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PSA density (Benson 1992)

PSA density

Compute Benson 1992 prostate-specific antigen density as serum PSA (ng/ml) divided by prostate volume (ml). Volume is length × width × depth × 0.5, or a caller-supplied volume.

LIVE $0.005 USDC GET /api/calc/psad

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

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

What it computes

Compute Benson 1992 prostate-specific antigen density as serum PSA (ng/ml) divided by prostate volume (ml). Volume is length × width × depth × 0.5, or a caller-supplied volume.

When to use

When an agent already has PSA and either a measured prostate volume or three orthogonal dimensions and must not invent a π/6 ellipsoid, diagnose cancer, or treat PSAD as a biopsy order.

When not to use

• Not a medical device. magent does not measure the gland or diagnose prostate cancer.
• Benson 1992 volume is length × width × depth × 0.5 (D1×D2×D3×1/2). This is not the π/6 ellipsoid.
• Provide psa_ng_ml with prostate_volume_ml (1-500 ml) or length_cm, width_cm, and depth_cm (each 1-20 cm), not both volume styles.
• Retrospective PSAD categories ≤0.05, >0.05 and <0.10, and ≥0.10 are Benson 1992 only. Not a biopsy order.

Formula

volume_ml = length_cm × width_cm × depth_cm × 0.5 (Benson: D1×D2×D3×1/2, not π/6); psad = psa_ng_ml / volume_ml

Citation

Title

Prostate specific antigen density: a means of distinguishing benign prostatic hypertrophy and prostate cancer

Authors

Benson MC, Whang IS, Pantuck A, Ring K, Kaplan SA, Olsson CA, Cooner WH

Source

J Urol. 1992;147(3 Pt 2):815-816

DOI

10.1016/s0022-5347(17)37393-7

Worked example

Also searched as

• PSA density
• prostate tumor volume
• PSAD
• prostate-specific antigen density
• Benson PSAD
• PSA divided by prostate volume
• BPH versus prostate cancer density

Try

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

/api/calc/psad?psa_ng_ml=4&length_cm=4&width_cm=4&depth_cm=4

Full URL: https://api.magentlab.com/api/calc/psad?psa_ng_ml=4&length_cm=4&width_cm=4&depth_cm=4

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/psad?psa_ng_ml=4&length_cm=4&width_cm=4&depth_cm=4"

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/psad 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": [
    {
      "depth_cm": "4",
      "length_cm": "4",
      "psa_ng_ml": "4",
      "width_cm": "4"
    },
    {
      "depth_cm": "4",
      "length_cm": "4",
      "psa_ng_ml": "4",
      "width_cm": "4"
    }
  ]
}

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/psad",
  "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": "Benson MC, Whang IS, Pantuck A, Ring K, Kaplan SA, Olsson CA, Cooner WH",
        "doi": "10.1016/s0022-5347(17)37393-7",
        "id": "benson-1992-psad",
        "pmid": "1371554",
        "source": "J Urol. 1992;147(3 Pt 2):815-816",
        "title": "Prostate specific antigen density: a means of distinguishing benign prostatic hypertrophy and prostate cancer"
      },
      "formula": "psad",
      "formula_expression": "volume_ml = length_cm × width_cm × depth_cm × 0.5 (Benson: D1×D2×D3×1/2, not π/6); psad = psa_ng_ml / volume_ml",
      "psa_ng_ml": 4.0,
      "benson_band": ">=0.10",
      "prostate_volume_ml": 32.0,
      "psad": 0.125,
      "depth_cm": 4.0,
      "length_cm": 4.0,
      "width_cm": 4.0
    },
    {
      "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": "Benson MC, Whang IS, Pantuck A, Ring K, Kaplan SA, Olsson CA, Cooner WH",
        "doi": "10.1016/s0022-5347(17)37393-7",
        "id": "benson-1992-psad",
        "pmid": "1371554",
        "source": "J Urol. 1992;147(3 Pt 2):815-816",
        "title": "Prostate specific antigen density: a means of distinguishing benign prostatic hypertrophy and prostate cancer"
      },
      "formula": "psad",
      "formula_expression": "volume_ml = length_cm × width_cm × depth_cm × 0.5 (Benson: D1×D2×D3×1/2, not π/6); psad = psa_ng_ml / volume_ml",
      "psa_ng_ml": 4.0,
      "benson_band": ">=0.10",
      "prostate_volume_ml": 32.0,
      "psad": 0.125,
      "depth_cm": 4.0,
      "length_cm": 4.0,
      "width_cm": 4.0
    }
  ]
}

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": "Benson MC, Whang IS, Pantuck A, Ring K, Kaplan SA, Olsson CA, Cooner WH",
    "doi": "10.1016/s0022-5347(17)37393-7",
    "id": "benson-1992-psad",
    "pmid": "1371554",
    "source": "J Urol. 1992;147(3 Pt 2):815-816",
    "title": "Prostate specific antigen density: a means of distinguishing benign prostatic hypertrophy and prostate cancer"
  },
  "formula": "psad",
  "formula_expression": "volume_ml = length_cm × width_cm × depth_cm × 0.5 (Benson: D1×D2×D3×1/2, not π/6); psad = psa_ng_ml / volume_ml",
  "psa_ng_ml": 4.0,
  "benson_band": ">=0.10",
  "prostate_volume_ml": 32.0,
  "psad": 0.125,
  "depth_cm": 4.0,
  "length_cm": 4.0,
  "width_cm": 4.0
}

Client errors (HTTP 400)

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

Related tools

• Gleason score — Sum caller-assigned Gleason 1974 primary and secondary histologic patterns (each 1-5) and return score 2-10. magent does not read slides. Not ISUP/Epstein 2016 Grade Groups.
• D'Amico — Apply the D'Amico 1998 JAMA clinically localized three-group rule to caller-assigned clinical T (t1c, t2a, t2b, t2c), Gleason sum 2-10, and PSA ng/mL, and return risk low, intermediate, or high. Does not assay PSA, assign Gleason, or compute CAPRA or NCCN groups.
• CAPRA — Apply Cooperberg 2005 Table 1 CAPRA points from caller-assigned preoperative PSA, Gleason primary/secondary, clinical T (t1/t2/t3a), percent positive biopsies, and age, and return the 0-10 score, Table 4 Kaplan-Meier band, and Table 4 5-year recurrence-free survival point estimate. Not a diagnosis.

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.