By providing this low-order attenuation model, we provide the flexibility to the problem for accurately estimating the sources.
The low-order attenuation model considered in this example is α = ρ-1 + βρ-2, with β as the tuning parameter.
The Chang method [ 26] is a very practical first-order attenuation correction algorithm.
This second-order attenuation of growth is equivalent to a logistic model, and a possible alternative approach would be to attenuate M(C t, S) according to an explicit logistic term with a carrying capacity.
The first order bulk attenuation rate constant for o-xylene was calculated to be 0.0025 d− 1 and a novel stable isotope-based first order model, which also accounted for the respective redox conditions, resulted in a slightly smaller biodegradation rate constant of 0.0019 d− 1.
Based on the quantified changes in total contaminant mass fluxes between the control planes, first-order natural attenuation rate constants could be estimated.
Based on the sparse set of monitoring wells, field scale mass fluxes and first-order natural attenuation rate constants of benzene, toluene, ethylbenzene, and o-xylene and p-xylene (BTEX) and low molecular weight polycyclic aromatic hydrocarbons (PAH) were estimated utilizing different point scale and also a new integral investigation method.
Applying a first-order uniform attenuation correction with the Chang algorithm resulted in accurate quantifications in our experiments, especially when combining together with scatter correction (–1.7% in the phantom study and from –6.3 to +4.3% in the animal study).
The detailed imaging parameters were as follows: 32-channel cardiac phased-array coil, TR/TE/FA = 3 matrix ms/10°, matrix 252 × 200, FOV 37.5 × 29.8 cm, SENSE factor 1.8, slice thickness = 3 mm, gap = −1.5 mm, linear k-space ordering, spectral attenuation with inversion recovery, acquired 133 sections, scan time 17.9 s, and breath-holding.
