A mathematical model is proposed to simulate the growth of a plant leaf. The tissue in the leaf is regarded as a viscous, incompressible fluid whose 2D expansion comes from the non-zero specific growth rate in area. The resulting system of equations are composed of the modified Navier-Stokes equations. A level set method is used to capture the expanding leaf front. Numerical simulations indicate qualitatively that different portions of the leaf expand at different rates, which is consistent with the biological observations in the growth of a plant leaf. Numerical results for the case of the Xanthium leaf growth are also presented.
(Note: the "life" of a leaf is measured by the leaf plastochron index (LPI), defined as:
where n denotes the nth oldest leaf of a Xanthium plant and L_n is the length of leaf n (measured in mm).)
LPI | Experimental data | Simulation result |
0.74 | 0.34 | 0.61 |
2.64 | 6.60 | 6.20 |
4.18 | 10.7 | 10.3 |
LPI | Experimental data | Simulation result |
2.64 | 1.353 | 1.353 |
4.18 | 1.146 | 1.164 |
leafgrow.mpeg
(size=8Mb)
Animation simulating the growing of a golden pothos leaf for 3 days.