We study dynamic light scattering using numerical techniques such as Monte Carlo and finite-difference time-domain (FDTD). These methods leverage recent advances in computational power to directly model dynamic light scattering in arbitrary three dimensional voxelized geometries. These approaches do not require assumptions about the degree of multiple scattering or the form of the autocorrelation function and are capable of rapidly evaluating the effects of changes in particle motion. We obtain depth-resolved vascular geometries using our two-photon microscope and assign each voxel location-appropriate optical properties. These simulations have been used to better understand the depth dependence of measured fluorescence signals and to quantify the effects of multiple scattering events on laser speckle contrast imaging (LSCI).
Laser speckle contrast imaging has become a ubiquitous tool for imaging blood flow in a variety of tissues. However, due to its widefield imaging nature, the measured speckle contrast is a depth integrated quantity and interpretation of baseline values and the depth dependent sensitivity of those values to changes in underlying flow has not been thoroughly evaluated. Using dynamic light scattering Monte Carlo simulations, the sensitivity of the autocorrelation function and speckle contrast to flow changes in the cerebral cortex was extensively examined. These simulations demonstrate that the sensitivity of the inverse autocorrelation time, 1/τc, varies across the field of view: directly over surface vessels 1/τc is strongly localized to the single vessel, while parenchymal ROIs have a larger sensitivity to flow changes at depths up to 500 μm into the tissue and up to 200 μm lateral to the ROI. It is also shown that utilizing the commonly used models the relate 1τc to flow resulted in nearly the same sensitivity to the underlying flow, but fail to accurately relate speckle contrast values to absolute 1/τc.
Few methods exist that can accurately handle dynamic light scattering in the regime between single and highly multiple scattering. We demonstrate dynamic light scattering Monte Carlo (DLS-MC), a numerical method by which the electric field autocorrelation function may be calculated for arbitrary geometries if the optical properties and particle motion are known or assumed. DLS-MC requires no assumptions regarding the number of scattering events, the final form of the autocorrelation function, or the degree of correlation between scattering events. Furthermore, the method is capable of rapidly determining the effect of particle motion changes on the autocorrelation function in heterogeneous samples. We experimentally validated the method and demonstrated that the simulations match both the expected form and the experimental results. We also demonstrate the perturbation capabilities of the method by calculating the autocorrelation function of flow in a representation of mouse microvasculature and determining the sensitivity to flow changes as a function of depth.
Speckle contrast imaging enables rapid mapping of relative blood flow distributions using camera detection of back-scattered laser light. However, speckle derived flow measures deviate from direct measurements of erythrocyte speeds by 47 ± 15% (n = 13 mice) in vessels of various calibers. Alternatively, deviations with estimates of volumetric flux are on average 91 ± 43%. We highlight and attempt to alleviate this discrepancy by accounting for the effects of multiple dynamic scattering with speckle imaging of microfluidic channels of varying sizes and then with red blood cell (RBC) tracking correlated speckle imaging of vascular flows in the cerebral cortex. By revisiting the governing dynamic light scattering models, we test the ability to predict the degree of multiple dynamic scattering across vessels in order to correct for the observed discrepancies between relative RBC speeds and multi-exposure speckle imaging estimates of inverse correlation times. The analysis reveals that traditional speckle contrast imagery of vascular flows is neither a measure of volumetric flux nor particle speed, but rather the product of speed and vessel diameter. The corrected speckle estimates of the relative RBC speeds have an average 10 ± 3% deviation in vivo with those obtained from RBC tracking.
Laser speckle contrast imaging (LSCI) is a powerful and simple method for full field imaging of blood flow. However, the depth dependence and the degree of multiple scattering have not been thoroughly investigated. We employ three-dimensional Monte Carlo simulations of photon propagation combined with high resolution vascular anatomy to investigate these two issues. We found that 95% of the detected signal comes from the top 700 μm of tissue. Additionally, we observed that single-intravascular scattering is an accurate description of photon sampling dynamics, but that regions of interest (ROIs) in areas free of obvious surface vessels had fewer intravascular scattering events than ROI over resolved surface vessels. Furthermore, we observed that the local vascular anatomy can strongly affect the depth dependence of LSCI. We performed simulations over a wide range of intravascular and extravascular scattering properties to confirm the applicability of these results to LSCI imaging over a wide range of visible and near-infrared wavelengths.
We develop an efficient method for accurately calculating the electric field of tightly focused laser beams in the presence of specific configurations of microscopic scatterers. This Huygens–Fresnel wave-based electric field superposition (HF-WEFS) method computes the amplitude and phase of the scattered electric field in excellent agreement with finite difference time-domain (FDTD) solutions of Maxwell’s equations. Our HF-WEFS implementation is 2–4 orders of magnitude faster than the FDTD method and enables systematic investigations of the effects of scatterer size and configuration on the focal field. We demonstrate the power of the new HF-WEFS approach by mapping several metrics of focal field distortion as a function of scatterer position. This analysis shows that the maximum focal field distortion occurs for single scatterers placed below the focal plane with an offset from the optical axis. The HF-WEFS method represents an important first step toward the development of a computational model of laser-scanning microscopy of thick cellular/tissue specimens.
Many materials, including biological tissue, attenuate light mostly by scattering. Because the scattered field is exquisitely sensitive to perturbations, control over the distribution of light after strong scattering is challenging. Though wavefront-shaping techniques enable arbitrary generation of light distributions within strongly scattering or turbid media in principle, the input wavefront necessary for the chosen light distribution is generally unknown. Using two different computational models, we demonstrate a technique called virtual aperture culling of the eigenmodes of a resonator (VACER), which uses weak spatial filtering mechanisms for noninvasive light focusing at arbitrary positions within turbid media. Compatibility with weak spatial filtering mechanisms is critical to innocuously focusing light within turbid media. One model represents an ideal system and could be physically implemented in some scenarios with digital optical phase conjugation, while the other model simulates phase conjugation via gain saturation, and its physical realization would operate fast enough to avoid the effects of speckle decorrelation in biological tissue. Modeling results establish that sound physical principles underlie VACER.
In vivo surface imaging of fluorescently labeled vasculature has become a widely used tool for functional brain imaging studies. Techniques such as phosphorescence quenching for oxygen tension measurements and indocyanine green fluorescence for vessel perfusion monitoring rely on surface measurements of vascular fluorescence. However, the depth dependence of the measured fluorescence signals has not been modeled in great detail. In this paper, we investigate the depth dependence of the measured signals using a three-dimensional Monte Carlo model combined with high resolution vascular anatomy. We found that a bulk-vascularization assumption to modeling the depth dependence of the signal does not provide an accurate picture of penetration depth of the collected fluorescence signal in most cases. Instead the physical distribution of microvasculature, the degree of absorption difference between extravascular and intravascular space, and the overall difference in absorption at the excitation and emission wavelengths must be taken into account to determine the depth penetration of the fluorescence signal. Additionally, we found that using targeted illumination can provide for superior surface vessel sensitivity over wide-field illumination, with small area detection offering an even greater amount of sensitivity to surface vasculature. Depth sensitivity can be enhanced by either increasing the detector area or increasing the illumination area. Finally, we see that excitation wavelength and vessel size can affect intra-vessel sampling distribution, as well as the amount of signal that originates from inside the vessel under targeted illumination conditions.
A linear coherent superposition method for estimating the plane wave far-field scattering pattern from multiple biological cells computed by the finite-difference time-domain (FDTD) method is presented. The method enables the FDTD simulation results of scattering from a small number of complex scatterers, such as biological cells, to be used to estimate the far-field pattern from a large group of those same scatterers. The superposition method can be used to reduce the computational cost of FDTD simulations by enabling a single large scattering problem to be broken into smaller problems with more practical computational requirements. It is found that the method works best in cases where there is little multiple scattering interaction between adjacent cells, so the far-field pattern of multicell geometry can simply be calculated as a phase-adjusted linear superposition of the scattering from individual cells. A strategy is also presented for choosing the minimum number of cells in cases with significant multiple scattering interactions between cells.
The FDTD method was used to simulate focused Gaussian beam propagation through multiple inhomogeneous biological cells. To our knowledge this is the first three dimensional computational investigation of a focused beam interacting with multiple biological cells using FDTD. A parametric study was performed whereby three simulated cells were varied by organelle density, nuclear type and arrangement of internal cellular structure and the beam focus depth was varied within the cluster of cells. Of the organelle types investigated, it appears that the cell nuclei are responsible for the greatest scattering of the focused beam in the configurations studied. Additional simulations to determine the optical scattering from 27 cells were also run and compared to the three cell case. No significant degradation of two-photon lateral imaging resolution was predicted to occur within the first 40 µm of imaging depth.
The growth of computing power has greatly improved our ability to extract quantitative information about complicated three-dimensional structures from microscope images. New hardware techniques are also being developed to provide suitable images for these tasks. However, a need exists for synthetic data to test these new developments. The work reported here was motivated by studies of embryo health, but similar needs exist across the field of microscopy. We report a rigorous computer model, based on Maxwell’s equations, that can produce the required synthetic images for bright-field, differential interference contrast, interferometric imaging, and polarimetric imaging. After a description of the algorithm, sample results are presented, followed by a discussion of future plans and applications.
We describe a novel Monte Carlo code for photon migration through 3D media with spatially varying optical properties. The code is validated against analytic solutions of the photon diffusion equation for semi-infinite homogeneous media. The code is also cross-validated for photon migration through a slab with an absorbing heterogeneity. A demonstration of the utility of the code is provided by showing time-resolved photon migration through a human head. This code, known as ‘tMCimg’, is available on the web and can serve as a resource for solving the forward problem for complex 3D structural data obtained by MRI or CT.
We introduce a novel and efficient method to provide solutions to inverse photon migration problems in heterogeneous turbid media. The method extracts derivative information from a single Monte Carlo simulation to permit the rapid determination of rates of change in the detected photon signal with respect to perturbations in background tissue optical properties. We then feed this derivative information to a nonlinear optimization algorithm to determine the optical properties of the tissue heterogeneity under examination. We demonstrate the use of this approach to solve rapidly a two-region inverse problem of photon migration in the transport regime, for which diffusion-approximation-based approaches are not applicable.
We combine the finite-difference time-domain method with pulse response techniques in order to calculate the light scattering properties of biological cells over a range of wavelengths simultaneously. The method we describe can be used to compute the scattering patterns of cells containing multiple heterogeneous organelles, providing greater geometric flexibility than Mie theory solutions. Using a desktop computer, we calculate the scattering patterns for common homogeneous models of biological cells and also for more complex representations of cellular morphology. We find that the geometry chosen significantly impacts scattering properties, emphasizing the need for careful consideration of appropriate theoretical models of cellular scattering and for accurate microscopic determination of optical properties.
We have examined the light-scattering properties of inhomogeneous biological cells through a combination of theoretical simulations and goniometric measurements. A finite-difference time-domain (FDTD) technique was used to compute intensity as a function of scattering angle for cells containing multiple organelles and spatially varying index of refraction profiles. An automated goniometer was constructed to measure the scattering properties of dilute cell suspensions. Measurements compared favorably with FDTD predictions. FDTD and experimental results indicate that scattering properties are strongly influenced by cellular biochemical and morphological structure.
Transscleral cyclophotocoagulation (TSCPC) is currently performed clinically as an effective treatment for end-stage glaucoma. We develop a theoretical model for the analysis of optical attenuation phenomena during TSCPC as a basis for selection of an optimal wavelength. A multilayered Monte Carlo model was developed to calculate the fluence and the rate of heat generation in each tissue layer for the wavelengths of Nd:YAG, diode, ruby, krypton yellow, and argon lasers. Of the five wavelengths under study, our theoretical results suggest that the diode laser wavelength offers the best penetration through the conjunctiva, sclera, and ciliary muscle and highest absorption within the ciliary pigment epithelium.
The finite-difference time-domain (FDTD) technique is used to compute light scattering from biological cells in two dimensions. Results are presented for the computed scattering patterns of cells containing multiple organelles. This method provides considerably more flexibility than Mie theory because of its ability to model inhomogeneous objects such as cells.
Using the finite-difference time-domain method, three-dimensional scattering patterns are computed for cells containing multiple organelles. The scattering cross section and average cosine of the scattering angle are computed for cells as a function of volume fraction of melanin granules and mitochondria. Results show that small organelles play a significant role in light scattering from cells, and the volume fraction of organelles affects both the total amount of scattered light and the angular distribution of scattered light.
The relationship between optical properties and image contrast in confocal imaging is investigated. A Monte Carlo simulation has been developed to analyze the effects of changes in scattering, index of refraction, and absorption in a three-layer medium. Contrast was calculated from the computed signal-to-background ratios for changes in tissue optical properties. Results show that the largest source of contrast is changes in refractive index.
The transfer function of a turbid medium such as biological tissue provides a method of analyzing the spatial resolution of a time-resolved tissue imaging system. A method is presented of calculating the transfer function with the use of a Monte Carlo simulation. The model allows the computation of the time-resolved line-spread function of a sample of thickness d from a simulation of thickness d/2 by use of reciprocity under certain conditions, and the transfer function can then be computed from the line-spread function. Results with this method agree with previously published theoretical and experimental results.