Ultrasound-modulated optical tomography: recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation

Abstract

We address a certain inverse problem in ultrasound-modulated optical tomography: the recovery of the amplitude of vibration of scatterers [p(r)] in the ultrasound focal volume in a diffusive object from boundary measurement of the modulation depth (M) of the amplitude autocorrelation of light [φ(r,τ)] traversing through it. Since M is dependent on the stiffness of the material, this is the precursor to elasticity imaging. The propagation of φ(r,τ) is described by a diffusion equation from which we have derived a nonlinear perturbation equation connecting p(r) and refractive index modulation [Δn(r)] in the region of interest to M measured on the boundary. The nonlinear perturbation equation and its approximate linear counterpart are solved for the recovery of p(r). The numerical results reveal regions of different stiffness, proving that the present method recovers p(r) with reasonable quantitative accuracy and spatial resolution.

Detection and estimation of liquid flow through a pipe in a tissue-like object with ultrasound-assisted diffuse correlation spectroscopy

“…The basic correlation diffusion is derived in [18] as an approximation to the transport equation modeling the decay of correlation, just as photon diffusion equation approximates radiative transport equation to model photon propagation through a multiple-scattering medium. The CDE describing the transport of Gr; τ through a turbid object, like the PVA slab of our experiments, is given by [19] −∇ · κ∇Gr; τ μ a 1∕3μ 0 s k 2 0 hΔr 2 r; τi b Gr; τ S 0 r 0 :…”

Ultrasound-modulated optical tomography: direct recovery of elasticity distribution from experimentally measured intensity autocorrelation

“…The typical mechanical property is the Young's modulus which influences the amplitude of oscillation of the scattering centers. In an earlier work [5], we demonstrated the recovery of pr, the distribution of the mean-squared amplitude of vibration of the scattering centers in the object undergoing nearly sinusoidal oscillation under local US forcing (i.e., pr hjA 2 rji, where Ar is the amplitude of vibration and hi represents averaging over a volume l 3 with l denoting the transport-mean-free path of photons) from M . The readily measured quantity in an experiment is g 2 r; τ on the boundary of the object, from which M (the experimental measurement) can be computed (see [6] for the relation between g 1 and g 2 ).…”

“…Since the local absorption coefficient μ a r, pr and nr influence M , it should be possible (at least theoretically) to recover all the above three parameters pertaining to the ROI from M . For this, a perturbation equation is set up from the correlation diffusion equation (CDE) describing the propagation of Gr; τ in a turbid medium [5], thus connecting the US-induced perturbations in the ROI [which are in nr and mechanical vibration of the scattering centers] to M , which is the perturbation of Gr; τ. This equation, relating pr nonlinearly to M (as in [5]), is solved either as it is, or, for ease of computation, after linearization at p 0.…”

“…For this, a perturbation equation is set up from the correlation diffusion equation (CDE) describing the propagation of Gr; τ in a turbid medium [5], thus connecting the US-induced perturbations in the ROI [which are in nr and mechanical vibration of the scattering centers] to M , which is the perturbation of Gr; τ. This equation, relating pr nonlinearly to M (as in [5]), is solved either as it is, or, for ease of computation, after linearization at p 0. The solution involves finding pr which minimizes εp 1 2 ‖M − M‖ 2 , where M is the experimentally measured modulation depth and M its computationally obtained counterpart [M may be looked upon as a function of pr].…”

Acousto-optic effect in random media

“…The image is created by scanning the focus of the beam and recording the intensity of the scattered light at a fixed detector. Tomographic imaging utilizes an inverse scattering method to reconstruct images of the optical properties of the medium [20,22,[29][30][31][32][33][34][35].…”