Improving the depth sensitivity of time-resolved measurements by extracting the distribution of times-of-flight

Abstract

Time-resolved (TR) techniques provide a means of discriminating photons based on their time-of-flight. Since early arriving photons have a lower probability of probing deeper tissue than photons with long time-of-flight, time-windowing has been suggested as a method for improving depth sensitivity. However, TR measurements also contain instrument contributions (instrument-response-function, IRF), which cause temporal broadening of the measured temporal point-spread function (TPSF) compared to the true distribution of times-of-flight (DTOF). The purpose of this study was to investigate the influence of the IRF on the depth sensitivity of TR measurements. TPSFs were acquired on homogeneous and two-layer tissue-mimicking phantoms with varying optical properties. The measured IRF and TPSFs were deconvolved using a stable algorithm to recover the DTOFs. The microscopic Beer-Lambert law was applied to the TPSFs and DTOFs to obtain depth-resolved absorption changes. In contrast to the DTOF, the latest part of the TPSF was not the most sensitive to absorption changes in the lower layer, which was confirmed by computer simulations. The improved depth sensitivity of the DTOF was illustrated in a pig model of the adult human head. Specifically, it was shown that dynamic absorption changes obtained from the late part of the DTOFs recovered from TPSFs acquired by probes positioned on the scalp were similar to absorption changes measured directly on the brain. These results collectively demonstrate that this method improves the depth sensitivity of TR measurements by removing the effects of the IRF.

Keywords: (170.3660) Light propagation in tissues; (170.3890) Medical optics instrumentation.

Fig. 1

Schematic of the two-layer phantom. Measurements for a homogeneous medium were acquired by removing the top layer and placing the emission and detection optodes 3 cm apart on the surface of the bottom layer.

Fig. 2

(a) TPSFs measured with the emission and detection probes positioned 3 cm apart on the surface of the homogeneous phantom. The curves were obtained by averaging 32 individual TPSFs, each acquired for 1s. The solid black curve is the TPSF measured at baseline (acquired at 800 kHz) and the cyan curve with the open circles is the TPSF acquired at the highest absorption coefficient (step 4 in Table 1). The dashed black curve is the instrument response function (IRF). Note, the amplitude of the IRF was divided by three for visualization purpose. (b) Corresponding DTOFs obtained by deconvolving the IRF and TPSFs shown in (a). Pathlength-resolved absorption changes (Δμ_a) recovered from the experimental TPSFs and the deconvolved DTOFs are shown in (c) and (d), respectively. The predicted Δμ_a from the simulated TPSFs and DTOFs are shown in (e) and (f), respectively.

Fig. 3

(a) TPSFs measured with the probes positioned on the surface of the two-layer phantom. Each curve is the average of 32 TPSFs. The black curve is the TPSF at baseline and the cyan curve with the open circles is the TPSF acquired with the largest μ_a value in the bottom layer (step 4 in Table 1). (b) DTOFs obtained by deconvolving the IRF and TPSFs. Absorption changes (Δμ_a) recovered from (c) the experimental TPSFs and (d) the corresponding DTOFs. Fig. (e) and (f) are the pathlength-resolved Δμ_a generated from (e) the simulated TPSFs and (f) the simulated DTOFs. The vertical dashed lines indicate the specific pathlengths used to obtain the data presented in Fig. 4.

Fig. 4

The absorption changes (Δμ_a) recovered from the two-layer media are plotted against Δμ_a in the bottom layer. The Δμ_a values are shown from early (red), middle (green) and late time-windows (blue) for experimental (a) TPSFs and (b) DTOFs, as well as for simulated (c) TPSFs and (d) DTOFs.

Fig. 5

(a) Normalized absorption changes for early (black) and late (blue) time-windows (width = 0.1 ns) obtained with the DTOFs recovered from the TPSFs measured by probes positioned on the pig’s scalp at a source-detector separation of 3 cm. (b) and (c) Comparison of the normalized absorption changes determined with the probes placed directly on the brain (red curve with circles) and the normalized Δμ_a(t) obtained from late time-window of the DTOFs acquired with the probes on the scalp, following two distinct ICG injections (blue and green). Note that the red curves in (b) and (c) are the same.