Time reversal optical tomography for locating targets in a highly scattering turbid medium

A time reversal optical tomography method to locate an extended tumor target embedded in a biological tissue, the method comprising steps of:

• illuminating a part of the biological tissue with light from an optical source, wherein the biological tissue comprises normal tissue that forms a background and at least one extended tumor target that defines a quantity of extended tumor targets,
• receiving an optical signal from the biological tissue resulting from the illuminating step, wherein the optical signal comprises perturbations in light intensity due to the at least one extended target, the optical signal being a fraction of fluorescence emitted by the at least one tumor;
• constructing, with a computer, a response data matrix K using the optical signal,
• calculating, using the computer, a time reversal (TR) matrix T=K†K, where K† is an adjoint of the response data matrix K, the TR matrix is of larger rank than the quantity of extended tumor targets;
• calculating eigenvalues and eigenvectors of the response data matrix K, including eigenvectors in signal subspace and noise subspace;
• separating the eigenvectors in signal subspace and noise subspace according to a L-curve regularization protocol that includes a step of identifying the eigenvectors in the signal subspace that exceeds a threshold ε;
• dividing the biological tissue into a predetermined number of voxels;
• calculating Green's function vectors (GFVs) both gd(Xp) and ∂αgd(Xp) (α=x, y, z) for a test target position Xp at a pth voxel of the predetermined number of voxels, for an absorptive test target, and a scattering test target, respectively;
• computing a pseudo-spectrum using the eigenvectors in the signal subspace that exceeds the threshold ε;
• generating a pseudo-image from the pseudo-spectrum;
• providing a location of the at least one extended tumor target by displaying the pseudo-image.

A time reversal optical tomography method to locate extended fluorescent tumor targets embedded in a biological tissue, the method comprising sequential steps of:

• placing the biological tissue under an optical source;
• illuminating a part of the biological tissue with light at wavelength λx from the optical source, wherein the biological tissue comprises normal tissue that forms a background and at least one extended tumor target that defines a quantity of extended tumor targets;
• receiving an optical signal from the biological tissue at wavelength λm resulting from the illumination step, wherein the optical signal comprises perturbations in light intensity due to the at least one extended tumor target, the optical signal being selected from (1) a fraction of the light received from the biological tissue, (2) a fraction of fluorescence emitted by the at least one extended tumor target and (3) combinations thereof;
• constructing, with a computer, a response data matrix K using the optical signal,
• calculating a time reversal (TR) matrix T=K†K, where K† is the adjoint of the response data matrix K, the TR matrix is of larger rank than the quantity of extended tumor targets;
• calculating the eigenvalues and eigenvectors of the response data matrix K, including eigenvectors in signal subspace and noise subspace;
• separating the eigenvectors in signal subspace and noise subspace according to a L-curve regularization protocol that includes a step of identifying the eigenvectors in the signal subspace that exceeds a threshold ε;
• dividing the biological tissue into a predetermined number of voxels;
• calculating Green's function vector (GFVs) gd(Xp) for a test target position Xp at the pth voxel;
• computing a pseudo-spectrum using the eigenvectors in the signal subspace that exceeds the threshold ε;
• generating a pseudo-image from the pseudo-spectrum;
• providing a location of the one or more extended tumor target by displaying the pseudo-image.