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Table 2.

Values and units of parameters used in the model

SymbolValueUnitDescription
Key (primary) parameters    
   V 1.12 mm3 Body volume (haemolymph and tissue compartments) 
   h0 2.5 mm Height of the cylindrical model 
   AM 0.4 mm2 Flow cross-sectional area of the medium flow 
   Δx 0.02 mm Thickness of the carapace lacuna 
   Φ 0.4  Tissue fraction of body volume 
   ζ 0.25  Fraction of total tissue in the central tissue cylinder 
   a0 0.0058 nmol s-1 mm-3 Volume-specific O2 consumption rate (whole body) 
   M 0.8333 mm3 s-1 Medium flow rate 
   H 0.0311 mm3 s-1 Perfusion rate 
   αM 0.0137 nmol mm-3 kPa-1 Solubility coefficient for O2 in water 
   αH 0.0123 nmol mm-3 kPa-1 Solubility coefficient for O2 in haemolymph 
   αT 0.0147 nmol mm-3 kPa-1 Solubility coefficient for O2 in tissue 
   DM 0.0020 mm2 s-1 Diffusion coefficient for O2 in water 
   DH 0.0015 mm2 s-1 Diffusion coefficient for O2 in haemolymph 
   DT 0.0010 mm2 s-1 Diffusion coefficient for O2 in tissue 
   g 0.0010 nmol s-1 mm-2 kPa-1 Permeability of the cuticular diffusion barrier 
   Δr 0.005 mm Radial distance between two grid points 
   Δh 0.1 mm Axial distance between two grid points 
   Δt ≤0.005 Time interval for numerical calculation 
Derived (secondary) parameters    
 0.120 mm Radius of the central tissue cylinder 
 0.280 mm Outer radius of the truncal haemolymph space 
 0.350 mm Outer radius of the peripheral tissue layer 
 0.500 mm Outer radius of the medium lacuna 
   r0 0.520 mm Outer radius of the carapace lacuna 
   a 0.015 nmol s-1 mm-3 Volume-specific O2 consumption rate (pure tissue) 
   νM 2.09 mm s-1 Flow velocity of the medium in the medium lacuna 
   νHC 0.13 mm s-1 Flow velocity of the haemolymph in the carapace lacuna 
   νHT 0.96 mm s-1 Flow velocity of the haemolymph in the trunk lacuna 
SymbolValueUnitDescription
Key (primary) parameters    
   V 1.12 mm3 Body volume (haemolymph and tissue compartments) 
   h0 2.5 mm Height of the cylindrical model 
   AM 0.4 mm2 Flow cross-sectional area of the medium flow 
   Δx 0.02 mm Thickness of the carapace lacuna 
   Φ 0.4  Tissue fraction of body volume 
   ζ 0.25  Fraction of total tissue in the central tissue cylinder 
   a0 0.0058 nmol s-1 mm-3 Volume-specific O2 consumption rate (whole body) 
   M 0.8333 mm3 s-1 Medium flow rate 
   H 0.0311 mm3 s-1 Perfusion rate 
   αM 0.0137 nmol mm-3 kPa-1 Solubility coefficient for O2 in water 
   αH 0.0123 nmol mm-3 kPa-1 Solubility coefficient for O2 in haemolymph 
   αT 0.0147 nmol mm-3 kPa-1 Solubility coefficient for O2 in tissue 
   DM 0.0020 mm2 s-1 Diffusion coefficient for O2 in water 
   DH 0.0015 mm2 s-1 Diffusion coefficient for O2 in haemolymph 
   DT 0.0010 mm2 s-1 Diffusion coefficient for O2 in tissue 
   g 0.0010 nmol s-1 mm-2 kPa-1 Permeability of the cuticular diffusion barrier 
   Δr 0.005 mm Radial distance between two grid points 
   Δh 0.1 mm Axial distance between two grid points 
   Δt ≤0.005 Time interval for numerical calculation 
Derived (secondary) parameters    
 0.120 mm Radius of the central tissue cylinder 
 0.280 mm Outer radius of the truncal haemolymph space 
 0.350 mm Outer radius of the peripheral tissue layer 
 0.500 mm Outer radius of the medium lacuna 
   r0 0.520 mm Outer radius of the carapace lacuna 
   a 0.015 nmol s-1 mm-3 Volume-specific O2 consumption rate (pure tissue) 
   νM 2.09 mm s-1 Flow velocity of the medium in the medium lacuna 
   νHC 0.13 mm s-1 Flow velocity of the haemolymph in the carapace lacuna 
   νHT 0.96 mm s-1 Flow velocity of the haemolymph in the trunk lacuna 

Data refer to a 2.5 mm-long, fasting D. magna without embryos in the brood chamber at food-free, normoxic conditions and to 20°C.

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