Definition of the parameters
A Cartesian reference landmark was defined: O was the center of the cup, Oz was the cranio-caudal axis, Oy was the lateral-medial axis, and Ox the postero-anterior axis.
JD is defined as the lateral translation distance of the femoral head center (CR) required for a head to dislocate from a socket (Figure 1). We used the formula by Sariali , reported below, to calculated JD, which is a function of 4 variables: a, b, R, offset.
JD = 2Rsin [(π/2 – Ψ – arcsin (offset/R)) / 2]
Ψ is the planar cup inclination angle measured on the frontal plane by using the following formula and corresponds to the projection of the abduction angle (α) on the frontal plane.
Ψ = arctan [tan(α) × cos(β)]
α is the cup abduction angle.
β is the cup anteversion angle on the cross-sectional plane.
R is the radius of the femoral head.
Offset is the femoral head offset and it is defined as the distance between the femoral head center (CR) and the cup opening plane. If the femoral head center is located inside the cup, the offset has negative value (femoral inset), whereas, if it is located outside the cup, the offset has positive value (Figure 2).
Knowing from Sariali that JD changes in function of cup abduction and anteversion angles, we decided to set the acetabular cup orientation with constant abduction angle (a) of 45° and constant anteversion angle (b) of 15°, which are within the safe zone described by Lewinnek et al..
Lateralization or medialization of the CR were defined as lateral or medial shift of the CR on frontal plane when using modDM or FB in comparison with DM, as reference.
All acetabular components used for this study were from the same manufacturer (Permedica Orthopaedics S.p.A.,Merate,Italy), in order to exclude product design variability between different brands from different manufacturers.
We studied two cementless press-fit acetabular cups which both featured a highly-porous random trabecular titanium structure, commercially named Traser®, manufactured by selective laser melting technology without solution of continuity on the bone-implant side of the cup.
The first implant was a conventional DM cup, named Acorn Traser® DM cup, with polar-flatted hemispherical profile, 0° cup opening plane and 2.5mm cylindrical equatorial extra-coverage. The CR of the femoral head had a medial eccentricity from the center of the polyethylene mobile liner.
The second implant was a standard titanium alloy press-fit modular cup, named Jump System Traser® cup, with a polar-flatted hemispherical profile which allowed for polyethylene or ceramic FB to be coupled with Ø28mm, 32mm, 36mm and 40mm femoral heads or for modDM inlay to be articulated with the same DM liner of the Acorn Traser® DM cup.
For measuring the distances of interest, the following landmarks were considered:
A: Center of DM liner.
C: Center of femoral head (CR).
D: Center of the ideal spherical cup outer profile.
E: intersection point between the cup opening plane and cup axis.
Offset was defined as the distance AE in case of DM and modDM, while as the distance CE in case of FB. Due to the medial eccentricity of the femoral head CR with DM and modDM, we used the center of the polyethylene mobile liner (A) as offset landmark, because when dislocating from the shell, the mobile liner acts like femoral head. R was the radius of the polyethylene mobile liner in case of DM and modDM, while the radius of the femoral head in case of FB (Figure 3).
To calculate the CR position change, it was measured the distance CD between the CR (C) and the geometric center (D) of the ideal spherical profile which better outline the outer profile of cup equatorial portion (Figure 3). This our convention was taken to choose a common landmark of the acetabular implant, in order to exclude design differences between DM cup and standard cup. The geometric center (D) of the ideal spherical cup profile, in fact should correspond to the center of the cup when achieving press-fit fixation into the acetabular cavity, leaving a more or less pronounced polar gap between the acetabular floor and the polar apex of the cup (D’). Thus, this center (D) approximately corresponds to the same landmark point referred to the acetabulum when implanting same-sized acetabular cups of different design. CD is then adjusted taking into account the cup frontal abduction angle Ψ, multiplying by cosΨ.
Technical 3D-models of the prosthetic components were used to simulate three configurations of acetabular implants: DM, modDM and FB, matched for same cup size (external diameter) in the range from size Ø48mm to size Ø64mm, which allowed the use of a 28mm femoral head diameter (Table 1).
In particular, DM cup was graphically coupled with DM liner and Ø28mm femoral head and then offset AE and distance CD were measured (Figure 3A).
Similarly, standard cup was graphically coupled with modular DM liner, DM liner and Ø28mm femoral head and offset AE and distance CD were then measured (Figure 3B).
Last, same standard cup was graphically coupled with 0° polyethylene or ceramic FB and different femoral head diameters according to the available matching (Table 1) and offset CE and distance CD were measured (Figure 3C).
Lateralization or medialization of the CR when using modDM (or FB) were defined as the difference between CD with modDM (or with FB) and CD with DM.
Graphical implant simulations were performed and distances of interest were measured by using modeling and drafting tools of software CAD NX Siemens 7.5, 2010.