Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method

Experimental imaging and Monte Carlo modeling of ultrafast pulse propagation in thin scattering slabs

SIGNIFICANCE

Most radiative transport problems in turbid media are typically associated with mm or cm scales, leading to typical time scales in the range of hundreds of ps or more. In certain cases, however, much thinner layers can also be relevant, which can dramatically alter the overall transport properties of a scattering medium. Studying scattering in these thin layers requires ultrafast detection techniques and adaptations to the common Monte Carlo (MC) approach.

AIM

We aim to discuss a few relevant aspects for the simulation of light transport in thin scattering membranes, and compare the obtained numerical results with experimental measurements based on an all-optical gating technique.

APPROACH

A thin membrane with controlled scattering properties based on polymer-dispersed TiO2 nanoparticles is fabricated for experimental validation. Transmittance measurements are compared against a custom open-source MC implementation including specific pulse profiles for tightly focused femtosecond laser pulses.

RESULTS

Experimental transmittance data of ultrafast pulses through a thin scattering sample are compared with MC simulations in the spatiotemporal domain to retrieve its scattering properties. The results show good agreement also at short distances and time scales.

CONCLUSIONS

When simulating light transport in scattering membranes with thicknesses in the orders of tens of micrometer, care has to be taken when describing the temporal, spatial, and divergence profiles of the source term, as well as the possible truncation of step length distributions, which could be introduced by simple strategies for the generation of random exponentially distributed variables.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium considering the polarization effect

Transient/time-dependent radiative transfer in a two-dimensional scattering medium is numerically solved by the discontinuous finite element method (DFEM). The time-dependent term of the transient vector radiative transfer equation is discretized by the second-order central difference scheme and the space domain is discretized into non-overlapping quadrilateral elements by using the discontinuous finite element approach. The accuracy of the transient DFEM model for the radiative transfer equation considering the polarization effect is verified by comparing the time-resolved Stokes vector component distributions against the steady solutions for a polarized radiative transfer problem in a two-dimensional rectangular enclosure filled with a scattering medium. The transient polarized radiative transfer problems in a scattering medium exposed to an external beam and in an irregular emitting medium are solved. The distributions of the time-resolved Stokes vector components are presented and discussed.

Overview of diffuse optical tomography and its clinical applications

Near-infrared diffuse optical tomography (DOT), one of the most sophisticated optical imaging techniques for observations through biological tissue, allows 3-D quantitative imaging of optical properties, which include functional and anatomical information. With DOT, it is expected to be possible to overcome the limitations of conventional near-infrared spectroscopy (NIRS) as well as offering the potential for diagnostic optical imaging. However, DOT has been under development for more than 30 years, and the difficulties in development are attributed to the fact that light is strongly scattered and that diffusive photons are used for the image reconstruction. The DOT algorithm is based on the techniques of inverse problems. The radiative transfer equation accurately describes photon propagation in biological tissue, while, because of its high computation load, the diffusion equation (DE) is often used as the forward model. However, the DE is invalid in low-scattering and/or highly absorbing regions and in the vicinity of light sources. The inverse problem is inherently ill-posed and highly undetermined. Here, we first summarize NIRS and then describe various approaches in the efforts to develop accurate and efficient DOT algorithms and present some examples of clinical applications. Finally, we discuss the future prospects of DOT.

Fast method of retrieving the asymmetry factor and scattering albedo from the maximum time-resolved reflectance of participating media

This research presents a parametric study of the time-resolved hemispherical reflectance of a semi-infinite plane-parallel slab of homogeneous, nonemitting, absorbing, and anisotropic scattering medium exposed to a collimated Gaussian pulse. The one-dimensional transient radiative transfer equation was solved by using the finite volume method. The internal reflection at the medium-air interface caused by the mismatch of the refractive indices was considered. In particular, this work focused on the maximum diffuse hemispherical reflectance. Three different optical regions were identified according to the dimensionless pulsewidth βct_p. The correlation between the normalized maximum hemispherical reflectance and βct_p was conformed to the Boltzmann function. The coefficients in the correlating functions of the match and mismatch refractive index cases were fitted as polynomial fitting functions of the single scattering albedo ω and Henyey-Greenstein asymmetric factor g. Thus, ω and g can be simultaneously reconstructed by the semi-empirical correlations without solving the forward model. In conclusion, the proposed method can potentially retrieve the asymmetry factor and single scattering albedo of participating media accurately and efficiently.

Polarization-sensitive hyperspectral imaging in vivo: a multimode dermoscope for skin analysis

Attempts to understand the changes in the structure and physiology of human skin abnormalities by non-invasive optical imaging are aided by spectroscopic methods that quantify, at the molecular level, variations in tissue oxygenation and melanin distribution. However, current commercial and research systems to map hemoglobin and melanin do not correlate well with pathology for pigmented lesions or darker skin. We developed a multimode dermoscope that combines polarization and hyperspectral imaging with an efficient analytical model to map the distribution of specific skin bio-molecules. This corrects for the melanin-hemoglobin misestimation common to other systems, without resorting to complex and computationally intensive tissue optical models. For this system's proof of concept, human skin measurements on melanocytic nevus, vitiligo, and venous occlusion conditions were performed in volunteers. The resulting molecular distribution maps matched physiological and anatomical expectations, confirming a technologic approach that can be applied to next generation dermoscopes and having biological plausibility that is likely to appeal to dermatologists.

Ex vivo proof-of-concept of end-to-end scaffold-enhanced laser-assisted vascular anastomosis of porcine arteries

OBJECTIVE

The low welding strength of laser-assisted vascular anastomosis (LAVA) has hampered the clinical application of LAVA as an alternative to suture anastomosis. To improve welding strength, LAVA in combination with solder and polymeric scaffolds (ssLAVA) has been optimized in vitro. Currently, ssLAVA requires proof-of-concept in a physiologically representative ex vivo model before advancing to in vivo studies. This study therefore investigated the feasibility of ex vivo ssLAVA in medium-sized porcine arteries.

METHODS

Scaffolds composed of poly(ε-caprolactone) (PCL) or poly(lactic-co-glycolic acid) (PLGA) were impregnated with semisolid solder and placed over coapted aortic segments. ssLAVA was performed with a 670-nm diode laser. In the first substudy, the optimum number of laser spots was determined by bursting pressure analysis. The second substudy investigated the resilience of the welds in a Langendorf-type pulsatile pressure setup, monitoring the number of failed vessels. The type of failure (cohesive vs adhesive) was confirmed by electron microscopy, and thermal damage was assessed histologically. The third substudy compared breaking strength of aortic repairs made with PLGA and semisolid genipin solder (ssLAVR) to repairs made with BioGlue.

RESULTS

ssLAVA with 11 lasing spots and PLGA scaffold yielded the highest bursting pressure (923 ± 56 mm Hg vs 703 ± 96 mm Hg with PCL ssLAVA; P = .0002) and exhibited the fewest failures (20% vs 70% for PCL ssLAVA; P = .0218). The two failed PLGA ssLAVA arteries leaked at 19 and 22 hours, whereas the seven failed PCL ssLAVA arteries burst between 12 and 23 hours. PLGA anastomoses broke adhesively, whereas PCL welds failed cohesively. Both modalities exhibited full-thickness thermal damage. Repairs with PLGA scaffold yielded higher breaking strength than BioGlue repairs (323 ± 28 N/cm(2) vs 25 ± 4 N/cm(2), respectively; P = .0003).

CONCLUSIONS

PLGA ssLAVA yields greater anastomotic strength and fewer anastomotic failures than PCL ssLAVA. Aortic repairs with BioGlue were inferior to those produced with PLGA ssLAVR. The results demonstrate the feasibility of ssLAVA/R as an alternative method to suture anastomosis or tissue sealant. Further studies should focus on reducing thermal damage.

Finite-difference time-domain analysis of time-resolved reflectance from an adult head model composed of multilayered slabs with a nonscattering layer

Finite-difference time-domain (FDTD) analysis has been used to predict the time-resolved reflectance from multilayered slabs with a nonscattering layer. Light propagation across the nonscattering layer was calculated based on the light intensity characteristics along a ray in free space. Additional equivalent source functions due to light from scattering regions across the nonscattering region were introduced into the diffusion equation and an additional set of the diffusion equation was solved by FDTD analysis by employing new boundary conditions. The formulation was used to calculate time-resolved reflectances of three- and four-layered slabs containing a nonscattering layer. The received light intensity and the mean time of flight estimated from the time-resolved reflectance are in reasonable agreement with previously reported experimental data and Monte Carlo simulations.

Retrieving skin properties from in vivo spectral reflectance measurements

A previously developed inverse method was applied to in vivo normal-hemispherical spectral reflectance measurements taken on the inner and outer forearm as well as the forehead of healthy white Caucasian and black African subjects. The inverse method was used to determine the thickness and melanin concentration in the epidermis, dermal blood volume fraction and oxygen saturation, and skin's spectral scattering coefficient. It was established that changes in melanin concentration due to racial difference and tanning, and differences in epidermal thickness and blood volume with anatomical location were detectable. The retrieved values were also consistent with independent measurements reported in the literature. The same method could be used for optical diagnosis of pathologies affecting the structure and pigmentation of human skin.

The forward and inverse problem in tissue optics based on the radiative transfer equation: a brief review

This note serves as an introduction to two papers by Klose et al. [Optical tomography using the time-independent equation of radiative transfer, Parts 1 (JQSRT 2002;72:691-713) and 2 (JQSRT 2002;72:715-732)] and provides a brief review of the latest developments in optical tomography of scattering tissue. We discuss advancements made in solving the forward model for light propagation based on the radiative transfer equation, in reconstructing scattering and absorption cross sections of tissue, and in molecular imaging of luminescent sources.

Implicitly causality enforced solution of multidimensional transient photon transport equation

A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided.

Multi-time-scale heat transfer modeling of turbid tissues exposed to short-pulsed irradiations

A combined hyperbolic radiation and conduction heat transfer model is developed to simulate multi-time-scale heat transfer in turbid tissues exposed to short-pulsed irradiations. An initial temperature response of a tissue to an ultrashort pulse irradiation is analyzed by the volume-average method in combination with the transient discrete ordinates method for modeling the ultrafast radiation heat transfer. This response is found to reach pseudo steady state within 1 ns for the considered tissues. The single pulse result is then utilized to obtain the temperature response to pulse train irradiation at the microsecond/millisecond time scales. After that, the temperature field is predicted by the hyperbolic heat conduction model which is solved by the MacCormack's scheme with error terms correction. Finally, the hyperbolic conduction is compared with the traditional parabolic heat diffusion model. It is found that the maximum local temperatures are larger in the hyperbolic prediction than the parabolic prediction. In the modeled dermis tissue, a 7% non-dimensional temperature increase is found. After about 10 thermal relaxation times, thermal waves fade away and the predictions between the hyperbolic and parabolic models are consistent.

Simulated parametric studies in optical imaging of tumors through temporal log-slope difference mapping

Numerical studies are conducted to evaluate the noninvasive imaging method of temporal log-slope difference mapping (TLSDM). Emphasis is placed on the parametric examination of tumor's size, enhanced absorption contrast ratio, and embedment depth on the imaging quality and accuracy. It is found that the imaging quality and accuracy are predominantly determined by the tumor size and its embedment depth. The TLSDM method can detect a small tumor of 10mm in size when the tumor is embedded at a shallow depth down to 10mm. With decreasing tumor size and/or increasing embedment depth, both image quality and accuracy worsen. The imaging method requires the enhanced absorption contrast ratio be 20:1 or above.

Optical imaging of breast tumor through temporal log-slope difference mappings

A novel optical temporal log-slope difference mapping approach is proposed for cancerous breast tumor detection. In this method, target tissues are illuminated by near-infrared (700-1000 nm) ultrashort laser pulses from various surface source points, and backscattered time-resolved light signals are collected at the same surface points. By analyzing the log-slopes of decaying signals over all points on the source-detection grid, a log-slope distribution on the surface is obtained. After administration of absorption contrast agents, the presence of cancerous tumors increases the decaying steepness of the transient signals. The mapping of log-slope difference between native tissue and absorption-enhanced cancerous tissue indicates the location and projection of tumors on the detection surface. In this paper, we examine this method in the detection of breast tumors in two model tissue phantoms through computer simulation. The first model has a spherical tumor of 6mm in diameter embedded at the tissue center. The second model is a large tissue phantom embedded with a non-centered spherical tumor 8mm in diameter. Monte Carlo methods were employed to simulate the light transport and signal measurement. It is shown that the tumor in both the tissue models will be accurately projected on the detection surface by the proposed log-slope difference mapping method. The image processing is very fast and does not require any inverse optimization in image reconstruction.