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Review Articles

The Kinematics of Biological Growth

[+] Author and Article Information
K. Garikipati

Department of Mechanical Engineering, Michigan Center for Theoretical Physics, and Center for Computational Medicine and Biology, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109-2125

Loss of mass is referred to as “resorption.”

These are the cells that produce the new mass.

While purely tangential growth, ρ¯n=0,ρ¯s0 is mathematically admissible; it does not appear that it is observed in Nature.

Appl. Mech. Rev 62(3), 030801 (Mar 31, 2009) (7 pages) doi:10.1115/1.3090829 History: Received June 15, 2008; Revised September 30, 2008; Published March 31, 2009

The kinematic aspects of biological growth models are reviewed by paying attention to the handful of crucial ideas on which modern treatments rest. Both surface and volumetric growth are considered. A critical appraisal is presented of the geometric and physical features of the models. Links are made to the mathematical treatment of growth and evolving interface phenomena in other physical problems. Computational issues are pointed out wherever appropriate.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

The initial growth surface Γ0 and the initial domain R0, current growth surface Γt, and intermediate growth surfaces Γτ

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Figure 2

Determination of the reference configuration of a material point at the instant of deposition on the surface Γt

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Figure 3

Admissibility of tangential surface growth velocities on nonsmooth surfaces

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Figure 4

The kinematics induced by the incompatible volumetric growth tensor Fg and its role in the multiplicative decomposition of the deformation gradient F=F¯eF̃eFg

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