Modelling spatially-resolved diffuse reflectance spectra of a multi-layered skin model by artificial neural networks trained with Monte Carlo simulations

: A robust modelling method was proposed to extract chromophore information in multi-layered skin tissue with spatially-resolved diﬀuse reﬂectance spectroscopy. Artiﬁcial neural network models trained with a pre-simulated database were ﬁrst built to map geometric and optical parameters into diﬀuse reﬂectance spectra. Nine ﬁtting parameters including chromophore concentrations and oxygen saturation were then determined by solving the inverse problem of ﬁtting spectral measurements from three diﬀerent parts of the skin. Compared to the Monte Carlo simulation accelerated by a graphics processing unit, the proposed modelling method not only reduced the computation time, but also achieved a better ﬁtting performance.


Introduction
Diffuse reflectance spectroscopy (DRS) is widely used to measure optical properties of tissue such as absorption and scattering coefficients. It is successfully applied for noninvasively characterization of biological tissue, morphological investigation, and diagnosis of diseases [1][2][3][4][5].
To extract optical properties from spectral measurements, an accurate model is required to resolve forward and inverse relationship between a set of optical properties and its corresponding diffuse reflectance spectra. The diffuse approximation was first introduced to analytically model the diffuse reflectance emitted from tissue [6]. However, the diffuse theory suffers from many limitations such as assumptions on high scattering medium and sufficiently large separations between the light source and the detector. Monte Carlo (MC) simulations have been developed and used as a gold standard approach to overcome the shortcomings of the diffuse theory [7]. Since the MC simulation relies on repeated random sampling to describe the radiative transfer process, it inevitably requires sufficient computation time to obtain accurate results. Some researchers have proposed many methods to accelerate simulations [8], but it is still time-consuming to inversely determine tissue optical properties, especially for superficial multi-layered tissue models.
Therefore, several methods based on pre-simulated MC databases have been proposed to obtain the diffuse reflectance and optical properties efficiently including semi-empirical/empirical models (SE/EMs), look-up table (LUT), inverse artificial neural network (I-ANN) and forward artificial neural network (F-ANN). For example, Yudovsky and Pilon provided a general semiempirical model for two-layered semi-infinite tissue based on two flux approximations [9, 10]. Parameters appearing in the analytic expressions were fitted to match results from MC simulations. The model would then be used to inversely resolve chromophore information for two-layered skin tissue. Fredriksson et al. proposed an efficient method of modelling the diffuse reflectance spectrum for three-layered skin tissue by linearly interpolating path length distributions from 72 base simulations [11]. Beer-Lambert's law was applied to calculate absorptions for each path length, and a total of nine fitting parameters were utilized to solve the inverse problem. Zhong et al. and Sharma et al. developed a look-up table based on two-layered MC simulations to inversely evaluate physiological characteristics of skin tissue [12,13]. The numerical model could efficiently and accurately determine volume fraction of melanin, volume fraction of blood, and oxygen saturation from spectral measurements. Wang et al. constructed I-ANN models trained with condensed MC simulations to directly obtain optical coefficients for a two-layered superficial tissue model [14]. F-ANN models were introduced by Yudovsky and Durkin to map a set of geometric properties and optical coefficients into spatial frequency domain diffuse reflectance [15,16]. Iterative curve-fitting method was then applied to find an optimal set of chromophore concentrations and oxygen saturation for a superficial two-layered skin model. The objective of this study is to present an efficient method capable of estimating scattering coefficients and chromophore information in multi-layered skin tissue from spatially-resolved diffuse reflectance spectra. First, F-ANN models trained with a pre-simulated database were built to map nine input parameters including three thicknesses and six optical coefficients into spatially-resolved diffuse reflectance spectra. Thicknesses of the stratum corneum and two other epidermal layers were measured by in vivo harmonic generation microscopy (HGM) [17], and in vivo diffuse reflectance spectra were obtained with a custom-built DRS system [18]. Nine fitting parameters appearing in wavelength-dependent expressions were then determined by solving the inverse problem of fitting spectral measurements. A flowchart of our proposed method is shown in Fig. 1.

Pre-simulated database
Multi-layered skin tissue was assumed to contain four homogenous layers (i.e., stratum corneum, intermediate epidermis without melanin, basal epidermis with melanin, and dermis). The stratum corneum was a keratinized superficial layer, and the intermediate epidermal layer consisted of the stratum granulosum and the stratum spinosum. A high concentration of melanin was located within the basal epidermal layer [17]. The geometric and optical parameters over visible wavelengths were considered to cover a wide range for the skin tissue model as summarized in Table 1 [19][20][21]. The thicknesses of the upper three layers varied from 5 to 30, 5 to 30, 10 to 60 µm respectively, and the thickness of the dermis was assumed to be infinite. The scattering coefficients of the lower two epidermal layers (µ s2 , µ s3 ) were set to have a fixed ratio, and the absorption coefficients of the upper two layers (µ a1 , µ a2 ) were assumed to be the same. Anisotropy factors of the Henyey-Greenstein scattering phase function (g x ) were selected to be 0.92, 0.75, 0.75 and 0.715 from upper to lower layers. All layers had an equal refractive index of 1.42.
Simulations of light transport in the multi-layered skin model were performed using public MCML code [22] with modifications to accelerate the computation by the graphics processing unit (GPU, GeForce GTX 1080) [23]. A Gaussian beam consisting of 100 million photons was used as the incident light perpendicular to the tissue surface. The diffuse reflectance remitted from the tissue surface was collected by three optical fibers which were separated from the source fiber by distances (SDS) of 0.22 mm, 0.45 mm and 0.73 mm, respectively. All fibers had a core diameter of 0.2 mm and a core refractive index of 1.457 with a numerical aperture of 0.26, and were in gentle contact with skin tissue. The nine input parameters (th 1 , th 2 , th 3 , µ a1 , µ s1 , µ s2 , µ a3 , µ a4 , µ s4 ) were randomly assigned within the setting range for each MC simulation, and a total of 30,000 samples were then created as a pre-simulated database.  The weights and biases in the model were tuned by minimizing the relative error between the estimated and the target reflectance. The log-sigmoid function was chosen as the transfer function to generate outputs for the subsequent layers including the final output layer. The scaled conjugate gradient algorithm was used to train the F-ANN models. During the training process, the database was randomly divided into three subsets (i.e., 70% for the training set, 15% for the validation set, and 15% for the testing set). The training set was used to optimize the models and estimate diffuse reflectance, the validation set was monitored to avoid overfitting, and the testing set was used to evaluate the performance of the trained models. The scattering coefficients of the upper two layers (µ s1 , µ s2 ) were both assumed to have a power law relation with the wavelength as commonly done for biological tissues [20]: where C x and b x are fitting parameters; λ is the wavelength in nm; g x is the anisotropy factor. Our previous study found a high scattering coefficient in the uppermost keratin layer of oral epithelial tissue using quantitative phase images of thin tissue slices. In addition, the scattering coefficients of the basal and intermediate layers approximately had a fixed ratio of 1.35 [24]. Since the depth-dependent morphology of epithelial cells in the oral epithelium is similar to that of epidermal cells in the skin and the scattering coefficient is highly correlated with the morphology, we assumed that the scattering coefficients of the basal and intermediate epidermal layers (µ s2 , µ s3 ) also had the same ratio. The absorptions of the upper two layers (µ a1 , µ a2 ) were assumed to be approximately the same as epithelial cells because these layers had negligible melanin [17,25]; as a result, the absorption coefficients could be expressed as: where µ a,e (λ) is the absorption coefficient measured from thin slices of bronchus epithelial tissue [26].
Melanin has a broad absorption spectrum exhibiting stronger absorption at shorter wavelengths. This dominant absorber was assumed to exist only in the basal layer of the epidermis whose absorption coefficient (µ a3 ) could be calculated as: where f m is the volume fraction of melanin and µ a,m (λ) is the absorption coefficient of melanin given by [27]:

. Dermis
The scattering coefficient of the dermis (µ s4 ) was also expressed as: where C 3 and b 3 are fitting parameters.
The absorption coefficient of the dermis (µ a4 ) was modeled as a combination of the absorption of blood, water and collagen [28]: where f b is the average volume fraction of blood; f w is the volume fraction of water which was assumed to have a fixed value of 70% [19]; µ a,b (λ), µ a,w (λ), µ a,c (λ) are the absorption coefficients of blood, water and collagen, respectively. The absorption coefficients measured from pure water and gelatin sheets with 100% collagenous protein were used for µ a,w (λ) and µ a,c (λ), respectively [28,29]. µ a,b (λ) is formed by summing the absorption coefficients of oxy-hemoglobin (µ a,oxy ) and deoxy-hemoglobin (µ a,deoxy ), which are given by [30]: µ a,oxy (λ) = 2.303ε oxy (λ)C heme S/64, 532 and (7) where ε oxy (λ) and ε deoxy (λ) are known molar extinction coefficients of oxy-hemoglobin and deoxy-hemoglobin, respectively; C heme represents the hemoglobin concentration of blood which is typically assumed to be 150 g/l; S (%) is the unknown oxygen saturation [30].

Iterative curve-fitting method
According to the review of the literature [19,28,31], the values of nine fitting parameters were constrained between the upper and lower bounds as shown in Table 2. The setting ranges of µ a3 and µ a4 in Table 1 were chosen to cover the values of the absorption coefficients generated by the bounded parameters ( f m , f b , S) while the fitting parameters for scattering coefficients ( were non-linearly constrained to ensure that the scattering coefficients would fall within the setting range of µ s1 , µ s2 and µ s4 . An initial guess of the fitting parameters was randomly assigned to generate optical coefficients based on Eqs. (1)-(8). The optical coefficients combined with the thicknesses obtained from HGM images were fed into the trained F-ANN models to estimate diffuse reflectance spectra. The Matlab built-in function "fmincon" then optimized the fitting parameters by minimizing an objective function which was defined as the root-mean-squared percent error between the estimated and the measured diffuse reflectance spectra: where l and k were the total number of fibers and wavelengths analyzed, respectively; R and r represented the estimated and the measured diffuse reflectance spectra. The fitting function stopped the optimization process when the current step size was less than a step tolerance of 10 −7 . The above random guess and fitting process were repeated for 100 times to find an optimal local minimum.
1 × 10 5 1 1 × 10 5 1 1 × 10 5 1 1% 0.0% 0.0% Upper bound 5 × 10 6 2 5 × 10 6 2 5 × 10 6 2 25% 0.5% 100% 2.5. Spatially-resolved diffuse reflectance spectra of skin tissue The diffuse reflectance spectra were acquired by a custom-built DRS system which shined white light (410-760 nm). The setup of the source and detectors was the same as those described in Sec. 2.1. We used a set of five homogeneous aqueous phantoms to calibrate the diffuse reflectance spectra and to establish calibration factors for removing the effects of non-uniform spectral response and background of the system. The tissue mimicking phantoms were made of known concentrations of polystyrene beads (Polysciences, Inc., Polybead Microspheres) and hemoglobin (Sigma-Aldrich, ferrous stabilized human hemoglobin). The calibration phantoms contained polystyrene beads with a diameter of 0.51±0.008 µm at concentrations of 9.10 × 10 10 , 5.60 × 10 10 , 3.64 × 10 10 , 2.28 × 10 10 , and 1.21 × 10 10 particles/ml, respectively. The first four phantoms and the last phantom also contained hemoglobin at concentrations of 0.056 and 0.1126 mg/ml respectively. Scattering coefficients and absorption coefficients of the phantoms were obtained using Mie theory and UV-visible absorption spectroscopy measurements, respectively. With the known optical coefficients, a linear calibration relation was then established by comparing the measured diffuse reflectance of the phantoms to the simulated diffuse reflectance. In this study, experiments using the DRS and the HGM system were approved by the Institutional Review Board at National Taiwan University Hospital, and the informed consent was obtained from healthy volunteers.

The training results of F-ANN models
The critical point of this study was to build F-ANN models that accurately mapped geometric and optical parameters into diffuse reflectance at several SDSs. There were two factors that greatly influenced the accuracy of F-ANN models: (1) the sample size used in the training process and (2) the coefficient of variation (CV) of MC simulations. We had used several sample sizes from 3,500 to 21,000 to train F-ANN models with 55 neurons for each hidden layer. The absolute relative error between the estimated and the target reflectance gradually converged to a minimum, and a total of 21,000 samples were enough to build robust F-ANN models without sacrificing the performance. The accuracy of F-ANN models for each SDS with various hidden neurons was summarized in Table 3. The errors of the best models were 1.28%±1.19%, 2.27%±2.40% and 3.59%±4.27% for the SDS of 0.22 mm, 0.45 mm and 0.73 mm, respectively. The curves of training, validation and testing error for each training epoch were depicted in Fig. 2(a).
In addition, the CV of MC simulations would induce the uncertainty in the F-ANN models to predict the diffuse reflectance. The value of CV at a specific reflectance value was estimated by conducting a random process for 20 times. The random process repeated 10 8 times an event of which the occurrence probability was equal to the probability of a photon collected by the fiber. The curve of CV versus reflectance was then obtained and plotted in Fig. 2(b). Furthermore, we used the F-ANN models with minimal errors to generate the diffuse reflectance for each sample in the training and the testing set. The curves of error versus reflectance in Fig. 2(b) were acquired by averaging the absolute relative errors of the samples in each reflectance bin of the histograms as shown in Figs. 2(c) and 2(d). The curves demonstrated that the error had a negative correlation with the value of the diffuse reflectance, and was highly correlated with the CV of MC simulations. According to Fig. 2(b), the error in the testing set reached around 30% at the reflectance of 10 −8 which occurred in highly absorbing media (i.e., µ a3 >300 and µ a4 >10). To solve this issue, 1177 samples in the database with the reflectance lower than 10 −7 at the SDS of 0.73 mm were re-simulated by launching one billion photons to reduce the variation in simulated diffuse reflectance. F-ANN models for the SDS of 0.73 mm were then re-trained and re-tested with the updated database. The results, as summarized in Table 3, showed that the mean and the standard deviation of the absolute relative errors of the best model decreased from 3.59%±4.27% to 3.19%±3.04%. Curves of the error versus the reflectance as depicted in Fig. 2(b) revealed that the error for the highly absorbing media decreased to about 8%. After the two-step training process, the F-ANN models had been prepared to solve the inverse problem.

Validations of F-ANN models with simulated DRS data
Fifteen sets of fitting parameters were randomly sampled to generate optical coefficients over a wavelength range of 410 to 760 nm. The generated coefficients combined with fixed thicknesses of 15, 15 and 30 µm for the upper three layers were used to model diffuse reflectance spectra. 3% random Gaussian noise was added to the spectral data to simulate experimental errors. The initial guess and the iterative curve-fitting method described in Sec. 2.4 were repeated for 100 times to find an optimal set of fitting parameters. Root-mean-squared percent errors of the recovered optical coefficients, absolute relative errors of the estimated chromophore concentrations and absolute errors of the oxygen saturation for 15 sets of MC-simulated data were summarized in Table 4. Curve fitting results of MC-simulated data were depicted in Fig. 3. The results revealed that the scattering coefficient of the stratum corneum (µ s1 ) had the largest root-mean-squared error on average among all the optical coefficients. The reason was that the stratum corneum was a highly forward-scattering and thin layer. The partial derivative of the objective function with respect to µ s1 was very low. Therefore, the recovering accuracy of µ s1 was susceptible to the noise interference. Based on the same reason, the recovering accuracies of µ s2 and µ s3 were also limited. This issue could be improved by using oblique fibers to enhance the sensitivity to the scattering coefficient of the epithelium [32,33]. On the contrary, µ a3 , µ a4 and µ s4 had great fitting accuracy since the objective function was sensitive to their variations. In addition, the means and standard deviations of the errors of the estimated chromophore information were 3.25%±2.87%, 3.59%±2.60% and 1.63%±1.40% for f m , f b , and S respectively. The theoretical evaluation validated that the proposed method could accurately extract the chromophore information with a high degree of accuracy.

The application of F-ANN models to extract chromophore information from in vivo experiments
Diffuse reflectance spectra of three different parts of the skin (i.e. face, ventral arm and dorsal arm) from three healthy human subjects were obtained by the DRS system described in Sec. 2.5. In our previous study, we found that the error of extracting optical coefficients from two-layered tissue phantoms would be reduced if the thickness information was known [34]. Therefore, HGM with sub-micrometer resolution was used to non-invasively measure the thicknesses of the stratum corneum and the other two epidermal layers (th 1 , th 2 , th 3 ). The F-ANN models were then applied to extract chromophore concentrations and oxygen saturation in the multi-layered skin tissue. After 100 times of the optimization process with different initial guesses, the optimal set of fitting parameters along with its corresponding diffuse reflectance spectra and optical coefficients was shown in Table 5 and Fig. 4. The fitting results indicated that the volume fraction of melanin ( f m ) in the epidermis varied from 8.23% to 17.5% which was defined as moderately pigmented skin [31]. The average volume fraction of blood ( f b ) in the dermis was around 0.2% [20] which was slightly lower than the typical value. The two dips in reflectance spectra at around 540 nm and 575 nm depicted in Fig. 4 corresponded to the high level of oxygen saturation (S) [30]. The stratum corneum had the strongest scattering property of all the layers, which was consistent with our previous research [24]. The scattering coefficients of the dermis were approximately from 150 to 60 cm −1 with the wavelengths ranging from 410 to 760 nm while the scattering coefficients of the lower two epidermal layers of the dorsal arm was greater than those of the face and the ventral arm. In addition, the fitted diffuse reflectance spectra showed a small mismatch from 450 nm to 700 nm in Fig. 4. Based on our previous studies, the mismatch would cause about 10% RMSE between the fitted and the measured diffuse reflectance spectra [18,33]. There were several factors that influenced the fitting performance for in vivo experiments: (1) optical properties of each layer in the skin model are not totally homogeneous, and (2) the tissue scattering phase function may be different from our assumption. The RMSE would be reduced if these issues were solved.
To further validate the F-ANN's performance, the MC simulation was implemented to generate diffuse reflectance spectra. The optical coefficients used in the forward simulations were derived from the fitting results of the F-ANN. The root-mean-squared percent error of the MC-simulated and the measured diffuse reflectance spectra was then calculated and denoted as RMSE' in Table  5. The results showed that the F-ANN models could accurately map the fitted parameters into the corresponding spectra since the diffuse reflectance spectra obtained from the F-ANN models and the MC simulations matched well as shown in Fig. 4. For comparison of the performance of solving the inverse problem, we implemented the identical fitting process once for each DRS measurement using MC simulations accelerated by the GPU (GPU-MC) to obtain diffuse reflectance. The fitting result of GPU-MC was also summarized in Table 5. The relative deviations between the chromophore information extracted by the two methods were about 10%, 35% and 10% for f m , f b , and S respectively. The RMSE revealed that the F-ANN had a better fitting performance than the GPU-MC. The primary reason was that the variation of MC simulations induced a noisy objective function, which prevented the RMSE from converging to an optimal minimum. Due to the noisy issue, finite differences of each fitting parameter should be carefully chosen to accurately calculate the gradients of the objective function. The issue can be improved by sacrificing the computation time for reducing the variation of MC simulations. In contrast, F-ANN models had a relatively smooth objective function. As a result, more than half of the tried initial guesses approached to the values with the minimal RMSE. Conclusively, the experiment showed that the F-ANN was a robust modelling method of solving the inverse problem, and the fitting speed of F-ANN models was approximately 1,000 times faster than that of GPU-MC simulations.

Discussion
This study presented detailed descriptions of using F-ANN modelling method to solve the inverse problem of fitting spatially-resolved diffuse reflectance spectra. The built models could forward map a wide range of input parameters into the diffuse reflectance and inversely determine the chromophore information in the superficial multi-layered skin tissue. In addition to training three F-ANN models, one for each SDS, we tested whether a single F-ANN model could describe different SDSs. Unfortunately, the result showed that the F-ANN model failed to describe different radiative transfer functions simultaneously. It indicated different radiative transfer functions could not share the same hidden layers. As a result, F-ANN models were built separately for each SDS. Despite the minor drawback, F-ANN shows distinct features and advantages over other methods summarized in Table 6. The gold standard approach, Monte Carlo simulations, can inversely resolve optical coefficients without suffering limitations from specific geometries of the tissue, light source or detectors. However, achieving small variations of MC simulations requires huge computation cost. Even though several techniques have been proposed to address the issue, it is still time-consuming to determine optical coefficients of superficial multi-layered tissue models using spatially-resolved DRS. For example, our previous studies showed that both scalable MC and GPU-MC simulations took around one day to iteratively curve-fit a set of spectra from a single measurement [32,33]. In contrast, the optimization process in the proposed modelling method is finished within a few minutes. Moreover, the variation of MC simulations may result in less desirable fitting results due to the noisy objective function. Loop-up-table is a numerical method of estimating new values of diffuse reflectance by interpolating a discrete set of known parameters. The accuracy could be very high when the database is sufficiently large and the variation of MC simulations is controlled [35,36]. The main disadvantage of the LUT method is that evenly spaced increments for each optical parameter of interest are required for the interpolation, which implies that the database tends to be very large. As a result, only three or four-dimensional LUT has been developed to extract physiological parameters and optical properties of two-layered tissue [12,13]. For example, Sharma et al. used 20 evenly spaced increments each for four free parameters to generate a database with 160,000 samples [13]. By contrast, F-ANN has an ability to efficiently solve the nonlinear relationship between input parameters and the target reflectance. The input parameters can be randomly sampled, and a smaller database is sufficient to generate a robust F-ANN model. I-ANN is a popular method that can directly determine optical coefficients without using any iterative optimization process. However, several studies showed that I-ANN models had large prediction errors [37][38][39][40][41][42]. To improve the accuracy, checking the uniqueness of mapping reflectance sets into corresponding optical parameters is needed [43]. Due to the uniqueness issue, the recovery ability of I-ANN models is limited to one or two-layered tissue. By contrast, the structure of the multi-layered F-ANN model was closer to real skin structures. It would provide more realistic information about the skin than one or two-layered tissue models [11]. Moreover, the I-ANN method lacks the advantage of using the prior knowledge of wavelength dependences of optical coefficients. A post-fitting process was needed to apply wavelength-dependent expressions to the predicted optical coefficients obtained from I-ANN models [14]. Although F-ANN requires more computation than I-ANN, it can avoid the uniqueness issue and improve both the accuracy and robustness of extracting optical properties using broadband spectra.
Compared to LUT, I-ANN and F-ANN modelling methods, semi-empirical/empirical methods require smaller databases to build forward models for diffuse reflectance emitted from the tissue. However, the disadvantage of SE/EMs is that they can only be applied to specific conditions. For example, several models assumed tissue to be a one-layered homogeneous turbid medium [44,45]; two-layered tissue models assumed either the upper or bottom layer to be strongly forward scattering [9, 10, 46,47]; multi-layered tissue models assumed that scattering properties are equal for all layers [11]. The numerical F-ANN model, by contrast, is versatile and not subject to the above limitations.
Due to the robustness and efficiency, F-ANN is a promising tool to replace time-consuming MC simulations for many applications. The proposed method can be used to extract optical properties for different kinds of biological tissues such as mucosa in the digestion track, the breast, brain, skin, subcutaneous fat and muscle tissues. Combined with wavelength-dependent expressions, the modelling technique is capable of solving chromophore information in multi-layered tissues. It is also well suited to be applied to the spatial-frequency-domain DRS [15,16], frequency-domain DRS [48], and image-based DRS such as modulated imaging [49] and hyperspectral imaging [50].

Conclusion
Spatially-resolved diffuse reflectance spectroscopy has been employed to analyze optical properties of biological tissue. This work presented a modelling method of extracting scattering coefficients, chromophore concentrations and oxygen saturation in multi-layered skin tissue based on F-ANN models for in vivo DRS measurements. Through the two-step training process, the models accurately mapped nine parameters including three thicknesses and six optical coefficients into diffuse reflectance spectra. The results showed that absolute relative errors of models were 1.28%±1.19%, 2.27%±2.40% and 3.19%±3.04% for the three optical fibers separated from the source fiber by distances of 0.22 mm, 0.45 mm and 0.73 mm, respectively. The built models were then used to extract optical properties of MC-simulated spectra for theoretical validations. It was shown that the F-ANN models could accurately estimate chromophore information while noise interference would affect the accuracy of recovering scattering properties of epidermal layers especially for the stratum corneum. To further demonstrate the model's applicability, diffuse reflectance spectra of three different parts of the skin (i.e. face, ventral arm and dorsal arm) were measured in vivo by a custom-built DRS system. The thicknesses of three epidermal layers were pre-determined by in vivo harmonic generation microscopic imaging. The chromophore information of the skin tissue was then obtained by iteratively curve-fitting the F-ANN models and estimating optical coefficients with known wavelength dependences. The experimental results demonstrated that the F-ANN models can significantly reduce the computation time with a better fitting performance compared to GPU-MC simulations. Due to the robustness and efficiency, F-ANN is a promising tool for many applications. In the future, we would implement F-ANN models for the diagnosis of diseases and characterization of physiological conditions of tissues.

Disclosures
The authors declare that there are no conflicts of interest related to this article.