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  • Legg-Calve-Perthes' disease: stress

    distribution in the hip joint articular

    surface after varisation osteotomy

    V. Antolic*, V. Kralj Iglic

  • 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 of the bone infarct by bone remodelling. The final result of LCPD is almost always 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 the LCPD. 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 the acetabulum 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 of the 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 the same surgeon (V. A.). X-ray parameters are recorded before and after the operation 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 in order to estimate the stress in the hip joint articular surface after the varisation osteotomy. In the model, the femoral head is represented by a sphere and the acetabulum is represented by a fraction of a spherical shell separated by a soft intermediate layer. The radius of the hip joint articular surface, r, is taken to be the mean of the radii of the radii of the femoral

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

  • Computational Biomedicine 257

    TABLE 1

    Preoperative, postoperative and normal (contralateral - no LCPD) side X-ray parameters: angle flccD (centrum-collum diapyseal angle), angle OACM, angle SCE , flLAT (angle of lateralization of the epiphysis), LAT-CE angle, r (half diameter of the femoral 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. NORMAL SIDE

    flCCD

    132 138 123

    111 112 110

    139 143 136

    tiACM

    54 58 48

    54 57 52

    45 47 41

    flCE

    16 30 7

    17 26 12

    28 33 20

    SLAT

    59 70 52

    41 50 32

    39 64 48

    LAT-CE

    43 56 30

    25 37 17

    27 37 18

    r

    3 3,6

    0 2.4

    3,2 3,6 2.6

    2,6 2,8 2.4

    MZ

    0,9 1,1 0,6

    0,9

    1,1 0

    0,5

    0,7

    3 0,2

    head sphere and the acetabular shell. The weight bearing area of the hip joint 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 surface bounded 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 is called the pole. The position of the pole (P) on the articular surface is

    determined in spherical coordinates (d,

  • 258 Computational Biomedicine

    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). 16 months after varisation from 139 to 118 degrees the X-ray contour of the femoral 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 and were 53 and 14 degrees, respectively. The MZ distance remains the same after 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 xz plane. The force ̂ is represented by its magnitude R and its the angle of inclination with respect to the x = 0 plane #R (Fig. 2).

    The unknown quantities; i.e. the value of the stress at the pole po and the coordinates of the pole 0 and

  • Computational Biomedicine 259

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

    tion osteotomy is calculated by using a simple static three dimensional model 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 muscles attachment 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 in the frontal plane of the body placed through the centers of both femoral heads. The weight-bearing area of the articular surface, i.e. the area where stress is different from zero (marked by shading), is taken as a portion of spherical surface bounded by the lateral and medial intersecting planes in- clined for angles -QCE and flM with respect to x = 0 plane. Symbol P denotes the pole of stress distribution determined by angles @ and 3> . Symbol 7? denotes the hip joint resultant force. The angle flR describes the inclination of the hip resultant force 7? with respect to x = 0 plane.

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

  • 260 Computational Biomedicine

    In this work the maximal value of the stress on the hip joint articular surface pmax is considered aa measure of stress. The value of pmax is taken to 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 taken at 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