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| | ==mechanics of the cell== | | ==mechanics of the cell== |
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| − | me 337 - [[mechanics of the cell]] <br> | + | me 339 - [[mechanics of the cell]] <br> |
| | fall 2007 | | fall 2007 |
| | tue thu 3:15-4:30 <br> | | tue thu 3:15-4:30 <br> |
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| | lecture notes finite element method - linear [http://biomechanics.stanford.edu/me337/kuhl_fem1.pdf (download)] <br> | | lecture notes finite element method - linear [http://biomechanics.stanford.edu/me337/kuhl_fem1.pdf (download)] <br> |
| | lecture notes finite element method - nonlinear [http://biomechanics.stanford.edu/me337/kuhl_fem2.pdf (download)] | | lecture notes finite element method - nonlinear [http://biomechanics.stanford.edu/me337/kuhl_fem2.pdf (download)] |
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| − | ==goals==
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| − | 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.
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| − |
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| − | ==syllabus==
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| − |
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| − | {| class="wikitable" style="text-align:center; width: 100%"
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| − | ! day !! date !! !! topic !! slides !! homework
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| − | | tue || apr || 03 || introduction - different forms of growth || [http://biomechanics.stanford.edu/me337/me337_s01.pdf s01] || [http://biomechanics.stanford.edu/me337/me337_wiki1.pdf h01] wiki growth
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| − | | thu || apr || 05 || tensor calculus - tensor algebra || [http://biomechanics.stanford.edu/me337/me337_s02.pdf s02] ||
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| − | | tue || apr || 10 || tensor calculus - tensor analysis || [http://biomechanics.stanford.edu/me337/me337_s03.pdf s03] || [http://biomechanics.stanford.edu/me337/homework_041207.pdf h02] tensors
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| − | | thu || apr || 12 || kinematic equations - growth || [http://biomechanics.stanford.edu/me337/me337_s04.pdf s04] ||
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| − | | tue || apr || 17 || balance equations – closed systems || [http://biomechanics.stanford.edu/me337/me337_s05.pdf s05]||
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| − | | thu || apr || 19 || balance equations – open systems || [http://biomechanics.stanford.edu/me337/me337_s06.pdf s06]|| example rocket propulsion
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| − | | tue || apr || 24 || constitutive equations – density growth || [http://biomechanics.stanford.edu/me337/me337_s07.pdf s07]|| example astronaut
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| − | | thu || apr || 26 || finite element method – density growth theory || [http://biomechanics.stanford.edu/me337/me337_s08.pdf s08] ||
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| − | | tue || mai || 01 || finite element method – density growth matlab || [http://biomechanics.stanford.edu/me337/me337_s09.pdf s09] || matlab density
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| − | | thu || mai || 03 || examples – density growth || [http://biomechanics.stanford.edu/me337/me337_s10.pdf s10] || example bone
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| − | | tue || mai || 08 || class project - growth of tennis player arms || [http://biomechanics.stanford.edu/me337/me337_s11.pdf s11] ||
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| − | | thu || mai || 10 || finite element method – density growth alternative || [http://biomechanics.stanford.edu/me337/me337_s12.pdf s12] ||
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| − | | tue || mai || 15 || constitutive equations – volume growth || [http://biomechanics.stanford.edu/me337/me337_s13.pdf s13] ||example tumor growth
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| − | | thu || mai || 17 || finite element method - volume growth theory || [http://biomechanics.stanford.edu/me337/me337_s14.pdf s14] ||
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| − | | tue || mai || 22 || finite element method - volume growth matlab || [http://biomechanics.stanford.edu/me337/me337_s15.pdf s15] ||
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| − | | thu || mai || 24 || examples - volume growth || [http://biomechanics.stanford.edu/me337/me337_s16.pdf s16] || [http://biomechanics.stanford.edu/me337/me337_wiki2.pdf h03] wiki growth
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| − | | tue || mai || 29 || examples - remodeling || [http://biomechanics.stanford.edu/me337/me337_s17.pdf s17] ||
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| − | | thu || mai || 31 || class project - growth of tennis player arms || [http://biomechanics.stanford.edu/me337/me337_s18.pdf s18] ||
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| − | | tue || jun || 05 || class project - discussion, presentation, evaluation || ||
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| − | |}
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| − |
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| − | ==matlab files==
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| − | voila!... just to get used to tensor notation and matlab <br>
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| − | [http://biomechanics.stanford.edu/me337/matlab_ex01.m matlab_ex01.m] ... the one with all the tensors
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| − | finally... here's the matlab nonlinear finite element code for density growth in bone! <br>
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| − | [http://biomechanics.stanford.edu/me337/matlab_bone.tar.gz matlab_bone.tar.gz] ... the one where u got it all
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| − | or... if you prefer to look @all the individual files <br>
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| − | i've tried to put comments to most of the variables, send me an email if you want moooore ;-)
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| − | [http://biomechanics.stanford.edu/me337/nlin_fem.m nlin_fem.m] ... the one and only <br>
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| − | [http://biomechanics.stanford.edu/me337/extr_dof.m extr_dof.m] ... the one which extracts element information from the global
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| − | field <br>
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| − | [http://biomechanics.stanford.edu/me337/assm_sys.m assm_sys.m] ... the one with the strange big A operator <br>
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| − | [http://biomechanics.stanford.edu/me337/res_norm.m res_norm.m] ... the one which tells you how far you are away from your ultimate goal <br>
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| − | [http://biomechanics.stanford.edu/me337/solve_nr.m solve_nr.m] ... the one with the solution to all problems <br>
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| − | [http://biomechanics.stanford.edu/me337/plot_int.m plot_int.m] ... the one to plot internal variables on the spatial/deformed configuration <br>
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| − | [http://biomechanics.stanford.edu/me337/plot_mat.m plot_mat.m] ... the one to plot the material/undeformed configuration <br>
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| − | [http://biomechanics.stanford.edu/me337/quads_2d.m quads_2d.m] ... the one with the 2d quadrillateral element <br>
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| − | [http://biomechanics.stanford.edu/me337/tetra_3d.m tetra_3d.m] ... the one with the 3d tetrahedral element <br>
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| − | [http://biomechanics.stanford.edu/me337/brick_3d.m brick_3d.m] ... the one with the 3d brick element <br>
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| − | [http://biomechanics.stanford.edu/me337/cnst_den.m cnst_den.m] ... the one with the constitutive equations for density growth <br>
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| − | [http://biomechanics.stanford.edu/me337/cnst_vol.m cnst_vol.m] ... the one with the constitutive equations for volume growth <br>
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| − | [http://biomechanics.stanford.edu/me337/updt_den.m updt_den.m] ... the one with yet another newton iteration to calculate the dnsity <br>
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| − | [http://biomechanics.stanford.edu/me337/updt_vol.m updt_vol.m] ... the one with yet another newton iteration to calculate the volume <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_humer.m ex_humer.m] ... the one with the example of the 3d humerus <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_femur.m ex_femur.m] ... the one with the example of the 2d femur <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_bimat.m ex_bimat.m] ... the one with the idealized humerus of cortical and trabecular bone <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_cylin.m ex_cylin.m] ... the one with the idealized humerus of trabecular bone <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_tubes.m ex_tubes.m] ... the one with the idealized humerus of cortical bone <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_beams.m ex_beams.m] ... the one with the example of a beam <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_punch.m ex_punch.m] ... the one with the example of a 3d punch <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_block.m ex_block.m] ... the one with the example of a 3d block <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_frame.m ex_frame.m] ... the one with the example of the 2d frame structure <br>
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| − | [http://biomechanics.stanford.edu/me337/ex_unity.m ex_unity.m] ... the one with the example of two 2d elements <br>
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| − | [http://biomechanics.stanford.edu/me337/mesh_sqr.m mesh_sqr.m] ... the one which meshes a square domain <br>
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| − | [http://biomechanics.stanford.edu/me337/num_grid.m num_grid.m] ... the other one from bex (thanx!) <br>
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| − | [http://biomechanics.stanford.edu/me337/in_humer.m in_humer.m] ... the one from bex to read the humerus input <br>
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| − | [http://biomechanics.stanford.edu/me337/data_humr1_elm.dat data_humr1_elm.dat] ... the coarse one with the humerus elements <br>
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| − | [http://biomechanics.stanford.edu/me337/data_humr1_nod.dat data_humr1_nod.dat] ... the coarse one with the humerus coordinates <br>
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| − | [http://biomechanics.stanford.edu/me337/data_humr2_elm.dat data_humr2_elm.dat] ... the fine one with the humerus elements <br>
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| − | [http://biomechanics.stanford.edu/me337/data_humr2_nod.dat data_humr2_nod.dat] ... the fine one with the humerus coordinates <br>
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| − | [http://biomechanics.stanford.edu/me337/in_femur.m in_femur.m] ... the one from bex to read the femur input <br>
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| − | [http://biomechanics.stanford.edu/me337/data_femur_elm.dat data_femur_elm.dat] ... the one with all the femur elements <br>
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| − | [http://biomechanics.stanford.edu/me337/data_femur_nod.dat data_femur_nod.dat] ... the one with all the femur coordinates <br>
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| − | ==bone example==
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| − | <div>
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| − | [[Image:matlab_bone.jpg|210px|left]]
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| − | {|
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| − | |for those of you who are interested in calculating the bone example from the literature [http://biomechanics.stanford.edu/me337/jacobs95.pdf (2)] and [http://biomechanics.stanford.edu/me337/kuhl03.pdf (3)], bex converted the bone file (you're awesome! thanx!) and now you could all run the bone with matlab! just download the gzipped archive above, unpack it, call the main file nlin_fem and type step,,50 to run 50 time steps to allow for density redistribution. you should then obtain the figure on the left... just throw me an email if it doesn't work! ... and yes, i know... the code's slow... so go'n get a cup of coffee... or try to re-code [http://biomechanics.stanford.edu/me337/cnst_den.m cnst_den.m] in terms of either spatial or material stresses & tangents by using voigt's matrix notation and speed up [http://biomechanics.stanford.edu/me337/quads_2d.m quads_2d.m] by using the traditional old-fashioned b-operator, it's maybe ugly in the code but a loaaad faster!
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| − | |}
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| − | </div>
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| − | <div class="spacer"> </div>
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| − |
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| − | ==additional reading==
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| − | don't feel forced to read all of this! it's just additional information that some of you might want to look at!
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| − | [http://biomechanics.stanford.edu/me337/taber95.pdf (1)] taber l: biomechanics of growth, remodeling, and morphogenesis, appl mech rew 48, 487-545, 1995
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| − | [http://biomechanics.stanford.edu/me337/jacobs95.pdf (2)] jacobs, cr, levenston me, beaupre gs, simo jc, carter dr: numerical instabilities in bone remodeling simulations: the advantages of a node-based finite element approach, j biomechanics 28, 449-459, 1995
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| − | [http://biomechanics.stanford.edu/me337/kuhl03.pdf (3)] 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
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| − | [http://biomechanics.stanford.edu/me337/rodriguez94.pdf (4)] rodriguez ek, hoger a, mc culloch a: stress-dependent finite growth in soft elastic tissues, j biomechanics 27, 455-467, 1994
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| − | [http://biomechanics.stanford.edu/me337/kuhl06.pdf (5)] 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 mechanobiol, available online first, DOI 10.1007/s10237-006-0062-x
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| − | ==class project - tennisplayers ==
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| − | [[motivation - density measurements of tennisplayer arms]] in [http://med.stanford.edu/profiles/Thor_Besier/ thor besier's lab] <br>
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| − | <div>
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| − | [[Image:humerus.jpg|210px|left]]
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| − | {|
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| − | |here's the current state of the tennis player arm density project: bex generated a finite element mesh from the humerus surface data that she got from [http://www.stanford.edu/group/nmbl/index.htm scott delp's neuromuscular biomechanics lab], cool! sorry ryan, this seems to be a male tennis player ;-( we've got two meshes, a coarse one and a fine one, modify the [http://biomechanics.stanford.edu/me337/in_humer.m in_humer.m] file to load either of the two. you might want to start with the coarse mesh [http://biomechanics.stanford.edu/me337/data_hum1_elm.dat data_hum1_elm.dat] and [http://biomechanics.stanford.edu/me337/data_humr1_nod.dat data_humr1_nod1.dat]. you can now download all the matlab files from [http://biomechanics.stanford.edu/me337/matlab_bone.tar.gz matlab_bone.tar.gz] and just change the input line from the femur to the humerus in the main file [http://biomechanics.stanford.edu/me337/nlin_fem.m nlin_fem.m]. the figure on the left has been generated by just applying three load steps, so far it's been just tension in the y-direction. it would be great if you could figure out how to apply the forces induced by the most important muscles, maybe for the right and left arm with and without the forces during the serve.
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| − | |}
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| − | </div>
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| − | <div class="spacer"> </div>
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| − |
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| − | ==... what we still need to do... ==
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| − | <div>
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| − | [[Image:to_be_done.jpg|210px|left]]
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| − | {|
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| − | |hey, i guess we agreed that it would be cool to have a study of the idealized cylindrial humerus model just to get some ideas about the loading and boundary conditions, right? the three figures on the left show you the three idealized model geometries, the humerus of cortical and trabecular bone [http://biomechanics.stanford.edu/me337/ex_bimat.m ex_bimat.m], the solid model of the trabecular bone [http://biomechanics.stanford.edu/me337/ex_cylin.m ex_cylin.m] and the cylicrical model of the cortical bone alone [http://biomechanics.stanford.edu/me337/ex_tubes.m ex_tubes.m]. try if you can run the examples! you can easily modify the geometry and discretization. the loading is a bit more challenging but we will discuss that in class today! <br>
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| − | |}
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| − | </div>
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| − | <div class="spacer"> </div>
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| − |
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| − | ==here's the literature you found==
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| − | [http://biomechanics.stanford.edu/me337/projects/muscle_woman.xls p00] ryan jackson <br>
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| − | [http://biomechanics.stanford.edu/me337/projects/haapasalo00.pdf p01]
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| − | [http://biomechanics.stanford.edu/me337/projects/jones77.pdf p02]
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| − | [http://biomechanics.stanford.edu/me337/projects/krahl94.pdf p03]
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| − | [http://biomechanics.stanford.edu/me337/projects/auerbach06.pdf p04] rebecca taylor <br>
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| − | [http://biomechanics.stanford.edu/me337/projects/benjamin06.pdf p05]
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| − | [http://biomechanics.stanford.edu/me337/projects/calbet97.pdf p06]
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| − | [http://biomechanics.stanford.edu/me337/projects/ducher05.pdf p07]
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| − | [http://biomechanics.stanford.edu/me337/projects/ducher06.pdf p08]
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| − | [http://biomechanics.stanford.edu/me337/projects/haapasalo00.pdf p09]
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| − | [http://biomechanics.stanford.edu/me337/projects/naraashizawa01.pdf p10]
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| − | [http://biomechanics.stanford.edu/me337/projects/nesbit06.pdf p11]
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| − | [http://biomechanics.stanford.edu/me337/projects/pearson04.pdf p12]
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| − | [http://biomechanics.stanford.edu/me337/projects/elliot03.pdf p13]
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| − | [http://biomechanics.stanford.edu/me337/projects/nikander06.pdf p14] chun hua zheng <br>
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| − | [http://biomechanics.stanford.edu/me337/projects/cowin87.pdf p15] nathaniel benz <br>
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| − | [http://biomechanics.stanford.edu/me337/projects/park04.pdf p16]
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| − | [http://biomechanics.stanford.edu/me337/projects/pieper98.pdf p17]
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| − | [http://biomechanics.stanford.edu/me337/projects/sabick04.pdf p18]
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| − | [http://biomechanics.stanford.edu/me337/projects/werner02.pdf p19]
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| − | [http://biomechanics.stanford.edu/me337/projects/crockett02.pdf p20]
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| − | [http://biomechanics.stanford.edu/me337/projects/osbahr02.pdf p21] julia chen <br>
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| − | [http://biomechanics.stanford.edu/me337/projects/gene_regulation01.pdf p22] joey doll <br>
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| − | [http://biomechanics.stanford.edu/me337/projects/nair0X.pdf p23] amir shamloo
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| − |
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| − | ==teaching evaluation==
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| − | thanks for your patience! i promise to improve on [http://biomechanics.stanford.edu/me337/teaching_me337_mine.pdf this...] <br>
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| − | thanx! i really do appreciate your input and [http://biomechanics.stanford.edu/me337/teaching_me337_class.pdf comments]!
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