The Resolution Matrix in Tomographic Multiplexing: Optimization of Inter-Parameter Cross-Talk, Relative Quantitation, and Localization

• Published in: IEEE transactions on biomedical engineering Vol. 66; no. 8; pp. 2341 - 2351
• Main Authors: Hou, Steven S., Bacskai, Brian J., Kumar, Anand T. N.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Algorithms; Asymptotic methods; Bayes methods; Bayes Theorem; Bayesian analysis; Biological activity; Biomedical measurement; Chemical compounds; Computer simulation; Crosstalk; Fluorescence; fluorescence tomography; Fluorophores; Inverse problems; lifetime multiplexing; Localization; Mimicry; Molecular imaging; Molecular Imaging - methods; Monte Carlo Method; Monte Carlo simulation; Multiplexing; Operators (mathematics); Optimization; Parameter estimation; Phantoms, Imaging; Quantitation; Spatial discrimination; Spatial resolution; Time domain analysis; time-resolved imaging; Tissues; Tomography; Tomography, Optical - methods
• ISSN: 0018-9294; 1558-2531; 1558-2531
• DOI: 10.1109/TBME.2018.2889043

Objective: We use a resolution matrix-based Bayesian framework to compare inversion methods for tomographic fluorescence lifetime multiplexing in a diffuse medium, such as biological tissue. Methods: We consider three inversion methods; an asymptotic time domain (ATD) approach, based on a multiexponential analysis of time domain data, a direct time domain (DTD) approach, which is a minimum error solution, and a cross-talk constrained time domain (CCTD) inversion, which is a solution to an optimization problem that minimizes both error and cross-talk. We compare these methods using Monte Carlo simulations and time domain fluorescence measurements with tissue-mimicking phantoms. Results: The ATD approach provides high accuracy of relative quantitation and spatial localization of two fluorophores embedded in a 18-mm thick turbid medium, with concentration ratios of up to 1:4.25. DTD leads to significant errors in relative quantitation and localization. CCTD provides improved quantitation accuracy over DTD, and better spatial resolution compared to ATD. We present a rigorous theoretical basis for these results and provide a complete derivation of the CCTD estimator. The Bayesian analysis also leads to a formula for rapid computation of the DTD inverse operator for large-scale tomography measurements. Conclusion: The ATD and CCTD inversion methods provide significant advantages over DTD for accurately estimating multiple overlapping fluorophores. Significance: Time domain fluorescence tomography, using zero cross-talk estimators, can serve as a powerful tool for quantifying multiple fluorescently labeled biological processes. The Bayesian framework presented here can be applied to general multiparameter inverse problems for the quantitative estimation of multiple overlapping parameters.