In-vivo multilaboratory investigation of the optical properties of the human head.

The in-vivo optical properties of the human head are investigated in the 600-1100 nm range on different subjects using continuous wave and time domain diffuse optical spectroscopy. The work was performed in collaboration with different research groups and the different techniques were applied to the same subject. Data analysis was carried out using homogeneous and layered models and final results were also confirmed by Monte Carlo simulations. The depth sensitivity of each technique was investigated and related to the probed region of the cerebral tissue. This work, based on different validated instruments, is a contribution to fill the existing gap between the present knowledge and the actual in-vivo values of the head optical properties.

Performance assessment of time-domain optical brain imagers, part 2: nEUROPt protocol.

The nEUROPt protocol is one of two new protocols developed within the European project nEUROPt to characterize the performances of time-domain systems for optical imaging of the brain. It was applied in joint measurement campaigns to compare the various instruments and to assess the impact of technical improvements. This protocol addresses the characteristic of optical brain imaging to detect, localize, and quantify absorption changes in the brain. It was implemented with two types of inhomogeneous liquid phantoms based on Intralipid and India ink with well-defined optical properties. First, small black inclusions were used to mimic localized changes of the absorption coefficient. The position of the inclusions was varied in depth and lateral direction to investigate contrast and spatial resolution. Second, two-layered liquid phantoms with variable absorption coefficients were employed to study the quantification of layer-wide changes and, in particular, to determine depth selectivity, i.e., the ratio of sensitivities for deep and superficial absorption changes. We introduce the tests of the nEUROPt protocol and present examples of results obtained with different instruments and methods of data analysis. This protocol could be a useful step toward performance tests for future standards in diffuse optical imaging.

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.

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.

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.

Retrieval procedure for time-resolved near-infrared tissue spectroscopy based on the optimal estimation method.

We propose the use of a retrieval procedure for time-resolved near-infrared tissue spectroscopy based on the 'optimal estimation' method. The aim of this retrieval method is to obtain an improved estimate of the target parameters compared with standard nonlinear least-squares routines, since the inverse problem dedicated to retrieve the optical properties of tissue is ill posed. A priori information on target and forward model parameters is used, so that a larger number of target parameters can be retrieved, and/or a better accuracy and precision can be achieved on the retrieved target parameters. The procedure has been tested on time-resolved simulated experiments generated, using solutions of the diffusion equation and with solutions of the radiative transfer equation reconstructed with Monte Carlo simulations. The results obtained show that, by using a priori information on target parameters, we have a smaller difference between retrieved values and true values, and lower retrieved error bars. Similarly, a more correct estimate of the errors of the forward model parameters improves the retrieval of the target parameters.

Carbon nanohorn-based nanofluids: characterization of the spectral scattering albedo.

The full characterization of the optical properties of nanofluids consisting of single-wall carbon nanohorns of different morphologies in aqueous suspensions is carried out using a novel spectrophotometric technique. Information on the nanofluid scattering and absorption spectral characteristics is obtained by analyzing the data within the single scattering theory and validating the method by comparison with previous monochromatic measurements performed with a different technique. The high absorption coefficient measured joint to the very low scattering albedo opens promising application perspectives for single-wall carbon nanohorn-based fluid or solid suspensions. The proposed approximate approach can be extended also to other low-scattering turbid media.PACS: 78.35.+c Brillouin and Rayleigh scattering, other light scattering; 78.40.Ri absorption and reflection spectra, fullerenes and related materials; 81.05.U- carbon/carbon-based materials; 78.67.Bf optical properties of low-dimensional, mesoscopic, and nanoscale materials and structures, nanocrystals, nanoparticles, and nanoclusters.

Effect of dependent scattering on the optical properties of Intralipid tissue phantoms.

The calibration of optical tissue-simulating phantoms remains an open question in spite of the many techniques proposed for accurate measurements of optical properties. As a consequence, a reference phantom with well known optical properties is still missing. As a first step towards a reference phantom we have recently proposed to use dilutions of Intralipid 20%. In this paper we discuss a matter that is commonly ignored when dilutions are prepared, i.e., the possibility of deviations from the simple linear relationships between the optical properties of the dilution and the Intralipid concentration due to the effects of dependent scattering. The results of an experimental investigation showed that dependent scattering does not affect absorption. As for the reduced scattering coefficient the effect can be described adding a term proportional to the square of the concentration. However, for concentrations of interest for tissue optics deviations from linearity remain within about 2%. The experimental investigation also showed that the microphysical properties of Intralipid are not affected by dilution. These results show the possibility to easily obtain a liquid diffusive phantom whose optical properties are known with error smaller than about 1%. Due to the intrinsic limitations of the different techniques proposed for measuring the optical properties it seems difficult to obtain a similar accuracy for solid phantoms.

Absorption and scattering properties of carbon nanohorn-based nanofluids for direct sunlight absorbers.

In the present work, we investigated the scattering and spectrally resolved absorption properties of nanofluids consisting in aqueous and glycol suspensions of single-wall carbon nanohorns. The characteristics of these nanofluids were evaluated in view of their use as sunlight absorber fluids in a solar device. The observed nanoparticle-induced differences in optical properties appeared promising, leading to a considerably higher sunlight absorption with respect to the pure base fluids. Scattered light was found to be not more than about 5% with respect to the total attenuation of light. Both these effects, together with the possible chemical functionalization of carbon nanohorns, make this new kind of nanofluids very interesting for increasing the overall efficiency of the sunlight exploiting device. PACS: 78.40.Ri, 78.35.+c, 78.67.Bf, 88.40.fh, 88.40.fr, 81.05.U.

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.

Intralipid: towards a diffusive reference standard for optical tissue phantoms.

Measurements of optical properties carried out at visible and NIR wavelengths on many samples of Intralipid 20% showed a high stability and surprisingly small batch-to-batch variations. Measurements have been carried out in a short time interval using samples from nine different batches with expiry dates spreading over ten years. For the specific reduced scattering coefficient, the values we have obtained, averaged over the nine batches, are 25.9, 21.2, and 18.4 mm(-1) at λ = 632.8, 751, and 833 nm, respectively, and the corresponding maximum deviations from the average were 2.2%, 1.1%, and 1.4%. For the absorption coefficient, we obtained values slightly smaller with respect to the absorption coefficient of pure water at 751 and 833 nm, and slightly larger at 632.8 nm. These results suggest that Intralipid 20% can be the first step towards a diffusive reference standard for tissue-simulating phantoms.

The use of India ink in tissue-simulating phantoms.

The optical properties of India ink, an absorber often used in preparation of tissue simulating phantoms, have been investigated at visible and near infrared wavelengths. The extinction coefficient has been obtained from measurements of collimated transmittance and from spectrophotometric measurements, the absorption coefficient from multidistance measurements of fluence rate in a diffusive infinite medium with small concentrations of added ink. Measurements have been carried out on samples of India ink from five different brands, and for some brands also from different batches. As also reported in previously published papers the results we have obtained showed large inter-brand and inter-batch variations for both the absorption and the extinction coefficient. On the contrary, our results showed small variations for the ratio between the absorption and the extinction coefficient. The albedo is therefore similar for all samples: The values averaged over all samples investigated were 0.161, 0.115, and 0.115 at λ = 632.8, 751, and 833 nm respectively, with maximum deviations of 0.044, 0.019, and 0.035. These results indicate that, using the values we have obtained for the albedo, it should be possible to obtain with uncertainty smaller than about 4% the absorption coefficient of a sample of unknown ink from simple measurements of extinction coefficient. A similar accuracy is not easily obtained with the complicated procedures necessary for measurements of absorption coefficient.

Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating.

We demonstrate the feasibility of time-resolved diffuse reflectance measurements at small source-detector separations using a single-photon avalanche diode operated in time-gated mode. Photon time distributions at an interfiber distance of 2 mm were obtained on a homogeneous tissue phantom with a dynamic range of 10(6) and collecting photons at arrival times up to 4 ns. Moreover, we were able to detect a local inhomogeneity deeply buried within a diffusive medium with better spatial resolution, higher signal intensity, and same contrast of a larger (20 mm) interfiber distance. Finally, the proposed approach proved valuable to detect in vivo a task-related brain activation.

Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model.

A diffusion-based model for photon migration through a three-layer medium is described. The main purpose of this work is to investigate the performance of a diffusion equation (DE)-based forward model for studying photon migration through a diffusive layered medium having a low scattering layer. This geometrical model can be used as a simple model of the adult head. Numerical results are shown for a set of values of the optical properties typical of the adult human head, where scalp and skull are lumped in the first layer while the second and third layer are associated with the cerebrospinal fluid (CSF) and the brain, respectively. Due to the presence of the CSF, which is a relatively clear layer, the diffusion-based model yields an approximate solution of photon migration. Nevertheless, comparisons with MC simulations show that the model can predict the total and the partial mean path length in the different layers with an error less than 20%. In particular, the partial mean path length in the third layer, representative of the brain, is calculated with an error less than 10% if the reduced scattering coefficient of the second layer, representative of the CSF, is assumed 0.25 mm(-1).

In vivo time-resolved reflectance spectroscopy of the human forehead.

We present an in vivo broadband spectroscopic characterization of the human forehead. Absorption and scattering properties are measured on five healthy volunteers at five different interfiber distances, using time-resolved diffuse spectroscopy and interpreting data with a model of the diffusion equation for a homogeneous semi-infinite medium. A wavelength-tunable mode-locked laser and time-correlated single-photon counting detection are employed, enabling fully spectroscopic measurements in the range of 700-1000 nm. The results show a large variation in the absorption and scattering properties of the head depending on the subject, whereas intrasubject variations, assessed at different interfiber distances, appear less relevant, particularly for what concerns the absorption coefficient. The high intersubject variability observed indicates that a unique set of optical properties for modeling the human head cannot be used correctly. To better interpret the results of the analysis of in vivo measurements, we performed a set of four-layer model Monte Carlo simulations based on different data sets for the optical properties of the human head, partially derived from the literature. The analysis indicated that, when simulated time-resolved curves are fitted with a homogeneous model for the photon migration, the retrieved absorption and reduced scattering coefficients are much closer to superficial layer values (i.e., scalp and skull) than to deeper layer ones (white and gray matter). In particular, for the shorter interfiber distances, the recovered values can be assumed as a good estimate of the optical properties of the first layer.

Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method.

In spite of many progresses achieved both with theories and with experiments in studying light propagation through diffusive media, a reliable method for accurate measurements of the optical properties of diffusive media at NIR wavelengths is, in our opinion, still missing. It is therefore difficult to create a diffusive medium with well known optical properties to be used as a reference. In this paper we describe a method to calibrate the reduced scattering coefficient, mu'(s) , of a liquid diffusive medium and the absorption coefficient, mu(a), of an absorbing medium with a standard error smaller than 2% both on mu'(s) and on mu(a). The method is based on multidistance measurements of fluence into an infinite medium illuminated by a CW source. The optical properties are retrieved with simple inversion procedures (linear fits) exploiting the knowledge of the absorption coefficient of the liquid into which the diffuser and the absorber are dispersed. In this study Intralipid diluted in water has been used as diffusive medium and Indian ink as absorber. For a full characterization of these media measurements of collimated transmittance have also been carried out, from which the asymmetry factor of the scattering function of Intralipid and the single scattering albedo of Indian ink have been determined.

Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. Time-resolved method.

In this paper, a general method to calibrate the absorption coefficient of an absorber and the reduced scattering coefficient of a liquid diffusive medium, based on time-resolved measurements, is reported. An exhaustive analysis of the error sources affecting the estimation is also performed. The method has been applied with a state-of-the-art time-resolved instrumentation to determine the intrinsic absorption coefficient of Indian ink and the reduced scattering coefficient of Intralipid-20%, with a standard error smaller than 1% and 2%, respectively. Finally, the results have been compared to those retrieved for the same compounds by applying a continuous wave method recently published, obtaining an agreement within the error bars. This fact represents a cross validation of the two independent calibration methods.

Heuristic Green's function of the time dependent radiative transfer equation for a semi-infinite medium.

The Green's function of the time dependent radiative transfer equation for the semi-infinite medium is derived for the first time by a heuristic approach based on the extrapolated boundary condition and on an almost exact solution for the infinite medium. Monte Carlo simulations performed both in the simple case of isotropic scattering and of an isotropic point-like source, and in the more realistic case of anisotropic scattering and pencil beam source, are used to validate the heuristic Green's function. Except for the very early times, the proposed solution has an excellent accuracy (> 98 % for the isotropic case, and > 97 % for the anisotropic case) significantly better than the diffusion equation. The use of this solution could be extremely useful in the biomedical optics field where it can be directly employed in conditions where the use of the diffusion equation is limited, e.g. small volume samples, high absorption and/or low scattering media, short source-receiver distances and early times. Also it represents a first step to derive tools for other geometries (e.g. slab and slab with inhomogeneities inside) of practical interest for noninvasive spectroscopy and diffuse optical imaging. Moreover the proposed solution can be useful to several research fields where the study of a transport process is fundamental.

Absorption and scattering perturbations in homogeneous and layered diffusive media probed by time-resolved reflectance at null source-detector separation.

We characterize the capability of time-resolved reflectance measurements at small source-detector separation (less than 5 mm) to localize small inhomogeneities embedded in an otherwise homogeneous or layered diffusive medium. By considering both absorption and scattering inhomogeneities, we demonstrate the improvement of this approach in terms of contrast and spatial resolution, as compared to more typical set-ups involving larger source-detection separations (few centimeters). Simulations are performed exploiting an analytical perturbation approach to diffusion theory and a four-layer heterogeneous time-resolved Monte Carlo code, considering realistic tissue geometries. Exhaustive investigation in the parameters space is reported.

Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging.

We propose a novel approach to imaging in diffusive media based on time-resolved reflectance measurements at null source-detector separation. This approach yields better spatial resolution and contrast as compared to the classical approach, which typically employs a separation of 20-40 mm. Results are obtained by an analytical perturbation approach to diffusion theory and on Monte Carlo simulations. Practical implementation with state-of-the-art technology and performance of a complementary approach based on the use of small but not null source-detector separation are also discussed.