*4.2. In Vivo Aging Study*

The explanted femoral head presented significant metal transfer across the whole implant except on apex areas, caused by the two dislocation events with consequent closed reduction procedures. Roughness values measured before and after chemical attack revealed that in the metal transfer area, approximately half of the measured roughness (0.154 μm vs. 0.079 μm in the cleaned sample) was due to the metal smearing and not eventual ceramic surface wear nor scratches on the ceramic surface. Hence, the roughness results reported by other groups in metal transfer areas (without removing the metal) may be questioned [11]. A picture of the retrieved head before and after the cleaning and identification of zones is provided in Figure 4. Zones A, B, C, D, and E are defined as stripe wear, transition area, main wear, metal transfer, and no wear (control area).

**Figure 4.** Picture of retrieved head before (**a**) and after (**b**) the cleaning and identification of zones.

No evidence was found of an increased monoclinic content led by metal transfer, whereas wear seemed to be more critically related to the monoclinic content: in wear areas, we found a higher monoclinic content (especially at the surface)—cf. Table 2. This result supports the interpretation that the discrepancy between in vitro and in vivo is related to shocks contributing to wear and stress-induced phase transformation rather than to metal transfer [15,22,23].

**Table 2.** Roughness values and values of Vm by XRD; Raman Vm values are determined as difference from E (non-wear case).


#### **5. Discussion**

*5.1. Use of Clarke/Adar and Katagiri Equations*

Our study clearly demonstrates that in the investigated materials (both for in vitro and in vivo aged specimens), the Clarke/Adar equation, and not the Katagiri equation, produced results that are in better accordance with the XRD measurements. This contradicts the current trend in the literature and suggests that the validity of Raman data in the literature is questionable. There is, in particular, a discrepancy with Tabares and Anglada's work [26], where on the basis of Raman and XRD measurements on several monoclinic/tetragonal powder mixtures, Katagiri's equation was deemed more suitable, whereas the Clarke/Adar equation underestimated the results. Tabares and Anglada explained this result with an intrinsic difference residing in the experimental procedure followed by Clarke and Adar: They used fracture surfaces of sintered samples in which the monoclinic phase was confined to a thin surface layer. Consequently, Clarke and Adar's specimens were affected by a concentration gradient in the depth direction, which caused the value of Vm measured by XRD to depend on the wavelength and the angle of incidence of the radiation. In other words, since Tabares and Anglada used different XRD settings for their calibration, the value of 0.97 for the k coefficient in Equation (1) is not valid in their case, and the Clarke/Adar equation underestimates Vm.

This, however, should also apply to our case. Interestingly, it is the Clarke/Adar equation that performs better in our case. One possible explanation is the fact that in our work, we carried out all measurements on sintered samples. It may be envisaged that the coefficient *k* = 2.2 obtained by Katagiri and confirmed by Tabares/Anglada for the Katagiri equation is valid only on powder mixtures, whereas the functional form including the tetragonal peak at ~265 cm−<sup>1</sup> (and *k* = 0.97) has to be taken for a sintered material, which is the case of the calibration performed by Clarke and Adar. Another possible explanation is the fact that both Clarke/Adar and Tabares/Anglada worked on monolithic zirconia (thus with a much lower penetration depth for XRD: around 5 μm).

A further proof that the Clarke/Adar equation, and not the Katagiri equation, has to be used for our setting is provided in Figure 5. The upper (blue) spectrum in Figure 6 belongs to an area (named area A) with a low Vm located at the apex of non-aged polished Delta head domes, whereas the lower spectrum (red) corresponds to regions with a high Vm (named area B) at the center of the ground bottom of aged heads and inserts. The spectrum in area A is associated with a Vm of 10.2% or 30.5% if calculated with the Clarke/Adar or Katagiri equation, respectively. The spectrum in area B corresponds to a Vm of 66.7% (Clarke/Adar) or 90.1% (Katagiri). Such a high monoclinic content as obtained from the Katagiri equation seems unlikely given the still very strong intensity of the tetragonal peak at ~265 cm<sup>−</sup>1. In a fully monoclinic material, the 265 cm−<sup>1</sup> peak is, in fact, absent [18].

The main intrinsic limitation of the Katagiri equation is evident from its functional form displayed in Equation (1): For the calculation of Vm, it considers two monoclinic peaks and only one tetragonal peak. Consequently, if the coefficient *k* is not correct for the investigated material, the contribution of the monoclinic peaks is disproportionately high. Very likely, for the investigated sintered material, the coefficient *k* should be higher. Based on a comparison with the Vm obtained here using the Clarke/Adar equation, a coefficient of *k* = 4.7 for the Katagiri equation is probably more realistic in the present case. The coefficient *k* is probably not only dependent on the materials used for the calibration but also on the type of Raman spectrometer used and on the depth profile of the monoclinic fraction. A careful analysis of the available literature, in fact, suggests that the Katagiri equation performs better on triple spectrometers [11,24,32], whereas the Clarke/Adar equation performs better on single spectrographs [15,21]. This might be explained by differences in the measured relative intensities by the different equipment.

#### *5.2. Spectral Quality and Fitting*

Further aspects that could lead to differences in the values of Vm published by various research groups are (i) the overall quality (in terms of the SNR) of the collected spectra and (ii) the procedure used for data regression. Let us first investigate the former aspect. Figure 6 reports two spectra collected on the same polished spot of a Delta head. One spectrum was taken with shorter acquisition times and less repetitions in order to obtain two spectra with very different SNRs. The low-SNR spectrum mimics the case in which a spectrum was taken focusing through the metal in an area affected by metal transfer on a retrieved implant (cf. Figure 3c in [13]). The high-SNR spectrum (black line) corresponds to a Vm of 14% or 34% (with the Clarke/Adar or Katagiri equation, respectively), whereas the low-SNR spectrum corresponds to a Vm of 19% or 41% (Clarke/Adar or Katagiri equation, respectively). Therefore, despite those spectra belonging to the same area, a difference of

~20% was obtained. In other words, using spectra with a low SNR (such as the ones taken in a metal transfer area without removing the metal) may produce an overestimation of the monoclinic content of about 20%.

**Figure 5.** Comparison of Raman spectra of Delta that underwent a low monoclinic transformation (blue line—area A) and a high monoclinic transformation (red line—area B). Peaks belonging to the monoclinic (m) and tetragonal (t) phases of the area used in the analysis are labeled on the upper (area A) spectrum. The area A spectrum is associated with Vm = 10% and 31% with the Clarke/Adar and Katagiri equations, respectively. In area B, the monoclinic content amounts to 67% and 90% (according to the Clarke/Adar and Katagiri equations, respectively). Such a high monoclinic content as obtained from the Katagiri equation seems unlikely given the still very strong intensity of the tetragonal peak at ~265 cm<sup>−</sup>1.

**Figure 6.** Raman spectra collected on Delta with different acquisition times in order to obtain different SNRs. The spectra were collected on the same point of a polished specimen surface, but the low-SNR spectrum mimics the case of a spectrum collected through a metal layer in correspondence with metal transfer.

Another issue that is often overlooked in the literature is the use of absolute or integrated intensities. In general, integrated intensities should be more suitable in low-Vm cases [27]. Nevertheless, the use of absolute intensities may seem attractive in cases in which a large fluorescence background is present. According to our analysis, using absolute instead of integrated intensities causes an overestimation of the monoclinic content

amounting to 26% for the Katagiri equation and up to 60% for the Clarke equation. Hence, use of integrated intensities is mandatory.

The latter result highlights the intrinsic weakness of the Clarke/Adar equation with respect to variations in the overall background of the spectrum, such as in the case of fluorescent emission. To highlight this aspect, we carried out a study in which we fitted the spectra using two different baselines, both in inserts and heads belonging to the investigated Delta implant components. Figure 7 shows the different baselines used in spectra collected on the rear of an insert (a, b) and on the apex of a head (c, d). These cases will be called Cups A and B and Heads A and B, henceforth. From Cup A, values of Vm of 53% and 84% were measured with the Clarke/Adar and Katagiri equations, respectively. The Vm for Cup B amounted to 64% with the Clarke/Adar equation and 84% with the Katagiri equation. Concerning the head, spectrum A had a Vm of 10% with the Clarke/Adar equation and 35% with the Katagiri equation. Head B produced a Vm of 15% with the Clarke/Adar equation and 34% with the Katagiri equation. Hence, choosing a different baseline brings about an error as high as 33% for the Clarke/Adar equation, whereas the Katagiri equation is more stable (maximum error ~3%). For the sake of clarity, we mention that in all spectra used for comparison in Figure 3 above, we used a 15 s acquisition time, 15 repetitions, and the same baseline used for background subtraction as that reported in Figure 7a.

Despite performing better than the Katagiri equation in the investigated samples, the Clarke/Adar equation thus seems to be more prone to errors. The reason resides in the use of the large tetragonal peak at ~265 cm<sup>−</sup>1, which is strongly influenced by the background and is largely affected by changes in the choice of the baseline for data regression. Hence, Katagiri's choice of excluding this peak from the analysis is not at all wrong; however, we demonstrate here that in this case, the coefficient *k* has to be recalibrated every time a new material (e.g., sintered instead of powders) or a new instrument is used. Moreover, any modification in both the data collection and treatment procedures risks introducing sources of errors that are non-negligible even in the case of the Katagiri equation. This suggests that the Vm values obtained by different research groups using different equipment and different data treatments can hardly be compared. The only way out of this issue is to define a standard procedure for the analysis of the monoclinic content in zirconia via Raman spectroscopy.
