Analytic evaluation of diffuse fluence error in multi-layer scattering media with discontinuous refractive index

A simple analytic method of estimating the error involved in using an approximate boundary condition for diffuse radiation in two adjoining scattering media with differing refractive index is presented. The method is based on asymptotic planar fluences and enables the relative error to be readily evaluated without recourse to Monte Carlo simulation. Three examples of its application are considered: (1) evaluating the error in calculating the diffuse fluences at a boundary between two media with differing refractive index and dissimilar scattering properties (2) the dependence of the relative error in a multilayer medium with discontinuous refractive index on the ratio of the reduced scattering coefficient to the absorption coefficient ms'/ma (3) the parametric dependence of the error in the radiant flux Js at the surface of a three-layer medium. The error is significant for strongly forward biased scattering media with non-negligible absorption and is cumulative in multi-layered media with refractive index increments between layers.Comment: 21 pages 7 Figures Text further revise

Analysis of diffusion theory and similarity relations for light reflectance by turbid media

Both diffusion theory and similarity relations for light reflectance by semi-infinite turbid media have been analyzed by comparing their computational results with Monte Carlo simulation results. Since a large number of photon packets are traced, the variance of the Monte Carlo simulation results is small enough to reveal the detailed defects of diffusion theories and similarity relations. We have demonstrated that both diffusion theory and similarity relations provide very accurate results when the photon sources are isotropic and one transport mean free path below the turbid medium surface or deeper. This analysis has led to a hybrid model of Monte Carlo simulation and diffusion theory, which combines the accuracy advantage of Monte Carlo simulation and the speed advantage of diffusion theory. The similarity relations are used for the transition from the Monte Carlo simulation to the diffusion theory

Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media

Light reflectance by semi-infinite turbid media is modeled by a hybrid of Monte Carlo simulation and diffusion theory, which combines the accuracy of Monte Carlo simulation near the source and the speed of diffusion theory distant from the source. For example, when the turbid medium has the following optical properties—absorption coefficient 1 cm^(-1), scattering coefficient 100 cm^(-1), anisotropy 0.9, and refractive-index-matched boundary—the hybrid simulation is 7 times faster than the pure Monte Carlo simulation (100,000 photon packets were traced), and the difference between the two simulations is within 2 standard deviations of the Monte Carlo simulation

Multiple-source optical diffusion approximation for a multilayer scattering medium

A method for improving the accuracy of the optical diffusion theory for a multilayer scattering medium is presented. An infinitesimally narrow incident light beam is replaced by multiple isotropic point sources of different strengths that are placed in the scattering medium along the incident beam. The multiple sources are then used to develop a multilayer diffusion theory. Diffuse reflectance is then computed using the multilayer diffusion theory and compared with accurate data computed by the Monte Carlo method. This multisource method is found to be significantly more accurate than the previous single-source method

Angular Distribution of Diffuse Reflectance in Biological Tissue

doi:10.1364/AO.46.006552We measured angular-resolved diffuse reflectance in tissue samples of different anisotropic characteristics. Experimental measurements were compared with theoretical results based on the diffusion approximation. The results indicated that the angular distribution in isotropic tissue was the same as in isotropic phantoms. Under normal incidence, the measured angular profiles of diffuse reflectance approached the Lambertian distribution when the evaluation location was far away from the incident point. The skewed angular profiles observed under oblique incidence could be explained using the diffuse model. The anisotropic tissue structures in muscle showed clear effects on the measurements especially at locations close to the light incidence. However, when measuring across the muscle fiber orientations, the results were in good agreement with those obtained in isotropic samples.This project was supported in part by National Science Foundation grant CBET-0643190, and the National Research Initiative of the USDA Cooperative State Research, Education, and Extension Service under grant 2006-35503-17619

Wavelength Tuneable Frequency Domain Photon Migration Spectrometer for Tissue-like Media

Frequency domain spectrometers use intensity modulated light to quantitatively interrogate turbid media. The modulation frequencies employed are in the radiofrequency range. Intensity modulated light launched into a turbid medium generates photon density fluctuations with wave like character that oscillates at the modulation frequency. These density fluctuations are named diffuse photon density waves, and it has been shown that the amplitude and phase of the photon density wave inside the medium depends on its optical properties. Hence by measuring the amplitude and phase of the photon density wave the optical properties of the medium can be estimated. This is the basic working principle of a frequency domain photon migration spectrometer. Frequency domain spectrometers fabricated with laser diodes are limited to discrete wavelengths thereby making compromises on the information about the media under test. In this research a wavelength tuneable frequency domain spectrometer was constructed by modulating the output intensity of a titanium: sapphire laser using an acousto-optic modulator. A low noise avalanche photodiode module in conjunction with a lock-in amplifier was used to measure the amplitude attenuation and phase lag inside a turbid sample. The frequency domain spectrometer was tested for accuracy and precision by estimating the optical properties of an important tissue simulation phantom, Intralipid , at a representative wavelength 790 nm. The results indicated that the spectrometer estimates absorption with an accuracy of 10%. The instrument estimates the absorption and reduced scattering coefficients with a precision of 3% and 6%, respectively. Optical properties of Intralipid were measured from 710-850 nm in the therapeutic window. The results were compared with published data measured by other methods and similar frequency domain techniques. The absorption coefficient agrees within 10% with results from a time domain measurement. The reduced scattering coefficient was within the error limits of other reported measurements. At 750 nm the reduced scattering agrees within 5% with the results from a continuous wave, time domain and within 1% from another frequency domain measurement, and at 811 and 849 nm this agreement is within 9%. A Mie theory prediction of the reduced scattering coefficient based on a measurement of the particle size distribution by a Mastersizer 2000 is larger than the frequency domain results by 6%. The spectrometer was used to determine the optical temperature coefficient of Intralipid , exploring its potential as a non invasive temperature monitoring device. The measured minute change in the absorption coefficient suggests a minimum observable temperature change of 4'C, which for most practical applications means that the precision needs to improve. The effect of glucose on the optical properties of Intralipid indicates that the absorption coefficient decreases steadily at 730 nm up to 1000mg/dL. The reduced scattering coefficient decreases with increasing glucose concentration at most of the wavelengths. This work quantified the absorption and reduced scattering of Intralipid over a larger wavelength range (in the therapeutic window) than before. This is the first time the effects of temperature on the optical properties of a turbid medium monitored with a frequency domain spectrometer. Specific information about the precision and accuracy which can be achieved with the current technology is documented. Current precision is not sufficient for many applications that would benefit from separation of absorption and scattering

Applying Mechanistic Understanding of Optical Absorption and Scattering Phenomena to Enhance the Spectroscopic Analyses of Pharmaceutical Materials

The dissertation uses spatially-resolved spectroscopy to separate absorption and scattering behaviors when NIR light interacts with pharmaceutical materials. The separated absorption and scattering were utilized to enhance mechanistic understanding of NIR diffuse reflectance spectroscopy and improve practical spectroscopic analysis in pharmaceutical applications. Near-Infrared (NIR) chemical imaging based spatially-resolved spectroscopy was used to measure radially-diffused reflectance on pharmaceutical materials. A Monte Carlo simulation based partial least square (PLS) model was constructed to determine the absorption and reduced scattering coefficients in pharmaceutical samples from the measured radially-diffused reflectance. The separated absorption and reduced scattering coefficients were combined with Monte Carlo simulation to provide understanding of the effects of physical properties (e.g., particle size and tablet density) on NIR spectral responses, including absorption and depth of penetration profiles. It was discovered that absorption and reduced scattering coefficients are the dominant factors in determining NIR absorbance and depth of penetration profiles, respectively. Both empirical measurements and Monte Carlo simulation were used to explore the photon radial movements in a chemical imaging setting. It is well understood that radial photon movements among adjacent pixels leaded to blurred 2-D chemical images. A Monte Carlo simulation based deconvolution filter was developed to sharpen a blurred feature in a 2-D image while maintaining the original chemical content of that feature. A new scattering correction method via the reduced scattering coefficient was proposed to specifically reduce physical interference with predictions of chemical properties. The wavelength- and absorption- dependent properties of the reduced scattering coefficient were found to allow specific suppression of physical interference and maintain the original chemical information. Combing the separated optical coefficients with contemporary efficient calibration approaches was found to simplify multivariate model calibration using a reduced calibration dataset, allowing parsimonious multivariate models, and reaching the same or even lower prediction error. To the author\u27s best knowledge, this work is the first example of the application of spatially-resolved spectroscopy to the pharmaceutical field. The enhanced understanding and improved spectroscopic analysis demonstrated in this dissertation is expected to provide groundwork for a wide variety of applications of spatially-resolved spectroscopy in pharmaceutical analyses

Improved mathematical and computational tools for modeling photon propagation in tissue

Thesis (Ph.D.)--Boston UniversityLight interacts with biological tissue through two predominant mechanisms: scattering and absorption, which are sensitive to the size and density of cellular organelles, and to biochemical composition (ex. hemoglobin), respectively. During the progression of disease, tissues undergo a predictable set of changes in cell morphology and vascularization, which directly affect their scattering and absorption properties. Hence, quantification of these optical property differences can be used to identify the physiological biomarkers of disease with interest often focused on cancer. Diffuse reflectance spectroscopy is a diagnostic tool, wherein broadband visible light is transmitted through a fiber optic probe into a turbid medium, and after propagating through the sample, a fraction of the light is collected at the surface as reflectance. The measured reflectance spectrum can be analyzed with appropriate mathematical models to extract the optical properties of the tissue, and from these, a set of physiological properties. A number of models have been developed for this purpose using a variety of approaches -- from diffusion theory, to computational simulations, and empirical observations. However, these models are generally limited to narrow ranges of tissue and probe geometries. In this thesis, reflectance models were developed for a much wider range of measurement parameters, and influences such as the scattering phase function and probe design were investigated rigorously for the first time. The results provide a comprehensive understanding of the factors that influence reflectance, with novel insights that, in some cases, challenge current assumptions in the field. An improved Monte Carlo simulation program, designed to run on a graphics processing unit (GPU), was built to simulate the data used in the development of the reflectance models. Rigorous error analysis was performed to identify how inaccuracies in modeling assumptions can be expected to affect the accuracy of extracted optical property values from experimentallyacquired reflectance spectra. From this analysis, probe geometries that offer the best robustness against error in estimation of physiological properties from tissue, are presented. Finally, several in vivo studies demonstrating the use of reflectance spectroscopy for both research and clinical applications are presented