Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 521-533 |
| Journal | Journal of Theoretical Biology |
| Volume | 212 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2001 |
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Consequences of forced convection for the constraints on size and shape in embryos. / Kranenbarg, S.; Verhagen, J.H.G.; Muller, M.; van Leeuwen, J.L.
In: Journal of Theoretical Biology, Vol. 212, No. 4, 2001, p. 521-533.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Consequences of forced convection for the constraints on size and shape in embryos
AU - Kranenbarg, S.
AU - Verhagen, J.H.G.
AU - Muller, M.
AU - van Leeuwen, J.L.
PY - 2001
Y1 - 2001
N2 - Previously, predictions of the maximum size of biological objects based on oxygen availability have been made for both zero and infinite water velocity around the object. In reality, however, water velocity is always intermediate between zero and infinity. We predicted maximum size and optimal shape of biological objects, pending the velocity of water around them. We assumed oxygen inside the object to be transported by diffusion and outside the object by diffusion and convection. Fick's first law of diffusion describes the inner transport. For the outer transport, we relied on semi-empirical relations between mass transport and flow conditions (Friedlander's equations). To keep mathematical complexity acceptable, we restricted ourselves to the analysis of a sphere and a cylinder in cross flow. If water velocity is low, a spherical shape is most favourable for gas exchange. If water velocity is high, an elongated and flattened shape is more favourable. A size-dependent intermediate velocity exists where shape does not matter (10-4ms-1for teleost embryos). Teleost embryos are typically exposed to flow velocities equal to or larger than 10-4ms-1, making an elongated shape more favourable than a spherical one. Although teleost eggs are typically spherical, the oxygen-consuming embryos inside are indeed elongated
AB - Previously, predictions of the maximum size of biological objects based on oxygen availability have been made for both zero and infinite water velocity around the object. In reality, however, water velocity is always intermediate between zero and infinity. We predicted maximum size and optimal shape of biological objects, pending the velocity of water around them. We assumed oxygen inside the object to be transported by diffusion and outside the object by diffusion and convection. Fick's first law of diffusion describes the inner transport. For the outer transport, we relied on semi-empirical relations between mass transport and flow conditions (Friedlander's equations). To keep mathematical complexity acceptable, we restricted ourselves to the analysis of a sphere and a cylinder in cross flow. If water velocity is low, a spherical shape is most favourable for gas exchange. If water velocity is high, an elongated and flattened shape is more favourable. A size-dependent intermediate velocity exists where shape does not matter (10-4ms-1for teleost embryos). Teleost embryos are typically exposed to flow velocities equal to or larger than 10-4ms-1, making an elongated shape more favourable than a spherical one. Although teleost eggs are typically spherical, the oxygen-consuming embryos inside are indeed elongated
U2 - 10.1006/jtbi.2001.2391
DO - 10.1006/jtbi.2001.2391
M3 - Article
VL - 212
SP - 521
EP - 533
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
IS - 4
ER -