TXRF Spectrometry for Investigating CaF₂:Nd³⁺,Y³⁺ Nanoparticle Diffusion in Tumoral Cancer 3D Spheroids

Abstract

Understanding the interactions of nanomaterials with complex tumour models is essential for advancing their use in nanomedicine. Calcium fluoride nanoparticles doped with neodymium and yttrium (CaF₂:Nd³⁺,Y³⁺) exhibit promising properties for biomedical applications, particularly for optical sensing and tagging. This study investigates their interaction with 3D cell spheroids derived from breast cancer, from Michigan Cancer Foundation-7 (MCF-7) and brain cancer, from Uppsala 87 Malignant Glioma (U-87 MG) cell lines as tumour models. Specific protocols have been developed in Total-reflection X-Ray Fluorescence (TXRF) to evaluate nanoparticles’ internalisation and diffusion within spheroids by quantifying the concentrations of Ca, Nd, and Y taken up by the cells. Minimal background interference enabled precise multi-element detection in low-volume biological samples, yielding very low detection limits and minimal uncertainties. The study demonstrates the effectiveness of TXRF for quantifying rare-earth-doped nanoparticles in 3D cancer models and reveals that, although both cell lines permit nanoparticle diffusion into cells, higher accumulation is observed in glioblastoma cell spheroids. A Weibull diffusion model was applied to help understand the observed internalisation kinetics of nanoparticles into U-87 MG and MCF-7 spheroids. The relevant differences suggest cell-line-dependent uptake behaviour, potentially influenced by differences in cellular architecture, the porosity of the generated spheroid, and its intercellular 3D microstructure. These findings highlight the importance of tumour-specific interactions in the investigation of nanoparticle systems for targeted cancer diagnostics and therapeutics.

1. Introduction

Rare-earth-doped nanoparticles (NPs) are increasingly recognised as valuable tools in nanomedicine for their distinctive optical properties, chemical stability, and low cytotoxicity [1]. Moreover, electronic shielding produces narrow emission bands, enabling deconvolution from other luminescent signals and making them valuable as optical sensors. Among these, calcium fluoride nanoparticles doped with neodymium and yttrium (CaF₂:Nd³⁺,Y³⁺) have been demonstrated for thermal sensing applications and as near-infrared optical labels [2,3].

To assess their suitability in biomedicine, it is essential to study their interactions with biologically relevant models. Three-dimensional (3D) cell spheroids provide an advanced in vitro system that more closely replicates the architecture and microenvironment of solid tumours than conventional two-dimensional (2D) cultures. As 3D structures, spheroids exhibit gradients of oxygen, nutrients, and pH, as well as realistic cell–cell and cell–matrix interactions, making them well-suited for evaluating nanoparticle diffusion kinetics in a more realistic manner [4]. In this study, adenocarcinoma breast cancer spheroids (MCF-7) and brain cancer spheroids (likely glioblastoma) (U-87 MG) were selected as representative models of two clinically significant cancer types with distinct biological characteristics. Understanding the extent to which CaF₂:Nd³⁺,Y³⁺ NPs interact with these 3D systems provides insights into cellular uptake, retention, and elemental distribution.

Since the ultimate application of these NPs is as optical sensors, mainly for thermometry, it is essential to quantify the amount of material internalised by the cells. NPs’ concentration in the sample directly affects the emission signal-to-noise ratio, which must be carefully evaluated and optimised to ensure reliable temperature readouts. A low internalised dose may result in insufficient signal, whereas excessive uptake can induce cytotoxic effects. Therefore, understanding the rules governing the material’s entry into the spheroids is a critical step in optimising nanosensor performance.

To investigate the NPs–spheroid interactions, Total-reflection X-Ray Fluorescence (TXRF) was employed for the first time with this nanoparticle type. TXRF is a highly sensitive, multi-elemental technique capable of detecting trace amounts of calcium, neodymium, and yttrium in biological samples. It requires minimal sample preparation and provides quantitative elemental analysis with excellent precision, making it particularly suitable for nanoparticle tracking in complex cell models. TXRF is widely applied across diverse scientific fields, including catalysis, biochemistry, materials science, and archaeometry [5,6,7,8,9,10,11,12,13,14,15,16], among others. In fact, previous studies have demonstrated its effectiveness for nanoparticle analysis and bio-sample quantification [17,18,19,20,21,22,23,24,25,26,27,28,29], highlighting its versatility and analytical robustness. Regarding nanoparticle interactions with biological samples, several applications are available, mostly focusing on Au nanoparticles and their detection in blood [30,31], quantification of cytotoxicity in cancer cells [32,33], or detection of their presence in tissues [20,34]. Work on spheroids is scarce and limited to micro X-Ray Fluorescence (µ-XRF) for nanoparticle localisation [35,36,37,38]. However, the sensitivity of TXRF enables accurate quantification of the total nanoparticle load within cell aggregates, information that becomes increasingly relevant as 3D spheroids are used as an intermediate model between monolayer culture and in vivo studies.

Working with three-dimensional biological samples (tissues) is challenging and has been addressed through lyophilisation [20] or by using histological sections [34], mainly to detect gold nanoparticles. Based on this background, the main goal of this work is to develop a rapid microanalytical method to quantify the uptake of CaF₂:Nd³⁺,Y³⁺ NPs and to compare their interactions in adenocarcinoma and glioblastoma spheroids. To do this, we have considered the most relevant parameters to describe the incubation treatments: time and NPs concentration in the medium. These findings will contribute to a better understanding of nanoparticle interactions in tumour-like environments and support their potential application in cancer nanotheranostics. To our knowledge, this is the first report of TXRF for studying nanoparticle uptake in complete 3D spheroid systems.

2. Results and Discussion

Three-dimensional tumour spheroids were treated with CaF₂: Nd³⁺,Y³⁺ nanoparticles as described in Section 3, and subsequently prepared for TXRF to quantify the amount of internalised material. Because this required complete digestion of both spheroids and nanoparticles, a dedicated micro-digestion and standardisation protocol was developed and validated before analysing the experimental results.

2.1. Qualitative Evaluation

Following the experimental workflow and after complete digestion of the spheroids (Section 3), the samples were qualitatively evaluated. Figure 1 shows the TXRF spectra obtained for U-87 MG and MCF-7 spheroids, both pure and treated with CaF₂:Nd³⁺,Y³⁺ NPs.

Figure 1. (a) Comparison of the elemental profile of U-87 MG spheroids incubated in the same way with (red) and without (blue) Ga spiked as an internal standard. (b) Comparison of the elemental profile detected of U-87 MG (blue) and MCF-7 (red) for three spheroids. (c) Comparison of the TXRF spectra of U-87 MG spheroids (blue) and MCF-7 spheroids (red) exposed to 750 ppm of CaF₂:Nd³⁺,Y³⁺ NPs for 48 h, digested and standardised with 333 ppb of Ga, both normalised to the K_α signal of Ga.

Figure 1a presents the elemental profile of U-87 MG spheroids incubated under identical conditions with (red) and without (blue) Ga spiked as an internal standard (IS), confirming that it does not interfere with any other elements from the sample. Figure 1b compares the elemental profile of U-87 MG (blue) and MCF-7 (red). Spectra show that the TXRF spectral lines of the elements associated with the samples, likely including trace impurities from cell culture medium, phosphate buffer saline solution (PBS), and the intracellular contents of the spheroids, were P-K_αβ, S-K_αβ, Cl-K_αβ, K-K_αβ, Ca-K_αβ, Ti-K_αβ, Fe-K_αβ, Cu-K_αβ, Zn-K_αβ, and Br-K_αβ. Additionally, Si-K_αβ, Ar-K_αβ, and Ga-K_αβ are present due to the quartz reflector, the air in the total-reflection chamber, and the internal standard, respectively. These spectra also indicate that the overall elemental profile is nearly identical across both cell lines; however, the abundances of several elements vary significantly between them, with S, Zn, and Br lower in the adenocarcinoma spheroids than in the glioblastoma ones.

Figure 1c shows the comparative TXRF spectra of the digested samples of U-87 MG (red) and MCF-7 (blue) spheroids treated with 750 ppm (µg/mL) of CaF₂:Nd³⁺, Y³⁺ NPs for 48 h, normalised to the K_α signal of the IS added. The comparison demonstrates the high analytical sensitivity of TXRF for detecting CaF₂:Nd³⁺, Y³⁺ NPs within the investigated cell spheroids. The well-resolved Ca-K_αβ, Nd-L, and Y-K_αβ signals are clearly observed in both spectra. Additionally, a significant difference in the amount of CaF₂:Nd³⁺, Y³⁺ NPs is observed, as indicated by the intensity of the signals related to the NPs’ components (Ca, Nd and Y). Thus, this qualitative approximation suggests that the NPs are more abundant in U-87 MG spheroids than in MCF-7 spheroids.

2.2. Baseline Elemental Profile of Control Spheroids

Three control samples of the U-87 MG cell line were specifically prepared to test the ability of TXRF to detect and quantify the cellular elemental composition. Control samples C1, C3, and C5 contain 1, 3, and 5 U-87 MG spheroids, respectively, and were resuspended in 20 μL, 60 μL, and 100 μL of water, respectively. Figure 2a shows the results obtained after sample preparation, as described in Section 3.2.2. The elements P, S, Cl, and K increase proportionally with the number of spheroids evaluated, indicating that they are correlated with the cellular composition of the spheroids. This observation is consistent with previous studies on cancer tissues, which demonstrate that TXRF is particularly sensitive to light elements in cells, such as P and S [8]. Interestingly, this technique has also shown that increased levels of K and, to a lesser extent, Cl are present in some cancer cells, distinguishing them from healthy tissues [9].

Figure 2. (a) Comparative spectra for 1 (blue), 3 (red), and 5 (green) U-87 MG spheroids, normalised to the Ga signal. (b) Linear correlation of the concentrations of the elements P, S, Cl, and K versus the number of spheroids (cells) evaluated.

The remaining elements show only aleatory variations, suggesting they may also be linked to other uncontrolled sources, including traces of cell culture medium and PBS. Notably, Y and Nd were not detected in these samples; thus, their concentrations are below the detection limits of 7 and 22 ppb (ng/mL), respectively. Ca was detected in the blank at a low concentration of 0.64 ppm, even in the C5 sample, indicating a negligible blank signal (<2%) for all cases evaluated. This is relevant in the next experiments, where NPs are quantified, as Ca is a constituent element.

Figure 2b shows the linear correlation between the concentrations of the elements P, S, Cl, and K and the number of spheroids (and thus, cells). This trend verifies several aspects. First, it demonstrates the ability of TXRF spectrometry to quantify intracellular elements. Second, the high correlation coefficients obtained (0.947–0.999) point to a linear relationship between the TXRF signal and the number of spheroids. This relationship can eventually be used as a rough estimate of the number of cells in an experiment, with K and P being the most sensitive indicators. However, this approximation must be used with caution, as the elemental composition of cells may vary between batches depending on their metabolic state or age. Third, interpolation to zero spheroids reveals residual traces of cell-culture medium and PBS (blank), with P = 9.22 ppm, S = 3.54 ppm, Cl = 2.75 ppm, and K = 10.34 ppm.

2.3. Analytical Parameters

2.3.1. Average Concentrations and Detection Limits

So far, we have observed that the detected elements are qualitatively derived from two primary sources. First, Ca, Nd, and Y correspond to the NPs investigated in the exposure-concentration and incubation-time experiments. Second, P, S, K, Ca, Fe, Cu, and Zn, come from the cellular composition of the spheroids, supplemented by induction and additional contributions from the culture medium and from PBS.

On this basis established for spheroid analysis, we can now proceed to quantify NP internalisation. It must be noted, though, that the halogens Cl and Br are not present now due to their aleatory loss by evaporation in the acid digestion and IS addition. The average concentrations obtained in parallel for three samples of U-87 MG spheroids exposed to 750 ppm of CaF₂:Nd³⁺,Y³⁺ NPs were used in this part of the study. Table 1 presents the average values, coefficients of variation (CVs), and detection limits (DLs). Detection limits were calculated by using the adaptation of the Poisson statistic to the counting measurement shown in Equation (1).

$$D{L}_x=3{\displaystyle \frac{C_x}{N_x}}\sqrt{N_B},$$

(1)

where C_x is the concentration of element x, associated with its net peak intensity N_x and the background intensity N_B, both expressed as net counts.

Table 1. Average concentration C, coefficient of variation CV, and detection limits DL obtained for the sample of U-87 MG glioblastoma spheroids (m = 3) exposed to 750 ppm of NPs during 48 h.

Element	C (µg/mL)	CV (%)	DL (µg/mL)
Ca	27.46	0.741	0.13
Y	5.29	0.091	0.02
Nd	0.95	0.035	0.05
P	34.60	1.85	1.11
S	2.74	0.360	0.62
K	22.00	0.845	0.17
Fe	0.100	0.021	0.021
Cu	0.050	0.017	0.011
Zn	0.090	0.019	0.009

The first group of elements (Ca, Nd, Y), originating from the investigated nanoparticles, appears at relatively low concentrations compared with endogenous elements such as P and K. Detection limits (DL) are low for most elements, ranging from 9 ppb for Zn to 1.11 ppm for P, showing the high sensitivity of the TXRF technique for this analytical application. When comparing DL with average concentrations, all measured values lie above their corresponding detection limits. For Ca, a concentration of 27.46 ppm was obtained after blank subtraction, with a DL of 0.13 ppm, indicating that the signal is well above the threshold in all cases. P has the highest concentration (34.56 ppm), whereas its detection limit (1.11 ppm) is relatively high compared with the others. This behaviour can be attributed to the lower sensitivity of P, evidenced by its low-energy K_α fluorescence signal at 2.01 keV. Ca and K also exhibit high concentrations, but low detection limits, indicating high detectability. Trace elements such as Cu, Zn, and Fe appear at very low concentrations, yet their detection limits are even lower, suggesting that they remain measurable with good sensitivity for evaluating cellular media contents.

2.3.2. Stoichiometric Recovery of CaF₂:Nd³⁺,Y³⁺ Nanoparticles

The CaF₂:Nd³⁺,Y³⁺ NPs were synthesised to obtain a molar ratio of 1:0.1:0.01 (Ca:Y:Nd), which implies a theoretical mass proportion of 88.3:10.05:1.6 weight percentage (wt%). This specific composition was selected based on previous studies describing the roles of Nd³⁺ and Y³⁺ in luminescence. It represents an optimal compromise that provides high thermal sensitivity (as the particles are used as thermal sensors) while keeping a good signal-to-noise ratio [2].

Based on the known mass proportion, TXRF was used to determine the stoichiometry of the synthesised nanoparticles under investigation. Two groups of aleatory samples were measured: first, seven samples of glioblastoma spheroids exposed to different concentrations of CaF₂:Nd³⁺,Y³⁺ NPs; and second, a group of five samples from different NP syntheses in aqueous solution to estimate their stoichiometry without distortion from bioaccumulation or digestion.

The results, presented in Table 2, indicate a perfect correlation between the theoretical NPs composition and the TXRF analytical results. Recovery rates ranging from 96% to 109% for the three phases of the NPs matrix (CaF₂, Nd, and Y) provide strong evidence of the reliability of the TXRF measurements. The uncertainties, expressed as coefficients of variation (CVs) in per cent, showed a clear dependence on concentration, with lower values observed at higher concentrations. When comparing the NPs after incubation and digestion with those directly synthesised in suspension, no analytical differences were detected. Thus, the comparison between the CaF₂, Y, and Nd results for both groups, NPs bioaccumulated in U-87 MG spheroids and colloidal suspension of NPs synthesised, is statistically equivalent within one standard deviation (see Table 2). The analytical values were as follows: for CaF₂ wt% results, 88.7 ± 1.3 versus 87.4 ± 0.6; for Y wt% results, 9.6 ± 1.1 versus 10.9 ± 0.6; and for Nd wt% results, 1.7 ± 0.3 versus 1.7 ± 0.2.

Table 2. Average stoichiometric NPs concentration C (wt%), standard deviation sd (wt%), coefficient of variation CV (%), and Recoveries (%) obtained for different U-87 MG spheroids treated with NPs (n = 7) (Up) and for NPs from different syntheses in suspension (n = 5) (Down).

	Element	Theo (wt%)	C (wt%)	sd (wt%)	CV (%)	Recovery (%)
NPs in U-87 MG Spheroids	CaF2	88.3	88.7	1.3	1.5	100.5
	Y	10.0	9.6	1.1	11.3	96.0
	Nd	1.6	1.7	0.3	15.3	106.3
NPs in Suspension	CaF2	88.3	87.4	0.6	0.7	99.0
	Y	10.0	10.9	0.6	5.5	109.0
	Nd	1.6	1.7	0.2	11.4	106.3

2.3.3. Spike-Recovery Assessment

In a broader context, spike-and-recovery validation is a technique used to assess the accuracy and recovery of analytical methods by adding a known amount of an analyte to a sample matrix. This procedure helps to evaluate the performance of the analytical method in the presence of potential matrix effects or when applied to new matrices. The spike-recovery percentage is a reliable indicator of the method’s accuracy in analytical methodology [39]. This aspect is particularly relevant in our case because no certified reference materials are available for CaF₂:Nd³⁺,Y³⁺ NPs interacting with specialised matrices such as MCF-7 and U-87 MG cell lines. To evaluate the recovery percentage of the Ca and Y constituents, two U-87 MG samples exposed to 750 ppm of NPs were used. After digestion, both samples were spiked with 5 ppm of Ca and Y using monoelemental standards with certified nominal concentrations of 1000 ppm from SCP Sciex (Ontario, Canada). Nd was not added because no suitable monoelemental reference standard was available. Under these conditions, the average recoveries were 109% for Ca and 102% for Y, respectively. Given that both values are close to 100%, we can assume that matrix interference can be considered negligible and that TXRF analytical accuracy is high.

2.3.4. Uncertainty Evaluation

Once the methodology was characterised, experiments were conducted to evaluate three primary sources of uncertainty in TXRF measurements: instrumental uncertainty (U_Ins), roughness uncertainty (U_Rough), and methodological uncertainty (U_meth). The uncertainties were assessed following the procedure described by Fernández-Ruiz [40]. In this approach, the empirical expanded TXRF uncertainties, U_x, expressed as a percentage for each element, x, can be evaluated with a 95% confidence level (k = 2) as:

$$U_x={\displaystyle \frac{100}{C_x}}\sqrt{{\displaystyle \frac{4}{n(n-1)}}{\sum }_{i=1}^n{\left(C_x^i-C_x\right)}^2},$$

(2)

where C_x is the average concentration value for element x, n is the sampling order, and Cⁱ_x is each concentration value obtained for element x. Instrumental uncertainty quantifies variability arising from the spectrometer, mechanical stability, acquisition spectra, deconvolution algorithm, and other instrumental parameters. To assess it, a single deposition was analysed three times (n = 3), with the reflector introduced, removed, and reinserted between measurements to adequately account for mechanical stability. Roughness uncertainty informs us about microscopic inhomogeneities in the sample layer deposited on the TXRF reflectors. It was calculated by analysing the same deposition at different relative positions between the reflector’s surface and the X-ray beam source. This was achieved by rotating the reflector position in 120° steps until a full rotation (n = 3) was completed. Finally, methodological uncertainty quantifies the global reproducibility of the methodology described in this study. To calculate it, three samples (n = 3) prepared in parallel were analysed. Figure 3 illustrates the sampling process used to estimate methodological uncertainties. The expanded uncertainties obtained for a sample containing five glioblastoma spheroids exposed to 750 ppm of CaF₂:Nd³⁺,Y³⁺ NPs are shown in Table 3.

Figure 3. Sampling process used to estimate the three uncertainty sources: methodology, roughness, and instrumental uncertainties.

Table 3. Methodological, roughness and instrumental expanded uncertainties obtained for the elements evaluated in the TXRF quantifications.

Element	UMeth (%)	URough (%)	UIns (%)
Ca	3.12	1.1	1.1
Y	4.20	2.5	1.6
Nd	9.60	6.8	6.0
P	9.40	6.3	1.8
S	10.60	6.8	4.1
K	4.43	3.3	0.8
Fe	8.51	3.6	6.5
Cu	14.56	3.4	4.2
Zn	13.98	2.4	4.0
Mean ± sd	10.2 ± 4.1	4.3 ± 2.1	3.5 ± 2.1

Figure 4 presents a global view of the uncertainties obtained for this TXRF protocol, including the three elements associated with the nanoparticles (Ca, Y, and Nd) and those related to the cellular composition (P, S, K, Fe, Cu, and Zn). The arrows indicate the average uncertainties for the methodological (blue), roughness (red), and instrumental (green) components. It is observed that the average uncertainties follow the trend:

$$10.2 \pm 4.1 > 4.3 \pm 2.1 > 3.5 \pm 2.1 ⟹ {\overline{U}}_{Meth}>{\overline{U}}_{Rough}>{\overline{U}}_{Ins,}$$

(3)

which is consistent with the expected behaviour of the evaluated uncertainty sources. In fact, this trend has also been reported previously for soil analysis using the suspension-assisted TXRF (SA/DSA-TXRF) methodology [41]. Nevertheless, the behaviour of the trace elements Fe, Cu and Zn deviates from this general pattern, showing U_Ins > U_Rough for all three elements (see Figure 3). This is a surprising fact from a sampling standpoint, probably related to the low concentrations of these elements (in the ppb range), which can increase variability and, combined with the deposition roughness, may lead to this anomalous behaviour. Additionally, the non-homogeneous 3D distribution of the TXRF depositions may play a role.

Figure 4. Uncertainties obtained for each element and for each expanded uncertainty are shown. Arrows indicate the average values for methodology (blue), roughness (red), and instrumental (green).

To better visualise this distribution, Figure 5 (left) shows an optical microscopy image of a 10 μL deposition from a U-87 MG control sample. Figure 5 (right) presents a 3D projection of the same image, generated with 3D Builder 20.0.4.0 software, illustrating the complex, rough morphology of the TXRF deposition. The Z-axis was derived from the grey-scale values of the original image. Thus, it does not represent the actual thickness of the sample at each XY point, but it helps visualise relative height differences. Figure 5 (right) reveals a pronounced volcanic morphology with a coffee-ring edge and significant thickness variations as a function of the deposition angle relative to the incident X-ray beam. This fact supports the explanation previously provided for the anomalous variability observed in the trace element measurements.

Figure 5. Left: optical microscope image of 10 μL deposition of a control sample of U-87 MG spheroids. Right: 3D projection of the same image made with the software 3D Builder 20.0.4.0.

2.3.5. Verification of the Deposition Chemical Homogeneity

One of the most critical aspects of TXRF quantification is ensuring that the spatial distributions of the analytes and the IS under evaluation are comparable. To assess this analytical aspect, µ-XRF was used to analyse the same U-87 MG depositions. The obtained results are shown in Figure 6, including 2D elemental maps of the most representative elements of the cellular composition (P, S, K, and Ca) together with Ga (the IS). The maps reveal that all elements are distributed in a ring shape, which colocalises with the IS, thereby preventing quantitative distortions in TXRF measurements due to spatial heterogeneity.

Figure 6. µ-XRF maps showing the spatial distribution of some elements associated with U-87 MG spheroids, together with Ga used as an IS in three different residues deposited on a TXRF quartz reflector.

2.4. Uptake of CaF₂:Nd³⁺,Y³⁺ Nanoparticles

After validating the TXRF methodology, the protocol was applied to investigate the intracellular diffusion of CaF₂:Nd³⁺,Y³⁺ NPs in U-87 MG and MCF-7 spheroids. For each cell line, the effects of NP concentration and exposure time were evaluated.

2.4.1. Concentration-Dependent Nanoparticle Uptake

As described in Section 3.2, four different NP concentrations were prepared in the cell culture medium and tested for internalisation in the spheroids. Based on the quantification of Nd and Y, the NPs concentrations measured in the spheroids are plotted in Figure 7a for both cell lines. Note that the data have been normalised to the number of spheroids in each sample. From these data, cellular uptake was calculated as:

$$Cellular Uptake \% = 100 \times {\displaystyle \frac{C_{NP} \left(\frac{\mu g}{Sph.mL}\right)}{C_0(\mu g/mL)}},$$

(4)

where C_NP represents the concentration of internalised NPs per spheroid, and C₀ is the starting concentration of NPs used during incubation.

Figure 7. (a) Mass of NPs internalised per spheroid and (b) cellular uptake of CaF₂:Nd³⁺,Y³⁺ NPs for U-87 MG (red) and MCF-7 (blue) spheroids versus NPs concentration added to the cell culture medium.

Figure 7 reveals significant differences in the interaction of CaF₂:Nd³⁺,Y³⁺ NPs with the two cell lines. The absolute amount of internalised NPs is significantly higher in U-87 MG spheroids than for MCF-7 ones (Figure 7a), reaching a four-fold increase at an incubation concentration of 750 ppm. In both cases, a saturation effect is observed as the NPs dose increases. If we focus on cellular uptake, U-87 MG spheroids also exhibit higher values than MCF-7 across all NP exposure doses. However, uptake percentage decreases linearly with increasing NP concentration during incubation, meaning that although more NPs interact with cells, a larger fraction remains in the culture medium and is removed during washing.

A possible explanation for the differences between cell lines lies in their distinct 3D morphologies and cell–cell adhesion characteristics. The final density of the spheroids depends on the culture method and can vary with several parameters, including passage number and culture medium. In our case, microscopic inspection shows that U-87 MG cells form coarse spheroids (Figure 8a–c), likely more porous than those formed by MCF-7 cells, which appear as compact and smooth spheres (Figure 8d–f). This observation is consistent with the findings of Froehlich et al. [42]. According to their classification, U-87 MG spheroids fall into an intermediate stage between compact aggregates and fully formed spheroids. This becomes clear during handling, as U-87 MG spheroids require longer to reach a stage where they can be manipulated without disintegrating.

Figure 8. Optical microscopy images of (a) 2D cell cultures of U-87 MG cell cultures, (b) a spheroid formed from 4.000 cells at day 4, and (c) a higher-magnification view of the spheroid edges. Equivalent optical images obtained for the MCF-7 cell line, including (d) the monolayer culture cells, (e) a spheroid grown under the same conditions, and (f) a magnified view of the spheroid edge.

In addition, U-87 MG spheroids tend to be larger, resulting in a 3-fold increase in the surface area exposed to the surrounding medium, which in turn increases the number of potential contact sites for NP interaction. As a result, the combined effects of increased porosity, surface roughness, intercellular spacing, and available surface area increase the likelihood of nanoparticle–cell interactions and facilitate intracellular diffusion, thereby explaining the results observed in Figure 8.

2.4.2. Time-Dependent Nanoparticle Uptake

Spheroids treated with NPs for different exposure times were prepared as described in Section 3.2. As in the previous section, the mass of NPs internalised per spheroid and the cellular uptake were calculated from TXRF measurements. The resulting values for both cell lines are plotted in Figure 9.

Figure 9. (a) Internalised mass per spheroid and (b) cellular uptake of CaF₂:Nd³⁺,Y³⁺ NPs for U-87 MG (red) and MCF-7 (blue) spheroids versus treatment time. Continuous lines are plotted as a guide for the eye.

Significant differences are again observed between the two cell lines, with values consistently higher in U-87 MG than in MCF-7 spheroids. In both cases, the logarithmic plot in Figure 9 underlines a progressive reduction in the rate at which NPs enter the spheroid. For MCF-7, a saturation stage is reached, where the internalised mass changes very little despite longer treatments. This behaviour is consistent with the gradual reduction in NP concentration in the culture medium due to internalisation, along with its accumulation, either intracellular or within the intercellular space.

2.4.3. Analysis of Nanoparticle Diffusion Dynamics

To further characterise the process, the NP uptake was fitted to a stretched-exponential function based on the Weibull diffusion model. Widely used in pharmacology to describe complex drug-release kinetics, it is particularly suitable for systems with radial geometry, which is the case here. Carr et al. [43] demonstrated that diffusion in such geometries is inherently multi-exponential; thus, a simple first-order model becomes inaccurate. Instead, the Weibull function provides a compact three-parameter model that captures the effective diffusive behaviour.

For the cumulative NPs content inside the spheroid as a function of time, the Weibull function can be expressed as:

$${C\left(t\right)}_{NPs}=C_{\infty }\left(1-e^{-{(t/\tau )}^{\beta }}\right)$$

(5)

where the parameters C_∞, τ and β have the following physical meaning: C_∞ reflects the maximum nanoparticle load achievable by the spheroid; τ represents the characteristic timescale of the diffusion process and depends on the effective diffusion coefficient and spheroid geometry; β determines the curvature of the kinetic profile and provides insight into the underlying transport mechanism. Values of β < 0.7 indicate sub-exponential kinetics, typically dominated by diffusion (linked to Fick’s law). Values of β between 0.7 and 1.1, correspond to near-exponential behaviour and suggest anomalous transport arising from the combined influence of several processes. Finally, values of β > 1.1 suggest accelerated transport, approaching sigmoidal kinetics and reflecting the likely contribution of additional uptake or active transport processes [44,45].

Figure 10 shows the nonlinear least-squares fit of the Weibull model (Equation (5)), weighted by the standard deviation of the measured NPs concentration within U-87 MG and MCF-7 spheroids.

Figure 10. Internalisation of CaF₂:Nd³⁺,Y³⁺ NPs in (a) U-87 MG and (b) MCF-7 spheroids versus treatment time of exposure. The Weibull fit model is shown as a blue line.

As shown in Figure 10, the Weibull model describes the diffusion kinetics of NPs in spheroids reasonably well. For U-87 MG spheroids (Figure 10a), the absence of a clear saturation stage within the experimental window reduces the robustness of the fit. Nevertheless, the extracted parameters are self-consistent: C_∞ = 2.1 ± 1.6 µg/Sph, τ = 57 ± 13 h and β = 1.82 ± 0.12. These values reveal accelerated kinetics, compatible with a globally sigmoidal profile, rather than a simple first-order behaviour. Although saturation was not reached, the larger C_∞ and longer τ values suggest a greater internalisation capacity than in MCF-7 spheroids. For MCF-7 spheroids (Figure 10b), the fitted parameters were C_∞ = 0.13 ± 0.03 µg/Sph, τ = 19 ± 12 h, and β = 0.68 ± 0.40. These values indicate sub-exponential (anomalous) kinetics, typically associated with diffusion-dominated transport. Consistent with this, the data indicate a relatively slow uptake, with only a modest fraction of the administered NPs dose retained at equilibrium.

3. Materials and Methods

3.1. XRF Instrumentation

Qualitative and quantitative TXRF analyses were performed with a benchtop S2 PicoFox TXRF spectrometer from Bruker Nano (Berlin, Germany), equipped with a Mo X-ray source working at 50 kV and 600 μA, a multilayer monochromator with 80% of reflectivity at 17.5 keV (Mo Kα), an XFlash SDD detector with a functional area of 30 mm², and an energy resolution better than 150 eV for 5.9 keV (Mn Kα). The commercial Spectra v.7.8.2 software package from Bruker was used for deconvolution, integration, and quantification. All the reagents used in this work were of suprapure quality. The ultrapure water used in this study was from a Milli-Q Element system (18.2 MΩ) from Millipore Merck KGaA, (Darmstadt, Germany). Microscopic images were obtained using a SMZ-800 binocular microscope from Nikon Europe (Amstelveen, Netherlands). The micro-X-Ray Fluorescence (µ-XRF) spectrometer used in this study was the M4 Tornado from Bruker Nano (Berlin, Germany), equipped with a 30W microfocus Rh X-ray tube and a polycapillary lens, yielding a spot size of approximately 20 μm. XRF detection was performed using an SDD with a 30 mm² detection area and an energy resolution of better than 145 eV for Mn Kα (5.9 keV). Mappings were performed using a step size of 25 μm and a time per step of 30 ms/pixel. The X-ray tube was operated at 50 kV and 500 μA without using a filter.

3.2. Sample Preparation

3.2.1. Synthesis of CaF₂:Nd³⁺,Y³⁺ Nanoparticles

The nanoparticles were synthesised using the hydrothermal method in a pressurised autoclave, as originally developed by Pedroni et al. [31] and recently modified by some of the authors [2]. These previous studies have shown that this synthesis produces citrate-stabilised nanoparticles of 14 ± 3 nm in size, with a homogeneous cubic phase, resulting in a cubic morphology (see Figure 11).

Figure 11. (a) TEM image illustrating the morphology and dimensions of the CaF₂:Nd³⁺,Y³⁺ NPs. (b) Corresponding particle size distribution obtained from 500 measurements and fitted with a log-normal function to estimate the nanoparticle diagonal size.

The synthesis has been developed using calcium chloride dihydrate >99%, Panreac (Barcelona, Spain), yttrium (III) chloride hexahydrate 99.99%, Sigma-Aldrich (Merck KGaA, Darmstadt, Germany), ammonium fluoride 98%, Acros (Thermo Fisher Scientific, Waltham, MA, USA), and neodymium (III) chloride hexahydrate 99.9%, Sigma-Aldrich (Merck KGaA, Darmstadt, Germany) as precursors and sodium citrate tribasic dihydrate 99.0%, Panreac (Barcelona, Spain) as a capping agent. All chemicals were purchased without further purification, and Milli-Q water was used as the solvent.

3.2.2. Cell Culture

Cell experiments were performed using human glioblastoma epithelial cells (U-87 MG) and human breast adenocarcinoma cells (MCF-7) supplied by Dr. Malou Henriksen-Lacey and Prof. Luis Liz-Marzán, from CIC BiomaGUNE (San Sebastián, Spain). Both cell lines were maintained in Dulbecco’s Modified Eagle’s Medium (DMEM) supplemented with 10% Fetal Bovine Serum (FBS) and 1% penicillin–streptomycin (P/S), all obtained from ThermoFisher (Waltham, Massachusetts, United States). Cultures were incubated at 37 °C in a Midi 40 incubator under 5% CO₂ conditions.

3.2.3. Spheroid Formation and Handling

To investigate the influence of incubation time and exposure concentration on CaF₂:Nd³⁺,Y³⁺ NPs, 3D spheroids were developed from both cell lines using a forced-floating method. Cells from 2D culture were counted using a Neubauer chamber. Approximately 4000 cells were seeded in an ultra-low-attachment (ULA) U-bottom 96-well plate (FaCellitate) in 200 µL of complete cell culture medium (day 0). After 48 h (day 2), compact spheroids had formed and could be easily handled for subsequent experimental procedures.

Despite optimisation of the culture protocol, spheroids can exhibit heterogeneity arising from minor cell clustering, well irregularities, or other factors. Thus, multiple replicates (m) were included in all experiments. Any ill-shaped spheroids identified on day 2 were discarded and not used in further experiments.

3.2.4. Nanoparticle Treatment of Spheroids

To incubate spheroids with NPs, the culture medium was removed and replaced with 200 µL of the desired NP concentration prepared in complete DMEM. The specific concentrations and incubation times depend on the experiment. Figure 12 illustrates spheroid development.

Figure 12. Scheme of the spheroid growth and NPs incubation process for experiments in which the incubation time was fixed at 48 h. Longer incubation times also began on day 2, but the NP-containing culture medium was removed at a different time.

To evaluate the effect of concentration, 20 spheroids per cell line were incubated separately with four NP concentrations: 1000 ppm (m = 4), 750 ppm (m = 8), 500 ppm (m = 4), and 200 ppm (m = 4). After 48 h, spheroids were washed twice with PBS and transferred in groups of four into separate vials for TXRF analysis. This results in one sample per concentration, with a duplicate at 750 ppm to assess repeatability.

Control samples consisted of untreated spheroids: three MCF-7 spheroids in 100 μL of water, and three U-87 MG control groups in water (C1: m = 1 in 20 μL; C3: m = 3 in 60 μL; C5: m = 5 in 100 μL). This control set enabled evaluation of TXRF analytical parameters, such as linearity and sensitivity.

To analyse nanoparticle internalisation over time, spheroids were treated at a fixed concentration of 164 ppm. Five spheroids per condition (m = 5) were incubated individually and washed with PBS, forming groups of seven different time points: 2, 4, 8, 16, 24, 48, and 72 h. In the U-87 MG set, the 2 h condition was repeated to evaluate reproducibility. In total, 35 MCF-7 spheroids and 40 U-87 MG spheroids were analysed.

For all experiments, the required number of spheroids was finally transferred from PBS into vials. Spheroids were then washed twice with 200 µL of Milli-Q water, with washes performed rapidly to preserve spheroid integrity and remove external nanoparticles efficiently from incubation. Finally, they were resuspended in Milli-Q water for TXRF measurement.

3.2.5. Spheroids Micro-Digestion and Standardisation

Following the NP incubation and washing protocol, 1 to 5 spheroids were micro-digested in each sample using suprapure nitric acid. The volume of HNO₃ added matched the volume of water already present in the sample (20, 60, 80, or 100 µL). Samples were then digested in a boiling water bath at 100 °C for 2 h, with the hot plate set to 120 °C. Figure 13 shows the home-designed micro-digestion system used for acid digestion of the spheroids and any remaining protein-rich culture medium.

Figure 13. Home-designed micro-digestion system including a boiling water bath to prepare the spheroid samples for TXRF.

Once cooled, samples were standardised by adding Ga at a concentration of 1 ppm as an IS, using a volume equal to the initial sample volume. This procedure resulted in a final dilution factor of three, reducing the Ga concentration to 0.333 ppm. Consequently, the same factor was applied to all initial elemental concentrations recovered from the spheroids. During TXRF sample processing, the Ga concentration (333 ppb) was renormalised to 1 ppm, allowing all elemental concentrations to be calculated relative to the original spheroid volume, V. Figure 14 summarises the complete workflow, including digestion, standardisation, and TXRF sample preparation.

Figure 14. Scheme of the micro-digestion and standardisation process of the analysed samples.

4. Conclusions

This work demonstrated that TXRF spectrometry is a powerful, practical, rapid, and accurate analytical technique for determining trace and rare-earth elements at low concentrations during the nanoparticle internalisation in 3D cellular systems. This was specifically demonstrated for U-87 MG and MCF-7 spheroids incubated with CaF₂:Nd³⁺,Y³⁺ nanoparticles.

Beyond the compositional elements of the investigated NPs (Ca, Nd, Y), TXRF enables highly sensitive quantification of cellular trace element content (P, S, K, Ca, Fe, Cu, and Zn) in low-volume biological samples, supporting its microanalytical capacity and suitability for nanoparticle-tracking studies in a 3D cancer model. A dedicated microdigestion protocol was developed, including a custom digestion system for microsamples.

The methodology was validated by evaluating average elemental concentrations (ranging from 50 ppb for Cu to 27.46 ppm for P), detection limits (11 ppb for Cu to 1.11 ppm for P), and coefficients of variation (always below 1.85%). The expanded uncertainty sources were quantified, with approximate values of U_Meth∼10.2 ± 4.1%, U_Rough∼4.3 ± 2.1%, and U_Ins∼3.5 ± 2.1%. Finally, recoveries relative to the theoretical NP composition and spike-and-recovery tests yielded both values of approximately 100%. These data confirm the accuracy, robustness, and absence of matrix interference in the developed TXRF method.

The method has been applied to investigate diffusion processes of CaF₂:Nd³⁺,Y³⁺ NPs in spheroids, evaluating two key parameters: exposure time and NP concentration. U-87 MG spheroids showed consistently higher NP accumulation than MCF-7 spheroids, reaching values up to four-fold greater. A saturation trend was observed versus exposure time and could be phenomenologically described by a Weibull model. In MCF-7 spheroids, the fitted parameters (C_∞ = 0.13 ± 0.03 µg/Sph, τ = 19 ± 12 h, and β = 0.68 ± 0.40) correspond to sub-exponential (diffusion-dominated), resulting in a modest NP retention. In U-87 MG, the parameters (C_∞ = 2.1 ± 0.6 µg/Sph, τ = 57 ± 13 h, and β = 1.82 ± 0.12) suggest an accelerated regime with substantial nanoparticle accumulation even without reaching saturation within the experimental time window. These differences suggest a cell-line-dependent uptake behaviour, potentially influenced by spheroid architecture, including roughness, porosity, and intercellular 3D microstructure. To confirm this explanation, additional measurements of spheroid surface morphology would help to quantify their effective area.

Finally, this study focuses on two representative cancer cell lines grown as 3D spheroids (U-87 MG, glioblastoma; MCF-7, adenocarcinoma) but sets the basis to be extended to alternative cell lines. Spheroids better reproduce tumour microstructure and metabolism than 2D cultures, enabling more realistic assessment of nanoparticle–cell interactions for nanotheranostic applications while remaining simplified in vitro systems. This is thus a route to be followed before progressing towards in vivo experimentation.