living matter lab


spring 18 - me337 - mechanics of growth


me 337 - mechanics of growth 18

rijk de rooij
ellen kuhl

tue/thu 10:30-11:50, GES-150
office hours tbd, 520-203
course announcement



in contrast to engineering structures, living matter shows 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, pok jm, mcwalter ej, gold ge, kuhl e. on high heels and short muscles: a multiscale model for sarcomere loss in the gastrocnemius muscle. j theor bio, 2015;365:301–310. (download)

eskandari m, pfaller mr, kuhl e. on the role of mechanics in chronic lung disease. materials, 2013;6:5639-5658. (download) (open access)

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

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 % final exam - closed book, closed notes, one single page cheat sheet
  • 20 % final project oral presentations - graded by the class
  • 20 % final project essay - graded by rijk and ellen


day date topic slides homework
tue apr 03 motivation - everything grows! s01
thu apr 05 basics maths - notation and tensors s02
tue apr 10 basic kinematics - large deformation and growth s03 h01
thu apr 12 kinematics - growing hearts s04
tue apr 17 kinematics - growing brains s05
thu apr 19 balance equations - closed and open systems s06
tue apr 24 basic constitutive equations - growing tumors s07
thu apr 26 volume growth - growing muscles s08 h02
tue may 01 volume growth - finite elements for growth s09
thu may 03 volume growth - growing arteries s10
tue may 08 volume growth - growing skin s11
thu may 10 volume growth - growing hearts s12
tue may 15 basic constitutive equations - growing bones s13
thu may 17 density growth - finite elements for growth s14 h03
tue may 22 density growth - wounds and brains s15
thu may 24 everything grows! - final prep s16
tue may 29 final
thu may 31 class projects - discussion, presentation, evaluation s19 h04
tue jun 05 class projects - discussion, presentation, evaluation
fri jun 08 final project reports 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