Tomographic Imaging Methods, Devices, and Systems

Abstract

A multispectral bioluminescence optical tomography algorithm makes use of a partial differential equation (PDE) constrained approach. A sequential quadratic programming (SQP) method is demonstrated that allows for solving both forward and inverse problems at once by updating the forward and inverse variables simultaneously at each step of the optimization iterations. Light propagation in biological tissue is modeled by using the equation of radiative transfer (ERT) and performance of the ERT-based PDE-constrained approach is modeled through numerical and experimental studies.

What is claimed is: 
     
         1 . A method for detecting a distribution of radiation sources inside an object, comprising:
 capturing image data responsively to radiation emitted from a surface of the object and converting the image data to radiation flux data representing radiation emitted at predefined portions of said surface, the converting including compensating for refractive index mismatch at the surface;   storing medium data representing a predicted distribution of radiation scattering properties inside the object; and   iteratively solving for a source distribution of said radiation sources that predicts the radiation emitted at the predefined portions, the solving including searching for an extremum of a multispectral Lagrangian functional representation of the independent source distribution and spectral radiance distribution; and   outputting data representing a source distribution resulting from said iteratively solving.   
     
     
         2 . The method of  claim 1 , further comprising storing source data representing an initial estimate of a distribution of radiation sources within said object, said iteratively solving being responsive to said initial estimate. 
     
     
         3 . The method of  claim 1 , further comprising storing flux data representing an initial estimate of a distribution of radiation within said object, said iteratively solving being responsive to said initial estimate. 
     
     
         4 . The method of  claim 1 , wherein the iteratively solving is effective to converge spectral radiance distribution and source distribution simultaneously such that the spectral radiance distribution is solved with a progressively smaller tolerance as the iteratively solving approaches the extremum. 
     
     
         5 . The method of  claim 1 , wherein the Lagrangian functional is derived from a Lagrangian formulation of a constrained optimization employing the Lagrangian multiplier method of finding an extremum of an objective function (the difference between predictions and measurements) subject to a linear constraint (discretized formulation of the radiation transfer equation). 
     
     
         6 . The method of  claim 1 , further comprising storing at least one emission parameter responsive to a sum-product over a substantial portion of range of wavelengths of the radiation emitted by said sources, said iteratively solving being responsive to said at least one emission parameter. 
     
     
         7 . The method of  claim 1 , wherein said sources are bioluminescent sources. 
     
     
         8 . The method of  claim 1 , wherein the iteratively solving accounts for reflection of radiation at said surface. 
     
     
         9 . A method for reconstructing a representation of a bioluminescent source distribution inside a subject using a partial differential equation (PDE) constrained algorithm, comprising:
 generating a model of bioluminescent source distribution based on light intensity measurements at respective wavelengths obtained at a surface of the subject; and   solving the inverse and forward problems in the model independently and simultaneously using a sequential quadratic programming (SPQ) method.   
     
     
         10 . The method of  claim 9 , wherein the sequential quadratic programming (SPQ) method updates forward and inverse variables simultaneously at each step of the reconstruction iterations. 
     
     
         11 . The method of  claim 9 , wherein the inverse problem includes finding a vector q(r) of bioluminescent sources inside the subject that minimizes differences between measurements and predictions. 
     
     
         12 . The method of  claim 9 , wherein the forward problem is modeled by the radiative transfer equation (ERT). 
     
     
         13 . The method of  claim 12 , wherein the vector q(r) includes all wavelength data. 
     
     
         14 . The method of  claim 9 , wherein the inverse problem is modeled by a Lagrangian function including Lagrangian variables. 
     
     
         15 . The method of  claim 14 , wherein the sequential quadratic programming (SPQ) method solves the inverse problem by minimizing the Lagrangian function. 
     
     
         16 . The method of  claim 12 , wherein the radiative transfer equation (ERT) includes spectral radiation intensity, absorption and scattering coefficients, total energy distribution, photon emission, and surface intensities as variables. 
     
     
         17 . The method of  claim 12 , wherein the sequential quadratic programming (SPQ) method solves the forward problem by determining total photon emission from spectral analysis over the spectral energy distribution of a bioluminescent source, employing a partially-reflective boundary condition, and using an unstructured finite volume method for discretization.