Three-dimensional computation of focused beam propagation through multiple biological cells

Modeling nonlinear optical microscopy in scattering media, part II. Radiation from focal volume to far-field: tutorial

The development and application of nonlinear optical (NLO) microscopy methods in biomedical research has experienced rapid growth over the past three decades. Despite the compelling power of these methods, optical scattering limits their practical use in biological tissues. This tutorial offers a model-based approach illustrating how analytical methods from classical electromagnetism can be employed to comprehensively model NLO microscopy in scattering media. In Part I, we quantitatively model focused beam propagation in non-scattering and scattering media from the lens to focal volume. In Part II, we model signal generation, radiation, and far-field detection. Moreover, we detail modeling approaches for major optical microscopy modalities including classical fluorescence, multi-photon fluorescence, second harmonic generation, and coherent anti-Stokes Raman microscopy.

Modeling nonlinear optical microscopy in scattering media, part I. Propagation from lens to focal volume: tutorial

The development and application of nonlinear optical (NLO) microscopy methods in biomedical research have experienced rapid growth over the past three decades. Despite the compelling power of these methods, optical scattering limits their practical use in biological tissues. This tutorial offers a model-based approach illustrating how analytical methods from classical electromagnetism can be employed to comprehensively model NLO microscopy in scattering media. In Part I, we quantitatively model focused beam propagation in non-scattering and scattering media from the lens to focal volume. In Part II, we model signal generation, radiation, and far-field detection. Moreover, we detail modeling approaches for major optical microscopy modalities including classical fluorescence, multi-photon fluorescence, second harmonic generation, and coherent anti-Stokes Raman microscopy.

Excitation and emission dual-wavelength confocal metalens designed directly in the biological tissue environment for two-photon micro-endoscopy

With the advantages of completely controlling the phase, amplitude, and polarization in subwavelength range, metalenses have drawn intensive attentions in high resolution two-photon micro-endoscopic fluorescence imaging system. However, chromatic dispersion and severe scattering of biological tissue significantly reduce excitation-collection efficiency in the traditional two-photon imaging system based on traditional metalenses designed in the air background. Here, an excitation and emission dual-wavelength confocal and polarization-insensitive metalens designed in the biological tissue environment was proposed by adopting the composite embedding structure and spatial multiplexing approach. The metalens with numerical aperture (NA) of 0.895 can focus the excitation (915 nm) and emission (510 nm) beams to the same focal spot in the mouse cortex. According to the theoretical simulation of two-photon fluorescence imaging, the lateral resolution of the collected fluorescent spots via the proposed metalens can be up to 0.42 µm. Compared to the metalens designed in the air environment, the collection efficiency of fluorescent spot is improved from 5.92% to 14.60%. Our investigation has opened a new window of high resolution and minimally invasive imaging in deep regions of biological tissues.

Simulation of penetration depth of Bessel beams for multifocal optical coherence tomography

Multifocal Bessel beam optical coherence tomography (MBOCT) combines the advantages of Bessel beam OCT and multifocal OCT to increase imaging depth. For MBOCT, the penetration depth of the Bessel beam in highly scattering biological tissue limits the final imaging depth. In this paper, we theoretically analyze the penetration depth of the Bessel beams with different parameters to explore which kind of Bessel beam is more suitable for MBOCT in a scattering medium. The finite-difference time-domain method is used to simulate the field distribution of Bessel beams in the medium. We find that the MBOCT for more focus based on a Bessel beam with a smaller Fresnel number N has higher penetration depth and light intensity when its lateral resolution is fixed. Moreover, the Bessel beam with N reversely closer to unity is more advantageous for penetrating the highly scattering medium for a certain imaging depth, and the Bessel beam has larger penetration depth when its lateral size is close to the size of the object to be imaged.

Plum pudding random medium model of biological tissue toward remote microscopy from spectroscopic light scattering

Biological tissue has a complex structure and exhibits rich spectroscopic behavior. There has been no tissue model until now that has been able to account for the observed spectroscopy of tissue light scattering and its anisotropy. Here we present, for the first time, a plum pudding random medium (PPRM) model for biological tissue which succinctly describes tissue as a superposition of distinctive scattering structures (plum) embedded inside a fractal continuous medium of background refractive index fluctuation (pudding). PPRM faithfully reproduces the wavelength dependence of tissue light scattering and attributes the "anomalous" trend in the anisotropy to the plum and the powerlaw dependence of the reduced scattering coefficient to the fractal scattering pudding. Most importantly, PPRM opens up a novel venue of quantifying the tissue architecture and microscopic structures on average from macroscopic probing of the bulk with scattered light alone without tissue excision. We demonstrate this potential by visualizing the fine microscopic structural alterations in breast tissue (adipose, glandular, fibrocystic, fibroadenoma, and ductal carcinoma) deduced from noncontact spectroscopic measurement.

Effect of scattering on coherent anti-Stokes Raman scattering (CARS) signals

We develop a computational framework to examine the factors responsible for scattering-induced distortions of coherent anti-Stokes Raman scattering (CARS) signals in turbid samples. We apply the Huygens-Fresnel wave-based electric field superposition (HF-WEFS) method combined with the radiating dipole approximation to compute the effects of scattering-induced distortions of focal excitation fields on the far-field CARS signal. We analyze the effect of spherical scatterers, placed in the vicinity of the focal volume, on the CARS signal emitted by different objects (2μm diameter solid sphere, 2μm diameter myelin cylinder and 2μm diameter myelin tube). We find that distortions in the CARS signals arise not only from attenuation of the focal field but also from scattering-induced changes in the spatial phase that modifies the angular distribution of the CARS emission. Our simulations further show that CARS signal attenuation can be minimized by using a high numerical aperture condenser. Moreover, unlike the CARS intensity image, CARS images formed by taking the ratio of CARS signals obtained using x- and y-polarized input fields is relatively insensitive to the effects of spherical scatterers. Our computational framework provide a mechanistic approach to characterizing scattering-induced distortions in coherent imaging of turbid media and may inspire bottom-up approaches for adaptive optical methods for image correction.

Characterization of wavefront errors in mouse cranial bone using second-harmonic generation

Optical aberrations significantly affect the resolution and signal-to-noise ratio of deep tissue microscopy. As multiphoton microscopy is applied deeper into tissue, the loss of resolution and signal due to propagation of light in a medium with heterogeneous refractive index becomes more serious. Efforts in imaging through the intact skull of mice cannot typically reach past the bone marrow ( ? 150 ?? ? m of depth) and have limited resolution and penetration depth. Mechanical bone thinning or optical ablation of bone enables deeper imaging, but these methods are highly invasive and may impact tissue biology. Adaptive optics is a promising noninvasive alternative for restoring optical resolution. We characterize the aberrations present in bone using second-harmonic generation imaging of collagen. We simulate light propagation through highly scattering bone and evaluate the effect of aberrations on the point spread function. We then calculate the wavefront and expand it in Zernike orthogonal polynomials to determine the strength of different optical aberrations. We further compare the corrected wavefront and the residual wavefront error, and suggest a correction element with high number of elements or multiconjugate wavefront correction for this highly scattering environment.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

Reconstruction of explicit structural properties at the nanoscale via spectroscopic microscopy

The spectrum registered by a reflected-light bright-field spectroscopic microscope (SM) can quantify the microscopically indiscernible, deeply subdiffractional length scales within samples such as biological cells and tissues. Nevertheless, quantification of biological specimens via any optical measures most often reveals ambiguous information about the specific structural properties within the studied samples. Thus, optical quantification remains nonintuitive to users from the diverse fields of technique application. In this work, we demonstrate that the SM signal can be analyzed to reconstruct explicit physical measures of internal structure within label-free, weakly scattering samples: characteristic length scale and the amplitude of spatial refractive-index (RI) fluctuations. We present and validate the reconstruction algorithm via finite-difference time-domain solutions of Maxwell's equations on an example of exponential spatial correlation of RI. We apply the validated algorithm to experimentally measure structural properties within isolated cells from two genetic variants of HT29 colon cancer cell line as well as within a prostate tissue biopsy section. The presented methodology can lead to the development of novel biophotonics techniques that create two-dimensional maps of explicit structural properties within biomaterials: the characteristic size of macromolecular complexes and the variance of local mass density.

Characterization of multiphoton microscopy in the bone marrow following intravital laser osteotomy

The bone marrow is an important site where all blood cells are formed from hematopoietic stem cells and where hematologic malignancies such as leukemia emerge. It is also a frequent site for metastasis of solid tumors such as breast cancer and prostate cancer. Intravital microscopy is a powerful tool for studying the bone marrow with single cell and sub-cellular resolution. To improve optical access to this rich biological environment, plasma-mediated laser ablation with sub-microjoule femtosecond pulses was used to thin cortical bone. By locally removing a superficial layer of bone (local laser osteotomy), significant improvements in multiphoton imaging were observed in individual bone marrow compartments in vivo. This work demonstrates the utility of scanning laser ablation of hard tissue with sub-microjoule pulses as a preparatory step to imaging.

Simulating the scanning of a focused beam through scattering media using a numerical solution of Maxwell's equations

A highly efficient method based on Maxwell's theory was developed, which enables the calculation of the scanning of a focused beam through scattering media. Maxwell's equations were numerically solved in two dimensions using finite difference time domain simulations. The modeling of the focused beam was achieved by applying the angular spectrum of plane waves method. The scanning of the focused beam through the scattering medium was accomplished by saving the results of the near field obtained from one simulation set of plane waves incident at different angles and by an appropriate post processing of these data. Thus, an arbitrary number of focus positions could be simulated without the need to further solve Maxwell's equations. The presented method can be used to efficiently study the light propagation of focused beam through scattering media which is important, for example, for different kinds of scanning microscopes.

Rapid computation of the amplitude and phase of tightly focused optical fields distorted by scattering particles

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.

Label-free and noninvasive optical detection of the distribution of nanometer-size mitochondria in single cells

A microfluidic flow cytometric technique capable of obtaining information on nanometer-sized organelles in single cells in a label-free, noninvasive optical manner was developed. Experimental two-dimensional (2D) light scattering patterns from malignant lymphoid cells (Jurkat cell line) and normal hematopoietic stem cells (cord blood CD34+ cells) were compared with those obtained from finite-difference time-domain simulations. In the simulations, we assumed that the mitochondria were randomly distributed throughout a Jurkat cell, and aggregated in a CD34+ cell. Comparison of the experimental and simulated light scattering patterns led us to conclude that distinction from these two types of cells may be due to different mitochondrial distributions. This observation was confirmed by conventional confocal fluorescence microscopy. A method for potential cell discrimination was developed based on analysis of the 2D light scattering patterns. Potential clinical applications using mitochondria as intrinsic biological markers in single cells were discussed in terms of normal cells (CD34+ cell and lymphocytes) versus malignant cells (THP-1 and Jurkat cell lines).

Maximum imaging depth of two-photon autofluorescence microscopy in epithelial tissues

Endogenous fluorescence provides morphological, spectral, and lifetime contrast that can indicate disease states in tissues. Previous studies have demonstrated that two-photon autofluorescence microscopy (2PAM) can be used for noninvasive, three-dimensional imaging of epithelial tissues down to approximately 150 μm beneath the skin surface. We report ex-vivo 2PAM images of epithelial tissue from a human tongue biopsy down to 370 μm below the surface. At greater than 320 μm deep, the fluorescence generated outside the focal volume degrades the image contrast to below one. We demonstrate that these imaging depths can be reached with 160 mW of laser power (2-nJ per pulse) from a conventional 80-MHz repetition rate ultrafast laser oscillator. To better understand the maximum imaging depths that we can achieve in epithelial tissues, we studied image contrast as a function of depth in tissue phantoms with a range of relevant optical properties. The phantom data agree well with the estimated contrast decays from time-resolved Monte Carlo simulations and show maximum imaging depths similar to that found in human biopsy results. This work demonstrates that the low staining inhomogeneity (∼ 20) and large scattering coefficient (∼ 10 mm(-1)) associated with conventional 2PAM limit the maximum imaging depth to 3 to 5 mean free scattering lengths deep in epithelial tissue.

Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues

The focal field distribution of tightly focused laser beams in turbid media is sensitive to optical scattering and therefore of direct relevance to image quality in confocal and nonlinear microscopy. A model that considers both the influence of scattering and diffraction on the amplitude and phase of the electric field in focused beam geometries is required to describe these distorted focal fields. We combine an electric field Monte Carlo approach that simulates the electric field propagation in turbid media with an angular-spectrum representation of diffraction theory to analyze the effect of tissue scattering properties on the focal field. In particular, we examine the impact of variations in the scattering coefficient (µ(s)), single-scattering anisotropy (g), of the turbid medium and the numerical aperture of the focusing lens on the focal volume at various depths. The model predicts a scattering-induced broadening, amplitude loss, and depolarization of the focal field that corroborates experimental results. We find that both the width and the amplitude of the focal field are dictated primarily by µ(s) with little influence from g. In addition, our model confirms that the depolarization rate is small compared to the amplitude loss of the tightly focused field.

Far-field superposition method for three-dimensional computation of light scattering from multiple cells

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.

Investigating the spectral characteristics of backscattering from heterogeneous spherical nuclei using broadband finite-difference time-domain simulations

Reflectance spectra measured from epithelial tissue have been used to extract size distribution and refractive index of cell nuclei for noninvasive detection of precancerous changes. Despite many in vitro and in vivo experimental results, the underlying mechanism of sizing nuclei based on modeling nuclei as homogeneous spheres and fitting the measured data with Mie theory has not been fully explored. We describe the implementation of a three-dimensional finite-difference time-domain (FDTD) simulation tool using a Gaussian pulse as the light source to investigate the wavelength-dependent characteristics of backscattered light from a nuclear model consisting of a nucleolus and clumps of chromatin embedded in homogeneous nucleoplasm. The results show that small-sized heterogeneities within the nuclei generate about five times higher backscattering than homogeneous spheres. More interestingly, backscattering spectra from heterogeneous spherical nuclei show periodic oscillations similar to those from homogeneous spheres, leading to high accuracy of estimating the nuclear diameter by comparison with Mie theory. In addition to the application in light scattering spectroscopy, the reported FDTD method could be adapted to study the relations between measured spectral data and nuclear structures in other optical imaging and spectroscopic techniques for in vivo diagnosis.