Time-resolved photon emission from layered turbid media

Criteria for the design of tissue-mimicking phantoms for the standardization of biophotonic instrumentation

A lack of accepted standards and standardized phantoms suitable for the technical validation of biophotonic instrumentation hinders the reliability and reproducibility of its experimental outputs. In this Perspective, we discuss general criteria for the design of tissue-mimicking biophotonic phantoms, and use these criteria and state-of-the-art developments to critically review the literature on phantom materials and on the fabrication of phantoms. By focusing on representative examples of standardization in diffuse optical imaging and spectroscopy, fluorescence-guided surgery and photoacoustic imaging, we identify unmet needs in the development of phantoms and a set of criteria (leveraging characterization, collaboration, communication and commitment) for the standardization of biophotonic instrumentation.

PV-MBLL algorithm for extraction of absolute tissue oxygenation information by diffuse optical spectroscopy

BACKGROUND AND OBJECTIVE

Tissue blood oxygenation contains critical information for biomedical studies and healthcare. The primary approach to extract the absolute value of tissue blood oxygenation (e.g., oxygen saturation) is spatial-resolved algorithm for near-infrared diffuse optical spectroscopy with continues-wave (CW) light, which require acquisition of the optical signals from multiple pairs of sources and detectors (S-D). This study reports the first attempt for absolute oxygenation measurement with single S-D pair of optical signals.

METHODS

A novel algorithm, namely, phantom-validation modified Beer-Lambert law (PV-MBLL), was created to fully utilize the optical signals from single S-D pair. This algorithm is combined with two-step phantom measurement to extract the absolute value of tissue oxygenation in CW system. The proposed PV-MBLL algorithm was compared with the conventional spatial-resolved algorithm on both step-varied liquid phantom and human experiment of cuff occlusion on arms. The one-way ANOVA analysis was performed to investigate the difference between the two algorithms.

RESULTS

By using the PV-MBLL algorithm, the reconstructed tissue absorption coefficient is highly accurate (not larger than 5.35% in error) over a wide range (0.02-0.20 cm^-1). By contrast, the spatial-resolved algorithm leads to much larger errors (up to 37.57% in error). Moreover, the responses of oxygen saturation to cuff occlusion differ significantly (p < 0.005) with the two algorithms.

CONCLUSIONS

The proposed PV-MBLL algorithm has promising potential for accurate acquisition of oxygenation information. Additionally, the single S-D pair greatly reduces the size of optical probe and instrument cost, thus it is highly appropriate for the tissues with small size and large curvature.

Development of thin skin mimicking bilayer solid tissue phantoms for optical spectroscopic studies

In vivo spectroscopic measurements have the proven potential to provide important insight about the changes in tissue during the development of malignancies and thus help to diagnose tissue pathologies. Extraction of intrinsic data in the presence of varying amounts of scatterers and absorbers offers great challenges in the development of such techniques to the clinical level. Fabrication of optical phantoms, tailored to the biochemical as well as morphological features of the target tissue, can help to generate a spectral database for a given optical spectral measurement system. Such databases, along with appropriate pattern matching algorithms, could be integrated with in vivo measurements for any desired quantitative analysis of the target tissue. This paper addresses the fabrication of such soft, photo stable, thin bilayer phantoms, mimicking skin tissue in layer dimensions and optical properties. The performance evaluation of the fabricated set of phantoms is carried out using a portable fluorescence spectral measurement system. The alterations in flavin adenine dinucleotide (FAD)-a tissue fluorophore that provides important information about dysplastic progressions in tissues associated with cancer development based on changes in emission spectra-fluorescence with varied concentrations of absorbers and scatterers present in the phantom are analyzed and the results are presented. Alterations in the emission intensity, shift in emission wavelength and broadening of the emission spectrum were found to be potential markers in the assessment of biochemical changes that occur during the progression of dysplasia.

Hemodynamic signals in fNIRS

Near-infrared spectroscopy (NIRS) was originally designed for clinical monitoring of tissue oxygenation, and it has also been developed into a useful tool in neuroimaging studies, with the so-called functional NIRS (fNIRS). With NIRS, cerebral activation is detected by measuring the cerebral hemoglobin (Hb), where however, the precise correlation between NIRS signal and neural activity remains to be fully understood. This can in part be attributed to the situation that NIRS signals are inherently subject to contamination by signals arising from extracerebral tissue. In recent years, several approaches have been investigated to distinguish between NIRS signals originating in cerebral tissue and signals originating in extracerebral tissue. Selective measurements of cerebral Hb will enable a further evolution of fNIRS. This chapter is divided into six sections: first a summary of the basic theory of NIRS, NIRS signals arising in the activated areas, correlations between NIRS signals and fMRI signals, correlations between NIRS signals and neural activities, and the influence of a variety of extracerebral tissue on NIRS signals and approaches to this issue are reviewed. Finally, future prospects of fNIRS are described.

Cerebral blood volume measurement using near-infrared time-resolved spectroscopy and histopathological evaluation after hypoxic-ischemic insult in newborn piglets

The aim of this study was to assess the relationship between the cerebral blood volume (CBV) measured by near-infrared time-resolved spectroscopy (TRS) and pathological change of the brain in a hypoxic-ischemic (HI) piglet model. Twenty-one anesthetized newborn piglets, including three sham controls, were studied. An HI event was induced by low inspired oxygen. CBV was measured using TRS (Hamamatsu TRS-10). Data were collected before, during, and 6h after the insult. CBV was calculated as the change from the end of the insult. The piglets were allowed to recover from anesthesia for 6h after the insult. At the age of 5 days, the brains of the piglets were perfusion-fixed, and histologic evaluations of brain tissue were performed. The extent of histopathological damage was graded in 0.5-unit intervals on a 9-step scale. CBV increments were well correlated with histopathological scores, especially at 1 and 3h after resuscitation. Spearman's rank-correlation coefficients at 1, 3, and 6h after resuscitation in the gray matter were 0.9016, 0.9127, and 0.6907, respectively. We conclude that an increased CBV after HI insult indicates more marked histological brain damage. CBV measurement immediately after resuscitation provides a more precise prediction of the histological outcome.

Automatic diagnosis of melanoma using machine learning methods on a spectroscopic system

Background

Early and accurate diagnosis of melanoma, the deadliest type of skin cancer, has the potential to reduce morbidity and mortality rate. However, early diagnosis of melanoma is not trivial even for experienced dermatologists, as it needs sampling and laboratory tests which can be extremely complex and subjective. The accuracy of clinical diagnosis of melanoma is also an issue especially in distinguishing between melanoma and mole. To solve these problems, this paper presents an approach that makes non-subjective judgements based on quantitative measures for automatic diagnosis of melanoma.

Methods

Our approach involves image acquisition, image processing, feature extraction, and classification. 187 images (19 malignant melanoma and 168 benign lesions) were collected in a clinic by a spectroscopic device that combines single-scattered, polarized light spectroscopy with multiple-scattered, un-polarized light spectroscopy. After noise reduction and image normalization, features were extracted based on statistical measurements (i.e. mean, standard deviation, mean absolute deviation, L₁ norm, and L₂ norm) of image pixel intensities to characterize the pattern of melanoma. Finally, these features were fed into certain classifiers to train learning models for classification.

Results

We adopted three classifiers – artificial neural network, naïve bayes, and k-nearest neighbour to evaluate our approach separately. The naive bayes classifier achieved the best performance - 89% accuracy, 89% sensitivity and 89% specificity, which was integrated with our approach in a desktop application running on the spectroscopic system for diagnosis of melanoma.

Conclusions

Our work has two strengths. (1) We have used single scattered polarized light spectroscopy and multiple scattered unpolarized light spectroscopy to decipher the multilayered characteristics of human skin. (2) Our approach does not need image segmentation, as we directly probe tiny spots in the lesion skin and the image scans do not involve background skin. The desktop application for automatic diagnosis of melanoma can help dermatologists get a non-subjective second opinion for their diagnosis decision.

Evaluation of cerebral circulation and oxygen metabolism in infants using near-infrared light

Bedside monitoring of cerebral circulation or oxygen metabolism in infants to appropriately manage circulation and establish the oxygen dose, aiming at improving the neurological prognosis, is needed in general clinical practice. Near-infrared spectroscopy is used for measurements of neonatal cerebral Hb oxygen saturation, cerebral blood volume, cerebral blood flow and cerebral metabolic rate of oxygen. Near-infrared time-resolved spectroscopy is particularly useful for bedside evaluation of cerebral circulation and oxygen metabolism because of its simple measurement procedure. Combined evaluation of cerebral blood volume and cerebral Hb oxygen saturation is expected to contribute to treatment centering on the brain in neonatal medical care.

A near-infrared spectroscopy computational model for cerebral hemodynamics

Near infrared spectroscopy (NIRS) is a technique used to detect and measure changes in the concentrations of oxygenated hemoglobin, deoxygenated hemoglobin, and water in tissues based on the differential absorption, scattering, and refraction of the near infrared light. In this imaging technique, the optical properties of tissues are reconstructed from the measurements obtained from the sensors located on the boundary. A computational method for the rapid noninvasive detection ∕ quantification of cerebral hemorrhage is described using the above procedure. CFD Research Corporation's finite volume computational biology code was used to numerically mimic the NIRS procedure by (i) noninvasively 'numerically penetrating' the brain tissues and (ii) reconstructing the optical properties the presence of water, oxygenated, and deoxygenated blood. These numerical noninvasive measurements are then used to predict the extent and severity of the brain hemorrhage. The paper also discusses ideas to obtain the location and the severity of a localized injury. Two-dimensional and three-dimensional simulations are performed as a proof of concept for the numerical formulation being feasible for the above mentioned detection/quantification. The results demonstrate that this numerical NIRS formulation can be used as a noninvasive technique for both qualitative and quantitative evaluation of cerebral hemodynamics.

Towards the next generation of near-infrared spectroscopy

Although near-infrared spectroscopy (NIRS) was originally designed for clinical monitoring of tissue oxygenation, it has also been developing into a useful tool for neuroimaging studies (functional NIRS). Over the past 30 years, technology has developed and NIRS has found a wide range of applications. However, the accuracy and reliability of NIRS have not yet been widely accepted, mainly because of the difficulties in selective and quantitative detection of signals arising in cerebral tissue, which subject the use of NIRS to a number of practical restrictions. This review summarizes the strengths and advantages of NIRS over other neuroimaging modalities and demonstrates specific examples. The issues of selective quantitative measurement of cerebral haemoglobin during brain activation are also discussed, together with the problems of applying the methods of functional magnetic resonance imaging data analysis to NIRS data analysis. Finally, near-infrared optical tomography--the next generation of NIRS--is described as a potential technique to overcome the limitations of NIRS.

Diffuse Optics for Tissue Monitoring and Tomography

This review describes the diffusion model for light transport in tissues and the medical applications of diffuse light. Diffuse optics is particularly useful for measurement of tissue hemodynamics, wherein quantitative assessment of oxy- and deoxy-hemoglobin concentrations and blood flow are desired. The theoretical basis for near-infrared or diffuse optical spectroscopy (NIRS or DOS, respectively) is developed, and the basic elements of diffuse optical tomography (DOT) are outlined. We also discuss diffuse correlation spectroscopy (DCS), a technique whereby temporal correlation functions of diffusing light are transported through tissue and are used to measure blood flow. Essential instrumentation is described, and representative brain and breast functional imaging and monitoring results illustrate the workings of these new tissue diagnostics.

Optical measurement of adipose tissue thickness and comparison with ultrasound, magnetic resonance imging, and callipers

Near-infrared spectroscopy is used to quantify the subcutaneous adipose tissue thickness (ATT) over five muscle groups (vastus medialis, vastus lateralis, gastrocnemius, ventral forearm and biceps brachii muscle) of healthy volunteers (n=20). The optical lipid signal (OLS) was obtained from the second derivative of broad band attenuation spectra and the lipid absorption peak (lambda=930 nm). Ultrasound and MR imaging as well as mechanical calliper readings were taken as reference methods. The data show that the OLS is a good predictor for ATT (<16 mm) with absolute and relative errors of <0.8 mm and <24%, respectively. The optical method compares favourably with calliper reading. The finding of a non-linear relationship of optical signal vs. ultrasound is explained by a theoretical two-layer model based on the diffusion approximation for the transport of photons. The crosstalk between the OLS and tissue hemoglobin concentration changes during an incremental cycling exercise was found to be small, indicating the robustness of OLS. Furthermore, the effect of ATT on spatially-resolved spectroscopy measurements is shown to decrease the calculated muscle hemoglobin concentration and to increase oxygen saturation.

Functional near-infrared spectroscopy: current status and future prospects

Near-infrared spectroscopy (NIRS), which was originally designed for clinical monitoring of tissue oxygenation, has been developing into a useful tool for neuroimaging studies (functional near-infrared spectroscopy). This technique, which is completely noninvasive, does not require strict motion restriction and can be used in a daily life environment. It is expected that NIRS will provide a new direction for cognitive neuroscience research, more so than other neuroimaging techniques, although several problems with NIRS remain to be explored. This review demonstrates the strengths and the advantages of NIRS, clarifies the problems, and identifies the limitations of NIRS measurements. Finally, its future prospects are described.

Intraoperative monitoring of depth-dependent hemoglobin concentration changes during carotid endarterectomy by time-resolved spectroscopy

By measuring the adult human head during carotid endarterectomy, we investigate the depth sensitivity of two methods for deriving the absorption coefficient changes (Dmu(a)) from time-resolved reflectance data to absorption changes in inhomogeneous media: (1) the curve-fitting method based on the diffusion equation (DE-fit method) and (2) the time-independent calculation based on the modified Lambert-Beer law (MLB method). Remarkable differences in the determined values of Dmu(a) caused by clamping the external carotid artery and subsequently clamping the common carotid artery were observed between the methods. The DE-fit method was more sensitive to mu(a) changes in cerebral tissues, whereas the MLB method was rather sensitive to mu(a) changes in the extracerebral tissues. Our results indicated that the DE-fit was useful for monitoring the cerebral blood circulation and oxygenation during neurosurgical operations. In addition, the combined evaluation of mu(a) changes with the DE-fit and MLB methods will provide us with more available information about the hemodynamic changes in the depth direction.

In vivo time-resolved reflectance spectroscopy of the human forehead

We present an in vivo broadband spectroscopic characterization of the human forehead. Absorption and scattering properties are measured on five healthy volunteers at five different interfiber distances, using time-resolved diffuse spectroscopy and interpreting data with a model of the diffusion equation for a homogeneous semi-infinite medium. A wavelength-tunable mode-locked laser and time-correlated single-photon counting detection are employed, enabling fully spectroscopic measurements in the range of 700-1000 nm. The results show a large variation in the absorption and scattering properties of the head depending on the subject, whereas intrasubject variations, assessed at different interfiber distances, appear less relevant, particularly for what concerns the absorption coefficient. The high intersubject variability observed indicates that a unique set of optical properties for modeling the human head cannot be used correctly. To better interpret the results of the analysis of in vivo measurements, we performed a set of four-layer model Monte Carlo simulations based on different data sets for the optical properties of the human head, partially derived from the literature. The analysis indicated that, when simulated time-resolved curves are fitted with a homogeneous model for the photon migration, the retrieved absorption and reduced scattering coefficients are much closer to superficial layer values (i.e., scalp and skull) than to deeper layer ones (white and gray matter). In particular, for the shorter interfiber distances, the recovered values can be assumed as a good estimate of the optical properties of the first layer.

Time-domain Green functions for diffuse light in two adjoining turbid half-spaces

Propagation of light emitted by an instantaneous source located above a plane interface between two semi-infinite turbid media is considered using the diffusion approximation. Green functions are derived for an instantaneous line source and an instantaneous point source by the method of Bellman et al. [Philos. Mag. 40, 297 (1949)], which is based on integral transforms. Both two-dimensional and three-dimensional Green functions for diffuse light have been obtained in the form of single integrals that allow for fast calculation of the specific intensity in the whole space. The influence of the optical parameters of the two media (diffusion coefficients, absorptions, and refractive indices) on the shapes of the contour lines of the specific intensity is analyzed.

Perturbation and differential Monte Carlo methods for measurement of optical properties in a layered epithelial tissue model

The use of perturbation and differential Monte Carlo (pMC/dMC) methods in conjunction with nonlinear optimization algorithms were proposed recently as a means to solve inverse photon migration problems in regionwise heterogeneous turbid media. We demonstrate the application of pMC/dMC methods for the recovery of optical properties in a two-layer extended epithelial tissue model from experimental measurements of spatially resolved diffuse reflectance. The results demonstrate that pMC/dMC methods provide a rapid and accurate approach to solve two-region inverse photon migration problems in the transport regime, that is, on spatial scales smaller than a transport mean free path and in media where optical scattering need not dominate absorption. The pMC/dMC approach is found to be effective over a broad range of absorption (50 to 400%) and scattering (70 to 130%) perturbations. The recovery of optical properties from spatially resolved diffuse reflectance measurements is examined for different sets of source-detector separation. These results provide some guidance for the design of compact fiber-based probes to determine and isolate optical properties from both epithelial and stromal layers of superficial tissues.

Simple algorithm for the measurement of absorption coefficients of a two-layered medium by spatially resolved and time-resolved reflectance

An inversion procedure for the recovery of absorption coefficients of a two-layered semi-infinite diffusive medium by use of time-resolved reflectance measured at two different source-detector distances is proposed. The inversion procedure is based on the property of the photon diffusion equation; i.e., the solution of the diffusion equation for the time-resolved reflectance measured at a longer source--detector distance coincides with that measured at a shorter one by a proper temporal, spatial, and intensity transformation. This inversion procedure, used together with the results of one set of Monte Carlo simulations, is validated as working well when the values of the scattering coefficients of the two layers and the thickness of the first layer are within a range of interest in tissue optics.

Extraction of depth-dependent signals from time-resolved reflectance in layered turbid media

We try a new approach with near-IR time-resolved spectroscopy, to separate optical signals originated in the upper layer from those in the lower layer and to selectively determine the absorption coefficient (mu(a)) of each layer in a two-layered turbid medium. The difference curve in the temporal profiles of light attenuation between a target and a reference medium is divided into segments along the time axis, and a slope of each segment is calculated to determine the depth-dependent mu(a). The depth-dependent mu(a) values are estimated under various conditions in which mu(a) and the reduced scattering coefficient (mu(s)') of each layer are changed with a Monte Carlo simulation and in phantom experiments. Temporal variation of them represents the difference in mu(a) between two layers when mu(s)' of a reference is the same as that of the upper layer of the target. The discrepancies between calculated mu(a) and the real mu(a) depend on the ratio of the real mu(a) of the upper layer to that of the lower layer, and our approach enables us to estimate the ratio of mu(a) between the two layers. These results suggest the potential that mu(a) of the lower layer can be determined by our procedure.

Reevaluation of near-infrared light propagation in the adult human head: implications for functional near-infrared spectroscopy

Using both experimental and theoretical methods, we examine the contribution of different parts of the head to near-IR (NIR) signal. Time-resolved spectroscopy is employed to measure the mean optical path length (PL), and the absorption (mu(a)) and reduced scattering (mu(s)') coefficients in multiple positions of the human head. Monte Carlo simulations are performed on four-layered head models based on an individual magnetic resonance imaging (MRI) scan to determine mu(a) and mu(s)' in each layer of the head by solving inverse problems, and to estimate the partial path length in the brain (p-PL) and the spatial sensitivity to regions in the brain at the source-detector separation of 30 mm. The PL is closely related to the thickness of the scalp, but not to that of other layers of the head. The p-PL is negatively related to the PL and its contribution ratio to the PL is 5 to 22% when the differential path length factor is 6. Most of the signal attributed to the brain comes from the upper 1 to 2 mm of the cortical surface. These results indicate that the NIR signal is very sensitive to hemodynamic changes associated with functional brain activation in the case that changes in the extracerebral tissue are ignorable.

Non-invasive imaging and characterisation of human foot by multi-probe laser reflectometry and Monte Carlo simulation

Diffusely backscattered signals from the human foot sole tissues of normal subjects (n = 5) were obtained by multiprobe laser reflectometry. The colour-coded images were constructed from data on the variation of normalised backscattered intensity (NBI), after interpolation and median filtering. The maximum and minimum NBI values at the arch and heel regions of the foot sole, respectively, were observed. The mean NBI at the arch region was significantly higher compared with that at other regions (p < 0.0001). The images of optical parameters of normal tissues show point-to-point variation, attributed to their compositional changes. The pattern of variation of the NBI of a diabetic subject (glucose level 170 mg dl(-1)) was associated with highly significant variation at the lateral sides of the fore- and middle-foot compared with that of normal subjects.

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.

Green functions for diffuse photon-density waves generated by a line source in two nonabsorbing turbid media in contact

Diffuse photon-density waves generated by an instantaneous line source that is parallel to the interface between two semi-infinite turbid media are studied by use of the diffusion approximation. For two nonabsorbing media the Green functions for diffuse light are obtained based on the Green functions for temperature fields that were derived with the Cagniard-de Hoop method. The boundary conditions for diffuse light take into account the discontinuity in the specific intensity at the interface between two media with different refractive indices. The results of the calculations of the specific intensities and the gradient lines for different sets of parameters are presented.

Characterization and imaging of compositional variation in tissues

The diffuse surface reflectance profiles of the goat's isolated heart, spleen, and adipose tissues by multiprobe laser reflectometer are measured. The normalized backscattered intensity values for adipose, heart, and spleen tissues at source-detector separation 0.2 cm, are 0.060, 0.021, and 0.003, respectively. The optical parameters of these tissues are determined by the best fit (chi2(0.99)) of their spatial profiles with that as obtained by Monte Carlo simulation by iterative procedure. As the optical parameters of these vary over a wide range, adipose and spleen tissues are treated as inhomogeneity of diameter 0.1, 0.2, or 0.3 cm, and placed inside the control (heart) tissue at different depths. Anisotropic simulation of light backscattering or photon depth distribution is significantly different for various tissues. The surface intensity profiles vary depending on the changes in tissue composition. From the horizontal scans of the subtracted images, the photon backscattering simulated images of control and combination of tissues are obtained. By analysis of peak intensity and full-width at half maximum, the type, location, and size of the tissue compositional variation are determined.

Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method

An exact solution of the time-dependent diffusion equation for the case of a two- and a three-layered finite diffusive medium is proposed. The method is based on the decomposition of the fluence rate in a series of eigenfunctions and upon the solution of the consequent transcendental equation for the eigenvalues obtained from the boundary conditions. Comparisons among the solution of the diffusion equation and the results of Monte Carlo simulations show the correctness of the proposed model.

Analysis of the spatial distribution of polarized light backscattered from layered scattering media

The scattering of polarized light from a two layer scattering medium is investigated using Monte Carlo simulations. First order and normalized second order moments are used to analyze the spatial properties of the emerging light in different polarization states. Linearly and circularly polarized illumination is used to probe different depths. Absorption and layer thickness are varied and it is demonstrated that the determination of these values is aided by the inclusion of polarization information. The lateral and depth localization of light by polarization subtraction is also quantified. Potential applications of these techniques are burn depth and melanoma thickness measurements.

Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness

A dual wavelength time-resolved reflectance system was developed for monitoring haemoglobin saturation noninvasively. At each wavelength, the time-resolved reflectance data were fitted to a diffusion model of light propagation in a homogeneous, semi-infinite medium to yield the absolute scattering and absorption coefficients. The absorption coefficients were then used to calculate haemoglobin saturation. A two-layer phantom containing human erythrocytes in a scattering solution in the bottom layer was used to study system performance under more realistic conditions. The top layer was chosen to simulate either skin or fat and the oxygenation of the bottom layer, which corresponded to muscle, was controlled. The thickness of the fat layer was varied from 1.5 to 10 mm to investigate the effects of increasing the top layer thickness. These results, obtained with the simple diffusion model, were compared with simultaneous measurements of oxygenation made directly in the bottom layer. Errors in estimating haemoglobin saturation with this method ranged from 5-11% depending on the thickness of the top layer and its optical properties.

Analytical approximate solutions of the time-domain diffusion equation in layered slabs

Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

Reconstruction of absorber concentrations in a two-layer structure by use of multidistance time-resolved reflectance spectroscopy

The characterization of a two-layer structure was investigated by use of time-resolved reflectance over a wide spectral range. We exploited the nonlinear dependence of the measured spectra on the upper-and lower-layer properties to formulate an algorithm for the recovery of absorber concentrations in both layers. The method assumes that the spectral features of the key absorbers are known, but it does not rely on a priori knowledge of the layer thickness. Phantom tests confirmed the accuracy of the estimate of the absorber concentrations to within 10% for thickness values ranging from 0.3 to 1.2 cm. Multidistance absorption spectra from 610 to 1000 nm were obtained in vivo from the forearms of human subjects, allowing us to estimate the concentration of key tissue constituents in a two-layer approximation. Good agreement between the reconstructed spectra and the experimental data taken from two volunteers with opposite predominance of adipose and muscular tissues demonstrated the validity of this approach.

Recovery of optical parameters in multiple-layered diffusive media: theory and experiments

Diffuse photon density waves have lately been used both to characterize diffusive media and to locate and characterize hidden objects, such as tumors, in soft tissue. In practice, most biological media of medical interest consist of various layers with different optical properties, such as the fat layer in the breast or the different layers present in the skin. Also, most experimental setups consist of a multilayered system, where the medium to be characterized (i.e., the patient's organ) is usually bounded by optically diffusive plates. Incorrect modeling of interfaces may induce errors comparable to the weak signals obtained from tumors embedded deep in highly heterogeneous tissue and lead to significant reconstruction artifacts. To provide a means to analyze the data acquired in these configurations, the basic expressions for the reflection and transmission coefficients for diffusive-diffusive and diffusive-nondiffusive interfaces are presented. A comparison is made between a diffusive slab and an ordinary dielectric slab, thus establishing the limiting distance between the two interfaces of the slab for multiple reflections between them to be considered important. A rigorous formulation for multiple-layered (M-layered) diffusive media is put forward, and a method for solving any M-layered medium is shown. The theory presented is used to characterize a two-layered medium from transmission measurements, showing that the coefficients of scattering, mu'(s) , and absorption, mu(a) , are retrieved with great accuracy. Finally, we demonstrate the simultaneous retrieval of both mu;(s) and mu(a).

Determining changes in NIR absorption using a layered model of the human head

A theoretical approach is presented to determine absorption changes in different compartments of a layered structure from distributions of times of flight of photons. In addition resulting changes in spatial profiles of time-integrated intensity and mean time of flight are calculated. The capability of a single-distance, time-domain method to determine absorption changes with depth resolution is tested on a layered phantom. We apply this method to in vivo measurements on the human head (motor stimulation, Valsalva manoeuvre) and introduce a small-sized time-domain experimental set-up suitable for bedside monitoring.

Quantifying the properties of two-layer turbid media with frequency-domain diffuse reflectance

Noncontact, frequency-domain measurements of diffusely reflected light are used to quantify optical properties of two-layer tissuelike turbid media. The irradiating source is a sinusoidal intensity-modulated plane wave, with modulation frequencies ranging from 10 to 1500 MHz. Frequency-dependent phase and amplitude of diffusely reflected photon density waves are simultaneously fitted to a diffusion-based two-layer model to quantify absorption (mu(a)) and reduced scattering (mu(s)') parameters of each layer as well as the upper-layer thickness (l). Study results indicate that the optical properties of two-layer media can be determined with a percent accuracy of the order of +/-9% and +/-5% for mu(a) and mu(s)', respectively. The accuracy of upper-layer thickness (l) estimation is as good as +/-6% when optical properties of upper and lower layers are known. Optical property and layer thickness prediction accuracy degrade significantly when more than three free parameters are extracted from data fits. Problems with convergence are encountered when all five free parameters (mu(a) and mu(s)' of upper and lower layers and thickness l) must be deduced.

Study of near infrared technology for intracranial hematoma detection

Although intracranial hematoma detection only requires the continuous wave technique of near infrared spectroscopy (NIRS), previous studies have shown that there are still some problems in obtaining very accurate, reliable hematoma detection. Several of the most important limitations of NIR technology for hematoma detection such as the dynamic range of detection, hair absorption, optical contact, layered structure of the head, and depth of detection are reported in this article. A pulsed light source of variable intensity was designed and studied in order to overcome hair absorption and to increase the dynamic range and depth of detection. An adaptive elastic optical probe was made to improve the optical contact and decrease contact noise. A new microcontroller operated portable hematoma detector was developed. Due to the layered structure of the human head, simulation on a layered medium was analyzed experimentally. Model inhomogeneity tests and animal hematoma tests showed the effectiveness of the improved hematoma detector for intracranial hematoma detection.

Diffusion coefficient in photon diffusion theory

The choice of the diffusion coefficient to be used in photon diffusion theory has been a subject of discussion in recent publications on tissue optics. We compared several diffusion coefficients with the apparent diffusion coefficient from the more fundamental transport theory, D(app). Application to point sources in turbid media, for which exact solutions are available, showed that D(app) has to be preferred. We give a simple equation to approximate D(app) for several phase functions that apply to tissue optics. Reasons for the remaining discrepancies in diffusion coefficients applied to time-resolved and time-averaged descriptions of photon propagation in homogeneous turbid media are discussed.

Investigation of two-layered turbid media with time-resolved reflectance

Light propagation in two-layered turbid media that have an infinitely thick second layer is investigated with time-resolved reflectance. We used a solution of the diffusion equation for this geometry to show that it is possible to derive the absorption and the reduced scattering coefficients of both layers if the relative reflectance is measured in the time domain at two distances and if the thickness of the first layer is known. Solutions of the diffusion equation for semi-infinite and homogeneous turbid media are also applied to fit the reflectance from the two-layered turbid media in the time and the frequency domains. It is found that the absorption coefficient of the second layer can be more precisely derived for matched than for mismatched boundary conditions. In the frequency domain, its determination is further improved if phase and modulation data are used instead of phase and steady-state reflectance data. Measurements of the time-resolved reflectance were performed on solid two-layered tissue phantoms that confirmed the theoretical results.

Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues

We analyse the limits of the diffusion approximation to the time-independent equation of radiative transfer for homogeneous and heterogeneous biological media. Analytical calculations and finite-difference simulations based on diffusion theory are compared with discrete-ordinate, finite-difference transport calculations. The influence of the ratio of absorption and transport scattering coefficient (mu(a)/mu'(s)) on the accuracy of the diffusion approximation are quantified and different definitions for the diffusion coefficient, D, are discussed. We also address effects caused by void-like heterogeneities in which absorption and scattering are very small compared with the surrounding medium. Based on results for simple homogeneous and heterogeneous systems, we analyse diffusion and transport calculation of light propagation in the human brain. For these simulations we convert density maps obtained from magnetic resonance imaging (MRI) to optical-parameter maps (mu(a) and mu'(s)) of the brain. We show that diffusion theory fails to describe accurately light propagation in highly absorbing regions, such as haematoma, and void-like spaces, such as the ventricles and the subarachnoid space.

Noninvasive determination of the optical properties of two-layered turbid media

Light propagation in two-layered turbid media having an infinitely thick second layer is investigated in the steady-state, frequency, and time domains. A solution of the diffusion approximation to the transport equation is derived by employing the extrapolated boundary condition. We compare the reflectance calculated from this solution with that computed with Monte Carlo simulations and show good agreement. To investigate if it is possible to determine the optical coefficients of the two layers and the thickness of the first layer, the solution of the diffusion equation is fitted to reflectance data obtained from both the diffusion equation and the Monte Carlo simulations. Although it is found that it is, in principle, possible to derive the optical coefficients of the two layers and the thickness of the first layer, we concentrate on the determination of the optical coefficients, knowing the thickness of the first layer. In the frequency domain, for example, it is shown that it is sufficient to make relative measurements of the phase and the steady-state reflectance at three distances from the illumination point to obtain useful estimates of the optical coefficients. Measurements of the absolute steady-state spatially resolved reflectance performed on two-layered solid phantoms confirm the theoretical results.

A solid tissue phantom for photon migration studies

A solid tissue phantom made of agar, Intralipid and black ink is described and characterized. The preparation procedure is fast and easily implemented with standard laboratory equipment. An instrumentation for time-resolved transmittance measurements was used to determine the optical properties of the phantom. The absorption and the reduced scattering coefficients are linear with the ink and Intralipid concentrations, respectively. A systematic decrease of the reduced scattering coefficient dependent on the agar content is observed, but can easily be managed. The phantom is highly homogeneous and shows good repeatability among different preparations. Moreover, agar inclusions can be easily embedded in either solid or liquid matrixes, and no artefacts are caused by the solid-solid or solid-liquid interfaces. This allows one to produce reliable and realistic inhomogeneous phantoms with known optical properties, particularly interesting for studies on optical imaging through turbid media.

Effect of the scattering delay on time-dependent photon migration in turbid media

We modified the diffusion approximation of the time-dependent radiative transfer equation to account for a finite scattering delay time. Under the usual assumptions of the diffusion approximation, the effect of the scattering delay leads to a simple renormalization of the light velocity that appears in the diffusion equation. Accuracy of the model was evaluated by comparison with Monte Carlo simulations in the frequency domain for a semi-infinite geometry. A good agreement is demonstrated for both matched and mismatched boundary conditions when the distance from the source is sufficiently large. The modified diffusion model predicts that the neglect of the scattering delay when the optical properties of the turbid material are derived from normalized frequency- or time-domain measurements should result in an underestimation of the absorption coefficient and an overestimation of the transport coefficient. These observations are consistent with the published experimental data.