Near-infrared light propagation in an adult head model. I. Modeling of low-level scattering in the cerebrospinal fluid layer

Adequate modeling of light propagation in a human head is important for quantitative near-infrared spectroscopy and optical imaging. The presence of a nonscattering cerebrospinal fluid (CSF) that surrounds the brain has been previously shown to have a strong effect on light propagation in the head. However, in reality, a small amount of scattering is caused by the arachnoid trabeculae in the CSF layer. In this study, light propagation in an adult head model with discrete scatterers distributed within the CSF layer has been predicted by Monte Carlo simulation to investigate the effect of the small amount of scattering caused by the arachnoid trabeculae in the CSF layer. This low scattering in the CSF layer is found to have little effect on the mean optical path length, a parameter that can be directly measured by a time-resolved experiment. However, the partial optical path length in brain tissue that relates the sensitivity of the detected signal to absorption changes in the brain is strongly affected by the presence of scattering within the CSF layer. The sensitivity of the near-infrared signal to hemoglobin changes induced by brain activation is improved by the effect of a low-scattering CSF layer.     

Near-infrared light propagation in an adult head model. II. Effect of superficial tissue thickness on the sensitivity of the near-infrared spectroscopy signal

It is important for near-infrared spectroscopy (NIRS) and imaging to estimate the sensitivity of the detected signal to the change in hemoglobin that results from brain activation and the volume of tissue interrogated for a specific source-detector fiber spacing. In this study light propagation in adult head models is predicted by Monte Carlo simulation to investigate the effect of the superficial tissue thickness on the partial optical path length in the brain and on the spatial sensitivity profile. In the case of source-detector spacing of 30 mm, the partial optical path length depends mainly on the depth of the inner skull surface whereas the spatial sensitivity profile is significantly affected by the thickness of the cerebrospinal fluid layer. The mean optical path length that can be measured by time-resolved experiments increases when the skull thickness increases whereas the partial mean optical path length in the brain decreases when the skull thickness increases. These results indicate that it is not appropriate to use the mean optical path length as an alternative to the partial optical path length to compensate the NIRS signal for the difference in sensitivity caused by variation of the superficial tissue thickness.     

Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging

An efficient computation of the time-dependent forward solution for photon transport in a head model is a key capability for performing accurate inversion for functional diffuse optical imaging of the brain. The diffusion approximation to photon transport is much faster to simulate than the physically correct radiative transport equation (RTE); however, it is commonly assumed that scattering lengths must be much smaller than all system dimensions and all absorption lengths for the approximation to be accurate. Neither of these conditions is satisfied in the cerebrospinal fluid (CSF). Since line-of-sight distances in the CSF are small, of the order of a few millimeters, we explore the idea that the CSF scattering coefficient may be modeled by any value from zero up to the order of the typical inverse line-of-sight distance, or approximately 0.3 mm(-1), without significantly altering the calculated detector signals or the partial path lengths relevant for functional measurements. We demonstrate this in detail by using a Monte Carlo simulation of the RTE in a three-dimensional head model based on clinical magnetic resonance imaging data, with realistic optode geometries. Our findings lead us to expect that the diffusion approximation will be valid even in the presence of the CSF, with consequences for faster solution of the inverse problem.     

Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than approximately 2%. The errors in the scattering phase functions are typically less than approximately 5%. The errors in the asymmetry factors are less than approximately 0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].     

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

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

Investigation of the effect of scattering agent and scattering albedo on modulated light propagation in water

A recent paper described experiments completed to study the effect of scattering on the propagation of modulated light in laboratory tank water [Appl. Opt.48, 2607 (2009)APOPAI0003-693510.1364/AO.48.002607]. Those measurements were limited to a specific scattering agent (Maalox antacid) with a fixed scattering albedo (0.95). The purpose of this paper is to study the effects of different scattering agents and scattering albedos on modulated light propagation in water. The results show that the scattering albedo affects the number of attenuation lengths that the modulated optical signal propagates without distortion, while the type of scattering agent affects the degree to which the modulation is distorted with increasing attenuation length.     

Determination of scattering volume fraction and particle size distribution in the superficial layer of a turbid medium by using diffuse reflectance spectroscopy

We have investigated the possibility of determining changes in the volume fraction of microstructure scatterers in the superficial tissue layers by using diffuse reflectance spectroscopy. To that extent we have built a two-layer optical phantom by using microparticles with various sizes in order to simulate the scattering properties of tissue microstructures. Reflectance spectral measurements were performed on a number of optical phantoms having different volume fractions of various microparticle sizes. An analytical model was developed using light-transport theory and fractal modeling approaches and was then fitted to the measured reflectance to calculate the volume fractions of the microparticles in phantoms. The results showed that we could measure changes in both the total volume fraction of the microparticles and in the overall size distribution of the microparticles with good accuracy (>80%). These results suggest the potential of using this method for measuring the volume fraction changes of tissue microstructure scatterers and applications in the detection of cancerous related morphological and structural changes.     

Shedding light on the adult brain: a review of the clinical applications of near-infrared spectroscopy

Near-infrared spectroscopy (NIRS) has potential as a non-invasive brain monitor in a wide range of clinical scenarios. In the last decade, there has been a rapid expansion of clinical experience using NIRS to monitor cerebral oxygenation, particularly in cardiac surgery, where there is some evidence that NIRS-guided brain protection protocols might lead to a reduction in peri-operative neurological complications. There are no data to support the wider application of NIRS to monitor cerebral oxygenation during routine anaesthesia and surgery, and its application in brain injury, where it might be expected to have a key monitoring role, is as yet undefined. Technological developments, including the introduction of broadband and time-resolved spectrometers that are capable of reliably measuring changes in oxidized cytochrome c oxidase, offer real potential for a single NIRS-based device to provide multi-site, regional monitoring of cerebral metabolic status as well as oxygenation and haemodynamics.     

Light scattering by a random distribution of particles embedded in absorbing media: diagrammatic expansion of the extinction coefficient

We address the problem of the modeling of the extinction coefficient into an absorbing medium, including a random distribution of identical scatterers of arbitrary size. We show that the extinction coefficient, including losses in the host medium, can be derived from a diagrammatic expansion arising from the rigorous multiple-scattering theory of electromagnetic waves in random media. While in previous approaches the contribution to the extinction coefficient due to the absorption in the host medium and due to the absorption and scattering by the particles were evaluated separately and heuristically, our approach is based on a derivation from first principles.     

Stimulated light scattering in transparent liquid particles: effect of the descartes ring

We consider some peculiarities of the evolution of processes of stimulated scattering in liquid transparent particles in the presence of ponderomotive action of a light field. We observed the occurrence of sharp deformations in the Descartes ring zone, which exceeds by more than 1 order of magnitude the deformations of the remaining particle surface. Investigation of the dynamics of the evolution of droplet deformations has made it possible to consider these deformations as the main cause of suppression of stimulated scattering indicated in the experiments. An analytical expression was derived to evaluate the decrease of the Q factor of droplet quasi-normal eigenmodes caused by perturbation of the particle shape from the spherical. Our study revealed that the larger the Q factor of the droplet eigenmodes, the greater the influence of surface deformation.     

Definition of the diffusion coefficient in scattering and absorbing media

We revisit the definition of the diffusion coefficient for light transport in scattering and absorbing media. From an asymptotic analysis of the transport equation, we present a novel derivation of the diffusion coefficient, which is restricted neither to low absorption nor to a situation in which the specific intensity is quasi-isotropic. Our result agrees with previous expressions of the diffusion coefficient in the appropriate limit. Using numerical simulations, we discuss the implications of the proper choice of the diffusion coefficient for time-dependent transport.     

Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons

We report on multidistance time-resolved diffuse reflectance spectroscopy of the head of a healthy adult after intravenous administration of a bolus of indocyanine green. Intracerebral and extracerebral changes in absorption are deduced from moments (integral, mean time of flight, and variance) of the distributions of times of flight of photons (DTOFs), recorded simultaneously at four different source-detector separations. We calculate the sensitivity factors converting depth-dependent changes in absorption into changes of moments of DTOFs by Monte Carlo simulations by using a layered model of the head. We validate our method by analyzing moments of DTOFs simulated for the assumed changes in absorption in different layers of the head model.     

Spatial distribution of single-photon and two-photon fluorescence light in scattering media: Monte Carlo simulation

Three-dimensional fluorescence spatial distributions under single-photon and two-photon excitation within a turbid medium are studied with Monte Carlo simulation. It is demonstrated that two-photon excitation has an advantage of producing much less fluorescence light outside the focal region compared with single-photon excitation. With the increase of the concentration of scattering particles in a turbid medium, the position of the maximum fluorescence intensity point shifts from the geometric focal region toward the medium surface. Further studies show that the optical sectioning property of two-photon fluorescence microscopy is degraded in thick turbid media or when the numerical aperture of an objective becomes low.     

On confocal Raman spectroscopy of semicrystalline polymers: the effect of optical scattering

A series of semicrystalline polymers has been prepared through morphological control. Each of these has an identical refractive index but a different, well-defined, scattering behavior. From existing geometrical optical theories of confocal Raman spectroscopy, these materials should behave identically. Initially, the extent of scattering in each system was assessed quantitatively, from the near-infrared through the visible wavelength range, by UV/visible spectroscopy. The effect of optical scattering on the variation of intensity of the Raman scattered radiation with subsurface position was then examined in all four materials; the effect of surface roughness was also considered in the highest clarity system. Where surface effects are removed through careful sample preparation and the materials are interrogated using identical optical systems to mitigate against the impact of refractive index mismatch and other optical effects, the Raman response is strongly affected by the scattering characteristics of each material. A simple empirical relationship has been determined that adequately described all our specimens.     

Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head

Near-infrared light propagation in various models of the adult head is analyzed by both time-of-flight measurements and mathematical prediction. The models consist of three- or four-layered slabs, the latter incorporating a clear cerebrospinal fluid (CSF) layer. The most sophisticated model also incorporates slots that imitate sulci on the brain surface. For each model, the experimentally measured mean optical path length as a function of source-detector spacing agrees well with predictions from either a Monte Carlo model or a finite-element method based on diffusion theory or a hybrid radiosity-diffusion theory. Light propagation in the adult head is shown to be highly affected by the presence of the clear CSF layer, and both the optical path length and the spatial sensitivity profile of the models with a CSF layer are quite different from those without the CSF layer. However, the geometry of the sulci and the boundary between the gray and the white matter have little effect on the detected light distribution.     

Effects of tissue surface curvature and incident light angle on diffuse correlation spectroscopy

Diffuse correlation spectroscopy is an emerging technique for the continuous, non-invasive monitoring of blood flow in biological tissues. However, the influence of oblique incidence and surface curvature has not been fully discussed. In this paper, we study the effects of the incident angle and surface curvature on diffuse correlation spectroscopy measurement and the blood flow index (BFI). For semi-infinite plane with lower absorption, oblique incidence angle has slightly stronger influence. Larger incident angles lead to high values and a reduced decay rate of the normalized electric field temporal autocorrelation. When the radius of curvature is more than 10?cm, the BFI estimation error reduced to less than 5% and very close to semi-infinite plane case. Besides, for the surface with small radius of curvature, larger incident angles sometimes may cause smaller estimated errors of the BFI. This work may help improve BFI estimation accuracy from diffuse correlation spectroscopy.     

Light scattering by a random distribution of particles embedded in absorbing media: full-wave Monte Carlo solutions of the extinction coefficient

We present a numerical investigation of the light scattering in an absorbing medium with randomly distributed scatterers. The extinction coefficient is derived from an ensemble of numerical solutions of Maxwell's equations for many different realizations of the system. Results are in good agreement with the predictions given by the effective medium theory under the independent-scattering approximation. Beyond the independent-scattering approximation, we explore the domain of validity of an effective medium theory that takes into account correlations between pairs of scatterers. A good agreement is obtained with a filling ratio up to 30% for scatterers with a relative refractive index contrast lower than 20% and size parameters near unity.     

Monte Carlo prediction of near-infrared light propagation in realistic adult and neonatal head models

In near-infrared spectroscopy and imaging, the sensitivity of the detected signal to brain activation and the volume of interrogated tissue are clinically important. Light propagation in adult and neonatal heads is strongly affected by the presence of a low-scattering cerebrospinal fluid layer. The effect of the heterogeneous structure of the head on light propagation in the adult brain is likely to be different from that in the neonatal brain because the thickness of the superficial tissues and the optical properties of the brain of the neonatal head are quite different from those of the adult head. In this study, light propagation in the two-dimensional realistic adult and neonatal head models, whose geometries are generated from a magnetic resonance imaging scan of the human heads, is predicted by Monte Carlo simulation. The sandwich structure, which is a low-scattering cerebrospinal fluid layer held between the high-scattering skull and gray matter, strongly affects light propagation in the brain of the adult head. The sensitivity of the absorption change in the gray matter is improved; however, the intensely sensitive region is confined to the shallow region of the gray matter. The high absorption of the neonatal brain causes a similar effect on light propagation in the head. The intensely sensitive region in the neonatal brain is confined to the gray matter; however, the spatial sensitivity profile penetrates into the deeper region of the white matter.     

Interface layer effect on the stress distribution of a wafer-bonded bilayer structure

The interface layer plays an important role in stress transfer in composite structures. However, many interface layer properties such as the modulus, thickness, and uniformity are difficult to determine. The model developed in this article links the influence of the interface layer on the normal stress distribution along the layer thickness with the layer surface morphology before bonding. By doing so, a new method of determining the interfacial parameter(s) is suggested. The effects of the layer thickness and the surface roughness before bonding on the normal stress distribution and its depth profile are also discussed. For ideal interface case with no interfacial shear stress, the normal stress distribution pattern can only be monotonically decreased from the interface. Due to the presence of interfacial shear stress, the normal stress distribution is much more complex, and varies dramatically with changes in the properties of the interface layer, or the dimensions of the bonding layers. The consequence of this dramatic stress field change, such as the shift of the maximum stress from the interface is also addressed. The size-dependent stress distribution in the thickness direction due to the interface layer effect is presented. When the interfacial shear stress is reduced to zero, the model presented in this article is also demonstrated to have the same normal stress distribution as obtained by the previous model, which does not consider the interface layer effect.