Eric Tinet

Phase function simulation in tissue phantoms: a fractal approach

Artificial media are needed for the calibration of optical diagnostic methods in order to work on reproducible, stable and well known samples. Since the scattering and absorption coefficients can easily be adjusted by using appropriate concentrations of scattering and absorbing components, the most difficult part in the design of a good tissue phantom is to obtain an actual phase function. The most common way to create phantoms is to use scattering microspheres of equal size, but the Mie phase function of such a phantom does not match the tissues real phase function. Moreover, we show in this paper that the similarity relations often used for the analysis of the results obtained with this type of phantom may sometimes be very inaccurate. The use of a mixture of different sized scattering particles is then considered, in order to imitate the whole phase function. However, as the determination of adequate sizes and concentrations is a difficult mathematical task, we describe a simple method to solve this problem. We first demonstrate that the extreme optical complexity of real biological samples could be simulated by a mixture of spheres with a fractal diameter distribution. Then, we present a few simple rules based on the knowledge of this fractal distribution, which can be used to obtain a realistic phase function with a limited number of sphere diameters.

FAST SEMIANALYTICAL MONTE CARLO SIMULATION FOR TIME-RESOLVED LIGHT PROPAGATION IN TURBID MEDIA

The statistical estimator concept, created in the nuclear engineering field, has been adapted to the elaboration of a new and fast semianalytical Monte Carlo numerical simulation for time-resolved light-scattering problems. This concept has also been generalized to the case of unmatched boundaries. The model, discussed in detail in this paper, contains two stages. The first stage is the information generator in which, for each scattering event, the contribution to the total reflectance and transmittance is evaluated and subtracted from the photon current energy. This procedure reduces the number of photons required to produce a given accuracy, which makes it possible to store all event positions and energies. In the second stage, called the information processor, the results of the first stage are used to calculate analytically any desired result. Examples are given for scattering slabs of isotropic or anisotropic scatterers when collimated-beam incidence is used. Reflections at the boundaries are taken into account. The results obtained either with this new method or with classical Monte Carlo methods are very similar. However, the convergence of our new model is much better and, because of the separation into two stages, any quantity related to the problem can be easily calculated afterward without recomputing the simulation.

Influence of the emission-reception geometry in laser-induced fluorescence spectra from turbid media.

Routine clinical detection of precancerous lesions by laser-inducedautofluorescence was recently demonstrated in several medicalfields. This technique is based on the analysis of complex spectrawith overlapping broad structures. However, in biological tissues, scattering and absorption are wavelength dependent, and the observedfluorescence signals are distorted when the illumination and detectiongeometry varies, making comparison of results from different groupsdifficult. We study this phenomenon experimentally in human tissuein a simple experiment: A fiber is used for the excitation and anidentical fiber is used for reception of the signal; both fibers aremaintained in contact with the tissue. We study the distortion ofthe spectra as a function of the distance between the twofibers. For correction of the spectra we show that it is possibleto use a fast and accurate ab initio Monte Carlo simulationwhen the spectral variations of the optical properties of the mediumare known. The main advantage of this simulation is itsapplicability even for complex boundary conditions or when the sampleconsists of several layers.

Real-space Green’s function calculation for the solution of the diffusion equation in stratified turbid media

We have derived the space-time Greens function for the diffusion equation in layered turbid media, starting from the case of a planar interface between two random scattering media. This new approach for working directly in real space permits highly efficient numerical processing, which is a decisive criterion for the feasibility of the inverse problem in biomedical optics. The results obtained by this method in the case of a two-layered medium are compared with Monte Carlo simulations.

The isometric force that induces maximal surface muscle deoxygenation.

Abstract To determine the external force that induces maximal deoxygenation of brachioradialis muscle 32 trained male subjects maintained isometric contractions using the elbow flexor muscles up to the limit time (isotonic part of the isometric contraction, IIC) and beyond that time for 120 s (anisotonic part of the isometric contraction). During IIC each subject maintained relative forces of either 25% and 70% maximal voluntary contraction (MVC), 50% and 100% MVC, or 40% and 60% MVC. Muscle oxygenation was assessed using a near infrared spectroscope, and expressed as a percentage of the reference value (ΔO2rest) which was the difference between the minimal oxygenation obtained after 6 min of ischaemia at rest and the maximal reoxygenation following the release of the tourniquet. During IIC at 25% MVC, muscle oxygenation decreased to 17 (SEM 3)% ΔO2rest, then it levelled off [25 (SEM 1)% ΔO2rest]. After the point at which target force could not be maintained, reoxygenation was very weak. During IIC at 40%, 50%, 60%, and 70% MVC, the lowest muscle oxygenation values were obtained after 15–20 s of contraction and corresponded to −18 (SEM 6), −59 (SEM 12) −31 (SEM 6), and −29 (SEM 6)% ΔO2rest, respectively. For the contraction at 100% MVC, the lowest oxygenation [−19 (SEM 9)% ΔO2rest] was obtained while force was decreasing (69% MVC). During the anisotonic part of the isometric contractions, the greatest reoxygenation rate was obtained after 50% MVC IIC (P < 0.001). Our results showed that during isometric elbow flexions between 25% and 100% MVC, there was no linear relationship between external force and muscle oxygenation, and that the maximal deoxygenation of the brachioradialis muscle was obtained at 50% MVC.

Real time optical coefficients evaluation from time and space resolved reflectance measurements in biological tissues

Quantitative and accurate determination of turbid media optical coefficients was achieved using time and space resolved measurements of diffuse backscattered light. The global analysis of the reflectance map registered on a streak camera was based on the diffusion approximation. This fast and practical method was tested on suspensions of latex microspheres in water, and the results were in good agreement with the Mie theory. Experiments were then performed on biological tissues. The total time required for the determination of the optical coefficients of a sample, essentially limited by the instrument integration time, consisted of a few seconds.

A new and easy way to perform time-resolved measurements of the light scattered by a turbid medium

We demonstrate that a low cost interferometric set-up and the analysis of the speckle fluctuations due to a wavelength modulated continuous source can be used to perform time-resolved measurements of the light scattered by a turbid medium. This method was tested on a solid scattering media with known optical coefficients. Our experimental results are in good agreement with Monte Carlo simulations.

Light propagation near turbid–turbid planar interfaces

The aim of this paper is to solve the diffusion equation in the case of two semi-infinite homogeneous scattering and absorbing media separated by a flat interface when a light source S is placed in one of these media. We present here a new approach which allows us to work directly in real space and to establish efficient analytical expressions for space and time resolved average intensity distributions in both media. The results obtained by this method are compared with Monte Carlo simulations. This new approach permits very efficient numerical processing, which is a decisive criterion for the study of light propagation in layered turbid media.

Ultimate spatial resolution with Diffuse Optical Tomography

We evaluate the ultimate transverse spatial resolution that can be expected in Diffuse Optical Tomography, in the configuration of projection imaging. We show how such a performance can be approached using time-resolved measurements and reasonable assumptions, in the context of a linearized diffusion model.

Monte Carlo evaluation of laser-induced fluorescence spectra modifications due to optical properties of the medium: Application to real spectra correction

Laser induced fluorescence has often been used as a diagnostic method. Unfortunately the fluorescence signal is modified during the photons migration towards the detector. The purpose of this study is to determine the alterations of the laser induced fluorescence spectra in white matter of adult brain due to the spectral variations of the optical coefficients (mu) a((lambda) ), (mu) s((lambda) ) and of the mean cosine of the scattering angle g((lambda) ).