 L (adult male fraction) 2. ΔNa = (0 + 0 − 160) / (42 + 1) = −160 / 43 = −3.7 mmol/L ## Also searched as - Adrogue Madias - delta Na infusate - change in serum sodium - hyponatremia infusate formula - hypernatremia infusate formula - sodium correction per liter ## Parameters - `sodium_mmol_l` (number, required): Measured serum sodium in mmol/L. Range 90-190. - `infusate_na_mmol_l` (number, required): Sodium concentration of 1 L of infusate in mmol/L (0-1000). Adrogué–Madias table examples: 5% dextrose 0; 0.9% NaCl 154; 3% NaCl 513. - `infusate_k_mmol_l` (number, optional): Potassium concentration of the same 1 L infusate in mmol/L (0-200). Omitted uses 0. Added to infusate sodium in the numerator. - `sex` (string, required): Sex used for adult and elderly TBW fractions. Ignored for the TBW fraction when pediatric=true (child fraction 0.6). - `age` (integer, required): Age in years. pediatric=false: integer 18-120; age ≥65 uses the elderly TBW fraction. pediatric=true: integer 0-17; TBW uses the child fraction 0.6. - `weight_kg` (number, optional): Weight in kilograms. Provide weight_kg or weight_lb. - `weight_lb` (number, optional): Weight in pounds. Converted as kg = lb * 0.45359237. - `pediatric` (boolean, required): true uses the child TBW fraction 0.6. false uses adult or elderly fractions from sex and age. Required; magent does not infer child vs adult from age. ## 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/adrogue_madias` 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": [ { "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" } ] } ``` Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/adrogue-madias Example 200: ```json { "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, "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, "sodium_mmol_l": 110.0, "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, "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, "sodium_mmol_l": 110.0, "tbw_fraction": 0.5, "tbw_l": 35.0 } ] } ``` ## Response fields - `formula` (string): adrogue_madias - `formula_expression` (string): Exact expression used - `sodium_mmol_l` (number): Measured serum sodium used - `infusate_na_mmol_l` (number): Infusate sodium used, mmol/L - `infusate_k_mmol_l` (number): Infusate potassium used (0 when omitted) - `weight_kg` (number): Normalized weight in kg - `sex` (string): male or female - `age_years` (integer): Age in years used - `pediatric` (boolean): true when the child TBW fraction 0.6 was used - `tbw_fraction` (number): TBW coefficient: children 0.6; adult male 0.6; adult female 0.5; elderly male 0.5; elderly female 0.45 - `tbw_l` (number): Total body water in L (fraction × weight_kg), 1 decimal - `delta_na_mmol_l` (number): Estimated change in serum Na after 1 L of infusate, 1 decimal - `citation` (object): Adrogué and Madias NEJM 2000 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": "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, "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, "sodium_mmol_l": 110.0, "tbw_fraction": 0.5, "tbw_l": 35.0 } ``` ## Errors - HTTP 400 `invalid_adrogue_sodium`: sodium_mmol_l must be a number from 90 to 190. Returned before settlement; you are not charged. - HTTP 400 `invalid_infusate_sodium`: infusate_na_mmol_l must be a number from 0 to 1000. Returned before settlement; you are not charged. - HTTP 400 `invalid_infusate_potassium`: infusate_k_mmol_l must be a number from 0 to 200 when provided. Returned before settlement; you are not charged. - HTTP 400 `invalid_sex`: sex must be female or male Returned before settlement; you are not charged. - HTTP 400 `invalid_age`: age must be an integer from 18 to 120 Returned before settlement; you are not charged. - HTTP 400 `invalid_weight`: weight_kg (1-500) or weight_lb (2-1100) is required Returned before settlement; you are not charged. - HTTP 400 `invalid_flag`: boolean clinical flags must be true or false 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 - [Sodium deficit](https://magentlab.com/docs/sodium-deficit) — Estimate sodium (cation) deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target. - [Free water deficit](https://magentlab.com/docs/free-water-deficit) — Estimate free water deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target. - [Corrected sodium](https://magentlab.com/docs/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. - 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 echoing accepted, payload, and extensions when present). - 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. - 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.