Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements

Efficiency scale for scattering luminescent particles linked to fundamental and measurable spectroscopic properties

Comparing the performance of molecular and nanoscale luminophores and luminescent micro- and nanoparticles and estimating achievable signal amplitudes and limits of detection requires a standardizable intensity scale. This initiated the development of the relative MESF (number of molecules of equivalent soluble fluorochromes) and ERF (equivalent reference fluorophores) scales for flow cytometry and fluorescence microscopy. Both intensity scales rely on fluorescence intensity values assigned to fluorescent calibration beads by an intensity comparison to spectrally closely matching fluorophore solutions of known concentration using a spectrofluorometer. Alternatively, the luminophore or bead brightness (B) can be determined that equals the product of the absorption cross section (σ_a) at the excitation wavelength (σ_a(λ_ex)) and the photoluminescence quantum yield (Φ_pl). Thereby, an absolute scale based on fundamental and measurable spectroscopic properties can be realized which is independent of particle size, material, and luminophore staining or labeling density and considers the sensitivity of the optical properties of luminophores to their environment. Aiming for establishing such a brightness scale for light-scattering dispersions of luminescent particles with sizes exceeding a few ten nanometers, we demonstrate how the brightness of quasi-monodisperse 25 nm, 100 nm, and 1 µm sized polystyrene particles (PSP), loaded with two different dyes in varying concentrations, can be obtained with a single custom-designed integrating sphere setup that enables the absolute determination of Φ_pl and transmittance and diffuse reflectance measurements. The resulting Φ_pl, σ_a(λ_ex), imaginary parts of the refractive index, and calculated B values of these samples are given in dependence of the number of incorporated dye molecule per particle. Finally, a unitless luminescence efficiency (LE) is defined allowing for the direct comparison of luminescence efficiencies of particles with different sizes.

Two-term scattering phase function for photon transport to model subdiffuse reflectance in superficial tissues

For Monte Carlo simulations of light transport in a variety of diffuse scattering applications, a single-scattering two-term phase function with five adjustable parameters is sufficiently flexible to separately control the forward and backward components of scattering. The forward component dominates light penetration into a tissue and the resulting diffuse reflectance. The backward component controls early subdiffuse scatter from superficial tissues. The phase function consists of a linear combination of two phase functions [Reynolds and McCormick, J. Opt. Soc. Am.70, 1206 (1980)10.1364/JOSA.70.001206] that were derived from the generating function for Gegenbauer polynomials. The two-term phase function (TT) accommodates strongly-forward anisotropic scattering with enhanced backscattering and is a generalization of the two-term, three-parameter Henyey-Greenstein phase function. An analytical inverse of the cumulative distribution function for scattering is provided for implementation in Monte Carlo simulations. Explicit TT equations are given for the single-scattering metrics g ₁, g ₂, γ, and δ. Scattering data from previously published bio-optical data are shown to fit better with the TT than other phase function models. Example Monte Carlo simulations illustrate the use of the TT and its independent control of subdiffuse scatter.

Phase function estimation from a diffuse optical image via deep learning

Objective. The phase function is a key element of a light propagation model for Monte Carlo (MC) simulation, which is usually fitted with an analytic function with associated parameters. In recent years, machine learning methods were reported to estimate the parameters of the phase function of a particular form such as the Henyey–Greenstein phase function but, to our knowledge, no studies have been performed to determine the form of the phase function. Approach. Here we design a convolutional neural network (CNN) to estimate the phase function from a diffuse optical image without any explicit assumption on the form of the phase function. Specifically, we use a Gaussian mixture model (GMM) as an example to represent the phase function generally and learn the model parameters accurately. The GMM is selected because it provides the analytic expression of phase function to facilitate deflection angle sampling in MC simulation, and does not significantly increase the number of free parameters. Main Results. Our proposed method is validated on MC-simulated reflectance images of typical biological tissues using the Henyey–Greenstein phase function with different anisotropy factors. The mean squared error of the phase function is 0.01 and the relative error of the anisotropy factor is 3.28%. Significance. We propose the first data-driven CNN-based inverse MC model to estimate the form of scattering phase function. The effects of field of view and spatial resolution are analyzed and the findings provide guidelines for optimizing the experimental protocol in practical applications.

Absorbance spectroscopy of light scattering samples placed inside an integrating sphere for wide dynamic range absorbance measurement

In the absorbance measurement of a sample that scatters light significantly, it is necessary to consider the effect of the attenuation of incident light due to scattering on the measured absorbance. Since the usual absorbance measurement with an integrating sphere (IS) cannot remove the influence of backscattering, we performed the absorbance measurement considering the light scattered to almost all solid angles by placing the sample inside the IS. Ni(NO₃)₂ and Co(NO₃)₂ aqueous solutions were used as non-scattering samples, and Ni(NO₃)₂ solutions mixed with submicrometer polystyrene spheres as scatterers were used as scattering samples. The sample-concentration dependence of the measured absorbance was investigated for the cell containing the sample placed at the entrance of or inside the IS. It was found that even inside the IS, the measured absorbance does not match the true absorbance because light is partially multiply transmitted through the sample or detected without being transmitted through the sample. Due to the latter reason, the saturated absorbance inside the IS was lower than that at the entrance. We derived the formula with three fitting parameters relating the measured and true absorbance taking these factors into account, which quantitatively reproduced the concentration dependence of the absorbance in the non-scattering sample. When the scattering samples were placed at the entrance and inside of the IS, the measured absorbance increased and decreased, respectively, compared to those without scatterers. This decrease in absorbance for the scattering samples inside the IS was also explained by the proposed formula slightly modified.

Imaging sub-diffuse optical properties of cancerous and normal skin tissue using machine learning-aided spatial frequency domain imaging

SIGNIFICANCE

Sub-diffuse optical properties may serve as useful cancer biomarkers, and wide-field heatmaps of these properties could aid physicians in identifying cancerous tissue. Sub-diffuse spatial frequency domain imaging (sd-SFDI) can reveal such wide-field maps, but the current time cost of experimentally validated methods for rendering these heatmaps precludes this technology from potential real-time applications.

AIM

Our study renders heatmaps of sub-diffuse optical properties from experimental sd-SFDI images in real time and reports these properties for cancerous and normal skin tissue subtypes.

APPROACH

A phase function sampling method was used to simulate sd-SFDI spectra over a wide range of optical properties. A machine learning model trained on these simulations and tested on tissue phantoms was used to render sub-diffuse optical property heatmaps from sd-SFDI images of cancerous and normal skin tissue.

RESULTS

The model accurately rendered heatmaps from experimental sd-SFDI images in real time. In addition, heatmaps of a small number of tissue samples are presented to inform hypotheses on sub-diffuse optical property differences across skin tissue subtypes.

CONCLUSION

These results bring the overall process of sd-SFDI a fundamental step closer to real-time speeds and set a foundation for future real-time medical applications of sd-SFDI such as image guided surgery.

Study of a laser echo in an inhomogeneous dust environment with a continuous field Monte Carlo radiative transfer model

A continuous field Monte Carlo radiative transfer model with an improved semianalytic approach is developed to study laser propagation in an inhomogeneous dust environment. In the proposed model, the photon step size can vary with the mass concentration of the dust environment. Additionally, the scattering properties of the dust particles are calculated with the T-matrix method and the T-matrix scattering phase function is applied to the Monte Carlo simulation with a rejection method. Using this model, the influences of the particle sizes and shapes on the backscattering properties are studied. Finally, the laser echoes simulated by our proposed model are compared with those of traditional Monte Carlo method and experimental results. Different mass concentration distributions indeed influence the simulated laser echo. The simulated results (of our proposed model) agree well with the measured data, demonstrating the effectiveness and accuracy of our approach for inhomogeneous media.

Direct measurement of the scattering coefficient

In general, the measurement of the main three optical properties (µ a , µ s and g) in turbid media requires a very precise measurement of the total transmission (TT), the total reflection (TR) and the collimated transmission (CT). Furthermore, an inverse algorithm such as inverse adding doubling or inverse Monte-Carlo-simulations is required for the reconstruction of the optical properties. Despite many available methods, the error free measurement of the scattering coefficient or the g-factor still remains challenging. In this study, we present a way to directly calculate the scattering coefficient from the total and collimated transmission. To allow this, it can be shown thatT T C T is proportional to e μ s ⋅ d for a wide range of optical properties if the sample is thick enough. Moreover, a set-up is developed and validated to measure the collimated transmission precisely.

Beyond diffuse correlations: deciphering random flow in time-of-flight resolved light dynamics

Diffusing wave spectroscopy (DWS) and diffuse correlation spectroscopy (DCS) can assess blood flow index (BFI) of biological tissue with multiply scattered light. Though the main biological function of red blood cells (RBCs) is advection, in DWS/DCS, RBCs are assumed to undergo Brownian motion. To explain this discrepancy, we critically examine the cumulant approximation, a major assumption in DWS/DCS. We present a precise criterion for validity of the cumulant approximation, and in realistic tissue models, identify conditions that invalidate it. We show that, in physiologically relevant scenarios, the first cumulant term for random flow and second cumulant term for Brownian motion alone can cancel each other. In such circumstances, assuming pure Brownian motion of RBCs and the first cumulant approximation, a routine practice in DWS/DCS of BFI, can yield good agreement with data, but only because errors due to two incorrect assumptions cancel out. We conclude that correctly assessing random flow from scattered light dynamics requires going beyond the cumulant approximation and propose a more accurate model to do so.

Precise determination of the optical properties of turbid media using an optimized integrating sphere and advanced Monte Carlo simulations. Part 2: experiments

Based on theoretical investigations of the light propagation within an integrating sphere, we developed an accurate method to determine the optical properties of scattering media using an integrating sphere-based setup. The method takes into account the exact sphere geometry as well as the different angular distributions of the reflected and transmitted light from the sample and the calibration standard. We tested our novelties successfully in theory with Monte Carlo simulations and in practice using a 3D printed and professionally coated integrating sphere. As a result, we were able to determine precisely the effective scattering coefficient, μs', and the absorption coefficient, μ_a, between 400 nm and 1500 nm in a range of μ_a=1e-3mm^-1 to 10mm^-1 and μs'=0.2mm^-1 to 100mm^-1. Usually, the accuracy was around 1% for μs' and around 3% for μ_a for turbid phantom media with an optical thickness τ=μs'd>1 and a transmittance signal >0.1%.

Angular reflectance of a highly forward scattering medium at grazing incidence of light

We study the angular distribution of light diffusely reflected from a turbid medium with large (compared to the light wavelength) inhomogeneities. Using Monte Carlo radiative transfer simulations, we calculate the azimuthally averaged bidirectional reflectance for an optically thick plane-parallel medium and analyze its dependence on the parameters of the scattering phase function. To model single scattering in the medium, we take advantage of the Reynolds-McCormick phase function. For grazing angles of incidence, we find that the angular distribution of reflected light becomes very sensitive to the angular profile of the scattering phase function. The more elongated the phase function, the more pronounced the peak that arises around the specular reflection angle. Comparison of our numerical results with an analytic solution of the radiative transfer equation is performed, and it is shown that the bidirectional reflectance can be decomposed into two contributions, namely, the diffusion contribution and the contribution from light experiencing multiple scattering through small angles. The latter relates directly to the angular profile of the scattering phase function and is responsible for the peak in the angular distribution of reflected light. An explicit analytic formula for the azimuthally averaged bidirectional reflectance is obtained.

Measurement of absorption in scattering media using objective laser speckle: application to blood oximetry

Multi-spectral imaging enables non-invasive sensing of chemical concentrations in biological tissue based on measurement of optical absorption, but invariably in the presence of high levels of scatter. Absorption is normally inferred from measurement of contrast of biological features, such as the vasculature, and so accuracy is degraded by the poorly characterized modulation-transfer function of the imaging optics and overlying tissue. We report how experimental characterization of the spectral variation of the tissue point-spread function and associated objective speckle pattern can be used to characterize the absorption spectrum and chromophore concentration, with a particular emphasis on determination of the ratio of oxygenated to deoxygenated hemoglobin within blood. Absorption measurements are determined purely by the geometry of the experiment, without degradation due to optical aberrations and associated light scatter. The technique offers enhanced and low-cost determination of in vitro or in vivo chromophore characterizations, including blood-gas analysis.

Absorption and Remission Characterization of Pure, Dielectric (Nano-)Powders Using Diffuse Reflectance Spectroscopy: An End-To-End Instruction

This paper addresses the challenging task of optical characterization of pure, dielectric (nano-)powders with the aim to provide an end-to-end instruction from appropriate sample preparation up to the determination of material remission and absorption spectra. We succeeded in establishing an innovative preparation procedure to reproducibly obtain powder pellet samples with an ideal Lambertian scattering behavior. As a result, a procedure based on diffuse reflectance spectroscopy was developed that allows for (i) performing reproducible and artifact-free, high-quality measurements as well as (ii) a thorough optical analysis using Monte Carlo and Mie scattering simulations yielding the absorption spectrum in the visible spectral range. The procedure is valid for the particular case of powders that can be compressed into thick, non-translucent pellets and neither requires embedding of the dielectric (nano-)powders within an appropriate host matrix for measurements nor the use of integrating spheres. The reduced spectroscopic procedure minimizes the large number of sources for errors, enables an in-depth understanding of non-avoidable artifacts and is of particular advantage in the field of material sciences, i.e., for getting first insights to the optical features of a newly synthesized, pure dielectric powder, but also as an inline inspection tool for massively parallelised material characterization.

Determining the optical properties of blood using He-Ne laser and double integrating sphere set-up

The behaviour of light interaction with biological tissue is determined by micro-optical parameters: refractive index (n), absorption coefficient (µa ), scattering coefficient (µs ), and anisotropy (g). The goal of this study is to measure the optical properties of normal whole blood using He-Ne laser (wavelength 632.8 nm).

The refractive index is measured using the traveller microscope. The integrating sphere method is used to measure the macro-optical parameters: total diffusive reflectance, transmittance, and collimated transmittance at wavelength 632.8 nm. The macro-optical parameters are fed to Inverse Adding Doubling (IAD) theoretical technique, to estimate the micro-optical parameters (µs , µa , g). An alternative practical method is used to measure the g value based on utilising the goniometric table. The study reveals that the refractive index (n) equals 1.395±0.0547, absorption coefficient (µa ) equals 2.37 mm−1, scattering coefficient (µs ) equals 55.69 mm−1, and anisotropy (g) equals 0.82.

In conclusion, these findings approved, in general, the applicability of the suggested experimental set up. The set up depend on using three devices: the integrating sphere method to estimate (µs , µa , g), traveller microscope (n) and goniometer (g).

Impact of the scattering phase function on the bulk reflectance of a turbid medium with large-scale inhomogeneities

We study the total bulk reflectance of a turbid medium with large (as compared to the light wavelength) inhomogeneities at grazing angles of light incidence. To model highly forward scattering in the medium, we take advantage of the Reynolds-McCormick scattering phase function. Using the scaling analysis for the small-angle radiative transfer equation, we derive simple analytical formulas for the total reflectance. For grazing incidence angles, we find a range of values of the medium transport coefficients where the total reflectance proves to be a universal function of a single parameter, which is expressed in terms of the incidence angle, the absorption coefficient, and the transport scattering one. The explicit form of this function is governed by the specific angular profile of the scattering phase function. The results obtained are verified by comparison with results of a direct numerical integration of the radiative transfer equation.

Lookup table-based sampling of the phase function for Monte Carlo simulations of light propagation in turbid media

Analytical expressions for sampling the scattering angle from a phase function in Monte Carlo simulations of light propagation are available only for a limited number of phase functions. Consequently, numerical sampling methods based on tabulated values are often required instead. By using Monte Carlo simulated reflectance, we compare two existing and propose an improved numerical sampling method and show that both the number of the tabulated values and the numerical sampling method significantly influence the accuracy of the simulated reflectance. The provided results and guidelines should serve as a good starting point for conducting computationally efficient Monte Carlo simulations with numerical phase function sampling.

Estimation of optical properties by spatially resolved reflectance spectroscopy in the subdiffusive regime

We propose and objectively evaluate an inverse Monte Carlo model for estimation of absorption and reduced scattering coefficients and similarity parameter ? from spatially resolved reflectance (SRR) profiles in the subdiffusive regime. The similarity parameter ? carries additional information on the phase function that governs the angular properties of scattering in turbid media. The SRR profiles at five source-detector separations were acquired with an optical fiber probe. The inverse Monte Carlo model was based on a cost function that enabled robust estimation of optical properties from a few SRR measurements without a priori knowledge about spectral dependencies of the optical properties. Validation of the inverse Monte Carlo model was performed on synthetic datasets and measured SRR profiles of turbid phantoms comprising molecular dye and polystyrene microspheres. We observed that the additional similarity parameter ? substantially reduced the reflectance variability arising from the phase function properties and significantly improved the accuracy of the inverse Monte Carlo model. However, the observed improvement of the extended inverse Monte Carlo model was limited to reduced scattering coefficients exceeding ?15??cm?1, where the relative root-mean-square errors of the estimated optical properties were well within 10%.

Polarized light interaction with tissues

This tutorial-review introduces the fundamentals of polarized light interaction with biological tissues and presents some of the recent key polarization optical methods that have made possible the quantitative studies essential for biomedical diagnostics. Tissue structures and the corresponding models showing linear and circular birefringence, dichroism, and chirality are analyzed. As the basis for a quantitative description of the interaction of polarized light with tissues, the theory of polarization transfer in a random medium is used. This theory employs the modified transfer equation for Stokes parameters to predict the polarization properties of single- and multiple-scattered optical fields. The near-order of scatterers in tissues is accounted for to provide an adequate description of tissue polarization properties. Biomedical diagnostic techniques based on polarized light detection, including polarization imaging and spectroscopy, amplitude and intensity light scattering matrix measurements, and polarization-sensitive optical coherence tomography are described. Examples of biomedical applications of these techniques for early diagnostics of cataracts, detection of precancer, and prediction of skin disease are presented. The substantial reduction of light scattering multiplicity at tissue optical clearing that leads to a lesser influence of scattering on the measured intrinsic polarization properties of the tissue and allows for more precise quantification of these properties is demonstrated.

Measuring absorption coefficient of scattering liquids using a tube inside an integrating sphere

A method for measuring the absorption coefficient μ_a of absorbing and scattering liquid samples is presented. The sample is injected into a small transparent tube mounted through an integrating sphere. Two models for determining the absorption coefficient using the relative optical output signal are described and validated using aqueous ink absorbers of 0.5 vol.% (0.3  mm^-1<μ_a<1.55  mm^-1) and 1.0 vol.% (1.0  mm^-1<μ_a<4.0  mm^-1) concentrations with 1 vol.% (μs'≈1.4  mm^-1) and 10 vol.% (μs'≈14  mm^-1) Intralipid dilutions. The low concentrations give μ_a and μ_s values, which are comparable with those of biological tissues. One model assumes a uniform light distribution within the sample, which is valid for low absorption. Another model considers light attenuation that obeys Lambert-Beer's law, which may be used for relatively high absorption. Measurements with low and high scattering samples are done for the wavelength range of 400-900 nm. Measured spectra of purely absorbing samples are within 15% agreement with measurements using standard transmission spectrophotometry. For 0.5 vol.% ink absorbers and at wavelengths below 700 nm, measured μ_a values are higher for samples with low scattering and lower for those with high scattering. At wavelengths above 700 nm, measured μ_a values do not vary significantly with amount of scattering. For 1.0 vol.% ink absorbers, measured spectra do not change with low scattering. These results indicate that the method can be used for measuring absorption spectra of scattering liquid samples with optical properties similar to biological absorbers, particularly at wavelengths above 700 nm, which is difficult to accomplish with standard transmission spectrophotometry.

Influence of multiple scattering and absorption on the full scattering profile and the isobaric point in tissue

Light reflectance and transmission from soft tissue has been utilized in noninvasive clinical measurement devices such as the photoplethysmograph (PPG) and reflectance pulse oximeter. Incident light on the skin travels into the underlying layers and is in part reflected back to the surface, in part transferred and in part absorbed. Most methods of near infrared (NIR) spectroscopy focus on the volume reflectance from a semi-infinite sample, while very few measure transmission. We have previously shown that examining the full scattering profile (angular distribution of exiting photons) provides more comprehensive information when measuring from a cylindrical tissue. Furthermore, an isobaric point was found which is not dependent on changes in the reduced scattering coefficient. The angle corresponding to this isobaric point depends on the tissue diameter. We investigated the role of multiple scattering and absorption on the full scattering profile of a cylindrical tissue. First, we define the range in which multiple scattering occurs for different tissue diameters. Next, we examine the role of the absorption coefficient in the attenuation of the full scattering profile. We demonstrate that the absorption linearly influences the intensity at each angle of the full scattering profile and, more importantly, the absorption does not change the position of the isobaric point. The findings of this work demonstrate a realistic model for optical tissue measurements such as NIR spectroscopy, PPG, and pulse oximetery.

Correction for tissue optical properties enables quantitative skin fluorescence measurements using multi-diameter single fiber reflectance spectroscopy

BACKGROUND AND OBJECTIVE

Fluorescence measurements in the skin are very much affected by absorption and scattering but existing methods to correct for this are not applicable to superficial skin measurements.

STUDY DESIGN/MATERIALS AND METHODS

The first use of multiple-diameter single fiber reflectance (MDSFR) and single fiber fluorescence (SFF) spectroscopy in human skin was investigated. MDSFR spectroscopy allows a quantification of the full optical properties in superficial skin (μa, μs' and γ), which can next be used to retrieve the corrected - intrinsic - fluorescence of a fluorophore Qμa,x(f). Our goal was to investigate the importance of such correction for individual patients. We studied this in 22 patients undergoing photodynamic therapy (PDT) for actinic keratosis.

RESULTS

The magnitude of correction of fluorescence was around 4 (for both autofluorescence and protoporphyrin IX). Moreover, it was variable between patients, but also within patients over the course of fractionated aminolevulinic acid PDT (range 2.7-7.5). Patients also varied in the amount of protoporphyrin IX synthesis, photobleaching percentages and resynthesis (>100× difference between the lowest and highest PpIX synthesis). The autofluorescence was lower in actinic keratosis than contralateral normal skin (0.0032 versus 0.0052; P<0.0005).

CONCLUSIONS

Our results clearly demonstrate the importance of correcting the measured fluorescence for optical properties, because these vary considerably between individual patients and also during PDT. Protoporphyrin IX synthesis and photobleaching kinetics allow monitoring clinical PDT which facilitates individual-based PDT dosing and improvement of clinical treatment protocols. Furthermore, the skin autofluorescence can be relevant for diagnostic use in the skin, but it may also be interesting because of its association with several internal diseases.

A new Monte Carlo program for simulating light transport through Port Wine Stain skin

A new Monte Carlo program is presented for simulating light transport through clinically normal skin and skin containing Port Wine Stain (PWS) vessels. The program consists of an eight-layer mathematical skin model constructed from optical coefficients described previously. A simulation including diffuse illumination at the surface and subsequent light transport through the model is carried out using a radiative transfer theory ray-tracing technique. Total reflectance values over 39 wavelengths are scored by the addition of simulated light returning to the surface within a specified region and surface reflections (calculated using Fresnel's equations). These reflectance values are compared to measurements from individual participants, and characteristics of the model are adjusted until adequate agreement is produced between simulated and measured skin reflectance curves. The absorption and scattering coefficients of the epidermis are adjusted through changes in the simulated concentrations and mean diameters of epidermal melanosomes to reproduce non-lesional skin colour. Pseudo-cylindrical horizontal vessels are added to the skin model, and their simulated mean depths, diameters and number densities are adjusted to reproduce measured PWS skin colour. Accurate reproductions of colour measurement data are produced by the program, resulting in realistic predictions of melanin and PWS blood vessel parameters. Using a modest personal computer, the simulation currently requires an average of five and a half days to complete.

Quantitative analysis of optical properties of flowing blood using a photon-cell interactive Monte Carlo code: effects of red blood cells' orientation on light scattering

Optical properties of flowing blood were analyzed using a photon-cell interactive Monte Carlo (pciMC) model with the physical properties of the flowing red blood cells (RBCs) such as cell size, shape, refractive index, distribution, and orientation as the parameters. The scattering of light by flowing blood at the He-Ne laser wavelength of 632.8 nm was significantly affected by the shear rate. The light was scattered more in the direction of flow as the flow rate increased. Therefore, the light intensity transmitted forward in the direction perpendicular to flow axis decreased. The pciMC model can duplicate the changes in the photon propagation due to moving RBCs with various orientations. The resulting RBC's orientation that best simulated the experimental results was with their long axis perpendicular to the direction of blood flow. Moreover, the scattering probability was dependent on the orientation of the RBCs. Finally, the pciMC code was used to predict the hematocrit of flowing blood with accuracy of approximately 1.0 HCT%. The photon-cell interactive Monte Carlo (pciMC) model can provide optical properties of flowing blood and will facilitate the development of the non-invasive monitoring of blood in extra corporeal circulatory systems.

Photon-cell interactive Monte Carlo model based on the geometric optics theory for photon migration in blood by incorporating both extra- and intracellular pathways

A photon-cell interactive Monte Carlo (pciMC) that tracks photon migration in both the extra- and intracellular spaces is developed without using macroscopic scattering phase functions and anisotropy factors, as required for the conventional Monte Carlos (MCs). The interaction of photons at the plasma-cell boundary of randomly oriented 3-D biconcave red blood cells (RBCs) is modeled using the geometric optics. The pciMC incorporates different photon velocities from the extra- to intracellular space, whereas the conventional MC treats RBCs as points in the space with a constant velocity. In comparison to the experiments, the pciMC yielded the mean errors in photon migration time of 9.8±6.8 and 11.2±8.5% for suspensions of small and large RBCs (RBC(small), RBC(large)) averaged over the optically diffusing region from 2000 to 4000 μm, while the conventional random walk Monte Carlo simulation gave statistically higher mean errors of 19.0±5.8 ( p < 0.047) and 21.7±19.1% (p < 0.055), respectively. The gradients of optical density in the diffusing region yielded statistically insignificant differences between the pciMC and experiments with the mean errors between them being 1.4 and 0.9% in RBC(small) and RBC(larger), respectively. The pciMC based on the geometric optics can be used to accurately predict photon migration in the optically diffusing, turbid medium.

In vitro assessment of optical properties of blood by applying the extended Huygens-Fresnel principle to time-domain optical coherence tomography signal at 1300 nm

A direct method for the measurement of the optical attenuation coefficient and the scattering anisotropy parameter based on applying the extended Huygens-Fresnel principle to optical coherence tomography images of blood is demonstrated. The images are acquired with a low-power probing beam at the wavelength of 1300 nm. Values of 12.15 mm⁻¹ and 0.95 are found for the total attenuation coefficient and the scattering anisotropy factor, respectively. Also, as a preliminary step, the optical refraction index is determined with a precision of two decimal numbers directly from optical coherence images. The total attenuation coefficient and the scattering anisotropy factor are determined with precisions within experimental error margins of 5% and 2%, respectively. Readable OCT signal is obtained for a maximum propagation of light into blood of 0.25 mm. At the maximum probed depth, the measured signal is almost 10³ smaller than its initial intensity when entering the sample.

A novel first principles approach for the estimation of the sieve factor of blood samples

Light may traverse a turbid material, such as blood, without encountering any of its pigment containing structures, a phenomenon known as sieve effect. This phenomenon may result in a decrease in the amount of light absorbed by the material. Accordingly, the corresponding sieve factor needs to be accounted for in optical investigations aimed at the derivation of blood biophysical properties from light transmittance measurements. The existing procedures used for its estimation either lack the flexibility required for practical applications or are based on general formulas that incorporate other light and matter interaction phenomena such as detour (scattering) effects. In this paper, a ray optics framework is proposed to estimate the sieve factor for blood samples. It employs a first principles approach to account for the distribution, orientation and shape of the cells that contain hemoglobin, the essential (oxygen-carrying) pigment found in human blood. Within this framework, ray-casting techniques are used to determine the probability that light can traverse a blood sample without encountering any of these cells. The predictive capabilities of the proposed framework are demonstrated through a series of in silico experiments. Its effectiveness is further illustrated by visualizations depicting the different blood parameterizations considered in the simulations.

Cultured human keratinocytes for optical transmission measurement

The challenges of measuring optical properties of human tissues include the thickness of the sample, homogenization, or crystallization from freezing of the tissue. This investigation demonstrates a method to avoid these problems by growing optically thin samples of human keratinocytes as a substitute for ex vivo epidermis samples. Several methods of growth were investigated. Resulting samples were measured on a spectrophotometer for transmission between 300 nm and 2600 nm. The efficacy of the cell growth was confirmed with histological examination of several cultured keratinocyte samples. Limitations were the requirement to measure samples immediately after removal from the incubation environment, and the absence of the irregular structures of normal skin such as hair and glands.

Measurement and numerical studies of optical properties of YAG:Ce phosphor for white light-emitting diode packaging

The optical properties of YAG:Ce phosphor were measured by a double-integrating-sphere system and calculated by Mie theory and Monte Carlo ray tracing to provide precise optical characterizations of YAG:Ce phosphor for white light-emitting diode (LED) packaging design. Measurement results showed that the phosphor presents strong absorption for blue light, high reflection for yellow light, and an isotropic emission pattern of converted light. The conversion efficiency and quantum efficiency for the saturated phosphor are around 70% and 87%, respectively. Based on the measurement results, the absorption coefficient, scattering coefficient, and anisotropy factor of the phosphor calculated by Mie theory were compared with those calculated by ray-tracing simulation to modify Mie theory to find a reasonable method that can easily obtain the optical constants of YAG:Ce phosphor. Comparisons revealed that Mie theory can predict the variation of the optical constants of phosphor, but the absorption and scattering cross sections should be multiplied with two fitting parameters. The fitting parameters have been given in this study and can be obtained by testing packaged LEDs with different phosphor concentrations.

Aggregation of red blood cells in suspension: study by light-scattering technique at small angles

Red blood cells (RBCs) in the presence of plasma proteins or other macromolecules have a tendency to form aggregates. Light-scattering technique was used to investigate the RBC aggregation process. A highly diluted suspension of RBCs was illuminated with a 632.8-nm HeNe laser. Angular-resolved measurements of light intensity scattered by an RBC suspension from a 200-microm thick optical glass cuvette during 10 min of their aggregation process were performed at 1 to 4 off-axis deg with a very high angular resolution, at hematocrits in the range of 3.5 x 10(-2) to 10(-1). The angular spreading of forward-scattered light at small angles during the RBC aggregation process was described in terms of a new, effective phase function model that has been used for fitting the experimental data. The aggregated RBCs' optical properties, such as effective scattering anisotropy and scattering cross section, were determined. The results were compared with prediction of Mie theory for equivolumetric spherical particles. The time dependence of the aggregates mean radius and of the mean number of cells per aggregate was also calculated. Last, the potential of the proposed technique (forward-scattering light technique) as a new quantitative investigation of cellular aggregation process was estimated.

Photochemical cross-linking for collagen-based scaffolds: a study on optical properties, mechanical properties, stability, and hematocompatibility

Collagen presents an attractive biomaterial for tissue engineering because of its excellent biocompatibility and negligible immunogenicity. However, some intrinsic features related to the mechanical stability and thrombogenicity limit its applications in orthopedic and vascular tissue engineering. Photochemical cross-linking is an emerging technique able to stabilize tissue grafts and improve the physicochemical properties of collagen-based structures. However, other important properties of collagen-based structures and the effect of processing parameters on these properties have not been explored. In this study, we aim to investigate the dose dependence of tensile and swelling properties on two parameters, namely, laser energy fluence and rose Bengal photosensitizer concentration. We also study the compression properties using cyclic compression test, long-term stability using subcutaneous implantation, and hematocompatibility using platelets adhesion test, of cross-linked collagen structures. Moreover, because limited optical penetration in turbid media is the major obstacle for light-based techniques, we also characterize the optical properties, which partially determine the effective optical penetration depth in collagen gel samples, during photochemical cross-linking. Laser energy fluence and rose Bengal concentration are important parameters affecting the cross-linking efficiency, which was characterized as the mechanical and the swelling properties, in a dose-dependent manner. Under the experimental conditions in this study, the peak fluence was 12.5 J/cm2 and the minimal rose Bengal concentration for effective cross-linking was >0.00008% (0.786 micromol). Photochemical cross-linking also enhanced the compression strength and long-term stability of collagen structures without compromising the tissue compatibility. Furthermore, photochemical cross-linking reduced platelet adhesion and abolished fibrin mesh formation, thereby improving the hematocompatibility of collagen structures. These results suggest the feasibility of using the photochemically cross-linked collagen structures for orthopedic and vascular tissue engineering. Finally, the effective optical penetration depth in collagen gel samples is wavelength and rose Bengal concentration dependent, and was approximately 12 mm at 514 nm at 0.001% (9.825 micromol), the rose Bengal concentration mostly used in this study.

Empirical model functions to calculate hematocrit-dependent optical properties of human blood

The absorption coefficient, scattering coefficient, and effective scattering phase function of human red blood cells (RBCs) in saline solution were determined for eight different hematocrits (Hcts) between 0.84% and 42.1% in the wavelength range of 250-1100 nm using integrating sphere measurements and inverse Monte Carlo simulation. To allow for biological variability, averaged optical parameters were determined under flow conditions for ten different human blood samples. Based on this standard blood, empirical model functions are presented for the calculation of Hct-dependent optical properties for the RBCs. Changes in the optical properties when saline solution is replaced by blood plasma as the suspension medium were also investigated.

Study on the error in the dynamic spectrum method relative with the pathlength factor as a function of wavelength

Utilizing near-infrared spectroscopy for non-invasive blood component concentration sensing has been a focusing topic in biomedical optics applications. The ease of use, low cost and portability of these methods is a clear advantage over the invasive blood component concentration sensing which is the main sensing method in the clinic application. However, there is no report about any successful non-invasive blood components (except the artery blood oxygen saturation) concentration detection techniques that can meet the requirements of clinic application. One of the most key difficulties is the influence of the individual discrepancy. Dynamic spectrum (DS) is a new measure method of non-invasive blood components concentration sensing presented recently. It can eliminate the individual discrepancy of the tissues except the pulsatile component of the artery blood (PCAB) theoretically. This indicates a brand new way to measure the blood components concentration and a potential to provide absolute quantitation of hemodynamic variables. One of the systematic errors in the calculation of the component changes from NIRS data of the dynamic spectrum is the absolute magnitudes and relative differences in pathlength factors as a function of wavelength. Monte Carlo simulations are used in this paper to examine the importance and mitigation methods of this error while the photoelectric pulse wave is detected on the finger tip. We found wavelength selection to be important variables in minimizing such errors, and replacing the average pathlength factor with the subsection pathlength factor appropriately could reduce the error to a small fraction (10%).

Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range

The optical parameters absorption coefficient, scattering coefficient, and the anisotropy factor of platelets (PLTs) suspended in plasma and cell-free blood plasma are determined by measuring the diffuse reflectance, total and diffuse transmission, and subsequently by inverse Monte Carlo simulation. Furthermore, the optical behavior of PLTs and red blood cells suspended in plasma are compared with those suspended in saline solution. Cell-free plasma shows a higher scattering coefficient and anisotropy factor than expected for Rayleigh scattering by plasma proteins. The scattering coefficient of PLTs increases linearly with the PLT concentration. The existence of physiological concentrations of leukocytes has no measurable influence on the absorption and scattering properties of whole blood. In summary, red blood cells predominate over the other blood components by two to three orders of magnitude with regard to absorption and effective scattering. However, substituting saline solution for plasma leads to a significant increase in the effective scattering coefficient and therefore should be taken into consideration.

Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions

The absorption coefficient mu(a), scattering coefficient mu(s), and anisotropy factor g of diluted and undiluted human blood (hematocrit 0.84 and 42.1%) are determined under flow conditions in the wavelength range 250 to 1100 nm, covering the absorption bands of hemoglobin. These values are obtained by high precision integrating sphere measurements in combination with an optimized inverse Monte Carlo simulation (IMCS). With a new algorithm, appropriate effective phase functions could be evaluated for both blood concentrations using the IMCS. The best results are obtained using the Reynolds-McCormick phase function with the variation factor alpha = 1.2 for hematocrit 0.84%, and alpha = 1.7 for hematocrit 42.1%. The obtained data are compared with the parameters given by the Mie theory. The use of IMCS in combination with selected appropriate effective phase functions make it possible to take into account the nonspherical shape of erythrocytes, the phenomenon of coupled absorption and scattering, and multiple scattering and interference phenomena. It is therefore possible for the first time to obtain reasonable results for the optical behavior of human blood, even at high hematocrit and in high hemoglobin absorption areas. Moreover, the limitations of the Mie theory describing the optical properties of blood can be shown.

High-resolution angle-resolved measurements of light scattered at small angles by red blood cells in suspension

Red blood cells (RBCs) scatter light mainly in the forward direction, where the scattering phase function has a narrow peak. We performed an experimental investigation into the angular distribution of light scattered by blood in the small-angle domain. A highly diluted suspension of RBCs (hematocrits in the range 5 x 10(-5)-10(-2)) was illuminated with a He-Ne laser with 633 nm wavelength. We focused our research on two main topics: the scattering efficiency of the RBCs given by the mean scattering cross section and the scattering anisotropy obtained from the angular distribution of the scattered photons. The collimated beam transmission and the angular distribution of scattered light were measured and compared with the predictions of the effective phase function model. The RBCs' mean scattering cross section and scattering anisotropy were obtained by fitting of the experimental data.

Effective phase function for light scattered by blood

The scattering process induced in blood by a collimated laser beam is theoretically investigated. An individual red blood cell (RBC) has a scattering phase function strongly peaked in the forward direction. For far-field experiments, the small scattering volumes can be considered as "macroscopic particles" characterized by an effective scattering phase function. Using the single-cell phase function as "input data" the angular distribution of light scattered at small angles by the whole scattering volume, containing RBCs in suspension, is calculated analytically. The angular dispersion of the light scattered by blood can be approximately described by the same formula used to characterize the light scattered by a single cell but with an effective, hematocrit-dependent anisotropy parameter.

Real-time absorption and scattering characterization of slab-shaped turbid samples obtained by a combination of angular and spatially resolved measurements

We present a fast and accurate method for real-time determination of the absorption coefficient, the scattering coefficient, and the anisotropy factor of thin turbid samples by using simple continuous-wave noncoherent light sources. The three optical properties are extracted from recordings of angularly resolved transmittance in addition to spatially resolved diffuse reflectance and transmittance. The applied multivariate calibration and prediction techniques are based on multiple polynomial regression in combination with a Newton--Raphson algorithm. The numerical test results based on Monte Carlo simulations showed mean prediction errors of approximately 0.5% for all three optical properties within ranges typical for biological media. Preliminary experimental results are also presented yielding errors of approximately 5%. Thus the presented methods show a substantial potential for simultaneous absorption and scattering characterization of turbid media.

Blood cell counting and classification by nonflowing laser light scattering method

We present a nonflowing laser light scattering method for automatically counting and classifying blood cells. A linear charge-coupled device (CCD) and a silicon photoelectric cell (which is placed behind a pinhole plate on the CCD) form a double-detector structure: the CCD is used to detect the scattered light intensity distribution of the blood cells and the silicon photoelectric cell to complete the focusing process. An isotropic sphere, with relative refractivity near 1, is used to model the blood cell. Mie theory is used to describe the scattering of white blood cells and platelets, and anomalous diffraction, red blood cells. To obtain the size distribution of blood cells from their scattered light intensity distribution, the nonnegative constraint least-squares (NNLS) method combined with the Powell method and the precision punishment method are used. Both numerical simulation and experimental results are presented. This method can be used not only to measure the mean and the distribution of red blood cell size, but also to divide the white blood cells into three classes: lymphocytes, middle-sized cells, and neutrocytes. The experimental results show a linear relationship between the blood cell (both white and red blood cells) concentration and the scattered light intensity, and therefore, the number of blood cells in a unit volume can be determined from this relationship.

Influence of cell shape and aggregate formation on the optical properties of flowing whole blood

We studied the influence of shape and secondary, or intercellular, organization on the absorption and scattering properties of red blood cells to determine whether these properties are of any practical significance for optical evaluation of whole blood and its constituents. A series of measurements of transmittance and reflectance of light from bovine blood in a flow cuvette was conducted with a 650-900-nm integrating sphere at shear rates of 0-1600 s(-1), from which the influence of cell orientation, elongation, and aggregate formation on the absorption (mu(a)) and the reduced scattering (mu(s)') coefficients could be quantified. Aggregation was accompanied by a decrease of 4% in mu(s)' compared with the value in randomly oriented single cells. Increasing the degree of cell alignment and elongation as a result of increasing shear rate reduced mu(s)' by 6% and mu(a) by 3%, evaluated at a shear rate of 1600 s(-1). Comparison with T-matrix computations for oblate- and prolate-shaped cells with corresponding elongation and orientation indicates that the optical properties of whole blood are determined by those of its individual cells, though influenced by a collective scattering factor that depends on the cell-to-cell organization. We demonstrate that cell morphological changes must be taken into consideration when one is conducting whole blood spectroscopy.

A scattering phase function for blood with physiological haematocrit

Though the optics of red blood cells as well as whole blood has been studied extensively, an effective scattering phase function for whole blood is still needed. The interference of waves scattered by neighbouring cells cannot be neglected in highly concentrated suspensions such as whole blood. As a result, the phase function valid for single erythrocytes may fail to describe a single scattering process in whole blood with physiological haematocrit (Hct approximately 0.4). In this study we compared the results obtained in goniophotometric measurements of blood samples with the results of angle-resolved Monte Carlo simulations. The results show that a Henyey-Greenstein phase function with an anisotropy factor of 0.972 is an adequate approximation for the effective scattering phase function of whole blood with high haematocrit at a wavelength of 514 nm.

Blood-flow measurements with a small number of scattering events

Results of simulations of the diffraction of a laser beam by a small blood vessel imbedded in scattering tissue are presented. The form of the spectra of biospeckle intensity fluctuations is analyzed. The Doppler shift of intensity fluctuations of scattered light is investigated as a function of the laser beam radius, the radius of the blood vessel, the depth of the vessel in the tissue, and the scattering characteristics of flowing blood. A formula that serves as the basis for a method of absolute measurements of blood-flow velocity is derived.

Multiple polynomial regression method for determination of biomedical optical properties from integrating sphere measurements

We present a new, to our knowledge, method for extracting optical properties from integrating sphere measurements on thin biological samples. The method is based on multivariate calibration techniques involving Monte Carlo simulations, multiple polynomial regression, and a Newton-Raphson algorithm for solving nonlinear equation systems. Prediction tests with simulated data showed that the mean relative prediction error of the absorption and the reduced scattering coefficients within typical biological ranges were less than 0.3%. Similar tests with data from integrating sphere measurements on 20 dye-polystyrene microsphere phantoms led to mean errors less than 1.7% between predicted and theoretically calculated values. Comparisons showed that our method was more robust and typically 5-10 times as fast and accurate as two other established methods, i.e., the inverse adding-doubling method and the Monte Carlo spline interpolation method.

Effect of multiple light paths on retinal vessel oximetry

Techniques for noninvasively measuring the oxygen saturation of blood in retinal arteries and veins are reported in the literature, but none have been sufficiently accurate and reliable for clinical use. Addressing the need for increased accuracy, we present a series of oximetric equations that explicitly consider the effects of backscattering by red blood cells and lateral diffusion of light in the ocular fundus. The equations are derived for the specific geometry of a scanning-beam retinal vessel oximeter; however, the results should also be applicable to photographic oximeters. We present in vitro and in vivo data that suggest the validity of these equations.