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Biomechanics of Joints,Ligaments and Tendons.

Course Text: Hamill & Knutzen (some inchapter 2 and 3, but ligament and tendonmechanics is not well covered in the text)Nordin & Frankel (Ch 2 & 3) or Hall (Ch. 5)

Hippocrates (460-377 B.C.)

“All parts of the body which have afunction, if used in moderation andexercises in labours to which each areaccustomed, thereby become healthy andwell-developed: but if unused and left idle,they become liable to disease, defectivein growth, and age quickly. This isespecially the case with joints andligaments, if one doe not use them.”

LeVay 1990. p30.

Joints

Review architecture of cartilaginous joints(specifically the vertebrae). We will lookat these again.

Review architecture of synovial joints. This will help with understanding the

structures we are discussing. Theanatomy of the synovial joint will not bespecifically examined.

Articular Cartilage

The joints of a mechanical device must beproperly lubricated. Articluar cartilage, adense white connective tissue coats (1-7mm thick) the ends of bones articulating atsynovial joints. It serves two purposes:

1: Spreads the load. Cartilage can reduce themaximum contact stress by 50% or more.

2: Reduces friction during movement.

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Articular cartilage has a combination of elastic andviscoeleastic properties. As load is applied,deformation increase with time, first in an elasticfashion, then with a slow creep. With the removal ofthe load there is an elastic recoil and the a slowrecovery to the base line.

Deform (strain)tissue by fixedamount

Load tissuewith constantstress (F/A).

Articular Fibrocartilage The function of fibrocartilage includes: Absorption and distribution of loads Improvement of the fit of articulating

surfaces. Increase in joint stability. Protection of the periphery of the

articulation. Lubrication.

Knee Menisci Stress distribution in anormal knee and in a kneewith the menisci removed.With the menisci removedthe contact area is limitedto the centre of the tibialplateau hence increasingthe stress.

In the average male theknees support 88% of thebody weight.

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Articular Connective Tissue Tendons and ligaments are much less extensible

than muscle and do not have the ability to contract. Made primarily of collagen fibres (with some elastin

fibres) they will return to their normal lengths whenunloaded.

However, there is an elastic limit (bone lecture) afterwhich the tendon or ligament will not return toresting length (region of plasticity - 2nd degreestrain). This will take time for the body to repair.

If the ligament completely fails (3rd degree strain)this can only be restored by surgery.

LigamentComposition

Fibre Arrangement

Tendon

Ligament

Skin

Ligament Crimp

Unloaded Ligament Loaded Ligament

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Collagen Fibres

Stress

Strain (percent)50 10

Collagen Fibres

Deformation Rangesmall 6 - 8%

Strength50% of that of cortical bone tested in

tension

Young’s ModulusYoung’s Modulus is the ratio of:

tensile stress / tensile strain

Young’s TensileModulus Strength

Tendon 2 x 109 1 x 108

Bone 1.7 x 1010 1.8 x 108

Carbon Steel 2 x 1011 3 x 109

Soft rubber c.106

Fibre Arrangement

Tendon

Ligament

Skin

Elastic Fibres(elastin and microfibrils)

Stress

Strain (percent)1000 200

Elastin Fibres

Deformation Range large >100%

(150% Fawcett 1986)

Strength weak

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Joint Stability

Stability to resist dislocation and damageto the ligaments, tendons and musclessurrounding a joint.

The shape of the articulating surfaces isimportant.

Some joints are obviously not designed tobe as stable as others as range of motioncan be compromised in a very stable joint.

The knee is agood exampleof a joint wherethe articulatingsurfaces arenot shaped likeeach other(although themenisciincreases thecontact area).

Tendons & Ligaments

Tendons and ligaments are predominantlymade up of collagen.

Hence their stress / strain relationship willmirror that of collagen.

The less-structured orientation of thecollagen in the ligaments will provideadditional elastic properties (directional)compared to tendons.

Load-elongation curve for rabbittendon tested to failure in tension

Load-Elongation Graph for PrimateLigament (Noyes 1977)

Load

Progressive failure of the anterior cruciate ligaments(cadaver knee tested in tension to failure at a physiologicstrain rate, Noyes 1977)

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Curve from previous slide divided into threeregions correlating with clinical findings

Repetitive stress causes failure at lower load thanthat required to cause failure in a single application.As a ligament undergoes cyclic loading it relaxationbehaviour results in continuously decreasing stress(protecting ligament from fatigue failure)……..

Hysteresisduring cyclicloading of aknee ligament.

……therefore, there is a time dependantincrease in elongation when a viscoelasticmaterial is subjected to a repetitive constantstress (cyclic creep).

Schematic representation of cyclic creepin the MCL of the knee

Con

trol

100% 100%

Imm

obiliz

ed 8

wee

ks

Rec

ondi

tione

d 5

mon

ths

Rec

ondi

tione

d 12

mon

ths

61%

79%

91%

50%

% of max.value

Max. load tofailure forprimate anteriorcruciateligamentsNoyes 1977 Maximum load to failure

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LigamentScar

0 weekspost

injury

LigamentScar

6 weekspost

injury

LigamentScar

14 weekspost

injury

Quantity not Quality? Eighteen weeks of remobilization were

necessary to reverse the detrimental effects ofa six-week immobilization on the structuralproperties of ligaments (Laros et al., 1971).

Structural properties nearly normal butmechanical properties of healed ligamentsalmost always remain inferior when comparedto normal tissue.

This is possible as the tissue accumulatesmass to compensate for inferior tissue quality.

Some areas of healed MCL were up to 2.5times larger than controls (Ohland et al., 1991)

Healed MCL exhibitsinferior mechanicalproperties after injury(intact state). Note thegraph opposite is a loadelongation curve for aMCL specimen

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This graph is a stress-strain curve for thefemur-MCL-tibiacomplex. Therefore thisgraph showsfundamental tissueproperties compared tothe previous specimenload-deformation curve.

Biomechanics of the Knee

Patellofemoral jointreaction force (P) isformed by the vectorsum of the force vectorof the quadricepstendon (FQ) and theforce vector of thepatellar tendon (FP).

Fc

FQ

Fc

FT

FQ

FT

As the knee flexes more force is required tomaintain balance and the compressive forceincreases due to tendon alignment (vectorresolution).

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Fc

FQ

Fc

FT

FQ

FT

Calculate FC if the angle between FQ and FT is90o, if the force in both tendons is 2,000 N.

Cosine LawR2 = FQ

2 + FP2 – 2(FQ)(FP)cosθ

R2= 20002 + 20002 – 2(20002)cos90o

R2 = 8,000,000 - (8,000,000)(0)

R2 = 8,000,000 – 0

R = √8,000,000 = 2,828 N

See the Problem Set Booklet foran example of vector resolutionfor the knee.

Full Squat

Crease at hip(a) is belowknee. So thighstend to justbreak belowparallel

Seated Knee Extension

If the hamstrings do not forcefully contract, the dominantquadriceps force acting on the knee will create considerableshear (red vector component).

Pelvis tends to rotate backfurthering the relaxation ofthe hamstrings

Relaxed Hamstring

Force on TibialTuberosity

shearingcomponent

Patella Tendon Rupture.Force in patella tendon λ 14.5 kN(17.5 x body weight)

Load weight 175 kgLoad weight 175 kg

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Knee Ligament Function Anterior Cruciate Ligament Injury

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PosteriorCruciateLigamentInjury

Joint Flexibility - Range of Motion Properties of soft connective tissues (collagen

and elastin) are crucial. Extensibility of muscles Elasticity of the articular capsules & fluidity of

discs Extensibility of the longitudinal ligaments Anatomical architecture of the articulations Resistance of the surrounding tissues. Collagen shortens in the absence of tension

but shows plasticity. Everyday movementkeeps ROM acceptable, but specializedstretching routines also help.