living matter lab


winter 19 - me337 - mechanics of growth


me 337 - mechanics of growth 19

oguz tikenogullari
ellen kuhl

winter 2019
tue/thu 10:30-11:50, 380-380W
office hours tbd, 520-203 / 520-204
course announcement



growth is a distinguishing feature of all living things. this course introduces the concept of living systems through the lens of mechanics. we discuss the basic continuum theory for living systems including the kinematics, balance equations, and constitutive equations and the computational modeling of growth phenomena including growing plants, remodeling bone, healing wounds, growing tumors, atherosclerosis, expanding skin, failing hearts, developing brains, and the effects of high performance training.

journal club

mechanics of growth on imechanica

class papers

harris tc, de rooij r, kuhl e. the shrinking brain: cerebral atrophy following traumatic brain injury. ann biomed eng, 2018;doi:10.1007/s10439-018-02148-2. (download)

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 jan 08 motivation - everything grows! s01
thu jan 10 basics maths - notation and tensors s02
tue jan 15 basic kinematics - large deformation and growth s03 h01
thu jan 17 kinematics - growing hearts s04
tue jan 22 kinematics - growing brains s05
thu jan 24 balance equations - closed and open systems s06
tue jan 29 basic constitutive equations - growing tumors s07 h02
thu jan 31 volume growth - growing muscles s08
tue feb 05 volume growth - finite elements for growth s09
thu feb 07 volume growth - growing arteries s10
tue feb 12 guest lecture - alain goriely s11 h03
thu feb 14 volume growth - growing skin s12
tue feb 19 volume growth - growing hearts s13
thu feb 21 basic constitutive equations - growing bones s14
tue feb 26 density growth - finite elements for growth s15
thu feb 28 everything grows! - final prep s16
tue mar 05 final
thu mar 07 density growth - wounds and brains
tue mar 12 class projects - discussion, presentation, evaluation s19
thu mar 14 class projects - discussion, presentation, evaluation
fri mar 15 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