Presenters. Muscle Modeling. John Rasmussen (Presenter) Arne Kiis (Host) The web cast will begin in a few minutes.

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1 Muscle Modelng If a part of my screen n mssng from your Vew, please press Sharng -> Vew -> Autoft The web cast wll begn n a few mnutes. Introducton (~5 mn) Overvew (~5 mn) Muscle knematcs (~10 mn) Muscle Models (~15 mn) Recrutment (~5 mn) Q&A sesson (~10 mn) Please check that your audo settngs correspond to the nstructons n the emal you have receved from us. Presenters John Rasmussen (Presenter) Arne Ks (Host)

2 Søren Tørholm Launch the Q&A panel here. Type your questons n the Q&A panel. Send the queston to Host, Presenter & Panelsts Notce the answer dsplays next to the queston n the Q&A box. You may have to scroll up to see t. Q&A Panel Muscle modelng overvew Muscle modelng Sngle muscles Redundant muscle systems Knematcs Muscle models Recrutment Va pont muscles Smple models (constant strength) Shortest path muscles Zajac -type two-element Hll-type three-element

3 AnyVaPontMuscle Pont-to-pont-to-pont muscles Fxed ponts on skeleton segments Numercally very effcent Cannot establsh and release contact AnyShortestPathMuscle: Example Bceps brach caput longum s an AnyShortestPathMuscle. It wraps on the humeral head The ntal wrap poston vectors spans the muscle The knematcs of the muscle has been solved

4 Multple wrappng muscles Most of the muscles n the upper body wrap over the bones. The shoulder muscle acton s very dfferent dependng on the posture of the body. AnyShortestPathMuscle defnton AnyShortestPathMuscle Muscle1 = { AnyMuscleModel &Model =.SmpleModel; AnyRefFrame &Org =.GlobalRef.M1Orgn; AnySurface &srf =.GlobalRef.CylCenter.WrapSurf; AnyRefFrame &Ins =.Arm.M1Inserton; SPLne.StrngMesh = 20; };

5 Muscle models AnyMuscleModel The smplest muscle model n the system Merely a constant strength ndependent of operatng characterstcs AnyMuscleModel SmpleModel = { F0 = 100; }; CE F T F T l MT

6 Muscle model types Hll models (A.V. Hll, , Nobel prze 1922). Phenomenologcal model based on experments wth frog muscles. Smple mathematcal expresson based on fber length and contracton velocty. Cross brdge models (A.F. Huxley, b. 1917, Nobel prze 1963) Based on the actual physology and bochemstry of muscle contracton Takes the form of dfferental equatons wth many nput parameters that are hard to fnd. Hll Huxley Muscle models n musculoskeletal smulaton Length, velocty, actvaton Muscle model Tradtonal muscle models Muscle force Length, velocty Muscle model Muscle strength Recrutment Muscle force Muscle models n nverse dynamcs

7 Zajac s Two-element muscle model AnyMuscleModel2ELn F T T CE F T l T0 l M l MT AnyMuscleModel2ELn Not exactly state-of-the-art, but smple and good for some purposes. Takes some amount of contracton dynamcs nto account. Dsregards passve elastcty Undesrable ablty to swtch the force off when the muscle s stretched passvely.

8 Three-element Hll model AnyMuscleModel3E CE Hll type contractle element, models the force/length and force/velocty characterstc PE Parallel elastc element, models the passve propertes. T Elastc tendon PE l l l SE CE SE CE F T γ Numercal soluton necessary! F T l T T0 PE l M d l MT Length / velocty plot

9 Force length relaton Ths means that t s very mportant to have the correct tendon length. Otherwse the muscle wll not work n the rght nterval of the for/length curve. Gastrocnemus strength as a functon of muscle length Force velocty relaton Gastrocnemus strength as a functon of muscle length

10 Demo: Passve muscle forces n bcyclng Example: Spne extenson

11 AnyBody wth smple muscle model 60% % Passve forces 2500 Muscle effort 40% 30% 20% EMG L5-S1 Force [N] % 500 0% 0% 10% 21% 31% 41% 52% 62% 72% 83% 93% Movement 0 0% 14% 28% 41% 55% 69% 83% 97% Tme [s] One-element model: Reasonable jont forces Two-element model: Also reasonable muscle actvtes Three-element model: Also dvson between actve and passve forces. Recrutment

12 Redundancy We have too many muscles. Ths creates a stuaton of statcal ndetermnacy. Brachals In statcally ndetermnate elastc problems, the load s dvded accordng to the elastcty of the structure. In bologcal systems, the load s dstrbuted by the central nervous system. Brachals BcepsBrach Brachoradals What do we know about muscle recrutment from experments? Muscles crossng the same jont cooperate when they can. Some muscles can be observed to work aganst the movement and perform negatve work. The pattern of muscle actvaton for repeated movements s very smlar. Ths ndcates that a ratonal crteron s behnd the recrutment. When the load over a jont s ncreased, the muscle tones also ncrease untl maxmum s reached. Brachals Bceps Brach Brachoradals

13 Internal forces Appled forces Equlbrum Jont reactons Muscle forces Cf = d, f ( M ) where f = [ f 0, ( R ) {1,.., n, f ( M ) ( M) } ] The matrx C s rectangular. Ths means that there are nfntely many solutons to the system of equatons. How to pck the rght one? Optmalty Mnmze G( ( ) f M Subject to Cf = d f ( M ) ) 0, Objectve functon. Dfferent choces gve dfferent muscle recrutment patterns. {1,.., n ( M ) }

14 Choces of objectve functon (M) G ( f ) = f N p p = 1: Ths wll fal to produce muscle synergsm for small loads. p > 1: Muscle synergsm but addtonal constrants are necessary to avod overloaded muscles p? 8: Maxmum synergsm, mnmum fatgue. All crtera wth p > 1 predct synergsm (and sometmes antagonsm) Mnmum fatgue formulaton Mnmze maxmum relatve muscle load or mnmze fatgue or maxmze endurance Mnmze Subject to Equlbrum equatons Muscles cannot pull f max( N Cf = d f ( M ) ), 0, Muscle force {1,.., n {1,.., n ( M ) ( M ) } Muscle strength as a functon of length and velocty. }

15 Bound formulaton and muscle strength Mn f,β β Muscle model: (Wednesday) Subject to Cf =d (M) f 0, 1,..., n ( M) f β, 1,..., n N (M) { } (M) { } T CE PE Muscle strength N as a functon of muscle length and velocty Iteratve soluton s necessary Yes Fnd muscle forces Elmnate unquely determned muscles Muscles Left? No Return soluton

16 Effects of the mn/max crteron Muscle Force (N) 1,80e+002 1,70e+002 1,60e+002 1,50e+002 1,40e+002 1,30e+002 1,20e+002 1,10e+002 1,00e+002 9,00e+001 8,00e+001 7,00e+001 6,00e+001 5,00e+001 4,00e+001 3,00e+001 2,00e+001 1,00e+001 0,00e+000 Muscles form groups 0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00 Tme (s) Muscles swtch n and out The envelope The envelope of muscle actvty s a good measure of fatgue. The envelope s very numercally stable. The envelope s a good choce of crteron for ergonomc desgn problems. 9,00e-001 8,00e-001 7,00e-001 6,00e-001 5,00e-001 4,00e-001 3,00e-001 2,00e-001 1,00e-001 0,00e+000 0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 Man.Study.Output.Abscssa.t 9,00e-001 8,00e-001 7,00e-001 6,00e-001 5,00e-001 4,00e-001 3,00e-001 2,00e-001 1,00e-001 0,00e+000 0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 Man.Study.Output.Abscssa.t

17 Inverse dynamcs assumptons Does not take actvaton dynamcs nto account. Sharper actvty knks Later onset compared to EMG Dsregards certan dynamc effects such as wobbly masses. Assumes that movements are voluntary and sklled. Some people beleve that QP recrutment s the best for low actvty Mn/max s the best for hgh actvty smulated EMG Addtonal nformaton References at At Tutorals Reference manual Download a free 30 day demo lcense Q&A sesson!