Single scattering by red blood cells

Influence of oxygen saturation on the optical scattering properties of human red blood cells in the spectral range 250 to 2,000 nm

The intrinsic optical parameters absorption coefficient mu(a), scattering coefficient micros, anisotropy factor g, and effective scattering coefficient micros were determined for human red blood cell (RBC) suspensions of hematocrit 33.2% dependent on the oxygen saturation (SAT O(2)) in the wavelength range 250 to 2,000 nm, including the range above 1,100 nm, about which there are no data available in the literature. Integrating sphere measurements of light transmittance and reflectance in combination with inverse Monte Carlo simulation were carried out for SAT O(2) levels of 100 and 0%. In the wavelength range up to 1,200 nm, the absorption behavior is determined by the hemoglobin absorption. The spectral range above the cells' absorption shows no dependence on SAT O(2) and approximates the absorption of water with values 20 to 30% below the respective values for water. Parameters micros and g are significantly influenced by the SAT O(2)-induced absorption changes. Above 600 nm, micros decreases continuously from values of 85 mm(-1) to values of 30 mm(-1) at 2,000 nm. The anisotropy factor shows a slight decrease with wavelengths above 600 nm. In the spectral regions of 1,450 and 1,900 nm where water has local absorption maxima, g shows a significant decrease down to 0.85, whereas micros increases.

Whole blood reflectance for assessment of hematologic condition and detection of angiographic contrast media

We present simple whole blood reflectance analyses in the range 500-900 nm, using intact whole blood to simultaneously quantify hematocrit and oxygen saturation from a single spectral reading. We applied these results for the development of an intravascular catheter-based reflectance sensing system to detect and remove contrast media injected during angiography so as to reduce the risk of complications associated with the injected contrast media. We further tested the practicality of the optical detection of angiographic contrast media in a pilot animal study in vivo. We successfully demonstrated the feasibility of real-time in vivo contrast detection and removal during angiography. Our simple method for the detection and removal of angiographic contrast media will facilitate the development of intravascular optical sensing systems.

Autofocusing and edge detection schemes in cell volume measurements with quantitative phase microscopy

We have proposed and demonstrated a very sensitive volume measurement scheme for a live cell with a quantitative phase microscopy (QPM) utilizing auto-focusing and numerical edge detection schemes. An auto-focusing technique with two different focus measures is applied to find the focus dependent errors in our live cell volume measurement system. The volume of a polystyrene bead sample with 3 mum diameter has been measured for the validity test of our proposed method. We have shown that a small displacement of an object from its focusing position can cause a large volume error. A numerical edge detection technique is also used to accurately resolve the boundary between a cell and its suspension medium. We have applied this method to effectively suppress errors by the surrounding medium of a single red blood cell (RBC).

Diffraction Phase Cytometry: blood on a CD-ROM

We demonstrate Diffraction Phase Cytometry (DPC) as a single shot, full-field, high throughput quantitative phase imaging modality, dedicated to analyzing whole blood smears. Utilizing a commercial CD as a sample substrate, along with dynamic spatial filtering via a liquid crystal spatial light modulator, we have developed a compact instrument capable of making quantitative, physiologically relevant measurements. To illustrate the ability of the system to function as a highly sensitive cytometer we imaged a large number (N=1,537) of live human erythrocytes in whole blood without preparation. We retrieved a comprehensive set of geometrical parameters including cell volume and surface area, which are not directly available using existing cytometers. Furthermore, we retrieved the minimum cylindrical diameter, through which red blood cells can pass, and deliver oxygen. These initial results prove the concept for an inexpensive lab-on-a-chip blood screening device.

Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses

We demonstrate the fabrication of integrated three-dimensional microchannel and optical waveguide structures inside fused silica for the interrogation and processing of single cells. The microchannels are fabricated by scanning femtosecond laser pulses (523 nm) and subsequent selective wet etching process. Optical waveguides are additionally integrated with the fabricated microchannels by scanning the laser pulse train inside the glass specimen. Single red blood cells (RBC) in diluted human blood inside of the manufactured microchannel were detected by two optical schemes. The first involved sensing the intensity change of waveguide-delivered He-Ne laser light (632.8 nm) induced by the refractive index difference of a cell flowing in the channel. The other approach was via detection of fluorescence emission from dyed RBC excited by Ar laser light (488 nm) delivered by the optical waveguide. The proposed device was tested to detect 23 fluorescent particles per second by increasing the flow rate up to 0.5 microl min(-1). The optical cell detection experiments support potential implementation of a new generation of glass-based optofluidic biochip devices in various single cell treatment processes including laser based cell processing and sensing.

Full-field laser-Doppler imaging and its physiological significance for tissue blood perfusion

Using Monte Carlo simulations for a semi-infinite medium representing a skeletal muscle tissue, it is demonstrated that the zero- and first-order moments of the power spectrum for a representative pixel of a full-field laser-Doppler imager behave differently from classical laser-Doppler flowmetry. In particular, the zero-order moment has a very low sensitivity to tissue blood volume changes, and it becomes completely insensitive if the probability for a photon to interact with a moving red blood cell is above 0.05. It is shown that the loss in sensitivity is due to the strong forward scatter of the propagating photons in biological tissues (i.e., anisotropy factor g = 0.9). The first-order moment is linearly related to the root mean square of the red blood cell velocity (the Brownian component), and there is also a positive relationship with tissue blood volume. The most common physiological interpretation of the first-order moment is as tissue blood volume times expectation of the blood velocity (in probabilistic terms). In this sense, the use of the first-order moment appears to be a reasonable approach for qualitative real-time blood flow monitoring, but it does not allow us to obtain information on blood velocity or volume independently. Finally, it is shown that the spatial and temporal resolution trade-off imposed by the CMOS detectors, used in full-field laser-Doppler hardware, may lead to measurements that vary oppositely with the underlying physiological quantities. Further improvements on detectors' sampling rate will overcome this limitation.

Quantitative interpretations of Visible-NIR reflectance spectra of blood

This paper illustrates the implementation of a new theoretical model for rapid quantitative analysis of the Vis-NIR diffuse reflectance spectra of blood cultures. This new model is based on the photon diffusion theory and Mie scattering theory that have been formulated to account for multiple scattering populations and absorptive components. This study stresses the significance of the thorough solution of the scattering and absorption problem in order to accurately resolve for optically relevant parameters of blood culture components. With advantages of being calibration-free and computationally fast, the new model has two basic requirements. First, wavelength-dependent refractive indices of the basic chemical constituents of blood culture components are needed. Second, multi-wavelength measurements or at least the measurements of characteristic wavelengths equal to the degrees of freedom, i.e. number of optically relevant parameters, of blood culture system are required. The blood culture analysis model was tested with a large number of diffuse reflectance spectra of blood culture samples characterized by an extensive range of the relevant parameters.

Quantitative phase evaluation of dynamic changes on cell membrane during laser microsurgery

The ability to inject exogenous material as well as to alter subcellular structures in a minimally invasive manner using a laser microbeam has been useful for cell biologists to study the structure-function relationship in complex biological systems. We describe a quantitative phase laser microsurgery system, which takes advantage of the combination of laser microirradiation and short-coherence interference microscopy. Using this method, quantitative phase images and the dynamic changes of phase during the process of laser microsurgery of red blood cells (RBCs) can be evaluated in real time. This system would enable absolute quantitation of localized alteration/damage to transparent phase objects, such as the cell membrane or intracellular structures, being exposed to the laser microbeam. Such quantitation was not possible using conventional phase-contrast microscopy.

Simplified spectraphotometric method for the detection of red blood cell agglutination

Human error is the most significant factor attributed to incompatible blood transfusions. A spectrophotometric approach to blood typing has been developed by examining the spectral slopes of dilute red blood cell (RBC) suspensions in saline, in the presence and absence of various antibodies, offering a technique for the quantitative determination of agglutination intensity [Transfusion39, 1051, 1999TRANAT0041-113210.1046/j.1537-2995.1999.39101051.x]. We offer direct theoretical prediction of the observed change in slope in the 660-1000 nm range through the use of the T-matrix approach and Lorenz-Mie theory for light scattering by dilute RBC suspensions. Following a numerical simulation using the T-matrix code, we present a simplified sensing method for detecting agglutination. The sensor design has been prototyped, fully characterized, and evaluated through a complete set of tests with over 60 RBC samples and compared with the full spectrophotometric method. The LED and photodiode pairs are found to successfully reproduce the spectroscopic determination of red blood cell agglutination.

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.

Optical microcirculatory skin model: assessed by Monte Carlo simulations paired with in vivo laser Doppler flowmetry

An optical microvascular skin model, valid at 780 nm, was developed. The model consisted of six layers with individual optical properties and variable thicknesses and blood concentrations at three different blood flow velocities. Monte Carlo simulations were used to evaluate the impact of various model parameters on the traditional laser Doppler flowmetry (LDF) measures. A set of reference Doppler power spectra was generated by simulating 7000 configurations, varying the thickness and blood concentrations. Simulated spectra, at two different source detector separations, were compared with in vivo recorded spectra, using a nonlinear search algorithm for minimizing the deviation between simulated and measured spectra. The model was validated by inspecting the thickness and blood concentrations that generated the best fit. These four parameters followed a priori expectations for the measurement situations, and the simulated spectra agreed well with the measured spectra for both detector separations. Average estimated dermal blood concentration was 0.08% at rest and 0.63% during heat provocation (44 degrees C) on the volar side of the forearm and 1.2% at rest on the finger pulp. The model is crucial for developing a technique for velocity-resolved absolute LDF measurements with known sampling volume and can also be useful for other bio-optical modalities.

Influence of shear rate on the optical properties of human blood in the spectral range 250 to 1100 nm

The intrinsic optical parameters-absorption coefficient mua, scattering coefficient mus, anisotropy factor g, and effective scattering coefficient mus'--are determined for human red blood cells of hematocrit 42.1% dependent on the shear rate in the wavelength range 250 to 1100 nm. Integrating sphere measurements of light transmittance and reflectance in combination with inverse Monte-Carlo simulation are carried out for different wall shear rates between 0 and 1000 s(-1). Randomly oriented cells show maximal mua, mus, and mus' values. Cell alignment and elongation, as well as the Fahraeus effect at increasing shear rates, lead to an asymptotical decrease of these values. The anisotropy factor shows this behavior only below 600 nm, dependent on absorption; above 600 nm, g is almost independent of shear rate. The decrease of mus' is inversely correlated with the hemoglobin absorption. Compared to randomly oriented cells, aggregation reduces all parameters by a different degree, depending on the hemoglobin absorption. It is possible to evaluate the influence of collective scattering phenomena, the absorption within the cell, and the cell shape.

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.

Optical diagnostic technology based on light scattering spectroscopy for early cancer detection

This article reviews the application of optical diagnostic technology based on light scattering spectroscopy for minimally invasive detection of precancerous and early cancerous changes in a variety of organs. Optical spectroscopic techniques have shown promising results in the diagnosis of diseases at the cellular scale. They do not require tissue removal, can be performed in vivo and allow for real-time diagnosis. While fluorescence and Raman spectroscopy are most effective in revealing the molecular properties of tissue, the novel technique, light scattering spectroscopy, is capable of characterizing the structural properties of tissue at the cellular and subcellular scale.

Optical measurement of cell membrane tension

Using a novel noncontact technique based on optical interferometry, we quantify the nanoscale thermal fluctuations of red blood cells (RBCs) and giant unilamellar vesicles (GUVs). The measurements reveal a nonvanishing tension coefficient for RBCs, which increases as cells transition from a discocytic shape to a spherical shape. The tension coefficient measured for GUVs is, however, a factor of 4-24 smaller. By contrast, the bending moduli for cells and vesicles have similar values. This is consistent with the cytoskeleton confinement model, in which the cytoskeleton inhibits membrane fluctuations [Gov et al., Phys. Rev. Lett. 90, 228101, (2003).

Observation of dynamic subdomains in red blood cells

We quantify the nanoscale structure and low-frequency dynamics associated with live red blood cells. The membrane displacements are measured using quantitative phase images provided by Fourier phase microscopy, with an average path-length stability of 0.75 nm over 45 min. The results reveal the existence of dynamic, independent subdomains across the cells that fluctuate at various dominant frequencies.

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.

Model function to calculate the refractive index of native hemoglobin in the wavelength range of 250-1100 nm dependent on concentration

The real part of the complex refractive index of oxygenated native hemoglobin solutions dependent on concentration was determined in the wavelength range 250 to 1100 nm by Fresnel reflectance measurements. The hemoglobin solution was produced by physical hemolysis of human erythrocytes followed by ultracentrifugation and filtration. A model function is presented for calculating the refractive index of hemoglobin solutions depending on concentration in the wavelength range 250 to 1100 nm.

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.

Diffraction phase microscopy for quantifying cell structure and dynamics

We have developed diffraction phase microscopy as a new technique for quantitative phase imaging of biological structures. The method combines the principles of common path interferometry and single-shot phase imaging and is characterized by subnanometer path-length stability and millisecond-scale acquisition time. The potential of the technique for quantifying nanoscale motions in live cells is demonstrated by experiments on red blood cells.

Phase function measurements on nonspherical scatterers using a two-axis goniometer

We present a two-axis goniometer for measuring the phase function of scattering media with an angular resolution of about 0.2 deg having 12 decades of dynamic range and covering almost the full solid angle. The setup is evaluated with polystyrene spheres and with perpendicularly and obliquely illuminated thin glass cylinders. The scattering pattern and its intensity distribution are in excellent agreement with analytical theory. A multiple scattering configuration composed of two parallel cylinders is also examined. Finally, the phase function of dentin slabs is measured and its dependence on the dental microstructure is discussed.

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.

Absorption and scattering coefficient dependence of laser-Doppler flowmetry models for large tissue volumes

Based on quasi-elastic scattering theory (and random walk on a lattice approach), a model of laser-Doppler flowmetry (LDF) has been derived which can be applied to measurements in large tissue volumes (e.g. when the interoptode distance is >30 mm). The model holds for a semi-infinite medium and takes into account the transport-corrected scattering coefficient and the absorption coefficient of the tissue, and the scattering coefficient of the red blood cells. The model holds for anisotropic scattering and for multiple scattering of the photons by the moving scatterers of finite size. In particular, it has also been possible to take into account the simultaneous presence of both Brownian and pure translational movements. An analytical and simplified version of the model has also been derived and its validity investigated, for the case of measurements in human skeletal muscle tissue. It is shown that at large optode spacing it is possible to use the simplified model, taking into account only a 'mean' light pathlength, to predict the blood flow related parameters. It is also demonstrated that the 'classical' blood volume parameter, derived from LDF instruments, may not represent the actual blood volume variations when the investigated tissue volume is large. The simplified model does not need knowledge of the tissue optical parameters and thus should allow the development of very simple and cost-effective LDF hardware.

Toward a velocity-resolved microvascular blood flow measure by decomposition of the laser Doppler spectrum

Tissue microcirculation, as measured by laser Doppler flowmetry (LDF), comprises capillary, arterial, and venous blood flow. With the classical LDF approach, it has been impossible to differentiate between different vascular compartments. We suggest an alternative LDF algorithm that estimates at least three concentration measures of flowing red blood cells (RBCs), each associated with a predefined, physiologically relevant, absolute velocity in millimeters per second. As the RBC flow velocity depends on the dimension of the blood vessel, this approach might enable a microcirculatory flow differentiation. The LDF concentration estimates are derived by fitting predefined Monte Carlo simulated, single-velocity spectra to a measured, multiple-velocity LDF spectrum. Validation measurements, using both single- and double-tube flow phantoms perfused with a microsphere solution, show that it is possible to estimate velocity and concentration changes, and to differentiate between flows with different velocities. Our theory is also applied to RBC flow measurements. A Gegenbauer kernel phase function (alpha(gk)=1.05; g(gk)=0.93), with an anisotropy factor of 0.987 at 786 nm, is found suitable for modeling Doppler scattering by RBCs diluted in physiological saline. The method is developed for low concentrations of RBCs, but can in theory be extended to cover multiple Doppler scattering.

Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements

The complex refractive index of highly concentrated hemoglobin solutions as they appear in red blood cells are determined in the wavelength range of 250 to 1100 nm using transmittance and Fresnel reflectance measurements. The determined real parts of the refractive indices are on average 0.02 units higher than the values found in the literature. The wavelength dependence of the measured data in the UV region differs from the calculated data using the Kramers-Kronig relation.

Erythrocyte structure and dynamics quantified by Hilbert phase microscopy

We present a new quantitative method for investigating red blood cell morphology and dynamics. The instrument integrates quantitative phase microscopy with an inverted microscope, which makes it particularly suitable for the noninvasive assessment of live erythrocytes. In particular, we demonstrate the ability of this approach to quantify noninvasively cell volume and dynamic morphology. The subnanometer path-length sensitivity at the millisecond time scales is exemplified by measuring the hemoglobin flow out of the cell during hemolysis.

In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: accuracy and resolution

Pulsed photoacoustic spectroscopy was used to measure blood oxygen saturation in vitro. An optical parametric oscillator laser system provided nanosecond excitation pulses over the wavelength range 740-1040 nm which were used to generate photoacoustic signals in a cuvette through which a saline suspension of red blood cells was circulated. The signal amplitude and the effective attenuation coefficient were extracted from the photoacoustic signals as a function of wavelength to provide photoacoustic spectra of the blood. From these, the relative concentrations of oxy- and deoxyhaemoglobin, and therefore blood oxygen saturation (SO2), were determined using forward models of the absorbed energy distribution based on diffusion theory. A standard linear model of the dependence of absorbance on the concentration of chromophores was also used to calculate the blood oxygen saturation from the signal amplitude spectra. The diffusion approximation model was shown to produce the highest accuracy in blood SO2. The photoacoustically determined oxygen saturation was found to have an accuracy of +/-4% SO2 for signal amplitude data and +/-2.5% SO2 for effective attenuation spectra. The smallest change in oxygen saturation that can be measured using this technique was +/-1% SO2.

Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy

We use near-infrared dynamic multiple scattering of light [diffusing-wave spectroscopy (DWS)] to detect the activation of the somato-motor cortex in 11 right-handed volunteers performing a finger opposition task separately with their right and left hands. Temporal autocorrelation functions g(1)(r,tau) of the scattered light field are measured during 100-s periods of motor task alternating with 100-s resting baseline periods. From an analysis of the experimental data with an analytical theory for g(1)(r,tau) from a three-layer geometry with optical and dynamical heterogeneity representing scalp, skull, and cortex, we obtain quantitative estimates of the diffusion coefficient in cortical regions. Consistent with earlier results, the measured cortical diffusion coefficient is found to be increased during the motor task, with a strong contralateral and a weaker ipsilateral increase consistent with the known brain hemispheric asymmetry for right-handed subjects. Our results support the interpretation of the increase of the cortical diffusion coefficient during finger opposition being due to the functional increase in cortical blood flow rate related to vasodilation.

A method to evaluate the effect of liposome lipid composition on its interaction with the erythrocyte plasma membrane

Lipid aggregates are considered promising carriers for macromolecules and toxic drugs. In order to fulfill this function, aggregates should have properties that ensure the efficient delivery of their cargo to the desired location. One of these properties is their stability in blood when accumulating in the targeted tissue. This stability may be affected by a number of factors, including enzymatic activity, protein adsorption, and non-specific lipid exchange between the aggregate and morphological blood components. Since blood cells in the majority consist of erythrocytes, their interaction with aggregates should be carefully analyzed. In this paper, we present a method that allows the exchange of lipid between liposomes and the erythrocyte plasma membrane to be evaluated. The extent of this exchange was measured in terms of the toxicity of a cationic lipid (DOTAP) incorporated into the liposome lipid bilayer, evaluated by plasma membrane mechanical properties. After liposomes were formed from DOTAP/PC or DOTAP/PE mixtures, erythrocyte plasma membranes were destabilized in a manner dependent on DOTAP concentration. A constant quantity of DOTAP mixed with various proportions of SM caused no such effect, indicating very limited lipid exchange with the cell membrane for such liposome formulations.

3-D simulation of light scattering from biological cells and cell differentiation

A 3-D code for solving the set of Maxwell equations with the finite-difference time-domain method is developed for simulating the propagation and scattering of light in biological cells under realistic conditions. The numerical techniques employed in this code include the Yee algorithm, absorbing boundary conditions, the total field/scattered field formulation, the discrete Fourier transformation, and the near-to-far field transform using the equivalent electric and magnetic currents. The code is capable of simulating light scattering from any real cells with complex internal structure at all angles, including backward scattering. The features of the scattered light patterns in different situations are studied in detail with the objective of optimizing the performance of cell diagnostics employing cytometry. A strategy for determining the optimal angle for measuring side scattered light is suggested. It is shown that cells with slight differences in their intrastructure can be distinguished with two-parameter cytometry by measuring the side scattered light at optimal angles.

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.

Oxygen saturation-dependent absorption and scattering of blood

We report on the scattering properties of oxygenated and deoxygenated whole blood from 250 to 1000 nm. We determine the complex refractive index of oxygenated and deoxygenated hemoglobin using a Kramers-Kronig analysis and optical coherence tomography measurements. Combining these data with Mie theory, the scattering properties are calculated. The strong oxygen saturation dependent scattering effects should be taken into account in the data analysis of optical oxymetry.

Beam propagation in sharply peaked forward scattering media

We calculate the radiance of a light beam propagating in a uniformly scattering and absorbing slab and determine the point-spread function. We do this by solving numerically the governing radiative transport equation by use of plane-wave mode expansions. When scattering is sharply peaked in the forward direction and it becomes difficult to solve the radiative transport equation, we replace it with either the Fokker-Planck or the Leakeas-Larsen equation. We also solve these equations by using plane-wave mode expansions. Numerical results show that these two equations agree with the radiative transport equation for large anisotropy factors. The agreement improves as the optical thickness increases.

Effect of dextran-induced changes in refractive index and aggregation on optical properties of whole blood

The purpose of the present study is to investigate systematically the mechanisms of alterations in the optical properties of whole blood immersed in the biocompatible agent dextran, and to define the optimal concentration of dextrans required for blood optical clearing in order to enhance the capability of light penetration depth for optical imaging applications. In the experiments, dextrans with different molecular weights and various concentrations were employed and investigated by the use of the optical coherence tomography technique. Changes in light attenuation, refractive index and aggregation properties of blood immersed in dextrans were studied. It was concluded from the results that the mechanisms for blood optical clearing are characteristic of the types of dextrans employed, their concentrations and the application stages. Among the substances applied, Dx500 at a concentration at 0.5 g dl(-1) gives the best result in improving light penetration depth through the blood. The increase of light transmission at the beginning of the addition of dextrans is mainly attributed to refractive index matching between the scattering centres and the ground matter. Thereafter, the transmission change is probably due to a dextran-induced aggregation-disaggregation effect. Overall, light scattering in the blood could be effectively reduced by the application of dextrans. It represents a promising approach to increasing the imaging depth for in vivo optical imaging of biological tissue, for example optical coherence tomography.

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.

Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture

A number of noninvasive fiber optic optical technologies are under development for real-time diagnosis of neoplasia. We investigate how the light scattering properties of cervical cells are affected by changes in nuclear morphology, DNA content, and chromatin texture, which occur during neoplastic progression. We used a Cyto-Savant computer-assisted image analysis system to acquire quantitative nuclear features measurements from 122 Feulgen-thionin-stained histopathologic sections of cervical tissue. A subset of the measured nuclear features was incorporated into a finite-difference time-domain (FDTD) model of cellular light scattering. The magnitude and angular distribution of scattered light was calculated for cervical cells as a function of pathologic grade. The nuclear atypia strongly affected light scattering properties. The increased size and elevated DNA content of nuclei in high-grade lesions caused the most significant changes in scattering intensity. The spatial dimensions of chromatin texture features and the amplitude of refractive index fluctuations within the nucleus impacted both the angular distribution of scattering angles and the total amount of scattered light. Cellular scattering is sensitive to changes in nuclear morphology that accompany neoplastic progression. Understanding the quantitative relationships between nuclear features and scattering properties will aid in the development of noninvasive optical technologies for detection of precancerous conditions.

A simple algorithm for in vivo ocular fundus oximetry compensating for non-haemoglobin absorption and scattering

An algorithm is introduced for the compensation of the influence of non-haemoglobin absorption as well as tissue scattering on blood spectra used in optical oximetry at the ocular fundus. The in vivo measured spectra were corrected by a linear transformation in order to match the reference spectra of fully oxygenated and reduced blood, respectively, at three isosbestic points (522 nm, 569 nm and 586 nm). The oxygen saturation can then be determined at a wavelength showing a high contrast between oxygenated and reduced haemoglobin (e.g., 560 nm). Reflection measurements at blood flowing through cuvettes were used to validate the algorithm. The oxygen saturation values were compared to measurements of the same samples at a laboratory haemoximeter. The mean deviation was found to be 2.65%.

Light paths in retinal vessel oxymetry

The oxygen utilization and, therefore, the metabolic state, of a distinctive area of the retina may be calculated from the diameter of the supplying artery and vein, the haemoglobin oxygenation, and the velocity of the blood. The first two parameters can be determined by imaging spectrometry at the patients ocular fundus. However, the reflected light emerging from a vessel followed different pathways through the ocular fundus layers and the vessel embedded in the retina. The contribution of the single pathways to the vessel reflection profile is investigated by a Monte Carlo simulation. Considering retinal vessels with diameters of 25-200 microm we found the reflection from a thin vessel to be determined by the single and double transmission of light at 560 nm. The backscattering from the blood column determines the reflectance in the case of a thick vessel. However, both components are in the same order of magnitude. This has to be considered in the calculation of the oxygen saturation of blood in retinal vessels from their reflection spectra.

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.

Calibration-free method to determine the size and hemoglobin concentration of individual red blood cells from light scattering

At present, hemoglobin concentration and the volume of an erythrocyte can be determined from the intensities of light scattered by an individual cell at fixed angular intervals. This method is used in modern hemoglobin analyzers, but it requires calibration of optical and electronic units by certified particles of known size and refractive index. We describe a method that is based on the parametric solution of an inverse light-scattering problem and does not require a calibration procedure. The method is based on the use of parameters of the entire angular light-scattering pattern, called an indicatrix here. These parameters do not depend on the absolute intensity of light scattering. The indicatrix parameters form approximating equations that relate these parameters to the size and the phase-shift parameters of the particle. The applicability of the method is demonstrated by measurement of the indicatrices of individual sphered erythrocytes. The indicatrices of the individual erythrocytes were measured with a scanning flow cytometer at an angular range of from 15 to 55 deg. The volume and the hemoglobin concentration have been calculated by use of the developed method and by fitting of the experimental indicatrices to the indicatrices calculated from the Mie theory.

A theoretical approach of the measurement of osmotic fragility of erythrocytes by optical transmission

The osmotic fragility of the erythrocyte membrane to hypotonic solutions is investigated theoretically. The fragility curves exhibit a strong transmittance rise. This variation is assumed to result from changes in the scattering properties of erythrocytes under dialysis resulting from swelling and hemolysis. The refractive indices of erythrocytes are obtained through the Lorentz-Lorenz relation based on hemoglobin and water contents. The scattering cross sections (needed to calculate the collimated transmittance) and the forward scattered intensity (needed to calculate the incoherent transmittance) are expressed according to the simple algebraic relations of the anomalous diffraction approximation. It is shown that swelling (or shrinking) has no influence on the collimated transmittance. Hemolysis alone causes the abrupt sigmoidal increase of the collimated transmittance with time. The possible transmittance increase (decrease) observed during swelling (shrinking) is due to incoherent transmittance and depends on the detecting solid angle value of the experimental setup.

Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope

The details of a model used to predict the scattering of a plane polarized wave by a spherical particle as observed with a microscope are presented. The model accounts for the effect of a refractive interface on the outgoing scattered field and determines the image produced by a lens with high numerical aperture. The predictions of the model are verified by direct comparison with the experimentally observed scattering from polystyrene spheres in a fluid.

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.

Light-scattering properties of undiluted human blood subjected to simple shear

An experimental investigation was performed into the effect of simple shear on the light-scattering properties of undiluted human blood. Undiluted human blood was enclosed between two glass plates with an adjustable separation between 30 and 120 microns and with one plate moving parallel to the other. For various shear rates and layer thicknesses, the angular light distribution and the collimated transmission were measured for 633-nm light. For shear rates above 150 s-1, the transmission results directly yielded a total attenuation coefficient of 120 mm-1. At lower shear rates the total attenuation followed an irregular pattern. From the angular intensity distributions, the anisotropy for single scattering was deduced by inverse Monte Carlo simulations. A continuous increase of the average cosine g with the shear rate was observed, with g in the range 0.95-0.975.

Scattering of he-ne laser light by an average-sized red blood cell

The scattering of He-Ne laser light by an average-sized human red blood cell (RBC) is investigated numerically. The RBC is modeled as an axisymmetric, low-contrast dielectric, biconcave disk. The interaction problem is treated numerically by means of a boundary-element methodology. The differential scattering cross sections (DSCS's) corresponding to various cell orientations are calculated. The numerical results obtained for the exact RBC geometry are compared with those corresponding to a scattering problem in which the cell is assumed to be either a volume-equivalent sphere or an oblate spheroid. A parametric study demonstrating the dependence of the DSCS on the wavelength of the incident wave and the cell's refractive index is presented.