Diffuse reflectance from a finite blood medium: applications to the modeling of fiber optic catheters

Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry

A noninvasive method to measure the optical properties of a diffusing and absorbing medium is described. Based on the spatially resolved measurement of diffuse reflectance at the sample surface, this method is particularly suitable for investigating the in vivo optical properties of biological tissues endoscopically in a clinical context. The sensitivity of the measurement is discussed, and two optical probes for two different clinical applications are presented. Preliminary measurements are performed on a nonbiological medium, which illustrate the possibilities of the proposed method. Finally, we report on in vivo measurements of the optical properties of the human esophageal wall at 630 nm.

Optical properties of ocular fundus tissues--an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation

Various models have been published calculating the light transport at the ocular fundus either for interpretation of in vivo reflectance measurements or for the prediction of photocoagulation effects. All these models took the absorption spectra of the pigments located at the ocular fundus, melanin, haemoglobin, xanthophyll, and the photoreceptor pigments, into account. However, light scattering inside the single fundus layers has not been investigated in detail and was, therefore, neglected in the calculations or only considered by very rough approximations. This paper presents measurements on specimens of retina, retinal pigment epithelium, choroid, and sclera using the double-integrating-sphere technique. Absorption coefficients, scattering coefficients, and anisotropy of scattering were calculated by an inverse Monte Carlo simulation from the measured collimated and diffuse transmittance and diffuse reflectance. Conclusions are drawn for the interpretation of fundus reflectance measurements, which are a useful tool in diagnostics and photocoagulation dosimetry.

Diffuse optics determination of hemoglobin derivatives in red blood cells and liposome encapsulated hemoglobin

High resolution optical absorption spectra of hemoglobin derivatives in red blood cells and phosphatidylcholine liposomes were calculated from diffuse reflection and transmission spectra by means of the one-dimensional diffusion approximation. The numerical technique of singular value decomposition was used to calculate the composition of red cell and liposome mixtures.

Experimental study of the effect of absorbing and transmitting inclusions in highly scattering media

Experimental results are presented for the cw reflected signal from a dense random medium containing inclusions of absorbing material or glass. It is shown that a glass inclusion is more difficult to detect than an absorbing one. A glass rod has two effects on the reflected signal: a waveguiding effect that reduces the signal and a transmission effect that increases it. The overall effect of the glass rod depends strongly on the distribution of light inside the sample around the inclusion and hence on the scattering liquid itself. This implies that for experiments modeling tissue interactions the parameters of scatterers used should be as close as possible to the tissue parameters.

Light-scattering technique for the study of orientation and deformation of red blood cells in a concentrated suspension

The backscattered and transmitted diagrams of He-Ne laser light illuminating a concentrated suspension of red blood cells (RBC's) are investigated. The shapes of these diagrams are closely related to the state of the suspension (at rest or submitted to a simple shear flow) and to the parameters that govern the non-Newtonian behavior of the blood suspension (such as the viscosity of the suspending medium and the volume concentration of the cells). An asymmetry in the backscattering diagram, which is absent on transmitted diagrams, is observed when the suspension is in a simple shear flow. This asymmetry is related to the deformation and orientation of the RBC's. The propagation of light through the suspension is modeled and a set of Monte Carlo simulations is performed to substantiate the inference that the relative variation of the backscattered flux is proportional to the gradients of deformation of the RBC's, and that such gradients must be known in order to apply a rheological model describing the non-Newtonian behavior of RBC membranes.

Multiple-scattering effects in transmission oximetry

To develop an algorithm for the spectrophotometric determination of the oxygen saturation in blood, a model for the transmission of light in a scattering and absorbing medium is developed, taking into account effects of multiple scattering. The computed results obtained by a Monte Carlo simulating program agreed well with those found by experiment. The results were compared with those obtained by the commonly used algorithm of transmission oximetry (based on Lambert-Beer's law) and it was found that the calibration curves obtained by this method were strongly dependent on the haematocrit and thickness of the sample. These curves were less reliable the lower the saturation of oxygen.

Characterization of absorption and scattering properties for various yeast strains by time-resolved spectroscopy

An understanding of the optical properties of biological media and cells is essential to the development of noninvasive optical studies of tissues. Unicellular organisms offer a unique opportunity to investigate the factors affecting light propagation, since they can be manipulated in ways impossible for more complex biological samples. In this study, we examined optical absorption and scattering properties of strongly multiple scattering yeast suspensions by means of near-infrared (NIR) time-resolved spectroscopy (TRS) and a sample substitution method. We determined the critical parameters for photon migration by varying the cell organelle content, the cell ploidy, the cell size, and the concentration of suspended cells. The results indicate that the photon absorption is insensitive to cell differentiation and that the cell volume is the primary factor determining light-scattering property.

Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction

In the present literature on ektacytometry, small angle light scattering by ellipsoidal red blood cells is commonly approximated by Fraunhofer diffraction. Calculations on a sphere with the size and relative refractive index of a red cell, however, show that Fraunhofer diffraction deviates significantly from exact Mie theory. Anomalous diffraction is found to be a much better approximation. The anomalous diffraction theory is used to calculate the intensity distribution of the light scattered by an ellipsoidally deformed red blood cell. The derived expression shows that the ellipticity of isointensity curves in forward scattered light are equal to the ellipticity of the red blood cell. The theoretical expression is fitted to the intensity patterns measured with an ektacytometer. For the small observation angles used in ektacytometry, the experimental results confirm the validity of the anomalous diffraction approach.

Prediction of sampling depth and photon pathlength in laser Doppler flowmetry

Monte Carlo simulation of photon migration in tissue was used to assess the sampling depth, measuring depth and photon pathlength in laser Doppler flowmetry. The median sampling depth and photon pathlength in skin, liver and brain tissue were calculated for different probe geometries. The shallowest median sampling depth found was 68 microns for a 120 microns diameter single fibre probe applied to a one-layered skin tissue model. By using separate transmitting and receiving fibres, the median sampling depth, which amounted to 146 microns for a 250 microns fibre centre separation, can be successively increased to 233 microns when the fibres' centres are separated by 700 microns. Total photon pathlength and thereby the number of multiple Doppler shifts increase with fibre separation, thus favouring the choice of a probe with a small fibre separation when linearity is more important than a large sampling depth. Owing mainly to differences in the tissue g-value and scattering coefficient, the median sampling depth is shallower for liver and deeper for brain, in comparison with skin tissue. For skin tissue, the influence on the sampling depth of a homogeneously distributed blood volume was found to be limited to about 1 per cent per percentage increase in tissue blood content, and may, therefore, be disregarded in most practical situations. Simulations show that the median measuring depth is strongly dependent on the perfusion profile.

Diffuse reflectance from turbid media: an analytical model of photon migration

To calculate the diffuse reflectance from a semi-infinite slab of tissue, we introduce a probability distribution function, f(n)(g), that a photon will escape from the tissue after n scattering events. This approach permits the separation of the phase dependence of scattering, described by the anisotropy coefficient, g, from the absorption, micro(alpha), and scattering, micro(s), coefficients in the calculation of diffuse reflectance. We demonstrate that f(n)(g) and g are related to each other through a universal probability function. The analytical form of this probability function is explored and used to obtain the diffuse reflectance from tissue. The diffuse reflectance calculated with this method is in excellent agreement with Monte Carlo simulations over the parameter range typically found in human tissue, even for the values in which diffusion theory is a poor approximation.

Condensed Monte Carlo simulations for the description of light transport

A novel method, condensed Monte Carlo simulation, is presented that applies the results of a single Monte Carlo simulation for a given albedo micro(s)/(micro(alpha) & micro(s)) to obtaining results for other albedos; micro(s) and micro(alpha), are the scattering and absorption coefficients, respectively. The method requires only the storage of the number of interactions of each photon with the medium. The reflectance and transmittance of turbid slabs can thus be found from a limited number of condensed Monte Carlo simulations. We can use an inversion procedure to obtain the absorption and scattering coefficients from the total reflectance and total transmittance of slabs. Remitted photon densities from a semi-infinite medium as a function of the distance between the light source and the detector for all albedos can be found even from the results of a single condensed Monte Carlo simulation. The application of similarity rules may reduce further the number of Monte Carlo simulations that are needed to describe the influence of the distribution of scattering angles on the results.

Reduced light-scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations

The reduced scattering cross section per unit of volume Sigma'(s) identical withSigma(s)(1 - g) is an important parameter to describe light propagation in media with scattering and absorption. Mie calculations of the asymmetry factor g for nonabsorbing spheres and Q(sca), the ratio of the scattering cross section Sigma(s) and the particle cross section, show that Q(sca)(1 - g) = 3.28x(0.37)(m - 1)(2.09) is true to within a few percent, when the Mie parameters for relative refractive index m and size x are in the ranges of 1 < m </= 1.1 and 5 < x < 50, respectively. A ratio of reduced scattering cross sections for radiation at two wavelengths is also independent of the size within the range mentioned, even for mixtures of different size spheres. The results seem promising for biomedical applications.

Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry

Photon diffusion theory is used to derive analytical expressions that relate the ac-dc intensity ratios measured by transmission-mode and reflectance-mode pulse oximeters to arterial oxygen saturation (SaO2). The effects of multiple scattering are examined by comparing the results of the photon diffusion analysis with those obtained using an analysis based on the Beer-Lambert law which neglects scattering. We show that the difference between the average lengths of the paths travelled by red and infrared photons makes the calibration curve of oximeters sensitive to the total attenuation coefficients of the tissue in the two wavelength bands, as well as to absorption by the pulsating arterial blood. Therefore, the shape of the calibration curve is affected by tissue blood volume, source-detector placement, and other variables that change the wavelength dependence of the attenuation coefficient of the tissue. After evaluating the relationship between SaO2 and the red/IR ac-dc ratio (R) under a variety of physiological conditions, we conclude that, for oximeters utilizing fixed calibration curves based on measurements obtained from normal subjects, errors introduced by interfering variables should be less than a few percent when SaO2 exceeds 70%. Predicted errors at lower oxygen saturation values are substantially greater because R is much more sensitive to interfering variables in this measurement range.

Monte Carlo modelling of light propagation in breast tissue

Light transport in three-dimensional plane-parallel tissue slabs has been modelled by Monte Carlo analogue simulation. The model design has allowed the study of transmission properties that are pertinent to imaging systems for the detection of breast cancer. An important aspect of the investigations is that they make use of data obtained from quantitative measurements of light scattering and absorption in normal and pathological breast tissues. It is shown that an imaging technique which used a raster scanning laser and detector arrangement and plane-parallel compression of the breast could have considerable advantages in terms of improved transmittance, spatial unsharpness and contrast. Time-of-flight gating of images is also found to be beneficial provided that the light intensities after temporal filtering remain adequate.

Gaussian beam spread in biological tissues

Flux density distributions were measured in large tissue sections illuminated with 633- and 1064-nm laser radiation delivered by an optical fiber. The results were modeled by solving the 2-D diffusion approximation for an incident Gaussian beam and fitting the data with nonlinear regression. It is shown that the radial average flux density is exponentially attenuated for an arbitrary incident irradiance profile.

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.

Monte Carlo modeling of light propagation in highly scattering tissues--II: Comparison with measurements in phantoms

Measurements of the fluence-depth distributions and of the diffuse reflectance of 633 nm light have been made in liquid media with optical properties similar to soft tissues. The results are compared with predictions of Monte Carlo computer calculations in order to test the adequacy of Monte Carlo modeling of light transport in tissue. Except at extremely high albedo, the experimental data and the Monte Carlo results agree well for the depth dependence of the fluence as a function of incident light beam diameter and optical absorption and scattering, and for the dependence of the diffuse reflectance on the albedo. The absolute experimental values for the fluence must be renormalized by a factor which varies with the albedo in order to match the model values, and the possible sources of this discrepancy are discussed.

Light propagation parameters for anisotropically scattering media based on a rigorous solution of the transport equation

New expressions are presented for light propagation in media for the whole range of absorption and for isotropic as well as for anisotropic scattering with an average cosine of the scattering angle between 0 and 0.9995. The method is based on the rigorous solution of the transport equation for Rayleigh-Gans scattering. The calculated angular intensity distribution was used to determine the absorption parameter K. Expressions for K and the backscattering parameter S are given that can be used to improve existing photon diffusion and two- or four-flux models.

Measurements and calculations of the energy fluence rate in a scattering and absorbing phantom at 633 nm

We have studied the influence of absorption, scattering, and refractive index of a phantom medium in conjunction with various beam diameters on the penetration depth of light at 633 nm. We used mixtures of Intralipid 10% (scattering medium) and Evans blue (absorbing medium). Measurements were performed in media with a scattering coefficient of 1 mm(-1), an anisotropy factor of 0.71, absorption coefficients of 1.3 x 10(-3), 0.01, and 0.05 mm(-1), and a refractive index of 1.33. The experimental results were compared with an analytical solution of the fluence rate based on diffusion theory. We found good agreement (deviations of <10%) between theory and experiment for incident beam diameters between 10 and 60 mm.

Toward absolute reflectance oximetry: I. Theoretical consideration for noninvasive tissue reflectance oximetry

The photon diffusion theory can yield quantitative estimation of tissue hemoglobin saturation, provided that the medium is homogeneous and that one calibration data is available. The error in detection of tissue OS of the gut mucosa ranged from 5 to 10% in oxygen saturation. In application to skin, the two-layer tissue model suggests that by properly designing the optical sensor and by appropriately selecting the illumination wavelengths, it is possible to capture mainly the light returning from the specific depth in tissue. Since the skin layer thickness is roughly in the order of 1 mm, the source and detector separation distance of approximately 3 mm or larger would ensure that the measured reflectance is truly returning from the deeper layer. When such reflectances are normalized to the blood-free reflectance obtained by squeezing the blood out of the tissue, the normalized reflectance truly represents the deeper layer characteristics. In application to head, since the skin and skull thickness is considerable large, separation distance of 40 mm or greater is required to ensure the reflectance is actually returning from the brain. Closely spaced optical sensor would measure the scattering and absorption characteristics of the skin and skull of the head. As for directional changes in optical propagation due to tissue inhomogeneities, multiple light sources at the equi-distance around the detector can be placed to average out the effect. The resultant reflectance can be analyzed based on the similar mathematical treatment as presented in this study. However, since the absolute reflectance level calculated by the theory and the actual reflectance for a given transducer geometry have some deviation, again one point calibration is required to close the gap between them. This can be accomplished through arterialization of the tissue and ventilating with pure oxygen to yield reflectance from tissue containing 100% saturated blood. As for hemoglobin content, isosbestic reflectance, for example at 805 nm, can be utilized to estimate tissue hemoglobin content. Once one point calibration is accomplished, reflectance changes thereafter due to changes in HbT and OST can be fairly accurately predicted by the photon diffusion theory in combination with linear analysis. Concerning separation of arterial and venous blood in tissue, the diastolic and systolic phases of the optical plethysmographic signal can be assumed to relate to venous or DC level, and to arterial or AC component. Since the four components, arterial and venous OS and Hb, are unknowns in the system, four equations or four wavelength measurements are required to sort out each effect.(ABSTRACT TRUNCATED AT 400 WORDS)

Diffusion model of the optical absorbance of whole blood

Photon-diffusion theory has had limited success in modeling the optical transmittance of whole blood. Therefore we have developed a new photon-diffusion model of the optical absorbance of blood. The model has benefited from experiments designed to test its fundamental assumptions, and it has been compared extensively with transmittance data from whole blood. The model is consistent with both experimental and theoretical notions. Furthermore, when all parameters associated with a given optical geometry are known, the model needs no variational parameters to predict the absolute transmittance of whole blood. However, even if the exact value of the incident light intensity is unknown (which is the case in many situations), only a single additive constant is required to scale experiment to theory. Finally, the model is shown to be useful for simulating scattering effects and for delineating the relative contributions of the diffuse transmittance and the collimated transmittance to the total optical density of whole blood. Applications of the model include oximetry and measurements of the arteriovenous oxygen difference in whole, undiluted blood.

New approaches to transillumination imaging

A review of the current state of transillumination imaging for the detection and diagnosis of breast cancer and the difficulties that impede more widespread acceptance of the methods is presented. An outline is given of the physical models that may be used to describe the propagation and scattering of light in a tissue matrix and how these models might be valuable in identifying imaging improvements. Some of the proposals for future imaging arrangements are described and the preliminary work on a system for light transmission computed tomography is presented.

Model for photon migration in turbid biological media

Various characteristics of photon diffusion in turbid biological media are examined. Applications include the interpretation of data acquired with laser Doppler blood-flow monitors and the design of protocols for therapeutic excitation of tissue chromophores. Incident radiation is assumed to be applied at an interface between a turbid tissue and a transparent medium, and the reemission of photons from that interface is analyzed. Making use of a discrete lattice model, we derive an expression for the joint probability gamma(n, rho)d2 rho that a photon will be emitted in the infinitesimal area d2 rho centered at surface point rho = (x, y), having made n collisions with the tissue. Mathematical expressions are obtained for the intensity distribution of diffuse surface emission, the probability of photon absorption in the interior as a function of depth, and the mean path length of detected photons as a function of the distance between the site of the incident radiation and the location of the detector. We show that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile. Results of relevant computer simulations are presented, and illustrative experimental data are shown to be in accord with the theory.

Light propagation in moderately dense particle systems: a reexamination of the Kubelka-Munk theory

A numerical method (NM) is developed to characterize radiative transfer in a moderately dense particle population, i.e., a suspension of concentration of <1-10% by volume. It assumes that the particles scatter in accord with the Mie equations, that the propagation of light over short distances is in accord with the exponential transmission law, and that the light flows in many (thirty-six) directions. For representative systems, predictions of the Kubelka-Munk theory (KMT) are compared with those of the NM; partial agreement is found. While this theory can be a useful tool, radiative transport in representative samples is found not to obey strictly either the assumptions for writing the basic differential equations of the KMT or those for solving them. The movement of diffuse light through an attenuating system is found to often collimate it, not to make it more diffuse as expected. This effect causes errors in absolute KMT predictions. New transport equations, like Schuster's, with four parameters instead of two are written and solved to obtain some new KMT equations. Their predictions are compared with those of the NM.

In vivo photometric analysis of hemoglobin

Since virtually all the oxygen carried by blood at normal hematocrit is reversibly bound to red blood cell hemoglobin, the distribution of oxygen within the microcirculation can be determined from measurements of hemoglobin concentration and hemoglobin oxygen saturation in vessels of the network. Photometric methods that rely on light absorption and scattering properties of blood are described. Criteria for selecting the wavelengths needed to analyze hemoglobin in the microcirculation are specified. Two theoretical descriptions of light absorption and scattering, multiple scattering theory and photon diffusion theory, are applied to the problem. Practical approaches to the determination of hemoglobin concentration and oxygen saturation in the microcirculation follow from these theoretical formulations. Technical aspects of microscope photometry including light sources, microscopy, and detection systems are described with special emphasis on the problem of glare. The importance of in vitro as well as in vivo calibrations is stressed, and several recent applications of a working system are discussed. Current problems as well as future developments of this methodology are delineated as a guide to future work in this area.

New methods for whole blood oximetry

New techniques for determining the hematocrit (Hct) and oxygen saturation (SO2) of whole blood from backscattered light measurements are described. First, theoretical and experimental results are presented which show that the empirical linear relationship between SO2 and the infrared-red backscattered light intensity ratio on which previous instruments have been based is an inadequate description primarily because it does not account for the strong effects of Hct and transducer geometry. Then it is shown that the ratio of backscattered intensities from two appropriately positioned infrared sources can be plotted against the infrared-red intensity ratio to produce a family of calibration curves from which SO2 and Hct can be independently determined. Finally, a practical implementation of an oximetry system which employs a microelectronic catheter-tip optical sensor and a microprocessor-based signal processor is proposed.

Scattering and absorption of turbid materials determined from reflection measurements. 1: theory

To allow the determination of scattering and absorption parameters of a turbid material from reflection measurements the relation of these parameters to the reflection has been described by two theoretical approaches. One approach is based on the diffusion theory which has been extended to include anisotropic scattering. This results in a reflection formula in which the scattering and absorption are described by one parameter each. As a second more general approach a Monte Carlo model is applied. Comparison of the results indicates the range of values of the scattering and absorption parameters where the computationally fast diffusion approach is applicable.

Fiber-optic scattering monitor for use with bulk opaque material

A method and apparatus is developed to monitor nondestructively the turbidity of colorless bulk material. The method employs illumination and measuring spots of equal and small sizes (radius r(m)) at the same site of the sample surface. The Kubelka-Munk scattering coefficient may be measured in nonabsorbing material but calibration is necessary. The range then is approximately l/(8r(m)) < S < 10/r(m). A flexibly connected miniature measuring head (r(m) approximately 0.13 mm) is connected to a lamp-detector unit by optical fibers. Polychromatic light from a xenon lamp is used. The present apparatus is especially designed for dental research, but biological tissues and also commercially available liquids, papers, and plastics can be monitored for their scattering behavior.

Model for laser Doppler measurements of blood flow in tissue

A theory is developed which relates quasi-elastic light scattering measurements to blood flow in tissue micro-vasculature. We assume that the tissue matrix surrounding the blood cells is a strong diffuser of light and that moving erythrocytes, therefore, are illuminated by a spatially distributed source. Because the surrounding tissue is considered to be stationary, Doppler shifts in the frequency of the scattered light arise only from photon interactions with the moving blood cells. The theory implies that the time decay of the photon autocorrelation function scales proportionally with cell size and inversely with mean translational speed. Analysis of multiple interactions of photons with moving cells indicates the manner in which spectral measurements additionally are sensitive to changes in blood volume. Predictions are verified by measurements of particle flow in model tissues.

Off-axis propagation of a laser beam in low visibility weather conditions

The role of non-small-angle scattering is examined for off-axis laser beam propagation under low visibility weather conditions. The near-axis radiance distribution function is obtained from a radiative transfer equation with the aid of the small-angle approximation. The contribution of the non-small-angle scattering is described via another transfer equation with the on-axis radiance as an external source, and this equation is solved in the diffusion approximation. Numerical results for radiational and advective fogs are presented to show the importance of non-small-angle scattering in the case of off-axis detection.

Backscattering of a picosecond pulse from densely distributed scatterers

A theoretical and experimental study of the backscattering characteristics of a picosecond pulse scattered from a dense diffusing medium is presented. The theory uses a diffusion solution to the time-dependent equation of radiative transfer and the formulation of a picosecond range-gating technique. The experimental system consists of a high-power laser range-gating system, based on a picosecond Kerr-effect shutter. The results of experiments carried out on aqueous solutions of latex microspheres agree well with the theoretical calculations, not only in the pulse shape but in the relative magnitudes of the pulse height for different particle sizes and concentrations.