## 2 Materials and Methods
### Implant Insertion Experiment without Soft Tissue  
For the first experiment, the desired free-free boundary condition was achieved by suspending the femur-implant structure via elastic bands. The response and excitation points were chosen at the extremity of the structure, on the implant neck. Measurements were taken in the Antero-Posterior (AP) and Medio-Lateral (ML) direction, at the femoral stem neck, as illustrated in Figure 1. At the response points, accelerometers (PCB 352A24, PCB Piezotronics) were attached with beeswax and at the excitation point impacts were performed using a modal hammer (PCB 086C03, PCB Piezotronics). Signal acquisition and processing was done by means of a signal acquisition device (Simcenter SCADAS, Siemens PLM) and signal processing software (Simcenter LMS Test.Lab, Siemens PLM).  
The artificial femur was prepared by the orthopedic surgeon. The preparation involved cutting and discarding the femoral head and creating the femoral cavity using the appropriate set of broaches, gradually enlarging the cavity up to broach size Wright 5.  
Following the femur preparation, the femoral stem was manually inserted into the femoral cavity. The FRF of the femur-implant structure was recorded and the distance between two fixed points, one located on the surface of the implant and one on the surface of the femur, were noted following each insertion hammer hit. These two fixed points are marked in red in Figure 1. The cumulative subsidence was obtained by subtracting  
Figure 1: Excitation and response locations on the implant neck.  
all measured distance values from the distance corresponding to the first insertion step. The Pearson Correlation Coefficient (PCC) and Frequency Response Assurance Criterion (FRAC), corresponding to each transition between two subsequent insertion steps, were calculated. For this calculation, the frequency range 0-3.5 kHz was considered. The insertion endpoint condition was fulfilled when the obtained PCC, corresponding to either the AP or ML direction, was equal or larger than 0.99.  
The definitions of the PCC and the FRAC are the following:  
\[\text{PCC}=\frac{\sum_{\ell=\text{a}}^{\text{b}}\Bigl{(}\left|\text{H(f)} \right|_{\text{N-1}}-\overline{\left|\text{H(f)}\right|_{\text{N-1}}}\Bigr{)} \cdot\Bigl{(}\left|\text{H(f)}\right|_{\text{N}}-\overline{\left|\text{H(f)} \right|_{\text{N}}}\Bigr{)}}{\sqrt{\sum_{\ell=\text{a}}^{\text{b}}\Bigl{(} \left|\text{H(f)}\right|_{\text{N-1}}-\overline{\left|\text{H(f)}\right|_{\text {N-1}}}\Bigr{)}^{2}}\cdot\sqrt{\sum_{\ell=\text{a}}^{\text{b}}\Bigl{(}\left| \text{H(f)}\right|_{\text{N}}-\overline{\left|\text{H(f)}\right|_{\text{N}}} \Bigr{)}^{2}}}, \tag{1}\]  
\[\text{FRAC}=\frac{\left|\sum_{\ell=\text{a}}^{\text{b}}\text{H(f)}_{\text{N-1 }}\cdot\text{H}^{\ast}(f)_{\text{N}}\right|^{2}}{\sum_{\ell=\text{a}}^{\text{ b}}\text{H(f)}_{\text{N-1}}\cdot\text{H}^{\ast}(f)_{\text{N-1}}\sum_{\ell=\text{a}}^{ \text{b}}\text{H(f)}_{\text{N}}\cdot\text{H}^{\ast}(f)_{\text{N}}}, \tag{2}\]  
where \(\text{H(f)}_{\text{N-1}}\) is the FRF measured at insertion step N - 1. H(f)N is the FRF measured at insertion step N. The frequency range spanning from a to b is considered to calculate the PCC and the FRAC.