living matter lab


winter 13 - me337 - mechanics of growth


ellen kuhl, alexander zollner
office hours thu 2:00-3:00, durand 217
course announcement

winter 2013
tue thu 11:00-12:15



in contrast to traditional engineering structures living structures show the fascinating ability to grow and adapt their form, shape and microstructure to a given mechanical environment. this course addresses the phenomenon of growth on a theoretical and computational level and applies the resulting theories to classical biomechanical problems like bone remodeling, hip replacement, wound healing, atherosclerosis or in stent restenosis. this course will illustrate how classical engineering concepts like continuum mechanics, thermodynamics or finite element modeling have to be rephrased in the context of growth. having attended this course, you will be able to develop your own problem-specific finite element based numerical solution techniques and interpret the results of biomechanical simulations with the ultimate goal of improving your understanding of the complex interplay between form and function.

journal club

mechanics of growth on imechanica

class papers

zöllner am, abilez oj, böl m, kuhl e. stretching skeletal muscle - chronic muscle lengthening through sarcomerogenesis. plos one, 2012;7(10):e45661. (download) (online)

pang h, shiwalkar ap, madormo cm, taylor re, andriacchi tp, kuhl e. computational modeling of bone density profiles in response to gait: a subject-specific approach. biomech model mechanobio, 2012;11:379-390. (download)

buganza tepole a, ploch cj, wong j, gosain ak, kuhl e. growing skin - a computational model for skin expansion in reconstructive surgery. j mech phys solids, 2011;59:2177-2190. (download)

taylor re, zheng ch, jackson pr, doll jc, chen jc, holzbaur krs, besier t, kuhl e. the phenomenon of twisted growth: humeral torsion in dominant arms of high performance tennis players. comp meth biomech biomed eng, 2009;12:83-93. (download)


  • 30 % homework - 3 homework assignments, 10% each
  • 30 % midterm - closed book, closed notes, one single page cheat sheet
  • 20 % final project oral presentations - graded by the class
  • 20 % final project essay - graded by instructor


day date topic slides homework
tue jan 08 motivation - everything grows! s01
thu jan 10 basics maths - notation and tensors s02 h01
tue jan 15 basic kinematics - large deformation and growth s03
thu jan 17 kinematics - growing hearts s04
tue jan 22 guest lecture - growing surfaces s05
thu jan 24 kinematics - growing leaflets s06
tue jan 29 basic balance equations - closed and open systems s07
thu jan 31 basic constitutive equations - growing muscle s08 h02
tue feb 05 basic constitutive equations - growing tumors s09
thu feb 07 volume growth - finite elements for growth - theory s10
tue feb 12 volume growth - finite elements for growth - matlab s11
thu feb 14 volume growth - growing skin s12
tue feb 19 basic constitutive equations - growing bones s13
thu feb 21 density growth - finite elements for growth s14 h03
tue feb 26 density growth - growing bones s15
thu feb 28 everything grows! - midterm summary s16
tue mar 05 midterm
thu mar 07 remodeling - remodeling arteries and tendons s18
tue mar 12 class project - discussion, presentation, evaluation s19 h04
thu mar 14 class project - discussion, presentation, evaluation
thu mar 14 written part of final projects due

final project

ASME SBC 2011.jpg

buganza a, wong j, kuhl e. computational modeling of mechanically driven skin growth due to different expander geometries, farmington, pennsylvania, 2011

matlab files

finally... here's the matlab code for growth

additional reading

(1) taber l. biomechanics of growth, remodeling, and morphogenesis, appl mech rew 48, 487-545, 1995
(2) kuhl e, menzel a, steinmann p. computational modeling of growth - a critical review, a classification and two new consistent approaches, computational mechanics 32, 71-88, 2003
(3) rodriguez ek, hoger a, mc culloch a. stress-dependent finite growth in soft elastic tissues, j biomechanics 27, 455-467, 1994
(4) kuhl e, maas r, himpel g, menzel a. computational modeling of arterial wall growth - attempts towards patient-specific simulations based on computer tomography, biomech model mechanobio 6, 321-331, 2007
(5) göktepe s, abilez oj, parker kk, kuhl e. a multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis.j theor bio 265: 433-442, 2010
(6) ambrosi d, ateshian ga, arruda em, cowin sc, dumais j, goriely a, holzapfel ga, humphrey jd, kemkemer r, kuhl e, olberding je, taber la, garikipati k. perspectives on biological growth and remodeling.j mech phys solids 59: 863-883, 2011
(7) zöllner am, buganza tepole A, kuhl e. on the biomechanics and mechanobiology of growing skin. j theor bio 297, 166-175, 2012
(8) menzel a, kuhl e. frontiers in growth and remodeling. mech res comm 42,1-14, 2012