living matter lab


winter 15 - me337 - mechanics of growth


me 337 - mechanics of growth 15

ellen kuhl
adrian buganza tepole, mona eskandari
office hours thu 3:00-4:00, durand 247
course announcement

office hours thu 3:00-4:00, durand 247
course announcement

winter 2015
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, 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 % 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 06 motivation - everything grows! s01
thu jan 08 basics maths - notation and tensors s02
tue jan 13 basic kinematics - large deformation and growth s03 h01
thu jan 15 kinematics - growing hearts s04
tue jan 20 project example - growing skin s05
thu jan 22 kinematics - growing brains s06
tue jan 27 balance equations - closed and open systems s07
thu jan 29 basic constitutive equations - growing muscle s08 h02
tue feb 03 basic constitutive equations - growing tumors s09
thu feb 05 volume growth - finite elements for growth s10
tue feb 10 volume growth - arteries s11
thu feb 12 project example - airway wall remodeling s12
tue feb 17 basic constitutive equations - growing bones s13
thu feb 19 density growth - finite elements for growth s14 h03
tue feb 24 density growth - growing wounds s15
thu feb 26 everything grows! - midterm summary s16
tue mar 03 midterm
thu mar 05 volume growth - growing hearts s18
tue mar 10 class projects - discussion, presentation, evaluation s19 h04
thu mar 12 class projects - discussion, presentation, evaluation
fri mar 13 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