Towards defining new nano-descriptors: extracting morphological features from transmission electron microscopy images

Abstract

Due to the important role of surface-related properties of NPs in their biological behavior, simple and fast methods that could precisely demonstrate accurate information about NPs' surface, structure and morphology are highly desirable. In this study a set of surface morphological nano-descriptors (size, shape, surface area, agglomeration state, curvature, corner count and aspect ratio) have been defined and extracted from Transmission Electron Microscopy (TEM) images of nanoparticles (NPs) by Digital Image Processing methods. The extracted data represent a thorough description of the surface and morphologies of NPs lying beyond their TEM images and can supply the data required for a nano-QSAR approach for predicting toxicity profiles of NPs. These nano-descriptors can provide a framework to further understand the mechanisms which govern the adverse effects of NPs in biological systems. Metallic nanostructures (gold, silver, palladium…) with different sizes (10 to 100 nm), shapes (cube, sphere, rod…) and characteristics were taken into account for which physicochemical indexes were reported. To the best of our knowledge, this is the first ever study that presents numerical values for properties such as shape and agglomeration state which significantly affect NPs behavior.

---

1. Introduction

Today with the developments in nanotechnology which has significantly improved the quality of life for human beings, it is important to address the possible consequences, as with any emerging technology. Computational approaches play an essential role in this risk assessment procedure due to their fast, in-expensive and high throughput methods. However, it must be noted that the negative impacts of NPs should be carefully considered and evaluated by gathering specialists in both experimental and theoretical fields. The large number of NPs and the variety of their characteristics including various sizes, shapes and coatings suggest that the only rational approach which avoids testing every single NP is to find a relationship between the physicochemical characteristics of NPs and their toxicity.^1,2 This approach, namely called Quantitative Structure–Activity Relationship of nanomaterials (nano-QSAR), statistically establishes a mathematical relationship between a measured profile of a set of nanostructures and their physicochemical properties (called “nano-descriptors”). Thus, through a nano-QSAR approach, one would be able to quantitatively predict the potential toxicity of a set of un-tested NPs based on experimental toxicological data available for a set of tested ones and therefore, prevent expensive and time-consuming empirical animal testing procedures for NPs risk assessment. However, since NPs significantly differ to their bulk counterparts, consequently, nano-QSAR differs to the well-known conventional QSAR approach (for which there are several commercial software available and large sets of molecular descriptors are calculated)³ and there is a need to develop QSAR models with a special insight to nanomaterials. Actually, some major obstacles impede the nano-QSAR approach such as: structural complexity and diversity of NPs, scarce and/or inconsistent empirical data and thus lack of available large scale datasets of NPs' toxicity, and finally lack of rational modeling procedures in describing the structural properties of these substances.⁴ Therefore, nano-specific descriptors responsible in determining the toxicity of nanostructures are markedly required. Developing these novel nano-descriptors could be a great challenge for computational experts. A number of research groups have already expressed computational and empirical nano-descriptors for revealing the behavior of nanomaterials.⁵ For example, Puzyn et al.⁶ presented a set of quantum mechanical descriptors for modeling the cytotoxicity of metal-oxide NPs to bacteria Escherichia coli. Martin et al.⁷ proposed two models predicting solubility of C₆₀ fullerene in n-octanol and n-heptane. Fourches et al.⁸ developed a quantitative nanostructure-activity relationship (QNAR) model to predict the cellular uptake of 109 NPs in PaCa2 cell. But none of them have yet succeeded to present numerical values for morphological properties of nanoparticles such as their shape or surface-related features. With this in mind, image processing, might be a great clue for extracting quantitative information about the structure of the investigated objects in NPs images and could be used to establish a link between this information and various non-visual properties of the objects.^9–12

In the present contribution, a set of novel image nano-descriptors were extracted from TEM images of NPs in order to reveal as much as information possible about their structural, morphological and surface properties. The extracted nano-descriptors can be used either as a final result (for example estimation of the aggregation state) or treated as an input for further analysis (such modeling NPs toxicity profile or cellular uptake). Furthermore, by combining these morphological image nano-descriptors with a series of experimentally assessed parameters of NPs (i.e., zeta potential, ionic strength, crystal structure, hydrophobicity, …) and even previously suggested QM descriptors, a favorable dataset could be provided for applying computational methods such as nano-QSAR in order to assess NPs potential risk to human health and the environment.

2. Methods

2.1. Dataset

An initial set of TEM images of metallic NPs were collected from our previous work¹³ and literature^14–21 to gather a diverse selection of different types of NPs including various sizes, shapes and comparable agglomeration states. Six representative TEM image candidates are shown in Fig. 1 and a larger set of the images can be seen in S1.† Because of the wide variety of NPs to be considered, consisting carbon based materials, metallic and metal oxide nanoparticles, quantum dots…, and owing to their structural heterogeneity, we herein focused on one of the above mentioned classes including metallic and metal oxide NPs due to their large number of recent toxicity reports.

Fig. 1 TEM images dataset including six different shape types of nanoparticles: (a) in spherical colloids,¹⁴ (b) Pt cuboctahedrons,¹⁵ (c) Pd triangular nanoplates,¹⁶ (d) Pd nanocubes,¹⁷ (e) Au dog bone-shaped nanocrystals¹⁸ and (f) Au nanorods.¹³

2.2. Descriptor generation by digital image processing

In order to develop morphological image nano-descriptors, the first step was to define appropriate descriptors from which maximum possible surface and structural information²² of NPs could be extracted. An initial set of surface descriptors was first defined as suggested by Puzyn et al.⁴ including size distribution, agglomeration state, shape, porosity and surface area. For each suggested descriptor, a number of different image processing codes were tested and applied to a pool of multiple TEM images (i.e., TEM of rods, spheres, cubes…) to achieve the most possible general code. Actually, one of the basic challenges herein was to provide general codes, i.e., codes with maximum accuracy for diverse TEM images and minimum erroneousness for noisy/blurred images. Moreover, general codes can be capable of defining thresholds for different kinds of images utilizing machine learning techniques. Several transitions were examined meanwhile to achieve the most appropriate code that could accurately find all the objects in an image and calculate the considered descriptors for them. In addition, a number of new features such as the amount of rigidity or curvature of the corners and some other possible informative parameters where proposed and defined throughout the process of calculating the previous mentioned descriptors which are fully introduced and discussed later. Digital image processing algorithms were coded and compiled by C++ language and GCC 4.6.1 in Linux, respectively.²³ In addition, some basic ideas on image processing were implemented from OpenCV and QT 5.2.1 libraries.^24,25 For each TEM image, an output folder was saved and exported containing the calculated nano-descriptors related to the considered image. The complete description of image processing steps are explained in the following.

3. Results and discussion

3.1. Overall algorithm

After importing a TEM image in .jpeg or .png format as input, the desired nano-descriptors were generated in an overall algorithm as follows: (1) initialization: including pre-processing steps to improve the image resolution, to remove the background and to find all the objects in the considered image; (2) calculating nano-descriptors (size, surface area, aspect ratio, corner count, agglomeration state, shape type and curvature); (3) removing outliers; (4) saving the output file.

3.2. Pre-processing step

The first step was to improve the image quality and find all the objects in that image to then calculate nano-descriptors for them. Thus, after reading the input image some image filters were applied to de-noise the image and sharpen the blurred edges of the objects in the image. The pre-processing was followed by employing morphological operators (erosion and dilation) to separate joined objects and eliminate very small ones (useless shapes which lack information). In the next step, thresholds were defined for background subtraction. For this purpose, the greyscale image was converted to binary image in which a threshold is calculated individually for each pixel based on its neighborhood pixels and reveals an array of zero and one values. Zero corresponds to the background pixels, while one corresponds to the presence of an object upon that pixel. By applying this mask on the initial image, the algorithm could successfully discriminate between the object and the background pixels. Fig. 2 illustrates the background subtraction process on a sample TEM image. Now, by applying the find contour process on the resulted image, the exact location of each object and its border could be detected. More information on the find contour algorithm can be found elsewhere.²⁶

Fig. 2 Pre-processing results in the initialization step: (a) original image, (b) threshold for background subtraction, (c) background subtracted image and (d) all the objects found in the image.

3.3. Nano-descriptors

After detecting all the objects in an image, seven nano-descriptors were calculated for each object in that image which are briefly defined below:

3.3.1. Size and surface area. Extracting the exact size of the NPs from an image processing insight avoids us from reporting imprecise and approximate values for NPs' size (when using just a simple ruler) and therefore, allows to scrutinize the real effect of particle size on NPs behavior. In this project, the size of each object was defined as the maximum distance between two points on the border of that object. Therefore, by finding the circumscribed rectangle of each object, we exported its length on account of the size of the object within it. The circumscribed rectangle around some objects in a sample TEM image are shown in Fig. 3. The aspect ratio descriptor could be also calculated by calculating the length/width ratio of the corresponding circumscribed rectangle. Since the TEM images reveal a two-dimentional representation of nanoparticles, the whole process on extracting morphological descriptors from TEM images is limited to information from 2D shapes. The surface area calculated herein is actually the surface area of a 2D cross section of the particle which can be calculated by counting the pixels beneath that shape. Thus, measuring the contour areas of each image would give the surface areas of the objects in that image individually and thus, exporting an average value as the representative surface area value for that image. This descriptor can be further used to detect outliers in an image, i.e., objects which don't match others (are rather too small or too big compared to most of the objects). The threshold for eliminating outliers is that objects with surface areas higher than twice of the mean surface are or lower than half of the mean surface area should be omitted from the image.

Fig. 3 Circumscribed rectangle depicted around each object.

3.3.2. Agglomeration state. Another important factor that can strongly influence the behavior of nanoparticles is their agglomeration state. An initial idea was to describe a standard value between zero and one as the agglomeration state of the particles in an image which respectively represent totally dispersed (particles far away from each other) or highly agglomerated particles (particles adjacent to each other). Therefore, in order to define this descriptor, the first step was to find the neighbors around each object in an image and then define a function related to both the distance and the number of neighbors. Thus, three nearest neighbors to each object were first found and a corresponding weight was then assigned to each of the neighbors in a descending order (i.e., a weight of 4 to the first nearest neighbor, a weight of 2 to the second nearest neighbor, and a weight of 1 to the third nearest neighbor). Then a weighted distance (D) was calculated from these three neighbors according to eqn (1):

Now, for each object in an image, an agglomeration value could be calculated from eqn (2):

In which D is the mean distance calculated by eqn (1) and S is the surface area of the corresponding object which has been measured in the surface area descriptor. Before reporting a mean value of the measured agglomeration values for all the objects in an image as a representative output, a much more accurate agglomeration value could be obtained if we would be able to count the number of neighbors around each object within a specific region and then calculate a weighted agglomeration state. With this weighted agglomeration state we could take into account images which included different agglomeration states in different areas within them. For this purpose, the next step was to depict a circle around the center of each object with a radius measured from eqn (3), and find the number of objects present in this criteria around each object.

In eqn (3), n corresponds to the total number of objects in the image. r will be calculated for each object separately and then a mean value will be used as the circle radius covering around each object in which the number of objects will be counted, as shown in Fig. 4. Finally, a representative agglomeration state value could be calculated from eqn (4):

Fig. 4 Finding the neighbors around each object in the determined region around it: (a) simple representation by a green shadowed circle around the central square, (b) true calculated region around each object determined by the software.

In this equation N_j corresponds to the number of neighbors in the defined criteria (explained above) around each object.

3.3.3. Corner count. With the aim of extracting further information from the TEM images, one idea was to reveal the exact number of corners of the objects. Though we already had an approximation of the number of corners throughout the shape descriptor defined above, we were looking for a more precise feature that could somehow reveal the amount of homogeneity or isotropy of the shapes. For example, if we consider two squares, we expect they both have four number of corners. This would be true just if we had two clean squares, with no noisy or damaged corners. But actually in the case of real samples, we rarely face such clean squares. Instead, the shapes include protrusions or depressions along their borders that bring about more or less number of expected corners. Therefore, by finding the exact number of the corners of the shapes (which we called it corner count), we will be able to disclose information about the shapes symmetry and could even discriminate precisely between objects within a same shape class. For this purpose the idea was to find the approximate polygon depicted around each shape and report its exact number of corners. It was found that the approximated polygon could precisely take into account interrupted edges of the noisy shapes.

3.3.4. Shape type. Shape, as a substantial parameter affecting the behavior of nanoparticles,^27–32 has been poorly taken into account in nanomaterial risk assessment studies suffering from the lack of a method to translate the shape type into numerical values. In the present contribution, we successfully defined shape descriptors that could distinguish between different shape types. For this purpose, due to our collected TEM image database, we defined six major classes for shape type including: rod, dog-bone, square, triangle, circle and hexagon. It must be kept in mind that since we are restricted to 2D images, we could offer 2D information for shape type; i.e., these shape types are in some cases common cross sections of different 3D nanostructures. Various algorithms were tested to distinguish between these six shapes. For example to decide whether a shape is a square or a triangle, one idea was to count the number of peaks appearing in the histogram of the tangent angle. As illustrated in Fig. 5, a triangle shape would exhibit three peaks due to three corners, while a square shape would expose four peaks.

Fig. 5 A method for discrimination between a square and a triangle using a 1-D functional representation of the shape boundary (the distance from the centroid is illustrated vs. the angle).³³

This idea worked out for clean squares/triangles, but in the case of noisy ones the algorithm failed to classify these shapes. The results for two TEM image samples are shown in Fig. 6. As it can be seen, the number of peaks in the histogram is notably influenced by the tiny noises in the shape border.

Fig. 6 Histograms resulted for the discrimination between (a) triangle¹⁵ and (b) square¹⁶ shaped TEM images.

Another challenge was to distinguish between a circle and a hexagon for which several ideas were tested. For example, one idea was based on a simple geometric theorem which states that only one circle crosses from any three individual points in a plane. Utilizing this basic geometric rule, our idea was to severally select three arbitrary points on the border of a circle or a hexagon and then calculate the radius of the circle crossing the three points each time. In the case of a circle, no matter where the three points are selected only one unique circle will cross from them that has a radius close to the radius of the initial circle (see the circle in Fig. 7a). In contrast, in the case of hexagon, if these points were selected close to each other, the crossing circle would have a big radius compared to when the points were selected far from each other (for example each point on a separate side of the hexagon) from which a small circle would be resulted (see the hexagon in Fig. 7b). Fig. 7 demonstrates this idea more clearly. As it could be seen, by depicting the histogram of the radius of the crossing circle for either a circle or a hexagon, two different patterns would be achieved consisting of just one peak in the case of a circle, but two or more peaks in the case of a hexagon. Again, this code was strongly influenced by noisy shapes and could not be generalized for most cases. Lots of other similar ideas were tested in order to attain a very precise general code for distinguishing between the six shape categorizes.

Fig. 7 A method for discrimination between a circle and a hexagon. For each shape, imagine a red dashed circle crossing three arbitrary points on the border of the considered shape. (a) In the case of a circle, the red crossing circle will always have a radius near the radius of the original circle, no matter where these three points are being chosen. Thus, only one peak will appear in the histogram of the red circle's radius. (b) But in the case of a hexagon, the red crossing circle can either have a small or a big radius, depending on the distance between the three random points: if the three points were chosen close to each other, the red crossing circle would have a big radius, but if the three points were chosen far from each other, the red crossing circle would have a small radius. Therefore, in the case of a hexagon, more than one peak will appear in the histogram of the red crossing circle's radius.

Finally, we investigated the idea of “template match” and defining six separate descriptors for different shapes, each explaining the amount of similarity of the images to one of the well-defined shape classes. In other words, each shape descriptor is a coefficient demonstrating the amount of similarity to each shape type. The more the similarity between an image and a specific shape class, the higher the value of its corresponding shape descriptor. For example, in the case of a TEM image including triangle shape NPs, the coefficient of the triangle descriptor will be close to one while the other five shape descriptors will have a value much lower than one (depending on the amount of being similar to/different from a triangle). By developing this idea, we were also able to consider similarities between different shape types. For example the value for the circle, the hexagon and the square descriptors will all be high in the case of a TEM image including hexagon-like NPs, because of the similarity between these three shape types.

For performing the template match discussed above, the algorithm first builds a template close to the size of each object in the image but with a specific shape type. For example it starts by building circles, then squares, then hexagons and so on till making all six shape templates. The constructed shape templates can be seen in S2.† Then it screens through the whole image, rotates the template (if necessary) and measures the amount of overlapping between the templates and the objects. The more the similarity between each shape template and the objects in an image, means the more matching between them and results in a higher coefficient for that specific shape descriptor. In more details, after defining a standard template for each of the six shape classes, a comparison between the surface areas of all the objects in the image and each template is performed separately and the objects are each re-sized in order to reach a surface area equal to the templates surface area. By overlaying a specific template on each object, a similarity value is defined from eqn (5):

The overlapping area is the number of pixels in common between that template and the object (matching area), while the surface area is the number of pixels beneath either the template or the object (which is expected to be the same due to the re-sizing step performed above). This similarity value lacks from the distinguishing ability between different shape types and actually needs to be more specified for different shape types (i.e., two shape templates with same surface areas may result in same similarity values, while they belong to different shape types). Thus, in order to comprise the shape type, a function of corner count was involved to complete the shape descriptor value as shown in eqn (6):

Shape descriptor = similarity × f(corner count) (6)

A Gaussian function was used for this purpose with a normal distribution around the number of corners of each template. For example, in the case of a square template, a Gaussian distribution with a mean value of four will be considered. If the corner count of the objects in the image were close to four, then the output of this function was a value next to one. In contrast, if the objects differed from a square and revealed a corner count far from four, then the output of the Gaussian function expresses this dissimilarity by revealing a value around zero. The more the similarity between the corner counts of the template and the objects, the more the value of the Gaussian function.

3.3.5. Curvature. The amount of curvature or rigidity of the corners might be another valuable parameter revealing lots of information about the way that particles gather around each other or how other molecules can attach to their surface. Thus, we defined a descriptor that could approximately report the amount of curvature of the corners. In order to have a comparable value between different images, we scaled this parameter between zero and one, corresponding to totally keen or totally curved (like circle) corners, respectively. Fig. 8 demonstrates a simple comparison between shapes with different curvatures. In order to calculate this descriptor, we investigated the idea of subtracting the measured surface area of each object (i.e. the surface area descriptor) from its desired surface area (the mathematical surface area calculated based of the geometry of each polygon).

Fig. 8 Simple demonstration of different curvature limits.

3.4. Output

Subsequently, after running all the above steps and calculating the nano-descriptors for each TEM image, the program reveals a matrix as an output in which the rows correspond to each TEM image and the columns are related to the image nano-descriptors. The nano-descriptors would be calculated for all the objects in each image (as shown in Table 1); but for reporting just one vector containing representative values of nano-descriptors calculated for each TEM image, a mean value of the nano-descriptors measured for every single object in an image was then calculated and reported (as shown in Table 2). As can be seen in Table 1, the rod-shape descriptor column has greater values than the other shape descriptors, consistent with its TEM image which belongs to gold nanorods. For a better visual perception of the extracted nano-descriptors, a number of the output shape descriptors are depicted close to their corresponding objects in a TEM image shown in Fig. 9. The final output file in the excel format could be used as an initial dataset for a nano-QSAR study or any other investigation related to morphological properties of nanomaterials.

Table 1 Nano-descriptors calculated for all the nanoparticles in TEM image in Fig. 2

Objects	Size	Surface area	Curvature	Aspect ratio	Corner count	Circle	Rod	Dogbone	Triangle	Square	Hexagon	Agglomeration state
1	24.0	416.5	0.211	1.143	8	0.905	0.267	0.236	0.700	0.567	0.792	0.006
2	55.0	1009.5	0.268	2.563	6	0.127	0.994	0.901	0.000	0.730	0.000	0.036
3	46.9	593.0	0.458	2.844	8	0.935	0.969	0.749	0.000	0.609	0.000	0.023
4	53.5	775.5	0.732	3.097	6	0.131	1.040	0.979	0.000	0.744	0.000	0.036
5	63.6	1238.5	0.368	2.871	6	0.125	1.003	0.951	0.000	0.682	0.000	0.065
6	68.2	1509.5	0.434	2.743	6	0.123	0.983	0.955	0.000	0.656	0.000	0.165
7	54.6	875.0	0.322	2.976	6	0.122	1.004	0.976	0.000	0.673	0.000	0.153
8	57.9	1026.0	0.425	2.832	7	0.619	1.014	0.807	0.000	0.750	0.000	0.098
9	64.7	1454.0	1.013	2.516	6	0.125	1.039	0.918	0.000	0.711	0.000	0.266
10	54.1	740.5	0.333	3.212	9	1.025	0.877	0.678	0.000	0.659	0.000	0.099
11	57.8	956.5	0.575	3.062	6	0.125	1.008	0.973	0.000	0.689	0.000	0.176
12	60.1	941.5	0.265	3.542	6	0.122	0.953	0.904	0.000	0.669	0.000	0.153
13	63.5	1385.0	0.447	2.538	6	0.131	0.986	0.943	0.000	0.756	0.000	0.170
14	43.1	1433.0	0.578	1.123	7	0.539	0.233	0.216	0.801	0.607	0.800	0.085
15	64.9	1211.0	0.318	3.075	6	0.121	0.967	0.938	0.000	0.654	0.000	0.088
16	50.6	550.0	0.089	3.831	7	0.584	0.343	0.314	0.000	0.682	0.000	0.064
17	45.0	1783.5	0.635	1.000	8	0.880	0.000	0.000	0.682	0.565	0.757	0.286
18	64.5	1272.0	0.781	2.857	6	0.125	0.985	0.943	0.000	0.697	0.000	0.113
19	59.7	1138.0	0.155	2.715	6	0.135	0.992	0.974	0.000	0.789	0.000	0.093
20	62.8	1215.0	0.513	2.759	7	0.589	0.968	0.845	0.000	0.709	0.000	0.033
21	54.1	1158.5	0.141	2.051	6	0.126	1.024	0.906	0.000	0.733	0.000	0.000

---

Table 2 Output matrix including nano-descriptors extracted from TEM images in Fig. 1

Image	Size	Surface area	Curvature	Aspect ratio	Corner count	Circle	Rod	Dogbone	Triangle	Square	Hexagon	Agglomeration state
a	11.9	115.9	0.919	0.997	7.263	0.759	0.095	0.088	0.750	0.561	0.764	0.123
b	16.8	196.9	0.896	1.160	7.012	0.560	0.256	0.232	0.769	0.627	0.780	0.275
c	25.9	497.6	0.577	1.117	6.034	0.321	0.194	0.203	0.750	0.637	0.701	0.225
d	13.9	138.1	0.758	1.165	6.465	0.395	0.328	0.319	0.872	0.657	0.831	0.223
e	27.1	204.8	0.182	1.695	8.851	0.352	0.832	0.796	0.352	0.762	0.355	0.217
f	55.6	1080.1	0.431	2.636	6.619	0.367	0.840	0.767	0.104	0.683	0.112	0.105

---

Fig. 9 Shape descriptor comparison between some of the objects in a TEM image; C, R, D, T, S and H respectively refer to circle, rod, dog-bone, triangle, square and hexagon nano-descriptor values.

4. Conclusion

The present contribution introduces a set of surface morphological nano-descriptors extracted from TEM images of NPs. These nano-descriptors including size, surface area, aspect ratio, curvature, corner count, shape type and agglomeration state, reveal as much as structural and surface related information as possible from the TEM images. The represented descriptors can provide informative data required for a thorough computational approach on nanomaterials, such as nano-QSAR. These descriptors can also be considered in a modeling procedure in order to assign the dominant factors affecting the toxicity of different types of NPs and consequently, be used to further understand the mechanisms which govern the adverse effects of NPs in biological systems. It must be kept in mind that the interaction of NPs with biological media is dynamic, and therefore it is impossible to monitor the real events taking place at the moment that NPs meet proteins, or actually reveal what the cell sees. But on the other hand, predicting the possible toxicity caused by NPs from their initial structure in TEM images previous to entering them into the biological media is noteworthy.

Acknowledgements

This work was supported by Sharif University of Technology Research Council. The authors wish to express their gratitude for the support of this project. In addition, the authors would like to thank Ali Foroughi-Pour for his special assistance on generating the image processing codes.

References

1. A. Gajewicz, B. Rasulev, T. C. Dinadayalane, P. Urbaszek, T. Puzyn, D. Leszczynska and J. Leszczynski, Adv. Drug Delivery Rev., 2012, 64, 1663.
2. B. Rasulev, A. Gajewicz, T. Puzyn, D. Leszczynska and J. Leszczynski, Towards Efficient Designing of Safe Nanomaterials: Innovative Merge of Computational Approaches and Experimental Techniques, RSC, 2012, ch. 10, pp. 220–256.
3. R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley-VCH, 2nd edn, 2009, vol. 41.
4. T. Puzyn, D. Leszczynska and J. Leszczynski, Small, 2009, 5, 2494.
5. P. R. Gil, G. Oberdörster, A. Elder, V. Puntes and W. J. Parak, ACS Nano, 2010, 4, 5527.
6. T. Puzyn, B. Rasulev, A. Gajewicz, X. Hu, T. P. Dasari, A. Michalkova, H. M. Hwang, A. Toropov, D. Leszczynska and J. Leszczynski, Nat. Nanotechnol., 2011, 6, 175.
7. D. Martin, U. Maran, S. Sild and M. Karelson, J. Phys. Chem. B, 2007, 111, 9853.
8. D. Fourches, D. Pu, C. Tassa, R. Weissleder, S. Y. Shaw, R. J. Mumper and A. Tropsha, ACS Nano, 2010, 4, 5703.
9. K. Artyushkova, S. Pylypenko, M. Dowlapalli and P. Atanassov, RSC Adv., 2012, 2, 4304.
10. K. P. Singh and S. Gupta, RSC Adv., 2014, 4, 13215.
11. S. Kucheryavski, Chemom. Intell. Lab. Syst., 2011, 108, 2.
12. C. Dahl and K. Esbensen, Chemom. Intell. Lab. Syst., 2007, 89, 9.
13. M. R. Hormozi-Nezhad, H. Robatjazi and M. Jalali-Heravi, Anal. Chim. Acta, 2013, 779, 14.
14. Y. Wang and Y. Xia, Nano Lett., 2004, 4, 2047.
15. K. M. Bratlie, H. Lee, K. Komvopoulos, P. Yang and G. A. Somorjai, Nano Lett., 2007, 7, 3097.
16. Y. Xiong, J. P. McLellan, J. Chen, Y. Yin, Z. Y. Li and Y. Xia, J. Am. Chem. Soc., 2005, 127, 17118.
17. Y. Xia, Y. Xiong, B. Lim and S. E. Skrabalak, Angew. Chem., Int. Ed., 2009, 48, 60.
18. L. Gou and C. J. Murphy, Chem. Mater., 2005, 17, 3668.
19. Y. Sun and Y. Zia, Science, 2002, 298, 2176.
20. X. Ye, L. Jin, H. Caglayan, J. Chen, G. Xing, C. Zheng, V. Doan-Nguyen, Y. Kang, N. Engheta, C. R. Kagan and C. B. Murray, ACS Nano, 2012, 6, 2804.
21. Y. Xia, B. Gates, Y. Yin and Y. Lu, Adv. Mater., 2000, 12, 693.
22. J. K. Beddow and T. P. Meloy, Advanced Particulate Morphology, CRC Press, Boca Raton, FL, 1977.
23. http://gcc.gnu.org, accessed December, accessed July 2013.
24. Willow Garage and Itseez, Intel Russia research center in Nizhny Novgorod, http://opencv.org, accessed January 2014.
25. http://qt-project.org, accessed July 2013.
26. S. Suzuki and K. Abe, CVGIP, 1985, 30, 32.
27. M. Muñoz-Mármol, J. Crespo, M. J. Fritts and V. Maojo, Nanomedicine: NBM, 2014 DOI:10.1016/j.nano.2014.07.006.
28. S. Wang, W. Lu, O. Tovmachenko, U. S. Rai, H. Yu and P. C. Ray, Chem. Phys. Lett., 2008, 463, 145.
29. B. D. Chithrani, A. A. Ghazani and W. C. W. Chan, Nano Lett., 2006, 6, 662.
30. A. M. Schrand, M. F. Rahman, S. B. Hussain, J. J. Schlager, D. A. Smith and A. F. Syed, Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol., 2010, 2, 544.
31. G. Bystrzejewska-Piotrowska, J. Golimowski and P. L. Urban, Waste Manage., 2009, 29, 2587.
32. S. Pal, Y. K. Tak and J. M. Song, Appl. Environ. Microbiol., 2007, 73, 1712.
33. R. C. Gonzalez and R. E. Woods, Digital Image Processing, Prentice Hall, 3rd edn, 2007.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra10375k

---