Direct-current-based image reconstruction versus direct-current included or excluded frequency-domain reconstruction in diffuse optical tomography

Figure of merit for task-based assessment of frequency-domain diffusive imaging

A figure of merit (FOM) for frequency-domain diffusive imaging (FDDI) is theoretically developed adapting the concept of Hotelling observer signal-to-noise ratio. Different from conventionally used FOMs for FDDI, the newly developed FOM considers diffused intensities, modulation amplitudes, and phases in combination. The FOM applied to Monte Carlo simulations of signal- and background-known-exactly problems shows unique characteristics that are in agreement with findings in the literature. We believe that a task based assessment using the FOM improves the characterization of FDDI systems and allows for complete system optimization.

Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. IV. Frequency-domain analysis

Part IV examines frequency-domain photon diffusion in a homogeneous medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to assess by analogical and finite-element methods the changes of AC amplitude, modulation depth, and phase with respect to the line-of-sight source-detector distance for a source and a detector located along the azimuthal or longitudinal direction on the concave or convex medium-applicator interface. By comparing to their counterparts along a straight line on a semi-infinite medium-applicator interface, for the same line-of-sight source-detector distance, it is found that: (1) the decay-rate of AC photon fluence is smaller along the azimuthal direction and greater along the longitudinal direction on the concave interface, (2) the decay-rate of AC photon fluence is greater along the azimuthal direction and smaller along the longitudinal direction on the convex interface, (3) the modulation depth along both azimuthal and longitudinal directions decays more slowly on the concave interface and faster on the convex interface, and (4) the phase along both azimuthal and longitudinal directions increases more slowly on the concave interface and faster on the convex interface.

Effect of noise on modulation amplitude and phase in frequency-domain diffusive imaging

We theoretically investigate the effect of noise on frequency-domain heterodyne and/or homodyne measurements of intensity-modulated beams propagating through diffusive media, such as a photon density wave. We assumed that the attenuated amplitude and delayed phase are estimated by taking the Fourier transform of the noisy, modulated output data. We show that the estimated amplitude and phase are biased when the number of output photons is small. We also show that the use of image intensifiers for photon amplification in heterodyne or homodyne measurements increases the amount of biases. Especially, it turns out that the biased estimation is independent of AC-dependent noise in sinusoidal heterodyne or homodyne outputs. Finally, the developed theory indicates that the previously known variance model of modulation amplitude and phase is not valid in low light situations. Monte-Carlo simulations with varied numbers of input photons verify our theoretical trends of the bias.

Noise characteristics of heterodyne/homodyne frequency-domain measurements

We theoretically develop and experimentally validate the noise characteristics of heterodyne and/or homodyne measurements that are widely used in frequency-domain diffusive imaging. The mean and covariance of the modulated heterodyne output are derived by adapting the random amplification of a temporal point process. A multinomial selection rule is applied to the result of the temporal noise analysis to additionally model the spatial distribution of intensified photons measured by a charge-coupled device (CCD), which shows that the photon detection efficiency of CCD pixels plays an important role in the noise property of detected photons. The approach of using a multinomial probability law is validated from experimental results. Also, experimentally measured characteristics of means and variances of homodyne outputs are in agreement with the developed theory. The developed noise model can be applied to all photon amplification processes.

Transrectal ultrasound-integrated spectral optical tomography of hypoxic progression of a regressing tumor in a canine prostate

The objective of this study was to evaluate if transrectal optical tomography implemented at three wavelength bands for spectral detection could monitor changes of the hemoglobin oxygen saturation (StO2) in addition to those of the total hemoglobin concentration ([HbT]) in lesions of a canine prostate, including an induced tumor modeling canine prostate cancer. Near-infrared (NIR) optical tomography was integrated with ultrasound (US) for transrectal imaging. Multi-spectral detection at 705_nm, 785_nm and 808_nm rendered measurements of [HbT] and StO2. Canine transmissible venereal tumor (TVT) cells were injected into the right lobe of a dog's prostate gland, which had a pre-existing cyst in the left lobe. Longitudinal assessments of the prostate were performed weekly over a 63-day duration by NIR imaging concurrent with grey-scale and Doppler US. Ultrasonography revealed a bi-lobular tumor-mass regressing from day-49 to day-63. At day-49 this tumor-mass developed a hypoxic core that became larger and more intense by day-56 and expanded further by day-63. The tumor-mass presented a strong hyper-[HbT] feature on day-56 that was inconsistent with US-visualized blood flow. Histology confirmed two necrotic TVT foci within this tumor-mass. The cyst appeared to have a large anoxic-like interior that was greater in size than its ultrasonographically delineated lesion, and a weak lesional elevation of [HbT]. On day-56, the cyst presented a strong hyper-[HbT] feature consistent with US-resolved blood flow. Histology revealed acute and chronic hemorrhage in the periphery of the cyst. The NIR imaging features of two other TVT nodules and a metastatic lymph node were evaluated retrospectively. Transrectal US-integrated spectral optical tomography seems to enable longitudinal monitoring of intra-lesional oxygenation dynamics in addition to the hemoglobin content of lesions in the canine prostate.

The utility of direct-current as compared to frequency domain measurements in spectrally-constrained diffuse optical tomography toward cancer imaging

This work investigates, by means of analytical and simulation studies, the performance of spectrally-constrained image reconstruction in Continuous-Wave or Direct-Current (DC) and Frequency Domain (FD) near-infrared optical tomography. A recent analytic approach for estimating the accuracy of target recovery and the level of background artifact for optical tomography at single wavelength, based on the analysis of parametric reconstruction uncertainty level (PRUL), is extended to spectrally-constrained optical tomography. The analytical model is implemented to rank three sets of wavelengths that had been used as spectral prior in an independent experimental study. Subsequent simulation appraises the recovery of oxygenated hemoglobin (HbO), deoxygenated hemoglobin (Hb), water (H2O), scattering amplitude (A), and scattering power (b) using DC-only, DC-excluded FD, and DC-included FD, based on the three sets of wavelengths as the spectral prior. The simulation results support the analytic ranking of the performance of the three sets of spectral priors, and generally agree with the performance outcome of DC-only versus that of DC-excluded FD and DC-included FD. Specifically, this study indicate that: 1) the rank of overall quality of chromophore recovery is Hb, H2O, and HbO from the highest to lowest; and in the scattering part the A is always better recovered than b. This outcome does suggest that the DC-only information gives rise to unique solution to the image reconstruction routine under the given spectral prior. 2) DC-information is not-redundant in FD-reconstruction, as the artifact levels of DC-included FD reconstruction are always lower than those of DC-excluded FD. 3) The artifact level as represented by the noise-to-contrast-ratio is almost always the lowest in DC-only, leading to generally better resolution of multiple targets of identical contrasts over the background than in FD. However, the FD could outperform DC in the recovery of scattering properties including both A and b when the spectral prior is less optimal, implying the benefit of phase-information in scattering recovery in the context of spectrally-constrained optical tomography.