Engineering aspects of the human knee joint : workshop, June 5th, 1978, Eindhoven

Engineering aspects of the human knee joint : workshop, June

5th, 1978, Eindhoven

Citation for published version (APA):

Brouwers, A., & Huiskes, H. W. J. (1978). Engineering aspects of the human knee joint : workshop, June 5th, 1978, Eindhoven. (BMGT; Vol. 78.300). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1978

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B M G r 7 8 . 3 0 0

E n g i n e e r i n g a s p e c t s o f the human knee joint

Workshop Eindhoven' J u n e 5 t h , 1 9 7 8

E I N D H O V E N U N I _{V E R S I T Y O F T E C H N O L O G Y}

Preface

This report describes a workshop on the engineering aspects of the knee joint, organised at the Eindhoven University of Technology on June 3th, 1978.

Such a workshop was proposed at a meeting of researchers in the bio engineering field, he1t at Utrecht on February 17th, 1977.

It was realised on the occasion of a visit by prof. Van C. Mow, Ph. ,D., widely acknowledged as an expert on biomechanics, especially on joint

lubrication and rheology of articular cartilage.

Virtually all Dutch scientists working on the biomechanics of the knee joint or its components participated in this workshop. It turned out to be a fruitful exchange of experiences worthwhile to repeat everyone cr

two years.

This workshop was focused mainly on the fundamental knowledge about the

knee joint. It was considered worthwhile to ~structuralizea next one

more from the clinical point of view, thus emphasizing more the application aspects of these engineering activities. The Twente University of

Technology was thought to be a good place for the realization of s~ch a

workshop.

This report, which contains abstracts about the presented research projects is ment to stimulate a broad communication in this field. The introductory chapter covers some basic aspects and viewpoints considered useful for such an interdisciplinary communication.

A survey is ;a1so given of the present topical research activities '~ithin

the Netherlands.

The variety in disciplines, the communication especially between physicians

and engineers, all this required special attention and good care of the

chairman. Here Rik Huiskes did a good job, contributing a great deal to the success of this day.

We are indebted to the participating scientists, students and others

interested for their clear presentation of information and their contribution to a mutual understanding.

Various typing and administrative aspects were attended by Mieke Barts and Marlies Lutkie.

A. Brouwers

Contact Group biomedical and health technology.

Eindhoven University of Technolo8Y, The Netherlands.

Contents

-2-BMCT 78.300

I. List of participants. 3

2. Introduction to "Engineering Aspects of the Human Knee Joint" 4

R. Huiskes, dept. Orthopaedic Surgery, University of Nijmegen.

3. "Biphasic Rheological Properties of Articular Cartilage". 9

V.C. Mow, Rensselaer Polytechnic lnst., Troy (N.Y.) U.S.A.

4. "The role of the synovial fluid in joint lubrication". 10

G. de Keizer, dept. Surgery, Maria Hospital, Tilburg.

5. "An asymptotic theory for thin layers of articular cartilage 12

with application to the knee joint".

H. Moes; Group Tribology, dept. Mech. Eng., University of Technology Twente.

6. "Measurement and mathematical description of the geometry of 13

the knee joint articular surfaces" •

.1. Wismans and P. Struben, Dept. Applied Mechanics, University

of Technology Eindhoven (presently: lnstituut voor Wegtransport TNO) and lcacia Hospital, Rotterdam.

7. "Aspects of the mechanical function of the menisci, experiments 15

on cadaveric pig knee joints".

P. Jaspers"A. de Lange, R. Huiskes and Tb.J.G. van Rens,

Dept. Orthopaedic Surgery, University of Nijmegen.

8. "The lubrication Mechanism for synovial Joints". 19

V.C. Mow, Rensselaer Polyt. lnst., Troy (N.Y.), U.S.A.

9. "The anatomical structure of the cruciate ligaments". 20

R. van Dijk, Dept. Orthop. Surgery, University of Nijmegen.

10. "Engineering aspects of the human knee joint". 22

A. Huson, Lab. Anatomy and Embryology, University of Leiden.

11. "A three-dimensional mathematical model of the human knee joint". 24

J. Wismans, F.E. Veldpaus, University of Technology Eindhoven.

12. "A Roentgen-stereophotogrammetric measurement system for three- 26

dimensional joint kinematics (Selvik-system)".

R. Huiskes, G. Selvik, Dept. of Orthop. Surgery, University of

List of participants

name address tel.

Akkermans, L.M.A. Brouwers, A. van Campen, D.H. Dakshina Murthy, H.B. van Dijk, R. Erens, J.M.N. Groot, G.S. Hamer, A.J.M. Huiskes, R. Huson, A. Jaspers, P. de Keizer, G. de Lange, A. Ligterink, D.L. Meijer, H.J.M. Moes, H. Mow, V.C. Poolla Murti Rappange, L. van Rens, Th.J.G Sauren, A.A.H.J. Scholten, P. Schouten, M. Snij ders, C. J. Spoor, C.W. Stalnaker, R. Struben, P.J. Veldpaus, F.E. Weidema, W.F. Wismans, J.

Academisch Ziekenhuis Utrecht Experimentele Heelkunde

TH Eindhoven

THTwente, afd. WB TH Delft (Tribologie)

Radboud Ziekenhuis, KUN, afd. Orthopaedie

TH Eindhoven OPG, Utrecht TH Eindhoven

Radboud Ziekenhuis, KUN, afd. Orthopaedie

RU Leiden, afd. Anatomie Radboud Ziekenhuis, KUN, afd. Orthopaedie

Maria Ziekenhuis, Tilburg Radboud Ziekenhuis, KUN, afd. Orthopaedie

TH Twente

TH Delft (Tribologie) TH Twente

RPI, Troy (N.Y.) U.S.A. Ruhr Univ. Bochum

4630 Bochum - Querenburg

West-Germany TH Eindhoven

Radboud Ziekenhuis, KUN, afd. Orthopaedie

TH Eindhoven TH Eindhoven TH Eindhoven TH Eindhoven

RU Leiden, afd. Anatomie

TNO, University of Michigan, USA

Ikazia Ziekenhuis Rotterd~1

RU Leiden TH Eindhoven

Ziekenhuis St. Annadal, RULg, Maastricht

Instituut voor Wegtransport TNQ

030 - 372251 040 - 475375 053 - 894189 015 - 786676 08819 - 3833 040 - 475009 030 - 938841 040 - 475352 080 - 513974 071 - 148333 080 - 514490 013 - 333600 080 - 514476 053 - 894008 053 - 894243 040 - 475352 080 - 514473 040 - 475385 040 - 475008 040 - 475181 040 - 475005 071 - 148333 010 - 201145 040 - 475385 043 - 866666 OJ5 - 569330

-4-2. Introduction to Engineering Aspects of the Human Knee Joint

R. Huiskes: Lab. for Experimental Orthopaedics, Dept. of Orthopaedic Surgery, University of Nijmegen, The Netherlands.

For those who only know the human body as something they carry along

and only know medicin from being a patient, it may sound pecu~iar

that the knee joint has engineering aspects. Indeed, engineers usually design structures, machines, methods, tools; taking into account the objects and boundary conditions of the specific field of application. Hence, one would not be amazed to hear that for instance mechanical engineers design artificial knee joints. This, however, is not an aspect of the knee joint, it is a replacement.

To be able to predict the functioning of his design, the engineer uses

experiments, but also theoretical considerations, based on me~hanics,

kinematics, materials sciences. To be able to design an artificial knee joint in proper fashion, he needs an engineering understanding of the function of this heavily loaded kinematical link in the human locomotor system. In other words: He searches descriptions of the joint-function in mechanical (mathematical) terms. This knowledge has not been provided for in traditional medicin and since it imp1ies the application of complicated methods and theories in which the engineer

has been trained, the field of Biomechanics develops and the l~nee does

have engineering aspects.

These aspects, however, are not only related to the designs of

artificial joints. As is being reflected by the recently started and fast developing cooperation between engineers, orthopaedic surgeons and functional anatomists, biomechanic methods have become accepted tools

~n fundamental research of the human locomotor system.

As a mechanical structure, the knee joint can schematically be described

as consisting of 3 bone parts (fig. I): a part of the thigh-cJne or

femur, a part of the shin-bone or tibia and the knee-cap or patella. The femoral and tibial parts are covered with articular cartilage and meet in two contact regions, one on the outer (lateral) side and one on the inner (medial) side. Between the medial and lateral pieces of

the tibia and femur (called condyli) , surrounding the direct contact

regions, we find the two half moon shaped cartilage structures called the menisci. The patella, on the inside also covered with articular

Quadriceps Muscle group Lateral Collatera Ligament Post. Cruciate Ligament Lateral Meniscus Femur Tibia Patella Tibia Ligament Fig. 2 Meniscus Fig. 1 Patella Condyli Tibial-Patellar ligament Posterior Cruciate Ligament Tibia

~

Femur Cruciate Ligaments~-""~--"""W

(

\.

\.

Anterior cruciate Meniscus

-*...

Adapted from: Kapandji, "The Physiology of the joints". 2nd ed. vol. 2. Churchill Livingstone, Edinburgh, London and New York (1970).

-6-

BMG'f 78.300

cartilage, glides over the femoral surface ~n a region soui;:\vhat above

and between the condyli. It is on one side connected with the important quadriceps muscle group and on the other side, by means of a ligament (a band consisting of strong collagen fibers) with the tibia.

The femoral and tibial bone parts are connected by various ligaments of which the most important are both cruciate ligaments, located

between the condyli, and both collateral ligaments, located along both s ides of the joint. (Fig. 2).

The motion between the femur and the tibia, roughly speaking a flexion-extension movement, is quite complicated and can hardly be compared

with a simple hinge. It is guided by the articular surfaces, the menisci, the patella and the ligaments. The geometrical properties of the parts and the non-linear, visco-elastic properties of the cartilage anc the ligaments have no doubt much influences on the kinematical behaviour. The articular cartilage is lubricated by and interacts with synovial fluid, a fluid of complicated chemical composition. The friction between the articular surfaces is many times smaller than would be possible

in technical circumstances; the lubricational mechanism ~s not yet

fully understood. During its physiological behaviour (walking etc.) the joint is heavy loaded through gravity, acceleration forces and muscle action. Forces that have to be transferred through the joint may be as high as seven times body weight, resulting in high stresses

in the components and on the articular surfaces. Stability has to be maintained by ligament constraints and muscle action, giving rise to elastic, or perhaps sometimes plastic, deformations.

In biomechanical research the kinematical and mechanical aspects of this structure are being investigated. It is being tried to describe the geometrical and mechanical material properties of the components mathematically as well as to evaluate the influences of these properties on the relations between loading, on one hand, and motion, deformation and stress distribution on the other hand.

The abstracts, presented in the following pages, reflect a cross-section of this research with respect to the intact knee joint and its components. Some of these research programms have a more general object, for instance the projects on joint lubrication and the

the studies on the mechanical function of the menisci or on tue

anatomical structure and mechanical function of the cruciate ligaments. Much use is being made of models, either material models or mathematical

(computer) models. With these models-schematic representations of

reality- the mechanical behaviour of the system or its components can be simulated and the influences of certain properties evaluated, as is often not possible with direct experiments.

Apart from purely a better fundamental understanding of the mechanical function of the knee joint and its components, the results of these research efforts contribute to the field of Orthopaedics.

Affections of the joint may have congenital causes (existing since

birth; growth deformaties), . pathological causes (diseases, for instance Rheumatoid Arthritis) or traumatical causes (accidental damages, for instance ligament ruptures or fracture of the bone components). Many diagnostical methods, in relation with these affections, have

mechanical aspects and most of the operational methods are essentially restorations of the joint in biomeohanical sense. Although of course many pure biological or biochemical factors play an important and complicating role.

Started about 10 years ago, the Orthopaedic Biomechanics discipline is expanding rapidly. Functions of bones, joints, ligaments and other components are investigated from a mechanical point of view in various recently erected Orthopaedic Biomechanics laboratories and Technical University departments and the results are being translated into

criteria for a variety of orthopaedic treatments. Much of this research is focussed on the knee joint. At the 24th Annual Meeting of the

American Orthopaedic Research Society in 1978 in Dallas, of the appro 200 papers presented, 72 concerned biomechanical research; 22 of these presented research work on general mechanics of joints or joint

components, of which 13 concerned exclusively the biomechanics of the knee joint and its components.

The group of Dutch scientists (orthopaedic surgeons, functioral anatomists and biomechanical engineers) working on the knee joint from a fundamental biomechanical point of view, is only small; small enough to gain from cooperation. It is hoped that after this

symposium the communication will be even more intensified.

Fig. 3 gives some information about Dutch institutions, where the knee joint is being investigated from an "engineering" point of view. '

&I)

/"f

/

Orthopaedic Knee Joint BMGT 78.300 T.J.J.H. Slooff. University of Nijmegen Dept. Orthopaedics, Lab. for Experimental Orthopaedics.

R.van Dijk, R. Huiskes, P. Jaspers, A. de Lange, TI ,J.G. van Rens,

• Experimental Evaluation of kinematics and stability • Mechanical. Consequences of

Knee Surgery.

of Limburg Dept. Orthopaedic Surgery

III •Structure and mec:lanical Function of the

I Knee Cruciate Ligaments

• Mechanical function of the Meniscus

A.J.M. Hamer, A.v.d. Linden

I

,

,

I

,

I

I

+

R. Bosma, D.lI. van Campen, H. Croon, H. Moes, students.

University of Technology rwente Dept. Mech. Eng.; Group Biomed. Eng.

V • Application of Simulation Models to Orthopaedic Methods of Diagnoses and Treatments.

~university

• fixation of Hinged Artifical KPee Joint • Kinematical Knee Simulator.

I •Rheology of Articular Cartilage • Lubrication of Joints

-8-~-

...

--~_

....

Fig. 3: Engineering aspects of the human knee joint Present research in The Netherlands

other

.--University of Tec.lmology Eindhoven

Dept. Hech. Eng.; Groups Applied Mechanics and Biomed. Eng.

A. llrouwers, J.D. Janssen, F.E. Veldpaus, students.

• Computer Simulation Nodels of the Knee Joint

Project groups Information exchange

Em

University of Leiucn

~Lab. Anatomy nnu Embryology A. Huson, C.W. Spoor, students.

"\.

II • funtional Anatomy of the Knee and Joints"

• Evaluation of Joint Kinematics.

~

3. Biphasic Rheological Properties of Art~cular Cartilage

Van C. Mow, Rensselaer Polytechnic Institute, Troy (N.Y.) U.S.A.

Articular cartilage is a biphasic material composed of a macromolecular solid matrix and water. The main constituents of the solid matrix are collagen and proteoglycan; together they comprise approximate:y 20% of the tissue substance by weight. It is of interest to investigate

the intrinsic material properties of this solid matrix since :ts ability to withstand the stresses and strains of joint function is intimately related to the health of the joint. It is also of interest to investigate the transport of the interstitial fluid since the rheological behaviour, such as creep and stress relaxation, of this tissue is intimately related to it.

Articular cartilage has been modeled as a binary mixture of an intrinsically incompressible solid matric and an intrinsically incompressible liquid. The interaction between these two media is given by either a linear or non-linear permeability function. The volumetric ratio of the solid content has been assumed to be either a constant or a variable function of depth from the surface. We have shown that these models can describe almost all the observed biphasic creep and stress relaxation behaviours of articular cartilage. Further, by using these models, we have been able to determine an intrinsic elastic modulus of the solid matrix.

-10- _{BMGT 78.300}

4. The Role of Synovial Fluid in Joint Lubrication

G. de Keizer; dept. General Surgery, Maria Ziekenhuis, Tilburg

The functioning of a normal joint is as that of a loaded bearing, which because of the absence of wear, must have an ideal lubrication.

Untill now no answer has been found to the question of the mechanism of normal joint lubrication. Not one of the current theories of joint

lubrication however takes account of the physical properties cf lubricant itself: the synovial fluid.

We measured the visco-elastic properties of 73 synovial fluid samples from normal and pathological joints by means of a cone and plate viscometer specially designed for this purpose (fig. 4). The results obtained may be summarized as follows:

Viscocity of synovial fluid shows a shear rate dependance whi~h is

greatest for fluids from normal joints (fig. 5).

Synovial fluid shows an elasticity which is greatest for fluios from normal joints.

Elasticity and viscosity changes are time independent.

These visco-elastic properties and those other factors that can influence the lubrication mechanism are combined in the theory of elasto-rheodynamic lubtication. This mode of joint lubrication is a full fluid film lubrication. Two aspects of the elasto-rheodynamic lubrication are discussed.

First: Because of an interaction of the roughnesses of the cartilagenous surface and the shear rate dependence of the synovial fluid there exists during sliding movements between the joint surfaces a non-isoliscous fluid film with a central plane of sliding and peripheral planes of squeezing.

A low resistance against sliding is combined with a high resistance against squeezing, at the same time, in the same film.

Second: During the peak loads in the stance phase of the walki.ng cycle the synovial fluid film will become thinner, not because of a squeezing out of fluid, but because of an elastic deformation of the film. After each peak load the film will elastically be restored.

The thesis by Coll. C.S. Groot from the University of Technology at Enschede is mentioned. He designed a mathematical model of joint

lubrication in which the shear rate dependence of synovial joint is accounted

for. With this advanced model he was able to calculate for the

~-~---2 - - - - 3 ·4 ~5 --6 7 8 Fig. 4

Schematische voorstellinM vun d(' synuvimetcr volgen~Vos en Theysp.. 1 ""' torsjcdroud 2. differentiaal membrunensysteem a.,verphtul.-';in~:-;lronsducer 4. doorboorde KcJeide· bus 5 _ groeveYourde drljfriem 6 _ mOllsb!r synoviule vlocistof 7""kegelvormlge

onder-zijdf' van de binnenbusIt _vt'rheven pluwuu up dr hodem vun de buitcnbus.

-Q a;

_"

0 ~ 0 :!E iii_w ... Z w 1';

...

_:!E iii 0 0 W III I > 3 5 10 2

3 0 SHEAR RATE IN SEC·

Fig. 5

Synovigrammen van twee mon8ters uit normole gewrichten. De van links naar rechts

dlliende lijnen zijn de krommen van de viscositelt.De stljgende van de normaalspanning. I w monster 2. Normaal Ilewricht. Patlllnl B uur overleden.

-12- BMGT 78.300

AN ASYMI'TOT IC 'I'ImORY FOR THIN LAYERS OF ARTICULAR CARTILAGE

WITII APPI.ICATION TO TilE KNEE JOINT.

If II. Mol's. 1l.1I. van Campen and R. Bosma.

bone diffusion, v

I

s ~~~.J-...J.._··t···skin (e) b layer(o)

f7777777

~//77

/

t

fluid film(P)--~ 1

L+..

···t·_·_·1···~··

I

N,A,F,C,L,

K

_{t ,}

K

_n

Figure: Deformed articular cartilage If Twente University of Technology,

Dept. of Mech. Eng., P.O. Box 217, Enschede

'ru~_~~!,*~k~~U~

areas. In both cases this model evp.n holds for lay-ers thicker than might be expected in joints. The validity of the small deformation assumption of the classical theory of elasticity has been chequed through an application to ~he knee joint. Immediately after loading for instance when the surfaces are separated by a layer of fluid

(i.e. forPc-a), this leads to about I nun maximum compression for layers of articular cartilage be-ing originally 5 nun thick.

From this example it can also be concluded that (see figure) the central part, i.e. the compressed area, imbibes fluid whereas everywhere else the fluid is expelled. Qui te ashtonishingly the net flow is equal to zere ; perhaps because it is im-possible to squeeze out a saturated fully emerged sponge without actually touching it: Squeezing the articular cartilage merely begins when in dUe time contact occurs between the two mating surfaces (i.e. forp' ~().

The lack of knowledge about most OF the physical

values appearing in this model is still a major handicap in its application. On the other hand, the model itself can be very helpful ir. designing new equipment for measuring the properties of artic-ular cartilage.

Analysis of the complete joint, including the fluid film. can quite well be performed by applying this model; one should be aware however that our knowl-edge about the physical properties of the synovial fluid is very limited.

Therefore a lot more research effort should be go-ing into the determination of thes~ properties. REFERENCES

I. Ling, F.F.; JOLT, 1974, 1'.449.

2. Mansour, J.C. and V.C. Mow; ASME Pap. No. 76 Lub-1.

J. Reynolds, 0.; Trans. Roy. Soc. 177 (PtI). 1886, p. 157.

4. Maroudas, A. and P.G. Bullough; Nature 219, 1968 p. 1260.

5. Love. A.E.H.; Atreatise on the mathematical theory of elasticity, 1944.

skin, 1'-11'-11.) inunediatply under the

v

P

Pc

E,

K -

..

Introduction.

The familiar mathematical models for articular cartilage like for instance the model as proposed by Ling (1974). neglect indispensable material properties, whereas the more satisfying models as applied by Mansour et.al. (1976) are rather com-plicated and hamper. the completp analysis of na-tural human joints (i.e. the analysis of two mat-ing surfaces both covered by a layer of articular cartilage coated with surface films and with a fluid film in between).

Therefore. a new model is proposed based on a thin layer approximation for a transversely isotropic material. in complete analogy with the Reynolds

(1886) equation for thin film lubrication. The introduction of a thin and. in

contradistinc-tion to Ling (1974), "permeable" skin covering the free surface of the articular cartilage layer as justified by the measurl'ments of Maroudas et.ai. (1968) appeared to be very helpful in the modeling process.

In this model visco-elastic behaviour of the solid material and various other effects still under dis-cussion have not yet been taken into account. There is no reason. however, why they should not be incorporated in future modeling.

The model.

The proposed model is:

JI

tr

v

2

cr+

S -

K.

bV·P -v'"0 (j' - cx2_{J:,'l.VIc;- _ _}p _T "P-C c V= -E~

0::

+f

s

_p

lb2V1c;-) with 0(2= {C(N+R)-F2}/2LC ~2={C(N+fl)-JFZJ/6FL ; ~ - £-E. ...

=

3£.

K..

/(3Kh+F'E.b) where

b - original uniform layer thickness, L

N,R.F.e,L- Love's (1944) elastic moduli. 1'1,-2

0- - tangential stress in th(' solid, 10'1.-2

S - increase in layer thickness, I.

K. -

mean value for tangential permeability,

F- 1T-IL4

diffusion velocity. LT-l

fluid pressure outside thp layer, 1'1.-2 risp in normal pressurp on thp layer due to contact. 1'1,-2

permeability of the normal permfability skin, F-1T- 1,4

Apart from the traditional assumptions in

elasti-d ty and hydrodynamic s SOOlP add i tionaI assumptions

had to 1)(' made; lor installl"l' a vl'ry sppcific rpla-tion between normal and tangpnti,l! jH'rm('nbility had to lH' int roduced (e.g. k.and K..constant:). Discussion and conclusions.

The validity of this modpl is sllpportpd by the calculated rpsults for hoth plastic impprvious layers and rigid porous layl'rs. two wpl I known

6. The three-dimensional $eometry of a knee joint and mathematical description of this geometry

*

J. Wismans, P. Struben.

University of technology Eindhoven and Department of Anatomy and Embryology, Leiden, The Netherlands.

A three-dimensional mathematical model, describing the mechanical behaviour of a knee joint has been developed. An important pat'ameter

in this model is the three-dimensional geometry of the joint-surfaces and the locations of the insertions of ligaments and capsule. Since these geometrical data could not be selected from literature, a device has been developed for measuring the positions of a number of points on the joint-surfaces of anatomical specimen. In this device the

z-coordinate of a point 1S measured as function of the (x,y)-coordinates

with a dial gauge. Also insertion-points of ligaments and capsule are measured in this way.

A polynomial in two variables and of degree p, is fitted to the measured data of a joint surface:

p Z

=

L i=1 i j a .. x y 1)

The coefficients a .. are calculated by using a least squares method. 1)

Fig. 6 shows the measured parts of the joint-surfaces and the

mathematical approximations of the femural joint-surfaces with a 4-degree function and the tibial joint-surfaces with a 2-4-degree function. The standard deviation of the measured points to these approximations

is about 0.5 rom. For clinical applications of the mathematical knee model research should be undertaken to find the relation between 2-dimensional x-ray pictures and the 3-2-dimensional geometry.

*

Fig.6: The knee joint with measured parts of the joint surfaces and the mathematical approximations.

...

o u c c

7. THE MECHANICAL FUNCTION OF THE MENISCUS, EXPERIMENTS ON CADA'JERIC PIG KNEE-JOINTS

P. Jaspers, A. de Lange, R. Huiskes and Th.J.G. van Rens.

Dept. of Orthop.Surgery, Univ. of Nijmegen, The Netherlands.

There should exist little doubt about the important functions of the meniscj with respect to the load carrying capacities of the knee joint.

From experiments of, for example, Krause, Walker and Kettelkamp, it has become clear that menisci enlarge the area over which lead can be transferred and from experiments of Blaimont we know that this area is used for load carrying indeed.

It was the object of our research program to evaluate in which way the material and geometrical aspects of the meniscus and the surroun-ding structures like joint cartilage, subchondral bone and li.gaments

influence the mechanical behaviour, the load transmission ia the knee.

Knowledge of this kind would be most helpful in the objective prediction of short- and long-term consequences of menisectomy. Pigs kLaes were chosen for the experiments, because of the favourable availability and the assumed pronounciated function of ·their menisci.

The joint, containing the above mentioned structures, was regarded as a ron-linear, visco-elastic mechanical system.

This system was being subjected to different loading types. The transient response of the system, being either displacements or

reaction force, was measured (fig.

7).

The different kinds of loading functions were: Constant loading rate, slow (ramp loading) and fast (step loading); repeated step loading, impact loading.

These experiments were carried out on the intact knees and repeated after menisectomy.

Based on the experimental results a rheological model was dt.veloped, consisting of non-linear springs and damping elements, related to the structures present; the characteristics of these elements were evaluated (fig. 8).

-16- BMGT 78.300

the knees were measured as function of loading, using X-ray ~ic·tures

after insertion of barium-sulfate. Both in intact knees as well as after menisectomy.

These measurements result in interesting data with respect to the area enlarging function of the meniscus. Also they are used to include the effect of the load carrying area in the model.

In order to be able to include geometrical aspects of the pig knee, some were imbedded in plastic, using a special technique, and

sliced; the slices were studied.

In order to acquire insight in what really happens in the knee joint after loading and in this way to be able to verify certain assumptions, made in the process of modelling, we made a high speed camera film of the joint during impact loading.

This film proved to give much interesting information, this film is shown.

As preliminary conclusions from this research work can be stated:

1. The menisci enlarge the load bearing area in the knee joint

conside-rably, $0 that:

2. after menisectomy the average contact stresses on the joint

surfaces may become up to 3 times higher, in normal functioning.

3. After menisectomy the two joint parts show considerable kinematic behaviour on loading, even when these parts are fixed as rigidly as possible; these movements are damped by the ligaments, so that: 4. the knee without meniscus becomes unstable, and:

5. the ligaments of a knee after menisectomy are subject to "heavy duty" in normal physiological functioning. They will frequently

be high stresses and stretched, perhaps even into the plastic region. 6. Although the kinematical behaviour makes it hard to interprete the

transient responses of the loading tests, a rheological model of

~he joint with realistic physical elements can be developed.

7. In such a model the function of the meniscus can be devided into two effects: A non-linear, but non-time dependent effect, related to the circumferential stretching and a linear visco-elastic effect related to the load-carrying area enlargement.

Although these experiments were carried out on pigs joints, it is felt that the general conclusions and the tendencies of the results will be

equally true for human joints.

We agree, however, that it would be worth while to repeat the experiments with some human joints.

di!'>placement cros!'>head

~

1

displacement between pins ] Sp(mm)

~

reac t ion lorce F ( kg F )

to

+ - -

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\

Fig. 7: The cadaveric p1g knee joint is deformed, with varying deformation speed , between the cross-heads of an Instron testing machine. Deplacements between the joint parts as well as reaction forces are measured.

SPECIFIED RHEOLOGIC MODEL

ellect 01 menisci

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- - central elastic arltcular

~ cartilage and elastic boo ,e meniscI (effect 2)

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periferal visco-elastic

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cartilage

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periferal elasltc articular cartilage and elastic bone

Fig. 8: Representation of a one-dimensional rheological model of the knee joint.

-18-menisci

a. Contact regions with intact menisci.

b. Contact regions after menisectomy

BMGT 78.300 ... 10 k~f ---. 40 kCj

f

_._._-- 80

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_ _ 160 k~F ._... ₁₀

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160

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Fig. 9: Contact regions between the joint parts, as function of applied force, with intact menisci and after menisectomy, as measured with roentgenological methods.

8. The Lubrication Mechanism for synovial Joints

V.C. Mow, Rensselaer Polytechnic Inst., Troy (N.Y.) U.S.A.

Synovial joints are nature's bearings. Their extraordinary

tribo-logical characteristics, a coefficient of friction 0.002 and

2

an articular cartilage wear rate 1 g/min at 1 MN/m , are better

than most man-made bearing systems. To date, no comprehensive lubrica-tion theory exists for animal joints.

The lubrication mechanisms within synovial joints are the results of a complex dynamic process involving the flow of a synovial fluid and deformation of articular cartilage. As a first step toward resolving this problem, a model for articular cartilage lubrication has been .established. This model is based upon the biphasic nature of articular cartilage and its known ultrastructural and material properties variation with depth. A steady moving load problem and a spatially fixed oscillatory load problem have been solved to

investigate the flux of the interstitial fluid. The detailed

nature of the calculated surface flux could be used to expl~in the

self-lubricating capability of articular cartilage. Our preliminary flow visualization studies tend to support these calculations.

-20-9. The anatomy and function of the cruciate ligaments

BMGT 78.300

R. van Dijk, Dept. of Orthopaedic Surgery, Univ. of Nijmegei"

In mechanical models of the knee-joint the cruciate ligaments are often described as lines, connecting attachment - points on femur and tibia. In reality the cruciates are thick structures, with different functional parts. In the literature of the last 70 years many opinions can be found about the tension of the cruciates during flexion and extension.

Anatomically one can distinguish in the anterior cruciate aii antero-medial part - the upper side - and a postero-lateral part - the under

side -, in the posterior cruciate an antero-lateral and a postero-medial part. In extension the postero-lateral part of the anterior cruciate and the postero-medial part of the posterior cruciate

is tense, during flexion the tension shifts anteriorly to th~

anterior-medial part of the anterior cruciate and to the antero-lateral part of the posterior cruciate. Thus during flexion and

extension some part of both cruciates is tense, this keeps ~he

knee stable in antero-posterior direction in all angles of flexion-extension.

Some other conclusions ca be drawn from the anatomy.

1. The course of the anterior cruciate becomes more horizontal during flexion, the posterior cruciate more vertical. Because of this the anterior cruciate seems a better check on anterior

movement of the tibia than the posterior cruciate in d~ing

the anterior drawer test.

2. There is very little torsion in the anterior cruciate ligament in extension, this increases during flexion.

3. The cruciate ligaments do not attach to the eminentiae inter-condylares, as often stated.

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-22-10. I':ngineering A!:lpects of the Human Knee Joint

BMGf 78.300

A. Huson; Lab. Anatomy and Embryology; University of Leiden.

The relation between several morphological and functional chdracteristics of the human knee joint can be described with the help of a model based upon a closed kinematic chain. Even a simple planar four-bar chain offers a remarkably efficient model. The development of this model started from the following principles.

1. Ligaments can be considered as links of a mechanism as long as they

are taut, and this condition will be fulfilled if the condylar

profiles which are in contact with each other have shapes which

correspond with the envelope curves of the ligamentary li~kage

system.

2. The cruciate ligaments have a leading position in the liglmentary steering-apparatus and the construction of the model can be started very efficiently with these two elements. Other ligaments can be added if their insertions are chosen at points which describe nearly circular parts of coupler curves. The insertion of the lateral

collateral ligament can be given such a position that its fibres are stretched only when the joint reaches full extension.

Typical features of the knee joint can be demonstrated by this model: e.g. the combination of rolling and sliding performed by thf femoral condyles being related to the arrangement of the ligaments and to the shape of the articular surfaces; the direction of the rolling movement being dependent on the arrangement of the guiding ligaments. It can be shown by variation of the structural characteristics of the model that the crossing arrangement of the central ligaments is an essential feature.

Furthermore lateral stability is partly effectuated by a central

eminence of the tibial plateau lying between the two femora1 _condyles.

This eminence must have rounded sides in order to allow rotation movements of the condyles whereas one of the halves of the tibial

plateau must be given a certain slant i f the crossing ligaments are to

be kept taut during the rotation. Fig. 11 is a photograph of a model

which illustrates this arrangement for an arbitrarily chosen flexion position of the femur. A careful inspection of the tibial articular surfaces ·of a number of human knee joints showed that there is indeed in most cases a typical slant of the lateral plateau, which corresponds well with the crossing pattern of the central ligaments,

-24- BMGT 78.300

11. A three-dimensional mathematical model of the human knee...1 oLlt

*

J. Wismans, 1".E. Veldpaus

University of Technology, Eindhoven, The Netherlands.

A three-dimensional analytical model of the knee joint 1S presented,

taking into account the geometry of the joint surfaces as well as geometry and material properties of the ligaments. Influence of menisci is neglected and it is assumed that the joint surfaces are rigid. The geometry of the joint surfaces are described matLamatically. On the femur an external loading can be prescribed, caused by patella, muscles, bodyweight and inertia. The ligaments are represented by a number of non-linear springs with material properties selected from

literature. This system (Fig. 12) is characterized by a set of 16

non-linear equations of which 10 represent the conditions of contact

and 6 the equilibrium conditions. These equations are solved

numerically and the results are presented in a graphical way. For a given three-dimensional loading (forces as well as moments) at various flexion-extension angles, the location of contactpoints, magnitude and direction of contact forces, magnitude of ligament elongation and ligament forces, position in space of the screw-axes and knee-stability are calculated. Calculations with the model are in good agreement with experiments described 1n literature. With the model the influence of several parameters on the mechanical and kinematical function is evaluated. It is found, for instance, in contradiction to what 1S often stated, that the geometry of the tibial joint surfaces is very important for the stability of the knee joint. The model can be used to develop criteria for orthopaedic implants and to evaluate surgical operations. The underlying theory can simply be generalized to develop mathematical models for other joints ..

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-26-

_BMGT

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12. The use of X-ray stereophotogrammetry for measurements of joint motion

R. Huiskes and G. Selvikx.

Dept. of Orthopaedic Surgery, Univ. of Nijmegen, The Netherlands x

Dept. of Anatomy, Univ. of Lund, Sweden.

Decision-making in Orthopaedic Surgery in matters of diagnosis or treatment is, as in other medical professions, often dependent on information from measurements. The muscelo-skeletal system, with

which the orthopaedic surgeon is concerned, can be regarded as a heavy loaded kinematical construction and in that frame of thought it is only logical that the information sought will be in terms of loads, movement (displacements) and (changes in) geometry.

Presently the clinical measurements, needed for this information

are usually based on conventional x-ray principles, meaning that the 3-dimensional geometry of the body is projected on a 2-dimensional plane and conclusions are derived from this projection.

Although for a number of cases this rough 2-D impression yields enough practical information, the accuracy of the results is often quite lowisometimes even too low for an adequate diagnosis. Moreover, many normal and pathological phenomena are essentially 3-dimensional

(e.g. joint function) so that 2-D measurements methods can not be expected to give enough information.

It has since long been recognized in Orthopaedics (as well as in

anatomical research) that 3-dimensional measurements of mov~ment

(dis-placement) and (changes in) geometry can be based on stereophotogrammetric X-ray principles, in short: Reconstruction of 3-D objects from two

2-D images.

Although measurements of this kind have been used in experiments, practical problems have always prohibited the use for clinical applications.

Recently, however, a measurement system based on the above mentioned

principles has been developed by Selvik (fig.

13).

This system, that can be used for experimental as well as clinical

applications, consists of computer programs, based on stereophotogrammetric and kinematic principles; extensif error analyses were included in the software and also special hardware was developed.

The problem of identification of a biological point on 2 images has been solved by introduction of bone markers, to be implanted in vivo with a special insertion-instrument.

By using a special reference system, no measurements concerning the relative position of the roentgenfoci have to be taken before, after ot during the procedure.

standard X-ray equipment is used and the roentgenograms can be measured fast and easy by non-specialists on a normal coordinate measuring table.

This "Selvik-system" has become available at our laboratory.

It is used in several research projects; among others, to evaluate

the 3-Dimensional kinematics of the knee joint (fig. 14) anrl

the elongational behaviour of the cruciate ligaments during the flexion-extension movement (project R. van Dijk) •

The work on the 3-dimensional kinematics of the knee joint, for which a grant has been acquired from the Nijmegen University

Research Pool, will be carried out in collaboration with the dept. Applied Mechanics, Eindhoven Univ. of Technology (ir. Hamer).

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Fig.14: Tracing from an X-ray stereo exposure of a cadaveric knee joint. Bone contours were drawn for both exposures; bone markers (.) are shown as well as markers from the reference

cage (x and +). Flexion angle is 60° After measurement of

the markers from the roentgenogram, the 3-dimensional positions of the bone parts, relative to each other, are evaluated, using computer programs.

-28- BMG'f 78.300

ROENTGEN

_{STEREOPHOTOGRAMMETRIC RECORDING}

STEP I

CALIBRATION CAGE _{SPINE EXAMINATION}STEP IT

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A measurement system, to be used in clinical and experimental orthopaedics, developed (hard-and software) by Dr.G. Selvik, University of Lund, Sweden.

The object is exposed on 2 roentgenograms, by foci in arbitrary position. A reference-cage, determinating the laboratory coordinate

system, is also exposed.

The 3-dimensional position of a point in the object can be recor.struc-ted, after measurement of the 2 roentgenograms, with the computer

,. "

program X-ray.

By application of 3 or more object points in bone parts, the position of the parts relative to each other at a given time can be measured and described.

Object points are inserted tantalum balls.

A method of high accuracy and great flexibility, useable in clinical and experimental investigations.