Giovanni Zaccanti

Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory.

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

Time-resolved spectroscopy of the human forearm

For spectroscopic purposes, the forearm is a conveniently large object to be investigated because consistent oxygenation and blood volume changes can be obtained. Human forearm spectral properties were investigated using picosecond near-IR laser spectroscopy. The behaviour of the temporal point spread function in resting conditions and during ischaemia, venous occlusion and exercise is reported. The effect of path length inaccuracy on muscle oxygen consumption, obtained by combining spectral data with the path length, is discussed.

Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation

The depth at which photons penetrate into a diffusive medium before being re-emitted has been investigated with reference to a semi-infinite homogeneous medium illuminated by a pencil beam. By using the diffusion equation analytical expressions have been obtained for the probability that photons penetrate at a certain depth before being detected, and for the mean path length they travel inside each layer of the medium. Expressions have been obtained both for the cw and the time domain, and simple approximate scaling relationships describing the dependence on the scattering properties of the medium have been found. For time-resolved measurements both the probability and the mean path length are expected to be independent of the distance from the light beam at which the detector is placed and of the absorption coefficient of the medium. The penetration depth increases as the time of flight increases. In contrast, for cw measurements both the probability and the mean path length strongly depend on the distance and absorption. The penetration depth increases as the distance increases or absorption decreases. The accuracy of the analytical expressions has been demonstrated by comparisons with cw experimental results. The penetration depth and the mean path length provide useful information, for instance, for measurements of tissue oxygenation and for functional imaging of muscle and brain. In particular, the depth reached by received photons provides overall information on the volume of the tissue actually investigated, while the mean path is strictly related to the sensitivity to local variations of absorption.

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.

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.PACS78.40.Ri, 78.35.+c, 78.67.Bf, 88.40.fh, 88.40.fr, 81.05.U.

Light Propagation through Biological Tissue and Other Diffusive Media

Acknowledgements Preface List of Acronyms List of Symbols 1. Introduction Part I: Theory 2. Scattering and Absorption Properties of Diffusive Media 2.1 Approach Followed in this Book 2.2 Optical Properties of a Turbid Medium 2.2.1 Absorption properties 2.2.2 Scattering properties 2.3 Statistical Meaning of the Optical Properties 2.4 Similarity Relation and Reduced Scattering Coefficient 2.5 Examples of Diffusive Media.

Transmission of a pulsed polarized light beam through thick turbid media: numerical results

We present numerical results on the change in polarization state of light pulses transmitted through thick turbid media. These results were obtained with a modified version of a previous Monte Carlo code that takes into account depolarization introduced by multiple scattering. The results have shown that for scattered received power pulse shape, polarization and total received power mainly depend on the transport cross section, σ(d), of the medium. The effect of the angular field of view of the receiver or of the distance between the diffusing medium and the receiver is shown, whereas the effect of the lateral displacement of the receiver elements proves to be of minor importance. An example of measurements showed a good agreement with numerical results, indicating the adequacy of our numerical code.

Independence of the diffusion coefficient from absorption: experimental and numerical evidence.

We investigated the dependence of the diffusion coefficient on the absorption coefficient by studying the propagation of light emitted by an isotropic source in an infinitely extended medium. Comparisons with both experimental and numerical results showed that the diffusion equation gives a better description of photon migration when the diffusion coefficient is assumed to be independent of absorption.

Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results

In our companion paper we presented a model to describe photon migration through a diffusing slab. The model, developed for a homogeneous slab, is based on the diffusion approximation and is able to take into account reflection at the boundaries resulting from the refractive index mismatch. In this paper the predictions of the model are compared with solutions of the radiative transfer equation obtained by Monte Carlo simulations in order to determine the applicability limits of the approximated theory in different physical conditions. A fitting procedure, carried out with the optical properties as fitting parameters, is used to check the application of the model to the inverse problem. The results show that significant errors can be made if the effect of the refractive index mismatch is not properly taken into account. Errors are more important when measurements of transmittance are used. The effects of using a receiver with a limited angular field of view and the angular distribution of the radiation that emerges from the slab have also been investigated.

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.