Muscle Forces
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A THREE-DIMENSIONAL MATHEMATICAL MODEL OF THE HUMAN KNEE JOINT Robert Scott Fijan B.S.in E:,gineering Sciences, University of Florida ( 1982) S.M. in Mechanical Engineering., Massachusetts Institute of Technology (1985) SUBMITTED IN PARTIAL FULFlLLMENT OF THE REQUIREMENTS FOR THE DEGREE OF LKXTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY April 1990 O Maswchusens ins^ tute of 'Technology Signature of nuthor ,r- - . ":p~tmcnt of ~ecdcalEngileering April 24, I990 Certified by Robert W. Mrrnn Rtsis Supervisor Approved by- -- Ain A. Sonin Chairman, Department Committee of Graduate Studics *ASSACH~~:TS INST!TU~ Cf rEIYNil: l\Gr A THREE-DIMENSIONAL R1 ATHEMATICAL MUDEL OF THE HUMAN KNEE JObT Subtttd to the Qcpmntof Mtchmcal Engincuing on A@ 2. 1M in partial Mfillmcnt of the quircnwnts for the dtgu of haof Ptulosophy in Mechanical Engmcmng Abstract A mathematical model of the human kr.:e joint is developed and applied to in vivo kinematic and dynamic measurements of gait to estimate joint contact and muscle forces. The four degree of freedom knee mdel includes muscles. ligaments, and taree- dimensional articular surface geometry md is developed as pan of a complete nine degree of bedom lower ext~mirymOde1. A method is developed for using a kinematic measurement system to generate a geornepic model of he articular surfaces of ihe tibia and femur. A novel me:+od is then employed to estimate and rcmove soft tissue motion cmn of in vivo knee hnemartcs by including gmbcconstraints. The estimated he kinematics arc incladed in a dynamic analysis to estimste the joint contact forces and mlixle forces. Sensiaviry to selected modeling and pmessing pmweten is discussed. Difficuities in satisfying dyr,amic quilibrium for all degrees of freedom of the knee model arc presented in msof the procedures for estimating knee joint kinematics without regard to dynamics. A mthcd is implemented to minimize these errors by iteratively adjusting the esfima!ed bite kinematics and muscle faxs ur.til convergence is &rained. A funher duction in best mrsis demonstrated by concum~:dyesnmting ldneinacics and dynamics. A joint stiffness and stability analysis for human joints is derived inc!uding specific nquircrnents for muscles. This analysis is initially applid to a single degree of freedom model of the human elbow joint to justify selection of t!!e muscle stiffness model and also to demonstrate that the method can successfully predict muscular ceconoaction due to subility constraints. The stability malysis is later applied to the knte 9s part of the muscle and joint force estharh dysis. For the experimental subject of this thesis, knee kinemstlcs arc estimated wih an accmcy between 2 and 6 mm and total forces in excess of 4.5 times body weight ar: estimated for the joint during she stance phase of gait. Theoretical predictions of the stability analysis applid to the eibwjoint match c~pccimentalmeasurements fairly closely, but funher improvements in muscle models ;ire required before the methods can be successfully employed for the knee. Tlesis Supervisor: Roben W. Mann Tltle : Whitaker Rofeswr of Biomabcal Engineering Bepmntof Mechanical Engineering MEMBERS OF THE COMMI7TEE Dr. G&n W. M*M (Chairman) Wraker Rofesxr of Bic#nebcal Enwnng Dcpmntof Mechanical Enpeemg Dr. William K. Ddee A ssociatc Professor Dcparmrnt of MccMcal Engineering Dr. Neville Hogan Pmfcs~ Dtpamaent of Mcchical Enwring Dr. Thanas A. McMahon hfcssor Division of Applied Sciences Hirrvard Universiry ACKNOWLEDGEMENTS I would like to thank Rofessor Mann for many years of suppon and guidance. He has always been willing to chscuss my thesis or any ohm concern as frequently as 1 des~red, yet he has also allow4 m the Frrcdom to go off and work on my own. I am ptcf~;for the opportunity of considering several different projects unal 1 found one which I really wanted to wsrk on. Most ~f all 1 wol~ldlike to thank him for king a positive role model. I have setn many exmplcs of his genuine concern for students and of hi; academ~c integrity. I havc always felt confident that he would give m sound advice, not of the most pers45lally bereficlal thing to do but of the right thing to do. Thanks also io thc sthcr mmbmof my thesis committee. Will Me,Neville Hogm. and Thar~asMchlahon. for helphg m to clarify exactly what I was aying to do and how I should go abut it My only regret is that I did na fonn my comarrirtbc linle sooner. Don Russel: and I have shadan office for four ycars now, and although our remh areas art different our common interest in dynamics has led to may interesting dwussions. He has been an excellent suurce for me to out new ideas or to tp)l to explain things that I think I understand. I also appreciate our many discussions abut topics rangng hpiano msuuction to daycare, with an ad&d knefit that I havc learned a little about Canada in the process. Don has also ken a source of information for the Macintosh. as well as a subject for the cibw txmnr. Special thanks to Mike Murphy, who initiated the project to study he normal Aumar, kntc in our lab and was insmmental in obtaining the fundmg. Pete Mansfield has been in cnarge of the TRACK systein and has kept it running about as long as I can remember (When I started this project. everything was running on a PDP 11/60!). Thanks to Pete and Pat tord fo: keeping the SUN computers working so 1 didn't have to worry abut them. Scott Banks helped me to find the best proccjurcs for mounting the arrays and was also willing to be a subject of the kinematic and dynamic experiments on numerous accasions. I appreciate his time very much. To all of the remaining members of the Newman Lab (Crispin, Greg, Kcita, Kjirste, Qang, Ted. etc.) hanks for malung it one of UK friendliest places to we. Two professors at the Univmity oi Florida, my undergraduate institution, also deserve thanks as they wert very influential in my decision to obtain my Ph.D. so that I coald become a pfesswr and have an impact on students' lives. Professor Charles Taylor spent a gtat chi of turn teaching me abut phototlaticity and holography, but more hpomtly I was very hpreud hy the respect his farmer students had for him. Dr. Knox Millsaps regularly got together with a small pupof students ir,clu&ng myself to guide us and encourage us in our careers. When I told him tha; I was interested in studying biomechanics, he told me "Well then you should go to M.I.T.and work for Bob Mann". Wisely, I followed hi^ advice. h general, his concern for students had a big impact on me. The world lost a very fine man wb--I he passed away a few months ago. I espcclally appmiate my parents, who have suppcmed me despite not completely undersmndmg why I spent so many yean here it .M.I.T. I recently heard one sidc of a relephone conversation of a student in our lab which sounded very farmliar. "k.mom. ... I don't blow mom I hope 1991. ...". Through all of the trylng circumstances rip parents have encountered in their own lives. I have always ken 100 percent confident that they would put their children first before any other priority. Their love means a lot to me and has pven me a smng sense of self-esteem even when my thesis was mt going as well as I would have ked. Most impmanfly, I would like to thank rnv wife Caroline. Throughout my time as a doctoral student she has been my source of support md encouragement She has worked very hard to help me to grow in the anas whcx 1 need to change, including facing nat to get organized and do the imponant things thy, mtha than wmking on inrmsting but tangential projects and putting off the essential work for later. I should have taken her advice some mom. During these past few months she has picked up the slack and maintained our fvnrly while allowing me to mcenuau on completing my thesis. Keeping our son Bobby in ordm while also taking care of our new baby daughter Elise is no easy task, especially in our small apartment. The years I have worked on my Ph.D. have cePtainly btcn more smssful for her than they have ken for rat, and I app~ciateand love her very much. Finally, my acknowledgements would be incomplete without mentioning that I kame a Christian while I was a student here at M.I.T.I came to the Boston area very arrogant ard prideful. Fonunatcly my pride was broken by the cross of Jesus Christ and not by M.I.T.A few verses from TkLving Bible arc very relevant to this. I Corinthians 3: 18 Stop fooling yourselves. If you count yourself above average in intelligence. as judged by the world's standards, you had better put this all aside and be a fool rather then let it hold you kkf~om the true wisdom from above. I Timothy 6:20,21 Keep out of foolish arguments with those who bast of their "knowledge" and thus prove their lack of it. Some of these people have missed the most impomt thing in life - they don't know God. This work was performed in the Eric P. and Evelyn E. Ncwman L.aboratory for Biomechanics and HumRehabilitation at M.I.T.Suppon was supplied by a National Science Foundation Fellowship, a Whitaker Health Sciences Fund Fellowship, NSF Grant Nurnkr 84 15430ET, NIDRR Granr Number H 133E80024 and the Whitaker Foundation.