Artificial neural network-based determination of denoised optical properties in double integrating spheres measurement

1. Introduction

A quantitative understanding of light propagation in biological tissues is essential in the field of biomedical optics for diagnostic and therapeutic applications.¹ Light propagation in biological tissues is mainly characterized by two optical parameters: the absorption coefficient ${\mu }_{\mathrm{\text{a}}}$ and the scattering coefficient ${\mu }_{\mathrm{\text{s}}}$.² The values of ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ are determined using a combination of spectroscopic measurements and inversion algorithms.³ To date, several methods have been developed to determine the ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ characteristics of various bio-tissues.⁴ In the spectroscopic measurements, a double integrating sphere (DIS) system allows the diffuse reflectance R and the total transmittance T to be measured simultaneously at the same point in a sample with high accuracy.^5,6 The combination of the DIS system with inversion algorithms is regarded as the gold standard for measurement of these optical properties.⁷

Several inversion techniques for ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ from the R and T characteristics measured by the DIS system have been established; examples include inverse adding doubling (IAD),⁸ the inverse Monte Carlo (IMC) method,⁹ lookup tables (LTs),¹⁰ and artificial neural network (ANN)^11,12 based methods. The IAD method, which is based on numerical solution of the radiation transport equation, offers high-speed inversion.¹³ The IMC method is based on an iterative calculation performed with the Monte Carlo (MC) model of light transport in tissues and calculates the optical properties accurately for a wide range of absorption and scattering coefficients.¹⁴ In the LT and ANN methods, the iterative processes required in the IAD and IMC methods are avoided and the calculation time can then be reduced significantly.^10,11,12 Although these methods have been used previously, the estimated ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values are affected by the measurement noise signals of both R and T.¹¹

The conventional approaches estimate ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values from measured R and T for each wavelength. The measured R and T values include random noise signals in the DIS measurements. These measurement noise signals thus affect the estimation of both ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ and reduce the accuracy of their determination. This measurement noise is unavoidable, and the effect increases as the measurement time for R and T decreases. Longer measurement times often lead to issues due to changes in the dryness of the bio-tissue, which lead to changes in the optical properties in the DIS measurement. To ensure that the ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values are determined accurately, a noise-resistant inversion technique is required.

In this work, we propose an ANN model with multiple wavelength inputs (mwANN) to determine the ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values of tissues with high noise robustness. The mwANN is based on the fact that the ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ spectra are theoretically defined as continuous functions in wavelength.² The measurement noise is reduced by using the continuity of the ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values between the target and neighboring wavelengths. The mwANN accepts the measured spectra of R and T for the target and neighboring wavelengths and outputs noise-reduced ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values at the target wavelength. To date, several ANN models have been demonstrated to provide a fast technique for determination of ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ and consideration of the wavelength-dependent anisotropy factor g and the refractive index n.¹² In addition to these functions, the mwANN enables noise-reduced estimation of both ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$. This improvement to the inversion process can shorten the DIS measurement time because of its high noise robustness, leading to measurements that can reduce the effects of sample desiccation and degeneration over time. This offers an advantage in providing accurate estimation without the need for equipment improvements for reducing the noise levels.

2. Materials and Methods

2.1. Neural network model

Figure 1 shows a schematic illustration of the mwANN that is proposed to determine the noise-reduced ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values at a target wavelength. The measured R and T values include measurement noise signals that depend on the DIS system and the measurement conditions. The measured R and T values at the target wavelength and several neighboring wavelengths are input into the mwANN model. The mwANN model reduces the estimation noise for both ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ at the target wavelength by learning the relevance and the continuity of these spectra. Estimated ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ spectra were obtained by varying the target wavelength.

The mwANN model, which has three hidden layers that incorporate batch normalization and a rectified linear unit (ReLU) function for activation, was then prepared. The mwANN model was tuned independently according to the noise conditions of the DIS system. The codes were implemented in Python and TensorFlow with the Keras module was used as the deep learning toolkit. Training was performed using Adam optimization. The mean squared error was then minimized as a loss function.

2.2. Dataset preparation

To construct a dataset, ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ spectra were generated using an approximation model and expressed as a function of the wavelength $\lambda$ [nm]. Several ${\mu }_{\mathrm{\text{a}}}$ spectra for biological tissues, denoted by ${\mu }_{\mathrm{\text{a}}}(\lambda )$, can be modeled using the ${\mu }_{\mathrm{\text{a}}}$ spectra of oxyhemoglobin (${\mu }_{{\mathrm{\text{a,HbO}}}_2}(\lambda )$), deoxyhemoglobin (${\mu }_{\mathrm{\text{a,Hb}}}(\lambda )$), water (${\mu }_{\mathrm{\text{a,W}}}(\lambda )$) and melanin (${\mu }_{\mathrm{\text{a,Mel}}}(\lambda )$), as shown below²:

where $S_{\mathrm{\text{B}}}$, $S_{\mathrm{\text{W}}}$ and $S_{\mathrm{\text{M}}}$ are scaling factors that indicate the blood, water and melanin volume fractions, respectively. $\alpha$ is the percentage of HbO₂ in the blood. ${\mu }_{\mathrm{\text{a,Mel}}}(\lambda )$ is calculated using the following equation¹⁵ :${\mu }_{\mathrm{\text{s}}}(\lambda )$ is calculated using the following equation with constants $a,b,c$ and d, which vary for different tissues¹⁶ : To simulate the measured $R(\lambda )$ and $T(\lambda )$ values, 15,000 sets of ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ were generated within the 370–800$$nm wavelength range. The scaling factors and the constants in Eqs. (1) and (3) were assigned randomly from the ranges given in Table 1 to cover a wide range of optical properties. The ranges of these factors were determined based on values from the literature.^16,17,18 To match the sampling pitch of the wavelength in the DIS measurements, the generated sets of ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ were interpolated using quadratic splines. The interpolated ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ were used after their spectral shapes were confirmed to be identical before and after the interpolation. From each set of these interpolated ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ values, the corresponding $R(\lambda )$ and $T(\lambda )$ values were then calculated using a Monte Carlo model of steady-state light transport in multi-layered tissues (MCML).¹⁹ The light propagation calculations were executed using CUDAMCML, which is graphics processing unit (GPU)-accelerated MCML software.²⁰ In the MCML calculations, the biological sample was assumed to be sealed between two glass slides to perform the DIS measurement.⁷ The values of n and g for the sample were set at 1.385 and 0.9, respectively, according to the literature.²¹ The thickness of the glass slide was set at 1.0$$mm. The n value of the glass slides was 1.524. The number of photon packets used in the MCML calculations was $1\times 10^6$. The sample thickness was set at 0.5$$mm in the numerical demonstration according to the literature²² or at an appropriate measured value in the experimental verification.

To simulate the measurement noise signals, noise signals based on the assumption of DIS measurement were added to the interpolated $R(\lambda )$ and $T(\lambda )$ values. $R(\lambda )$ and $T(\lambda )$ are obtained via three optical measurements, comprising a white light reference measurement, a dark reference measurement and a sample measurement, using the DIS system. The dark reference measurements for $R(\lambda )$ or $T(\lambda )$ were taken experimentally 20 times over the wavelength range of the dataset to obtain the variance at each wavelength as the detection noise signals. The detection noise distributions were assumed to be Gaussian noise. The noise variance of $R(\lambda )$, denoted by ${\sigma }_{\mathrm{\text{noise}}}^2(R)$, and that of $T(\lambda )$, denoted by ${\sigma }_{\mathrm{\text{noise}}}^2(T)$, were calculated via error propagation using the variances of the detection noise signals. Gaussian noise signals with variances of ${\sigma }_{\mathrm{\text{noise}}}^2(R)$ and ${\sigma }_{\mathrm{\text{noise}}}^2(T)$ were generated randomly and then added to the interpolated $R(\lambda )$ and $T(\lambda )$ values. Therefore, a database consisting of 15,000 sets of ${\mu }_{\mathrm{\text{a}}}(\lambda )$, ${\mu }_{\mathrm{\text{s}}}(\lambda )$, noise-added $R(\lambda )$ and noise-added $T(\lambda )$ values was constructed. Several databases were prepared by changing ${\sigma }_{\mathrm{\text{noise}}}^2(R)$ and ${\sigma }_{\mathrm{\text{noise}}}^2(T)$ during the evaluation of the noise robustness.

For a training dataset, target wavelengths were assigned randomly for each set in the constructed database. The ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ values at the assigned target wavelengths and the continuous noise-added $R(\lambda )$ and $T(\lambda )$ sequences with the same number of wavelengths as the mwANN inputs were then extracted. The training dataset, which consisted of 15,000 pairs of inputs and outputs from the mwANN shown in Fig. 1, was thus constructed. For the test dataset, 1,000 sets of ${\mu }_{\mathrm{\text{a}}}(\lambda )$, ${\mu }_{\mathrm{\text{s}}}(\lambda )$, noise-added $R(\lambda )$ and $T(\lambda )$ values were generated using the same procedure that was used for the database for the training dataset.

2.3. Accuracy evaluation

To evaluate the noise reduction performance, the signal-to-noise ratio (SNR) was used. The SNRs of the estimated ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values were calculated independently using the following equation²³ :

where ${\sigma }_x^2$ is the variance of the true ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ values. ${\sigma }_e^2$ is the variance of the estimation error, which is described as the absolute error between the true and estimated ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ values.

Comparisons of the noise robustness of the proposed mwANN to the IMC method, a one-wavelength ANN (owANN) and a combination of a Gaussian filter (GF) and the owANN were performed. In the IMC method, ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ were determined using the methodology presented in the literature.²⁴ In the IMC method, n and g were assumed to be constant at all wavelengths and were set at 1.385 and 0.9. In the owANN, 12,000 sets of a meshed training dataset of ${\mu }_{\mathrm{\text{a}}}$, ${\mu }_{\mathrm{\text{s}}}$, R and T were used for training, as described in the literature.¹¹ To have the same ranges for the optical properties that were used as the training dataset for the mwANN, the ranges of ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ were 0–3 mm${}^{-1}$ and 0–120 mm${}^{-1}$, respectively, and the intervals for ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ were 0.03 mm${}^{-1}$ and 1 mm${}^{-1}$, respectively. For the combination of the GF and owANN, R and T values that had been denoised using a GF were input to the owANN, and the values of ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ were estimated. Within the parameter ranges, the ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values were divided into each interval size and all possible different combinations were then generated.

2.4. Sample measurement using DIS system

To measure $R(\lambda )$ and $T(\lambda )$, a DIS system was used. Our DIS experimental setup was previously described in detail.²⁴ Briefly, a xenon lamp (L2273 and C8849, Hamamatsu Photonics, Japan) was used as the white light source. The light was focused onto the sample surface into a 1$$mm diameter spot. The sample was placed between the reflectance and transmittance spheres (CSTM-3P-GPS-033SL, Labsphere). The integrating spheres had ports with a diameter of 10$$mm. The diffusely reflected and transmitted light was detected through an optical fiber (CUSTOM-PATCH-2243142, Ocean Optics) connected to a spectrometer (MAYP10161, Maya2000-Pro, Ocean Optics).

Chicken breast tissue was prepared for the measurements. Frozen chicken breast tissue was cut into thin slices with dimensions of approximately 1$$cm × 1$$cm to cover the ports of the integrating spheres. The thickness of the chicken breast tissue was 2.0$$mm. The sample thickness was measured at three points using a micrometer (MDE-25MX, Mitutoyo, Japan) and averaged. The sample was then sandwiched between two glass slides using spacers to minimize any change in the optical properties due to compression. The tissue was then sealed with glue to prevent desiccation from occurring during the measurements. The above procedures had been completed within 10$$min and the measurement was performed immediately after sample preparation. To compare the performance of IMC and the mwANN, a single sample was prepared. The exposure time was set at 500$$ms and the number of scans averaged in the measurement was set at 1 or 100.

3. Results

3.1. Noise reduction in determination of absorption and scattering coefficients

To demonstrate the noise reduction, the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ values were estimated by the trained mwANN, which accepted 31 wavelengths from the simulated $R(\lambda )$ and $T(\lambda )$ spectra measured using the DIS system. Initially, ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra generated in the same manner shown in Sec. 2.2 were defined as the true values. From the generated ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra, the simulated $R(\lambda )$ and $T(\lambda )$ spectra were obtained. Figure 2(a) shows a set of the simulated $R(\lambda )$ and $T(\lambda )$ spectra. The ${\sigma }_{\mathrm{\text{noise}}}^2(R)$ and ${\sigma }_{\mathrm{\text{noise}}}^2(T)$ values were determined to be $2.10\times 10^{-5}$ and $3.32\times 10^{-5}$, respectively. Figure 2(b) shows the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra calculated using the IMC and mwANN methods. When compared with the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra obtained by the IMC method, the results from the mwANN method showed good agreement with the true values. The spectra estimated by the IMC method showed less accuracy, particularly at wavelengths around 400$$nm, where light absorption by the hemoglobin was notably strong. This led to the small values that were determined for both $R(\lambda )$ and $T(\lambda )$ within this wavelength range.²⁵ In contrast, the spectra estimated via the mwANN method showed high accuracy with almost no dispersions. Figures 3(a) and 3(b) show the estimation errors for the IMC and mwANN methods, respectively. The average estimation errors for the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra were 0.013$$mm${}^{-1}$ and 1.59$$mm${}^{-1}$ for the IMC method and 0.010$$mm${}^{-1}$ and 0.48$$mm${}^{-1}$ for the mwANN method, respectively. The accuracy of the optical properties estimated from the noised R and T values was improved.

3.2. Evaluation of the number of input wavelengths

To evaluate the relationships between the SNR and the number of input wavelengths, simulated measured $R(\lambda )$ and $T(\lambda )$ spectra were prepared by assuming that the number of scans to be averaged in the DIS measurement was 1 or 100. For the number of scans to be averaged of 1, ${\sigma }_{\mathrm{\text{noise}}}^2(R)$ and ${\sigma }_{\mathrm{\text{noise}}}^2(T)$ were $1.58\times 10^{-4}$ and $2.10\times 10^{-4}$, respectively. For the number of scans to be averaged of 100, ${\sigma }_{\mathrm{\text{noise}}}^2(R)$ and ${\sigma }_{\mathrm{\text{noise}}}^2(T)$ were $2.46\times 10^{-6}$ and $3.28\times 10^{-6}$, respectively. Figure 4 illustrates the relationship between the SNR and the number of input wavelengths. When the neighboring wavelengths were not taken into account (i.e., one wavelength was input), the SNR was low for both measurement conditions, indicating that the noise reduction procedure had not functioned. In contrast, as the number of input wavelengths increased, the SNR was observed to improve for both ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$. This improvement occurred because use of a greater number of input wavelengths meant that more spectral shape changes could be trained and used for the estimation process. The use of multiple wavelengths as inputs is useful as an approach to noise reduction for the optical properties. For numbers of input wavelengths greater than 11, the SNRs of the ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values estimated from the measurement with one scan exceeded the SNR obtained when 100 scans were averaged without consideration of the neighboring wavelengths (i.e., when one wavelength was input), thus indicating the feasibility of reducing the measurement time by applying the DIS.

3.3. Evaluation of noise robustness

To evaluate the noise robustness of the proposed method, the estimation accuracies obtained for each noise level when using the IMC method, the owANN method, the GF method and the mwANN method with 51 input wavelengths were compared. Figure 5(a) shows the relationship between the SNR and the noise level ${\sigma }_{\mathrm{\text{noise}}}^2$. ${\sigma }_{\mathrm{\text{noise}}}^2$ was defined as ${\sigma }_{\mathrm{\text{noise}}}^2=({\sigma }_{\mathrm{\text{noise}}}^2(R)+{\sigma }_{\mathrm{\text{noise}}}^2(T))/2$. The mwANN method showed a higher SNR and better estimation accuracy when compared with the IMC, owANN and GF methods, except in the case where ${\sigma }_{\mathrm{\text{noise}}}^2$ was near zero. The SNR, which tended to decrease with increasing noise levels, was improved by using the multi-wavelength model, and the high SNR was retained. The IMC and owANN methods both showed a significant reduction in their SNR characteristics, indicating reduced noise robustness. The mwANN method was more robust to the measurement noise than the other methods. Even at high noise levels, the mwANN method was able to reduce the noise and determine the optical properties accurately. Figure 5(b) shows the coefficient of determination ($R^2$) characteristics with the varying noise levels. The mwANN method kept the $R^2$ at the same level (more than 0.99) as the estimated results from noise-free data (${\sigma }_{\mathrm{\text{noise}}}^2=0$) with the IMC method, even at high noise levels. The difference between the true and estimated values was maintained at the same level as the noiseless case, indicating that the mwANN method reduces noise without smoothing out the information of the actual ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$.

3.4. Experimental verification

The ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra of the chicken breast tissue were estimated from experimental $R(\lambda )$ and $T(\lambda )$ characteristics measured using the DIS system for experimental verification. Figure 6(a) shows the $R(\lambda )$ and $T(\lambda )$ spectra of the chicken breast tissues when measured with the number of scans to be averaged of 1 or 100. The acquisition time for the $R(\lambda )$ and $T(\lambda )$ spectra for one scan can be shortened to 1/100 of that for 100 scans. Figure 6(b) shows the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra obtained via the IMC method when using measured data that were averaged over 100 scans. A strong absorption peak was observed at approximately 412$$nm and smaller peaks were observed at approximately 548$$nm and 575$$nm. These peaks were considered to be derived from hemoglobin. Some blood vessels might be included in the chicken breast tissue sample. The ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectrum decreased monotonically with increasing wavelength, which was attributed to a reduction in the Rayleigh scattering contribution and an increase in Mie scattering. Figures 6(c) and 6(d) show the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra determined from $R(\lambda )$ and $T(\lambda )$ when measured with one scan by the IMC and mwANN methods, respectively. The mwANN method reduced the effects of noise propagation on the measurement of both $R(\lambda )$ and $T(\lambda )$. The resulting ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra showed values that were closer to the spectra shown in Fig. 6(b). The small absorption peaks produced by hemoglobin at approximately 548$$nm and 575$$nm were identified more clearly by the mwANN method than by the IMC method. These results indicate that the mwANN model can reduce the number of scans required for the DIS measurements, and thus contributes to reduction of the measurement time required to perform spectroscopy.

3.5. Adaptability evaluation

To evaluate the adaptability of the trained mwANN, the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra of human subcutaneous fat were estimated based on previously reported $R(\lambda )$ and $T(\lambda )$ results.²⁴ In the previous work,²⁴ the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ spectrum has a peak for bilirubin at 475$$nm, i.e., a spectrum with a shape that differs from that for hemoglobin absorption. Figure 7 shows the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra obtained by the IMC and mwANN methods. In the ${\mu }_{\mathrm{\text{a}}}$ spectrum that was analyzed using the IMC method, the absorption peaks of hemoglobin were observed at wavelengths of approximately 415$$nm, 450$$nm and 574$$nm, while the peak for bilirubin was observed at 475$$nm. Although spectra with bilirubin absorption bands were not included among the training datasets, the mwANN method was still able to estimate the absorption peak. The ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectrum also showed agreement between the IMC and mwANN methods. The peaks of other absorbers could be estimated because the spectral shape changes in R and T were trained appropriately.

4. Discussion

An ANN model that used R and T values at multiple wavelengths as inputs was constructed for noise-reduced measurement of the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra. The numerical and experimental results demonstrated that the mwANN was robust to measurement noise and that it improved the estimation accuracy of ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ from the noised $R(\lambda )$ and $T(\lambda )$ characteristics. The use of multiple wavelengths as inputs is an effective approach for noise reduction and can be applied regardless of the actual noise level. In addition, accurate ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra can be calculated from $R(\lambda )$ and $T(\lambda )$ when measured using a small number of scans in the DIS system, which contributes to reduced DIS measurement times. There are few restrictions with regard to the biological tissues to which the mwANN can be applied because absorption peaks that are not considered in the optical properties model for the dataset can be estimated.

In the mwANN method, noise reduction was achieved by focusing on the nature of the continuity of the absorption and scattering spectra of the biological tissues. The proposed mwANN method was applied over the visible to near-infrared wavelength range in this study. The same algorithm can be used to estimate ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ over other wavelength ranges, as long as an appropriate training dataset is prepared. In the construction of the training dataset, the main optical absorbers in biological tissues (i.e., hemoglobin, oxyhemoglobin, water and melanin) were considered. Because the optical properties were estimated from spectral changes in $R(\lambda )$ and $T(\lambda )$, absorption bands that were not considered as part of the training data were also detected, as shown in Fig. 7. Other absorption peaks may be detected, along with that of bilirubin.

The results from the owANN and mwANN methods were compared as shown in Fig. 5. When using the owANN method, the $R^2$ values of the estimated ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ were 0.9684 and 0.9905, respectively, for the simulated $R(\lambda )$ and $T(\lambda )$ when assuming DIS measurements with 100 scans. The mwANN method estimated the ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ spectra more accurately, with $R^2$ values of 0.9944 and 0.9932, respectively. The mwANN method determined ${\mu }_{\mathrm{\text{a}}}(\lambda )$ and ${\mu }_{\mathrm{\text{s}}}(\lambda )$ with higher $R^2$ values than the owANN method, even in measurements performed with measurement noise variance that was 60 times larger. The mwANN model was more robust to noise signals when compared with the owANN model. The mwANN can shorten the acquisition time by using measured data that have been averaged over smaller numbers of scans in the DIS system. At least three measurements are required for $R(\lambda )$ or $T(\lambda )$ in conventional DIS measurements, making the measurement time relatively long.²⁶ Prolonged measurements might lead to changes in the optical properties of the biological sample. Zhu et al. reported that the absorption coefficient of porcine liver tissue increased over time because of the weight loss and water loss caused by drying.²⁷ By using the mwANN method, it is expected that the reduced DIS measurement time requirement will enable measurements that minimize any changes in the optical properties caused by the sample conditions.

Although the input to the mwANN will need to be modified, an ANN-based approach with multiple wavelength inputs could be implemented for in vivo measurements when using broadband wavelengths. In diffuse reflection spectroscopy (DRS), the absorption and scattering coefficient spectra were estimated by the IMC²⁸ and ANN²⁹ methods from spatially resolved diffuse reflectance. Generally, the SNR in DRS decreases with increasing source-detector separation, or with increasing distance between the optical fibers that deliver and collect the light.³⁰ The potential for noise reduction when using an ANN-based approach may provide a higher SNR for in vivo optical properties. Furthermore, the time required to perform in vivo spectroscopy can be reduced, thus contributing to real-time measurement of the optical properties.

5. Conclusions

This study has presented an ANN-based method for noise-resistant determination of the optical properties of biological tissues. The ANN was trained to output ${\mu }_{\mathrm{\text{a}}}$ and ${\mu }_{\mathrm{\text{s}}}$ values at a target wavelength based on the inputs of R and T at the surrounding wavelengths. The ANN-based method demonstrated better noise reduction performance than the conventional methods in this field. Furthermore, in vitro experiments showed that the ANN can contribute to the performance of short-time DIS measurements and can be applied to samples with absorption peaks that are not included in the dataset. This method will improve the accuracy of optical properties determination and will enable DIS measurements with minimized effects from changes in the optical properties over time.

Acknowledgments

This work was supported by the Japan Society for the Promotion of Science KAKENHI (Grant numbers: 20H04549 and 19K12822) and the Japan Science and Technology Agency ACT–X (Grant Number: JPMJAX21K7).

Conflicts of Interest

The authors have no conflicts of interest relevant to this article.