Multi-modulated frequency domain high density diffuse optical tomography

Abstract

Frequency domain (FD) high density diffuse optical tomography (HD-DOT) utilising varying or combined modulation frequencies (mFD) has shown to theoretically improve the imaging accuracy as compared to conventional continuous wave (CW) measurements. Using intensity and phase data from a solid inhomogeneous phantom (NEUROPT) with three insertable rods containing different contrast anomalies, at modulation frequencies of 78 MHz, 141 MHz and 203 MHz, HD-DOT is applied and quantitatively evaluated, showing that mFD outperforms FD and CW for both absolute (iterative) and temporal (linear) tomographic imaging. The localization error (LOCA), full width half maximum (FWHM) and effective resolution (ERES) were evaluated. Across all rods, the LOCA of mFD was 61.3% better than FD and 106.1% better than CW. For FWHM, CW was 6.0% better than FD and mFD and for ERES, mFD was 1.20% better than FD and 9.83% better than CW. Using mFD data is shown to minimize the effect of inherently noisier FD phase data whilst maximising its strengths through improved contrast.

Fig. 1.

A. (z plane) and B. (x plane) A schematic diagram of the source-detector placement on top of the phantom, as well as the orientation of the movable rod which contains the contrast anomaly. For contrast anomaly measurements, the anomaly is centred at x = y = 0 mm and z = -15 mm. C. A photo of the phantom with the rod inserted. The sources and detectors are placed on the phantom using a 3d printed cap. D. A graph showing the log of the intensity as a function of source-detector separation at three modulation frequencies.

Fig. 2.

A diagram of how each performance metric [13, 24] is calculated. A. The LOCA is given by the distance between the centre of the contrast anomaly and the maximum recovery of absorption coefficient in the reconstructed image. B. The FWHM is given by the maximum distance between any two nodes that are more than or equal to 50 $\mathrm{\%}$ of the maximum of the reconstructed image. C. The ERES is twice the maximum distance between the centre of the contrast anomaly and any node that is more than or equal to 50 $\mathrm{\%}$ of the maximum of the reconstructed image.

Fig. 3.

A. A schematic of which source-detector pairs are used for the data shown in Fig. 3(B). B. Log Intensity and Phase measurements of the reference rod volume and contrast anomaly of rod 7. NN1 measurement is between Source 2-Detector 7 of 13 mm separation and NN2 measurement is between Source 4-Detector 7 of 29 mm separation.

Fig. 4.

The standard deviation (left y-axis, circle ticks) and contrast (right y-axis, cross ticks) of the measurements shown in Fig. 3. The standard deviation is that of the reference measurement. For intensity the contrast is the log ratio of the mean anomaly measurement to the mean reference measurement and is dimensionless. For phase, the contrast is the difference between the mean anomaly measurement and the mean reference measurement.

Fig. 5.

Box plots of the log ratio of intensity data of the reference rod ( $I_0$ ) volume and contrast anomaly ( $I(t)$ ) of rod 7. NN1 measurement is between Source 2-Detector 7 of 13 mm separation and NN2 measurement is between Source 4-Detector 7 of 29 mm separation. Measurements are shown at the three modulation frequencies, 78 MHz, 141 MHz and 203 MHz.

Fig. 6.

Box plots of the difference of phase data of the reference rod ( ${\varphi }_0$ ) volume and contrast anomaly ( $\varphi (t)$ ) of rod 7. NN1 measurement is between Source 2-Detector 7 of 13 mm separation and NN2 measurement is between Source 4-Detector 7 of 29 mm separation. Measurements are shown at the three modulation frequencies, 78 MHz, 141 MHz and 203 MHz.

Fig. 7.

Single step tomographic reconstructions from rod 3, 5 and 7 (R3, 5 and 7 respectively) using CW, FD and mFD data respectively at 830 nm. For each reconstructed image, two views are shown, firstly the z plane at z = -15 mm and secondly the x plane at x = 0 mm. The colour bar scales are the same for each given rod. The solid black lines indicate the spatial constraints of the imaging metrics.

Fig. 8.

Iterative (4 iterations) tomographic reconstructions from rod 3, 5 and 7 (R3, 5 and 7 respectively) using CW, FD and mFD data respectively at 830 nm. For each reconstructed image, two views are shown, firstly the z plane at z = -15 mm and secondly the x plane at x = 0 mm. The colour bar scales are the same for each given rod. The solid black lines indicate the spatial constraints of the imaging metrics.

Fig. 9.

Iterative tomographic reconstructions from rod 3, 5 and 7 (R3, 5 and 7 respectively) using CW (8 iterations), FD (6 iterations) and mFD (4 iterations) data respectively at 830 nm. For each reconstructed image, two views are shown, firstly the z plane at z = -15 mm and secondly the x plane at x = 0 mm. The colour bar scales are the same for each given rod. The solid black lines indicate the spatial constraints of the imaging metrics.