legg-calve-perthes' disease: stress ^faculty of electrical ... · clinical cases of...

Legg-Calve-Perthes' disease: stress

distribution in the hip joint articular

surface after varisation osteotomy

V. Antolic*, V. Kralj Iglic<\ A. Iglic & F. Srakar*

^ University Clinical Hospital for Orthopaedics,

Zaloska 9, 61000 Ljubljana, Slovenia

^Faculty of Electrical and Computer Engineering,

Trzaska 25, 61000 Ljubljana, Slovenia

^Institute of Biophysics, Medical Faculty,

Lipiceva 2, 61000 Ljubljana, Slovenia

ABSTRACT

Biomechanical influences of the varisation osteotomy performed on 7clinical cases of Legg-Calve-Perthes' disease with lateral subluxation of theflattened femoral epiphysis are studied. For this purpose, a three dimen-sional mathematical model of the hip joint articular surface is used, takinginto account the spherical shape of the femoral head and of theacetabulum inner surface before and after the operation. The model as-sumes that stress on the hip joint articular surface is proportional to thecosine of the angle between the pole of the stress distribution and anypoint on the articular surface sphere.

The average varisation in our series was 20 degrees, and the maximal stressdecreased for about 20%. In all the cases a significant improvement in thesphericity of the femoral head epiphysis was observed one year after theoperation, presumably because the lateralized part of the epiphysis isplaced under the acetabular roof after varisation osteotomy. Plasticremodelling of the femoral head is thus enhanced. Acetabulum was slightlydysplastic before the operation and did not change after varisation.

INTRODUCTION

In Legg-Calve-Perthes' disease (LCPD), a lack of vascularity in theproximal femoral epiphysis occurs before adolescence. So far the reasonsfor it remain undiscovered. In the initial stage of the LCPD (lasting a few

Transactions on Biomedicine and Health vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3525

256 Computational Biomedicine

months) the bony part of the epiphysis disintegrates due to bone infarc-tion, which leads to flattening of the epiphysis. The second-fragmentation-stage of the LCPD (lasting for 1-2 years) is characterized by the healing ofthe bone infarct by bone remodelling. The final result of LCPD is almostalways an enlarged femoral head which can lack sphericity. The final situa-tion depends on the age at onset, on the severity and extension of the vas-cular lesion and on the therapy efficiency.

There still is some controversy regarding optimal treatment of theLCPD. In milder forms of the disease a non-weight bearing and/or abduc-

tion brace or cast may suffice. In cases where the whole epiphysis is ef-

fected and lateral subluxation of the flattened epiphysis occurs, operative

measures are necessary including pelvic or varisation osteotomies. The

goal of all these treatments is containment of the femoral head by theacetabulum in the weight bearing position. Thus remodelling of the

femoral head is expected to occur by a process called biological plasticity(capability of the femoral head to remodel to spherical shape when encal-

luped to the spherical acetabulum) [3].

In this work stress distribution in the acetabular articular surface (in-

cluding the lateralized part of the epiphysis) before and after the varisation

osteotomy are estimated for one-legged stance using a 3-D mathematical

model of the hip joint articular surface [6]. Additionally, 7 clinical cases ofthe LCPD where varisation osteotomy was performed are discussed.

METHODS

Seven patients with LCPD and lateral subluxated epiphysis are in-cluded in the study. The average duration of the LCPD before the opera-tion was 15 months and all were in the group IV according to Catteral [3].

The average age at the operation was 8,8 years (min. 7,0 and max. 12,1

years). In all the cases the varus osteotomy was performed in 1991 by thesame surgeon (V. A.). X-ray parameters are recorded before and after theoperation at an average interval of 12 month (max. 18 and min. 1 month).

(Table 1). Fig. 1 represents typical X-ray before and after the varisation os-

teotomy.

A three dimensional mathematical model of the hip joint [6] is used inorder to estimate the stress in the hip joint articular surface after thevarisation osteotomy. In the model, the femoral head is represented by asphere and the acetabulum is represented by a fraction of a spherical shellseparated by a soft intermediate layer. The radius of the hip joint articularsurface, r, is taken to be the mean of the radii of the radii of the femoral


Computational Biomedicine 257

TABLE 1

Preoperative, postoperative and normal (contralateral - no LCPD) side X-rayparameters: angle flccD (centrum-collum diapyseal angle), angle OACM, angle SCE ,flLAT (angle of lateralization of the epiphysis), LAT-CE angle, r (half diameter of thefemoral head) and MZ distance (see also Fig. 1), measured according to Tonnis[lO] for the 7 patients. The average, maximal and minimal values of angles OccD ,#ACM , flCE and tiLAT are represented in degrees, while r and MZ are given in cm.

PREOP

max.,min.POSTOP

max.,min.NORMALSIDE

flCCD

132138 123

111112 110

139143 136

tiACM

5458 48

5457 52

4547 41

flCE

1630 7

1726 12

2833 20

SLAT

5970 52

4150 32

3964 48

LAT-CE

4356 30

2537 17

2737 18

r

33,6

02.4

3,23,6 2.6

2,62,8 2.4

MZ

0,91,1 0,6

0,9

1,10

0,5

0,7

30,2

head sphere and the acetabular shell. The weight bearing area of the hipjoint articular surface, i.e. the area where the stress on the articular surface

is different from zero, is taken to be a portion of the spherical surfacebounded by the lines of intersection of the spherical surface with two

planes, the lateral and the medial intersecting plane (Fig. 2). The lateral

intersecting plane is inclined for #CE (the angle of Wiberg; [11]) in the

lateral direction with respect to the x = 0 plane and the medial intersecting

plane is inclined for #M in the medial direction with respect to x = 0 plane

(Fig. 2). The point of minimal distance between the sphere and the shell iscalled the pole. The position of the pole (P) on the articular surface is

determined in spherical coordinates (d,<p ) by two angles 0 and <5 (Fig. 2).

Although shear stress in the hip joint due to friction is also present inthis case, it is supposed to be negligibly small and so only the stress in nor-mal direction is considered. This is a reasonable assumption for the case,where the acetabular and femoral head spheres are smooth and well lubri-cated. For a system satisfying the above assumptions, the stress in the hipjoint articular surface is proportional to the pole of the stress distribution(Fig. 2):

p = po cos y (1)

where po is the value of p at the pole and y is the angle between any pointon the surface and the pole [2]. The articular stress integrated over theweight bearing area yields the resultant hip joint force:



Fig. 1. (A,B): A case of LCPD at a 8 years old boy (group IV according to Catteral).The lateralized and flattened epiphysis before operation (A, arrow). 16months after varisation from 139 to 118 degrees the X-ray contour of thefemoral epiphysis is round (B). Due to varisation the lateralized epiphysis(arrow) is under the acetabulum (see also Fig. 4) and the angle of lateral iza-tion of the epiphysis (LAT) decreased from 56 degrees (A) to 40 degrees(B). The angles ACM and CE did not change because of the operation andwere 53 and 14 degrees, respectively. The MZ distance remains the sameafter the operation. See also Table 1 for symbols.

J*pdX = g (2)

Regarding the direction of the hip joint contact force it was found out

[5,7] that in one legged stance 7? lies almost in the frontal plane of the body(xz plane in Fig. 2), therefore in this work is considering to lie in the xzplane. The force is represented by its magnitude R and its the angle ofinclination with respect to the x = 0 plane #R (Fig. 2).

The unknown quantities; i.e. the value of the stress at the pole po andthe coordinates of the pole 0 and <& (Fig. 2), are determined by solving thevector integral equation (2) as it is described in detail by Iglid et. al. [6].



In the hip joint force # for the changed femoral geometry after varisa-

tion osteotomy is calculated by using a simple static three dimensionalmodel of the adult human hip in one-legged stance position [5,7].

Different femoral neck-femoral shaft angles #CCD after varisation os-

teotomy are included in the model by variation of the greater trochanter

space position relative to the center of the femoral head. This is mathe-

matically simulated by changing the reference coordinates of the musclesattachment points on the greater trochanter [1, 8, 9].

While the lateral angle #CE is determinated from the hip geometry, the

medial angle #M is determined at the point where the cosine function of

the stress distribution reaches the value of 0. In other words, #M is rotated

in the clockwise direction from the pole of the stress distribution for n/2.

Fig. 2. Schematic representation of the hip joint articular surface [6]. The rectan-gular Cartesian coordinate system is oriented so that its x and z axis lie inthe frontal plane of the body placed through the centers of both femoralheads. The weight-bearing area of the articular surface, i.e. the area wherestress is different from zero (marked by shading), is taken as a portion ofspherical surface bounded by the lateral and medial intersecting planes in-clined for angles -QCE and flM with respect to x = 0 plane. Symbol P denotesthe pole of stress distribution determined by angles @ and 3> . Symbol 7?denotes the hip joint resultant force. The angle flR describes the inclinationof the hip resultant force 7? with respect to x = 0 plane.



In this work the maximal value of the stress on the hip joint articularsurface pmax is considered aa measure of stress. The value of pmax is takento be po if the pole is located inside the surface bounded by the intersect-ing planes, while, the maximal value of the stress distribution pmax is takenat the acetabular rim, if the pole is located outside this surface.

RESULTS

X-ray analysis (Table 1) revealed an average varisation of about 20

degrees. Lateralization of the epiphysis (LAT) decreased similarly for

about 20 degrees. Lateralization of the epiphysis returned to normal values

2.5

2.0

1.5

14

12

10

3.0

2.5

2JO130 120 110 100 90 130 120 110 100 90 130 120 110 100 90

Fig. 3. The magnitude of the hip joint resultant force (R), the angle of the inclinationof the hip joint resultant force (-OR ) and the maximal value of stress in thehuman hip joint articular surface (pmax) as functions of the femoral neck-femoral shaft angle (-OCCD )• Parameters used in calculations are: r = 2.6cm, -dee = 25 degrees and body weight WB = 800 N.

after the operation. The angles #CE , #ACM and #MZ did not change after

the operation. The involved femoral head was enlarged (Table 1). In all 7cases the sphericity of the operated femoral head, determined by the con-tour of the epiphysis on X-ray significantly improved.

Fig. 3 shows the dependence of the magnitude of the hip joint resultantforce (R), the angle of the inclination of the hip joint resultant force (#R )

and the maximal value of the stress in the human hip joint articular surface

(pmax) on the femoral neck-femoral shaft angle #CCD . It can be seen in

Fig. 3 that #R increases with decreasing angle #CCD, while R and pmax

decrease with decreasing angle #CCD .



Fig. 4 shows the distribution and corresponding maximal value (pmax)of stress in the human hip joint articular surface calculated for two dif-ferent values of angle #CCD (130 degrees and 110 degrees).

Fig. 4 shows also the area of the femoral head which becomes loadedafter the varisation osteotomy.

DISCUSSION AND CONCLUSIONS

The goal of any treatment of the Legg-Calve Perthes'disease is contain-

ment of the femoral head by the acetabulum in normal body position. Con-tainment may be achieved through surgery, casts and orthosis [3].

Pnm=3.MO«Pd

Fig. 4. The distribution and corresponding maximal value (pmax) of stress in thehuman hip joint articular surface calculated for two different values neck-femoral shaft angle flccD (130 degrees and 110 degrees). The area of thefemoral head which becomes loaded after the varisation osteotomy ismarked. Parameters used in calculations are the same as in Fig. 3. The sym-bol GT stands for the greater trochanter.

Varisation osteotomy of the proximal femur places the abnormallylateralized part of the epiphysis under the acetabulum. The lateralized partof the epiphysis is placed under the calup in the weight bearing position. Inthis way the molding forces of the acetabulum stimulate the regenerationof the capital femoral epiphysis and remodelling of the femoral head oc-curs. All these leads to spherical shape. This means that the femoral headis biologically plastic and is capable to take over the spherical shape of theacetabulum. This work shows that varisation osteotomy also decreases thestress in the hip joint which is also favourable (Figs. 3, 4).



The observation period in this study is relatively short, but it can be

concluded that sphericity of the femoral head significantly improved after

varisation osteotomy of the proximal femur in all clinical cases considered.Hip unloading after varisation may have additional favourable long term

effects. Varisation did not influence the minor acetabular dysplasia whichwas present before the operation.

REFERENCES

1. AntoliC, A., IgliC, A., Srakar, F., Herman, S., MaCek Lebar, A., Brajnik, D.Transposition of the greater trochanter: A mathematical analysis. In: Recentadvances in computer methods in biomechanics and biomedical engineering,Swansea, (Middleton, J., Pande, G.N. and Williams, K.R., eds.), Books andJournals International Ltd., Swansea (UK), 280-287, 1992.

2. Brinckmann, P., Frobin, W. and Hierholzer, E. Stress on the articular surface ofthe hip joint in healthy adults and persons with idiopathic osteoarthrosis of the hipjoint. J. Biomechanics 14, 149-156, 1981.

3. Crenshaw, A.H. Campbell's Operative Orthopaedics. Mosby, C. Co., St. Louis,Washington, Toronto, 1987.

4. Dostal, W. F., Andrews, J. G. A three - dimensional biomechanical model of thehip musculature. J. Biomechanics, 14, 803-812, 1981.

5. IgliC, A., Srakar, F., AntoliC, V., Kralj IgliC, V. and Batagelj, V., Mathematicalanalysis of Chiari osteotomy, Acta. Orthop. lugosl., Vol. 20, pp. 35-39, 1990.

6. IgliC, A., Kralj IgliC, V., AntoliC, V., Srakar, F. and StaniC, U. Effect of theperiacetabular osteotomy on the stress on the human hip joint articular surgace.IEEE Trans. Rehab. Engr. (in press), 1993.

7. IgliC, A., Srakar, F. and AntoliC, V. The influence of the pelvic shape on thebiomechanical status of the hip, Clin. Biomech., (in press), 1993.

8. IgliC, A., Srakar, F., AntoliC, A., Brajnik, D., MaCek Lebar, A. Biomechanicalanalysis of various greater trochanter positions. Ital. J. Orthop. Traumatol., (inpress), 1993.

9. Srakar, F., IgliC, A., AntoliC, V. and Herman, S. Computer simulation ofperiacetabular osteotomy, Acta. Orthop. Scand., Vol. 63, pp. 411-412, 1992.

10. Tonnis, D. Congenital dysplasia and dislocation of the hip in children and adults.pp. 110-142. Springer Verlag Berlin, Heidelberg, 1987.

11. Wiberg, G., Mechanisch-funktionelle Faktoren als Ursache der Arthritisdeformans im Httft- und Kniegelenk, Z. Orthop., Vol. 75, pp. 261-285, 1945.


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