# Kt/V

Kt/V

Status: LIVE
Price: $0.005 USDC
`GET /api/calc/kt_v`
HTML: https://magentlab.com/docs/kt-v
Markdown: https://magentlab.com/docs/kt-v.md

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

## What it computes

Compute the Daugirdas 1993 second-generation logarithmic single-pool variable-volume Kt/V from pre- and post-dialysis BUN, session length, ultrafiltration volume, and post-dialysis weight.

## When to use

When an agent needs the published 1993 logarithmic Kt/V and must not invent adequacy targets, substitute equilibrated eKt/V or stdKt/V, or compute a urea reduction ratio.

## When not to use

- Not a medical device.
- Not a dialysis prescription.
- Daugirdas 1993 second-generation single-pool variable-volume Kt/V only. This is not equilibrated eKt/V, not stdKt/V, and not a urea-reduction-ratio tool.
- Does not assign KDOQI or other adequacy targets. Those cuts are not in Daugirdas 1993.
- Weight is post-dialysis body weight (W). magent does not estimate urea distribution volume.

## Formula

```
Kt/V = -ln(R - 0.008 * t) + (4 - 3.5 * R) * UF / W
```

## Citation

[Second generation logarithmic estimates of single-pool variable volume Kt/V: an analysis of error](https://doi.org/10.1681/ASN.V451205)
Daugirdas JT
J Am Soc Nephrol. 1993;4(5):1205-1213
DOI: [10.1681/ASN.V451205](https://doi.org/10.1681/ASN.V451205)

## Worked example

### Pre BUN 80, post BUN 24, 4 h, UF 2 L, 70 kg

Given: `post_bun_mg_dl=24, pre_bun_mg_dl=80, session_hours=4, uf_l=2, weight_kg=70`

1. R = 24 / 80 = 0.3
2. R - 0.008 * 4 = 0.268
3. -ln(0.268) ≈ 1.3172
4. (4 - 3.5 * 0.3) * 2 / 70 ≈ 0.0843
5. round to 2 decimals → 1.40


## Also searched as

- Kt/V
- Daugirdas Kt/V
- single-pool Kt/V
- spKt/V
- hemodialysis Kt/V
- variable-volume Kt/V
- Daugirdas 1993 Kt/V
- urea kinetic Kt/V

## Parameters

- `pre_bun_mg_dl` (number, required): Predialysis blood urea nitrogen in mg/dL (1-200). Required with post_bun_mg_dl.
- `post_bun_mg_dl` (number, required): Postdialysis blood urea nitrogen in mg/dL (1-200). Required with pre_bun_mg_dl.
- `session_hours` (number, required): Hemodialysis session length in hours (1.0-8.0). Daugirdas 1993 t.
- `uf_l` (number, required): Ultrafiltration volume in litres (0-15). Daugirdas 1993 UF.
- `weight_kg` (number, optional): Post-dialysis body weight in kilograms (1-500). Provide weight_kg or weight_lb, not both.
- `weight_lb` (number, optional): Post-dialysis body weight in pounds (2-1100). Converted as kg = lb × 0.45359237. Provide weight_kg or weight_lb, not both.

## 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/kt_v`
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": [
    {
      "post_bun_mg_dl": "24",
      "pre_bun_mg_dl": "80",
      "session_hours": "4",
      "uf_l": "2",
      "weight_kg": "70"
    },
    {
      "post_bun_mg_dl": "24",
      "pre_bun_mg_dl": "80",
      "session_hours": "4",
      "uf_l": "2",
      "weight_kg": "70"
    }
  ]
}
```

Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/kt-v

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/kt_v",
  "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": "Daugirdas JT",
        "doi": "10.1681/ASN.V451205",
        "id": "daugirdas-1993",
        "pmid": "8305648",
        "source": "J Am Soc Nephrol. 1993;4(5):1205-1213",
        "title": "Second generation logarithmic estimates of single-pool variable volume Kt/V: an analysis of error"
      },
      "formula": "daugirdas_1993",
      "formula_expression": "Kt/V = -ln(R - 0.008 * t) + (4 - 3.5 * R) * UF / W",
      "weight_kg": 70.0,
      "kt_v": 1.4,
      "post_bun_mg_dl": 24.0,
      "pre_bun_mg_dl": 80.0,
      "session_hours": 4.0,
      "uf_l": 2.0
    },
    {
      "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": "Daugirdas JT",
        "doi": "10.1681/ASN.V451205",
        "id": "daugirdas-1993",
        "pmid": "8305648",
        "source": "J Am Soc Nephrol. 1993;4(5):1205-1213",
        "title": "Second generation logarithmic estimates of single-pool variable volume Kt/V: an analysis of error"
      },
      "formula": "daugirdas_1993",
      "formula_expression": "Kt/V = -ln(R - 0.008 * t) + (4 - 3.5 * R) * UF / W",
      "weight_kg": 70.0,
      "kt_v": 1.4,
      "post_bun_mg_dl": 24.0,
      "pre_bun_mg_dl": 80.0,
      "session_hours": 4.0,
      "uf_l": 2.0
    }
  ]
}
```

## Response fields

- `formula` (string): daugirdas_1993
- `formula_expression` (string): Exact expression used
- `pre_bun_mg_dl` (number): Predialysis BUN used in mg/dL
- `post_bun_mg_dl` (number): Postdialysis BUN used in mg/dL
- `session_hours` (number): Session length used in hours
- `uf_l` (number): Ultrafiltration volume used in litres
- `weight_kg` (number): Post-dialysis body weight used in kg (after conversion)
- `kt_v` (number): Daugirdas 1993 single-pool variable-volume Kt/V, 2 decimals
- `citation` (object): Daugirdas 1993 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": "Daugirdas JT",
    "doi": "10.1681/ASN.V451205",
    "id": "daugirdas-1993",
    "pmid": "8305648",
    "source": "J Am Soc Nephrol. 1993;4(5):1205-1213",
    "title": "Second generation logarithmic estimates of single-pool variable volume Kt/V: an analysis of error"
  },
  "formula": "daugirdas_1993",
  "formula_expression": "Kt/V = -ln(R - 0.008 * t) + (4 - 3.5 * R) * UF / W",
  "weight_kg": 70.0,
  "kt_v": 1.4,
  "post_bun_mg_dl": 24.0,
  "pre_bun_mg_dl": 80.0,
  "session_hours": 4.0,
  "uf_l": 2.0
}
```

## Errors

- HTTP 400 `invalid_bun`: bun_mg_dl must be a number from 1 to 200. Returned before settlement; you are not charged.
- HTTP 400 `invalid_dialysis_hours`: session_hours must be a number from 1.0 to 8.0 (Daugirdas 1993). Returned before settlement; you are not charged.
- HTTP 400 `invalid_ultrafiltration`: uf_l must be a number from 0 to 15 (Daugirdas 1993 ultrafiltration volume in litres). 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_urea_ratio`: post_bun_mg_dl must be < pre_bun_mg_dl and R - 0.008 * t must be > 0 (Daugirdas 1993). 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

- [CKD-EPI 2021 eGFR](https://magentlab.com/docs/egfr) — Compute race-free CKD-EPI 2021 creatinine eGFR in mL/min/1.73m2.
- [Cockcroft–Gault CrCl](https://magentlab.com/docs/crcl) — Compute Cockcroft–Gault creatinine clearance in mL/min using total body weight.

## 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.
- 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.