Flux density calibration in diffuse optical tomographic systems.

The solution of the forward equation that models the transport of light through a highly scattering tissue material in diffuse optical tomography (DOT) using the finite element method gives flux density (Φ) at the nodal points of the mesh. The experimentally measured flux (Umeasured) on the boundary over a finite surface area in a DOT system has to be corrected to account for the system transfer functions (R) of various building blocks of the measurement system. We present two methods to compensate for the perturbations caused by R and estimate true flux density (Φ) from Umeasuredcal. In the first approach, the measurement data with a homogeneous phantom (Umeasuredhomo) is used to calibrate the measurement system. The second scheme estimates the homogeneous phantom measurement using only the measurement from a heterogeneous phantom, thereby eliminating the necessity of a homogeneous phantom. This is done by statistically averaging the data (Umeasuredhetero) and redistributing it to the corresponding detector positions. The experiments carried out on tissue mimicking phantom with single and multiple inhomogeneities, human hand, and a pork tissue phantom demonstrate the robustness of the approach.

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

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.

Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography.

PURPOSE: A computationally efficient algorithm (linear iterative type) based on singular value decomposition (SVD) of the Jacobian has been developed that can be used in rapid dynamic near-infrared (NIR) diffuse optical tomography. METHODS: Numerical and experimental studies have been conducted to prove the computational efficacy of this SVD-based algorithm over conventional optical image reconstruction algorithms. RESULTS: These studies indicate that the performance of linear iterative algorithms in terms of contrast recovery (quantitation of optical images) is better compared to nonlinear iterative (conventional) algorithms, provided the initial guess is close to the actual solution. The nonlinear algorithms can provide better quality images compared to the linear iterative type algorithms. Moreover, the analytical and numerical equivalence of the SVD-based algorithm to linear iterative algorithms was also established as a part of this work. It is also demonstrated that the SVD-based image reconstruction typically requires O(NN2) operations per iteration, as contrasted with linear and nonlinear iterative methods that, respectively, require O(NN3) and O(NN6) operations, with "NN" being the number of unknown parameters in the optical image reconstruction procedure. CONCLUSIONS: This SVD-based computationally efficient algorithm can make the integration of image reconstruction procedure with the data acquisition feasible, in turn making the rapid dynamic NIR tomography viable in the clinic to continuously monitor hemodynamic changes in the tissue pathophysiology.