Optical sampling depth in the spatial frequency domain

Abstract. 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.

[1]  W. W. Engle,et al.  Concept of spatial channel theory applied to reactor shielding analysis , 1977 .

[2]  B. Wilson,et al.  Forward-adjoint fluorescence model: Monte Carlo integration and experimental validation. , 1997, Applied optics.

[3]  Fengshan Liu,et al.  Influence of polydisperse distributions of both primary particle and aggregate size on soot temperature in low-fluence LII , 2006 .

[4]  Dongqi Wang,et al.  Chirality of Graphene Oxide–Humic Acid Sandwich Complex Induced by a Twisted, Long-Range-Ordered Nanostructure , 2016 .

[5]  A. Cox,et al.  An experiment to measure Mie and Rayleigh total scattering cross sections , 2002 .

[6]  Alessandro Torricelli,et al.  There’s plenty of light at the bottom: statistics of photon penetration depth in random media , 2016, Scientific Reports.

[7]  Vasan Venugopalan,et al.  Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media. , 2004, Journal of biomedical optics.

[8]  C. Burch,et al.  Localization of absorbers in scattering media by use of frequency-domain measurements of time-dependent photon migration. , 1994, Applied optics.

[9]  Guruprasad Raghavan,et al.  Feasibility of spatial frequency-domain imaging for monitoring palpable breast lesions , 2017, Journal of biomedical optics.

[10]  Jing Wang,et al.  Mesoporous Silica‐Coated Gold Nanorods as a Light‐Mediated Multifunctional Theranostic Platform for Cancer Treatment , 2012, Advanced materials.

[11]  Hai Huang,et al.  Absorption and Scattering Cross Section of Regular Black Holes , 2014 .

[12]  T. Binzoni,et al.  Depth sensitivity of frequency domain optical measurements in diffusive media. , 2017, Biomedical optics express.

[13]  J. E. Hoogenboom,et al.  A new effective Monte Carlo Midway coupling method in MCNP applied to a well logging problem , 1998 .

[14]  Yahya Sefidbakht,et al.  Homology modeling and molecular dynamics study on Schwanniomyces occidentalis alpha-amylase , 2017, Journal of biomolecular structure & dynamics.

[15]  L. Tayebi,et al.  Normalization of doxorubicin release from graphene oxide: New approach for optimization of effective parameters on drug loading , 2017, Biotechnology and applied biochemistry.

[16]  Yanzhi Xia,et al.  Fabrication and characterization of a triple functionalization of graphene oxide with Fe3O4, folic acid and doxorubicin as dual-targeted drug nanocarrier. , 2013, Colloids and surfaces. B, Biointerfaces.

[17]  Bernard Choi,et al.  Quantitative long‐term measurements of burns in a rat model using Spatial Frequency Domain Imaging (SFDI) and Laser Speckle Imaging (LSI) , 2017, Lasers in surgery and medicine.

[18]  Zhouyi Guo,et al.  Graphene oxide based surface-enhanced Raman scattering probes for cancer cell imaging. , 2013, Physical chemistry chemical physics : PCCP.

[19]  Anthony J. Durkin,et al.  Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain. , 2005, Optics letters.

[20]  Yushen Jin,et al.  Graphene oxide modified PLA microcapsules containing gold nanoparticles for ultrasonic/CT bimodal imaging guided photothermal tumor therapy. , 2013, Biomaterials.

[21]  Chong-Yun Park,et al.  X-ray absorption spectroscopy of graphite oxide , 2008 .

[22]  A E Profio,et al.  Light transport in tissue. , 1989, Applied optics.

[23]  J. E. Hoogenboom,et al.  A midway forward-adjoint coupling method for neutron and photon Monte Carlo transport , 1999 .

[24]  S. Krishnan,et al.  Nanoparticle-mediated hyperthermia in cancer therapy. , 2011, Therapeutic delivery.

[25]  Vasan Venugopalan,et al.  Sampling tissue volumes using frequency-domain photon migration. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Bruce J. Tromberg,et al.  Quantitative In Vivo Imaging of Tissue Absorption, Scattering, and Hemoglobin Concentration in Rat Cortex Using Spatially Modulated Structured Light , 2009 .

[27]  Shaoqin Liu,et al.  Photothermal ablation cancer therapy using homogeneous CsxWO3 nanorods with broad near-infra-red absorption. , 2013, Nanoscale.

[28]  Xavier Intes,et al.  Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency. , 2011, Medical physics.

[29]  Yuanming Zhou,et al.  Synthesis and optical properties of gold nanorods with controllable morphology , 2016, Journal of physics. Condensed matter : an Institute of Physics journal.

[30]  S. Jacques.  Optical properties of biological tissues: a review , 2013, Physics in medicine and biology.

[31]  C. Geiss,et al.  An introduction to probability theory , 2008 .

[32]  Hui Zhang,et al.  Immuno gold nanocages with tailored optical properties for targeted photothermal destruction of cancer cells. , 2007, Nano letters.

[33]  Jerome Spanier,et al.  Coupled Forward-Adjoint Monte Carlo Simulations of Radiative Transport for the Study of Optical Probe Design in Heterogeneous Tissues , 2007, SIAM J. Appl. Math..

[34]  Anthony J. Durkin,et al.  Postoperative Quantitative Assessment of Reconstructive Tissue Status in a Cutaneous Flap Model Using Spatial Frequency Domain Imaging , 2011, Plastic and reconstructive surgery.

[35]  L Wang,et al.  MCML--Monte Carlo modeling of light transport in multi-layered tissues. , 1995, Computer methods and programs in biomedicine.

[36]  H. Dai,et al.  Ultrasmall reduced graphene oxide with high near-infrared absorbance for photothermal therapy. , 2011, Journal of the American Chemical Society.

[37]  S. N. Cramer.  Forward-adjoint Monte Carlo coupling with no statistical error propagation , 1995 .

[38]  G. Wagnières,et al.  Determination of tissue optical properties by steady-state spatial frequency-domain reflectometry , 1998, Lasers in Medical Science.

[39]  J. Coleman,et al.  High-yield production of graphene by liquid-phase exfoliation of graphite. , 2008, Nature nanotechnology.

[40]  Venkataramanan Krishnaswamy,et al.  Sub-diffusive scattering parameter maps recovered using wide-field high-frequency structured light imaging. , 2014, Biomedical optics express.

[41]  Carole K Hayakawa,et al.  Coupled forward-adjoint Monte Carlo simulation of spatial-angular light fields to determine optical sensitivity in turbid media , 2014, Journal of biomedical optics.

[42]  L. Tayebi,et al.  Functionalized R9–reduced graphene oxide as an efficient nano-carrier for hydrophobic drug delivery , 2016 .

[43]  K. Prather,et al.  Exploring the Mechanism of Biocatalyst Inhibition in Microbial Desulfurization , 2013, Applied and Environmental Microbiology.

[44]  Xiang Zhang,et al.  A graphene-based broadband optical modulator , 2011, Nature.

[45]  Anthony J. Durkin,et al.  In vivo measurements of cutaneous melanin across spatial scales: using multiphoton microscopy and spatial frequency domain spectroscopy , 2015, Journal of biomedical optics.

[46]  J. Eduard Hoogenboom,et al.  Exact Monte Carlo perturbation analysis by forward-adjoint coupling in radiation transport calculations , 2001 .

[47]  D. Roblyer,et al.  Optical property uncertainty estimates for spatial frequency domain imaging. , 2018, Biomedical optics express.

[48]  H Szmacinski,et al.  Frequency domain imaging of absorbers obscured by scattering. , 1992, Journal of photochemistry and photobiology. B, Biology.

[49]  Descriptive parameter for photon trajectories in a turbid medium. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[50]  Alwin Kienle,et al.  Model-based analysis on the influence of spatial frequency selection in spatial frequency domain imaging. , 2015, Applied optics.

[51]  G. Wallace,et al.  Processable aqueous dispersions of graphene nanosheets. , 2008, Nature nanotechnology.

[52]  M. L. Williams,et al.  Generalized Contributon Response Theory , 1991 .

[53]  S. A. Mikhailov,et al.  Non-linear electromagnetic response of graphene , 2007, 0704.1909.

[54]  George H. Weiss,et al.  Statistics of Penetration Depth of Photons Re-Emitted From Irradiated Tissue , 1989 .

[55]  P. Jain,et al.  Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: applications in biological imaging and biomedicine. , 2006, The journal of physical chemistry. B.

[56]  Khalid Nawaz,et al.  Solvent-exfoliated graphene at extremely high concentration. , 2011, Langmuir : the ACS journal of surfaces and colloids.

[57]  Min Yi,et al.  Achieving concentrated graphene dispersions in water/acetone mixtures by the strategy of tailoring Hansen solubility parameters , 2013 .

[58]  J. R. Frisvad,et al.  Importance sampling the Rayleigh phase function. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[59]  Bruce J Tromberg,et al.  Diffuse optical imaging using spatially and temporally modulated light. , 2012, Journal of biomedical optics.

[60]  B. Wilson,et al.  Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths. , 1995, Applied optics.

[61]  A. Welch,et al.  A review of the optical properties of biological tissues , 1990 .

[62]  Bruce J Tromberg,et al.  Characterization of nonmelanoma skin cancer for light therapy using spatial frequency domain imaging. , 2015, Biomedical optics express.

[63]  Fengshan Liu,et al.  Effect of aggregation on the absorption cross-section of fractal soot aggregates and its impact on LII modelling , 2010 .

[64]  Bernard Choi,et al.  Spatial frequency domain imaging of burn wounds in a preclinical model of graded burn severity , 2013, Journal of biomedical optics.

[65]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[66]  Vasan Venugopalan,et al.  Accurate and efficient Monte Carlo solutions to the radiative transport equation in the spatial frequency domain. , 2011, Optics letters.

[67]  B. Chance,et al.  Photon migration in the presence of a single defect: a perturbation analysis. , 1995, Applied optics.

[68]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[69]  W. V. van Gunsteren,et al.  Validation of the GROMOS 54A7 Force Field with Respect to β-Peptide Folding. , 2011, Journal of chemical theory and computation.

[70]  C. R. Chris Wang,et al.  Gold Nanorods: Electrochemical Synthesis and Optical Properties , 1997 .

[71]  R. Stafford,et al.  Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[72]  Jonathan F. Lovell,et al.  Ablation of Hypoxic Tumors with Dose-Equivalent Photothermal, but Not Photodynamic, Therapy Using a Nanostructured Porphyrin Assembly , 2013, ACS nano.

[73]  B. Cady,et al.  A Comparison of Ink-Directed and Traditional Whole-Cavity Re-Excision for Breast Lumpectomy Specimens With Positive Margins , 2001, Annals of Surgical Oncology.

[74]  H.J.C.M. Sterenborg,et al.  Skin optics , 1989, IEEE Transactions on Biomedical Engineering.

[75]  Jerome Spanier,et al.  Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

[76]  E. Gelbard,et al.  Monte Carlo Principles and Neutron Transport Problems , 2008 .

[77]  J. Haselgrove,et al.  Photon hitting density. , 1993, Applied optics.

[78]  G. Weiss,et al.  Statistics of the depth probed by cw measurements of photons in a turbid medium , 1998 .

[79]  Jan Leen Kloosterman,et al.  Analysis of Correlated Coupling of Monte Carlo Forward and Adjoint Histories , 2001 .

[80]  Kaushal Rege,et al.  Spatiotemporal temperature distribution and cancer cell death in response to extracellular hyperthermia induced by gold nanorods. , 2010, ACS nano.

[81]  Pramod C. Nair,et al.  An Automated Force Field Topology Builder (ATB) and Repository: Version 1.0. , 2011, Journal of chemical theory and computation.

[82]  Yongdoo Choi,et al.  Gold nanorod-photosensitizer complex for near-infrared fluorescence imaging and photodynamic/photothermal therapy in vivo. , 2011, ACS nano.

[83]  Yanyu Zhao,et al.  Feasibility of spatial frequency domain imaging (SFDI) for optically characterizing a preclinical oncology model. , 2016, Biomedical optics express.

[84]  Anthony J. Durkin,et al.  Quantitation and mapping of tissue optical properties using modulated imaging. , 2009, Journal of biomedical optics.