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Modellering af optagelse af organiske stoffer i grøntsager og frugt

Bilag A
Generic one-compartment model for uptake into aerial plant parts ("TGD-blad")

Trapp & Matthies (1995) proposed a dynamic one-compartment model for to estimate the uptake of organic chemicals by foliar vegetation. The model is a strict simplification of former work (Trapp et al. 1994). It is the model currently used in European risk assessment EUSES (EC 1996a), and proposed for CSOIL (the Netherlands, Versluijs et al. 1998).

Mass balance for aerial plants

The model assumes that anthropogenic organic chemicals are only taken up passively, i.e., by diffusion and advection. Processes considered are translocation to shoots, gaseous deposition on leaves, volatilization from leaves, metabolism and degradation processes, and dilution by exponential growth.

The mass balance is:

Change of chemicals mass in the aerial plant parts =

+ flux from soil via xylem to the shoots
± gaseous flux from/to air
- photodegradation - metabolism

Expressed in mathematical terms:

dmL/dt = d(CL× VL)/dt
= Q · TSCF · CW + A · g · (CA - CL/KLA) - kE · mL

Equation 1


where

mL is the mass of chemical in the leaves
CL is the concentration
VL is the volume of the leaves (default 0.002 m3)
Q is the amount of transpired water per time (default 1 L/d)
A is the leaf surface area (default 5 m2),
g is the leaf to air conductance (default 0.001 m/s)
CA is the concentration of chemical in air
kE is an elimination rate (1/s)


Assuming that the growth is exponential with the rate kG (default 0.035 d-1) and assuming that the ratios A/VL and Q/VL are constant, it follows for the change of the concentration with time dCL/dt:

dCL/dt=
-[A · g/(KLA · VL)+kE+kG] · CL + CW · TSCF · Q/VL + CA · g A/VL

Equation 2

Analytical solution for constant conditions

Taking the parameters on the right side of the equation as constants yields a linear differential equation of first order with the general solution:

dCL/dt = -a × CL + b Equation 3


where

a = A · g/(KLA · VL) + kE + kG (sink terms) Equation 4
b = CW · TSCF · Q/VL + CA · g A/VL (source terms) Equation 5

With an initial CL(0) the analytical solution of the equation is:

CL(t) = CL(0) · exp(-a · t) + b /a [1 - exp(-a · t)] Equation 6


The steady-state concentration (t à infinite, dCL/dt à 0) is:

CL(t à infinite) = b /a Equation 7


The time to reach steady-state (95%) is:

t(95%) = - ln 0.05/a Equation 8

Limitations

The approach was developed for non-ionic organic substances only. Calculated concentrations correspond to the aerial plant compartment, mainly foliage. Concentrations in fruit can deviate greatly. Exponential growth is assumed. This is only valid for plants that are harvested before maturation, e.g. green fodder, green vegetables and lettuce. Deposition by aerosols, which is not considered, can be important for particle-bound compounds. The empirical parameters used in the equation (KLA, TSCF) were derived from a small number of experiments. The given parameterization is not for a specific plant, but represents average values. Moreover, properties were taken as constant. This is comfortable for the mathematical solution of the equation, but is not very realistic and can lead to error. The equation is of a generic type and not necessarily applicable for real situations.

Although these limitations had been clearly stated by the authors, the model is used for all chemicals in the current risk assessment approach of the EU, although applicable only for a minority. This has been criticized (Trapp & Schwartz 2000).

 

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