# Acid-base assessment (Berend) Acid-base assessment (Berend) Status: LIVE Price: $0.005 USDC `GET /api/calc/abg` HTML: https://magentlab.com/docs/abg Markdown: https://magentlab.com/docs/abg.md Not a medical device. Not a diagnosis, dose, or listing recommendation. ## What it computes Apply the Berend 2014 physiological stepwise assessment: pH acidemia or alkalemia, Table 1 primary metabolic versus respiratory process, anion gap, optional albumin-corrected gap, and printed delta-delta. ## When to use When an agent has arterial pH, PaCO2, bicarbonate, sodium, and chloride and needs Berend 2014 stepwise labels and numeric intermediates. ## When not to use - Not a medical device and not a diagnosis. magent does not assay arterial blood gas, assign a cause, or replace clinical context. - Not a ventilator setting, oxygen prescription, or bicarbonate dose. - Expected PaCO2 in metabolic acidosis is the Table 1 Winters secondary response (1.5×HCO3+8±2), not a treatment target. Standalone Winters is the related winters tool. - Anion gap uses Na−Cl−HCO3. High versus normal uses Berend's example upper reference of 12 mmol/L; the paper states the laboratory range is analyzer-specific. - Albumin correction uses Figure 1 (2.5 mmol/L per 1 g/dL decrease). Berend does not print a reference albumin; this tool uses 4.0 g/dL as the decrement baseline and does not reverse-correct hyperalbuminemia. - Delta-delta is returned only when the anion gap is high. Both ketoacidosis (1:1) and lactic (0.6) printed equations are returned; magent does not pick one from lactate. - Does not compute A-a difference, osmolal gap, or urinary anion gap. ## Formula ``` Berend 2014: acidemia if pH<7.38; alkalemia if pH>7.42; metabolic acidosis if pH<7.38 and HCO3<22; metabolic alkalosis if pH>7.42 and HCO3>26; respiratory acidosis if pH<7.38 and PaCO2>42; respiratory alkalosis if pH>7.42 and PaCO2<38; anion_gap=Na-Cl-HCO3 (high if >12); albumin-corrected AG=AG+2.5*(4.0-albumin) when albumin<4.0 g/dL; metabolic acidosis expected PaCO2=1.5*HCO3+8±2; metabolic alkalosis expected PaCO2=0.7*(HCO3-24)+40±2; acute respiratory acidosis HCO3 +1 per 10 mm Hg PaCO2 above 40; chronic +4 to +5; acute respiratory alkalosis HCO3 -2 per 10 mm Hg PaCO2 below 40; chronic -4 to -5; ketoacidosis delta-delta=ΔAG-ΔHCO3; lactic delta-delta=0.6*ΔAG-ΔHCO3 (simple if -5 to 5) ``` ## Citation [Physiological Approach to Assessment of Acid-Base Disturbances](https://doi.org/10.1056/NEJMra1003327) Berend K, de Vries APJ, Gans ROB N Engl J Med. 2014;371:1434-1445 DOI: [10.1056/NEJMra1003327](https://doi.org/10.1056/NEJMra1003327) ## Worked example ### Berend 2014 Patient 1 saline acidosis Given: `bicarbonate_mmol_l=18, chloride_mmol_l=115, paco2_mm_hg=39, ph=7.28, sodium_mmol_l=135` 1. pH 7.28 < 7.38 → acidemia 2. HCO3 18 < 22 with acidemia → metabolic acidosis; PaCO2 39 is not >42 → not a Table 1 respiratory primary 3. anion_gap = 135 − 115 − 18 = 2.0 mmol/L (not >12 → normal anion-gap) 4. expected PaCO2 = 1.5 × 18 + 8 = 35.0 mm Hg (band 33.0–37.0) 5. measured PaCO2 39.0 > 37.0 → additional respiratory acidosis ## Also searched as - Berend acid-base - acidemia alkalemia - stepwise acid-base - physiological acid-base - delta delta anion gap - albumin-corrected anion gap - arterial blood gas assessment ## Parameters - `ph` (number, required): Arterial pH (6.80-7.80). Acidemia if pH<7.38; alkalemia if pH>7.42 (Berend 2014 Table 1). - `paco2_mm_hg` (number, required): Arterial PaCO2 in mm Hg (8-120). Respiratory acidosis if pH<7.38 and PaCO2>42; respiratory alkalosis if pH>7.42 and PaCO2<38. - `bicarbonate_mmol_l` (number, required): Plasma bicarbonate in mmol/L (2-55). Metabolic acidosis if pH<7.38 and HCO3<22; metabolic alkalosis if pH>7.42 and HCO3>26. - `sodium_mmol_l` (number, required): Serum sodium in mmol/L (110-160). Used for anion gap Na-Cl-HCO3. - `chloride_mmol_l` (number, required): Serum chloride in mmol/L (70-130). Used for anion gap Na-Cl-HCO3. - `albumin_g_dl` (number, optional): Serum albumin in g/dL (1-6). When supplied and below 4.0 g/dL, anion gap is increased by 2.5 mmol/L per 1 g/dL decrease (Figure 1). Omitted skips the correction. - `lactate_mmol_l` (number, optional): Serum lactate in mmol/L (0-30) when supplied. Echoed only; magent does not pick keto vs lactic delta-delta from lactate. Both printed equations are returned when the anion gap is high. ## 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/abg` 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": [ { "bicarbonate_mmol_l": "18", "chloride_mmol_l": "115", "paco2_mm_hg": "39", "ph": "7.28", "sodium_mmol_l": "135" }, { "bicarbonate_mmol_l": "18", "chloride_mmol_l": "115", "paco2_mm_hg": "39", "ph": "7.28", "sodium_mmol_l": "135" } ] } ``` Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/abg Example 200: ```json { "count": 2, "path": "/api/calc/abg", "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": "Berend K, de Vries APJ, Gans ROB", "doi": "10.1056/NEJMra1003327", "id": "berend-2014-acid-base", "pmid": "25295502", "source": "N Engl J Med. 2014;371:1434-1445", "title": "Physiological Approach to Assessment of Acid-Base Disturbances" }, "formula": "abg", "formula_expression": "Berend 2014: acidemia if pH<7.38; alkalemia if pH>7.42; metabolic acidosis if pH<7.38 and HCO3<22; metabolic alkalosis if pH>7.42 and HCO3>26; respiratory acidosis if pH<7.38 and PaCO2>42; respiratory alkalosis if pH>7.42 and PaCO2<38; anion_gap=Na-Cl-HCO3 (high if >12); albumin-corrected AG=AG+2.5*(4.0-albumin) when albumin<4.0 g/dL; metabolic acidosis expected PaCO2=1.5*HCO3+8±2; metabolic alkalosis expected PaCO2=0.7*(HCO3-24)+40±2; acute respiratory acidosis HCO3 +1 per 10 mm Hg PaCO2 above 40; chronic +4 to +5; acute respiratory alkalosis HCO3 -2 per 10 mm Hg PaCO2 below 40; chronic -4 to -5; ketoacidosis delta-delta=ΔAG-ΔHCO3; lactic delta-delta=0.6*ΔAG-ΔHCO3 (simple if -5 to 5)", "secondary_response": "additional respiratory acidosis", "anion_gap_class": "normal", "anion_gap_mmol_l": 2.0, "bicarbonate_mmol_l": 18.0, "chloride_mmol_l": 115.0, "criteria": [ { "value": 7.28, "factor": "acidemia", "met": true }, { "value": 7.28, "factor": "alkalemia", "met": false }, { "value": 18.0, "factor": "metabolic_acidosis", "met": true }, { "value": 18.0, "factor": "metabolic_alkalosis", "met": false }, { "value": 39.0, "factor": "respiratory_acidosis", "met": false }, { "value": 39.0, "factor": "respiratory_alkalosis", "met": false }, { "value": 2.0, "factor": "high_anion_gap", "met": false }, { "value": 2.0, "factor": "normal_anion_gap", "met": true } ], "disorders": [ "acidemia", "metabolic acidosis", "normal anion-gap acidosis", "additional respiratory acidosis" ], "paco2_mm_hg": 39.0, "ph": 7.28, "ph_status": "acidemia", "primary_process": "metabolic acidosis", "sodium_mmol_l": 135.0, "expected_paco2_high_mm_hg": 37.0, "expected_paco2_low_mm_hg": 33.0, "expected_paco2_mm_hg": 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": "Berend K, de Vries APJ, Gans ROB", "doi": "10.1056/NEJMra1003327", "id": "berend-2014-acid-base", "pmid": "25295502", "source": "N Engl J Med. 2014;371:1434-1445", "title": "Physiological Approach to Assessment of Acid-Base Disturbances" }, "formula": "abg", "formula_expression": "Berend 2014: acidemia if pH<7.38; alkalemia if pH>7.42; metabolic acidosis if pH<7.38 and HCO3<22; metabolic alkalosis if pH>7.42 and HCO3>26; respiratory acidosis if pH<7.38 and PaCO2>42; respiratory alkalosis if pH>7.42 and PaCO2<38; anion_gap=Na-Cl-HCO3 (high if >12); albumin-corrected AG=AG+2.5*(4.0-albumin) when albumin<4.0 g/dL; metabolic acidosis expected PaCO2=1.5*HCO3+8±2; metabolic alkalosis expected PaCO2=0.7*(HCO3-24)+40±2; acute respiratory acidosis HCO3 +1 per 10 mm Hg PaCO2 above 40; chronic +4 to +5; acute respiratory alkalosis HCO3 -2 per 10 mm Hg PaCO2 below 40; chronic -4 to -5; ketoacidosis delta-delta=ΔAG-ΔHCO3; lactic delta-delta=0.6*ΔAG-ΔHCO3 (simple if -5 to 5)", "secondary_response": "additional respiratory acidosis", "anion_gap_class": "normal", "anion_gap_mmol_l": 2.0, "bicarbonate_mmol_l": 18.0, "chloride_mmol_l": 115.0, "criteria": [ { "value": 7.28, "factor": "acidemia", "met": true }, { "value": 7.28, "factor": "alkalemia", "met": false }, { "value": 18.0, "factor": "metabolic_acidosis", "met": true }, { "value": 18.0, "factor": "metabolic_alkalosis", "met": false }, { "value": 39.0, "factor": "respiratory_acidosis", "met": false }, { "value": 39.0, "factor": "respiratory_alkalosis", "met": false }, { "value": 2.0, "factor": "high_anion_gap", "met": false }, { "value": 2.0, "factor": "normal_anion_gap", "met": true } ], "disorders": [ "acidemia", "metabolic acidosis", "normal anion-gap acidosis", "additional respiratory acidosis" ], "paco2_mm_hg": 39.0, "ph": 7.28, "ph_status": "acidemia", "primary_process": "metabolic acidosis", "sodium_mmol_l": 135.0, "expected_paco2_high_mm_hg": 37.0, "expected_paco2_low_mm_hg": 33.0, "expected_paco2_mm_hg": 35.0 } ] } ``` ## Response fields - `formula` (string): abg - `formula_expression` (string): Berend 2014 printed steps - `ph` (number): Arterial pH used, 2 decimals - `paco2_mm_hg` (number): Arterial PaCO2 used, 1 decimal - `bicarbonate_mmol_l` (number): Plasma bicarbonate used, 1 decimal - `sodium_mmol_l` (number): Serum sodium used, 1 decimal - `chloride_mmol_l` (number): Serum chloride used, 1 decimal - `anion_gap_mmol_l` (number): Na - Cl - HCO3 in mmol/L, 1 decimal - `anion_gap_class` (string): high if anion gap >12 mmol/L (Berend example upper reference); else normal - `ph_status` (string): acidemia, alkalemia, or normal - `primary_process` (string): Table 1 primary metabolic and/or respiratory process label - `disorders` (array): Berend 2014 disorder labels as strings - `expected_paco2_mm_hg` (number): Table 1 expected PaCO2 when a metabolic primary is present. Omitted otherwise. - `expected_paco2_low_mm_hg` (number): Expected PaCO2 minus 2 mm Hg. Omitted when expected PaCO2 is omitted. - `expected_paco2_high_mm_hg` (number): Expected PaCO2 plus 2 mm Hg. Omitted when expected PaCO2 is omitted. - `secondary_response` (string): appropriate, additional respiratory acidosis, or additional respiratory alkalosis versus the metabolic expected PaCO2 ±2 band. Omitted when no metabolic primary. - `hco3_change_per_10_mm_hg` (number): Change in HCO3 per 10 mm Hg PaCO2 from 40 when a respiratory primary is present. Omitted otherwise. - `respiratory_secondary` (string): acute, chronic, additional metabolic acidosis, or additional metabolic alkalosis when the printed per-10 mm Hg band is met. Omitted when no respiratory primary or the ratio is between printed bands. - `albumin_g_dl` (number): Serum albumin when supplied. Omitted when albumin_g_dl is not given. - `albumin_corrected_anion_gap_mmol_l` (number): Anion gap plus 2.5 mmol/L per 1 g/dL albumin decrease from 4.0 g/dL. Omitted when albumin is omitted. - `lactate_mmol_l` (number): Serum lactate when supplied. Omitted when lactate_mmol_l is not given. - `delta_ag_mmol_l` (number): Anion gap minus 12 (albumin-corrected when albumin is supplied). Omitted when anion gap is not high. - `delta_hco3_mmol_l` (number): 24 minus HCO3. Omitted when anion gap is not high. - `delta_delta_ketoacidosis_mmol_l` (number): ΔAG − ΔHCO3. Omitted when anion gap is not high. - `delta_delta_lactic_mmol_l` (number): 0.6×ΔAG − ΔHCO3. Omitted when anion gap is not high. - `mixed_metabolic_ketoacidosis` (string): Printed Δ-Δ ketoacidosis mixed-metabolic label. Omitted when AG is not high. - `mixed_metabolic_lactic` (string): Printed Δ-Δ lactic mixed-metabolic label. Omitted when AG is not high. - `criteria` (array): Tree rows for acidemia, alkalemia, primary processes, and anion-gap class - `citation` (object): Berend 2014 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": "Berend K, de Vries APJ, Gans ROB", "doi": "10.1056/NEJMra1003327", "id": "berend-2014-acid-base", "pmid": "25295502", "source": "N Engl J Med. 2014;371:1434-1445", "title": "Physiological Approach to Assessment of Acid-Base Disturbances" }, "formula": "abg", "formula_expression": "Berend 2014: acidemia if pH<7.38; alkalemia if pH>7.42; metabolic acidosis if pH<7.38 and HCO3<22; metabolic alkalosis if pH>7.42 and HCO3>26; respiratory acidosis if pH<7.38 and PaCO2>42; respiratory alkalosis if pH>7.42 and PaCO2<38; anion_gap=Na-Cl-HCO3 (high if >12); albumin-corrected AG=AG+2.5*(4.0-albumin) when albumin<4.0 g/dL; metabolic acidosis expected PaCO2=1.5*HCO3+8±2; metabolic alkalosis expected PaCO2=0.7*(HCO3-24)+40±2; acute respiratory acidosis HCO3 +1 per 10 mm Hg PaCO2 above 40; chronic +4 to +5; acute respiratory alkalosis HCO3 -2 per 10 mm Hg PaCO2 below 40; chronic -4 to -5; ketoacidosis delta-delta=ΔAG-ΔHCO3; lactic delta-delta=0.6*ΔAG-ΔHCO3 (simple if -5 to 5)", "secondary_response": "additional respiratory acidosis", "anion_gap_class": "normal", "anion_gap_mmol_l": 2.0, "bicarbonate_mmol_l": 18.0, "chloride_mmol_l": 115.0, "criteria": [ { "value": 7.28, "factor": "acidemia", "met": true }, { "value": 7.28, "factor": "alkalemia", "met": false }, { "value": 18.0, "factor": "metabolic_acidosis", "met": true }, { "value": 18.0, "factor": "metabolic_alkalosis", "met": false }, { "value": 39.0, "factor": "respiratory_acidosis", "met": false }, { "value": 39.0, "factor": "respiratory_alkalosis", "met": false }, { "value": 2.0, "factor": "high_anion_gap", "met": false }, { "value": 2.0, "factor": "normal_anion_gap", "met": true } ], "disorders": [ "acidemia", "metabolic acidosis", "normal anion-gap acidosis", "additional respiratory acidosis" ], "paco2_mm_hg": 39.0, "ph": 7.28, "ph_status": "acidemia", "primary_process": "metabolic acidosis", "sodium_mmol_l": 135.0, "expected_paco2_high_mm_hg": 37.0, "expected_paco2_low_mm_hg": 33.0, "expected_paco2_mm_hg": 35.0 } ``` ## Errors - HTTP 400 `invalid_abg`: ABG acid-base inputs must match Berend 2014 pH, PaCO2, bicarbonate, sodium, chloride, albumin, and lactate as published. 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 - [Winters' formula](https://magentlab.com/docs/winters) — Compute expected arterial PCO2 in metabolic acidosis from plasma bicarbonate using the Albert–Winters 1967 formula. - [Anion gap](https://magentlab.com/docs/anion-gap) — Compute the serum anion gap from sodium, chloride, and bicarbonate, with or without potassium, using the Emmett–Narins 1977 formulas. formula 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 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.