Image reconstruction for bioluminescence tomography

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed by our group. While the forward imaging model is described by the diffusion approximation, BLT is the inverse problem to recover an internal bioluminescent source distribution subject to Cauchy data for the diffusion equation. This inverse source problem is ill-posed and does not yield the unique solution in the general case. The uniqueness problem under practical constraints was recently studied by our group. It was found that all the inverse source solutions can be expressed as the unique minimal energy source solution plus a nonradiating source. We demonstrate that the minimal energy source solution is not physically favorable for bioluminescence tomography, although the minimal energy constraint is utilized in other applications. To find a physically meaningful unique solution, adequate prior knowledge must be utilized. Here we propose two iterative approaches in this work. The first one is a variant of the well-known EM algorithm. The second one is based on the Landweber scheme. Either of the methods is suitable for incorporating knowledge-based constraints. We discuss several issues related to the implementation of these methods, including the initial guess and stopping criteria. Also, we report our numerical simulation results to demonstrate the feasibility of bioluminescence tomography.

[1]  Ming Jiang,et al.  Development of iterative algorithms for image reconstruction , 2002 .

[2]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[3]  C. Contag,et al.  It's not just about anatomy: In vivo bioluminescence imaging as an eyepiece into biology , 2002, Journal of magnetic resonance imaging : JMRI.

[4]  Bertolt Eicke.  Iteration methods for convexly constrained ill-posed problems in hilbert space , 1992 .

[5]  Ashutosh Sabharwal,et al.  Convexly constrained linear inverse problems: iterative least-squares and regularization , 1998, IEEE Trans. Signal Process..

[6]  Y. Y. Belov,et al.  Inverse Problems for Partial Differential Equations , 2002 .

[7]  A. Klose,et al.  Quasi-Newton methods in optical tomographic image reconstruction , 2003 .

[8]  S. Gambhir,et al.  Molecular Imaging of Cardiac Cell Transplantation in Living Animals Using Optical Bioluminescence and Positron Emission Tomography , 2003, Circulation.

[9]  H. Malcolm Hudson,et al.  Accelerated image reconstruction using ordered subsets of projection data , 1994, IEEE Trans. Medical Imaging.

[10]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[11]  Yair Censor,et al.  Finding the projection of a point onto the intersection of convex sets via projections onto half-spaces , 2003, J. Approx. Theory.

[12]  R. Weissleder,et al.  Fluorescence molecular tomography resolves protease activity in vivo , 2002, Nature Medicine.

[13]  A J Devaney,et al.  Inverse source problem and minimum-energy sources. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  Anton P. McCaffrey,et al.  Advancing Molecular Therapies through In Vivo Bioluminescent Imaging , 2003, Molecular imaging.

[15]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[16]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[17]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[18]  A. Welch,et al.  A review of the optical properties of biological tissues , 1990 .

[19]  S. Arridge.  Optical tomography in medical imaging , 1999 .

[20]  Ming Jiang,et al.  Convergence of the simultaneous algebraic reconstruction technique (SART) , 2003, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[21]  A. Söling,et al.  Bioluminescence imaging in vivo – application to cancer research , 2003, Expert opinion on biological therapy.

[22]  M. Bertero,et al.  Projected Landweber method and preconditioning , 1997 .

[23]  B. Rice,et al.  In vivo imaging of light-emitting probes. , 2001, Journal of biomedical optics.

[24]  Daniel E. Hall,et al.  Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging. , 2000, Neoplasia.