Optical Interaction Coefficients Research Articles

Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning

Monte Carlo (MC) simulations are being used extensively in the field of medical biophysics, particularly for modeling light propagation in tissues. The high computation time for MC limits its use to solving only the forward solutions for a given source geometry, emission profile, and optical interaction coefficients of the tissue. However, applications such as photodynamic therapy treatment planning or image reconstruction in diffuse optical tomography require solving the inverse problem given a desired dose distribution or absorber distribution, respectively. A faster means for performing MC simulations would enable the use of MC-based models for accomplishing such tasks. To explore this possibility, a digital hardware implementation of a MC simulation based on the Monte Carlo for Multi-Layered media (MCML) software was implemented on a development platform with multiple field-programmable gate arrays (FPGAs). The hardware performed the MC simulation on average 80 times faster and was 45 times more energy efficient than the MCML software executed on a 3-GHz Intel Xeon processor. The resulting isofluence lines closely matched those produced by MCML in software, diverging by only less than 0.1 mm for fluence levels as low as 0.00001 cm(-2) in a skin model.

Measurements of the optical properties of tissue in conjunction with photodynamic therapy

A simple optical dosimeter was used to measure the light intensity in rat liver and muscle in vivo with fibers positioned at different depths to investigate whether the light penetration changed during photodynamic therapy (PDT). The results were then correlated with measurements of the three optical-interaction coefficients µ(s), µ(a) and g for wavelengths in the range 500-800 nm for PDT-treated and nontreated rat liver and muscle tissue in vitro. Adistinct increase in the absorption coefficient was seen immediately after treatment, in agreement with the decreasing light intensity observed during the treatment, as measured with the optical dosimeter. The collimated transmittance was measured with a narrow-beam setup, and an optical integrating sphere was used to measure the diffuse reflectance and total transmittance of the samples. The corresponding optical properties were obtained by spline interpolation of Monte Carlo-simulated data. To ensure that the measured values were correct, we performed calibration easurements with suspensions of polystyrene microspheres and ink.

The Calibration of fibre optic probes used for light dosimetry measurements during photodynamic therapy

We describe the calibration of fibre optic probes used to perform in vivo light dosimetry studies during the treatment of skin lesions by photodynamic therapy. Results from six individual detectors show that the linearity of the calibration and the calculated radiant energy fluence rate within a liquid phantom are independent of the type and sensitivity of the probe. The method of calibration is also shown to yield the optical interaction coefficients of the phantom.

Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements

When a picosecond light pulse is incident upon a turbid medium such as tissue, the temporal distribution of diffusely reflected and transmitted photons depends on the optical absorption and scattering properties of the medium. From diffusion theory it is possible to derive analytic expressions for the pulse shape in terms of the optical interaction coefficients of a homogeneous semi-infinite medium. Experimental tests of this simple model in tissue-simulating liquid phantoms of different geometries are presented here. The results of these tests show that, in a semi-infinite phantom, the application of the diffusion model provides estimates of the absorption and transport-scattering coefficients that are accurate to better than 10%. Comparable accuracy was also obtained with this simple model for finite slab, cylindrical, and spherical volumes as long as the objects were of sufficient size. For smaller volumes the absorption coefficient was overestimated because of the significant loss of photons at the bounda ries of the object.

Optical properties of Intralipid: a phantom medium for light propagation studies.

Intralipid is an intravenous nutrient consisting of an emulsion of phospholipid micelles and water. Because Intralipid is turbid and has no strong absorption bands in the visible region of the electromagnetic spectrum, and is readily available and relatively inexpensive, it is often used as a tissue simulating phantom medium in light dosimetry experiments. In order to assist investigators requiring a controllable medium that over a finite range of wavelengths is optically equivalent to tissue, we have compiled previously published values of the optical interaction coefficients of Intralipid, most of which were measured at a wavelength of 633 nm. We have extended the measurements of the absorption and reduced scattering coefficients from 460 to 690 nm and the total attenuation coefficient from 500 to 890 nm. These measurements show that, for stock 10% Intralipid, the absorption coefficient varies from 0.015 to 0.001 cm-1 between 460 and 690 nm, the reduced scattering coefficient varies from 92 to 50 cm-1 between 460 and 690 nm, the total attenuation coefficient varies from 575 to 150 cm-1 between 500 and 890 nm, and the average cosine of scatter varies from 0.87 to 0.82 between 460 and 690 nm. With these data, we discuss the design of an optically tissue-equivalent phantom consisting of Intralipid and black India ink.

The propagation of optical radiation in tissue. II: Optical properties of tissues and resulting fluence distributions

This paper is the second of two reviewing the propagation of electromagnetic radiation of wavelength 0.25–10μm in tissue. This part begins with a discussion of how the fundamental optical interaction coefficients of tissue may be measured. Both direct methods, in which the coefficients are measured for optically thin samples, and indirect methods, in which the coefficients are inferred from measurements on bulk samples are described. The difficulties inherent in both types of measurement are outlined. Next the wavelength dependence of the scattering and absorption coefficient is discussed, both from a heuristic point of view and by illustration from current literature. We illustrate how the optical spectrum can be divided into regions where the propagation of light is dominated by absorption or scattering effects. Finally we show how the distribution of light fluence in these spectral regions is dramatically different and illustrate the important features of these distributions.

In vivo measurement of the optical interaction coefficients of human tumours at 630 nm

The light distribution within a treatment volume is determined by the source geometry (e.g. superficial or interstitial illumination) and the optical interaction coefficients of the irradiated tissue. The authors have measured the energy fluence rate at various points within tumours undergoing irradiation with 630 nm light for photodynamic therapy for several source geometries. The relative positions of source and detector fibres were determined using CT scanning techniques. The results of the measurements were then applied to solutions of the diffusion theory which allowed the determination of the absorption coefficient ( Sigma a=30.5+or-16 m-1), the reduced scattering coefficient ( Sigma s=941+or-735 m-1), the effective attenuation coefficient ( Sigma eff=261+or-49 m-1) and the build-up coefficient which relates surface irradiance to the energy fluence rate at depth (k=1.6+or-0.6).

A program for calculating and plotting soft-X-ray optical interaction coefficients for molecules

Comprehensive tables for atomic scattering factor components f 1 and f 2 were compiled by Henke et al. for the extended photon region of 350–10000 eV. Accurate calculations of optical interaction coefficients for absorption, reflection and scattering by material systems (e.g. filters, multi-layers, etc.), which have widespread application, can be based simply upon the atomic scattering factors for the elements comprising the material, except near the absorption threshold energies. These calculations based upon the weighted sum of f 1 and f 2 for each atomic species present can be very tedious if done by hand. This led us to develop Optical Constants Grapher (OCG), a user-friendly program to perform these calculations on an IBM PC or compatible computer. By entering the chemical formula, density and thickness of up to six molecules, values of f 1, f 2, mass absorption, transmission efficiencies, attenuation lengths, mirror reflectivities and complex indices of refraction can be calculated and plotted as a function of energy or wavelength. This program and its user's manual are available from the authors.

Monte Carlo modeling of light propagation in highly scattering tissue--I: Model predictions and comparison with diffusion theory.

Using optical interaction coefficients typical of mammalian soft tissues in the red and near infrared regions of the spectrum, calculations of fluence-depth distributions, effective penetration depths and diffuse reflectance from two models of radiative transfer, diffusion theory, and Monte Carlo simulation are compared for a semi-infinite medium. The predictions from diffusion theory are shown to be increasingly inaccurate as the albedo tends to zero and/or the average cosine of scatter tends to unity.