Margareta Nordin Basic Biomechanics Musculoskeletal System

7/30/2019 Margareta Nordin Basic Biomechanics Musculoskeletal System

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Progress in restoring ftrnction has pa=lleled our gai"in knowledge of the musctrloskelell $rstem and thenature of its disabilities. Observation,'thought, a'dexperience wene srrfficient to solve some pfubl"o,".Further :ulsweJs evolved e.' n'e becamu o.or" cogni-zant of und:tly-,g p1+ologv and phy,siology. tu6.yof the remaining problemJ art'ait i$ app[Ltion ofbiomectranical prirrciples. 'A major detersrinant of eftective function is theforce tolerance and mobilitv of the skeletal systeur.Increass n the intensiry or activity of alr age go"p,and extended h'man longevitv "i- pr"=orti"g newdemands "" -ggs phvsical qpariuo. to devel"op anaPPropriate dinical resPonse,biomechanical infoizra-tion must b" ".quired and the knowledge translatedinto therapeutic guidelines.'t'ictor Frankel has been a leader in both theseendeavors- FIis contribution to biomechanical re-search is attested to by his extensive publications.This text represnEs his second effort to introducbiomechanical knort'ledge into patient care- It is not asimple task- lvlargareta Nordin has ioined trim in ttrisresPonsibility for prodtcing a new text. Her ' volve-ment has contrrbuted to thJ informative stvle used tolt'"tpret complex data. The value of this ,"*, JJ;been enha'ced by the added breadth pro'idud by theconEibutors.The "tt*eering profession has developed themea-ns or identifying- the forces, motions, and tiss'e

FOREWORDTO THFIRSTEDITIOresPonses n human firnction. A considerable arof information has been providd, but this inftion is disPrsed in a wide variety of publicatioruis often coudred in engrneering terrrinology uniar to dinicians.This book on the basic biomechanics of thectrloskeletal system brings together the crknowledge and Presents it in a cle"r, conversastlrle- ft" !T of engineering terrdnolory is restto that whidr is necessary to express essenriacepts- Presentation of the literature is both incland selective. The major contributions to each:rre cited :$ sPeeificreferences, and other sourcidentified as recoulmended reading.while the text is primarily a- compendiruinformation and illustrations of biomechanical pples that:rrredinically pertinent, a small portionobook desaibes the'me:rns for calctrtating jointmusde forces- This is presented lucidly *itti minmathematical formulae and very cleardiagramste,++ques :ue descriH in a way that makesusable by the interested clinici:ln.This book is a well conceived bridge betengineering concepts and dinical practici. It shprovide orttropaediqts, physical and occnpathelaPists, and other hiallh professionals wyglki"g hol'ledge of biomechlnical principlesfut in the evaluation and treatment of musctrlost"I dysfunction.

facquelin Petr!, M


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This book has been written to serve as an introduc-tion to biomechanics for those who deal with disor-ders of the musculoskeletal system- The work is theresult of ?5 _years of experience in biomechanicseducation and many conferencs wittr colleatues inthe fields of orthopaedic surgery, physical rherapy,occarpational therapy, bioengin*ri"i ertonomics,and other allied specialties.Biomechanics uses raws of physics and errgineer-ing concepts to dessibe motibn-'ndeqton. 6y thevarious bodl setments and the forces actir,g or, th"r"body parts during nonnar daily activities. The inter-relationship of force and motion is importa.t, andmust be understood if rational heaturent programsane o be.Spptied to muscrrloskeletatdisorders. Dele-terious effecG-*ly be produced if the forcesacting onthe areas with disorders rise to hith revers d'lngexerciseor activity"The pu{pose of this volume is to acqgaint thereaders with the force-motion relatior,ships withinthe musctrJoskeletal system and the vario's tech-nioues used to understand these relationships.The volusre is intended to be usd as a textbook_,either conjunction with a biomechanics courseor for independent sfudy. The references a.d sug_gested readings at the end of each chaptercan be ufili-gd to amplify the discussions in these.cnaPters.Although we undertook an extensivereview of thervorld literature on biomechanics in preparing thisbook, it has not been our purpose to pubrish a reviewof the material- Rather, wL hive selectedexasrples toillustrate the..gtr.9pts needed for a basicknowledgeof musculoskeretaf biomechanics. In add.itior, wehave developed important engineering conceptsthroughout the volume. The text *iII srveas a gurdet? " 1""p"r understanding of musctrloskeretalbiome-chanics gained through Frrther read.ing,analvsis of

PREFAcasematerial, artd independent rese.uch. The imadon presented should also gurde the read-s"ft"g the literatnre on biomechanics. No attehas been made to disctrss theftpy, as it was notPuPose to over this area. Rather, we have descthe undedying basis for rational therapeutictrarns.This book has been strengthened by the wormany excellent contributing authors. ;\n initialtion on the international system of meaflrremserves as :rn introduction to the physical measments used throughout the book. -The reader neno more ftan a basic knowledge of mathematicfuIIy comPnehend the material in the book, butimportant to first review the section on the SI sysand its application to biomechartics.The five drapters in Part One of the book deal wthe biomechanics of the tissues and stnrcttrres ofmuscrrloskeletal system: biomechanics of bone,mechanics of artictrlar cartila Be, biomechanicstendons and -ligaments, biomechanics of penphneryes, and biomechartics of skeletal muscle. Tsection has been exPanded from the first eCitioSve the reader:rn understanding of the differencemechanical behavior among the principal tisscomposing the musculoskeletal system.

The ten drapters in Part Two cover the biomechics or' the maior joints of the musculoskeletalsystEachof thesechapters contains an anatomic overvfollorved by a discussion of the biomechanicsspeto- he partictrlar ioint or ioint complex. In thi; nedition chapters on the biomechanics of the cervspine' the biomechanics of the wrist, and the biomchanicsof the hand have been added.we feel that our efforts h *l-ti.g and expandthis book will be iustified if it biings aboutincreasedawarenessof the importance of bio-echaics and engendersdiscussion.Margareta NorcVictor H. Fran


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ACKNOWLEDGMENThis book rt'as made possible through the efforts ofall the contributors. Their outstanding knowledge,their understanding of the basic concepts of biome-chartics, and their wealth of experierrcehave broughtboth breadth and depth to this worlc We:rnehonoredand gratefuI for their contributions and for fteirdevoted work in preparing and finalizing this newedition. We are deeply saddenedby th" recent deathof one contributor, Carl Carlstedt, who finalized hischapter from his hospital bed, near the end of trisvaliant stmggle with leukemia.A book of this size, with its large nunber offigr*s, legends, and references,czrnnotbe producedwithout editorial efforts. laude Yelle's intense effortsshine throughout the entire booL Not only did shefunction as a trzrmmarian and stylist, but her logicalpattern of thinking had a great deal to do wittl thefinal organization of the book.IGis" Forssn and Hugh Nachartie, illustrators,h'ene vital, energetic, and never-failing members ofour publication team. Their quick Fasp of theconcepts to be illustrated and the datity of their artwork weFeof the greatest importance in the produc-tion of ttris book.

Our colleagues in the O.*pational and lndustrOrthopaedic Center of the Hospital for Ioint DiseaOrthopaedic Institute functioned as critical reviewof the chapters. A sFdat thanlcs is extendedMohamad Parnianpour for his iilraluable assistanOur sincerest thanks also-goes to Shdly Bade, OsCartas, Narlia Greenidge, Irura Gitsevitch, ManHalpern, foan IGlur, Ali Sheikhzadeh, I.rdy TruciPat Tnriello, IGthy Viola, and Sherri Weiser. InDepartment of Orthopaedic Surger4, lrene Co*pbeAbe Moshel, and Alisa Rivera deserve our greatappreciation for their valuable help. We thank luRaymond and Ffita{y Winter for word processassistanceand consbnrctive sugtestions. We Erreamost gratefuI to Drs. AIex Nonrurn, PauI Bisson, aSterrenLubin for supplying vital roentgenoFamsthe new edition.This new edition of the book was supporthroughout its production by the Research aDevelopment Foundation of the Hospital for JoDiseasesOrthopaedic Institute and the hospitalministration, to whom we forward our sincergratitude.To all who helped, hiardigt tack!

Ma5garetaNordVictor H. Fran


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FAOI JOSEPH BEJJANT. M.D.. D.E'[/I., MA.,ResearchProfessorand DirectorHuman PerformanceAnatysistaboraroryNernrYork UniversityNew Yorfc New YorkarrtCorisuftant in Occupattmaf OmfropaedicrElectrodiagnosis,Mcirr Anat)4sis, d Ans ldedicineCARL A. CARLSTEDT, M.D., Ph.D.fGrolirska trstituteHuddinge HospinlStocfnolm,SwedenarxlReseardtFeflowDepartment of BioengineeringHospial for Joint Diseasesorfiopaedic fn*iu.neNew York,New YorkDENNIS R. CARTER,Ph.D.AssociareProfessorof MechanicatEngineeringSunford UnivenirySpnford, CatifomiaVICTOR H. FRANKEL M.D., Ph.D.PresidentHospial for Joint Diseasesorthopaedic lrtsdu.rtechairmaru Depanmenr of odropaedc g.lrge4yNew York, New york

andProfesrcrof OrrhopaeOic urgeryNew York Univers,rySdtoof of MedicineNew york, New yorkMICIT \ELA. KELLY. M.D.Assisranrprofessorof Offropaedic grrgeryCoflegeof phpiciars and furgeonsCofumbiaUniversityNew York,New yorkJOF{AN M. F. TANDSMEER, prof. Dr.ProfessorEmerinJsDeparrmenrof Anatomy and EmOryoroglRrjksUniversiteirLeiden,HollandANARGARETAUNDH, M.D., R.P.T.,Ph.D.Depanmenrof RehabifhadonMedicineSantgrenHospitaf - --'s" rUnrversiryof GothenburgGotnenburg.Sweden

Ph.D. @RAN LUNDBORG. M.D.. Ph.D.Prdesss aN ChairmanDivbion d l{urd LlrgeryDepartrrrrt d OrthopaedicsUUwrvty of lrrndUtfr, SucdenatrtLaboravy of ExperimernalBiolosyDepartrrrnt d Anatomyt lrUver:rry of CrcfienburgGotherU.rg, Surcden

FREDERICKA. MATSEN III. M.D.Professorand Chainnan@artnrnt of OrfiopaedicsUniveniry of WashingrtonSeatde,Washirgton

VAAI c. MOW, Ph.D.DirectorNov Ytrk Onhopaedic Hospial Researcfr aboratoryProfessorof Mecl'ranicafEngineer-ing nd ortlropaedicBioengineering:fffrffiT"nMedicaf centerNeul Yq*, New York

MARGARETA NORDIN, R.P.T., Dr. Sci.fJrectorOcapaoonal and frxCctrial Ortlropaedic CenterFbspital for Jcint Diseasesordrcpaedic lrudnltef\h^/ Yqfc f\h^/ YorkaNProgramDirectorPrrogram f Ergonomicsand Occupadonal BiomecfnniNeur Y6k UniversityNew Yqk, NerryYork

I.ARS PETERSON, M.D., Ph.D.AssociaceProfessorDepanmenr of Orfiopaedic furgnryEast HospiafC:otfrerourg,Sweden

CONTRIBUTO


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XiV CONTRIBUTORS

'I'IARK I. PITMAN, M.D.Chief of SPors MedicirPAnendir physician, Departmerrt of ortrropaedic $rgetyHospitat or Joirn Diseases dropaedk lrsdufieNernrYorK New YorkandAssi$ant Clinic;t Prroftsor of OrtlroPaedic 9rgeryNernrYork Unirrcrsity Schoolof MedcineNew YorK New YorkCHRISTOPHER S. PROCTOR' M'D'ResearchFellowNerrvyork orfropaedic Hospital Re


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{-

CONTEN

Sf: THE INTER|\AT|O,\AL STSTEMOF UNTTSDennis R- C-arter

part oneEIOMECFTANICS F TISSUES ND STRUCTURES F THEM USCULOSKELEXALSYSTEM

I. BIOMECI-{ANICS F BONEMargareta Nordin, victor H. Frankel

z' BtoMEcFtANfcsoF ARTtcutARCARTTLAGEVan C- Mow, Christopher s. proctor, MichaerA. KeIl'

3' BtoMEcFtANlcsoF TENDONSAAJDL|GA,\TENTSCarl A. Carlstedt, Margareh Nordin

4' BloMEcFtANtcsoF pERfpHERAtNERvEsBjorn Rydevik, G6ran Lundborg, Richard skarak

5' BfoMEct{ANfcs oF sKELFTAIMuscLEMark I. pitman, Lars peterson

pan twoBIOMECFT,\NICS OF JOIIG6. BIOMECT-{ANICSOF THE KNEE

Margareta Nordin, Victor H" Frankel

rI


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xlri coMENrS7. BIOMECI.{ANICSF THE HIP

Margareta Nordin, Victor H' Frankel

8. BIOMECH/qNICSOF THE A IKLEVictor H. Frankel, Margareta Nordin

9. BIOMECFLANICS F THE FOOTG. lames Samrnarco

IO. BIOMECI.UANICSF TI-IELUMBARSPINEMargareta Lindh

I I. BIOMECFTANICSF THE CERVICALSPINEIlan ShaPiro, Victor H. Frankel

12. BIOMECI.I,ANICSF THE SHOULDERJosephD. Zuckerman, rederick ' Matsentr

I3 . BIOMECFI.,ANICSF THE ELBOWJosephD. Zuckerm:I1, Frederick A- Matsen III

14. BIOMECFLANICSF THE WRISTStevenSruchin

. a . ' A r5. etoMecHA lcs oF THE {ANDFadiJ. Beiiani, ohanM. F- Landsmeer

GLOSSARY F BIOMECF1ANICAL ERMS

INDEX


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The need for establisning systems of weights andmeasures for use in bt'ilding, making clotf,es, andengaging in simple trade "ia .o*oi"rce was rec-or:nized by primitive societies. The Bible and earlvrecords from Babylonian and Eglptian civilizationsindicate that man first used parts-of his body andcommon elements in his environment to establ.ishsimple svstems of measurement. Time was com-monlv measuredby p.riods of the sun. At the time'[ Noah, . l-"t s,h was measured in terms of thecrrbit, which was equivalent to the dishnss fromthe elbow to the tip of the middle finger. A span,(quivatent to one half a cubit, was taken as thedistance from the tip of the thumb to the tip of thelittle finger with the hand fuIly spread. For smalrermeasurements the digrt, or width of the thumb,rvas used- For measurements of volumes or fluidcapacities, containers were fi.tled with seeds, whictrrvere then poured out and counted to establish the"lume of the container in terms of the n'rrrber ofsr.t-ds t could holci.Prirr.itive societies found that th"y could deter_mine if one object rvas heavier thin ariother bvplacing th: two_obiectson a balance.The Babyro"i;;retined this,,olruqy_" uy barancingan object with aset of standard, *"u-porirnua stones. These stones|sre probably the fusi standards, and the measure-ment later evolved nto the er,Irish legarstone, whicht'r the imperial svstem is "qii*raleni to 14 pounds6l-27 nervtons).The Eglprians and the Greeksboth used the wheateedas the sta'dard for the smalrestunit of rveight.hisconcepte'olved into the unit of the gEain,whichs srill t""d toclav ,. . i*rr.J-"pprications. The Arabsshblished a standard of weights fo r precious stonesnd metalsbasedoi-tt " weight of a smanbean catedcarob' a measurementwhich has evorved into theresenrunit of the carat.

Sl: THINTERNATIONSYSTEMOUNIDennisR.Ca

lncreasing trade among tribes and nations cathe measuring svrstemsdeveloped by early civtions to become intermixed. Measuring ltandwere widely disseminated by the Romans. AsRoman soldiers marched in their conquests,distawere measured in terms of the pace, which wadistance between the points *here one foot sthe ground on successivesteps.A pacewas therequivalent to two steps.

THE ENGUSH SYSTEMThe E"glish system of weights and measevolved from me-*5ing systems used bv the Blonians, Eglptians, Rorna'1, Angro-sa:


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xl/iii sf:THE NTERNATTONALysTEMF uNrrsment of a foot was established as one third the lengthof the measuring stick, and an inch was establishedas one-thirty-sixth of the standard yard. King EdwardII apparently found this new measuring system to beconfusing and passed a stafute decreeing an inch tobe equivalent to "three barleycorns, round and dry.,,The English system of measurement evolved andbecame refined primarily through royal decrees. TheearlyTudor rulers established 220 yards as equivalentto 1 furlong. In the sixteenth century, eueen Ehza-beth I changed the traditional Roman mile from 5,000to 5,280 feet, making the mile equivalent to exactty Bfurlongs. In 1824the English Parliament legalized ihenew standard yard, which was based on the mea-surements taken from a brass bar with a gold buttonne;r each end. A single dot was engraved on eachbutton, and the yard was taken to 6e the distancebetween the two engraved dots.The English colonization and dominance of worldcommerce in the seventeenth, eighteenth, and nine-teenth centuries served to spread- the English systemof _weights and measures throughout the world,includi.g the American colonius. Athough refined insome ways to meet the demands of commerce, thesystem has remained essentially unchange,c.

THE METRICSYSTEMIn the early eighteenth century no uniformsystem of weights and measures existed on theEuropean continent. Measurements not only differed

frorn country to country, but also from town to town.P_gi"g the French Revolution in r7g0, Kirg Louisu and the National Assembly of France pissed adecree calling on the French Academy of sciencesnd the Royal society of London to ,,,ceduce anstandard for all of the measures and allThe English, however, did not participatethis undertaking, and so the French alone set outestablish a new and uniform system of measures.result was the metric system.In 1793 the French gorr"*ment adopted a stan-system of measurement based or, the meter,was defined as one ten-millionth of the dis-from the North pole to the equator on a linethrough Paris, All other linear measurementsestablished as decimal fractions of the meter.metric unit of mass was established as the gr"rr,was defined as the mass of L cubic centimeterwater at its temperafure of maximum density. Theof fluid capicity was named the ,,ritre,, and

defined as the volume contained by a cube whichmeasured one tenth of a meter on each side.Most Frenchmen thought that the new metricsystem of measurement was confusing and expendeda great deal of effort converting from the new systemto the familiar measuring system of yards and feetthat had been used previously. Widespread resis-tance to the new system forced Napoleon to renouncethe metric system in 1872. In 7837, however, Francereturned to the metric system in the hope that itwould spread throughout the world.In the nineteenth century, the metric system foundfavor among scientists because (1) it was an interna-tional system, (2) the units were independentlyreproducible, and (3) its use of a decimal systemgreatly simplified calculations. The British systemhad been designed for trade and commerce, but themetric system appeared to have significant advan-tages in the areas of engineering and science.In the latter haU of the nineteenth century, scien-tific advances necessitated the development of bettermetric standards. In L875 an international treafy, theTreaty of the Meter, established well-defined mefricstandards for length and mass. In addition, thepermanent machinery for further refinements of themetric system was established. This treaty wassigned by L7 countries. By 1900, 35 nations hadofficially adopted the metric system.At the time the Treaty of the Meter was signefl, aPermanent secretariat, the International Bureau ofWeights and Measures, was established in Sdwes,France, to coordinate the exchange of informationabout the metric system. The diptomatic organuattonconcerned with the metric system is the GeneralConference of weights and Measures, which meetsperiodically to ratify improvements in the system andthe standards. In L960, the general ionferenceadopted an extensive revision una simplification ofthe system. This modernued metric lystem wasnamed Le systeme International d'unites (Interna-tional system of units), and was given the interna-tional abbreviation SI. The general conferenceadopted improvements and additions to the sI sys-tem in L964, L968, 79T1,and I9TS.Between L965 and LgTz, the united Kingdom,Australia, Canada, New zealand,, and tt ur,/otherEnglish-sp:3king countries adopted the metric sys-tem- rn 1975, the united states Congress passed inuMetric Conversion Act, providing foithe idopUon ofthe SI metric system as the predominant ryit"* ofmeasurement units. Today, nearly the entire worldeither is using the metric system or is committed to itsadoptiorl.


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THE SI METRIC SYSTEMThe systeme nternational d'unites (sr), themodernmetric system, has evolved nto the mostexacting ystemof measures evised. n thissecrion,the 5I units of measurernent used in the scienceofmechanicsare described. SI trnits used in electricaland light scienceshave been omitted for the sake ofsimplicit-v-The SI units can be considered in three groups: (1)the basegnits; (Z) the supplementry uniL; and (3)the derired units (Fig. 1)- The baseunits are a smallgroup of standard measr.rrementswhich have beenarbitrarilv defined. The base unit for length is themetef i*), and the base unit of mass is the"kiJogr;(kg). The base units for time and temperahrreari thesecond (s) and the kelvin (R, respectively. Definj-tions of the base units have become increasi"gtysophisticatedin resPonse to the expanding needs "i.,aapabilitiesof the scien"fic couununity glUte l). Fore,xample' the meter is now defined in terms of the

wavelength of radiation emitted from the krlr;ptondatom.The radian (rad) is a supplementary unit tomeasurep.laneangles. This unit, like the b.se units,is arbitrarily defined (Table 1). Although the radian isthe SI unit for plane angte, the unit of th" degreehasbeen retained for general use, since it i; firmlv

FtG. .fhe fnreradonalSysrem f Unis.

5l:Tl':3 NTE:)nION.- SYSTE:IAFUNITS Xiestablishedand '.ridely used around the rvorld.degree is eguivalent to , lg0 rad,N{ost units of the sI system are derived unimeaning that ther are established rom the baseunin accordance with ftrndamental physical principlesome of these units are e(pressed in terms or theb.runits from which th"y are derived. Examples aarea, speed,artd acceleration,which are exptlssedthe SI units of squ;re meters (m2),meters per seco(mr's),and meters per secondsquared (m/it), respetively.Other derived units are similarly established frothe baseunits but h]-" beengiven special names (sFig- I and Table 1). These ,rnits ;rre defined througthe use of firndarnental eqgatioru of physical laws-coniunction with the arbiuarily definia 3t baseunitFor o


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SI :THE NTERNATIONALYSTEMF UNITS nltation was purportedly spurred by being hit on thehead by an apple falling from a tree. If is perhapspoetic justice that the SI unit of one newton isapproximately equivalent to the weight of a medium-sized apple. Newton was knighted in 1705by eueenM"ry for his monumental contributions to science.The unit of pressure and stress, the pascal, wasnamed after the French physicist, mathematici?il,and philosopher Blaise Pascal (1,629-1612). pascalconducted important investigations on the character-istics of vacuums and barorneters and also invented amachine which would make mathematical calcula-tions. His work in the area of hydrostatics andhydrodynamics helped luy the foundation for thelater development of these scientific fields. In addi-tion to his scientific pursuits, Pascal was passionatelyinterested in reliFon and philosophy and thus wrot-eextensively on a wide range of subjects.The base unit of temperafure, the kelvin, wasnamed in honor of Lord William Thomson Kelvin(L824-790n He was of Scottish-Irish descent, andhis given name was william Thomson. He waseducated at the University of Glasgow and Cam-

TABLE2SI PREFIXESPREFIX SYMBOL MEANING EXPONENOR POWEexapetateragigamegaki fhectodeka

decicentim i f l imicronanopicofemtoatto

EPTGMkhda

dcml-rnpfa

quintilfonquadrilliontrilfonbi f ionmilfionthousandhundredten

BASEUNITtenthhundredththousandthmilfonthbilfonthrilf onthquadrilfonthquintrillionrh

l 0 r 8l 0 r slot2l 0erc6t dl02l 0 ll 0 -rc-2Io- 3I 0- 6| 0- el0 - t2l 0 - r sf 0 - r 8

TABLE3SI UNITSNAMED AFTERSCTENTTSTSSYMBOL UNIT OUANTIry SCIENTIST COUNTRY FBIRTH DATESAC"CFHHzJK

NoPaSTVWwb

amperecoulombdegreeCelsiusfaradhenryhenzjoulekefvinnewtonoh mpascalsiemenstesfa

efectriccurrentelectric chargetemperaureelectric capaciyinductive resistancefrequencyenergytemperature

forceefectricresistancepressure/stressefectricconductance

magnetic flux density

electricalpotentiafpowermagnetic flux

Ampere, Andre-MarieCoulomb, CharfesAugustin deCelsius,AndersFaraday,MichaelHenry, JosephHeru, Heinrich RudofphJoufe, James PrescottThomson, Wifliam

fater Lord KelvinNewton, Si r saacOhm, Georg SimonPascaf.BlaiseSiemens,KarlWilhelm,

laterSi rWilf iamTesla,Nikola

Volta, Count Afessandrowatt, JamesWeber, Wilhelm Eduard

FranceFranceSwedenEnglandUnitedStatesGermanyEnglandEnglandEnglandGermanyFranceGermany(EnglandfCroatia(UnitedStatesfItalyScotlandGermany

t775- 836t736- I806t70t 17441791- 86 71797 18781857 1894r8 r8 - 889182+-1907| 642- 727t7B7 1854| 623- | 6621823-1883r856- 1943t745-1827t736- 8 9r804 -1891

voltwattweber


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;11jii Sl:THE NTERNATIONALYSTEM F UNITSbridgeUniversityand early n his careernvestigatedthe thermalpropertiesof steamat a scientificabora-tory in Paris"At the age of 32 he returnedto theUniversity of Glasgou/ to accept the chair of NaturalPhilosophy. His rieeting with |ames |oule in lg41stimulated interesting discussions on the nature ofheat which eventually led to the establishment ofThomson's absolute scale of temperature, the Kelvinscale. In recognition of Thomson's contributions tothe field of thermodynamics, King Edward VII con-ferred on him the title of Lord Kelvin.The conunonly used unit of temperafure, thedegree Celsius, was named after the Swedish astron-omer and inventor Anders Celsius (170L-L7M).Celsius was appointed professor of astronomy at theUniversity of Uppsala at the age of 29 and remainedat the university until his death"'!, years later. In L742he described the centigrade thermometer in a paperprepared for the Swedish Academy of Sciences. The

name of the centigrade temperature scale was offi-cially changed to Celsius in L948.CONVERTINGTO SI FROM OTHERUNITSOF MEASUREMENTTable 4 has been provided to allow conversionof measurements expressed n English and non-Slmetric units into SI units. One fundamental sourceofconfusion in converting from one system to anotheris that two basic ypes of measurement systems exist.In the "physical" system (such as SI) the units oflength, time, and massare arbitrarily defined, andother units (induding force) are derived from thesebaseunits, In "technical" or "guurtational" systems(suchas he English system) he units of length, time,and force are arbitrarily defined, and other units(including mass) are derived from these base units.Sincethe units of force in gravitational systemsare in

TABLE+CONVERTINGTO St FROM OTHERUNITSLENGTHTo convert o meters mfmultiply in byftydmifeAREATo convert o squaremeters m'lmuttipty inz byft'zyd'VOLUMETo conven o cubic meters mtlmultipty in3 byftn

ydt(Note:A liter is equivalent o I m' x l0-3.)MASSTo convert o kilograms kglmultiply fb byslugkgfszm- |DENSIryTo convento kg/m3multipty tb/in3 byfbldMOMENT OF INERTIATo convert o kg mt or, equivalently,o Nm seczmuttipty lo rt2 byfb in2kgf s2mFORCETo convert o newtons NlmutriPty kgf (:kpl bytb f

0.a2540.30480.9144r609.3

6.4s 6x to-40.09290.8361

t 5387 t0-s0.02830.7646

0.+53614.5949.8067

27,680r6 . 08

0.04212.9264 l0-49.8067

by 50360096,+o0

by 0.30480.27780.4+70

by 0.30+8

PRESSUREND STRESSTo conven o pascafsPal or,equivafently,o N/mzmuttiply lbf/inz by 6894.8kgflmz 9.8067mm Hg 133.32ENERGY.WORK,AND MOMENT OF FORCETo conven o oufes (Jl or, equivafently,o Nm t.mutriply ft fbf by 1.3558in lbf 0. 13 0kgf m 9.8067Btu 1055.caf 4.1868TIMETo convert o seconds sf

multiply minhdSPEEDTo convento m/smultiply fuskmlhmile/hACCELERATIONTo convento mlszmultiply ftlszTEMPERATURE

To convert o degreesCelsiusfromdeg K: degC: de gK - 273.15ftom deg F: deg C : 5/9 (degF - 3ZlPLANEANGLETo convert o radians radlmultiply degrev by nlt80 (or0.017452t (or 6.283219.80674.4482


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n SI :THE NTERNATIONALYSTEMF UNITSTABLEDEFINITIONS OF SI UNITSmeter mlkilogram kg)second sfkelvin Kf

BASESI UNITSThe meter is the length equal to 1,650,763.73 avelengths n vacuum of the radiarioncoffesponding o theUansition etween he levels2p,o and 5ds of the k rypton6 atom.The kilogram s the unit of massand is equal o the massof the international rototypeof the kilogram.The second s the durationof 9,192131,770 eriodsof the radiailonconesponding o the transitionbetween hetwo hyperfineevelsof the groundstateof the cesium_133tom.The kelvin,a unit of thermo-dynamicemperature,s rhe fraction 11273.16f the thermodynamicemperature fthe triplepoinr of warer.

radian {rad) SUPPLEMENTARYIUNITThe adians heplane nglebetweenwo radiiof a circlewhichsubtend n thecircumferencen arcequal nlengtho the radius.newron (Nl

pascal (Pal

joule (J )

waft (wldegree Cefsius "C f

DERIVEDSI UNITS wlTH SPECIALNAMESThe newton is that Force hich, when applied o a massof one kilogram,gives t an acceleration f one meterpersecondsquared.N = I kgm/s2.The pascal s the pressure roducedby a forceof one newton applied.with uniformdistribution, veran areaofone squaremeter. Pa= I N/m2.The oule is the work done when the point of applicationof a force of one newton is displaced hrough adistance f one meter n the directionof the force. J = I Nm.The wafi is the powerwhich in one secondgives ise o the energyof one oule. I w = I J/s. .The degreecelsius s a unit of thermodynamicemperature nd is equivalento K - 273.15.

The SI unit of pressureand stresss the pascal pa).Pressure is defined in hydrostatics as the forcedivided by the areaof force application. Mathemati-cally this t"r, be expressed sPressure q*area

The sI unit of pressure, he pascal pa), is thereforedefined in terms of the basesI units as1pa:1ry.1 m 2

}lthough the SI base unit of temperature is thekelvin, the derived unit of degree Celiius ("C or c) ismuch more commonly used. The degree Celsius isequivalent to the kelvin in magnitude, but theabsolute value of the Celsius scale differs from that ofthe Kelvin scale such that "C _ K ZTg.15.When the SI system is used in a wide variety ofmeasurements, the quantities expressed in terms ofthe base, supplemer,tul, or derived units may beeither very large or very small. For example, the areaon the head of a pin is an extremely small numberwhen expressed in terms of square meters (*t). onthe other hand, the weight of a whale is an extremelylarge number when expressed in terms of newtons

(N). To accommodate the convenient representationof small or large quantities, a system of prefixes hasbeen incorporated into the SI system (Table 2). Eachprefix has a fixed meaning and can be used'with all SIunits. When used with the name of the unit, theprefix indicates that the quantity described is beingexpressed in some multiple of ten times the unitused. For example, the millimeter (mm) is used torepresent one thousandth (10-3) of a meter and aSgapascal (GPa) is used to denote one billion (10')pascals.

one of the more interesting aspects of the sIsystem is its use of the names of famous scientists asstandard units. In each case, the unit was namedafter a scientist in recognition of his contribution tothe field in which that unit plays a major role. Table3 lists a number of SI units and the scientist for whicheach was named.The unit of force, the newton, was named in honorof the English scientist Sir IsaacNewton (1624-LT2n.He was educated at Trinity College at Cambridge andlater returned to Trinity College as a profesior ofmathematics. Early in his career he made fundamen-tal contributions to mathematics which formed thebasis of differential and integral calculus. His othermajor discoveries were in the fields of optics, ashon-omy, gravitation, and mechanics. His work in gravi-


15/43

rfact the weightsof standard masses,conversion to SIis dependentuPon the accelerationof massdue to theEartl-,'s ravity. By international agreement the accel-

Sf:THE NTERr,tAflor{AL YSTEMOF UNrTseration dubeen","d:rT:iln,'*#:fl"1;'ffifactors in Table 4.

BIBUOGRAPF{YFcirr. I- L-: sI Metic Flandbook. New yorrg chartes scribner,sSons, gn- Pennycrrick, C. I.: Handy Matrices of Unit Conversionfor Biology and Medranics. Ne* york, Iotrn wil.y ard son world Heal$ O$anization. The SI for the Healtr hoftsC'enerra,World Health qBarriza6on, lg;n.


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panBIOMECH NICSOFAND STRUCTURESITflUSCULOSKELETAL

TISSUOF THSYST


17/43

The purpose of the skeletal qrstem is to protectinternal organs, provide ritrd icinematic rinl6 andmurle attachnrent sites, ana facilitate muscle action'tnd t'*cdy movemenl Bone trasunique siruct.oal andnrtrhanical groperties that allow it io cary out theser'lt"s' Bone is among the bod/s turdest stnrct'res,'nlv dentin and enasrel in the teeth being harder. Itis ()ne of the most dynasdc and metaboEllly activetissues -. *.. body and remains active throughoutlifc- A highlv vasgular tissue, it has -rn excetentt"lpacit)' for self-repair and ctn alter its properties andt''nfigu:ation in t"tpot t" to changes '; mechanicaltlcmand- Fo1 *.o,pi.,,."h"og, in bone dersity are'()mmonly observed after Ft.ar of diilse and ofrcatlv increased *: o*g, in bone shape :rreote'd during fracturS hearini"r,a after certain or)er-tt,ns' Thus, bon" adapts* a" mechanicat demandslacedon it .This chapter des,qibes the composition and stmc-ure of bone dszue, the mechanical prcperties ofone' and $,e--uetnvior of bone trnder differentoading conditio*- various hctors that affect theechanicalbehavio, of bone ir, ,.iuo and in vivo arerlso di_


18/43

BIOMECHANICSF NSSUESND STRUCTURESF THE MUSCULOSKELETALYsTEMproteoglycans (PGs). The GAGs ser:\reas a cementingsubstance between layers of mineralized collageifibers. These GAGs, along with various nonco[Jgu-nous glycoproteins, constitute about svo of the "*iu-ellular matrix. (The structure of PGs, which are vitalcomponents of articular cartila ge, is described indetail in Chapter 2.)Water is fairly abundant in live bone, account-ing for up to 25% of its total weight. About gsvoof the water is found in the organic matrix, aroundthe collagen fibers and ground substance, and in thehydration shells surrounding the bone crystals. Theother L57o s located in canals and cavities that housebone cells and carry nutrients to the bone tissue.At the microscopic level, the fundamental struc-fural unit of bone is the osteon, ot haversian system(Fig. t-1). At the center of each osteon is a smallchannel, called a haversian canal, that contains bloodvessels and nen/e fibers. The osteon itself consists ofa concentric series of layers (lamellae) of mineralizedmatrix surrounding the central canal, d configurationsimilar to growth rings in a tree trunk.Along the boundaries of each layer, or lamella, aresmall cavities known as lacunae, each containing one

CANALICULIOSTEOCYTE

LACUNACIRCUMFERENTIALIAMELLAEHAVERSIANSYSTEMSCEMENT INEINTERSTITIALLAMELLAETRABECULAE

HAVERSIANCANALS

VOLKMANN'SCANALS

bone cell, or osteocyte (see Fig. l-tc). Numeroussmall channels, calea canali*-li, rad.iate from eachlacrrna/ connecting the lacunae of adjacent lamellaeand ultimately reaching the haversian canal. Cellprocesses extend from the osteorytes into the cana-liculi, allowing nufrients from the blood vessels in thehaversian canal to reach the osteocytes.At the periphery of each osteon is a cement line, anarrow area of cementlike ground substance com-posed primarily of glycosaminoglycans. The canalic-uli of the osteon do not pass this cement Line. Like thecanaliculi, the collagen fibers in the bone matrixinterconnect from one lamella to another within anosteon but do not cross the cement line. Thisintertwining of collagen fibers within the osteonundoubtedly increases the bone's resistance to me-chanical stress and probably explains why the cementline is the weakest portion of the bone's microstruc-ture (Dempster and Colemdrr, L960;Evans and Bang,Le67).A typicalosteons about200micrometerspm) ndiameter.Hence everypoint in the osteon s no morethan 100F.m rom the centrally ocatedblood supply.In the long bones, the osteonsusually run longitudi

BLOODVESSEL

F I G . - IA. The fine structureof bone is iflustratedschematicalfyn a section f theshaft/of longbone depictedwithout inner marrow.Theos-teons, r haversianystems,reapparent s hestructuraf nits of bone. fn the centerof theosteons re the haversian anafs,which formthemainbranches f thecirculatoryetwork nbone.Each steonsboundedby a cement ine.One osteon sshown exten ing romthe bone(20x1. Adapted rom Bassen, 965.lB, Eachosteonconsists f famefae, concentric ingscomposedof mineralmatrixsurrouning thehaversiancanaf (Adaptedfrom Tortora andAnagnostakos,9g4.lC. Along rhe boundariesof the lamelfaeare small cavities nown aslacunae, achof whichcontains singfe onecelf, r osteoqrte. adiatin from he acunae retiny canafs, r canaliculi,nto which the ryto-pfasmicprocesses f the osteoq/tesextend.(Adapted from Tortora and AnagnostakoS,te8+.1BRANCHESOFPERIOSTEALBLOODVESSELS

LAMELLAE


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nally, but they branch frequently and anastomoseextensively with each other.Interstitial lamellae span the regions between com-plete osteons (see Fig. 1-1A). Th"y are continuouswith the osteons and are just the same material in adifferent geometric configuration. As in the osteons,

no point in the interstitiat lamellae is farther than 100pm from its blood supply. The interfaces betweenthese lamellae contain an array of lacunae in whichosteorytes lie and from which canaliculi extend.At the macroscopic level, all bones are composedof two types of osseous tissue: cortical, or compact,bone and cancellous, or trabecular, bone (Fig. l-Z).Cortical bone forms the outer shell, or cortex, of thebone and has a dense structure similar to that ofivory. Cancellous bone within this shell is composedof thin plates , ot trabeculae, in a loose mesh struc-ture; the interstices between the trabeculae are filledwith red marrow. Cancellous bone tissue is arrangedin concentric lacunae-containing lamellae, but it doesnot contain haversian canals. The osteorytes receivenutrients through canaliculi from blood vessels pass-irg through the red marrow. Cortical bone alwayssurrounds cancellous bone, but the relative quantityof each Vpe varies among bones and within individ-ual bones according to functional requirements.

FrG.1 -2Frontal ongitudinal section through thehead, neck, greater trochanter,and prox-imaf shaft of an aduft femur. Cancellousbone, with it s trabecufae oriented in alattice, l ies within the shell of corticalbone. (Reprinted with permission fromGray, H. . Anatomy of the Human Body.l3th American Ed . Edired by C. D.Clemente. Philadelphia"Le a & Febiger,le8s.)

BIOMECHANICS F BONE

Since the lamellar pattern and material composi-tion of cancellous and cortical bone appear identical,the basic distinction between the two is the degree ofporosify. Biomechanically, the two bone types can beconsidered as one material whose porosify anddensity vary over a wide range (Carter and Hayes,1977b). The difference in the porosif of cortical andcancellous bone can be seen in cross sections fromhuman tibiae (Fig. 1-3). The porosity ranges from 5to 30Vo n cortical bone and from 30 to over 90Vo ncancellous bone. The distinction between porouscortical bone and dense cancellous bone is somewhatarbitrary.All bones are surroundedby a dense fibrousmembrane called the periosteum (see Fig. 1-1A). It souter layer is permeated by blood vessels and nen/efibers that pass into the cortex via Volkmann's canals,connecting with the haversian canals and extendi*gto the cancellous bone. An inner, osteogenic layercontains bone cells responsible for generating newbone during growth and repair (osteoblasts). Theperiosteum covers the entire bone except for the jointsurfaces, which are covered with articular cartilage.In the long bones, a thinner membrane, the endos-teum, lines the central (medullary) cavity, which isfilled with yellow fut!y marrow. The endosteum

ff* ^&--*#*frdt


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(t BIOMECHANICSF TISSUESND STRUCTURESF THEMUSCULOSKELETALYSTEM

contains osteoblasts and also giant multinucleatedbone cells called osteoclasts, which play a role in theresorytion of bone.

BIOMECF{ANICAL ROPERTIES FBONEBiomechanically, bone tissue may be regarded

as a two-phase (biphasic) composite material, withthe mineral as one phase and the collagen andground substance as the other. In such materials (anonbiologic example is fiberglass)-in which astrong, brittle material is embedded in a weaker,more flexible one-the combined substances arestronger for their weight than either substance alone(Bassett, 7965).Functionally, the most important mechanical prop-erties of bone are its strength and stiffness. These andother characteristics can best be understood for bone,or any other structure, by examining its behaviorunder loadinB, r.e., under the influence of externally

applied forces. Loading causes a deformation, or achange in the dimensions, of the structure. When aload in a known direction is imposed on a structure,the deformation of that structure can be measuredand plotted on a load-deformation curve. Muchinformation about the strength, stiffness, and othermechanical properties of the structure can be gainedby examining this cun/e.

FrG. -3r{. Reflected-fghtphotomicrographfcorticalbone from a human tibia(+}xl. (Courtesy f Dennis R.Carter,Ph.D.lB. Scanningelectronphoto-micrograph f cancelfous one froma human tibia {30 ,. (Courtesy fDennisR.Caner, h.D.|

A hypothetical load-deformation curve for a some-what pliable fibrous structure, such as a long bone, isshown in Figure "1,-4. The initial (straight line)portion of the curye, the elastic region, reveals theelasticify of the structure, i.e., its capacity,for return-

PI.ASTICREGION CtULTIMATEFAILUREPOINTYIELD ,/ DPOINToJ I ENERGYDEFORMATIONFIG. _4Load-deformationurue ar a structure omposedof a some-whatpf ablematerial. a load sappliedwithin he elasticange

of the structureA to B on the curvefand is then refeased,opermanent eformation ccurs.f loading scontinued ast heyieldpoint B) nd nto hestructure'sfasticange B o Con thecurvefand the load is then released, ermanentdefoimationresults.heamountof permanent eformationhatoccursf thestructures foaded o point D in the plastic egion and thenunfoadeds representedy the distance etweenA and D,. lfloadingcontinues ithin the pfastic ange, n ultimate ailurepoint C) s reached.

fIIfIIffIr

F8F


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ing to its original shape after the load is removd. Asthe load is applied, deformation occurs but is notpermanen| the structure recovers its original shapewhen unloaded. As loading continues, the outermostfibers of the structure begin to yield at some point.This yield point signals the elastic limit of thestructure. As the load exceeds this limit, the structureexhibits plastic behavior, reflected in the second(curved) portion of the curve, the plastic region. Thestructure will no longer return to its original dimen-sions when the load has been released; some residualdeformation will be permanent. If loading is progres-sively increased, the structure will fail at some point(bone will fracture). This point is indicated by theultimate failure point on the curve.Three parameters for determinirg the strength of astructure are reflected on the load-deformation curve:(1) the load that the structure can sustain beforefailing, (2) the deformation that it can sustain beforefailing, and (3) the energy that it can store beforefailing. The strength in terms of load and deforma-tion, or ultimate strength, is indicated on the curve bythe ultimate failure point. The strength in terms ofenergy storage is indicated by the size of the areaunder the entire curve. The larger the area is, thegreater the energy that builds up in the structure asthe load isr applied. The stiffness of the strucfure isindicated by the slope of the curve in the elasticregion. The steeper the slope is, the stiffer thematerial.

The load-deformation curye is useful for determin-irg the mechanical properties of whole structuressuch as a whole bone, an entire ligament or tendon,or a metal implant. This knowledge is helpful in thestudy of fracture behavior and repair, the response ofa strucfure to physical stress, or the effect of varioustreatment programs; however, characterizing a boneor other structure in terms of the material thatcomposes 7t, independent of its geome{r, requiresstandardization of the testing conditions and the sizeand shape of the test specimens. Such standardizedtesting is useful for comparing the mechanical prop-erties of two or more materials, such as the relativestrength of bone and tendon tissue or the relativestiffness of various materials used in prostheticimplants. More precise units of measure can be usedwhen standardized samples are tested, i.., the loadper unit of area of the sarnple (stress) and the amountof deformation in terms of the percentage of changein the sample's dimensions (strain). Tha curve gen-erated is a stress-strain curve.Stress is the load, or force, per unit area thatdevelops on a plane surface within a structure in

BIOMECHANICS F BONE

response to externally applied loads. The three unitsmost commonly used for measuring stress in stan-dardtzed samples of bone are newtons Per centimetersquared (NI/cm2); newtons per meter squared, orpascals (N/m2, Pu); and meganewtons per metersquared, or me gapascals(MN/m2, MPa).Strain is the deformation (change in dimension)that develops within a strucfure in resPonse toexternally applied loads. The two basic tyPes of strainare linear strain, which causes a change in the lengthof the specimen, and shear strain, which causes achange in the angular relationships within the struc-ture. Linear strain is measured as the amount oflinear deformation (lengthening or shorted^g) of thesample divided by the sample's original length. It is anondimensional parameter expressed as a percentage(for example, centimeter per centimeter). Shear strainis measured as the a*onttt of angular change (^y)n aright angle lying in the plane of interest in thesample. It is expressed in radians (one radian equalsapproximately 57.3 degrees) (International Society ofBiomechanics, 1988).

Stress and strain values can be obtained for boneby placing a stan dardtzed specimen of bone tissue ina testing jig and loading it to failure (Fig. 1-5). Thesevalues can then be plotted on a stress-strain curve

FfG. -5Standardized one specimen n a testing machine.The strain nthe segment of bone between the two gauge arms s measuredwith a straingauge. The stress s calculated rom the totaf foadmeasured. Courtesy f Dennis R. Carter,Ph.D.)


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g BTOMECHA.N|CSF n55UE5AND STRUCTURESF rHE MUSCULOSKEJTAL YSTEM(Fig. 1-6). Th e regions of this cr.rn'e re similar tothose of the load-deformation curve. Loads in theelastic region do not causeperrnanent cieformation,but once the yield point is exceeded,some deforma-tion is permanent. The strength of the material interms of enerry storage is represented by the areaunder the entire curve. The stiffness is representedby the slope of the curve in the elastic region. A valuefor stiffness is obtained by dividing the stress at anypoint in the elastic (straight line) portion of the curveby the strain at that point. This value is called themodulus of elasticity (Young's modulus). Stiffermaterials have higher moduli.Mechanical properties differ in the two bone t1pes.Cortical bone is stiffer than cancellous bone, with-standing greater stressbut less strain before failure.Cancellous bone in vitro does not fracture until thestrain exceeds 75Vo,but cortical bone fracttrreswhenthe strain exceeds ZVa.Becauseof its porous stnrc-ture, cancellousbone hasa large capacity for energystorage(Carter and Hayes, 1975).Stress-strain curves for cortical bone, met-|, andglass llustrate the differences n mechanicalbehavioramong these materials (Fig. L-n The variations instiffness are reflected in the different slopes of thecurves in the elastic region. Metal has the steepestslopeand is thus the stiffestmaterial.

FlG. | -7Sress-straincun/sfor three materials.Meal has rhe stesfope n rhe etasric egionand is thus the sdffestmaterielasticporcionof trrecune br menf is a suaightfine, ndilineartyetasucbefravior.The fact dut meaf has a long pregion irrdicates fiat trris tlpical ducdle material deexrensivcly efore ailure.Gla


23/43

micromechanical et'ents at yield. Yield.ing in metal(tested n teruion,-or pulled) is causedUy pLil flowand formation of prastic rlp lines; ,fup n ,., areiormed when the molecul"r oi the lattice srrrcture ofmetal dislocate' Yieldingin bone (tested in tension) iscaused by debonding of the osteons at the cementlines and microfriactrrre.lvlaterials are classified as brittle or ductile depend-ing on the extent of deformation before failure.'Ct *is a t'"ical brittle material, and soft metal is a tlet-ductile material- The difference in the "o,o#t ofdeforrration is reflected in the fractrrre surfacesof thehvo materi* -(Hg- l-g). when pieced together aftertrachue, the ductile material *iit not conform to itsorigrnal shaPe whereas the brittle material will. Bonee.xhibits more brittte or more ductile behavior de-pelding on its age 9-o,*ger bl"being more ducrile)and the rate at whidr it is loaded (b"i" being morebrittle at higher loading speeds). IBecausethe stmchrre of Uor,e is dissimilar in thetransverseand the longitudinal directions, it exhibitsdifferent mechariicat pioperties when loaded alongdifferent axes, a characteristic known as arrisotropy.Figure l-9 shows the variations in strength andsriffness for cortical bone samples from a humanfemoral shaft, tested in tension in four d.irections(Frankel and Burstein rg70). The 'alues for bothparameters.T highest for the sampres oaded in thelongitudinal direcfion. Although the relatior,ship be_trveen loading_patterns and tf," mechanical prop"r_ties of bone throughout the skereton is ..*t"*er),complX, it cat g".'-*rally be said that bone strengthand stiffness are gre-atest n the direction in whichloads are most co'uncnty imposed (Franker andBurstein, 1970).BIOMECT{ANTCALBEFI,AWOROFBONEThe mechanicalbehavior of bone-its behaviorunder the influence of forces and moments-isaftected by its mechallcal properties, its geometriccharacteriiHcs,the roading ;-,odeapplied, the rateofuadi.g, and the fr"qr"ncy of loadirg.BON-EBEF{,AVIOR NDER VARIOUSLOADING MODESForces and moments can b" "pplied to a stmc-ure in various dite.dons, producing tension, com_ression, bendi f,g, shear, 'torsion, and combinedoadits (Fig- 1- l0i. &rne in rivo is subjected to al l of

EiCMECHAAJICSOF EONE

l iDUCTILEFRACTURE

FlG. I _gFracure surftcesof sarnplesof a ducrile anda britde mThe broken frneson fte dr,rcrifemateriat indicate tfrelengfi of dre sampfe.before ft deformed. The bride mdeformedrcry lirde befureftacnrre.

these loading modes- The folrowing descriptiothese *d- appb' to strrcturr in equilibri,.rrest or moring at a T"rTt speed); oaaing proan internal deforrning effect'on the structure.TersimDudry teruile .l*dTg, equal and oppIoads are applied outward Fo^ the strrface ostmchrre' and tensrle shess and strain result ithe sbnrchre- Tensrle stness can be thoughtErany small forces directed away from the surfathe stnrchrre- ldaximal tensile stress occurspJT" perpsrdicular to the applied load (Fig. 1under tens.le loading, the rt*.t ,," lengthensnarrows- At the microscopic level, the far,rre manism for bone tissue loaded in tension is ma

ctCNUTccFCn

STRATNFfc . t -9Anisotroplc e-avio of c3nicalbone specrmens toma humfemoral s|Eft :esred in rension (puiledl in four direcrfongirudinalL,- lted 30 cegreeswirh respec o g1eneurafof dre bone. =:ed & decrees.and rransverseTl. (DataFrankel nd B,-iern lg73

-\-.-/:>-l;lLJIJ">57

@f T


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t o BtoMEcHANrcsF TrssuEs NDsrRUCfuREsF THEMUSCULOSKELETALYSTEM

vUNLOADED TENSION -.COMPRESSIONBENDING

SHEARFrG. - l0Schematicepresentation

FrG. - 12Reflectedight photomicrographf a human corficalbonspecimenestedn tension30 }.Arrowsndicate ebondingthe cement inesand pullingout of th e osteons.CourtesDennisR.Carter, h.D.)

F t G . - t 3Tensile racture hrough the calcaneus roduced by suocontractionf th e triceps uraemuscle uringa tennismatc{Courtesyf Robert . Winquist,M.D.)

CompressionDuring compressive loading, equal and oPPo

site loads are applied toward the surface of thstructure and comPressive stress and strain resuinside the strucfure. Compressive stress can bthought of as many small forces directed into th

F t G . - t lTensileoading.

a a vD-t:tryLt4>TORSION COMBINEDLOADINGof various oading modes.

debonding at the cement lines and pulling out of theosteons (Fig. L-Lz).

Clinic ally, fractures produced by tensile loadingare usually seen in bones with a large ProPortion ofcancellous bone. Examples are fractures of the base ofthe fifth metatarsal adjacent to the attachment of theperoneus brevis tendon and fracfures of the calca-neus adjacent to the attachment of the Achillestendon. Figure 1- L3 shows a tensile fracture throughthe calcaneus; intense contraction of the triceps suraemuscle produced abnormally high tensile loads onthe bone.

nilUU


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FlG.1- t4ComPressiveoading.

surface of the structure. Maximal compressive stressoccurs on a plane PerPendicular to the applied load(Fig. 1,-1,4).Under comPressive loading the structureshortens and widens. At the microscopic level, thefailure mechanism fof bone tissue loaded in comPres-sion is mainly oblique cracking of the osteons (Fig.1- 15).

Ctinically, compression fractures are commonlyfound in the vertebrae, which are subjected to highcompressive loads. These fractures are most oftenseen in the elderly, whose bones weaken as afunction of apng. Figure 1,-1,5 shows the shortetitgand widening that took place in a human vertebrasubjected to a high comPressive load. In a joint,compressivb loading to failure can be produced byabnormally strong contraction of the surroundingmuscles. An example of this effect is Presented inFigure L-L7; bilateral subcapital fractures of thefemoral neck were sustained by u patient undergoingelectroconvulsive therapy; strong confractions of themuscles around the hip joint comPressed the femoralhead against the acetabulum.

F f G . - 1 5Scanning lectron hotomicroraph fa human coftical bone specimentested n compression30x).Arrowsindicateobliquecracking f the os -teons.(Courtesy f Dennis R. Carter,Ph.D. l

BIOMECHANICS F BONE

F f G . -16Compressionractureof a human first umbar vertebra. hevertebra asshortened nd widened.

l l


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l2 B|OMECHAN|CSF TTSSUESND STRUCTURESF THEMUSCULOSKELETALYSTEM

FrG. - t7Bilaterafubcapital ompressionracturesf the emoral ecksna patientwho underwent lectroconvulsiveherapy.

ShearDuring shear loading, a load is applied parallel

to the surface of the structure, and shear stress andstrain result inside the structure. Shear stress can bethought of as many small forces acting on the surfaceof the structure on a plane Parallel to the applied load(Fig. 1-18). A structure subjected to a shear loaddeforms internally in an angular manner; right angleson a plane surface within the strucfure becomeobtuse or acute (Fig. L-L9). Whenever a structure issubjected to tensile or comPressive loading, shearstress is produced. Figure L-20 illustrates angulardeformation in structures subjected to these loadingmodes.

Clinic ally, shear fracfures are most often seen incancellous bone. Examples are fracfures of the femo-ral condyles and the tibial plateau. A shear fracture ofthe tibial plateau is shown in Figure L-zL.

FtG. - t8Shear oading.

BEFORE OADING UNDERSHEAR OADIFfG. - 19When a structures loaded n shear, ines originally t riangleson a pfanesurfacewithin the structurehange horientation, nd the angle becomesobtuseor acute.Tangular deformation ndicatesshear strain. (Adapted rFrankel ndBurstein11970.1

Human adult cortical bone exhibits different vues for ultimate stress under compressive, tensiand shear loading (Fig. L-22). Cortical bone cwithstand greater stress in comPression than tension and greater stress in tension than in she(Reilty and Burstein, 1975).The value for the stiffneof a material under shear loading is known as tshear modulus rather than the modulus of elastici

Bending f.In bendirrg, loads are applied to a structure in

manner that causes it to bend about an axis. Whenbone is loaded in bendin1, it is subjected to combination of tension and comPression. Tens

+t tUNLOADED UNDERTENSILELOADING

UNDERCOMPRESSIVELOADING

FtG. -20Thepresencef shear train n a structureoadedn tensionain compressions indicated y angular eformation.AdapfromFrankel ndBurstein,970.'l

+

t

LUNDERSHEAR OADI

r t t


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looF 150=ct)fr 1oocrFct)

,,:

FfG. -21Shearand compressionractureoF the lateraf ibial plateau.{Courtesyf Steven ubin,M.D.)

FfG. | -2 2Ultimatestress or human adult corticafbone specimens estedin compression, ension,an d shear {average f data from Reillyan d Burstein, 1975l|. haded area indicatesultimate stress orhuman aduft cancellousbone with an apparentdensiryof 35o/otested n tension and compression Carter,1979).

FfG. | -23Cross section of a bone subjected to bending, showingdistribution of stressesaround tne neutral axis. Tensilestresses ct on the Superiorside, and compressiveStressesact on the inferior side. The stressesare highest at theperipheryof the bone an d lowest near he neutrafaxis.Th etensile and compressiveStresses re Unequal because hebone is asymmetrical.

BOMECHANICSF BONE | 3stressesand strains act on one side of the neutral axis,and compressive stressesand strains act on the otherside (Fig. 1,-23); there are no stresses and strainsalong the neutral axis. The magnitude of the stressesis proportional to their distance from the neutral axisof the bone. The farther the stresses are from theneutral axis, the higher their magnitude. Becausebone is asymmetrical, the tensile and comPressivestressesmay not be equal.Bending may be produced by three forces (three-point bending) or four forces (four-point bending)(Fig. 1,-24). Fractures produced by both tyPes ofbending are commonly obsenred clinically, Particu-larly in long bones.Three-point bending takes place when three forcesacting on a structure Produce two equal moments,each being the product of one of the two peripheralforces and its perpendicular distance from the axis ofrotation (the point at which the middle force isapplied) (seeFig. 1,-24A). If loading continues to theyield point, the structure, if homogeneous and sym-metrical, will break at the Point of application of themiddle force.A typical three-Point bending fracture is the "boottop" fracture sustained by skiers. In the "boot toP"fracture shown in Figure 1 -25, one bending momentacted on the proximal tibia as the skier fell fonnrardover the top of the ski boot. An equal mornent,produced by the fixed foot and ski, acted on the distaltibia. As the proximal tibia was bent fonvard, tensilestressesand strains acted on the Posterior side of thebone and compressive stresses and strains acted onthe anterior side. The tibia and fibula fractured at thetop of the boot. Since adult bone is weaker in tensionthan in compression, failure begins on the sidesubjected to tension. Immature bone may fail first incompression, and a buckle fracfure may result on thecompressive side.Four-point bending takes place when two forcecouples acting on a structure produce two equalmoments. A force couPle is formed when two parallelforces of equal magnitude but oPPosite direction areapplied to a structure (see Fig. '1,-248). Because the

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l4 BIOMECHANICSF TISSUESND STRUCTURESF THE MUSCULOSKELFTALYSTEM

rnagnitude of the bending moment is the samethroughout the area between the fwo force couples,the stmcture breaks at its weakest point. An exampleof a four-point bending fracture is shown in FigureI-26. A stiff knee joint was manipulated incorrectlyduring rehabilitation of a patient with a femoralfracture. Duting the manipulation, the posterior kneejoint capsule and tibia formed one force couple andthe femoral head and hip joint capsule formed theother. As a bending moment was applied to thefemur, the bone failed at its weakest point, theorigrnal fracture site.

FrG. -25Lateral oentgenogram f a "boot top" fracture roducedbythree-point ending. Courtesyf Robert . Winquist,M.D.)

FrG. -2+Two ypes f bending..Three-pointending.Four-pointending.

TorsionIn torsion, a load is applied to a structure in a

manner that causes it to twist about an axis, and atorque (or moment) is produced within the structure.When a strucfure is loaded in torsion, shear stresseare distributed over the entire structure. As inbendin1, the magnitude of these stresses is ProPortional to their distance from the neqtral axis (FigL-27). The farther the stresses are from the neutralaxis, the higher their magnitude.

Under torsional loading, maximal shear stresseact on planes parallel and PerPendicular to theneutral axis of the structure. In addition, madmaltensile and compressive sfresses act on a planediagonal to the neutral axis of the structure. FigUre1-28 illustrates these planes in a small segment obone loaded in torsion.

The fracture pattern for bone loaded in torsionsuggests that the bone fails first in shear, with theformation of an initial crack parallel to the neutral axisof the bone. A second crack usually forms along theplane of maximal tensile stress. Such a pattern can beseen in the experimentally produced torsional fracfure of a canine femur shown in Figure L 29.

Combined LoadingAlthough each loading mode has been consid-ered separately,living bone is seldom loaded in onemode only. Loading of bone in vivo is complex for

two principal reasons: bones are constantly subjectedto multiple indeterminate loads, and their geometricstrucfure is irregular. Measurement in vivo of the

A

B


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A BFfG. -26r{ . Duringmanipulation f a stiff kneeduring ractureehabili-tation, our-pointbendingcaused he femur o fracture t itsweakestpoint, he originaf racture ite.B. Lateral oentgeno-gramof the fracturedemur. Counesy f KajLundborg,M.D.)

BIOMECHANICS F BONE T5

SHEARCOMPRESSION

TENSION

FfG. -28Schematicepresentation1'a mall egment f bone oadedntorsion.Maximalshearstressesct on planes parallelandperpendicularo th eneutral xis.Maximal ensife ndcompres-sivestressesct on planesdiagonalo t his axis.

FrG. -2 9Experimentalfyroduced orsional racture f a canine emur.The shortcrack arrow)parallef o the neutralaxisrepresentsshearailure;he ractureneat a30-degreengle o theneutrafaxis epresentshe pfaneof maximalensife tress.

strains on the anteromedial surface of a human adulttibia during walking and jogstg demonstrated thecomplexity of the loading patterns during thesecommon physiologic activities (Lanyon et dl., 1975).Stress values calculated from these strain measure-ments by Carter (1978) showed that during normalwalking the stresses were comPressive during heelstrike, tensile during the stance phase, and againcompressive during push-off (F ig. 1-30A). Values forshear stresswere relatively high in the later portion ofthe gait cycle, denoting significant torsional loaditg.This torsional loading was associated with externalrotation of the tibia during stance and push-off.During jogpng the stress pattern was quite differ-ent (Fig. 1-308). The compressive stresspredomineit-ing at toe strike was followed by high tensile stressduring push-off. The shear stress was low through-

FfG. -2 7Crosssectionof a ryfinder oaded in torsion,showingdistributionof shearstresses round the neutral axis.magnitudeof the stressess highestat the periphery fryf nderand owestnear he neutral xis.

theThethe


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WALKING (1.4 m/sec)STRESS_- TENSTLE-. - @UPRESSI\IE- SIGAR (EXTEFlll ,ni

at i la I \ .o t

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I t rI t-I tI to

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i'.. rt al ' . . 1| --jl al lI i"..

. a| \ 4 . .t \t tai t'-\ /

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l 6432

EIOMECI{ANIC5CF NSSUESND SIRUCTURESF T}JEMUSCULOSKELEI'ALYSTEM1 2

G.o - 13EoutF1CT'

RNAL ROTATION}

TS TS.TO BFrG. -3011. Calculated ucses on the ancromedialconex of a hurnan adult tibia durirg wdking.HS-heel strike:FF-foot llat;FlO-heel-ofr TO-toeofr S-virq. {After .arDon t al..1975; ounesy f DennisR C-aner,h.D.lB. Calculated resses n fte anteromedialortexof anadufthumantibb during qgirg.TS-toe srike;TO-toeotr hfter Lanlonet al- 1975;courtesy f DennisR.Caner,Ph.D.l t

out the stride, denoting minimal torsional loadingproduced by slight external and internal rotation ofthe tibia in an alternating pattern. The increase inspeed from slorv walking to jogpng increased boththe stress and the strain on the tibia (I-anyon et al.,L975).This increa* in strain with greater speed wasconfirmed in studies of locomotion in sheep, whichdemonstrated a fivefold increase n strain values fromslow walking to fast trotting (Lanyon and Bourn,1979).Clinical exarrrination of fracture patterns indicatesthat few fractures are producd by one loading modeor even by hvo modes. lndeed, most frachrres areproduced Ly " cornbination of several oading modes.

INFLUENCEOF MUSCLEACTIVIW ONSTRESS ISTRIBUTIONN BONEWhen bone is loaded in vivo, contraction of themusdes attached to the bone alters the stressdistri-bution in the bone. This musde contractiondecreases

JOGGING (22 m/sec)

STRESS. -IE}ISiLE

-.- @UFRESSIVE- $An GXTERI{AL ROTATIOiO- slGAlR (INTERNAL ROTATION)

or eliminates tensile sress on the bone by prodcompressive stress that neutralizes it either paor totally.The effect of muscle contraction can be illusin a tibia zubjected to three-point bending. 1-31A represents the l"g of a skier who is forward, zubjecting the tibia to a bending moHigh tensile stress is produced on dre poaspect of the Hbda,and high compressive streon the anterior aspect. Contraction of thesurae muscle produces great comPressive strthe posterior aspect (Fig. 1-3lB), neutralizt4great tensile sfress and therebv protecting thfrom failnre in tension. ThiS musde contractioresult in higher comprressivestress on the astrrface of the tibia. Adult bone can usually withthis stress,but imrnahue bone, which is weakefail in compression.Musde contraction produces a similar effecthip joint (Fig. 1-32). During locomotion, bemoments aneapplied to the femoral neck and stress s produced on the superior cortex-Contr

e 6o-EE4UJEF(t, 2HS FFHO FIO STO

A


31/43

t

ABFfG. -3 |A. Disribmion of cornpressir'eaN tersite $resses n a dbiasubleced to firee-point bending. 8. Conracion of trrericepssuraemuscleproduceshigh cqnpressirrre rcsson trtepo*erioraspecLneuualang dre hgh tensilestress.

FtG. _32stress rsrnbuuonn a fernoral recksubjecredo bending.whenine -oluteusnecrusmuscre s refaxedfopl. tensile tress cE onine sucerlorcorTex nd compressive ress acE on dre inferiorcciex' conc'actonof drismuscle bonomfneuralizesrle ensile: l ieSS.

EfoMECFrN|CSOF BONEof the gluteus medius musde produces comprestress that neutralizes this tensile stress, with theresult that neither compressive nor tensile stresson the superior cortex. Thus, the uruscle contracallows the femoral neck to zustain higt er loadswould otherwise be possible-

RATEDEPENDENCY N BONEBecause bone is a viscoetasfic material,biomechanical behavior varies with the rate at wthe bone is loaded (Le., the rate at rryirictr he loaapplied and removed). Bone is stiffer and sustaihigher load to failure when loads are appliedhigher rates. Bone also stores morre energy befailure at higho loading rates, provided tnat thrates are within the physiologic range.The loaddeformation curves in Figure l-33 sthe difference in the mechanical properties of pacanine tibiae tested in vitro at a high and a veryloading_ ate, 0.01.second and 200 seconds, restively (Sammarcoet aI., l97L)- The amount of enistored before failure approximately doubled athigher loading rate. The load to failure almdoubld, but the deformation to failure didchange significantly. The bone was about sa% stat the high"r speed.The loading rate is dinically significant becausinfluences both the fracture pattern and the auroof soft tissue damage at fnacture. When a b

fracfures, the stored energy is released. At aloading rate, the ener6y can dissipate throughformation of a single crack; the bone and soft tiss

FfG. r -33Ratedependencyof bone is demonsrrated n paireC caubiae estedat a high arrt a low foad,ng are-The oad ro faand he energystored o faifureafrpst doubledat d'rehigh rlAdapted tom Sammarco r al., lg7l.l

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LOADINGRATEO.O1 EC

DEFORTATION


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T8 BIOMECHANICSF NSSUESND STRUCIUREsF THEMUSCULOSKELETALYSTEM

remain relatively intact, and there is little or nodisplacement of the bone fragments. At a highloading rate, however, the greater energy storedcannot dissipate rapidly enough through a singlecrack, and comminution of bone and extensive softtissue damage result. Figure 7-34 shows a humantibia tested in vitro in torsion at a high loadin g rate;numerous bone fragments were produced, and dis-placement of the fragments was pronounced.

FrG. -35Tensile trainvalues rom a humanadult tibia during ogging{Lanyon t al., 19751avebeenpfottedon a stress-strainurueforbonesamplesested o failuren tension. smallproponionof the otalenergy torage apacity f thebone sutilize duringthisnormalphysiologicctiviiy.

FtG. -34Human ibia experimentaflyested ofailuren torsion ta high oading ateDisplacement f the numerous ragmentswas pronounced.

Clinically, bone fractures fall into three generalcategories asedon the amount of energy releasedatfracture: low-energf high-energy, and very high-energy. A low-enerry fracture is exemplified by thesimple torsionalski fracture; ahigh-energyfracture soften sustained during automobile accidents; and avery high- energy fracture is produded by veryhigh- muzzle velocity gunshot.only a smallproportion of the total energy storagecapacity of bone is utilized during normal activity.Figure 1-35 illustrates ust how little of this capacityis used during the normal physiologic activity ofjogsrg.

FATIGUEOF BONE UNDERREPETITIVEOADINGBone racturescan be produced by u single oadthat exceedsthe ultimate strength of the bone orby repeatedapplications of a load of lower magni-tude. A fracture causedby repeatedapplications ofa lower load is called a fatigue fracture and is Vpi-cally produced either by few repetitions of a highload or by many repetitions of a relatively normalload.The interpluy of load and repetition for anymaterial can be plotted on a fatigue curye (Fig. l-g1).For some materials (somemetals, for example), thefatigue curve is asymptotic, indicating that if the load

U)@utEFa

PHYSIOLOGIC

STRAIN


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BIOMECFTANICSF EONEfracture in the lower extremities is outlinedfollowing schema:

ooJ

FtG. -lE--The inrerplayof load dfr repetidm is represen*ct qt a faog*CUn/.

STRENUOUS XERCISE

IFATIGUED IIUSCLE^/- \'\

Loss oF sHo{ }1.RED GAITSOREING.CIPACITY /\ /ABNORMALOADINGILTEREDSTRESS

/OISTRIBUTIONs kepl below a certain level theoretiolly, trematerial will remain intact, no matter how manyrepetitions. For bone tested in vito, the curve is notasymPtotic- When bone is s,tbiected to repetitive lowloads, it may sustain fatigue microfractires (C-arterand Hayes, l9T7a). Testing of bone in vitro alsoreveals that bone fatigues rapi


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20 BIOMECI.IANIG OF I65UE5 AND STRUCTURESF fiE MUSCT'LOSKELETATIsIEM

2x2ll

moment of inertia is the width (B) multiplied by thecube of the h.ight (H1 dividedby 12:B . H 3t2

Because of its large area moment of inertia, beasr IIIcan wiftstand four times more load in bending thanbearn I-A third facbr, the length of the bone, influencsthe strength and stiffness in bending. The longer thebone is, the greater the magnitude of the bendingmoment caused by the application of a force. In a

BEAM A

FfG. | -37Three beams of equal area brx diffeshapessubjecred o bending.Fs recangooss secdors. fie area moment of inerucahrlarcd ry fie formuraB: $ raheret 2tfn widtrt aN H. trte height The amqnent of ineniafor beamI is elZ: for betf, lUlZ: aN for beam ltl. 64112.Adafiorn FrankefaN Bursrein l970-t

1x4til

rectangutar stnrcture, the magnitude of the stresproduced at the point of application of the bendimoment is proportional to the length of the stmcttrFigure l-38 dqplcts the forces acting on two beawift the same width and height but different lengthbeam B is twice as long as bearn A. The bendimoment for the longer beasr is twice ilrat for tshorter bearu coruiequently, the stress magnitudttuoughout the beam is twice as high.Becauseof their leogth, the long bones of the sketon are subjected to high bending moments and,high teruile and compressive stresses.Their tubu

FlG. | -39Eearn B is rwice as fong as beam Asr.rsEins wice fie berxling momenl Henfie $ress rnagniude firo4hour beam Btwice as high. fAdapred from FrankelBur$ein. 1970.1

STRESSMAGNITUDES

BEAM B-.L-.-JI STRESSMAGNTTUDE 2S


35/43

shape gives them the ability to resist bending mo-ments in all directions. Theseboneshavea largeareamoment of inertia becausemuch of the bone tissue sdistributed at a distance from the neutral a)ds.The factors that affect bone strength and stiffnessin torsion are the same ones that operate n bendingthe cross-sectionalarea and the distribution of boneHssuearound a neutrial axis. The quantity that takesinto account these two factors in torsiornl loading isthe polar moment of inertia. The larger the polarmoment of inertia is, the stronger and sfitrd thebone. 'Figure 1-39 shows distal and proximal cnosssections of a tibia subjected to torsional loading.Although the proximal section has a slightly surallerbony area than does the distal section, it tras a muchhigher polar moment of inertia becausemuch of thebone tissue is distributed at a distance from theneutral ilds. The distal section, while it has a largerbony area, is subjected to much high"r shear stressbecausemuch of the bone tissue is distributed closeto the neutral axis. The magnifude of the shear stressin the distal section is approximately double that inthe proximal section. Clinically, torsiornl fractrrres ofthe tibia conrmonly occrr distally.when bone begins to heal after ftactnre, bloodvesselsand connective tissue from the periosteusrmigrate inlo the region of the fracture, forrting a cuffof dense fibrous tissue, or callus, anound the fr"ct rrusite, which stabiti-es that area (Fig. l-40A). Thecallus significantly increases the ate and polarmoments of inertia, thereby increasing the strengthand stiffness of the bone in bending and torslonduring the healing period. As the fracture heals and,h: bone gradually regains its norrnal strength, thecallus cuff is progressively resorbed and th" bonereturns to as near its normal size and shape aspossible Fig. l-4OB).certain surgical procedures produce defects thatgreatly weaken the bone, partiarlarty in tonsion.These defects fall into two categories: those whoselength is less than the diameteiof the bone (stressraisers)and those whose length exceedsthe bonediarneter open section defects).

o't"'I,Til:T:HllH::HffifiH il*trength is reduced because the stresses imposedduring loading_ re prevented from beirg distributeds1'ehlt throufhout the bone and instead becomeconcentratedaround the defect. This defect is anaL.Bouso a rock in a stream, which diverts the water,producing high water turburence around it (Fig.

EIOMECFdAT'.IICSF BONE 2

FfG. t -39Disribtttion of sfiear stress in two cross secrionsof a ribsubjeced to tqsirnal loadlng. The proximaf section (Al frashigher morrfem d Frnia dran does fre disal secion (BbecausemoreWry nEterial is distributedaway from trre netrraxis.fAdapted un frankel and Bursrein, 971.l

1-41). The wealcening effect of a stress raiser ipartictrlarly marked under torsional loading the totadecrease n bone strength in this loading mode careach60Vo.Bnrstein and associates(1972)showed the effect ostress raisers pTdrced by screws and by emptscrew holes on the eneqty storage capacity of rabbbones tested in torsion at a high loading rate. Thimmediate eftct of drilling a hole and insertingscnew n a rabbit femnr was a74vo decrease n energstoragecapacity. After 8 weel$, the stress raiser effecproduced W the scrervrsand by the holes withoutscrrewshad disappeared completely becausethe bonhad resrodele& bone had been laid down around thescrews to stabilize them, and the empty screw holehad been fiUed in with bone. In femora from whichthe screws had been removed immediately befortesting howetrer, the energy storage capacity of thebone decreased by 50%, mainly because the bonetissue arund the scnew sustained microdamageduring screw removal (Fig. !-42).An open section defect is a discontinuity in thebone caused by s,rrgrcal remorral of a piece of bonelonger than the bone's diameter (for example, by thectrtting of a slot during a bone biopsy). Because heouter surfaceof the bone cross section is no longecontinuous, the bone's abitity to resist loads isdtered, partiorlarly in torsion.

V(-V.A.-.F v\-o'rl\\-/\B


36/43

22 BIOMECHANICS F NSSUESND STRUCTURESF THE MUSCULOSKELF|ALYSTEM

FfG. | -4 1Stress oncentrationaround a defecgsuch a defect sanalogousto a rock in a stream.

In a normal bone subjected to torsion, the shearstress is distributed throughout the bone and acts toresist the torque. This stress pattern is illustrated inthe cross section of a long bone shown in Figure1-43A. (A cross section with a continuous outer

FtG. -40A, Earlycallus ormation n a femoraf racture ixed with anintramedullaryaif.B, Ninemonthsafter njury he fracture asheafed nd mostof the callus uf fhasbeen esorbed.Counesyof Robert . WinquistM.D.)

0 1 2 3 4 5 6 7 8 WEEKSFtG. -42Effect f screwsandof emptyscrewhofeson theenergy toragecapacity f rabbit emora.The energystorage or experimentafanimals sexpresseds a percentagef thetotal energy toragecapacityfor controf animals. When screws were removedimmediately efore esting, he energystoragecapacityde-creased y 50o/o.AdaptedromBurstein t af., 1972.)

surface is called a closed section.) In a bone with anopen section defect, only the shear stress at theperiphery of the bone resists the applied torque. Asthe shear stress encounters the discontinuity , it isforced to change direction (Fig. L-438). Through-

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37/43

,nrN\t'Y'//'rr/(

_ _ : I\ t

FlG. | -4 5A patient sustained a tibialproduced open section defectafter operation.

BIOMECHANICSF BONE 23

fracture hrough a surgicallywhen she rippeda few weeks

BFtG. -43Stress attern n an open and closedsectionunder orsionalloading. . In the cfosed ection, ll he shear tressesistsheapplied orque.B. fn the opensection, nf y he shear tress tthe periphery f the bone resistshe applied orgue. AdaptedfromFrankel ndBurstein,970.1

out the interior of the bone, the stress runs parallel toto the applied torqu, and the amount of bone tissueresisting the load is greatly decreased.In torsion tests in vitro of human adult tibiae, anopen section defect reduced the load to failure andenergy storage to failure by as much as 90%. Thedeformation to failure was diminished by about 70Vo(Frankel and Burstein, 1970) (FiS. 1-M).

Clinically, surgical removal of a piece of bone cangreatly wdaken the bone, particularly in torsion.Figure 7-45 is a roentgenogram of a tibia from whicha graft was removed for use in an arthrodesis of thehip. A few weeks after operation, the patient trippedwhile twisting in an attempt to rescue the Christmasham from toppling onto the floor, and the bonefractured through the defect.

FtG. | -+ 4Load-deformation curves for human adult tibiae tested in vitrounder torsional oading.The controlcurve epresents tibia withno defecg he open sectioncuryerepresents tibia with an opensection defect. (Adapted rom Frankeland Burstein,1970.1

oo

BONE REMODELINGBone has the ability to rernodel, by altering its

size, shape, and structure, to meet the mechanicaldemands placed on it. This phenomenon, in whichbone gains or loses cancellous and/or cortical bone inresponse to the level of stress sustained, is summa-rized as Wolff 's law, which states that bone is laiddown where needed and resorbed where not needed(Wolff , 7892).If, because of partial or total imm obllization, boneis not subjected to the usual mechanical stresses,periosteal and subperiosteal bone is resorbed (Jenkinsand Cochrdn, 7969) and strength and stiffness de-crease. This decrease in bone strength and stiffnesswas shown by Kazarian and Von Gierke (1969), whoirnmobilized Rhesus monkeys in full-body casts for 60days. Subsequent compressive testing in vitro of thevertebrae from the immobilized monkeys and fromcontrols showed up to a threefold decrease in load to

CONTROL

DEFORMATION


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24 BIOMECHANICSF TISSUESND STRUCTURESF IHE MUSCULOSKELETALYSTEM

oofractureadheared.hebone nderh" il#fiJ$,:Jff: l",: 3:l^?-ff]: l r:- q-""i"dteornd hediameterfFudiaphysisu.u*Lryi:ffiHit*:' *fj"::'^": : :*-'l :! " ":;i,,.uai mreatlydecreaesbones rength,parricular; ;f i:Tilg#i. 1o,,1:o-1,^ l#ol."Jt" ;F; l ;;ioments of inertia. A 2AVodecrease n bone diamerilT#iH"',i"":":ffi1'1,1suggest hat rigid plates should be removea short{t:::^[::yl:,lf heared lJ berorei; bonehamarkedlydiminishedn size.sucha ,cecr";;;ffi:

:i:" *_i:l"l1m::Tl_"Tud bysecondarysteopsis,which urther#eakensnu-;;;;i6rrnr:i[:;1980) 1vr '*Lrtr (t L dr'An imprant may cause bone hypurfrophy at itattachment sites el exampreof bohe hypertrophyaround screws s illusfrated in Figure r-4g. A naplate was applied to a femoral neck fracture, and thebonehyperirophied around the screws n response othe increased oad at these sites Hrpertrophy mayalso result if bone is repeatedry ,"u;".ted to highmechanical stresseswithin the normal physiologicrange.Hypertrophy ofnormal adult bone n responsto strenuousexerciiehasbeenobserved Jones t ar.7977;Dal6n and Olsson, I9T4; Huddleiton et aI.7980)'ashas an increasen bonedensity (NilssonandWestlin, 1g7I). ---'d.'-1-potitive correlation exists between bone massand body weight. A greater body weight has beenassociated ith a argei bot " mass Exne"r t ar . i,g7g)conversely,a prolorigedcondition of weightlessnesssuch as that experienced,curing space travel, has

FtG. _4 7AnteroposteriorIAt and ateraltBf roenrge ograms f an ulnaafterplateremoval how a decreasedone diameter ue toesorption f the bone underthe plate.cancelf zatian f thecortexand he presence f screwhores rsoweaken he bone.{Courtesyf MarcMartens,M.D.f

Ffc. | _+6Load-deformationcuruesorvertebralegmenE5 o L7 fromnormal and immoblizedRhesusmonkeys.fAdapted romKazarianndVonGierke,.969.)

failure uld energy sjolage capaciv in the vertebraethat had been immobilizEd, ,,iffr,um was also signif_icantly decreasedFig. I_4'6).An implant that remainsfirmry attached o a boneafter a fracfure has healed may arso diminish thestrength and stiffnessof the bone. In the caseof aplate fixed to the bonewith screws, he plateand thebone share he roadl'.proporuons det"r*i'ed by thegeometryand materialp-roperties f eachstructure.Alarge plate, carryilg high t,ouJr,unroads he bone toa great extenu the bone then atrophies n response othis diminished load. (The bone may hypertrophy atthe bone-screw interface in an attempt to reducemicromotion of the screws.)Bone resorption under a prate is ilrustrated inFigure 1-47 A compressionplate made of a material

IMMOBILIZED

DEFORMATTON


39/43

BloMECHANlcsF BONE 25been found to resultweight-bearirg bonesGazenkoet dl., 1981).

in a decreased bone mass in(Rambaut and |ohnston, 1979;

DEGENERATIVECI.I,ANGESN BONEASSOCTATEDWITH AGINGA progressive loss of bone density has beenobserved aJ part of the normal aging Process. Thelongitudinal trabeculae become thinner, and some of

the transverse trabeculae are resorbed (Siffert andLevy, 1981) (Fig. I-49). The result is marked reduc-tionin the amount of cancellous bone and thinning ofcortical bone. This decrease in the total amount ofbone tissue and the slight decrease in the size of thebone reduce bone strength and stiffness.Stress-strain curves for specimens from humanadult tibiae of two widely differing ages tested intension are shown in Figure 1-50. The ultimate stresswas approximately the same for the young and theold bone. The old bone specimen could withstandonly half the strain that the young bone could,indicatitg greater brittleness and a reduction inenergy storage caPacitY.

FfG. | -+ 8 ' 'Roentgenogram f a fractured emoralneck o which a nail platewas applied. Loadsare transmitted rom the plate io the bonevi a the screws.Bone has been laid down around the screws obear hese oads.

FtG. -49Vertebralross ectionsromautopsy pecimensfyoung Af and old Bf boneshowa markedreduction n cancellous one in the latter. Reprinted ith permissionrom Nordin,B.E.C.:MetabolicBoneand StoneDisease. dinburgh, hurchill ivingstone,973.1. Bone eductionwith aging s schematicallyepicted. s normalbone (top) ssubjectedo absorptionshadedareafduring he agingprocess,he ongitudinalrabeculaeecome hinner ndsome ransversetrabeculae isappearbottom). Adaptedrom Siffert nd Levy,1981.)

j'ffiqffiffilu4ltnnB


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26 BIOMECI{ANICSFNSSUESND STRUCruREFTHEMTSCULOSKEI..ETALYsTEM

FtG. | -50stress-srain cun es for sampfg of aduft lrurnan dbbe of nnovudelydifferingages ested n tersion. (Adapred iom Br.rrsreintal., 1976.1

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SUMII/IARY1. Bone is a two-phas composite material, inor-ganic mineral salts b.irg one phase and anorganic matrix of collagen and ground strbstancrethe other. The inoanic component makes bonehard and rigtd, whereas the oqganic componentgives bone its flexibility and resilience.2- Microscopic"fly, the fundarnental stmctural unitof bone is the ost@n, or haversian qlsteul,composed of concntric layers of mineralizedmatrix srurounding a central canal containingblood vessels and nerve f

Margareta Nordin Basic Biomechanics Musculoskeletal System

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