Haber Time Scaling
Integrate piecewise concentration×time and express equivalent duration under the n=1 Haber assumption; toxicodynamic recovery and concentration-dependent exponents are excluded.
Description
Sum piecewise-constant concentration-time exposure and convert it to equivalent hours at a reference concentration.
Haber-style scaling treats concentration multiplied by time as an exposure summary. Equal concentration-time products are equivalent under that arithmetic, but equal toxic effects require an appropriate concentration-time relationship; other toxic-load models use different exponents.1
This tool assumes the simple concentration-time form with concentration exponent one. Each supplied concentration is constant for its paired duration. The total is divided by a positive reference concentration to express an equivalent number of reference hours.
All concentrations, including the reference, must use the same unit. If concentrations are mg/m³ and durations are hours, the integral is mg·hour/m³. EquivalentReferenceHours is a duration under the chosen arithmetic, not a recommended exposure time.
When to use Haber Time Scaling
Use it to reconcile a prepared segmented concentration history or express its concentration-time total at a chosen reference concentration.
How to use Haber Time Scaling and interpret its calculation
- Enter aligned, nonempty concentrationSegments and segmentDurationsHours lists with nonnegative values.
- Enter positive referenceConcentration in the same concentration unit and run the calculation.
- Read concentrationTimeIntegral and equivalentReferenceHours. Evaluate whether simple concentration-time equivalence is appropriate before making a biological comparison.
integral = Σ(C_i × hours_i); equivalent hours = integral/reference concentration The implementation sums rectangular, constant-concentration intervals rather than interpolating timestamped observations.
Interval order does not affect this sum, and the reference is a rescaling value rather than an exposure limit retrieved by the tool. No ventilation, retention, body mass, or concentration exponent is an input.
{
"input": {
"concentrationSegments": [
10,
20
],
"segmentDurationsHours": [
1,
2
],
"referenceConcentration": 5
},
"output": {
"concentrationTimeIntegral": 50,
"equivalentReferenceHours": 10
}
}Zero concentration or duration contributes zero. All-zero intervals are accepted and yield zero equivalent hours. Doubling the reference concentration halves equivalent hours without changing the integral. A zero reference is rejected.
Limitations and assumptions
Equal totals can arise from very different peaks and schedules. The model does not account for recovery, accumulation, saturation, peak-driven toxicity, or a chemical-specific toxic-load exponent other than one.
It does not retrieve acute guideline levels, assess an endpoint, or infer an allowable exposure duration. Gaps and overlapping intervals cannot be identified from durations alone.
Alternative or Complementary methods
A retained inhalation-dose model includes breathing volume and retention, while a reference-concentration adjustment applies a separate schedule and dosimetric interpretation. Select the exposure metric required by the assessment.
References
-
Standing Operating Procedures for Developing Acute Exposure Guideline Levels for Hazardous Chemicals (2001) — U.S. Environmental Protection Agency
Similar or alternative tools
- Inhalation Dose
Calculate retained inhaled mass and a body-mass-normalized amount.
- Reference Concentration
Apply supplied schedule and dosimetric factors to a concentration point of departure.