A novel multinuclear solid-state NMR approach for the characterization of kidney stones

Abstract The spectroscopic study of pathological calcifications (including kidney stones) is extremely rich and helps to improve the understanding of the physical and chemical processes associated with their formation. While Fourier transform infrared (FTIR) imaging and optical/electron microscopies are routine techniques in hospitals, there has been a dearth of solid-state NMR studies introduced into this area of medical research, probably due to the scarcity of this analytical technique in hospital facilities. This work introduces effective multinuclear and multidimensional solid-state NMR methodologies to study the complex chemical and structural properties characterizing kidney stone composition. As a basis for comparison, three hydrates ( n=1 , 2 and 3) of calcium oxalate are examined along with nine representative kidney stones. The multinuclear magic angle spinning (MAS) NMR approach adopted investigates the 1H , 13C , 31P and 31P nuclei, with the 1H and 13C MAS NMR data able to be readily deconvoluted into the constituent elements associated with the different oxalates and organics present. For the first time, the full interpretation of highly resolved 1H NMR spectra is presented for the three hydrates, based on the structure and local dynamics. The corresponding 31P MAS NMR data indicates the presence of low-level inorganic phosphate species; however, the complexity of these data make the precise identification of the phases difficult to assign. This work provides physicians, urologists and nephrologists with additional avenues of spectroscopic investigation to interrogate this complex medical dilemma that requires real, multitechnique approaches to generate effective outcomes.


Introduction
Kidney stones (KSs) are a major health problem in industrialized countries. For example, the medical costs associated with the treatment of nephrolithiasis in France exceeds EUR 800 million annually. The study of KSs is presently at the heart of a concerted multidisciplinary axis of research involving physicians, physical chemists and spectroscopists . Nevertheless, the nucleation and growth of KSs remains largely unknown, and the associated mechanism is based mainly on assumption and incomplete evidence; hence, more thorough and wide-ranging structural investigations are still required (Sherer et al., 2018;. The growth of KSs is clearly a multifactorial problem, with their chemical composition and morphology presenting considerable variability due to the extreme complexity of the in vivo reaction media in which they are formed. The resultant biological materials exhibit very different characteristics as they can emanate from wide-ranging pathological scenarios, including bacterial infection, genetic predispositions, diabetes mellitus and bowel diseases (Bazin et al., 2012). Hence, KSs can be considered as being real examples of hybrid organic-inorganic nanocomposite materials.
The main mineral components comprising hydrated calcium oxalates are the monohydrate CaC 2 O 4 · H 2 O (whewellite -COM) and dihydrate CaC 2 O 4 · 2H 2 O (weddellite -COD) species, although amorphous calcium oxalate can also be observed (Gehl et al., 2015;Ruiz-Agudo et al., 2017). The trihydrate form, CaC 2 O 4 · 3H 2 O (caoxite -COT) is almost never observed in vivo but can be synthesized in an aqueous solution. COD is characterized by a zeolitic structure exhibiting a true structural challenge. It is considered as being one of the very few natural MOFs (metal organic frameworks; Huskić et al., 2016;Dazem et al., 2019), and its chemical formula is better represented by CaC 2 O 4 · (2 + x)H 2 O (x ≤ 0.5; Petit et al., 2018). "Structural" and "zeolitic" water molecules are, therefore, distinguished. Calcium phosphates and other mineral phases can also be detected in KSs, i.e., hydroxyapatite (Ca 10 (PO 4 ) 6 (OH) 2 ), which may be partially carbonated, brushite (CaHPO 4 · 2H 2 O) or struvite (NH 4 MgPO 4 · 6H 2 O; Gardner et al., 2021). The organic components (from a few percent to a major fraction) include, e.g., proteins (collagen among them), uric acid, lipids, triglycerides, etc. The nature of the organic-inorganic interfaces remain largely unknown to date. This chemical and structural complexity at several scales requires the use of a wide variety of characterization methods. Recently, elaborate experiments took advantage of the last development in TEM (transmission electron microscopy; Gay et al., 2020) and of synchrotron radiation (Bazin et al., 2012). In hospitals, optical microscopy, Fourier transform infrared (FTIR), FTIR microscopy, SEM (scanning electron microscopy) and X-ray diffraction are used in routine mode. Curiously, solid-state NMR has been used very rarely in the context of KSs (and other pathological cal-cifications), apart from sparse 13 C and 31 P studies (Bak et al., 2000;Jayalakshmi et al., 2009;Reid et al., 2011Reid et al., , 2013Li et al., 2016;Dessombz et al., 2016), which is unlike other human hard tissues such as bones and teeth. This is probably due to the fact that solid-state NMR instruments are not widely available in hospital settings. It is also stressed that some KSs are small so that the intrinsic lack of sensitivity associated to NMR may be a drawback. Other nuclei, such as 1 H and 43 Ca, can act as potential NMR targets. However, 1 H solid-state NMR remains a rather specialized technique because of the relative inefficiency of magic angle spinning (MAS) in producing really high-resolution data from most systems. 43 Ca (I = 7/2) is particularly insensitive (as a result of its extremely low natural abundance, ∼ 0.14 %, and low γ , −1.8028 × 10 7 rad s −1 T −1 , 57.2 MHz at 20 T).
In this work, a comprehensive multinuclear solid-state NMR approach is presented that facilitates the detailed structural analysis of KSs and the related synthetic hydrated calcium oxalate phases (COM, COD and COT) associated with their composition. The synthetic phases were obtained by carefully controlling the precipitation of calcium salts in aqueous solutions, as described below in Sect. 6 (Leroy, 2016). In total, nine KSs were studied systematically, with some of them exhibiting similar NMR fingerprints. The spectra of five of them (KS1 → KS5) are presented here. They come from the KS collection of the Tenon hospital (Paris, France) led by Michel Daudon (the collection counts tens of thousands of samples from all origins, exhibiting the largest variety of size, chemical composition and morphology worldwide). Our main goal here is to reach out to the physician community and, more specifically, nephrologists, urologists and biologists. NMR methods are presented at a moderate to high magnetic field (i.e., 7.0 to 16.4 T MHz) in order to make them much more widely accessible. Occasionally, further developments at an ultra-high magnetic field (up to 35.2 T) are proposed to the user. Particular emphasis is placed on high-resolution 1 H MAS NMR, with homonuclear decoupling and the complete interpretation of spectra based on structural data, and 43 Ca MAS NMR. To the best of our knowledge, these nuclei have never been used as spectroscopic probes for KS studies (apart from a unique 43 Ca MAS NMR study by Bowers and Kirkpatrick, 2011). A complete experimental protocol is then presented for the reconstruction of 13 C NMR spectra, including organic/inorganic and/or rigid/mobile components. Finally, the intriguing role of phosphates in KSs is partially deciphered by 2D 1 H− 31 P heteronuclear correlation (HETCOR) MAS NMR experiments despite the low phosphate content in KSs.  (Samoson, 2019), with an ultra-high magnetic field, up to 35.2 T, (Gan et al., 2017), in order to average the strong dipolar couplings. Indeed, the homogeneous character of the homonuclear dipolar interaction implies poor MAS efficiency at low to moderate spinning frequencies (Schmidt-Rohr and Spiess, 1994; note that the temperature increase, inside a 0.7 mm diameter rotor, is estimated to be roughly 20 • C in the fast/ultra-fast regime, i.e., ν rot > 30 kHz). This point is of prime importance as calcium oxalate structures may undergo subtle structural modifications upon heating (Deganello, 1981;Shepelenko et al., 2019; see also Sect. 6). More generally, for a 2.5 mm probe, the temperature increase is < 5 • C at 5 kHz, and 40 • C at 30 kHz. For a 7 mm probe, the order of magnitude is 5 • C at 5 kHz. However, such leading edge equipment is not widely available. An alternative is to use the CRAMPS sequence at a moderate spinning frequency (ν rot < 12 kHz; Paruzzo and Emsley, 2019). The DUMBO sequence (Decoupling Using Mind-Boggling Optimization) belongs to the CRAMPS family (Lesage et al., 2003). Using this approach, the internal temperature increase remains moderate for all rotor diameters. Moreover, this methodology can be successfully implemented on almost all magnets. Moreover, larger rotor diameters may be used, which can be interesting in terms of sensitivity. To the best of our knowledge, synthetic COM, COD and COT samples were never investigated by 1 H highresolution solid-state NMR. The corresponding spectra are presented in Fig. 1. At ν rot = 12 kHz, standard 1 H MAS NMR spectra (Fig. 1a) are all characterized by very broad and almost featureless line shapes. Such spectral fingerprints are not useful for analytical purposes due to the strong overlap of the resonances. DUMBO decoupling leads to a drastic increase in resolution and to very characteristic features for each synthetic hydrate.
The COT crystallographic structure exhibits six inequivalent sites for protons (Heijnen et al., 1985), whereas only three resonances are clearly observed at δ iso ( 1 H) = 3.36, 5.95 and 6.53 ppm (parts per million; Fig. 1a). A realistic assumption is that some resonances are so close that they cannot be distinguished even under DUMBO decoupling. It has been shown previously (Eckert et al., 1988;Pourpoint et al., 2007) Table A1 in the Appendix), namely 1.668-1.679 Å/1.809-1.837 Å/1.957-1.978 Å. It is stressed here that the distances were obtained after extensive optimization of the geometry of the COT structure at density functional theory (DFT) level (the same comment holds for the COM and COD structures; see Sect. 6). According to the literature (Pourpoint et al., 2007), a variation in O−H ... O of ∼ 0.3 Å is related to a δ iso ( 1 H) variation of ∼ 3.5 ppm, which is in rather good agreement with the results presented here (i.e., the shorter the distance, the higher the isotropic 1 H chemical shift). We mention also (Table A1) that each proton of the structure is involved in a relatively high number of H ... O contacts (from three to four, with O−H ... O ≤ 3 Å). The 3Å cut-off is realistic when considering "weak" H bonds (Steiner, 2002). In other words, the shortest O−H ... O distance directly dictates δ iso ( 1 H), whereas the number of H ... O contacts is more representative of the electrostatic/dispersion contributions at a given H position (Steiner, 2002). As all protons of COT are characterized by a large number of H ... O contacts, we assume a certain character of "rigidity" in the structure at room temperature and very limited local dynamics (Fig. 3c). Under this simple assumption, at most three resolved δ iso ( 1 H) are expected due to similarities in O−H ... O distances (see above), which is in good agreement with the experimental data ( Fig. 1a). Therefore, the 1 H COT assignments are the following, using the numbering given in Table A1: 3.36 ppm for H1/H6, 5.95 ppm for H3/H5 and 6.53 ppm for H2/H4. We note that partial deuteration could be of great help in increasing the resolution further.
In the case of COM, the four H crystallographic sites (H11, H12, H21 and H22; Deganello, 1981) Table A1). Therefore, a less rigid structure is expected at room temperature (when compared to COT). Rapid flips of H 2 O molecules could lead to partial averaging of δ iso ( 1 H) of protons belonging to the same molecule (Fig. 3). Using the numbering given in Table A1, the average O−H ... O distances for H11/H12 and H21/H22 are very similar (i.e., 1.802 and 1.795 Å, respectively). A unique resonance is therefore expected, which is in full agreement with the 1 H DUMBO MAS NMR spectrum of COM (one resonance centered at 5.26 ppm; Figs. 1a and 2). Data obtained at 100 K . COM is always obtained as a final product, as shown by the X-ray powder diffraction (XRD). Subtle variations are observed, depending on the degree of the disorder present, as demonstrated very recently by Shepelenko et al. (2019).
The 1 H spectrum of COD (Fig. 1a) is a priori complex, as it corresponds to the superposition of structural and zeolitic water molecules (Tazzoli and Domeneghetti, 1980;Izatulina et al., 2014). It is much broader than the spectra corresponding to COM and COT. More specific features centered at δ iso ( 1 H) = 4.11, 5.17 and ∼ 6.5 (shoulder) ppm are observed (Fig. 1a). When compared to the COT spectrum, the spectral resolution decreases, as expected, from the partial disorder of the zeolitic water molecules.  16 (H 2 O) 3 ). The water molecules located in the channels of the zeolitic structure are represented in italics in the preceding formula. Taking into account the number of H ... O contacts (in full analogy with the approach described above for COM and COT), among the 19 water molecules, seven molecules are considered as being less rigid (or potentially mobile), of which four of them are structural and three are zeolitic. The remaining 12 water molecules are considered as being rigid. Typical example of rigid (H4) and less rigid (H33/H34) water molecules are presented in Fig. 3b. From Fig. 2, it is then possible to predict the expected ranges of δ iso ( 1 H) for COD. The rules applied are that rigid water molecules correspond to two distinct δ iso ( 1 H) (line 4), whereas less rigid water molecules correspond to a single average δ iso ( 1 H) (averaging of line 5 gives line 6; averaging of line 7 gives line 8). The sum of lines 4, 6 and 8 (in blue) corresponds to the expected 1 H spectrum for COD. On this basis, it is expected (i) that δ iso ( 1 H) is distributed over a much larger range when compared to COM and COT and (ii) that some maxima should be observed (at least two, corresponding to large number of overlapping triangles in Fig. 2). Points (i) and (ii) are in very good agreement with the experimental observations. All in all, the relative predicted positions for δ iso ( 1 H) resonances are in agreement with the experimental data for COM, COD and COT (bottom of Fig. 2), validating the proposed assignments.
As a first conclusion of this section, 1 H DUMBO MAS NMR spectra for COM, COD and COT correspond to use-  (Table A1 and Sect. 6). The effect of eventual local dynamics in the case of the "less rigid" structure is taken into account. For line 1, the structure of COT is considered as being "rigid" (plain green circles). On the basis of the shortest O−H. . .O distance, the six inequivalent protons can be associated in three groups. To each group, a single average δ iso ( 1 H) is assigned. A total of three lines for COT is predicted (represented by the three vertical green solid lines). For line 2, the structure of COM is considered as being less rigid (open squares), while for line 3 the corresponding averaged distances are represented by plain squares. A single average δ iso ( 1 H) is associated as the averaged distances are very close. A total of one line for COM is predicted. The COD case is shown in lines 4 to 8, where COD exhibits both rigid (plain triangles; line 4) and less rigid water molecules (open triangles in line 5 for the four structural water molecules and in line 7 for the three zeolitic water molecules). For line 6, the corresponding averaged distances for the structural water molecules are represented by plain triangles, and for line 8, the corresponding averaged distances for the zeolitic water molecules are represented by plain triangles. A continuum of δ iso ( 1 H) is predicted for COD. The vertical blue dashed lines correspond to the expected limits of δ iso ( 1 H). The two vertical solid blue lines correspond to local maxima, adding lines 4, 6 and 8. At the bottom, the superposition of the 1 H DUMBO MAS NMR spectra for COM (red), COD (blue) and COT (green; see Fig. 1a) is shown. The solid and dashed lines connect the experimental data and the predicted δ iso ( 1 H).
ful fingerprints for analytical purposes as they are clearly characteristic for each phase. Such fingerprints can be used for the analysis of 1 H NMR spectra of KSs (see below). We emphasize that 1 H spectra with an excellent signal-tonoise ratio were obtained within minutes. As δ iso ( 1 H) values are very sensitive to H-bond networks and to local motional averaging, studies performed on synthetic COM, COD and COT were necessary prior to the detailed analyses of KSs. Nevertheless, the following comments have to be made at this stage: (i) first, the 1 H DUMBO MAS methodology (ν rot = 12 kHz, 700 MHz) is comparable to the very fast MAS/very high magnetic field approach (ν rot ∼ 80 kHz, 850 MHz) without any multiple pulses decoupling. In Fig. 1b, the 1 H MAS NMR spectra of COM are presented at various fast/very fast rotation frequencies, from ν rot = 40 to ∼ 80 kHz. As in the case of the DUMBO MAS approach, a single resonance (with a small shoulder) was observed, showing a continuously decreasing linewidth with increasing the MAS frequency. The linewidth obtained at ∼ 80 kHz is still broader than the one observed under DUMBO MAS  Table A1. Color code: red is O, black is C and light pink is H.
conditions. In Fig. 1c, the two approaches are compared in the case of COD. The resolution is slightly enhanced under very fast MAS at 79 kHz, but it remains comparable to DUMBO conditions at 12 kHz. More importantly, the relative intensities are not strictly preserved, indicating that some distortions of the line shapes may occur under DUMBO conditions. It follows that only semi-quantitative data can be extracted, at best, in the case of complex mixtures of hydrated calcium oxalate phases. Moreover, dynamics at room temperature may impact the efficiency of the DUMBO decoupling.
Finally, two KSs (KS1 and KS2) were studied by 1 H DUMBO MAS NMR ( Fig. 1d and e). In the case of KS1, a mixture of COM and COD is immediately detected (in full agreement with FTIR and XRD; not shown here). As stated above, a slight deviation of δ iso ( 1 H) for COM is observed. A semi-quantitative analysis of the COM/COD proportions is possible and could be systematically compared to FTIR analyses (as routinely obtained in hospitals). In addition to COM and COD resonances, the 1 H DUMBO MAS NMR spectrum of KS2 exhibits small new contributions that can be attributed to organic moieties (such as proteins). In this case, a semiquantitative analysis of the KSs appears more difficult to perform. Working at much higher magnetic field, 35.2 T (Gan et al., 2017), and under ultra-fast MAS ( 100 kHz) should lead to increased resolution and easier direct quantification of the spectra. Finally, we mention the fact that DUMBO experiments may be sensitive to local dynamics, especially in the intermediate regime (Paruzzo and Emsley, 2019). It may involve some discrepancies between 1 H and 13 C NMR data in terms of quantification (see Sect. 4).

T
Another KSs sample, KS3, that was studied contained a large proportion of organic moieties (as shown by FTIR). Another option to increase the 1 H NMR resolution is to implement standard Hahn echoes with increasing delays, τ , (up to several milliseconds) and synchronization with the MAS fre- quency. The magnetization associated to the protons characterized by short T * 2 ( 1 H) will dephase very rapidly. 1 H MAS echoes (ν rot = 30 kHz) for KS3 are presented in Fig. 4. From XRD data (not shown here) confirmed by 13 C CP MAS NMR data (see Sect. 4), KS3 contains COM as a major mineral phase. For long τ , sharp lines (associated to mobile components) were obtained, whereas the broader COM component, around 5.2 ppm, was totally suppressed. δ iso ( 1 H) values agree with unsaturated fatty acids (δ iso ( 1 H) ∼ 5.25 ppm; Ren et al., 2008). The presence of triglycerides is excluded as the CH and CH 2 resonances of the glycerol backbone (δ iso ( 1 H) ∼ 5.0 and 4.0 ppm, respectively) were not detected.
Such a level of resolution allowed for the implementation of J-MAS-derived pulse schemes, such as the 1 H− 1 H double quantum-filtered (DQF) correlation spectroscopy (COSY) MAS experiment (based on isotropic J ( 1 H− 1 H) couplings). This experiment is part of the toolbox for a more general dynamics-based spectral editing research topic applied to biological solids (Mroue et al., 2016;Matlahov and van der Wel, 2018;Gopinath and Veglia, 2018). The 1 H− 1 H DQF COSY MAS spectrum is presented in Fig. 5a for KS3. All resonances of the mobile fatty acid chains were assigned in a straightforward way, demonstrating the pertinence of this through-bond correlation experiment. On the other hand, dipolar-based double quantum (DQ) experiments can be implemented to establish through-space proximities between protons (such as back to back or BABA; Feike et al., 1996).
It is a distinct advantage to perform such experiments under very fast MAS (here 79 kHz). Indeed, the spectral resolution is drastically increased, leading to an easier observation of the correlation peaks. The 1 H− 1 H DQ BABA MAS NMR spectrum of KS3 is presented in Fig. 5b. The 1 H resonance corresponding to the COM phase is clearly evidenced on the 1 H projection and on the 2D diagonal (red arrows). Moreover, red dashed ovals indicate correlations involving the protons of the immobile proteins contained in KS3 (essentially the 1 H N − 1 H α , 1 H α − 1 H β regions). 1 H spin diffusion experiments should help to highlight actual correlations between the organic and inorganic components at the interface (Schmidt-Rohr and Spiess, 1994).

Natural abundance 4Ca solid-state NMR experiments
Natural abundance solid-state 43 Ca MAS NMR spectroscopy remains a challenge. Indeed, the NMR characteristics of this quadrupolar nucleus (I = 7/2) are clearly unfavorable, as natural abundance is 0.14 % and low γ (ν 0 = 57.2 MHz at 20 T). Nevertheless, the following four main experimental approaches have been successfully developed during the last few years: (i) using large volume rotors (7 mm; ∼ 400 mg of sample) at high magnetic field (20 T), under moderate MAS (∼ 5 kHz) and implementing DFS (double frequency sweep) excitation scheme (Sect. 6); (ii) using much smaller rotors (3.2 mm; ∼ 20 mg of sample at ultra-high magnetic field (35.2 T) and under moderate/fast MAS (∼ 18 kHz); (iii) using dynamic nuclear polarization (DNP) to strongly enhance the 43 Ca polarization, usually in the indirect mode (from 1 H to 43 Ca); (iv) using labeling in 43 Ca (starting from an enriched calcite precursor; Laurencin et al., 2021;Smith, 2020;Laurencin and Smith, 2013). Here, we follow the approach in (i), which is by far the easiest to implement in most NMR facilities worldwide (as long as a low γ probe is available).
The first contributions related to the study of synthetic calcium oxalates hydrates by 43 Ca MAS NMR spectroscopy were proposed by Wong et al. (2006) for COT and by Bowers and Kirkpatrick (2011) for the three hydrated phases. The latter claimed that the COM line shape could be attributed to an averaged Gaussian signal due to a local disorder in the structure (Tazzoli and Domeneghetti, 1980). Colas et al. (2013) demonstrated that a high signal-to-noise ratio is necessary to extract reliable quadrupolar parameters from natural abundance 43 Ca MAS NMR spectra and reinvestigated the COM phase. Instead of a Gaussian contribution, two distinct resonances were evidenced, which is in agreement with the crystallographic data (δ iso ( 43 Ca) = −2.6 ppm, C Q = 1.50 MHz, η Q = 0.60; δ iso ( 43 Ca) = 0.7 ppm, C Q = 1.60 MHz, η Q = 0.70). The 43 Ca MAS NMR spectra of COM, COD and COT, recorded at 20.0 T, are presented in Fig. 6a. All spectra were obtained in natural abundance in a reasonable amount of experimental time (∼ 2 h for COM and COT; ∼ 4 h for COD). The 43 Ca NMR fingerprints obtained allow for unambiguous distinctions of the three phases. The sharpest line (characterized by the smallest C Q ) is observed for COT (one unique crystallographic site). For this particular phase, second-order quadrupolar broadening is efficiently suppressed at 20 T, leading directly to δ iso ( 43 Ca) = −0.1 ppm. This value is slightly different from the one reported by Wong et al. (2006; i.e., −4.2 ppm). Such a discrepancy can be attributed to a difference in chemical shift referencing (Gervais et al., 2008). The associated quadrupolar parameters for COT (Wong et al., 2006) were C Q = 1.55 MHz, η Q = 0.72. C Q is probably overestimated, as such a value would definitely produce second-order quadrupolar broadening under MAS at 20.0 T (see above the quadrupolar parameters for COM). Finally, a rather featureless spectrum is obtained for COD (one crystallographic site), exhibiting a much larger linewidth than for COT (δ iso ( 43 Ca) ∼ −2.6 ppm, C Q ∼ 1.60 MHz, η Q ∼ 0.20). We assign this broadening to the distribution of zeolitic water molecules (leading consequently to a slight distribution of δ iso ( 43 Ca)). Hence, it is demonstrated that natural abundance 43 Ca MAS NMR spectroscopy is useful for characterizing hydrated calcium oxalate phases. The use of moderate MAS is sufficient to retrieve a satisfactory resolution as characteristic C Q ( 43 Ca) are usually small/very small (< 1.8 MHz). However, the δ iso ( 43 Ca) range covered by these three phases is making this NMR parameter less sensitive to distinguishing the hydrates. This comes from the fact that δ iso ( 43 Ca) is mainly determined by the coordination of the Ca atoms and the mean < Ca−O > distances. These parameters are almost identical for COM, COD and COT (eight-fold coordination for COM and COD; seven-fold coordination for COT; range of averaged Ca−O distances, i.e., 2.47-2.49 Å). This last comment is rather in contradiction with previous conclusions proposed in the literature (Bowers and Kirkpatrick, 2011).
The natural abundance 43 Ca MAS NMR spectra of KS1 and KS2 are presented in Fig. 6b. They are largely similar to the COD spectrum overall. The contribution of a COM component is hardly discernable (though it is present, especially in KS1; see Fig. 7). As stated above, the structure of COM is subject to subtle structural variations which could lead to the overlap of the two 43 Ca resonances. In other words, though interesting in principle, natural abundance 43 Ca MAS NMR spectroscopy (inherently associated with the limited signalto-noise ratio) should not be used as a first solid-state NMR tool of investigation for KSs. However, 43 Ca NMR would benefit from working at a ultra-high magnetic field (35 T) in order to drastically increase the resolution and enhance 43 Ca NMR analytic capabilities. 4 Back to 13 C NMR: spectral edition and reconstruction of spectra 13 C NMR data related to synthetic calcium oxalate phases and KSs are the most represented in the literature. This is probably due to the fact that the spectral resolution is high under MAS and that CP (cross-polarization) MAS experiments can easily be implemented even at low or moderate magnetic field. Typical 13 C CP MAS NMR spectra for COM and COD are presented in Fig. 7. A total of four isotropic resonances are observed for COM, as expected from XRD data (Colas et al., 2013), and one unique broader resonance is observed for COD, as expected from XRD data, considering the disorder associated to the zeolitic water molecules. Such a disorder has an impact on the resolution of the 13 C NMR spectra.
It is observed that the chemical shift range of interest is very restricted (∼ 4 ppm from 167 to 171 ppm), corresponding to ∼ 0.8 % of the whole 13 C isotropic chemical shift range. 13 C CP MAS NMR spectra for KS1 and KS2 are also presented in Fig. 7. The presence of COM and COD components is clearly evidenced and could be quantified if necessary (by increasing the signal-to-noise ratio, S/N, significantly). The S/N is adequate here for coarse quantification. For better accuracy, a longer experimental time will be necessary. Moreover, NMR experiments will be combined with denoising techniques developed recently by Laurent and Bonhomme (2020).
As a matter of fact, a single experiment at fixed contact time (usually > 5 ms) is sufficient, in principle, for quantitative purposes, as 1 H− 13 C dipolar couplings are comparable for all 13 C sites (differences in relative intensities can be evidenced at much short contact time, i.e., < 0.5 ms). The case of KS3 is by far more complex. As stated in Sect. 1, a given KS may include a complex organic component containing lipids, triglycerides, membrane components, glycoproteins (like the Tamm-Horsfall protein) and glycosaminoglycans, among other species (Reid et al., 2011). The approximate chemical composition of KS3 is ∼ 10 % proteins, ∼ 20 %-25 % COM and ∼ 65 % amorphous silica (Dessombz et al., 2016). In Fig. 8, we propose a robust protocol to reconstruct the 13 C MAS NMR spectra starting from well-identified subspectra. At a short contact time (0.8 ms), all carbon-containing species are detected, corresponding to both sharp and broad lines (Fig. 8a).
Then, a T 1ρ ( 1 H) filter was applied by increasing the contact time by a factor of ∼ 10, leading to the drastic reduction in the intensities of the broad components. The four resonances of COM are clearly observed (insert in Fig. 8b). COD is absent, which is in agreement with powder XRD and FTIR data. It follows that the proton spin baths corresponding to COM and the broad components are independent; spin diffusion and domain size measurements could be implemented as complementary experiments (Schmidt-Rohr and Spiess, 1994). The 1D 1 H− 13 C refocused INEPT J-MAS NMR sequence (Fig. 8c) allowed a selective extraction of the mobile components corresponding to the fatty acids (see also Fig. 5a). The unsaturated nature is clearly evidenced by the shift at δ iso ( 13 C) ∼ 130 ppm. Finally, the 13 C CP MAS NMR spectrum ( Fig. 8a; bottom) could be reconstructed with resonances from (i) the COM phase and its associated spinning sidebands (in red), (ii) fatty acids characterized by very sharp lines (in purple) (iii) and proteins (in brown; Cavanagh et al., 2007), for which a precise attribution cannot be given at this stage.  Bak et al. (2000) used 31 P MAS and CP MAS experiments to evidence phosphate-containing phases in KSs. The presence of phosphate groups in KSs is not unusual and is observed mainly by FTIR (Fig. A1). However, their exact chemical nature remains unclear. Phosphates in KSs can correspond to (i) mineral phases, such as substituted (carbonated) hydroxyapatite (Ca 10 (PO 4 ) 6 (OH) 2 ), brushite (CaHPO 4 · 2H 2 O) or struvite (NH 4 MgPO 4 · 6H 2 O), and (ii) organic phosphates present in phospholipids (in the cell membrane) and/or DNA, RNA and adenosine triphosphate (ATP) molecules (Butusov and Jernelöv, 2013). Usually, phosphates are found as minor components in KSs, making 31 P NMR attractive given the high inherent signal sensitivity of 31 P (which is also an I = 1/2 nucleus). A total of six KSs (exhibiting COM as the major phase and the apparent absence of phosphate phases by powder XRD) were studied here. The representative 31 P MAS and CP MAS NMR spectra of the KSs are presented in Fig. 9. The 31 P NMR fingerprint of KS4 is specific (Fig. 9a), whereas KS5 has a 31 P fingerprint analogous to four other KSs (Fig. 9b). The acquisition time is ∼ 2 to 3 h, demonstrating that the amount of phosphate species is indeed small in all samples. One notes a large distribution of δ iso ( 31 P), corresponding not only to structural disorder but also to strong chemical variability. In order to facilitate the assignment of δ iso ( 31 P), 1 H− 31 P HETCOR CP MAS NMR experiments under active temperature control (T = −20 • C) were implemented as well (Fig. 9c). In total, three clear correlations were observed, i.e., δ iso ( 31 P) = 4.6 ppm ↔ δ iso ( 1 H) = 8.7 ppm, δ iso ( 31 P) = 4.6 ppm ↔ δ iso ( 1 H) = 5.7 ppm and δ iso ( 31 P) ∼ 0.25-0.30 ppm ↔ δ iso ( 1 H) ∼ 5.0 ppm. Reasonable assignments are the following (Godinot et al., 2016): (i) the peak centered at δ iso ( 31 P) = 4.6 ppm is assigned to struvite, i.e., NH 4 MgPO 4 · 6H 2 O (Bak et al., 2000). The correlation centered at δ iso ( 31 P) = 4.6 ppm ↔ δ iso ( 1 H) = 8.7 ppm (ammonium groups) is attributed to PO 3− 4 /NH + 4 . The correlation centered at δ iso ( 31 P) = 4.6 ppm ↔ δ iso ( 1 H) = 5.7 ppm concerns water molecules. It is interesting to note that the amount of struvite is extremely small (almost absent in the 31 P MAS NMR spectrum of KS4 and KS5; Fig. 9a and b). (ii) The resonance at δ iso ( 31 P) = 0.3 ppm may be attributed to phosphates in phospholipids (in this case, δ iso ( 31 P) is in the ∼ 1 to −1 ppm range). However, correlations with δ iso ( 1 H) < 3 ppm are almost absent (such resonances should be characteristic for long alkyl chains in phospholipids). Consequently, we assign the 31 P resonance to inorganic (hydrated) orthophosphates. (iii) δ iso ( 31 P) ∼ 2.7 ppm could be potentially assigned to amorphous calcium phosphate with a rather small (rather unusual) level of protonation (this resonance is underestimated in the CP MAS experiment; Fig. 9a). (iv) δ iso ( 31 P) 0 ppm resonances are assigned to pyro-and/or polyphosphates. The 13 C CP MAS NMR spectra and 31 P (MAS and CP MAS) NMR spectra of all samples studied here are given in Figs. A3 and A4, respectively.

Syntheses of hydrated calcium oxalate, kidney stones samples and NMR methods
Synthesis. Calcium chloride (CaCl 2 ) and sodium oxalate (Na 2 C 2 O 4 ) were purchased from Sigma-Aldrich and used as received. All syntheses were carried out using distilled water. For COM, at 40 • C, equimolar aqueous solutions of Na 2 C 2 O 4 and CaCl 2 (0.1 mol. L −1 ) were added simultaneously, dropwise, in a few milliliters of water under magnetic stirring. The mixture was left mixing under these conditions during 2 h before filtration and was then washed with cold water before drying under air. For COD, a Na 2 C 2 O 4 aqueous solution (0.1 mol. L −1 ) and a CaCl 2 solution (1.0 mol. L −1 , Ca/Ox = 10) were prepared the day prior to the reaction and stored between 2-6 • C overnight. The solution of Na 2 C 2 O 4 was added dropwise to the CaCl 2 solution in an ice bath (T < 7 • C) under magnetic stirring. The mixture was left under stirring for 15 min before filtration and was then washed with cold water before drying under air. For COT, in an ice bath, two equimolar (0.001 mol. L −1 ) aqueous solutions of Na 2 C 2 O 4 and CaCl 2 were slowly added simultaneously, dropwise, in a few milliliters of water under vigorous magnetic stirring. The mixture was left under stirring for 15 min before filtration and was then washed with cold water before drying under air. All COM, COD and COT samples were obtained as white fine powders. COD and COT were rapidly stored between 2-6 • C, while COM could be stored at ambient temperature. Kidney stones. The samples were provided by Michel Daudon (Tenon Hospital, Paris, France). The choice of the diameter of the used NMR rotor was dictated by the initial size of the KSs and the implemented experiments. In the case of large KSs, smaller pieces were studied as powders by NMR.
NMR methods. Warning: the COM structure is highly sensitive to temperature variations (≥ 15 • C). The lowest MAS frequencies have to be implemented for all investigated nuclei and active regulation of the sample temperature (Bruker BCU-Xtreme cooling unit). Most of the 1 H MAS and DUMBO MAS NMR spectra presented in Fig. 1 were obtained at 700 MHz (Bruker AVANCE III spectrometer), using a 2.5 mm Bruker MAS probe spinning the sample at 12 kHz (20 to 40 scans; 10 s recycle delay for quantitative measure-ments; 10 • C in temperature; t 90 • ( 1 H) = 3.0 µs; 24 µs duration of the shape length at 113 kHz radio frequency (RF) field). The DUMBO experiment was first set up with glycine as a test sample (including the scaling of the isotropic chemical shift) and then optimized for each compound. Some 1 H MAS NMR spectra were obtained at 850 MHz, using a 1 mm JEOL MAS probe (spinning the sample up to 79 kHz; four scans; 3 s recycle delay; t 90 • ( 1 H) = 1.70 µs). Synchronized Hahn echoes (Fig. 4) were performed at 700 MHz, using a 2.5 mm Bruker MAS probe spinning the sample at 30 kHz (64 scans; 5 s recycle delay; t 90 • ( 1 H) = 2.8 µs; no active regulation of the temperature in order to increase local dynamics; the increase in temperature is estimated to ∼ 40 • C). The 1 H− 1 H DQF COSY MAS NMR experiment (Fig. 5) was performed at 700 MHz, using a 2.5 mm Bruker MAS probe at 30 kHz (32 scans; 2 s recycle delay; t 90 • ( 1 H) = 2.8 µs; 256 increments in t 1 dimension; no active regulation of the temperature in order to increase local dynamics and magnitude mode). The 1 H− 1 H SQ-DQ BABA MAS NMR experiment (Fig. 5) was performed at 850 MHz, using a 1 mm JEOL MAS NMR probe spinning the sample at 79 kHz (16 scans; 3 s recycle delay; t 90 • ( 1 H) = 1.70 µs; two BABA loops, 426 increments in t 1 dimension and no active regulation of the temperature). All 1 H NMR spectra were referenced using adamantane (1.85 ppm) as a secondary reference. All natural abundance 43 Ca NMR spectra (Fig. 6) were obtained at 850 MHz (Bruker AVANCE III spectrometer), using a 7 mm low-γ Bruker MAS single channel NMR probe spinning the sample at 3 to 5 kHz. A DFS (double frequency sweep; Iuga et al., 2000) enhancement scheme, followed by a 90 • selective pulse of 1.5 µs, was used (DFS pulse length of 2 ms, RF ∼ 8 kHz and a convergence sweep from 400 to 50 kHz; 5600 to 18 000 scans; 0.8 s recycle delay). All 43 Ca chemical shifts were referenced at 0.0 ppm to a 1.0 mol. L −1 aqueous solution of CaCl 2 (Gervais et al., 2008). The 1 H− 13 C RAMP (ramped amplitude) CP MAS experiments (Fig. 7) 664 C. Leroy et al.: A novel multinuclear solid-state NMR approach for characterizing kidney stones were obtained at 700 MHz (Bruker AVANCE III spectrometer) using a 2.5 mm Bruker MAS double resonance NMR probe spinning the sample at 5 kHz (600 to 1200 scans; 3 s recycle delay; t 90 • ( 1 H) = 3.1 µs; 2 to 8 ms contact time). The 13 C MAS NMR spectra presented in Fig. 8 were obtained at 300 MHz (Bruker AVANCE III spectrometer) using a 7 mm Bruker MAS double resonance NMR probe spinning the sample at 5 kHz (328 scans; 3 s recycle delay; t 90 • ( 1 H) = 5.2 µs; 0.8 and 9.0 ms contact time; refocused IN-EPT MAS: 6000 scans; 3 s recycle delay; 5.2 and 3.2 µs π/2 pulse on 1 H and 13 C respectively; no active regulation of the temperature). All 13 C NMR spectra were referenced using adamantane (38.48 ppm) as a secondary reference. 31 P 1D and 2D NMR spectra presented in Fig. 9 were obtained at 700 MHz (Bruker AVANCE III spectrometer) using a 2.5 mm Bruker MAS double resonance NMR probe spinning the sample at 30 kHz (≈ 4000 scans for high-power 1 H decoupling experiments and ≈ 3700 for CP MAS experiments; recycle delay: 10 s for high-power 1 H decoupling experiments; 30 • flip angle; 3 s for CP MAS experiments; t 90 • ( 1 H) = 2.0 µs; 5.0 ms contact time for CP MAS experiments). For the 1 H− 31 P HETCOR RAMP CP MAS experiment, the number of scans was 400, the recycle delay was 3 s, t 90 • ( 1 H) = 2.0 µs, the contact time was 5.0 ms, with 96 increments in t 1 dimension, and there was an active regulation of the temperature at −20 • C.
Relaxation of crystallographic structures. Starting from the crystallographic data, COM (Daudon et al., 2009), COD (Tazzoli and Domeneghetti, 1980) and COT (Basso et al., 1997) structures were relaxed at DFT level. The unit cell parameters and the atomic positions were optimized, as previously described for COM (Colas et al., 2013). The Vienna Ab initio Simulation Package (VASP) was used Hafner, 1993, 1994;Kresse and Furthmüller, 1996). The corresponding crystallographic information files (CIFs) are available upon request.

Conclusions and perspectives
This study has demonstrated that the solid-state NMR technique offers a complementary characterization approach for the study of kidney stones and related synthetic model systems. The 1 H DUMBO MAS NMR technique provides unambiguous identification of the different calcium oxalate hydrate phases. This experiment is a rapid-measurement technique which can be easily adapted to yield semi-quantitative data. For the first time, the natural abundance 43 Ca MAS NMR data from the three calcium oxalate hydrate phases have been presented together; these data exhibited sufficient signal to noise to facilitate a complete structural interpretation in agreement with crystallographic data. The extension of this approach to the study of KSs was attempted, showing that a real signal could be measured but with relatively limited discrimination between the different KSs samples. The deconvolution of the 1 H and 13 C MAS NMR data into assigned subspectra aided the interpretation of the data describing the whole system, thus demonstrating that KSs materials are usually a complex association of organic and inorganic components. Additional 31 P MAS NMR studies provided further insight into the composition of the low-level phosphates which are ubiquitous and difficult to characterize in KSs. The development of solid-state NMR, in combination with modern computational DFT and machine learning approaches, would be able to characterize the complex heterogeneous biomaterials such as KSs without ambiguity (Tielens et al., 2021). As part of on-going studies building on the observations here, systematic NMR studies of a large range of KSs from the Tenon Hospital's collection is being undertaken to develop new diagnosis NMR approaches that could impact on developing novel treatments.       Data availability. All the data are shown in all the figures of the paper. The CIFs of COM, COD and COT structures are available upon request from the corresponding author.
Author contributions. CL performed all syntheses and recorded most of the NMR spectra in strong collaboration with CB, DL and DI. CG and FT performed all DFT optimizations. FB and LB-C were deeply involved in the interpretation of the NMR spectra, with the help of MES and JVH. MD, EL and DB provided the KS sample and interpreted the data as both physicians and a physical chemist, respectively. CB wrote the article, with the support of the coauthors.