Excretion Half-Life Calculator

Fit actual independently resolved excretion-only remaining-pool logmass versus time and invert negative slope. Not total elimination half-life from metabolism+excretion or half-life from two unconstrained points; first-order model/correct pool external.

Description

An excretion-only half-life model uses observations of a separately resolved remaining pool.

An excretion-only half-life model uses observations of a separately resolved remaining pool.^[1]

A decreasing log-mass fit supports a conditional first-order estimate without establishing all elimination pathways.

When to use Excretion Half-Life Calculator

Use this tool to calculate or review the supplied observations under the stated rules. Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.

How to use Excretion Half-Life Calculator and understand its results

Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.
Enter actualElapsedTimesHours, actualIndependentlyResolvedExcretedPoolRemainingMass, using the field meanings and rules below, then run the tool.
Read result.observedLogDecaySlopePerHour, result.conditionalFirstOrderExcretionHalfLifeHours. Use the units and subtraction order below to interpret each value; retain negative differences where returned.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
actualElapsedTimesHours	Actual elapsed times hours	list of number	Required
actualIndependentlyResolvedExcretedPoolRemainingMass	Actual independently resolved excreted pool remaining mass	list of number	Required

Supply at least two aligned finite strictly increasing times and strictly positive remaining masses. Negative time coordinates are accepted. Fit ordinary least squares to natural-log remaining mass against time, with a free intercept. The fitted slope must be negative, although every neighboring mass need not decrease. Return the slope and derived half-life without fit uncertainty.

slope=Σ((t_i−mean(t))(ln(m_i)−mean(ln(m))))/Σ((t_i−mean(t))²); halfLife=−ln(2)/slope

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Qualified observed calculation or explicit reference	object
result.observedLogDecaySlopePerHour	Fitted natural-log remaining-mass slope per hour; required to be negative.	number
result.conditionalFirstOrderExcretionHalfLifeHours	Minus ln(2) divided by the fitted negative log-mass slope, in hours.	number

json

{
  "input": {
    "actualElapsedTimesHours": [
      0,
      1,
      2
    ],
    "actualIndependentlyResolvedExcretedPoolRemainingMass": [
      8,
      4,
      2
    ]
  },
  "output": {
    "result": {
      "observedLogDecaySlopePerHour": -0.6931471805599452,
      "conditionalFirstOrderExcretionHalfLifeHours": 1.0000000000000002
    }
  }
}

Limitations and assumptions

Chemical identity, route, assay, exposure basis and reference applicability are caller-established. The output supplies no causal conclusion, universal toxicity threshold or authoritative regulatory determination.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use One-Compartment AUC Calculator: A one-compartment exponential model describes concentration decline using an initial concentration and elimination rate. For a complementary comparison, use Maintenance Dose Calculator: A maintenance-mass scenario relates a clinician-established average concentration target to clearance, interval and bioavailability.

References

Excretion Half-Life Calculator — tool.io

Similar or alternative tools

One-Compartment AUC Calculator
A one-compartment exponential model describes concentration decline using an initial concentration and elimination rate.
Maintenance Dose Calculator
A maintenance-mass scenario relates a clinician-established average concentration target to clearance, interval and bioavailability.