The Myriophyllum model is derived from the Lemna TKTD model by
Klein et al. (2021). The Myriophyllum model is mathematically equivalent
to the Tier 2C version of the Lemna model by Klein et al. (2021),
cf. Lemna_SETAC(). Recommended settings for Tier 2C are k_photo_fixed=TRUE
and k_resp=0 (Klein et al. 2021).
In particular, the growth model is a simple exponential growth model,
which is considered to be the typical situation for a laboratory macrophyte
study. Instead of frond numbers as for Lemna, the biomass is also returned as
total shoot length (TSL) in simulation results.
Consequently, the model has the additional parameter r_DW_TSL
(dry weight per total shoot length ratio) instead of r_DW_FN (dry weight
per frond number ratio).
Myrio()an S4 object of type MyrioExpScenario
The model has two state variables:
BM, Biomass (g dw m-2 for field studies or mg dw for lab)
M_int, Mass of toxicant in plant population (mass per m2, e.g. ug m-2)
Growth model
k_photo_max, Maximum photosynthesis rate (d-1), default: 0.47
Concentration response (Toxicodynamics)
EC50_int, Internal concentration resulting in 50% effect (ug L-1)
E_max, Maximum inhibition (-), default: 1
b, Slope parameter (-)
Internal concentration (Toxicokinetics)
P, Permeability (cm d-1)
r_A_DW, Area per dry-weight ratio (cm2 g-1), default: 1000
r_FW_DW, Fresh weight per dry weight ratio (-), default: 16.7
r_FW_V, Fresh weight density (g cm-3), default: 1
r_DW_TSL, Dry weight per total shoot length ratio (g (field) or mg (lab) dw cm-1)
K_pw, Partitioning coefficient plant:water (-), default: 1
k_met, Metabolisation rate (d-1), default: 0
None.
Default values for parameter boundaries are set for all parameters by expert
judgement, for calibration purposes. Values can be modified using set_bounds().
Simulation results will contain the state variables
It is possible to amend the output of simulate() with additional model
quantities that are not state variables, for e.g. debugging purposes or to
analyze model behavior. To enable or disable additional outputs, use the
optional argument nout of simulate(). As an example, set nout=2 to
enable reporting of the acceleration factor (MV) and the mobilization flux
(pC). Set nout=0 to disable additional outputs (default).
The available output levels are as follows:
nout >= 1: C_int, internal concentration (mass per volume)
nout >= 2: TSL, total shoot length (?)
nout >= 3: f_photo, photosynthesis dependency function (-)
Growth and TK/TD
nout >= 4: C_int_unb, unbound internal concentration (mass per volume)
nout >= 5: C_ext, external concentration (mass per volume)
Derivatives
nout >= 6: dBM, biomass derivative (g dw m-2 d-1)
nout >= 7: dM_int, mass of toxicant in plants derivative (mass per m2 d-1)
The arguments to ODE solver deSolve::ode() control how model equations
are numerically integrated. The settings influence stability of the numerical
integration scheme as well as numerical precision of model outputs. Generally, the
default settings as defined by deSolve are used, but all deSolve settings
can be modified in cvasi workflows by the user, if needed. Please refer
to e.g. simulate() on how to pass arguments to deSolve in cvasi
workflows.
Some default settings of deSolve were adapted for this model by expert judgement to enable precise, but also computationally efficient, simulations for most model parameters. These settings can be modified by the user, if needed:
hmax = 0.1
Maximum step length in time suitable for most simulations.
Supported effect endpoints include BM (biomass) and r (average growth rate during simulation). The effect on biomass is calculated from the last state of a simulation. Be aware that endpoint r is incompatible with biomass transfers.
Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.
The biomass transfer feature assumes that always a fixed amount of
biomass is transferred. Transfers can occur at any fixed point in time or
in regular intervals. During a transfer, the biomass is reset to the
transferred amount and additional compartments can be scaled 1:1 accordingly,
to e.g. reflect the change in internal toxicant mass when biomass is modified.
Transfer settings can be modified using set_transfer().
If a transfer occurs, simulation results of that time point will report the model state
before the transfer. Be aware that if transfers are defined using the
interval argument, the transfers will always occur relative to time point
zero (t = 0). As an example, setting a regular transfer of seven days,
interval = 7, will result at transfers occurring at time points which are
integer multiplicates of seven, such as t=0, t=7, t=14 and so forth.
The starting and end times of a scenario do not influece when a regular
transfer occurs, only if it occurs.
Klein J., Cedergreen N., Heine S., Reichenberger S., Rendal C., Schmitt W., Hommen U., 2021: Refined description of the Lemna TKTD growth model based on Schmitt et al. (2013) - equation system and default parameters. Report of the working group Lemna of the SETAC Europe Interest Group Effect Modeling. Version 1, uploaded on 22. Sept. 2021. https://www.setac.org/group/effect-modeling.html
Macrophyte-models, Transferable, Scenarios
Other Myriophyllum models:
Myrio_log(),
Myriophyllum-models
Other macrophyte models:
Lemna_SETAC(),
Lemna_Schmitt(),
Macrophyte-models,
Myrio_log()