Application of transfer learning for rapid calibration of spatially resolved diffuse reflectance probes for extraction of tissue optical properties

Abstract

Significance: Treatment planning for light-based therapies including photodynamic therapy requires tissue optical property knowledge. This is recoverable with spatially resolved diffuse reflectance spectroscopy (DRS) but requires precise source-detector separation (SDS) determination and time-consuming simulations.

Aim: An artificial neural network (ANN) to map from DRS at multiple SDS to optical properties was created. This trained ANN was adapted to fiber-optic probes with varying SDS using transfer learning (TL).

Approach: An ANN mapping from measurements to Monte Carlo simulation to optical properties was created with one fiber-optic probe. A second probe with different SDS was used for TL algorithm creation. Data from a third were used to test this algorithm.

Results: The initial ANN recovered absorber concentration with $\mathrm{RMSE}=0.29\mu M$ (7.5% mean error) and ${\mu }_s^{\text{'}}$ at 665 nm (${\mu }_{s,665}^{\text{'}}$) with $\mathrm{RMSE}=0.77{\mathrm{cm}}^{-1}$ (2.5% mean error). For probe 2, TL significantly improved absorber concentration (0.38 versus $1.67\mu M$ RMSE, $p=0.0005$) and ${{\mu }^{\text{'}}}_{s,665}$ (0.71 versus $1.8{\mathrm{cm}}^{-1}$ RMSE, $p=0.0005$) recovery. A third probe also showed improved absorber (0.7 versus $4.1\mu M$ RMSE, $p<0.0001$) and ${\mu }_{s,665}^{\text{'}}$ (1.68 versus $2.08{\mathrm{cm}}^{-1}$ RMSE, $p=0.2$) recovery.

Conclusions: TL-based probe-to-probe calibration can rapidly adapt an ANN created for one probe to similar target probes, enabling accurate optical property recovery with the target probe.

Keywords: Monte Carlo simulation; diffuse reflectance spectroscopy; machine learning; neural network; transfer learning.

Fig. 1

Image of the distal face of probe 1 showing the $200\mu \mathrm{m}$ diameter fibers. The source fiber ($S$) and detector fibers ($D1$ to $D8$) are denoted using orange circles. The outside diameter is abbreviated as “OD.”

Fig. 2

Initial ANN (${\mathrm{ANN}}_1$) for optical property extraction, which was created by combining ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ ensemble and ${\mathrm{ANN}}_{\mathrm{MC}1\text{-}\mathrm{OP}}$ ensemble.

Fig. 3

TL to create ${\mathrm{ANN}}_{\text{target}(\text{probe})}$ from ${\mathrm{ANN}}_1$ by retraining the output layer of ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$. Although the TL algorithm was applied to all ANN of the ${\mathrm{ANN}}_{\mathrm{EXP}1\text{-}\mathrm{MC}1}$ ensemble, only one ANN is shown here for clarity.

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.

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.

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.

Fig. 7

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

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.

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.

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.

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.

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.

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.