2.1.

Carbon Nanoparticles and Their Characterization

In this study, nano-graphene oxide (NGO) particles¹⁷ and detonation nanodiamond G01 (PlasmaChem, Germany) were used. NGO nanoparticles were synthesized by oxidizing nanographite in a $3:1$ sulfuric to nitric acids mixture at a temperature of 130°C. The reaction supernatant was collected by removing the graphitic carbon residue by centrifugation. The supernatant was neutralized by the addition of sodium hydroxide. The neutralized solution was dialyzed for 2 days against water.¹⁷ Below, they are called CD.

Nanodiamonds G01 were prepared by controlled dry detonation synthesis followed by purification. The bulk powder density of the sample was $0.69\mathrm{g}/{\mathrm{cm}}^3$, the primary particle size was about 4 nm.

Bidistilled deionized water was used for the preparation of aqueous suspensions of carbon nanoparticles. Aqueous suspensions of CD with a concentration of $0.1\mathrm{g}/\mathrm{l}$ and aqueous suspension of ND with a concentration of $1\mathrm{g}/\mathrm{l}$ were prepared. Suspensions were treated for 2 h in an ultrasonic bath (Bandelin Sonorex rk 31).

Measurements of the sizes of CD and ND in water suspensions were carried out by the method of dynamic light scattering using correlator-goniometer system ALV-CGS-5000/6010 (Langen, Germany), equipped with a He-Ne laser (at a wavelength of 633 nm, output power 20 mW). For numerical processing of the correlation functions, the software package CONTIN was used. Measurements showed that the majority of the CD particles in water had dimensions of $6-9\mathrm{nm}$, and 88% of the ND particles in the suspension had a size of 35 nm.

2.2.

Biological Media

As a biological media, chicken egg white was chosen. This choice is justified by the fact that delivery of nanoparticles directly into the cell is provided, as the whole egg white is a single cell. Also the choice is associated with representative natural fluorophores in the egg white.

In subsequent experiments, in order to improve the reliability of the trained neural network toward changes in biological objects, egg whites of different stages of development and from different vendors were used.

2.3.

Quantum Efficiency and Photostability of Carbon Nanoparticles

For the use of fluorescence nanoparticles in biological applications, high quantum yield, photostability and low toxicity are required.

2.3.2.

Photostability of aqueous suspensions of carbon particles

We carried out a comparative analysis of the temporal stability of the fluorescence of water suspensions of CDs, the typical detonation ND, and organic dye Alexa Fluor 488 with the same concentration, $0.3\mathrm{g}/\mathrm{l}$.

A cuvette with a suspension of nanoparticles was fixed in the cell holder and constantly exposed to laser radiation (argon laser, at a wavelength of 488 nm, power density in cuvette about $10\mathrm{W}/{\mathrm{cm}}^2$ in a defocused beam) for 2 h. Spectra were measured every 15 min in the spectral range 500 to 800 nm using a photomultiplier tube (PMT) (Hamamatsu, H-8259-01) in photon counting mode. The geometry of the experiment and the experimental conditions were exactly the same for all samples. Spectra were corrected for laser power, data acquisition time, sensitivity of the PMT, and absorption of samples.

Figure 1 shows the dependence of the integral intensity of the fluorescence of the studied suspensions as a function of irradiation time. The experimental results clearly demonstrate the advantages of photostability of carbon nanoparticles as compared with the organic dye.

Fig. 1

Dependence of the integral fluorescence intensity of carbon dots (CDs), nanodiamonds (NDs) and dye Alexa Fluor 488 as a function of time of the laser irradiation of the suspensions.

3.1.

Laser Spectrometer

Fluorescence and Raman signals from aqueous suspensions of nanoparticles and biological objects containing nanoparticles were excited by a diode laser (at a wavelength of 405 nm, power incident on the sample $\sim 50\mathrm{mW}$). Spectra were recorded by PMT (Hamamatsu, H-8259-01) in the range 430 to 750 nm. The practical spectral resolution was 0.5 nm. The temperature of the samples was stabilized at $22.0\pm 0.1°\mathrm{C}$. Spectra were corrected for the laser power and data acquisition time. Further, mathematical data processing consisted of the subtraction of the background caused by light scattering in the cuvette with the sample and normalization of the obtained spectra by the area under the Raman valence band of water.

3.2.

Analysis of the Fluorescence Spectra of Egg White with Introduced Carbon Nanoparticles

Figures 2 and 3 show Raman and fluorescence spectra of egg white, water suspensions of CD and ND, and egg white with introduced nanoparticles. The relatively narrow band near 470 nm is the Raman valence band of OH-groups either of water or of biological media (percentage of water in the egg white is about 85%) under excitation at a wavelength of 405 nm. This band is caused by the valence vibrations of molecular OH-groups (wavenumber of this band maximum is $3400{\mathrm{cm}}^{-1}$ and width is about $400{\mathrm{cm}}^{-1}$).

Fig. 2

Raman and fluorescence spectra of water, egg white, aqueous suspensions of CD and egg white containing CD.

Fig. 3

Raman and fluorescence spectra of water, egg white, aqueous suspensions of ND and egg white containing the ND.

The spectrum of autofluorescence of egg white in the studied range consists of several bands: an intense broad structureless band in the range 430 to 730 nm with a maximum at 480 nm, and weaker bands with maxima at 640 nm, 655 to 660 and 675 nm. It is known⁴ that the basic fluorescence band of egg white is formed by the fluorescence contributions of pyridoxine, NADF, flavins, and lipo pigments. Weak fluorescence bands near 640 to 670 nm are caused by the fluorescence of porphyrins.

As seen from Figs. 2 and 3, when excited at a wavelength of 405 nm, CDs exhibited fluorescence in the spectral region between 430 and 680 nm with a maximum near 500 to 505 nm, while NDs emit in the region 430 to 680 nm with a maximum near 520 to 525 nm. Egg white emits in the region 420 to 700 nm with a maximum which varies for different eggs within 480 to 520 nm (see below). Thus, the fluorescence spectra of nanoparticles and egg white are largely overlapping structureless bands. They differ in the position of the maximum and the position and extent of the fluorescence spectral bands. These characteristics are the basis for the extraction of the fluorescent signal of the nanocarbon particles.

Obviously, if the concentration of nanoparticles in the egg white changes, the band of the integral fluorescence varies significantly for several reasons. The main reasons are as follows: (1) when the concentration of nanoparticles changes, the intensity of the fluorescence of individual particles changes and (2) due to the interactions of CD and ND with components of the egg white, both the fluorescence of the egg white and that of nanoparticles change. These interactions are very complex and still not well understood in part because the carbon nanoparticles have been relatively recently synthesized. Using conventional methods, it is impossible to construct a mathematical model of the change of the overall fluorescence of an egg white and nanoparticles as a function of their concentrations (for example, during movement of nanoparticles in biotissue). This means that traditional mathematical methods cannot solve either the direct problem of spectra modeling, or the inverse problem of extracting the fluorescent contribution of varying amount of nanoparticles against a background fluorescence of egg white. Therefore, the algorithms of ANNs have been used.

4.1.

Multilayer Perceptron

In this study, we use the most widespread type of ANNs such as the multilayer perceptron (MLP). The elementary unit used to construct a MLP is a so-called formal neuron, a unit with several inputs and a single output. Each of the inputs is characterized by its own weight coefficient, $w_j$. The value $y$ at the output of a neuron is calculated as a weighted sum of the values $x_j$ at its inputs, put through a nonlinear function $F$ called activation function:

Now, identical neurons, different only by their weights, are combined into blocks, which are used to create layers. Each neuron is connected with each of the neurons in the preceding and the next layers (fully connected scheme) (Fig. 4). The signal is fed, according to Eq. (1), from the input of the first layer of the MLP to the output of the last one.

Fig. 4

Multilayer perceptron.

The first layer of an MLP is called the input layer, as it is used to feed data into the MLP, and serves as the input for the whole network. There are as many neurons in the input layer as there are features describing each of the processed data samples. The neurons of the input layer perform no calculations; they simply distribute the input signal to all the neurons of the next layer. The last layer of an MLP is called the output layer; it serves as the output of the whole network. There are as many neurons in the output layer as there are values that are to be simultaneously determined for each data sample. One or several layers between the input and the output layers are called hidden layers. The numbers of neurons in the hidden layer(s) determine the complexity of the network; it can be estimated by some half-empirical equations, but often it is determined by trial and error.

When the MLP is applied, its output depends on the values of the weight coefficients $w$ (1). Hence, to provide correct answers for an MLP, it should be trained prior to its application. This is done by analyzing the answers of the MLP on the samples of the training set of data, for which the correct (desired) answers are known, with subsequent tuning of the weight coefficients. The goal of training is to minimize the average error of the MLP over the training set by changing the values of the weight coefficients of all the neurons. Most often this is performed by the so-called error backpropagation algorithm, which performs gradient descent in the space of weight coefficients.⁴⁶

4.2.

Use of Artificial Neural Networks to Solve Inverse Problems

Application of ANN for solving inverse problems of optical spectroscopy is possible using three approaches: “model,” “quasi-model,” and “experiment-based.”⁴⁸

In the “model” approach to obtain a learning sample for ANN training, one applies an existing analytical or computational model of the solution of the direct problem. In the presence of such a model, it is possible to provide the required representativity of all the datasets necessary for ANN training (description of the necessary datasets into which the total learning sample should be divided is provided in Sec. 5.3). However, the quality of solution in this case depends on the adequacy of the model used. In situations where the development of an adequate model is impossible because of the complexity of the object, this approach is not feasible.

In the “quasimodel” approach, in order to obtain representative datasets, simulated spectra are used. Unlike the “model” approach in which the data for the learning sample are calculated according to the known analytical expression describing the spectra, in the “quasimodel” approach, first a parametric “quasimodel” describing the spectra on the basis of a small set of experimental data is constructed, and then it is used to compute the data for the learning sample. Obviously, in this way, a sufficient number of patterns can be obtained providing a good representativity of all sets for ANN training. However, the accuracy of solving the inverse problem with the “quasimodel” approach largely depends on two factors: (1) the error of the “quasimodel” used for the calculation (i.e., correspondence of the selected or calculated “quasimodel” with reality) and (2) differences of the noise in calculated patterns and the noise in real experimental data.

In the “experiment-based” approach, experimental data are used to train the neural network. The disadvantage of this approach is the low representativity of sets because getting a very large amount of experimental material is very time consuming. The main advantages of this approach include: training neural network directly on the experimental data taking all molecular interactions into account, and the fact that the network is trained on real experimental noise, which increases the accuracy of the solution of inverse problems.

As was mentioned above, a problem of recognition of the nanoparticles’ fluorescence in the presence of the background fluorescence of egg white cannot be solved based on the “model” approach due to the lack of a correct analytical description of the fluorescence spectra of nanoparticles and the egg white. In addition, because the object of the study is a living biological material and its state can vary significantly with time, it is especially important to train the ANN on real signals of objects containing noise. Thus, in this paper, the inverse problem was solved by ANN in the framework of the “experiment-based” approach.

5.1.

Experimental Learning Sample for Artificial Neural Networks

Two series of Raman and fluorescence spectra were obtained for two different egg whites containing CD. The CD concentration varied in the range from 0 to $20\mu \mathrm{g}/\mathrm{ml}$ with increments of 0.75 and $1.5\mu \mathrm{g}/\mathrm{ml}$. Three series of three egg whites containing ND were obtained. The concentration of ND varied from 0 to $30\mu \mathrm{g}/\mathrm{ml}$ with increments of 1, 1.5, and $3\mu \mathrm{g}/\mathrm{ml}$.

To improve the stability of the solution relative to the biological object model, different series of spectra were recorded with different egg whites. As seen from Fig. 5, such an approach is justified since the fluorescence spectra of different egg whites are significantly different. At that position and shape of integral fluorescence band of pyridoxine, NADF, flavins, lipo pigments (430 to 730 nm), and band of porphyrins (640 to 670 nm) remain practically unchanged.

Fig. 5

Fluorescence spectra for different egg whites: a, b, c—egg whites from different vendors; d—egg white after 3 weeks.

Figure 6 shows examples of the experimental Raman and fluorescence spectra of egg whites with different concentrations of nanoparticles. As seen from Fig. 6, the water Raman valence band (in the region 470 nm) and fluorescence bands of porphyrins (bands near 640 to 670 nm) practically do not change while the fluorescence contribution of CD in the integral fluorescence band in the region 430 to 600 nm changes. The obtained datasets for CD and ND were used for the training of ANN.

Fig. 6

One of the series of Raman and fluorescence spectra of egg whites with different concentrations of introduced carbon dots.

5.2.

Preliminary Processing of Input Data

The considered problem in its original formulation is characterized by an extremely unfavorable ratio of the number of patterns in the training set (30 to 45) and the number of input features (651 points–wavelengths of spectra). Therefore, an important area of research is the use of algorithms to reduce the input dimensionality of the problem, i.e., to reduce the number of input features.

Previous studies made by the authors of this work⁵⁵ showed that one of the most effective ways to reduce the dimensionality of the spectroscopic data is the aggregation of the channels of a spectrum. Newly generated features represent the sum of the intensities in several adjacent channels of the spectrum. Apart from the possibility of improving the quality of the problem solutions, this approach, if successful, may allow the use of much less expensive equipment with a significantly lower spectral resolution.

In this paper, two methods have been explored in order to decrease the dimensionality of the input data: channel aggregation, and selection of the most significant features based on the standard deviation of the values in a channel, proportional to the amount of information contained in that channel.

These studies are important not only from the viewpoint of increasing the sensitivity of the method, but also from a practical point of view. Thus, the aggregation of every four channels corresponds to a coarsening of the spectral resolution of the registration devices by four times (from 0.5 to 2 nm). The spectral range of registration is usually chosen in a way to include the entire bands of interesting objects. Discarding insignificant input features allows one to select the most informative region of the spectra and to use the device with registration in the more narrow spectral range.

5.3.

Results of Using Artificial Neural Networks

For the correct realization of the “experiment-based” approach to ANN training, the learning sample containing the experimental data must be divided into three datasets: training, test, and examination. The training set is used for actual ANN training; the test set—for periodic testing of the network during the learning process in order to determine the moment of termination of the training and to prevent network overtraining; the examination set—to check the quality of the network on an independent dataset. In this paper, this partitioning was carried out randomly in the ratio of $70:20:10$ (training-test-examination). As a result, for the spectra of egg white containing CD, the partitioning of $31:8:4$ (total 43 patterns) was obtained, and for the spectra of egg white with ND–$45:12:6$ (total 63). For an unbiased evaluation of the quality of the networks, averaging over 10 random partitionings was conducted for each type of dimensionality reduction of the input data.

To solve this problem, we used a three-layer perceptron (with 10 neurons in the single hidden layer), trained by the error backpropagation algorithm⁴⁶ with the following parameters: the hyperbolic tangent transfer function in the hidden and output layers, learning rate 0.01, moment 0.5, the initial dispersion of weights 0.3, random order of presentation of patterns, and stop after 100,000 training events after the minimum of the average error on the test dataset. The software package NeuroShell 2⁵⁶ was used for all calculations.

Tables 1 and 2 show the best results of ANN applied to examination sets for different experimental series, for various partitionings into training, test, and examination sets, and after averaging over 10 partitionings, for the original dataset and after the use of the methods of dimensionality reduction for the space of input features. As seen, the error on the examination set for the initial array of data for CD is on the average $2.2\mu \mathrm{g}/\mathrm{ml}$, and for ND–$4\mu \mathrm{g}/\mathrm{ml}$. The high value of the coefficient of multiple determination $R^2$ should be noted. It indicates effective ANN training.

Table 1

Results for average error on examination set for the best partitioning.

Table 2

Results of averaging over 10 different partitionings: mean ± standard deviation.

As seen from these results, both methods used to reduce the dimensionality of input feature space decrease the error. In the case of aggregation, significant features are concentrated in a smaller number of channels without loss of representativity. In the case of discarding insignificant features, the same principle operates: the network is trained better when more information is concentrated in fewer input features without loss of representativity. Table 1 shows the best results, which were obtained by aggregation over four channels. However, the removal of uninformative channels turned out to be more effective. As a result, the average error on the examination set decreased by one and a half times.

The obtained results show that, on average, the error of determination of the concentration of nanoparticles in the studied volume on the examination set for CD is half as much as for ND. It was expected since, first, the quantum yield of CD for the used excitation wavelength (405 nm) is approximately 6.5 times higher than the quantum yield of ND. Second, the size of ND is several times larger than the size of CD, which causes more intense scattering of light by nanoparticles, and this, in turn, can introduce an additional error in the registration of the spectra.

Thus, the results of the use of ANN showed the principle possibility of solving the problem of separation of the fluorescent contribution of carbon nanoparticles from the background autofluorescence. After reducing the dimensionality of the input data feature space, the attained accuracy of determination of the concentration (on examination set) in the studied volume is up to $2\mu \mathrm{g}/\mathrm{ml}$ for CD and $3\mu \mathrm{g}/\mathrm{ml}$ for ND, which is also equal to the minimum detectable concentration of nanoparticles.

5.4.

Prospects of the Proposed Method

In this study, the successful detection of fluorescent nanoparticles in biological objects using ANN was demonstrated. The presented method is fast, sensitive, inexpensive, and nondestructive. Obviously, in this case it is possible to operate with blood, skin, subsurface vessels, lymph nodes, excretas, and cells in vivo and in vitro. In our study, the suggested method was elaborated for fluorescent nanodiamond particles and CDs. However, this method can be also used to work with other fluorescent nanoparticles having fluorescence spectra different from the fluorescence spectra of natural biofluorophores, even to a small degree. Note that the suggested method of using ANN is very sensitive. It may provide good optical visualization not only for nanoparticles having a strong fluorescence as a result of some pretreatment (e.g., nanodiamonds after creation of vacancies by electron bombardment or surface modification), but also for nanoparticles with less intense fluorescent properties (detonation nanodiamonds). In this paper, this can be seen from the comparison of the results of ANN application for CD and detonation ND.

As the elaborated method not only provides optical visualization of nanoparticles in biological tissue, but also allows an estimation of their concentration, it can be used for monitoring the distribution of nanoparticles in biomaterial and of their excretion from the organism. This is especially important when nanoparticles (e.g., nanodiamonds or nanocomposites based on nanodiamonds) are used not only as fluorescent biomarkers, but also as drug carriers.^{10,12,15,20,22,24} ANNs allow not only the detection of the fluorescent signal of nanoparticles carrying drugs or without drugs against the background of autofluorescence, but also the distinguishing of fluorescence spectra of nanoparticles in both states. This means that the suggested method is capable of providing all the necessary stages of a biomarker “job”: monitoring of address delivery, of drug release degree, and of excretion of nanoparticles from the organism.

It should be noted that for each type of biomaterial and nanoparticles, it is necessary to obtain a new experimental database and to retrain the ANN. However, such retraining is performed only once, whereupon the trained ANN can be repeatedly used to solve this specific problem, providing express solution of this problem in real-time experiments.

Unfortunately, so far it is impossible to obtain a fluorescence signal from the deeper layers of the biological system. However, the elaborated method can be also used for detection of signals from deeper layers of bio-objects (for example, when x-ray sources of excitation are used).