# MELD 3.0 (Kim 2021) MELD 3.0 Status: LIVE Price: $0.005 USDC `GET /api/calc/meld_3` HTML: https://magentlab.com/docs/meld-3 Markdown: https://magentlab.com/docs/meld-3.md Not a medical device. Not a diagnosis, dose, or listing recommendation. ## What it computes Compute the Kim 2021 MELD 3.0 integer from sex, bilirubin, INR, creatinine, sodium, albumin, and dialysis. ## When to use When an agent needs the published Kim 2021 MELD 3.0 integer and must not invent a listing order, substitute original MELD, or substitute MELD-Na. ## When not to use - Not a medical device. - Not a transplant listing or allocation order. - Kim 2021 MELD 3.0 only. This is not original MELD (Kamath 2001) and not MELD-Na (OPTN 2016). - Applies Kim 2021 lab bounds: creatinine 1.0–3.0 mg/dL (dialysis sets 3.0), bilirubin and INR floor 1.0, sodium 125–137 mmol/L, albumin 1.5–3.5 g/dL. - Does not cap the integer at 40. Kim 2021 did not presume an allocation cap. - Does not assign exception scores or listing priority. ## Formula ``` meld_3 = round(1.33*(female) + 4.56*ln(bilirubin) + 0.82*(137 - Na) - 0.24*(137 - Na)*ln(bilirubin) + 9.09*ln(INR) + 11.14*ln(creatinine) + 1.85*(3.5 - albumin) - 1.83*(3.5 - albumin)*ln(creatinine) + 6) ``` ## Citation [MELD 3.0: The Model for End-Stage Liver Disease Updated for the Modern Era](https://doi.org/10.1053/j.gastro.2021.08.050) Kim WR, Mannalithara A, Heimbach JK, Kamath PS, Asrani SK, Biggins SW, et al. Gastroenterology. 2021;161(6):1887-1895.e4 DOI: [10.1053/j.gastro.2021.08.050](https://doi.org/10.1053/j.gastro.2021.08.050) ## Worked example ### Male floors: bili 1, INR 1, Cr 1, Na 137, albumin 3.5 Given: `albumin_g_dl=3.5, bilirubin_mg_dl=1, creatinine_mg_dl=1, dialysis=false, inr=1, sex=male, sodium_mmol_l=137` 1. Kim 2021 bounds leave bilirubin, INR, and creatinine at 1.0; sodium at 137; albumin at 3.5. Male so female = 0. Not dialysis. 2. ln(1) = 0, so bilirubin, INR, creatinine, sodium, and albumin terms vanish. 3. meld_3 = round(6) → 6 ## Also searched as - MELD 3.0 - MELD 3 - Kim 2021 MELD - model for end-stage liver disease 3.0 - MELD three point zero - female sex MELD - albumin MELD 3.0 ## Parameters - `sex` (string, required): Sex used in the Kim 2021 female term (female adds 1.33). - `bilirubin_mg_dl` (number, optional): Total bilirubin in mg/dL (0.1-40). Provide this or bilirubin_umol_l. Kim 2021 floors at 1.0. - `bilirubin_umol_l` (number, optional): Total bilirubin in µmol/L (2-684). Converted as mg/dL = µmol/L / 17.1. - `inr` (number, required): INR (0.8-10). Kim 2021 floors at 1.0. - `creatinine_mg_dl` (number, optional): Serum creatinine in mg/dL (0.1-20). Provide this or creatinine_umol_l. Kim 2021 floors at 1.0 and caps at 3.0. - `creatinine_umol_l` (number, optional): Serum creatinine in µmol/L (9-1768). Converted as mg/dL = µmol/L / 88.42. - `sodium_mmol_l` (number, required): Serum sodium in mmol/L (110-160). Kim 2021 clamps 125-137. - `albumin_g_dl` (number, optional): Serum albumin in g/dL (1.0-6.0). Provide this or albumin_g_l. Kim 2021 clamps 1.5-3.5. - `albumin_g_l` (number, optional): Serum albumin in g/L (10-60). Converted as g/dL = g/L / 10. - `dialysis` (boolean, required): Dialysis twice in the prior week. true sets creatinine used to 3.0 (Kim 2021 ceiling). ## 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/meld_3` 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": [ { "albumin_g_dl": "3.5", "bilirubin_mg_dl": "1", "creatinine_mg_dl": "1", "dialysis": "false", "inr": "1", "sex": "male", "sodium_mmol_l": "137" }, { "albumin_g_dl": "3.5", "bilirubin_mg_dl": "1", "creatinine_mg_dl": "1", "dialysis": "false", "inr": "1", "sex": "male", "sodium_mmol_l": "137" } ] } ``` Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/meld-3 Example 200: ```json { "count": 2, "path": "/api/calc/meld_3", "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": "Kim WR, Mannalithara A, Heimbach JK, Kamath PS, Asrani SK, Biggins SW, et al.", "doi": "10.1053/j.gastro.2021.08.050", "id": "kim-2021", "pmid": "34454066", "source": "Gastroenterology. 2021;161(6):1887-1895.e4", "title": "MELD 3.0: The Model for End-Stage Liver Disease Updated for the Modern Era" }, "formula": "kim_meld_3_2021", "formula_expression": "meld_3 = round(1.33*(female) + 4.56*ln(bilirubin) + 0.82*(137 - Na) - 0.24*(137 - Na)*ln(bilirubin) + 9.09*ln(INR) + 11.14*ln(creatinine) + 1.85*(3.5 - albumin) - 1.83*(3.5 - albumin)*ln(creatinine) + 6)", "albumin_g_dl": 3.5, "inr": 1.0, "bilirubin_mg_dl": 1.0, "creatinine_mg_dl": 1.0, "sex": "male", "sodium_mmol_l": 137.0, "female": false, "bilirubin_used_mg_dl": 1.0, "creatinine_used_mg_dl": 1.0, "dialysis": false, "inr_used": 1.0, "sodium_used_mmol_l": 137.0, "albumin_used_g_dl": 3.5, "meld_3": 6 }, { "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": "Kim WR, Mannalithara A, Heimbach JK, Kamath PS, Asrani SK, Biggins SW, et al.", "doi": "10.1053/j.gastro.2021.08.050", "id": "kim-2021", "pmid": "34454066", "source": "Gastroenterology. 2021;161(6):1887-1895.e4", "title": "MELD 3.0: The Model for End-Stage Liver Disease Updated for the Modern Era" }, "formula": "kim_meld_3_2021", "formula_expression": "meld_3 = round(1.33*(female) + 4.56*ln(bilirubin) + 0.82*(137 - Na) - 0.24*(137 - Na)*ln(bilirubin) + 9.09*ln(INR) + 11.14*ln(creatinine) + 1.85*(3.5 - albumin) - 1.83*(3.5 - albumin)*ln(creatinine) + 6)", "albumin_g_dl": 3.5, "inr": 1.0, "bilirubin_mg_dl": 1.0, "creatinine_mg_dl": 1.0, "sex": "male", "sodium_mmol_l": 137.0, "female": false, "bilirubin_used_mg_dl": 1.0, "creatinine_used_mg_dl": 1.0, "dialysis": false, "inr_used": 1.0, "sodium_used_mmol_l": 137.0, "albumin_used_g_dl": 3.5, "meld_3": 6 } ] } ``` ## Response fields - `formula` (string): kim_meld_3_2021 - `formula_expression` (string): Exact expression used - `sex` (string): female or male - `female` (boolean): true when the Kim 2021 female term applies - `bilirubin_mg_dl` (number): Input bilirubin in mg/dL - `inr` (number): Input INR - `creatinine_mg_dl` (number): Input creatinine in mg/dL - `sodium_mmol_l` (number): Input sodium - `albumin_g_dl` (number): Input albumin in g/dL - `dialysis` (boolean): Dialysis flag - `bilirubin_used_mg_dl` (number): Bilirubin after Kim 2021 floor of 1.0 - `inr_used` (number): INR after Kim 2021 floor of 1.0 - `creatinine_used_mg_dl` (number): Creatinine after Kim 2021 1.0-3.0 bounds; dialysis forces 3.0 - `sodium_used_mmol_l` (number): Sodium after Kim 2021 125-137 clamp - `albumin_used_g_dl` (number): Albumin after Kim 2021 1.5-3.5 clamp - `meld_3` (integer): Kim 2021 MELD 3.0, nearest integer - `citation` (object): Kim 2021 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": "Kim WR, Mannalithara A, Heimbach JK, Kamath PS, Asrani SK, Biggins SW, et al.", "doi": "10.1053/j.gastro.2021.08.050", "id": "kim-2021", "pmid": "34454066", "source": "Gastroenterology. 2021;161(6):1887-1895.e4", "title": "MELD 3.0: The Model for End-Stage Liver Disease Updated for the Modern Era" }, "formula": "kim_meld_3_2021", "formula_expression": "meld_3 = round(1.33*(female) + 4.56*ln(bilirubin) + 0.82*(137 - Na) - 0.24*(137 - Na)*ln(bilirubin) + 9.09*ln(INR) + 11.14*ln(creatinine) + 1.85*(3.5 - albumin) - 1.83*(3.5 - albumin)*ln(creatinine) + 6)", "albumin_g_dl": 3.5, "inr": 1.0, "bilirubin_mg_dl": 1.0, "creatinine_mg_dl": 1.0, "sex": "male", "sodium_mmol_l": 137.0, "female": false, "bilirubin_used_mg_dl": 1.0, "creatinine_used_mg_dl": 1.0, "dialysis": false, "inr_used": 1.0, "sodium_used_mmol_l": 137.0, "albumin_used_g_dl": 3.5, "meld_3": 6 } ``` ## Errors - HTTP 400 `invalid_sex`: sex must be female or male Returned before settlement; you are not charged. - HTTP 400 `invalid_bilirubin`: bilirubin_mg_dl (0.1-40) or bilirubin_umol_l (2-684) is required Returned before settlement; you are not charged. - HTTP 400 `invalid_inr`: inr must be a number from 0.8 to 10 Returned before settlement; you are not charged. - HTTP 400 `invalid_creatinine`: creatinine_mg_dl (0.1-20) or creatinine_umol_l (9-1768) is required Returned before settlement; you are not charged. - HTTP 400 `invalid_sodium`: sodium_mmol_l must be a number from 110 to 160 Returned before settlement; you are not charged. - HTTP 400 `invalid_albumin`: albumin_g_dl (1-6) or albumin_g_l (10-60) 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 - [MELD](https://magentlab.com/docs/meld) — Compute the Kamath 2001 model for end-stage liver disease (MELD) integer from creatinine, bilirubin, INR, and cholestatic or alcoholic etiology. - [MELD-Na](https://magentlab.com/docs/meld-na) — Compute OPTN/UNOS 2016 MELD and MELD-Na from creatinine, bilirubin, INR, sodium, and dialysis. - [Child–Pugh](https://magentlab.com/docs/child-pugh) — Compute the Child–Turcotte–Pugh cirrhosis severity score from bilirubin, albumin, INR, encephalopathy, and ascites. ## 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.