4.5. The Separation Function
4.5.1. Summary
In my previous AlloClassic stem, the longitudinal edges of the anchoring zone were strictly rectilinear as for the stems of ZweymĂŒller of first generation. The passage from the distal part of the anchoring zone towards the pyramidal tip was carried out too abruptly.
The femoral diaphyse was to support the totality of bending stresses whereas a few millimetres higher this diaphyse was rigidified by the presence of the stem. This short transition zone was still likely to be overloaded and to cause some pains. The purpose of the Separation Function introduced into stems SL Plus is to gradually distribute on a wider zone the passage of the prothesed diaphyse towards the empty diaphyse. The Separation Function is modelled by a subtractive exponential curve which is also one of the components of the Calcar Polynom Deckner.
4.5.2. A solution provided by the continuity of the form
I think it was the sudden change of pressure on the bone that could be causing many of femur thickenings observed under the tip of the stems. For me, the pressure exerted by the stem on the bone should decrease gradually over a long enough distance instead of abruptly cancel.
I wanted to make modeling a gradual separation between the area prepared by rasping and the distal tip of the stem, like a plane taking off gently from the runway.
It is the Separation Function. It is consisted arc of a very flattened defined and normalized exponential curve as the preceding functions which is connected to the Fixation Function and whose abscissa are directed in the opposite direction.
This Separation Function respects the Law of the Positive Derivates and the resulting curve also has a continuous second derivative.
4.5.3. The Separation Function
is also an additive exponential curve with real exponent. The local coordinate system has its vector V oriented negatively. The first derivative of this curve is zero in the vicinity of the origin of its local coordinate system also ensuring the continuity of the entire contour of the stem. The shift in the origin of its landmark is such that the distal zone of the stem relies less and less on the bone to effect a gradual transition towards the zone of the diaphysis which is no longer at all stiffened by the prosthesis.
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