A \ B strain gauges
4.2 M kl mechanical design
4.2.2 Structural modifications
In order to house the gauges and electronics within cavities inside the prosthesis, certain modifications were required to be made to the structure. The cavities also provided reduced stiffiiess in the prosthesis at the sites where strains were to be measured, in order to increase the sensitivity o f the strain gauges to applied load. The cavities were not large enough to cause sufficiently high strains for the structure to fail however [#4.2.3], and the modified prosthesis design was fatigue tested to ensure safety [#4.2.5]. The instrumented prostheses were made in two sections: a standard instrumented part and a subject-specific part, figure 4.9. The instrumented part was machined axisymmetrically to become the IM stem and
43
cobalt-chrom e alloy femoral head
titanium alloy shaft Subject-specific part
\\
shaft cavity and strain gauges
\ l /
Standard (instrum ented) part
127
stem tip cavity and strain gauges
Figure 4.9 Mkl instrumented prosthesis showing the instrumented part and the subject-specific part. These are finally welded together after instrumentation.
main shaft. The 30mm diameter shaft was machined integral with the stem, which tapered from a diameter of 14mm at the shoulder to 12mm along a length of 95mm and then extended cylindrically for a further 30mm. The shaft was hollowed out to a depth of 65mm with a wall thickness of 2.5mm, and the tip of the stem to a depth of 25mm with a wall thickness of 1mm. A 5mm diameter hole was gun drilled axially to connect the two cavities, and honed to eliminate possible stress raisers. Three longitudinal flutes were then carved into the stem
surface, at 120° spacing, of different lengths (to minimise stress concentrations at the runouts) and to a maximum depth of 1 mm, and a lug was spigotted into the flat face of the shoulder on what was thereafter defined as the medial side. These two features, the grooves and the lug, were standard practice at the time to prevent rotation of the stem in the cement. The shaft section was designed to be just long enough to house the main electronic circuit, having allowed sufficient length at the ends for the shoulder and spigot. The stem dimensions are larger than would normally be used, and it was accepted that this might necessarily restrict the choice of subject to those having large IM cavities. The slightly larger shaft diameter was desirable to allow sufficient room for the implant electronics whilst ensuring adequate wall thickness for safety, and would not restrict subject choice. All abrupt changes in section were appropriately radiused.
The tip of the stem was significantly modified due to its additional role as the interface between the prosthesis and the implant coil [#4.2.6]. Additional titanium components were machined for this arrangement, as shown in figure 4.10.
Figure 4.10 The implant coil wound on a ferrite former, and the mechanical parts comprising the stem tip assembly: end cap, split collars and endplug.
The subject-specific part of the prosthesis consisted of a cobalt-chrome alloy femoral head, spigotted onto a neck and proximal shaft machined from titanium alloy. The offset of the centre of the head from the shaft axis was fixed (43mm), and the proximal shaft length customised for the required resection length.
4.2.3 Stress analysis and factors of safety
The above geometrical modifications to the prosthesis were made in order to maximise the sensitivity to axial force and yet keep within the maximum stresses which could be tolerated in the prosthesis for a given factor of safety. The achievable force sensitivity was thus determined by safety considerations as well as by the available dynamic range of the instrumentation [#4.3.2, #4.4.4.2]. The following calculations were used to establish the maximum stresses which would be applied to the various sections under worst case loading conditions, ignoring the effects of stress concentration. Considering an axis-symmetric tubular structure such as is shown in figure 4.11, loaded with force F acting along a loadline as shown, the compressive and bending stresses at any point P within the structure distant y from the neutral axis may be readily calculated as follows:
load line
neutral axis
F
p
Figure 4.11 Load line offset from and at an angle to the neutral axis of an axis- symmetric tubular structure.
Compressive stress ac = Fcosa / Tr(R^-r^)--- (4.2.1) Bending stress ob = Fxy cosa / 1 (4.2.2) where r, R are the internal and external tube radii, x is the distance from the loadline to the neutral axis at the point P, and I is the second moment o f of the cross-section, given by
I = 7t( r
V )
/ 4 = 7i( R^-r^)( R V ) / 4 (4.2.3)The combined compressive and bending stress at P is therefore given by:
CTb + ac = (Fcosa / n( R^-r^)) * (1 + 4xy / (R^+r^)) --- (4.2.4) and the ratio o f bending to compressive stress at P is given by:
aB / ac = 4xy / (R^+r^) (4.2.5) Thus for the loading condition shown in figure 4.11, where the loadline passes outside the structure at P, the bending stress is greatest on the outer surface (y = R) and Qb is always greater than twice ac, the ratio increasing with the loadline offset. The bending stress therefore predominates, and the design must therefore primarily allow safe bending stresses to occur under adverse loading conditions. Figure 4.12 gives the dimensions of the prostheses supplied to the two subjects, IM and DG. The offset distances x q, x r and x t (at the levels o f the Gauges, stem
Root and stem Tip respectively) may simply be calculated from the geometry, and these together with the other relevant data are tabulated below at the 3 sections in each prosthesis (Table 4.4). The prostheses differ primarily in their shaft lengths, which are determined by the amount o f bone which required replacement. Figures are also tabulated for a ‘normal’ solid prosthesis o f the same resection level as for subject DG, for comparison. The compressive and bending stresses are calculated
45' ^ 43 (41) resected bone R16 173 (108) weld
shaft cavity and strain gauges
26^5
(31.1) 22.5 (27.2) bone cement 127 (130)Stem tip cavity and strain gauges 235 (296) load line 13.7 (18.5) 108 (166) 14.5 (174.7)
Figure 4.12 Modified Mkl prosthesis showing principal dimensions for subject IM (dimensions in brackets for subject DG).
at the 3 sections for each prosthesis, and a 'factor o f safety' derived for each section. This is calculated using the material manufacturer's figure for 'direct- stress zero minimum fatigue limit' for smooth specimens, 690MPa [#4.2.5], The shaft inside and outside diameters were determined empirically, the resulting geometry allowing sufficient space for the electronics as well as providing an adequate safety margin as shown in the Table.
These factors o f safety allow no margin for stress concentration due to sharp edges, poor polishing, or inadequately radiused changes in section. However, the tabulated figures also assume that all the applied stress is carried by the prosthesis, which is unrealistic, particularly at the tip cavity. In practice, if the bone resorbs away from the shoulder, the weakest part is the stem root, for which the lowest factor of safety is 2.8. In addition, due to their larger stem root diameter, the instrumented prostheses are stronger at this level than those routinely used in limb salvage, where mechanical failure (and, notably, stem root fracture) is a rare occurrence. Subject Location on prosthesis OD ID I X y Safety factor mm mm mm"^ mm mm MPa MPa - IM Shaft gauges 25 20 11321 26.5 12.5 12.7 65.8 8.8 Stem root 14 5 1855 22.5 7.0 16.8 191.0 3.3 Tip cavity* 12 10 527 13.7 6.0 65.1 351.0 1.7 DG Shaft gauges 25 20 11321 31.1 12.5 12.7 113 7.7 Stem root 14 5 1855 27.2 7.0 16.8 230.9 2.8 Tip cavity* 12 10 527 18.5 6.0 65.1 474.0 1.3 Solid Shaft gauges 25 0 19175 31.1 12.5 4.6 45.6 13.7 implant Stem root 12 0 1018 27.2 6.0 19.9 360.7 1.8
Tip cavity* 10 0 491 18.5 5.0 28.7 423.9 1.5 *at the change in section between the tip cavity and the stem hole
Table 4.4: Geometry, axial and bending stresses, and factors of safety at mid shaft, stem root and stem tip for 2.25kN applied force. Figures are given for the two instrumented proximal femoral replacements and for a standard implant, and assume no contribution to the stiffness from the bone or cement.
The prosthesis of subject DG is theoretically rather more prone to failure than that o f subject IM, due to the smaller resection as discussed in #4.2.1 above, although still with a factor o f safety o f 2.8 at the stem root.
4.2.4 Welding
All implanted instrumentation except the inductive coil is housed within hermetic cavities sealed by welding. In the M kl device, two circumferential welds and one planetary weld are required for hermeticity. These are respectively i) the shaft of the instrumented part to the customised upper shaft (figure 4.12), ii) the stem tip cavity to the endplug (figure 4.14), and iii) the feedthrough to the endplug (figure 4.14). The first plan was to use Tungsten Inert Gas (TIG) welding. In the TIG process, a tungsten electrode is maintained a fixed distance from the weldpiece, and an arc is struck between them in an Argon environment. Certain weld parameters (arc current pulse waveform, upslope and downslope) are controlled electronically during the weld. TIG welding equipment is semi-portable and welds can be carried out in the laboratory. Setups can be easily and quickly adjusted, and little skill is needed. However, TIG arcs create a large weldpool and produce high temperatures at some distance from the weld site compared to other precision welding techniques. In the case of deep welds the 'heat affected zone' is extensive, and more metal is melted than with other methods. The excessive heat generated requires heatsinking o f temperature-critical regions. This method was therefore only suitable for the welds at the stem tip, since these were small and required little depth (<2mm) of penetration.
For the main circumferential weld, at the junction of the instrumented and upper shaft, the joint shoulder is 5mm deep, and therefore a penetration depth of 6mm or more was required. The electron beam process was chosen for this weld, since this technique gives excellent penetration with minimal heat affected zone. Electron beam (e-beam) welding requires substantial plant and is unsuitable for carrying out in the laboratory. It was convenient to have both circumferential joints e-beam welded, as this allowed the temperature in the tip cavity to be reduced during the
welding process. So that the welds could be made during the same despatch, the prosthesis was completely instrumented and assembled except for the implant coil which was assembled finally due to its vulnerability to mechanical damage. The weld sites were cleaned with alcohol and the mating parts assembled. Since a medially positioned anti-rotation lug, spigotted onto the shoulder, would be used to orientate the prosthesis during surgery, the upper shaft was anteverted w.r.t. the instrumented part by the usual 10° in order to restore the anatomical neck angle. The prosthesis was despatched for welding in this orientation. Upon its return the prosthesis was thoroughly polished.