Forward solvers for photon migration in the presence of highly and totally absorbing objects embedded inside diffusive media

In this paper, after a critical review of the literature, we present two forward solvers and a new methodology for description of photon migration in the presence of totally absorbing inclusions embedded in diffusive media in both time and CW domains. The first forward solver is a heuristic approach based on a higher order perturbation theory applied to the diffusion equation (DE) [denoted eighth-order perturbation theory (EOPT)]. The second forward solver [denoted eighth-order perturbation theory with the equivalence relation (EOPTER) ] is obtained by combining the EOPT solver with the adoption of the equivalence relation (ER) [J. Biomed. Opt.18, 066014 (2013)]. These forward solvers can possibly overcome some evident limitations of previous approaches like the theory behind the so-called banana-shape regions or exact analytical solutions of the DE in the presence of highly or totally absorbing inclusions. We also propose the ER to reformulate the problem of a totally absorbing inclusion in terms of another inclusion having a finite absorption contrast and a re-scaled volume. For instance, we have shown how this approach can indeed be used to simulate black inclusions with the Born approximation. By means of comparisons with the results of Monte Carlo simulations, we have shown that the EOPTER solver can model totally absorbing inclusions with an error smaller than about 10%, whereas the EOPT solver shows an error smaller than about 20%, showing a performance largely better than that observed with solvers proposed previously.

Light diffusion in quenched disorder: role of step correlations

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via nonscattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.

Nondestructive optical detection of monomer uptake in wood polymer composites

A noninvasive method to assess the local monomer concentration within a wooden matrix, post monomer impregnation, by time-resolved diffuse optical spectroscopy is demonstrated. A data analysis technique for improving accuracy, which takes account of changes in the refractive index during the monomer uptake, has been employed. This technique can be potentially applied in the wood industry for the study of polymer composites as well as in cultural heritage science for noninvasively monitoring the penetration of chemical compounds used for consolidation or conservation purposes.

Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation

We present the experimental implementation and validation of a phantom for diffuse optical imaging based on totally absorbing objects for which, in the previous paper [J. Biomed. Opt.18(6), 066014, (2013)], we have provided the basic theory. Totally absorbing objects have been manufactured as black polyvinyl chloride (PVC) cylinders and the phantom is a water dilution of intralipid-20% as the diffusive medium and India ink as the absorber, filled into a black scattering cell made of PVC. By means of time-domain measurements and of Monte Carlo simulations, we have shown the reliability, the accuracy, and the robustness of such a phantom in mimicking typical absorbing perturbations of diffuse optical imaging. In particular, we show that such a phantom can be used to generate any absorption perturbation by changing the volume and position of the totally absorbing inclusion.

Non-contact in vivo diffuse optical imaging using a time-gated scanning system

We report on the design and first in vivo tests of a novel non-contact scanning imaging system for time-domain near-infrared spectroscopy. Our system is based on a null source-detector separation approach and utilizes polarization-selective detection and a fast-gated single-photon avalanche diode to record late photons only. The in-vivo tests included the recording of hemodynamics during arm occlusion and two brain activation tasks. Localized and non-localized changes in oxy- and deoxyhemoglobin concentration were detected for motor and cognitive tasks, respectively. The tests demonstrate the feasibility of non-contact imaging of absorption changes in deeper tissues.

Optical identification of subjects at high risk for developing breast cancer

A time-domain multiwavelength (635 to 1060 nm) optical mammography was performed on 147 subjects with recent x-ray mammograms available, and average breast tissue composition (water, lipid, collagen, oxy- and deoxyhemoglobin) and scattering parameters (amplitude a and slope b) were estimated. Correlation was observed between optically derived parameters and mammographic density [Breast Imaging and Reporting Data System (BI-RADS) categories], which is a strong risk factor for breast cancer. A regression logistic model was obtained to best identify high-risk (BI-RADS 4) subjects, based on collagen content and scattering parameters. The model presents a total misclassification error of 12.3%, sensitivity of 69%, specificity of 94%, and simple kappa of 0.84, which compares favorably even with intraradiologist assignments of BI-RADS categories.

Phantoms for diffuse optical imaging based on totally absorbing objects, part 1: Basic concepts

The design of inhomogeneous phantoms for diffuse optical imaging purposes using totally absorbing objects embedded in a diffusive medium is proposed and validated. From time-resolved and continuous-wave Monte Carlo simulations, it is shown that a given or desired perturbation strength caused by a realistic absorbing inhomogeneity of a certain absorption and volume can be approximately mimicked by a small totally absorbing object of a so-called equivalent black volume (equivalence relation). This concept can be useful in two ways. First, it can be exploited to design realistic inhomogeneous phantoms with different perturbation strengths simply using a set of black objects with different volumes. Further, it permits one to grade physiological or pathological changes on a reproducible scale of perturbation strengths given as equivalent black volumes, thus facilitating the performance assessment of clinical instruments. A set of plots and interpolating functions to derive the equivalent black volume corresponding to a given absorption change is provided. The application of the equivalent black volume concept for grading different optical perturbations is demonstrated for some examples.

Recipes to make organic phantoms for diffusive optical spectroscopy

Three recipes are presented to make tissue constituent-equivalent phantoms of water and lipids. Different approaches to prepare the emulsion are proposed. Nature phantoms are made using no emulsifying agent, but just a professional disperser; instead Agar and Triton phantoms are made using agar or Triton X-100, respectively, as agents to emulsify water and lipids. Different water-to-lipid ratios ranging from 30% to 70% by mass were tested. A broadband time-resolved diffuse optical spectroscopy system was used to characterize the phantoms in terms of optical properties and composition. For some water/lipid ratios the emulsion fails or the phantom has limited lifetime, but in most cases the recipes provide phantoms with a high degree of homogeneity [coefficient of variation (CV) of 4.6% and 1.5% for the absorption and reduced scattering coefficient, respectively] and good reproducibility (CV of 8.3% and 12.4% for absorption and reduced scattering coefficient, respectively).

Note: Comparison between a prism-based and an acousto-optic tunable filter-based spectrometer for diffusive media

This paper compares two continuously tunable systems for time-resolved spectroscopy of diffusive media based on a supercontinuum laser source. Two approaches for spectral selection are considered relying either on a dispersive prism or on a commercial acoustic-optic tunable filter (AOTF) device. The comparison was performed first in terms of extracted power and spectral response function, then in terms of distortions introduced in the retrieved absorption and scattering spectra. Simulations and experiments on diffusive phantoms confirmed that, besides narrower FWHM in the AOTF bandpass, the prism solution is superior with respect to the distortions produced on the recovered spectra.

Time-resolved diffuse optical tomography using fast-gated single-photon avalanche diodes

We present the first experimental results of reflectance Diffuse Optical Tomography (DOT) performed with a fast-gated single-photon avalanche diode (SPAD) coupled to a time-correlated single-photon counting system. The Mellin-Laplace transform was employed to process time-resolved data. We compare the performances of the SPAD operated in the gated mode vs. the non-gated mode for the detection and localization of an absorbing inclusion deeply embedded in a turbid medium for 5 and 15 mm interfiber distances. We demonstrate that, for a given acquisition time, the gated mode enables the detection and better localization of deeper absorbing inclusions than the non-gated mode. These results obtained on phantoms demonstrate the efficacy of time-resolved DOT at small interfiber distances. By achieving depth sensitivity with limited acquisition times, the gated mode increases the relevance of reflectance DOT at small interfiber distance for clinical applications.

Absorption spectroscopy of powdered materials using time-resolved diffuse optical methods

In this paper a novel method, based on time-resolved diffuse optical spectroscopy, is proposed to measure the absorption of small amounts of nanostructured powder materials independent of scattering. Experimental validation, in the visible and near-infrared spectral range, has been carried out on India Ink<sup/>particles. The effectiveness of the technique to measure scattering-free absorption is demonstrated on carbon nanotubes. The comparison between the absorption spectra acquired by the proposed method and conventional measurements performed with a commercial spectrophotometer is discussed.

Effects of tissue heterogeneity on the optical estimate of breast density

Breast density is a recognized strong and independent risk factor for developing breast cancer. At present, breast density is assessed based on the radiological appearance of breast tissue, thus relying on the use of ionizing radiation. We have previously obtained encouraging preliminary results with our portable instrument for time domain optical mammography performed at 7 wavelengths (635-1060 nm). In that case, information was averaged over four images (cranio-caudal and oblique views of both breasts) available for each subject. In the present work, we tested the effectiveness of just one or few point measurements, to investigate if tissue heterogeneity significantly affects the correlation between optically derived parameters and mammographic density. Data show that parameters estimated through a single optical measurement correlate strongly with mammographic density estimated by using BIRADS categories. A central position is optimal for the measurement, but its exact location is not critical.

Time-resolved diffuse optical spectroscopy up to 1700 nm by means of a time-gated InGaAs/InP single-photon avalanche diode

We present a new compact system for time-domain diffuse optical spectroscopy of highly scattering media operating in the wavelength range from 1100 nm to 1700 nm. So far, this technique has been exploited mostly up to 1100 nm: we extended the spectral range by means of a pulsed supercontinuum light source at a high repetition rate, a prism to spectrally disperse the radiation, and a time-gated InGaAs/InP single-photon avalanche diode working up to 1700 nm. A time-correlated single-photon counting board was used as processing electronics. The system is characterized by linear behavior up to absorption values of about 3.4 cm(-1) where the relative error is 17%. A first measurement performed on lipids is presented: the absorption spectrum shows three major peaks at 1200 nm, 1400 nm, and 1700 nm.

Single-fiber diffuse optical time-of-flight spectroscopy

We demonstrate interstitial diffuse optical time-of-fight spectroscopy based on a single fiber for both light delivery and detection. Detector saturation due to the massive short-time reflection is avoided by ultrafast gating of a single photon avalanche diode. We show that the effects of scattering and absorption are separable and that absorption can be assessed independently of scattering. Measurements on calibrated liquid phantoms and subsequent Monte Carlo-based evaluation illustrate that absorption coefficients can be accurately assessed over a wide range of medically relevant optical properties. Our findings pave the way to simplified and less invasive interstitial in vivo spectroscopy.

Non-contact time-resolved diffuse reflectance imaging at null source-detector separation

We report results of the proof-of-principle tests of a novel non-contact tissue imaging system. The system utilizes a quasi-null source-detector separation approach for time-domain near-infrared spectroscopy, taking advantage of an innovative state-of-the-art fast-gated single photon counting detector. Measurements on phantoms demonstrate the feasibility of the non-contact approach for the detection of optically absorbing perturbations buried up to a few centimeters beneath the surface of a tissue-like turbid medium. The measured depth sensitivity and spatial resolution of the new system are close to the values predicted by Monte Carlo simulations for the inhomogeneous medium and an ideal fast-gated detector, thus proving the feasibility of the non-contact approach for high density diffuse reflectance measurements on tissue. Potential applications of the system are also discussed.

Fast-gated single-photon counting technique widens dynamic range and speeds up acquisition time in time-resolved measurements

In many time-domain single-photon measurements, wide dynamic range (more than 5 orders of magnitude) is required in short acquisition time (few seconds). We report on the results of a novel technique based on a time-gated Single-Photon Avalanche Diode (SPAD) able to increase the dynamic range of optical investigations. The optical signal is acquired only in well-defined time intervals. Very fast 200-ps gate-ON transition is used to avoid the undesired strong signal, which can saturate the detector, hide the fainter useful signal and reduce the dynamic range. In experimental measurements, we obtained a dynamic range approaching 8 decades in few minutes of acquisition.

Functional tomography using a time-gated ICCD camera

We present a system for near infrared functional tomography based on a single pulsed source and a time-gated camera, for non-contact collection over a large area. The mean penetration depth of diffusely reflected photons is dependent on the arrival time of photons, but not on the source-detector distance. Thus, time-encoded data can be used to recover depth information while photon exiting point is exploited for lateral localization. This approach was tested against simulations, demonstrating both detection and localization capabilities. Preliminary measurements on inhomogeneous phantoms showed good detection sensibility, even for a low optical perturbation, and localization capabilities, yet with decreasing spatial resolution for increasing depths. Potential application of this method to in vivo functional studies on the brain is discussed.

Annealing Studies of Visible Light Emission from Silicon Nanocrystals Produced by Implantation

The annealing behavior of silicon implanted SiO2 layers is studied using continuous and time-gated photoluminescence (PL). Two PL emission bands are observed. A band centered at 560 nm is present in as implanted samples and it is still observed after 1000 °C annealing. The emission time is fast (0.2 -2 ns). A second band centered at 780 nm further increases when hydrogen annealing was performed. The emission time is long (1 μs - 0.3 ms).

Time-resolved diffuse optical spectroscopy: a differential absorption approach

A method is presented for the estimate of spectral changes in the absorption properties of turbid media from time-resolved diffuse optical spectroscopy. The method relies on the hypothesis of constant scattering over the wavelength range of interest, but no limitations come from the sample size and shape as the method is derived directly from the Beer-Lambert law. The effects of a moderate spectral dependence of the scattering properties and of the non-ideal instrument response function were investigated theoretically, and the results were confirmed experimentally, showing that the method can be profitably applied in cases of practical interest.

Noninvasive assessment of breast cancer risk using time-resolved diffuse optical spectroscopy

Breast density is a recognized strong and independent risk factor for breast cancer. We propose the use of time-resolved transmittance spectroscopy to estimate breast tissue density and potentially provide even more direct information on breast cancer risk. Time-resolved optical mammography at seven wavelengths (635 to 1060 nm) is performed on 49 subjects. Average information on breast tissue of each subject is obtained on oxy- and deoxyhemoglobin, water, lipids, and collagen content, as well as scattering amplitude and power. All parameters, except for blood volume and oxygenation, correlate with mammographic breast density, even if not to the same extent. A synthetic optical index proves to be quite effective in separating different breast density categories. Finally, the estimate of collagen content as a more direct means for the assessment of breast cancer risk is discussed.

The impact of morphology on light transport in cancellous bone

In recent years, optical techniques based on diffusion approximation have demonstrated their ability to gain rich spectral information about bone. However, these methods normally assume homogeneity, while cancellous bone and marrow form a highly heterogeneous two-phase medium. This paper studies the limitations of this assumption, and quantifies the role of microstructure on long-range transport properties. The propagation of light pulses through trabecular bone is calculated by Monte Carlo simulation of the scattering and absorption in reconstructions of bone samples obtained from x-ray micro tomographic scans. The time-resolved responses are then fitted with the analytical response of a homogeneous material to obtain the apparent transport properties. These properties are used to test different homogenization equations that have been postulated in the past for heterogeneous tissues and to check their accuracy. The results show that nonlinearity and crosstalk between absorption and scattering are statistically significant, although their impact is relatively small. More importantly, we found that the weight of the components is not only affected by their volume fractions, but need to be corrected by other morphologic measures like trabecular spacing or connectivity density. These deviations from the homogeneous assumption are stronger for scattering than for absorption. In conclusion, the average optical properties of cancellous bone are strongly determined by its microstructure, meaning that optical techniques are a valid method for tissue evaluation, but careful consideration of structure-related perturbation sources is required.

Diffuse optical spectroscopy of breast tissue extended to 1100 nm

The feasibility of in vivo measurements in the range of 1000 to 1100 nm and the potential benefits of operation in that wavelength range for diagnostic applications are investigated. To this purpose, an existing system for time-resolved diffuse spectroscopy is modified to enable in vivo studies to be carried out continuously from 600 to 1100 nm. The optical characterization of collagen powder is extended to 1100 nm and an accurate measurement of the absorption properties of lipid is carried out over the entire spectral range. Finally, the first in vivo absorption and scattering spectra of breast tissue are measured from 10 healthy volunteers between 600 and 1100 nm and tissue composition is evaluated in terms of blood parameters and water, lipid, and collagen content using a spectrally constrained global fitting procedure.