2.1 Instrumental neutron activation analysis

When a sample is subjected to a high neutron flux, it emits gamma rays, following the decay of radioactive elements which have been produced. The energy and intensity of these gamma rays are directly related to the nature and concentration of the elements present in the sample. This technique has been used to investigate different kinds of biological entities, such as hair [13], liver [14], kidney stones [15,21], gallstones [16], cortical and trabecular bones [17,18,22], human prostate [19], human nails [20], human thumbnails [26] or urine [28].

Several investigations have also been dedicated to kidney stones [34,35]. C. Koeberl and P.M. Bayer [34] have for example determined the presence of rare-earth elements in brain tissues and in kidney stones. Rare-earth elements have an exogenous origin, being mainly incorporated into the human body via ingestion of food or by inhalation of dust particles. The data suggest that rare-earth elements are trapped in kidney stones, by a slow accumulation process. In [35], D. Gompertz et al. have compared biochemical indicators of renal dysfunction with liver and kidney cadmium levels measured by neutron activation analysis in a group of 37 cadmium smelters.

2.2 Neutron powder diffraction (NPD)

Scattering processes between neutrons and atoms are also used by scientists to study matter [36–40]. Neutrons are electrically neutral and interact only weakly with matter, and have, as a result, a penetration depth of several centimeters. Unlike X-rays, they do not interact with the electronic cloud of an atom, but with its nucleus: the strength and character of this neutron–nucleus interaction is characterised by the so-called neutron scattering length. This parameter varies irregularly from one nucleus to another. In particular, it is quite large for light elements like hydrogen, carbon, nitrogen or oxygen, which are almost invisible to X-rays (Fig. 1). Neutrons are thus an important tool in the investigation of the location and dynamics of protons, an essential aspect in many biological processes.

Elastic scattering, or diffraction, describes a process in which the incident and the scattered neutrons have the same energy. The scattering angle θ (as defined in Fig. 2) gives information, through Bragg’s law, on the periodicity of the atomic arrangement (i.e. crystal unit cell parameters). The intensity of the Bragg peaks is related to the cell symmetry and atomic positions within the crystal unit cell.

As shown in Fig. 2, a neutron powder diffraction (NPD) pattern is simply a recording of the intensity of diffraction (in neutron counts) versus the diffraction angle θ.

A typical example of a neutron powder diffractometer is the G4.1 instrument, located at the French neutron source Orphée. The Orphée reactor produces a white neutron beam (broad distribution of wavelengths) and a monochromator is used to select the desired wavelength. The monochromator is commonly a single crystal of germanium or silicon; on the G4.1 beamline, a vertically focusing pyrolytic graphite monochromator is used. The detector is an 800-cell multidetector covering a 2θ range spanning 80°, which collects all reflections simultaneously, thus increasing the data acquisition speed (Fig. 3).

Rietveld refinement [41] is the most common method used for the determination of crystal structures from X-ray or neutron diffraction data. A theoretical diffraction pattern is calculated based on a proposed model, and compared with the experimental data. Gradual changes are introduced into the model, to minimize the difference between the observed and calculated patterns (Fig. 2). This is usually performed using a computer software package such as FullProf, Jana2006, or GSAS [41].

Rather straightforward experimentally, powder diffraction provides after data refinement a wealth of information, not only about the detailed atomic arrangement, but also about the size, the residual strains and the morphology of the powder particles. For instance, the broadening of the diffraction peaks can be the result of two physical factors, either a small particle size or residual microstrain, whose effects can be analyzed separately [42]. The size of nanocrystals can therefore be estimated after analysis of the peak profiles. This can be of clinical importance, as in [43], in which U. Vetter et al. have pointed out significant modifications of the apatite crystal sizes in the bones of patients with osteogenesis imperfecta.

Regarding the orientation of the nanocrystals within a bulk material, diffraction also provides key information: Bacon and Goodship [44] have shown through neutron diffraction that the long bones of animals have the c-axes of their apatite crystals preferentially oriented to withstand stresses. Recent experimental developments combining a monochromatic X-ray beam (<30 μm) with a charge-coupled device camera allow a relatively easy quantification of crystal alignment in bone tissue [45].

3.1 Cystine kidney stones

Recently we have published a neutron powder diffraction (NPD) and FE-SEM investigation on cystinuria [47]. Worldwide, the incidence of cystinuria is about 1:7000 births and represents a major medical problem, because of stone recurrence and the risk to induce renal failure. This genetic disease comes from a mutation in renal epithelial cell transporters [48–53]. More precisely, two different types of cystinuria may be distinguished according to genetics: type A cystinuria, due to mutations along the SLC3A1 gene encoding the rBAT heavy subunit, and type B cystinuria, with mutations in the SLC7A9 gene encoding for light subunit b^0,+ AT [54]. In both A and B cystinuria, mutations result in a deficient reabsorption of the dibasic amino acids and cystine [54,55]. The excessive amount of cystine in urine leads to a high risk of cystine precipitation, and to the formation of stones as a consequence of the poor solubility of this amino acid.

Regarding cystine kidney stones, two morphological types, namely Va and Vb, exist [56–58]. The surface of the first kind of stone (type Va, Fig. 4a) is homogeneous, granular, made of crystals with blunt angles, and is commonly observed in untreated cystinuric patients. When cystinuria is treated with alkali or/and thiol therapy, a second type of cystine kidney stone may appear (type Vb, Fig. 4b).

The salient point of this study comes from NPD, and lies in the result that only the usual alkaline therapy with sodium bicarbonate reduces significantly the growing process of cystine crystals. All the other therapies, namely alkalinization with other salts (Foncitril, Alcaphor, potassium citrate) and thiol therapy (sulfhydryls) based on tiopronine, d-penicillamine or on captopril treatments, seem inefficient. A similar conclusion is obtained through FE-SEM observations. In conclusion, all observations agree that only the usual alkaline therapy with sodium bicarbonate reduces the size of both crystals and crystallites, while other medical treatments only alter the surface of the crystallites.

3.2 Calcium oxalate kidney stones

In western countries, calcium oxalate (CaO_x) is the main component of more than 70% of all kidney stones [59,60]. Among the different crystalline forms, calcium oxalate monohydrate (COM – CaC₂O₄–H₂O), or whewellite, is the most frequent [61–63]. COM kidney stones are related to hyperoxaluria (too much oxalate present in the urine), while excess of calcium (hypercalciuria) in urine leads to the formation of calcium oxalate dihydrate (COD – CaC₂O₄–2H₂O) [64]. Of note, a third species exists, namely calcium oxalate trihydrate (COT – CaC₂O₄–3H₂O – caoxite), which has been observed – rarely – in patients treated with drug containing a precursor of oxalate [65].

Hyperoxaluria may have different origins, from dietary to genetic [57]. At the macroscopic scale, significant differences exist. Intermittent hyperoxaluria of dietary origin corresponding to idiopathic stone formers leads to stones with a dark-brown smooth or mammillary surface; for primary hyperoxaluria [66–72] stones have a surface with a mulberry-shaped aspect of cream or pale yellow–brown color [57]. These different kinds of hyperoxaluria lead to the same whewellite chemical phase.

To compare the structural characteristics of the stones at the mesoscopic and nanometric scale, NPD and FE-SEM studies were carried out [73]. The crystal structure of whewellite was first revisited using single-crystal neutron diffraction at room temperature. Then, whewellite stones corresponding to different kinds of hyperoxaluria were examined, at the mesoscopic scale with FE-SEM, and at the nanometric scale with NPD (Fig. 5). The results show that, although the various whewellite kidney stones exhibit similar neutron diffraction patterns, significant differences exist at the mesoscopic scale, which explains the polymorphism of whewellite stones observed at the macroscopic scale. Combined NPD and FE-SEM datasets therefore define a completely new medical diagnosis of primary hyperoxaluria [74], a rare inherited disease, leading to recurrent nephrolithiasis, nephrocalcinosis, systemic oxalosis, and renal failure, ultimately requiring combined kidney and liver transplantation.

3.3 Struvite kidney stones

Unlike more common calcium kidney stones, struvite stones [75–80] are formed by bacterial waste products during a kidney or urinary tract infection (UTI). Struvite kidney stones can lead to rapid obstruction, hydronephrosis, recurrent pyelonephritis, and decreased kidney function; owing to the urine decomposition process, large (cm) kidney stones can grow over a period of a few weeks. Urea-splitting bacteria such as Proteus, Staphylococcus, Pseudomonas, Providencia, and Klebsiella generate struvite kidney stones [81–83]. In addition, urease-negative bacteria like those with weak urease activity, such as some strains of Escherichia coli, may also be involved in the formation of struvite renal calculi, although urease-positive bacteria seem to play a greater role. If these organisms leave their imprints at the surface of kidney stones made of apatite, the presence of such imprints has not been found at the surface of struvite kidney stones. Moreover, in a stone containing both carbonated apatite and struvite components, bacterial imprints were observed on the carbonated apatite but not on the struvite part.

NPD can provide an understanding of this apparent contradiction between clinical data gathered at the hospital and observations obtained through FE-SEM [84]. A typical diffraction pattern collected for a struvite kidney stone is compared in Fig. 6 with the pattern of an apatite kidney stone. Even if the background level was high (owing to the large hydrogen content of the biological samples), the high quality of the signal-to-noise ratio allows one to perform a complete Rietveld-type refinement, with an analysis of the crystallite size for both samples. While struvite kidney stones consisted of quite large nanocrystals (250 nm), as expected from the well-defined diffraction peaks (Fig. 6), crystallites in carbonated calcium phosphate apatite kidney stones are much smaller, ∼50 nm. To explain the absence of bacterial imprints at the surface of struvite kidney stones, an analogy with a man walking on a beach can be drawn: if the beach is made of sand, footprints may be observed, but if the beach is made of stone, no footprints will be seen. Therefore, a relationship between the size of bacteria and the size of nanocrystals becomes relevant when looking for bacterial imprints: bacterial imprints may appear with small calcium carbonated apatite nanocrystals, rather than with large struvite nanocrystals. This result obtained through neutron diffraction has a major clinical significance. Neutron diffraction diagrams validate an approach in which infection leads to the presence of struvite kidney stones or the presence of bacterial imprints at the surface of Ca phosphate apatite even if infection is asymptomatic. Indeed, for several patients without any symptoms related to infection (negative urinary test, no fever…) and which have kidney stones without struvite or Ca apatite with a high carbonation rate, observations through Field Emission Scanning Electron Microscopy (FE-SEM) point out the presence of bacterial imprints. Antibiotic therapy starts immediately, avoiding major kidney infection, which can lead to the loss of the kidney function and thus to dialysis and kidney graft.

3.4 Apatite kidney stones and ab initio simulation

Regarding nanometer scale particles, it is also possible to build neutron (or X-ray) diffraction intensity I(q) through Debye scattering [85–91].

In this equation, I(q) is the angle dependent intensity from coherent scattering, the sums over i and j are over all the atoms, R_ij is the distance between the atoms i and j, and b_i and b_j are the neutron scattering lengths of the different atoms i and j. It is quite easy to build a structural model for particles displaying different morphologies (cylinders, spheres, etc.) and to calculate the scattering intensity. More precisely, A. Guagliardi et al. [92] have used the hexagonal P6₃/m structure [93–95] as the building block for constructing a family of nanocrystals.

Following this approach, it is possible to calculate scattering profiles for different particle shapes, and match them to experimental data (Fig. 7, in the case of nanocrystals of Ca phosphate apatite). The next step will be to study the effect of other parameters, such as cationic substitution in the nanocrystals investigated.