A fluorescence optical tomography approach that extends time reversal optical tomography (TROT) to locate fluorescent targets embedded in a turbid medium is introduced. It uses a multi-source illumination and multi-detector signal acquisition scheme, along with TR matrix formalism, and multiple signal classification (MUSIC) to construct pseudo-image of the targets. The samples consisted of a single or two small tubes filled with water solution of Indocyanine Green (ICG) dye as targets embedded in a 250 mm × 250 mm × 60 mm rectangular cell filled with Intralipid-20% suspension as the scattering medium. The ICG concentration was 1μM, and the Intralipid-20% concentration was adjusted to provide ~ 1-mm transport length for both excitation wavelength of 790 nm and fluorescence wavelength around 825 nm. The data matrix was constructed using the diffusely transmitted fluorescence signals for all scan positions, and the TR matrix was constructed by multiplying data matrix with its transpose. A pseudo spectrum was calculated using the signal subspace of the TR matrix. Tomographic images were generated using the pseudo spectrum. The peaks in the pseudo images provided locations of the target(s) with sub-millimeter accuracy. Concurrent transmission TROT measurements corroborated fluorescence-TROT findings. The results demonstrate that TROT is a fast approach that can be used to obtain accurate three-dimensional position information of fluorescence targets embedded deep inside a highly scattering medium, such as, a contrast-enhanced tumor in a human breast.
Time Reversal Optical Tomography (TROT) is developed to locate extended target(s) in a highly scattering turbid
medium, and estimate their optical strength and size. The approach uses Diffusion Approximation of Radiative Transfer
Equation for light propagation along with Time Reversal (TR) Multiple Signal Classification (MUSIC) scheme for
signal and noise subspaces for assessment of target location. A MUSIC pseudo spectrum is calculated using the
eigenvectors of the TR matrix T, whose poles provide target locations. Based on the pseudo spectrum contours, retrieval
of target size is modeled as an optimization problem, using a "local contour" method. The eigenvalues of T are related to
optical strengths of targets.
The efficacy of TROT to obtain location, size, and optical strength of one absorptive target, one scattering target, and
two absorptive targets, all for different noise levels was tested using simulated data. Target locations were always
accurately determined. Error in optical strength estimates was small even at 20% noise level. Target size and shape were
more sensitive to noise. Results from simulated data demonstrate high potential for application of TROT in practical
biomedical imaging applications.
Optical imaging using independent component analysis (OPTICA) and time reversal optical tomography (TROT)
approaches are used to detect, locate, and obtain cross-section images of two tumor pieces inside a model human breast
assembled using ex vivo human breast tissues and configured as a semi-cylindrical slab of uniform thickness. The
experimental arrangement realized a multi-source probing scheme to illuminate an end face (source plane) of the slab
sample using 750 nm, 800 nm and 830 nm beams of laser light. A multi-detector signal acquisition scheme measured
transmitted light intensity distribution on the other end face (detection plane). This combined multi-source probing and
multi-detector sensing approach culminated in multiple spatial and angular views of the sample necessary for target
localization. The perturbations in light intensity distribution in the detection plane were analyzed using both the OPTICA
and the TROT approaches to obtain locations of the tumor pieces. A back-projection technique with OPTICA provided
cross-section images and estimates of cross section of the targets within the sample. The estimated locations and
dimensions of targets are in good agreement with the results of a corroborating magnetic resonance imaging experiment
and known values.
Time reversal optical tomography (TROT) approach is used to detect and locate absorptive targets embedded in a highly
scattering turbid medium to assess its potential in breast cancer detection. TROT experimental arrangement uses multi-source
probing and multi-detector signal acquisition and Multiple-Signal-Classification (MUSIC) algorithm for target
location retrieval. Light transport from multiple sources through the intervening medium with embedded targets to the
detectors is represented by a response matrix constructed using experimental data. A TR matrix is formed by multiplying
the response matrix by its transpose. The eigenvectors with leading non-zero eigenvalues of the TR matrix correspond to
embedded objects.
The approach was used to: (a) obtain the location and spatial resolution of an absorptive target as a function of its
axial position between the source and detector planes; and (b) study variation in spatial resolution of two targets at the
same axial position but different lateral positions. The target(s) were glass sphere(s) of diameter ~9 mm filled with ink
(absorber) embedded in a 60 mm-thick slab of Intralipid-20% suspension in water with an absorption coefficient μa~
0.003 mm-1 and a transport mean free path lt~ 1 mm at 790 nm, which emulate the average values of those parameters
for human breast tissue. The spatial resolution and accuracy of target location depended on axial position, and target
contrast relative to the background. Both the targets could be resolved and located even when they were only 4-mm
apart. The TROT approach is fast, accurate, and has the potential to be useful in breast cancer detection and localization.
The backscattering of circularly polarized (CP) light has been investigated using experiments and an analytical cumulant
solution of the vector radiative transfer equation. The expression of the exact spatial cumulants of light distribution
function has been derived. Both experimental and theoretical studies show that the helicity of the incident circular
polarization is maintained in the light backscattered from large particle suspensions. Reflection from an embedded target
inside the turbid medium reverses the helicity of the incident circular polarization. Polarization memory imaging makes
use of this difference in helicity between light reflected from the target and that from the scattering medium and
significantly enhances the image contrast by selecting out the circularly cross-polarized light. We experimentally
demonstrate the superior image quality for target inside large polystyrene particle suspensions in water.
A new algorithm based on multi-static data and vector subspace classification to eigenvectors of a round-trip matrix is introduced for optical imaging and localization of objects embedded in a turbid medium. The transport of light from multiple sources through excitation of the embedded objects to the array of detectors is represented by a response matrix that can be constructed from experimental data. The 'round-trip (RT) matrix’ is constructed by multiplying the response matrix by its transpose for continuous-wave (adjoint matrix for frequency domain) illumination. Mathematically, the RT matrix is equivalent to transfer of light from the sources via the embedded objects to the array of detectors and back, and is similar to the time-reversal matrix used in the general area of array processing for acoustic and radar time-reversal imaging. The eigenvectors with leading non-zero eigenvalues of the RT matrix correspond to embedded objects, which are orthogonal to the vectors in the noise subspace. The vector subspace method along with Green’s functions calculated from an appropriate model for light propagation through turbid media is then used to determine the locations of the embedded objects. We tested this algorithm in simulation for light transmitting through a 50 l tr thick (l tr ~ 1 mm is transport mean free path) parallel slab turbid medium with up to six embedded absorptive objects. The method was able to globally locate all six objects with surprising accuracy. This “round-trip tomographic imaging” approach is fast, applicable to different geometries and to different forward models.
Time-sliced and quasi continuous wave two-dimensional (2-D)transillumination imaging methods were used with independent component analysis (ICA) to generate three-dimensional (3-D)tomographic maps of absorbing and scattering inhomogeneities embedded in tissue-like turbid media. The thickness of the turbid media in both the cases was approximately 50 times the transport mean free path. The experimental arrangement for time-sliced optical imaging used 150-fs, 1 kHz repetition-rate, 800-nm light pulses from a Ti:sapphire laser system for sample illumination, and an ultrafast gated intensified camera system (UGICS) providing a minimal gate duration of 80 ps for recording 2-D images. Quasi continuous wave (CW) imaging used 784-nm CW output of a diode laser as the light source and a cooled charge coupled device (CCD) camera for recording 2-D images. Translation stages were used to scan the samples over an array of points in the x-y plane. The temporal profile of the transmitted pulse was used to extract the average optical properties of the media. An independent component separation of the signal, in conjunction with diffusive photon migration theory was used to locate the embedded inhomogeneities. An improved lateral and axial localization of the inhomogeneity over the result obtained by common photon migration reconstruction algorithm is achieved.
We report on the effect of the nonlinear multiple passage on optical
imaging of an absorption inhomogeneity of finite size deep inside
a turbid medium based on a cumulant solution to radiative transfer.
An analytical expression for the nonlinear correction factor is derived. Comparison to Monte Carlo simulations reveals an excellent agreement. The implication on optical imaging is discussed.
A linear forward model of light propagation in turbid media for three dimensional (3D) optical tomography is formed based on the analytical cumulant solution of the Boltzmann radiative transfer equation., for time resolved, CW, and frequency-domain measurements in parallel slab geometry. This forward model is more accurate than the forward model based on the diffusive approximation. An inverse algorithm is developed, based on a fast 3D hybrid-dual-Fourier tomographic approach using multiple detectors and multiple sources in parallel geometry, which incorporates the cumulant radiative transfer model. The inverse algorithm runs fast that can produce a 3D image of a turbid medium with more than 20,000 voxels in 1-2 minutes using a PC computer. A 3D image is presented using simulated data.
We present an analytical solution of the distribution function and the density distribution for the Boltzmann photon transport equation in an infinite uniform isotropic medium. This solution is quantitatively accurate up to the second order cumulant approximation. The solution shows a clear picture of the time evolution of particle migration, from near ballistic, through snake-like, and then into the diffusive regime.
An inverse image reconstruction approach that makes use of an algorithm based on the diffusion approximation of the radiative transport theory and a sequence of picosecond-duration slices of transmitted two-dimensional (2D) light intensity distribution for fast 3D image reconstruction is presented. The results of simulation and experiment for a cylindrical geometry are presented. Object localization in the lateral dimensions is better than that in the axial direction. The observed difference in axial and lateral resolutions are analyzed by introducing the concept of "longitudinal sensitivity".
A novel inverse algorithm, which combines a 2D matrix inversion with a 1D Fourier transform inversion, is designed for obtaining an image of 3D hidden objects in scattering media. The existence of 2D boundaries, on which source- detector pairs are located around, violates the condition for using a 3D Fourier transform inverse imaging. This effect has been handled in our approach. This method greatly reduces the computational burden, compared to standard 3D matrix inversion methods. The result of image of hidden objects using time- resolved simulated data is presented.
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