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.

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.

Radiance backscattered by a strongly scattering medium in the high spatial frequency limit.

We study the radiative transfer of a spatially modulated plane wave incident on a half-space composed of a uniformly scattering and absorbing medium. For spatial frequencies that are large compared to the scattering coefficient, we find that first-order scattering governs the leading behavior of the radiance backscattered by the medium. The first-order scattering approximation reveals a specific curve on the backscattered hemisphere where the radiance is concentrated. Along this curve, the radiance assumes a particularly simple expression that is directly proportional to the phase function. These results are inherent to the radiative transfer equation at large spatial frequency and do not have a strong dependence on any particular optical property. Consequently, these results provide the means by which spatial frequency domain imaging technologies can directly measure the phase function of a sample. Numerical simulations using the discrete ordinate method along with the source integration interpolation method validate these theoretical findings.

Single-shot interferometric measurement of cavitation bubble dynamics.

We demonstrate an interferometric method to provide direct, single-shot measurements of cavitation bubble dynamics with nanoscale spatial and temporal resolution with results that closely match theoretical predictions. Implementation of this method reduces the need for expensive and complex ultra-high speed camera systems for the measurement of single cavitation events. This method can capture dynamics over large time intervals with sub-nanosecond temporal resolution and spatial precision surpassing the optical diffraction limit. We expect this method to have broad utility for examination of cavitation bubble dynamics, as well as for metrology applications such as optorheological materials characterization. This method provides an accurate approach for precise measurement of cavitation bubble dynamics suitable for metrology applications such as optorheological materials characterization.

Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media: erratum.

This erratum corrects the relative error plots and references in our paper [J. Opt. Soc. Am. A31, 301 (2014)JOAOD60740-323210.1364/JOSAA.31.000301].

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.

Multi-scale silica structures for improved HIV-1 Capsid (p24) antigen detection.

Silica (SiO2) micro- and nanostructures fabricated with pre-stressed thermoplastic shrink wrap film have been shown to yield far-field fluorescence signal enhancements over their planar or wrinkled counterparts. The SiO2 structures have previously been used for improved detection of fluorescently labelled proteins and DNA. In this work, we probe the mechanism responsible for the dramatic increases in fluorescence signal intensity. Optical characterization studies attribute the fluorescence signal enhancements to increased surface density and light scattering from the rough SiO2 structures. Using this information, we come up with a theoretical approximation for the enhancement factor based off the scattering effects alone. We show that increased deposition thickness of SiO2 yields improved fluorescence signal enhancements, with an optimal SiO2 thin layer achieved at 20 nm. Finally, we show that the SiO2 substrates serve as a suitable platform for disease diagnostics, and show improved limits of detection (LOD) for the human immunodeficiency virus type 1 (HIV-1) p24 antigen.

Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media.

We examine the relative error of Monte Carlo simulations of radiative transport that employ two commonly used estimators that account for absorption differently, either discretely, at interaction points, or continuously, between interaction points. We provide a rigorous derivation of these discrete and continuous absorption weighting estimators within a stochastic model that we show to be equivalent to an analytic model, based on the radiative transport equation (RTE). We establish that both absorption weighting estimators are unbiased and, therefore, converge to the solution of the RTE. An analysis of spatially resolved reflectance predictions provided by these two estimators reveals no advantage to either in cases of highly scattering and highly anisotropic media. However, for moderate to highly absorbing media or isotropically scattering media, the discrete estimator provides smaller errors at proximal source locations while the continuous estimator provides smaller errors at distal locations. The origin of these differing variance characteristics can be understood through examination of the distribution of exiting photon weights.

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.

Hydrodynamic determinants of cell necrosis and molecular delivery produced by pulsed laser microbeam irradiation of adherent cells.

Time-resolved imaging, fluorescence microscopy, and hydrodynamic modeling were used to examine cell lysis and molecular delivery produced by picosecond and nanosecond pulsed laser microbeam irradiation in adherent cell cultures. Pulsed laser microbeam radiation at λ = 532 nm was delivered to confluent monolayers of PtK2 cells via a 40×, 0.8 NA microscope objective. Using laser microbeam pulse durations of 180-1100 ps and pulse energies of 0.5-10.5 µJ, we examined the resulting plasma formation and cavitation bubble dynamics that lead to laser-induced cell lysis, necrosis, and molecular delivery. The cavitation bubble dynamics are imaged at times of 0.5 ns to 50 µs after the pulsed laser microbeam irradiation, and fluorescence assays assess the resulting cell viability and molecular delivery of 3 kDa dextran molecules. Reductions in both the threshold laser microbeam pulse energy for plasma formation and the cavitation bubble energy are observed with decreasing pulse duration. These energy reductions provide for increased precision of laser-based cellular manipulation including cell lysis, cell necrosis, and molecular delivery. Hydrodynamic analysis reveals critical values for the shear-stress impulse generated by the cavitation bubble dynamics governs the location and spatial extent of cell necrosis and molecular delivery independent of pulse duration and pulse energy. Specifically, cellular exposure to a shear-stress impulse J≳0.1 Pa s ensures cell lysis or necrosis, whereas exposures in the range of 0.035≲J≲0.1 Pa s preserve cell viability while also enabling molecular delivery of 3 kDa dextran. Exposure to shear-stress impulses of J≲0.035 Pa s leaves the cells unaffected. Hydrodynamic analysis of these data, combined with data from studies of 6 ns microbeam irradiation, demonstrates the primacy of shear-stress impulse in determining cellular outcome resulting from pulsed laser microbeam irradiation spanning a nearly two-orders-of-magnitude range of pulse energy and pulse duration. These results provide a mechanistic foundation and design strategy applicable to a broad range of laser-based cellular manipulation procedures.

In vivo multiphoton NADH fluorescence reveals depth-dependent keratinocyte metabolism in human skin.

We employ a clinical multiphoton microscope to monitor in vivo and noninvasively the changes in reduced nicotinamide adenine dinucleotide (NADH) fluorescence of human epidermal cells during arterial occlusion. We correlate these results with measurements of tissue oxy- and deoxyhemoglobin concentration during oxygen deprivation using spatial frequency domain imaging. During arterial occlusion, a decrease in oxyhemoglobin corresponds to an increase in NADH fluorescence in the basal epidermal cells, implying a reduction in basal cell oxidative phosphorylation. The ischemia-induced oxygen deprivation is associated with a strong increase in NADH fluorescence of keratinocytes in layers close to the stratum basale, whereas keratinocytes from epidermal layers closer to the skin surface are not affected. Spatial frequency domain imaging optical property measurements, combined with a multilayer Monte Carlo-based radiative transport model of multiphoton microscopy signal collection in skin, establish that localized tissue optical property changes during occlusion do not impact the observed NADH signal increase. This outcome supports the hypothesis that the vascular contribution to the basal layer oxygen supply is significant and these cells engage in oxidative metabolism. Keratinocytes in the more superficial stratum granulosum are either supplied by atmospheric oxygen or are functionally anaerobic. Based on combined hemodynamic and two-photon excited fluorescence data, the oxygen consumption rate in the stratum basale is estimated to be ∼0.035 µmoles/10(6) cells/h.

Analysis of relative error in perturbation Monte Carlo simulations of radiative transport.

Significance: Perturbation and differential Monte Carlo (pMC/dMC) methods, used in conjunction with nonlinear optimization methods, have been successfully applied to solve inverse problems in diffuse optics. Application of pMC to systems over a large range of optical properties requires optimal "placement" of baseline conventional Monte Carlo (cMC) simulations to minimize the pMC variance. The inability to predict the growth in pMC solution uncertainty with perturbation size limits the application of pMC, especially for multispectral datasets where the variation of optical properties can be substantial. Aim: We aim to predict the variation of pMC variance with perturbation size without explicit computation of perturbed photon weights. Our proposed method can be used to determine the range of optical properties over which pMC predictions provide sufficient accuracy. This method can be used to specify the optical properties for the reference cMC simulations that pMC utilizes to provide accurate predictions over a desired optical property range. Approach: We utilize a conventional error propagation methodology to calculate changes in pMC relative error for Monte Carlo simulations. We demonstrate this methodology for spatially resolved diffuse reflectance measurements with ±20% scattering perturbations. We examine the performance of our method for reference simulations spanning a broad range of optical properties relevant for diffuse optical imaging of biological tissues. Our predictions are computed using the variance, covariance, and skewness of the photon weight, path length, and collision distributions generated by the reference simulation. Results: We find that our methodology performs best when used in conjunction with reference cMC simulations that utilize Russian Roulette (RR) method. Specifically, we demonstrate that for a proximal detector placed immediately adjacent to the source, we can estimate the pMC relative error within 5% of the true value for scattering perturbations in the range of [-15%,+20%]. For a distal detector placed at ∼3 transport mean free paths relative to the source, our method provides relative error estimates within 20% for scattering perturbations in the range of [-8%,+15%]. Moreover, reference simulations performed at lower (µs'/µa) values showed better performance for both proximal and distal detectors. Conclusions: These findings indicate that reference simulations utilizing continuous absorption weighting (CAW) with the Russian Roulette method and executed using optical properties with a low (µs'/µa) ratio spanning the desired range of µs values, are highly advantageous for the deployment of pMC to obtain radiative transport estimates over a wide range of optical properties.

MCCL: an open-source software application for Monte Carlo simulations of radiative transport.

The Monte Carlo Command Line application (MCCL) is an open-source software package that provides Monte Carlo simulations of radiative transport through heterogeneous turbid media. MCCL is available on GitHub through our virtualphotonics.org website, is actively supported, and carries extensive documentation. Here, we describe the main technical capabilities, the overall software architecture, and the operational details of MCCL.

Corneal transparency and scleral opacity arises from the nanoarchitecture of the constituent collagen fibrils.

While human scleral and corneal tissues possess similar structural morphology of long parallel cylindrical collagen fibrils, their optical characteristics are markedly different. Using pseudospectral time-domain (PSTD) simulations of Maxwell's equations, we model light propagation through realistic representations of scleral and corneal nanoarchitecture and analyze the transmittance and spatial correlation in the near field. Our simulation results provide differing predictions for scleral opacity and corneal transparency across the vacuum ultraviolet to the mid-infrared spectral region in agreement with experimental data. The simulations reveal that the differences in optical transparency between these tissues arise through differences in light scattering emanating from the specific nanoscale arrangement and polydispersity of the constituent collagen fibrils.

Analysis of single Monte Carlo methods for prediction of reflectance from turbid media.

Starting from the radiative transport equation we derive the scaling relationships that enable a single Monte Carlo (MC) simulation to predict the spatially- and temporally-resolved reflectance from homogeneous semi-infinite media with arbitrary scattering and absorption coefficients. This derivation shows that a rigorous application of this single Monte Carlo (sMC) approach requires the rescaling to be done individually for each photon biography. We examine the accuracy of the sMC method when processing simulations on an individual photon basis and also demonstrate the use of adaptive binning and interpolation using non-uniform rational B-splines (NURBS) to achieve order of magnitude reductions in the relative error as compared to the use of uniform binning and linear interpolation. This improved implementation for sMC simulation serves as a fast and accurate solver to address both forward and inverse problems and is available for use at http://www.virtualphotonics.org/.

Accurate and efficient Monte Carlo solutions to the radiative transport equation in the spatial frequency domain.

We present an approach to solving the radiative transport equation (RTE) for layered media in the spatial frequency domain (SFD) using Monte Carlo (MC) simulations. This is done by obtaining a complex photon weight from analysis of the Fourier transform of the RTE. We also develop a modified shortcut method that enables a single MC simulation to efficiently provide RTE solutions in the SFD for any number of spatial frequencies. We provide comparisons between the modified shortcut method and conventional discrete transform methods for SFD reflectance. Further results for oblique illumination illustrate the potential diagnostic utility of the SFD phase-shifts for analysis of layered media.

Examination of axonal injury and regeneration in micropatterned neuronal culture using pulsed laser microbeam dissection.

We describe the integrated use of pulsed laser microbeam irradiation and microfluidic cell culture methods to examine the dynamics of axonal injury and regeneration in vitro. Microfabrication methods are used to place high purity dissociated central nervous system neurons in specific regions that allow the axons to interact with permissive and inhibitory substrates. Acute injury to neuron bundles is produced via the delivery of single 180 ps duration, lambda = 532 nm laser pulses. Laser pulse energies of 400 nJ and 800 nJ produce partial and complete transection of the axons, respectively, resulting in elliptical lesions 25 mum and 50 mum in size. The dynamics of the resulting degeneration and regrowth of proximal and distal axonal segments are examined for up to 8 h using time-lapse microscopy. We find the proximal and distal dieback distances from the site of laser microbeam irradiation to be roughly equal for both partial and complete transection of the axons. In addition, distinct growth cones emerge from the proximal neurite segments within 1-2 h post-injury, followed by a uniform front of regenerating axons that originate from the proximal segment and traverse the injury site within 8 h. We also examine the use of EGTA to chelate the extracellular calcium and potentially reduce the severity of the axonal degeneration following injury. While we find the addition of EGTA to reduce the severity of the initial dieback, it also hampers neurite repair and interferes with the formation of neuronal growth cones to traverse the injury site. This integrated use of laser microbeam dissection within a micropatterned cell culture system to produce precise zones of neuronal injury shows potential for high-throughput screening of agents to promote neuronal regeneration.

Laser cavitation rheology for measurement of elastic moduli and failure strain within hydrogels.

We introduce laser cavitation rheology (LCR) as a minimally-invasive optical method to characterize mechanical properties within the interior of biological and synthetic aqueous soft materials at high strain-rates. We utilized time-resolved photography to measure cavitation bubble dynamics generated by the delivery of focused 500 ps duration laser radiation at λ = 532 nm within fibrin hydrogels at pulse energies of Ep = 12, 18 µJ and within polyethylene glycol (600) diacrylate (PEG (600) DA) hydrogels at Ep = 2, 5, 12 µJ. Elastic moduli and failure strains of fibrin and PEG (600) DA hydrogels were calculated from these measurements by determining parameter values which provide the best fit of the measured data to a theoretical model of cavitation bubble dynamics in a Neo-Hookean viscoelastic medium subject to material failure. We demonstrate the use of this method to retrieve the local, interior elastic modulus of these hydrogels and both the radial and circumferential failure strains.

Optical sampling depth in the spatial frequency domain.

We present a Monte Carlo (MC) method to determine depth-dependent probability distributions of photon visitation and detection for optical reflectance measurements performed in the spatial frequency domain (SFD). These distributions are formed using an MC simulation for radiative transport that utilizes a photon packet weighting procedure consistent with the two-dimensional spatial Fourier transform of the radiative transport equation. This method enables the development of quantitative metrics for SFD optical sampling depth in layered tissue and its dependence on both tissue optical properties and spatial frequency. We validate the computed depth-dependent probability distributions using SFD measurements in a layered phantom system with a highly scattering top layer of variable thickness supported by a highly absorbing base layer. We utilize our method to establish the spatial frequency-dependent optical sampling depth for a number of tissue types and also provide a general tool to determine such depths for tissues of arbitrary optical properties.

Examination of laser microbeam cell lysis in a PDMS microfluidic channel using time-resolved imaging.

We use time-resolved imaging to examine the lysis dynamics of non-adherent BAF-3 cells within a microfluidic channel produced by the delivery of single highly-focused 540 ps duration laser pulses at lambda = 532 nm. Time-resolved bright-field images reveal that the delivery of the pulsed laser microbeam results in the formation of a laser-induced plasma followed by shock wave emission and cavitation bubble formation. The confinement offered by the microfluidic channel constrains substantially the cavitation bubble expansion and results in significant deformation of the PDMS channel walls. To examine the cell lysis and dispersal of the cellular contents, we acquire time-resolved fluorescence images of the process in which the cells were loaded with a fluorescent dye. These fluorescence images reveal cell lysis to occur on the nanosecond to microsecond time scale by the plasma formation and cavitation bubble dynamics. Moreover, the time-resolved fluorescence images show that while the cellular contents are dispersed by the expansion of the laser-induced cavitation bubble, the flow associated with the bubble collapse subsequently re-localizes the cellular contents to a small region. This capacity of pulsed laser microbeam irradiation to achieve rapid cell lysis in microfluidic channels with minimal dilution of the cellular contents has important implications for their use in lab-on-a-chip applications.