Scattering Size Distribution Research Articles

Wavelength-dependent backscattering measurements for quantitative real-time monitoring of apoptosis in living cells

Apoptosis--programmed cell death--is a cellular process exhibiting distinct biochemical and morphological changes. An understanding of the early morphological changes that a cell undergoes during apoptosis can provide the opportunity to monitor apoptosis in tissue, yielding diagnostic and prognostic information. There is avid interest regarding the involvement of apoptosis in cancer. The initial response of a tumor to successful cancer treatment is often massive apoptosis. Current apoptosis detection methods require cell culture disruption. Our aim is to develop a nondisruptive optical method to monitor apoptosis in living cells and tissues. This would allow for real-time evaluation of apoptotic progression of the same cell culture over time without alteration. Elastic scattering spectroscopy (ESS) is used to monitor changes in light-scattering properties of cells in vitro due to apoptotic morphology changes. We develop a simple instrument capable of wavelength-resolved ESS measurements from cell cultures in the backward direction. Using Mie theory, we also develop an algorithm that extracts the size distribution of scatterers in the sample. The instrument and algorithm are validated with microsphere suspensions. For cell studies, Chinese hamster ovary (CHO) cells are cultured to confluence on plates and are rendered apoptotic with staurosporine. Backscattering measurements are performed on pairs of treated and control samples at a sequence of times up to 6-h post-treatment. Initial results indicate that ESS is capable of discriminating between treated and control samples as early as 10- to 15-min post-treatment, much earlier than is sensed by standard assays for apoptosis. Extracted size distributions from treated and control samples show a decrease in Rayleigh and 150-nm scatterers, relative to control samples, with a corresponding increase in 200-nm particles. Work continues to correlate these size distributions with underlying morphology. To our knowledge, this is the first report of the use of backscattering spectral measurements to quantitatively monitor apoptosis in viable cell cultures in vitro.

The effect of scatterer size distribution on the backscatter coefficient.

The bias and variance of mean scatterer size estimates made from backscatter coefficients might be reduced by incorporating an estimate of scatterer size distribution into the parameter estimation scheme. Current estimation schemes generally assume a single scatterer size representing the volume‐weighted mean diameter of a distribution. When the mean interrogation frequency has a ka value near 0.8 for the mean scatterer size, and the size distribution is relatively narrow, the results are unbiased. However, consideration of the distribution of sizes may improve scatterer size estimation, especially at frequencies for which ka > 1. A phantom of 2% (dry weight) agar spheres (with diameters between 90 and 125 μm) in a 3.4% agar background was scanned over a broad frequency range using several transducers, and the backscatter coefficients were estimated from these data. When accounting for the size distribution, the mean square error between the measured and theoretical backscatter coefficients over the frequency range of 3–14 MHz was reduced by at least 50% in the size range of interest. These results suggest that accounting for the size distribution in backscatter models will significantly improve the ability to parametrize the backscatter coefficient. [Work supported by NIH CA111289]

Nature of defect clusters in neutron-irradiated iron-based alloys deduced from small-angle neutron scattering

Small-angle neutron scattering (SANS) was applied to investigate Fe-based model alloys with intentionally varied Cu levels. The aims are to provide size distributions of scatterers and to interpret deviations of the measured ratio of magnetic and nuclear scattering cross-sections from the ratios calculated for pure vacancy clusters and pure Cu clusters. For the case of the low-Cu alloy the SANS results indicate the average scatterer to be an Fe–Cu–vacancy cluster of about 1 nm radius, the composition of which is constricted according to given inequalities. For the case of the Cu-enriched alloy the SANS results are consistent with Cu-rich clusters of about 1.5 nm radius containing 15% vacancies per bcc lattice site.

A Polydisperse Sphere Model Describing the Propagation ofLight in Biological Tissue

A polydisperse sphere model with the complex refractive index isemployed to describe the propagation of light in biological tissue. Thescattering coefficient, absorption coefficient and scattering phasefunction are calculated. At the same time, the inverse problem onretrieving the particles size distribution, imaginary part of therefractive index and number density of scatterers is investigated. Theresult shows that the retrieval scheme together with the Chahine algorithmis effective in dealing with such an inverse problem. It is alsoclarified that a group of parameters including the scatteringcoefficient, absorption coefficient and phase function are associatedwith another group including the refractive index, particle sizedistribution and number density of scatterers, which is a problemdescribed in two different ways and the anisotropy factor is not anindependent variable, but is determined by the phase function.

Image reconstruction of effective Mie scattering parameters of breast tissue in vivo with near-infrared tomography

A method for image reconstruction of the effective size and number density of scattering particles is discussed within the context of interpreting near-infrared (NIR) tomography images of breast tissue. An approach to use Mie theory to estimate the effective scattering parameters is examined and applied, given some assumptions about the index of refraction change expected in lipid membrane-bound scatterers. When using a limited number of NIR wavelengths in the reduced scattering spectra, the parameter extraction technique is limited to representing a continuous distribution of scatterer sizes, which is modeled as a simple exponentially decreasing distribution function. In this paper, image formation of effective scatterer size and number density is presented based on the estimation method. The method was evaluated with Intralipid phantom studies to demonstrate particle size estimation to within 9% of the expected value. Then the method was used in NIR patient images, and it indicates that for a cancer tumor, the effective scatterer size is smaller than the background breast values and the effective number density is higher. In contrast, for benign tumor patients, there is not a significant difference in effective scatterer size or number density between tumor and normal tissues. The method was used to interpret magnetic resonance imaging-coupled NIR images of adipose and fibroglandular tissues, and it indicated that the fibroglandular tissue has smaller effective scatterer size and larger effective number density than the adipose tissue does.

Low-coherence light-scattering calculations for polydisperse size distributions

The calculation of angular light-scattering distributions is considered for low-coherence light incident on a polydisperse particle size distribution of scatterers. As low-coherence light is now commonly used in interferometry schemes when applied to biomedical imaging, the difference between detecting scattered intensity and interferometrically detecting the scattered field is examined. An expression is derived that allows the presence of multiple wavelengths lambda and particle sizes d to be described by a single distribution in the size parameter x = pi d/lambda, which simplifies numerical calculations. The applicability of this expression is examined numerically.

The reflection of ultrasound from partially contacting rough surfaces

Ultrasound is commonly used to detect and size cracks in a range of engineering components. Modeling techniques are well established for smooth and open cracks. However, real cracks are often rough (relative to the ultrasonic wavelength) and closed due to compressive stress. This paper describes an investigation into the combined effects of crack face roughness and closure on ultrasonic detectability. A contact model has been used to estimate the size and shape of scatterers (voids) at the interface of these rough surfaces when loaded. The response of such interfaces to excitation with a longitudinal ultrasonic pulse over a wide range of frequencies has been investigated. The interaction of ultrasound with this scattering interface is predicted using a finite-element model and good agreement with experiments on rough surfaces is shown. Results are shown for arrays of equi-sized scatterers and a distribution of scatterer sizes. It is shown that the response at high frequencies is dependent on the size, shape, and distribution of the scatterers. It is also shown that the finite-element results depart from the mass-spring model predictions when the product of wave number and scatterer half-width is greater than 0.4.

Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo

A method for estimating Mie theory scattering parameters from diffuse light tomography measurements in breast tissue is discussed. The approach provides an estimate of the mean particle size and number density given assumptions about the index of refraction change expected in lipid-membrane-bound scatterers. When using a sparse number of wavelengths in the reduced scattering spectra, the parameter extraction technique is limited to representing a continuous distribution of scatterer sizes that appears to be dominated by an exponential decrease with increasing particle size. The fitting method is tested on simulated data and then on Intralipid-based tissue-phantom data, giving a mean particle size of 93+/-17 nm, which is in excellent agreement with expectations. The approach is also applied retrospectively to breast tissue spectra acquired from normal healthy volunteers, where the average particle size and number density were found to be in the range of 20 to 1400 nm. Grouping of the data based on radiographic breast density, as a surrogate measure of tissue composition yielded values of 20 to 65, 25 to 200, 140 to 1200, and 150 to 1400 nm, respectively, for the four BI-RADS (American College of Radiology Breast Imaging Reporting and Data System) density classifications of extremely dense, heterogeneously dense, scattered, and fatty. These results are consistent with the microscopic characteristics of each breast type given the expected progression from predominantly collagenous connective tissue (extremely dense category) to increasing proportions of glandular epithelium and fat (intermediate density categories) to predominantly fat (fatty category).

PRINSAS– a Windows-based computer program for the processing and interpretation of small-angle scattering data tailored to the analysis of sedimentary rocks

PRINSASis a Windows program that takes as input raw (post-reduction) small-angle neutron and small-angle X-ray scattering (SANS and SAXS) data obtained from various worldwide facilities, displays the raw curves in interactive log–log plots, and allows processing of the raw curves. Separate raw SANS and ultra-small-angle neutron scattering (USANS) curves can be combined into complete scattering curves for an individual sample. The combined curves can be interpreted and information inferred about sample structure, using built-in functions. These have been tailored for geological samples and other porous media, and include the ability to obtain an arbitrary distribution of scatterer sizes, the corresponding specific surface area of scatterers, and porosity (when the scatterers are pores), assuming spherical scatterers. A fractal model may also be assumed and the fractal dimension obtained. A utility for calculating scattering length density from the component oxides is included in the program.

Modelling optical properties of soft tissue by fractal distribution of scatterers

Abstract A knowledge of the local refractive index variations and size distribution of scatterers in biological tissue is required to understand the physical processes involved in light-tissue interaction. This paper describes a method for modelling the complicated soft tissue, based on the fractal approach, permitting numerical evaluation of the phase functions and four optical properties of tissue—scattering coefficient, reduced scattering coefficient, backscatter-ing coefficient, and anisotropy factor—by the use of the Mie scattering theory. A key assumption of the model is that refractive index variations caused by microscopic tissue elements can be treated as particles with size distribution according to the power law. The model parameters, such as refractive index, incident wavelength, and fractal dimension, that are likely to affect the predictions of optical properties are investigated. The results suggest that the fractal dimension used to describe how biological tissue can be approximated by particle distribution is highly dependent on how the continuous distribution is discretized. The optical properties of the tissue significantly depend on the refractive index of tissue, implying that the refractive index of the particles should be carefully chosen in the model in order accurately to predict the optical properties of the tissue concerned.

Modelling optical properties of soft tissue by fractal distribution of scatterers

A knowledge of the local refractive index variations and size distribution of scatterers in biological tissue is required to understand the physical processes involved in light-tissue interaction. This paper describes a method for modelling the complicated soft tissue, based on the fractal approach, permitting numerical evaluation of the phase functions and four optical properties of tissue—scattering coefficient, reduced scattering coefficient, backscatter-ing coefficient, and anisotropy factor—by the use of the Mie scattering theory. A key assumption of the model is that refractive index variations caused by microscopic tissue elements can be treated as particles with size distribution according to the power law. The model parameters, such as refractive index, incident wavelength, and fractal dimension, that are likely to affect the predictions of optical properties are investigated. The results suggest that the fractal dimension used to describe how biological tissue can be approximated by particle distribution is highly dependent on how the continuous distribution is discretized. The optical properties of the tissue significantly depend on the refractive index of tissue, implying that the refractive index of the particles should be carefully chosen in the model in order accurately to predict the optical properties of the tissue concerned.

Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics

We have studied the optical properties of mammalian cell suspensions to provide a mechanistic basis for interpreting the optical properties of tissues in vivo. Measurements of the wavelength dependence of the reduced scattering coefficient and measurements of the phase function demonstrated that there is a distribution of scatterer sizes. The volumes of the scatterers are equivalent to those of spheres with diameters in the range between ~0.4 and 2.0 mum. Measurements of isolated organelles indicate that mitochondria and other similarly sized organelles are responsible for scattering at large angles, whereas nuclei are responsible for small-angle scattering. Therefore optical diagnostics are expected to be sensitive to organelle morphology but not directly to the size and shape of the cells.

Optical scattering properties of soft tissue: a discrete particle model

We introduce a micro-optical model of soft biological tissue thatpermits numerical computation of the absolute magnitudes of itsscattering coefficients. A key assumption of the model is that therefractive-index variations caused by microscopic tissue elements canbe treated as particles with sizes distributed according to a skewedlog-normal distribution function. In the limit of an infinitelylarge variance in the particle size, this function has the samepower-law dependence as the volume fractions of the subunits of anideal fractal object. To compute a complete set of opticalcoefficients of a prototypical soft tissue (single-scatteringcoefficient, transport scattering coefficient, backscatteringcoefficient, phase function, and asymmetry parameter), we apply Mietheory to a volume of spheres with sizes distributed according to thetheoretical distribution. A packing factor is included in thecalculation of the optical cross sections to account for correlatedscattering among tightly packed particles. The results suggest thatthe skewed log-normal distribution function, with a shape specified bya limiting fractal dimension of 3.7, is a valid approximation of thesize distribution of scatterers in tissue. In the wavelength range 600 </= lambda </= 1400 nm, the diameters of the scatterers thatcontribute most to backscattering were found to be significantlysmaller (lambda/4-lambda/2) than the diameters of the scatterersthat cause the greatest extinction of forward-scattered light(3-4lambda).

On the Retrieval of Particle Size Distributions from Small-Angle Scattering Data: the Influence of Statistical Data Dispersion

The problem of the retrieval of the particle size distribution of scatterers from small-angle scattering experiments with noisy data is addressed. Gaussian-like particle size distributions of noninteractive spheres are used as illustrative examples. A numerical corrector method, previously reported by the present authors, is used for the retrieval process. The achievable information in real space is investigated with the help of numerical experiments, the solution of which is known in advance. Cases are solved assuming three different functional dependences of noise with scattering vector, which simulate experimental conditions. The method proves to be powerful in retrieving the correct information with noisy data. The reliability of the process is established as a function of noise level and particle size.

First-order statistics of pulsed-sinusoid backscatter from random media: basic elements of an exact treatment

In ultrasonic imaging systems, the instantaneous pressure at the transducer face during echo reception is typically comprised of many superimposed reflections of a pulse resembling an amplitude-modulated sinusoid. Generally, these reflections are randomly shifted in phase and randomly scaled in amplitude. Moreover, each reflected pulse may have been distorted by passage through a nonuniform medium. The first-order amplitude statistics of such a waveform have long been considered of interest. The backscatter formation process has often been modeled as a random walk in two dimensions. For simplicity, the effects of amplitude-phase dependence and scatterer size distribution have not been fully included in previous work. In most cases of interest this is physically justified; but, given a strongly non-Rayleigh random medium, experience has shown that more accurate expressions may be required. This paper points to the essentials of such an improved analysis. The effects of pulse structure and scatterer size distribution on the statistical properties of the individual step of the random walk are considered de novo. Simulation results are described.

Model of optical coherence tomography of heterogeneous tissue

A comprehensive model of optical coherence tomography (OCT) is described that includes the interference effects that produce speckle in images of dense heterogeneous tissue. It is based on the extended Huygens–Fresnel formulation of beam propagation in a turbulent atmosphere, adapted to the analysis of OCT. Incorporated in the model is a fractal description of the size distribution of scatterers in tissue. We demonstrate its application in the simulation of images of tissue volumes containing high-contrast targets embedded in a mixture of two sizes of particles. The simulated images show the degradation of image quality caused by speckle noise, along with the benefits of employing a light source with a short coherence time and an objective lens with a high numerical aperture. Based on model results, an estimate of the maximum probing depth is given in terms of the design variables of an OCT scanner and the optical properties of the tissue.

Measurement of cavitation damage in isothermally crept Al/SiC p composites using small-angle neutron scattering

Small-angle neutron scattering is shown to enable the detection of cavities in strained Al/SiC p composites. An iterative method based upon analytically calculated scatterer size distribution functions is introduced. Generally, this method allowed the determination of scatterer shapes with little initial knowledge of their exact geometry. It is suggested that fewer cavities are nucleated during tensile testing than during creep tests. Larger reinforcement sizes are demonstrated to raise the rate of void growth, but to lower the overall number of generated cavities. Composite pre-fatiguing is shown to increase significantly the number of nucleated voids.

Porosity by small-angle X-ray scattering (SAXS): comparison with results from mercury penetration and nitrogen adsorption

For several materials showing type-IV nitrogen adsorption behavior, the scatterer size distribution calculated from small-angle X-ray scattering (SAXS) data are shown to be consistent with pore size distributions (POSDS) calculated from nitrogen adsorption, over the range of pore radii from 2.0 to 20 nm. However, since neither pores nor particles are present as a dilute phase, it is not possible to assign unambiguously the SAXS distribution to either pores or particles.

Parametric ultrasound imaging from backscatter coefficient measurements: Image formation and interpretation

A broadband method for measuring backscatter coefficients σ b and other acoustic parameters is described. From the σ b measurements, using a commercially-available imaging system, four high-resolution parametric ultrasound images are formed in a C-scan image plane. Scatterer size images are computed from the frequency dependence of σ b and a correlation model function that describes the structure and elastic properties of the medium. Scattering strength images are computed from the absolute magnitude of σ b . Chi-square images are generated to display how well the correlation model represents the interrogated medium. Integrated backscatter coefficient images are formed over the transducer bandwidth. All four images are generated simultaneously and compared with the corresponding B-mode image. Test samples with known physical properties were used to demonstrate experimentally that accurate parametric images are possible if an accurate correlation model is used. Local variations in attenuation, the center frequency and bandwidth of the transducer, and the distribution of scatterer sizes greatly influence the accuracy of estimates and the appearance of the image, thus demonstrating the importance of these factors in parametric image interpretation.

Parametric Ultrasound Imaging from Backscatter Coefficient Measurements: Image Formation and Interpretation

A broadband method for measuring backscatter coefficients sigma b and other acoustic parameters is described. From the sigma b measurements, using a commercially-available imaging system, four high-resolution parametric ultrasound images are formed in a C-scan image plane. Scatterer size images are computed from the frequency dependence of sigma b and a correlation model function that describes the structure and elastic properties of the medium. Scattering strength images are computed from the absolute magnitude of sigma b. Chi-square images are generated to display how well the correlation model represents the interrogated medium. Integrated backscatter coefficient images are formed over the transducer bandwidth. All four images are generated simultaneously and compared with the corresponding B-mode image. Test samples with known physical properties were used to demonstrate experimentally that accurate parametric images are possible if an accurate correlation model is used. Local variations in attenuation, the center frequency and bandwidth of the transducer, and the distribution of scatterer sizes greatly influence the accuracy of estimates and the appearance of the image, thus demonstrating the importance of these factors in parametric image interpretation.