### Electron Microscopy

With a routinely achievable resolution of a few nanometers and an open view (no specific labeling required, no *a priori* information required), electron microscopy and especially TEM provides an unrivaled insight into the cellular ultrastructure. Besides a number of physicochemical characteristics of electron-dense NPs such as aggregation state, size and shape, TEM exclusively provides answers for the following questions in nanomedicine: where exactly is a NP localized (e.g., inside or outside of a cell membrane and/or in which organelle); and how many NPs are inside a compartment of choice.

Electrons, the electromagnetic source in electron microscopy, do not penetrate a sample deeper than a few 100 nm, which raises the requirement for ultrathin sectioning. In contrast with LSM, where entire cells and even tissues can be studied *in toto* and slices can be obtained by nondestructive optical sectioning, TEM requires the reduction of the sample thickness to ultrathin sections of about 50–100 nm. Nonetheless, accurate quantification in 3D based on 2D sections is provided by a set of geometrical tests known as stereology.^{[65,66]} Using proper sampling schemes, stereological tools provide unbiased information on number,^{[67,68]} length,^{[69,70]} surface^{[71,72]} and volume.^{[73,74]} Furthermore, stereological quantification provides absolute numbers, which can be put in relation to a control but can also be used for universal comparison. Stereology is hereby the method of choice for quantifying cellular particle numbers in 3D from 2D microscopic images.

Counting particles is fast assuming that the NPs are smaller than the section thickness (~50 nm) and cannot be sectioned by ultramicroscopy, which is the case for most metallic NPs. Since TEM provides projections, the number of particles in the micrographs can be directly related to the volume of the section. If successive sections were cut, the volume of the cell, and by extension the average volume of the cell line can be estimated using the Cavalieri principle^{[74,75]} where a point grid is placed randomly over the successive sections and the number of points that hit the cell (or any other region of interest) is counted (Figure 3). This yields a scientifically relevant reference space (e.g., the total volume of the phagosomes or the volume of the cell). It is a fundamental principle in stereology to always estimate the reference space,^{[76]} since treatments (e.g., with NPs) might influence the cellular homeostasis and lead to an alteration in reference space biasing in all downstream quantifications.^{[77]}

Figure 3.

**Example of disector count of crocidolite asbestos fibers in a human blood monocyte-derived macrophage in a tomographic data set.** Two slices from a tomographic stack, parallel and aligned and 57 nm apart in axial direction are compared. Five fibers are present in the reference plane but are absent in the lookup plane and three such events are observed *vice versa*. Fibers present in both slices are irrelevant. A systematic point grid with an area per point of 75,000 nm^{2} placed randomly over the image has 18 hits inside phagosomes (red crosses). Using the director formula, this amounts to 52 crocidolite asbestos fibers per μm^{3} phagosome. Due to the low counts, this relative number is highly imprecise (but unbiased) and more counts – based on proper sampling – are required in order to increase the precision of this estimate. For simplicity of the example, we assumed an invariable phagosome throughout the axial span of 57 nm (a typical ultrathin section thickness). If the study was extended to entire cells and fibers, the number of fibers/cell or the average mass of asbestos per cell could be estimated in a similar way. Scale bar: 250 nm.

If particles are larger than the section thickness (~50 nm) they will appear over two or more sections, which is the case for polystyrene microbeads or long fibers. The disector^{[68]} should be used to count such particles/fibers. The disector method counts 'tops' and 'bottoms' of objects and thereby avoids counting the same object again, assuring unbiased results. Naturally, the disector can also be applied to other recognizable structures, such as mitochondria,^{[78]} synapses^{[79]} or nuclei.^{[80]} Alternatively, the stereological design of Elsaesser and colleagues^{[81]} allows for quantifying cellular NP number by TEM using the fractionator principle.^{[82]} This straightforward approach correlates the total number of intracellular particles per sample with the total cell number per sample. The approach is designed for convex cells in suspension but not for adherent cells.

If particles are randomly distributed over all compartments, then number of particles per compartment is expected to be proportional to its volume. This is the principle the relative deposition index (RDI)^{[83]} is based on (Figure 4). Significant alterations from the randomly distributed model will reveal a likeliness of particles for a specific compartment.^{[8,84]} Therefore, the RDI identifies the preferred compartment/organelles of (nano)particles.^{[85,86]}

Figure 4.

**Example of the calculation of a relative deposition index.** A systematic point grid (crosses) is randomly placed over the micrograph and was manually color coded for intersections with the nucleus (blue), cytosol (yellow), vesicles (red) and extracellular space (black). The points quantify the relative size of each compartment. The particles are made evident by arrows and similarly color coded were counted as well. A model of the expected particle number is calculated assuming random distribution of the gold NP (number of observed intersections for a compartment × total number of observed AuNP/total number of observed intersections, for example, 124 × 25/280 = 11.1 for the compartment 'cytoplasm') and placed in relation to the observations. RDI equals the observed number of NP in a compartment divided by expected number of NP by the random model, for example, 6/11.1 = 0.54 for the compartment 'cytoplasm'). A χ^{2} analysis calculated for 3 degrees of freedom (from [r – 1] × [k – 1], where r is the number of compartments or rows [4] and k is the number of columns, 2) between the observed (O) situation and the expected (E) random model reveals a much larger statistic (181.1) which than the boundary value (16.3 for df = 3 and p = 0.001) and therefore significant differences between random model and the observations (calculated as [O–E]^{2}/E). Approximately 93% of the statistic is explained by the vesicles. Hence, particles are not randomly distributed but concentrate in vesicular organelles. Scale bar = 100 nm.

Although conducting stereological tests requires little or no expertise, proper sampling is of utmost importance in stereology since it assures unbiased results.^{[87–89]} The primary sampling approach in stereological procedures is an equal probability method known as systematic random sampling: the sampling at a random spot on the sample. Images are sampled in a systematic (e.g., meandering) manner at predefined, fixed distances, known as the sampling interval. Stereological approaches are mathematically designed to yield unbiased, accurate estimates independent from the distribution state of the objects of interest. Decreasing homogeneity can be accompanied with a decrease in sampling efficiency; that is, the time needed to produce an estimate with a certain precision. Advanced sampling techniques^{[90]} cater for estimates of rare or clustered events, which can be the case for NPs uptake quantification.^{[91]} High-throughput procedures are emerging with advances in image processing routines. Sampling efficiency can be optimized using the 'do more less well' principle,^{[92]} not the methodical variation but the biological variation is the major determinant of overall efficiency. Therefore, in order to increase the sampling efficiency, and with it the precision of the quantification, time and money should be invested in upstream (include more animals or cell culture replicates) rather than downstream (individual micrographs).

Ultrathin serial sections of the sample are a requirement in order to use the Cavalieri estimator and also the disector relies on parallel consecutive sections. But ultramicroscopy of serial sections is challenging, requiring knowledge and technical experience. Alternatively, the requirement for serial sections can be met by electron tomography. Although a relatively recent add-on, most TEM instrumentation is equipped with the necessary hardware to perform electron tomography.^{[93]}

Since TEM offers an open view, it does not convey biochemical information in the way fluorescent markers in light microscopy can. Furthermore, the requirement for a water-free sample and ultrathin sample thickness (<200 nm, usually around 50 nm) prevents the study of living cells in the TEM. Stereology is not limited to TEM. Therefore, light microscopy and TEM are often combined: although sample preparation for light microscopy can be as challenging as for TEM, certain prerequisites can be easier met, e.g., serial sections can be obtained by laser scanning microscopy.^{[94,95]}

Nanomedicine. 2014;9(12):1885-1900. © 2014 Future Medicine Ltd.

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