Medications · LIVE

Biologically effective dose

Compute Fowler 1989 biologically effective dose from equal-fraction count, dose per fraction in Gy, and a caller-assigned tissue α/β, without a time or repopulation term.

LIVE $0.005 USDC GET /api/calc/bed

Markdown: /docs/bed.md · Canonical: https://magentlab.com/docs/bed

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

What it computes

Compute Fowler 1989 biologically effective dose from equal-fraction count, dose per fraction in Gy, and a caller-assigned tissue α/β, without a time or repopulation term.

When to use

When an agent already has n, d, and tissue α/β and must not invent a radiotherapy prescription, apply T_k or T_pot, or treat the result as EQD2.

When not to use

• Not a medical device. Not a radiotherapy prescription or treatment plan. magent does not plan radiotherapy.
• Fowler 1989 BED without a time or repopulation term. Does not apply overall-time T_k or T_pot (those are later Fowler and other papers).
• Does not convert BED to EQD2 or normalized total dose. Caller supplies n, d_gy, and tissue alpha_beta; magent does not assign α/β.
• Rejects non-positive n×d or α/β. n 1-50, d_gy 0.5-30, alpha_beta 1-20 are magent clamps, not bands published as input limits in Fowler 1989.

Formula

bed_gy = n * d_gy * (1 + d_gy / alpha_beta)

Citation

Title

The linear-quadratic formula and progress in fractionated radiotherapy

Authors

Fowler JF

Source

Br J Radiol. 1989;62(740):679-694

DOI

10.1259/0007-1285-62-740-679

Worked example

Also searched as

• BED
• biologically effective dose
• linear quadratic formula
• Fowler BED
• alpha beta ratio
• fractionated radiotherapy BED
• LQ model BED
• dose per fraction BED

Try

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

/api/calc/bed?n=30&d_gy=2&alpha_beta=3

Full URL: https://api.magentlab.com/api/calc/bed?n=30&d_gy=2&alpha_beta=3

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/bed?n=30&d_gy=2&alpha_beta=3"

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/bed 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": [
    {
      "alpha_beta": "3",
      "d_gy": "2",
      "n": "30"
    },
    {
      "alpha_beta": "3",
      "d_gy": "2",
      "n": "30"
    }
  ]
}

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/bed",
  "items": [
    {
      "n": 30,
      "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": "Fowler JF",
        "doi": "10.1259/0007-1285-62-740-679",
        "id": "fowler-1989",
        "pmid": "2670032",
        "source": "Br J Radiol. 1989;62(740):679-694",
        "title": "The linear-quadratic formula and progress in fractionated radiotherapy"
      },
      "formula": "bed",
      "formula_expression": "bed_gy = n * d_gy * (1 + d_gy / alpha_beta)",
      "alpha_beta": 3.0,
      "bed_gy": 100.0,
      "d_gy": 2.0
    },
    {
      "n": 30,
      "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": "Fowler JF",
        "doi": "10.1259/0007-1285-62-740-679",
        "id": "fowler-1989",
        "pmid": "2670032",
        "source": "Br J Radiol. 1989;62(740):679-694",
        "title": "The linear-quadratic formula and progress in fractionated radiotherapy"
      },
      "formula": "bed",
      "formula_expression": "bed_gy = n * d_gy * (1 + d_gy / alpha_beta)",
      "alpha_beta": 3.0,
      "bed_gy": 100.0,
      "d_gy": 2.0
    }
  ]
}

Response

Example JSON

Machine form of the same example. Frozen fixture. Not a live lookup.

{
  "n": 30,
  "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": "Fowler JF",
    "doi": "10.1259/0007-1285-62-740-679",
    "id": "fowler-1989",
    "pmid": "2670032",
    "source": "Br J Radiol. 1989;62(740):679-694",
    "title": "The linear-quadratic formula and progress in fractionated radiotherapy"
  },
  "formula": "bed",
  "formula_expression": "bed_gy = n * d_gy * (1 + d_gy / alpha_beta)",
  "alpha_beta": 3.0,
  "bed_gy": 100.0,
  "d_gy": 2.0
}

Client errors (HTTP 400)

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

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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. 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.