Function ComputeTAveSeconds

Modules/PET/src/mitkSUVCalculationHelper.cpp:252–267

Closed-form average count-rate time per IBSI-SUV recommendation (suv_text.txt:820-826): T_ave = (1/lambda) * ln((lambda * T) / (1 - exp(-lambda * T))) with lambda = ln(2) / T_half and T = ActualFrameDuration. Physically: a non-decay-corrected voxel value is the count rate averaged over the frame; T_ave is the time inside the frame at which the *instantaneous* count rate equals that average. As

  // We use std::expm1(-lambda*T) instead of (1 - exp(-lambda*T)) for
  // numerical stability when lambda*T is small.
  double ComputeTAveSeconds(double frameDurationSeconds, double halfLifeSeconds)
  {
    if (frameDurationSeconds <= 0.0 || halfLifeSeconds <= 0.0
        || !std::isfinite(frameDurationSeconds) || !std::isfinite(halfLifeSeconds))
    {
      mitkThrowException(mitk::InvalidDICOMPropertyValueException)
        << "ComputeTAveSeconds requires positive, finite frame duration and "
           "half-life (got T=" << frameDurationSeconds
        << " s, T_half=" << halfLifeSeconds << " s).";
    }
    const double lambda = std::log(2.0) / halfLifeSeconds;
    const double lambdaT = lambda * frameDurationSeconds;
    // (1 - exp(-lambdaT)) computed stably as -expm1(-lambdaT).
    const double denom = -std::expm1(-lambdaT);
    return (1.0 / lambda) * std::log(lambdaT / denom);
  }
}