Health

Trough Level Estimator (Cmin = Cmax · e^(-kτ))

Predict the trough concentration Cmin from a measured peak concentration Cmax during therapeutic drug monitoring (TDM): Cmin = Cmax · e^(-kτ), where k = ln2 / t½ and τ is the time from the peak to the next dose. Inputs are the measured peak, the elimination half-life, and the dosing interval. Also reports the fraction of the peak remaining at the trough and the peak-to-trough drop. This tool takes a measured Cmax (the TDM workflow), unlike drug-half-life-dose (which derives C0 from Dose/Vd) and dosing-interval-designer (which outputs a dimensionless peak/trough ratio, not an absolute concentration). Valid for one-compartment first-order elimination with the peak measured post-distribution. Not medical advice.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/trough-level-estimator' \
  -H 'Content-Type: application/json' \
  -d '{"cmax":15,"halfLife":8,"tau":8,"decimalPlaces":4}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/trough-level-estimator

Parameters

Name	Type	Required	Description
cmax	number	Yes	Measured peak plasma concentration (post-distribution). Must be positive.
halfLife	number	Yes	Elimination half-life. Must be positive.
tau	number	Yes	Dosing interval — time from the measured peak to the next dose. Must be positive.
decimalPlaces	number	No	—

Response format

JSON result

JSON

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-trough-level-estimator": {
      "name": "trough-level-estimator",
      "description": "Predict the trough concentration Cmin from a measured peak concentration Cmax during therapeutic drug monitoring (TDM): Cmin = Cmax · e^(-kτ), where k = ln2 / t½ and τ is the time from the peak to the next dose. Inputs are the measured peak, the elimination half-life, and the dosing interval. Also reports the fraction of the peak remaining at the trough and the peak-to-trough drop. This tool takes a measured Cmax (the TDM workflow), unlike drug-half-life-dose (which derives C0 from Dose/Vd) and dosing-interval-designer (which outputs a dimensionless peak/trough ratio, not an absolute concentration). Valid for one-compartment first-order elimination with the peak measured post-distribution. Not medical advice.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=trough-level-estimator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "trough-level-estimator",
    "arguments": {
  "cmax": 15,
  "halfLife": 8,
  "tau": 8,
  "decimalPlaces": 4
}
  }
}

Browse tools Open tool