2.3.1.

Creation and validation of ${\mathit{ANN}}_{\mathit{EXP}\mathit{1}\text{-}\mathit{MC}\mathit{1}}$ network

The ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ network was an ensemble of 10 individual ANNs as shown in Fig. 2. To balance between training time and optimized TL performance with a limited amount of data, we opted for an ensemble approach with 10 individual ANNs for the ${\mathrm{ANN}}_{\mathrm{EXP}\text{-}\mathrm{MC}1}$ network (see Fig. S3 in the Supplementary Material for more details). As the goal was to enable rapid TL on this ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ network with a limited dataset, a simpler network structure was utilized than that described below for ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$.

To train the individual ANNs of the ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ network, an 80% train, 20% validation split was performed on the ${\mathrm{TV}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ dataset described in the section “Probe 1 dataset,” with different random initializations for each ANN. Weight initialization used the Glorot uniform initialization method.¹⁷ Experimental reflectance spectra were treated as arrays of independent data points, with no knowledge of wavelength entering training. Training and validation data were randomly sampled from this concatenated, wavelength-independent dataset. The input signals (experimental reflectance intensity) were not scaled. However, as the outputs (simulated reflectance intensity) of different fibers were of vastly different magnitudes, they were rescaled to [0, 1] range using min–max normalization. Each individual ANN was comprised of an input layer with 8 fully connected neurons (one neuron for each SDS), 5 hidden layers with 30 fully connected neurons in each layer, along an output layer comprising 8 fully connected neurons, resulting in a total of 4238 trainable parameters for each ANN. This optimal number of hidden layers and number of neurons in these layers was found using KerasTuner,¹⁶ and the details of which are provided in Fig. S1 in the Supplementary Material. The hidden layers used rectified linear unit (ReLU) activation, and the output layer employed a linear activation function. Training was continued for up to 1000 epochs. An early stopping callback was implemented to halt training if there was no improvement in the validation loss for 50 epochs, preventing overfitting. The model that demonstrated the best performance on the validation set during training was restored and saved. The Adam optimizer with a mean-squared-error (MSE) cost function was used with a learning rate of 0.0005.

2.3.2.

Creation and validation of ${\mathit{ANN}}_{\mathit{MC}\mathit{1}\text{-}\mathit{OP}}$ network

The optimal ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$ network was an ensemble of 5 ANNs, each with 6 hidden layers as depicted in Fig. 2. The details of the optimization are provided in Fig. S2 in the Supplementary Material. The ${\mathrm{TV}}_{\mathrm{MC}1\text{-}\mathrm{OP}1}$ dataset described in Sec. 2.5.2 was used to train this network. Both the input and output data were scaled to [0, 1] range during training, using the known range of simulated data. During inference, the outputs of the network were scaled back to the original, absolute range using inverse scaling to obtain absolute values of optical properties. The dataset was randomly divided into training set (80%) and test set (20%). An automated algorithm called deep jointly informed neural networks (DJINN)¹⁸ was used for automatic selection of the best ANN structure and hyperparameters without the need for time-consuming manual searching. DJINN automatically determined the near-optimal hyperparameters for our dataset, which were 250 epochs, batch size of 4916, and a learning rate of 0.007. By automating hyperparameter tuning and network structure selection, DJINN enabled us to obtain a high-performance model more efficiently. DJINN employed the Adam optimizer to minimize the MSE loss function. Each hidden layer utilized the ReLU activation function, and linear activation was applied to the output layers.

Finally, ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ and ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$ were integrated end-to-end to form the initial ANN (${\mathrm{ANN}}_1$) as illustrated in Fig. 2. To independently assess its performance, we subjected ${\mathrm{ANN}}_1$ to evaluation using a distinct test dataset ($E_{\mathrm{EXP}1\text{-}\mathrm{OP}1}$) that was not included in training or validation. The performance of ${\mathrm{ANN}}_1$ was evaluated based on its ability to accurately predict both absorption (${\mu }_a$) and reduced scattering (${\mu }_s^{\prime }$) coefficients. Predicted absorption spectra were fitted with the known chromophore basis function to retrieve absorber concentration. Predicted reduced scattering coefficient was fitted with a power-law relationship of the form ${\mu }_s^{\prime }=a{(\lambda /{\lambda }_0)}^{-b}$, where $a$ and $b$ are the fitting coefficients, $\lambda$ corresponds to wavelength in nm, and ${\lambda }_0$ is a normalization wavelength. This ${\mathrm{ANN}}_1$ served as the basis for the TL technique discussed in the next section.

2.5.1.

Phantom experiments and associated datasets

Three stages of phantom data were collected using three different probes. In all phantoms, methylene blue (Akorn, Inc., Lake Forest, Illinois, United States) was used as the absorber and Intralipid 20% (Fresenius Kabi AG, Bad Homburg, Germany) was used as the scatterer. Appropriate amounts of MB and Intralipid were mixed with 300 mL of distilled water (DI) in a black spray-painted container (Rust-Oleum Flat Black, Vernon Hills, Illinois, United States) to create the phantoms described in the sections “Probe 1 dataset,” “Probe 2 dataset,” and “Probe 3 dataset.” Concentration ranges of each component were selected to encompass the optical property range pertinent to our clinical application.^4,5 Separate MB and Intralipid stocks were used for data collection for each separate probe, with each stock characterized as described below.

In order to calculate the necessary volumes of Intralipid and MB to add to DI water to achieve the desired optical properties, absorption (${\mu }_a$) spectra of MB, scattering (${\mu }_s$) spectra of Intralipid, and scattering anisotropy coefficients ($g$) for Intralipid were required. The first two were measured using a commercial spectrophotometer (Cary 50 Varian, Santa Clara, California, United States). To determine the scattering anisotropy of each Intralipid stock, we created 30 phantoms with ${\mu }_s=25$, 37.5, 62.5, 75, and $125{\mathrm{cm}}^{-1}$ at 665 nm, each of which had ${\mu }_a=0.05$, 0.1, 0.25, 0.5, 0.75, and $1.0{\mathrm{cm}}^{-1}$ at 665 nm from each stock. These phantoms were distinct from those used for training and/or validation. An iterative fitting algorithm was used to determine $g$ by minimizing the difference between experimental signal and corresponding simulated signal obtained from the MC library described in Sec. 2.5.2. The calculated $g$ values were similar to the literature values^20,21 and showed small interstock variation. This small variation was relevant as it considerably affected the quality of fitting of the algorithm. This was expected because of the relatively small SDS present in our probes, making them considerably more sensitive to variations in scattering anisotropy. Hence, it was important for us to determine the value of $g$ for each Intralipid stock rather than relying on the fixed values from the literature.

Our experimental phantom data collection process is briefly described here, the details of which can be found in our earlier work.⁴ We first allowed the source lamp to reach a steady state over $\sim 30\min$. Calibration measurements were taken using a 3-in. calibration sphere to account for fiber throughput and lamp power variation. The probe was then placed in contact with the liquid phantom while continuously stirring. Light was emitted into the phantom using the source fiber, and diffuse reflectance spectra were collected through each of the detector fibers. For both the calibration measurements and phantom measurements, corresponding dark measurements were taken and subtracted. Then the dark corrected spectra were normalized by the corresponding dark corrected calibration data for each detection fiber to obtain the final DRS. Each spectrum consisted of 316 wavelengths (500 to 740 nm).

Sections “Probe 1 dataset,” “Probe 2 dataset,” and “Probe 3 dataset” detail phantom datasets and their optical properties where TV, TL, and $E$ denote training and validation, TL, and testing datasets, respectively. Figure 4 visually represents these datasets with blue, green, and orange denoting training, TL, and test sets, respectively. The subscript associated with each dataset is divided into two parts, with the first part indicating the input and the second part indicating the output of each dataset. EXP, MC, and OP, respectively, denote experimental reflectance intensity, simulated reflectance intensity, and optical properties. The numerical value in the subscript specifies the probe or MC library utilized in generating the dataset.

Fig. 4

Data for different probes and their corresponding optical property ranges. The blue, green, and orange colors correspond to training, TL, and test datasets, respectively.

2.5.2.

Monte Carlo dataset

A Monte Carlo (MC) model for probe 1 was constructed for optical property retrieval from diffuse reflectance spectra. A detailed account is of this is available in our previous publication.⁴ In summary, we generated the MC library (${\mathrm{MC}}_1$) by conducting GPU accelerated MC simulations across a wide range of parameter combinations, encompassing values for absorption coefficient (${\mu }_a$) from 0.0001 to $25{\mathrm{cm}}^{-1}$ and scattering coefficient (${\mu }_s$) from 1 to $250{\mathrm{cm}}^{-1}$. These simulations were carried out using a refractive index of $n=1.37$ and employed the Henyey–Greenstein phase function with a scattering anisotropy factor ($g$) of 0.7, resulting in reduced scattering coefficients (${\mu }_s^{\prime }$) from 0.3 to $75{\mathrm{cm}}^{-1}$ for the MC library. The simulations were executed using ${10}^8\text{photon}$ packets. The computations were performed on a Quadro RTX6000 GPU equipped with 24 GB of GPU memory (NVIDIA Corporation, Santa Clara, California, United States), which took about 7 days to run all optical property combinations. This MC library was used to create a ${\mathrm{TV}}_{\mathrm{MC}1\text{-}\mathrm{OP}1}$ dataset where the inputs were simulated reflectance intensity at eight fibers and outputs were corresponding absorption coefficients (${\mu }_a$) and reduced scattering coefficients (${\mu }_s^{\prime }$).

3.1.1.

Training and performance of ${\mathit{ANN}}_{\mathit{EXP}\mathit{1}\mathit{\text{-}}\mathit{MC}\mathit{1}}$ ensemble

Figure 5 demonstrates the progression of both training and validation losses (MSE) against the number of epochs for a representative ANN (ANN #1) selected from the ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ ensemble. The plot illustrates the convergence of the ANN as training proceeded, with training and validation losses closely aligning. Early stopping callback halted the training at 544 epochs.

Fig. 5

Loss (MSE) versus epochs for ANN #1 of the ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ ensemble. Blue and red colors correspond to training and validation loss, respectively.

The performance of the ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ ensemble was evaluated on the entire ${\mathrm{TV}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ dataset to ensure that it properly captured the relationship between experimental and simulated reflectance signals across all detector fibers. Figure 6 demonstrates that the ensemble accurately learned the relationship between input and outputs. The RMSE and MAPE values were small across all fibers, as detailed in Table 2. The ensemble’s performance was evaluated on the entire ${\mathrm{TV}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ dataset.

Fig. 6

Performance of ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ for (a)–(h) detector fibers 1 to 8. Red dots indicate predictions and solid black lines denote perfect prediction. The units for simulated reflectance signals are detected photon weight.

Table 2

RMSE and MAPE for predicted simulated reflectance signal across eight detector fibers.

3.1.2.

Training and performance of ${\mathit{ANN}}_{\mathit{MC}\mathit{1}\text{-}\mathit{OP}}$ ensemble

Figure 7 shows the training loss (MSE) versus number of epochs for the ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$ ensemble, demonstrating training convergence.

Fig. 7

Loss (MSE) versus epoch for ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$ ensemble. Blue color corresponds to training loss.

The performance of the ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$ ensemble on its test set is depicted in Fig. 8. Absorption coefficient (${\mu }_a$) was predicted with a small $\mathrm{RMSE}=0.087{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=290\%$). This elevated MAPE can be attributed to discrepancies arising from very small absorption coefficients (${\mu }_a<0.01{\mathrm{cm}}^{-1}$). For ${\mu }_a>0.01{\mathrm{cm}}^{-1}$, RMSE was $0.091{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=6.4\%$). Reduced scattering coefficient (${\mu }_s^{\prime }$) was predicted with a small $\mathrm{RMSE}=0.48{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=1.1\%$). These low RMSE values indicate that ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$ successfully learned the relationship between simulated reflectance intensity and corresponding optical properties.

Fig. 8

Predicted (a) absorption coefficients (${\mu }_a$) and (b) reduced scattering coefficients (${\mu }_s^{\prime }$). Red dots represent predictions and solid black lines denote perfect prediction.

3.1.3.

Performance of the initial ANN (${\mathit{ANN}}_{\mathit{1}}$)

The performance of the initial ANN (${\mathrm{ANN}}_1$) on the test set ($E_{\mathrm{EXP}1\text{-}\mathrm{OP}1}$) is presented in Fig. 9. The absorption and reduced scattering spectra predictions from ${\mathrm{ANN}}_1$ for a representative phantom (with ${\mu }_s=100{\mathrm{cm}}^{-1}$ at 665 nm and ${\mu }_a$ values of 0.05, 0.1, 0.25, 0.5, 0.75, and $1.0{\mathrm{cm}}^{-1}$ at 665 nm) from the test dataset are illustrated in Figs. 9(a) and 9(b). The predicted absorption and reduced scattering spectra were fitted using the procedure mentioned in Sec. 2.3.2, resulting in highly accurate fitting.

Fig. 9

Predicted (a) absorption spectra and (b) reduced scattering spectra for a representative phantom. Solid lines, open circles, and dashed lines correspond to known, predicted, and fitted spectra, respectively, whereas colors indicate MB concentration. Predicted (c) MB concentration and (d) ${\mu }_s^{\prime }$ at 665 nm across phantoms. Predictions are denoted by red dots and solid black lines denote perfect prediction. Symbols indicate mean recovered values across all phantom measurements at that value, and error bars correspond to standard deviation across phantoms with identical optical properties. Error bars are included in all cases but are not always visible.

Figure 9(c) illustrates that ${\mathrm{ANN}}_1$ accurately predicted the MB concentration of the phantoms in the test dataset with a small $\mathrm{RMSE}=0.29\mu \mathrm{M}$ (MAPE = 7.46%). It also performed well in predicting the reduced scattering coefficient (${\mu }_s^{\prime }$) across all wavelengths, as evidenced by a low $\mathrm{RMSE}=1.08{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=3.6\%$). The reduced scattering coefficient at 665 nm (${\mu }_{s,665}^{\prime }$) was predicted with $\mathrm{RMSE}=0.77{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=2.54\%$), which is shown in Fig. 9(d).

3.2.1.

Performance of initial ANN (${\mathit{ANN}}_{\mathit{1}}$) on Probe 2 data without transfer learning

To assess the performance of ${\mathrm{ANN}}_1$ for data collected with another probe, we evaluated its performance on the $E_{\mathrm{EXP}2\text{-}\mathrm{OP}2}$ dataset. Figures 10(a) and 10(b) illustrate the absorption and reduced scattering spectra predictions of ${\mathrm{ANN}}_1$ for a representative phantom from $E_{\mathrm{EXP}2\text{-}\mathrm{OP}2}$. ${\mathrm{ANN}}_1$ predicted much higher absorption than known absorption for this phantom as evident from Fig. 10(a). The MB concentration and fitted reduced scattering spectra were obtained by the same methods described in Sec. 3.1.3.

Fig. 10

Predicted (a) absorption spectra and (b) reduced scattering spectra for a representative phantom measured with probe 2 using the neural network trained on probe 1 data (${\mathrm{ANN}}_1$) show poor quality extraction of optical properties. Solid lines, open circles, and dashed lines correspond to known, predicted, and fitted spectra, respectively, and colors indicate MB concentration. Predicted (c) MB concentration and (d)  ${\mu }_s^{\prime }$ at 665 nm across phantoms also show poor performance, where predictions are denoted by red dots and solid black lines denote perfect prediction. Error bars are included in all cases but are not always visible.

The failure of ${\mathrm{ANN}}_1$ to accurately predict MB concentration from probe 2 data can be seen in Fig. 10(c), which shows the performance of ${\mathrm{ANN}}_1$ for the entire $E_{\mathrm{EXP}2\text{-}\mathrm{OP}2}$ dataset. The MB concentration of phantoms was recovered with a large $\mathrm{RMSE}=1.67\mu \mathrm{M}$ (MAPE = 154.84%). It also performed worse in predicting the reduced scattering coefficient (${\mu }_s^{\prime }$) across all wavelengths as evidenced by comparably higher $\mathrm{RMSE}=2.2{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=4.85\%$). The reduced scattering coefficient at 665 nm (${\mu }_{s,665}^{\prime }$) was predicted with $\mathrm{RMSE}=1.76{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=5.14\%$), as shown in Fig. 10(d). These results indicate that employing ${\mathrm{ANN}}_1$, which was trained using probe 1 data, for optical property extraction from data collected by probe 2 results in large errors in predictions, particularly for absorption.

3.2.2.

Feature extraction

From the results of Sec. 3.2.1, it is evident that usage of the initial ANN (${\mathrm{ANN}}_1$) for probe 2 data leads to highly inaccurate prediction of optical properties. To adapt ${\mathrm{ANN}}_1$ to probe 2, we employed a feature extraction TL technique.

Number of training spectra versus performance

Figure 11 presents the prediction error for TL models created from different-sized TL training datasets on the $E_{\mathrm{EXP}2\text{-}\mathrm{MC}1}$ dataset. Initially, we employed 30 spectra, constituting the entire ${\mathrm{TL}}_{\mathrm{EXP}2\text{-}\mathrm{MC}1}$ dataset, to establish our baseline performance (error = 0.021). Subsequently, we reduced the TL dataset to 10 spectra, consisting of the lowest (${\mu }_a=0.05{\mathrm{cm}}^{-1}$) and highest absorption (${\mu }_a=1{\mathrm{cm}}^{-1}$) coefficients at 665 nm for each scattering condition. These 10 spectra were selected as they constitute the outermost boundaries of the ${\mathrm{TL}}_{\mathrm{EXP}2\text{-}\mathrm{MC}1}$ dataset. Figure 11 demonstrates that using these 10 spectra for TL leads to identical error compared to that of using all 30 spectra (0.021 versus 0.021), indicating that the 20 intermediate spectra can be discarded from the TL dataset without loss in the performance.

Fig. 11

Prediction error for ${\mathrm{ANN}}_{\mathrm{TL}}$ models created from TL datasets with varying number of training spectra. The $X$ axis denotes the number of spectra in the TL dataset, and the $Y$ axis denotes the prediction error. Solid bars represent mean values across all combinations of the specified number of spectra, with error bars corresponding to standard deviation.

Smaller subsets of these 10 spectra were then used for TL, ranging from 1 to 5 spectra. Prediction error for a given number of spectra was calculated for all combinations selected from these 10 spectra, in order to determine mean error. Figure 11 illustrates that performance worsens as we employ fewer spectra for TL. Notably, there is a significant difference in error between using 2 and 3 spectra (0.034 versus 0.024, $p=0.0009$), whereas the error between 3 and 4 spectra was not significantly different (0.024 versus 0.022, $p>0.99$). We therefore included three spectra in our TL dataset.

Performance of ${\mathit{ANN}}_{\mathit{\text{target}}(\mathit{2})}$ on Probe 2 data

This algorithm was applied to ${\mathrm{ANN}}_1$ to create ${\mathrm{ANN}}_{\text{target}(2)}$ for probe 2 and its performance was evaluated on $E_{\mathrm{EXP}2\text{-}\mathrm{OP}2}$. Figures 12(a) and 12(b) illustrate the absorption and reduced scattering spectra predictions of ${\mathrm{ANN}}_{\text{target}(2)}$ for a representative phantom from $E_{\mathrm{EXP}2\text{-}\mathrm{OP}2}$. We observe much better agreement between the known and predicted spectra for both absorption and reduced scattering compared to the incorrect insertion of probe 2 data into ${\mathrm{ANN}}_1$.

Fig. 12

Predicted (a) absorption spectra and (b) reduced scattering spectra for a representative phantom measured with probe 2 after TL. Solid lines, open circles, and dashed lines correspond to known, predicted, and fitted spectra, respectively, whereas colors indicate MB concentration. Predicted (c) MB concentration and (d)  ${\mu }_s^{\prime }$ at 665 nm across phantoms, where predictions are denoted by red dots and solid black lines denote perfect prediction. Error bars are included in all cases but are not always visible.

The ability of ${\mathrm{ANN}}_{\text{target}(2)}$ to accurately predict MB concentration can be seen in Fig. 12(c), which shows the performance of ${\mathrm{ANN}}_{\text{target}}$ for the entire $E_{\mathrm{EXP}2\text{-}\mathrm{OP}2}$ dataset. The MB concentration of phantoms was recovered with a small $\mathrm{RMSE}=0.38\mu \mathrm{M}$ (MAPE = 24.82%). It also showed superior performance in predicting the reduced scattering coefficient (${\mu }_s^{\prime }$) across all wavelengths as evidenced by low $\mathrm{RMSE}=0.88{\mathrm{cm}}^{-1}$ (MAPE = 3.68%). The reduced scattering coefficient at 665 nm (${\mu }_{s,665}^{\prime }$) was predicted with $\mathrm{RMSE}=0.71{\mathrm{cm}}^{-1}$ (MAPE = 3.01%), which is shown in Fig. 12(d).

Overall, ${\mathrm{ANN}}_{\text{target}(2)}$ exhibited significantly improved performance on the $E_{\mathrm{EXP}2\text{-}\mathrm{OP}2}$ dataset in comparison to ${\mathrm{ANN}}_1$ both in predicting MB concentration ($p=0.0005$) and reduced scattering coefficient at 665 nm ($p=0.0005$).

3.2.3.

Application of TL algorithm to Probe 3

The performance of ${\mathrm{ANN}}_1$ on probe 3 data ($E_{\mathrm{EXP}3\text{-}\mathrm{OP}3}$) is shown in Figs. 13(a) and 13(b) as the pre-TL prediction. The MB concentration prediction error was huge, with a $\mathrm{RMSE}=4.1\mu \mathrm{M}$ ($\mathrm{MAPE}=361.08\%$). For phantoms with ${\mu }_a>0.1{\mathrm{cm}}^{-1}$, MB concentration was predicted with $\mathrm{RMSE}=4.06\mu \mathrm{M}$ ($\mathrm{MAPE}=124.51\%$). Prediction of the reduced scattering coefficient (${\mu }_s^{\prime }$) across all wavelengths was also poor, with $\mathrm{RMSE}=2.47{\mathrm{cm}}^{-1}$ (MAPE = 5.68%). The reduced scattering coefficient at 665 nm (${\mu }_{s,665}^{\prime }$) was predicted with an $\mathrm{RMSE}=2.08{\mathrm{cm}}^{-1}$ (MAPE = 5.45%) as shown in Fig. 13(b).

Fig. 13

Predicted (a) MB concentration and (b)  ${\mu }_s^{\prime }$ at 665 nm for phantoms measured with probe 3 for both before (pre-TL) and after (post-TL) the application of TL. Pre-TL and post-TL predictions are denoted by red dots and blue squares, respectively, whereas solid black lines denote perfect prediction. Error bars are included in all cases but are not always visible.

The TL algorithm described in the section “Selection of spectra and creation of TL algorithm” was applied to ${\mathrm{ANN}}_1$ to create ${\mathrm{ANN}}_{\text{target}(3)}$ for probe 3 and its performance was also evaluated on $E_{\mathrm{EXP}3\text{-}\mathrm{OP}3}$, which are shown in Figs. 13(a) and 13(b) as the post-TL prediction. The MB concentration of phantoms was recovered with a $\mathrm{RMSE}=0.73\mu \mathrm{M}$ ($\mathrm{MAPE}=61.89\%$), as depicted in Fig. 13(a). This high MAPE can be attributed to mismatch in prediction of low-absorption phantoms for which slight mismatch in prediction causes huge MAPE values. For phantoms with ${\mu }_a>0.1{\mathrm{cm}}^{-1}$, MB concentration was predicted with $\mathrm{RMSE}=0.72\mu \mathrm{M}$ ($\mathrm{MAPE}=22.8\%$). It was also able to predict reduced scattering coefficient (${\mu }_s^{\prime }$) across all wavelengths with a low $\mathrm{RMSE}=1.67{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=4.11\%$). The reduced scattering coefficient at 665 nm (${\mu }_{s,665}^{\prime }$) was predicted with $\mathrm{RMSE}=1.68{\mathrm{cm}}^{-1}$ ($\mathrm{MAPE}=5.43\%$), which is shown in Fig. 13(b).

${\mathrm{ANN}}_{\text{target}(3)}$ exhibited significantly improved performance on the $E_{\mathrm{EXP}3\text{-}\mathrm{OP}3}$ dataset in comparison to ${\mathrm{ANN}}_1$ for MB concentration prediction ($p<0.0001$), whereas prediction of the reduced scattering coefficient at 665 nm was not significantly improved ($p=0.2$).