Convergence
Sensitivities of implant seating force and introducer stresses to time-step and element-length were very low (< 3.5%), indicating temporal and spatial convergence of the model.
Load transfer (nominal parameter magnitudes)
For the nominal parameter magnitudes, the impact force between hammer and introducer (Fig. 1) had a peak of ∼30kN and a period of ∼0.1ms (magenta line), similar to clinical magnitudes. This led to an oscillating force between introducer and implant (orange line) with an amplitude of ¼ - ⅓ of the peak applied force and a similar period (∼0.1ms, 8kHz). Seating (black line) occurred during ∼10 force reversals between introducer and implant and took ∼10 times longer than the hammer impaction period. The magnitude of the seating force was ∼10% of the applied force and ∼30% of the force acting between introducer and implant. Once the stem had seated, the force between introducer and implant reduced by ∼50% and the vibration frequency increased (22kHz). A single deflection of the bone (Fig. 1B) was observed with a soft tissue force of 3 orders of magnitude less than the impaction force (∼44N) and with a period 3 orders of magnitude greater (∼0.25s).
Figure 1C (and Additional file 1) show the stress distributions through the hammer and introducer during implantation for the nominal parameter values and seating lasted ∼2ms. Maximum stress in the hammer acted in compression at its tip during impaction. Maximum stresses in the introducer were compressive and occurred during the hammer strike. This impaction stress wave moved distally along the introducer (at the speed of sound in the introducer ~ 6000m/s, which is observed by a slight diagonal shape to the right from proximal to distal for the blue compression plot), with a similar magnitude to the impaction stress but with a narrower period and reflected at each end of the introducer. Following seating of the implant (∼2ms), vibrations perpetuated in the introducer and hammer, but with much smaller amplitudes and higher frequencies (hammer 42kHz, introducer 22kHz).
Sensitivities
Figure 2 shows sensitivities of introducer stresses and seating forces to parametric variations. For example, -50% would imply that increasing the input variable by 100% from the nominal would decrease the output by 50% of the nominal value. With the aim of decreasing introducer stresses (blue bars), without reducing implant seating (grey bars) blue bars should be negative and grey bars should not. Reducing the applied energy and number of hits would reduce stresses but would also decrease seating (“surgeon” parameters). However, stresses decreased with increasing hammer diameter, length and density, which are all directly related to increasing hammer mass (“Hammer” parameters). The opposite is observed for introducer length and density (“Introducer” parameters), suggesting introducer mass should be decreased. However reducing the mass by decreasing the introducer diameter increases stresses, due to the reduced cross sectional area. Increased implant-bone implantation resistance (e.g. stem roughness) increased the seating force without increasing stresses in the introducer, perhaps allowing less energy to be applied (“Implant” parameters). Introducer stresses can be decreased by decreasing the implant mass and increasing the effective bone mass (“Implant” parameters). Sensitivities of implant seating and introducer stresses to material stiffness of the hammer and introducer are rather low. Increasing hammer tip stiffness seems to increase introducer stresses and might better be avoided. These sensitivities are presented below in greater detail, with some analysis of their interactions.
Hammer and Introducer
Sensitivity results suggested that parameters increasing hammer mass and decreasing the introducer mass fulfilled the aims of increasing seating and decreasing introducer stresses (Fig. 2). Effects of hammer density on load transfer are shown in Fig. 3A, and are representative of the effects of the other variables related to mass. Increasing hammer density decreases the peak applied force because the hammer velocity is decreased to maintain constant kinetic energy of impaction. This reduces force peaks and stresses in the introducer. However, the impact period is increased and this seems to increase seating and increase the rate of seating somewhat.
Increasing the length and density of the introducer had the opposite of the desired effects (Fig. 3B) so they should perhaps be reduced, but without reducing the diameter, which had a very strong influence on increasing stresses. These results are the opposite of those for the hammer, as can be seen by the increase in peak applied force and period for increasing introducer density, which increases stresses in the introducer but decreases seating, which also takes longer, due to the lower frequency of the vibrations.
Hammer tip stiffness and surgeon parameters.
Increasing the hammer tip stiffness, applied energy and number of hits (separately) increased introducer stresses, as well as implant seating (Fig. 2 and Additional files 1–3). These outcomes tend to be related to increased peak applied forces. Peak forces increase with hammer tip stiffness, while their period decreases (Fig. 4, magenta lines) and this results in greater seating forces, that increase with consecutive impaction, but also to greater stresses in the introducer (Compare varied hammer tip stiffness in Additional files 2&3 with nominal clinical tip stiffness in Additional file 1 to observe dynamically the more distinct and shorter wavelength reflected waves for increasing tip stiffness). This seating behaviour is summarised in Fig. 5 for a larger range of hammer tip stiffnesses and two applied energy levels. For tip stiffnesses greater than 0.021GPa, consecutive impactions led to progressive seating. The plot suggests an interaction between applied energy and number of hits. These parameters are the responsibility of the surgeon. Doubling the energy increased seating by the same proportion for all hammer tip stiffnesses (constant vertical shift on the log scale Fig. 5). Thus, less energy can be applied with more hits to achieve the same seating. This reduces introducer stresses by 30%.
Introducer stresses
Introducer stresses appear to be related to the magnitude of the peak applied force. This relationship is plotted for all variations made in this study (Fig. 6). The main outliers are the two for variations in the diameter of the introducer, which has an overriding effect on stresses by changing the cross-sectional area.
Implant
Increasing the resistance to stem insertion into the bone (rougher implant surface, better bone quality) increases the implant seating force (anchorage force), without influencing the introducer stress magnitudes during seating (Fig. 7) because impaction force magnitudes are unaffected. The rate at which seating occurs increases, with less oscillations before seating. Seating and introducer stresses are rather insensitive to implant mass.
Patient Parameters
Implant seating and Introducer stresses were rather insensitive to patient parameters. It is noted that impaction and implant seating are completed long before significant motion of the bone occurs (Fig. 1C), so that the bone effectively acts as a rigid boundary during seating. However, further analysis (Fig. 8) suggests that for an effective bone masses of less than 6kg seating reduces dramatically because the inertia of the bone is no longer great enough for it to act as a rigid base during implant seating. In this case, soft tissue parameters would start to affect bone deflection and implant seating, although they would not be expected to affect implant stresses. Soft tissue forces were relatively low (< 50N) compared to body weight.
Realistic Materials
Materials had little effect on stresses for a given geometry but PEEK was more likely to break due to its lower strength (Fig. 9). Increasing the diameter of the soft material (PEEK) reduced stresses and restored seating to the magnitudes for other materials.