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Computational tools for inversion and uncertainty estimation in respirometry. PLoS One 2021; 16:e0251926. [PMID: 34019586 PMCID: PMC8139500 DOI: 10.1371/journal.pone.0251926] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2020] [Accepted: 05/06/2021] [Indexed: 11/22/2022] Open
Abstract
In many physiological systems, real-time endogeneous and exogenous signals in living organisms provide critical information and interpretations of physiological functions; however, these signals or variables of interest are not directly accessible and must be estimated from noisy, measured signals. In this paper, we study an inverse problem of recovering gas exchange signals of animals placed in a flow-through respirometry chamber from measured gas concentrations. For large-scale experiments (e.g., long scans with high sampling rate) that have many uncertainties (e.g., noise in the observations or an unknown impulse response function), this is a computationally challenging inverse problem. We first describe various computational tools that can be used for respirometry reconstruction and uncertainty quantification when the impulse response function is known. Then, we address the more challenging problem where the impulse response function is not known or only partially known. We describe nonlinear optimization methods for reconstruction, where both the unknown model parameters and the unknown signal are reconstructed simultaneously. Numerical experiments show the benefits and potential impacts of these methods in respirometry.
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Campos-Delgado DU, Gutierrez-Navarro O, Salinas-Martinez R, Duran E, Mejia-Rodriguez AR, Velazquez-Duran MJ, Jo JA. Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach. PLoS One 2021; 16:e0248301. [PMID: 33735228 PMCID: PMC7971520 DOI: 10.1371/journal.pone.0248301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 02/23/2021] [Indexed: 11/18/2022] Open
Abstract
The deconvolution process is a key step for quantitative evaluation of fluorescence lifetime imaging microscopy (FLIM) samples. By this process, the fluorescence impulse responses (FluoIRs) of the sample are decoupled from the instrument response (InstR). In blind deconvolution estimation (BDE), the FluoIRs and InstR are jointly extracted from a dataset with minimal a priori information. In this work, two BDE algorithms are introduced based on linear combinations of multi-exponential functions to model each FluoIR in the sample. For both schemes, the InstR is assumed with a free-form and a sparse structure. The local perspective of the BDE methodology assumes that the characteristic parameters of the exponential functions (time constants and scaling coefficients) are estimated based on a single spatial point of the dataset. On the other hand, the same exponential functions are used in the whole dataset in the global perspective, and just the scaling coefficients are updated for each spatial point. A least squares formulation is considered for both BDE algorithms. To overcome the nonlinear interaction in the decision variables, an alternating least squares (ALS) methodology iteratively solves both estimation problems based on non-negative and constrained optimizations. The validation stage considered first synthetic datasets at different noise types and levels, and a comparison with the standard deconvolution techniques with a multi-exponential model for FLIM measurements, as well as, with two BDE methodologies in the state of the art: Laguerre basis, and exponentials library. For the experimental evaluation, fluorescent dyes and oral tissue samples were considered. Our results show that local and global perspectives are consistent with the standard deconvolution techniques, and they reached the fastest convergence responses among the BDE algorithms with the best compromise in FluoIRs and InstR estimation errors.
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Affiliation(s)
- Daniel U. Campos-Delgado
- Facultad de Ciencias, Universidad Autonoma de San Luis Potosi, San Luis Potosi, Mexico
- Instituto de Investigacion en Comunicacion Optica, Universidad Autonoma de San Luis Potosi, San Luis Potosi, Mexico
- * E-mail:
| | - Omar Gutierrez-Navarro
- Department of Biomedical Engineering, Universidad Autonoma de Aguascalientes, Aguascalientes, Mexico
| | | | - Elvis Duran
- Department of Biomedical Engineering, Texas A&M University, College Station, Texas, United States of America
| | | | | | - Javier A. Jo
- School of Electrical and Computer Engineering, University of Oklahoma, Norman, Oklahoma, United States of America
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Campos-Delgado DU, Gutierrez-Navarro O, Rico-Jimenez JJ, Duran E, Fabelo H, Ortega S, Callicó GM, Jo JA. Extended Blind End-member and Abundance Extraction for Biomedical Imaging Applications. IEEE ACCESS : PRACTICAL INNOVATIONS, OPEN SOLUTIONS 2019; 7:178539-178552. [PMID: 31942279 PMCID: PMC6961960 DOI: 10.1109/access.2019.2958985] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In some applications of biomedical imaging, a linear mixture model can represent the constitutive elements (end-members) and their contributions (abundances) per pixel of the image. In this work, the extended blind end-member and abundance extraction (EBEAE) methodology is mathematically formulated to address the blind linear unmixing (BLU) problem subject to positivity constraints in optical measurements. The EBEAE algorithm is based on a constrained quadratic optimization and an alternated least-squares strategy to jointly estimate end-members and their abundances. In our proposal, a local approach is used to estimate the abundances of each end-member by maximizing their entropy, and a global technique is adopted to iteratively identify the end-members by reducing the similarity among them. All the cost functions are normalized, and four initialization approaches are suggested for the end-members matrix. Synthetic datasets are used first for the EBEAE validation at different noise types and levels, and its performance is compared to state-of-the-art algorithms in BLU. In a second stage, three experimental biomedical imaging applications are addressed with EBEAE: m-FLIM for chemometric analysis in oral cavity samples, OCT for macrophages identification in post-mortem artery samples, and hyper-spectral images for in-vivo brain tissue classification and tumor identification. In our evaluations, EBEAE was able to provide a quantitative analysis of the samples with none or minimal a priori information.
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Affiliation(s)
- D U Campos-Delgado
- Faculty of Sciences, Universidad Autonoma de San Luis Potosi, SLP, México
| | - O Gutierrez-Navarro
- Biomedical Engineering Department, Universidad Autonoma de Aguascalientes, AGS, México
| | - J J Rico-Jimenez
- Department of Biomedical Engineering, Texas A& M University, College Station, TX, USA
| | - E Duran
- Department of Biomedical Engineering, Texas A& M University, College Station, TX, USA
| | - H Fabelo
- Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain
| | - S Ortega
- Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain
| | - G M Callicó
- Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain
| | - J A Jo
- Department of Biomedical Engineering, Texas A& M University, College Station, TX, USA
- School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK, USA
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Sagar MAK, Dai B, Chacko JV, Weber JJ, Velten A, Sanders ST, White JG, Eliceiri KW. Optical fiber-based dispersion for spectral discrimination in fluorescence lifetime imaging systems. JOURNAL OF BIOMEDICAL OPTICS 2019; 25:1-17. [PMID: 31833280 PMCID: PMC6907392 DOI: 10.1117/1.jbo.25.1.014506] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2019] [Accepted: 11/20/2019] [Indexed: 06/10/2023]
Abstract
The excited state lifetime of a fluorophore together with its fluorescence emission spectrum provide information that can yield valuable insights into the nature of a fluorophore and its microenvironment. However, it is difficult to obtain both channels of information in a conventional scheme as detectors are typically configured either for spectral or lifetime detection. We present a fiber-based method to obtain spectral information from a multiphoton fluorescence lifetime imaging (FLIM) system. This is made possible using the time delay introduced in the fluorescence emission path by a dispersive optical fiber coupled to a detector operating in time-correlated single-photon counting mode. This add-on spectral implementation requires only a few simple modifications to any existing FLIM system and is considerably more cost-efficient compared to currently available spectral detectors.
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Affiliation(s)
- Md Abdul Kader Sagar
- University of Wisconsin–Madison, Laboratory for Optical and Computational Instrumentation, Madison, Wisconsin, United States
- University of Wisconsin–Madison, Biomedical Engineering Department, Madison, Wisconsin, United States
| | - Bing Dai
- University of Wisconsin–Madison, Laboratory for Optical and Computational Instrumentation, Madison, Wisconsin, United States
| | - Jenu V. Chacko
- University of Wisconsin–Madison, Laboratory for Optical and Computational Instrumentation, Madison, Wisconsin, United States
| | - Joshua J. Weber
- University of Wisconsin–Madison, Laboratory for Optical and Computational Instrumentation, Madison, Wisconsin, United States
| | - Andreas Velten
- University of Wisconsin–Madison, Laboratory for Optical and Computational Instrumentation, Madison, Wisconsin, United States
| | - Scott T. Sanders
- University of Wisconsin–Madison, Mechanical Engineering Department, Madison, Wisconsin, United States
| | - John G. White
- University of Wisconsin–Madison, Laboratory for Optical and Computational Instrumentation, Madison, Wisconsin, United States
| | - Kevin W. Eliceiri
- University of Wisconsin–Madison, Laboratory for Optical and Computational Instrumentation, Madison, Wisconsin, United States
- University of Wisconsin–Madison, Biomedical Engineering Department, Madison, Wisconsin, United States
- University of Wisconsin–Madison, Medical Physics Department, Madison, Wisconsin, United States
- Morgridge Institute for Research, Madison, Wisconsin, United States
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Walsh AJ, Sharick JT, Skala MC, Beier HT. Temporal binning of time-correlated single photon counting data improves exponential decay fits and imaging speed. BIOMEDICAL OPTICS EXPRESS 2016; 7:1385-99. [PMID: 27446663 PMCID: PMC4929649 DOI: 10.1364/boe.7.001385] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Revised: 03/15/2016] [Accepted: 03/15/2016] [Indexed: 05/06/2023]
Abstract
Time-correlated single photon counting (TCSPC) enables acquisition of fluorescence lifetime decays with high temporal resolution within the fluorescence decay. However, many thousands of photons per pixel are required for accurate lifetime decay curve representation, instrument response deconvolution, and lifetime estimation, particularly for two-component lifetimes. TCSPC imaging speed is inherently limited due to the single photon per laser pulse nature and low fluorescence event efficiencies (<10%) required to reduce bias towards short lifetimes. Here, simulated fluorescence lifetime decays are analyzed by SPCImage and SLIM Curve software to determine the limiting lifetime parameters and photon requirements of fluorescence lifetime decays that can be accurately fit. Data analysis techniques to improve fitting accuracy for low photon count data were evaluated. Temporal binning of the decays from 256 time bins to 42 time bins significantly (p<0.0001) improved fit accuracy in SPCImage and enabled accurate fits with low photon counts (as low as 700 photons/decay), a 6-fold reduction in required photons and therefore improvement in imaging speed. Additionally, reducing the number of free parameters in the fitting algorithm by fixing the lifetimes to known values significantly reduced the lifetime component error from 27.3% to 3.2% in SPCImage (p<0.0001) and from 50.6% to 4.2% in SLIM Curve (p<0.0001). Analysis of nicotinamide adenine dinucleotide-lactate dehydrogenase (NADH-LDH) solutions confirmed temporal binning of TCSPC data and a reduced number of free parameters improves exponential decay fit accuracy in SPCImage. Altogether, temporal binning (in SPCImage) and reduced free parameters are data analysis techniques that enable accurate lifetime estimation from low photon count data and enable TCSPC imaging speeds up to 6x and 300x faster, respectively, than traditional TCSPC analysis.
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Affiliation(s)
- Alex J. Walsh
- National Research Council, JBSA Fort Sam Houston, Texas, 78234, USA
- 711th Human Performance Wing, Human Effectiveness Directorate, Bioeffects Division, Optical Radiation Bioeffects Branch, Air Force Research Lab, JBSA Fort Sam Houston, Texas, 78234, USA
| | - Joe T. Sharick
- Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee, 37235, USA
| | - Melissa C. Skala
- Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee, 37235, USA
| | - Hope T. Beier
- 711th Human Performance Wing, Human Effectiveness Directorate, Bioeffects Division, Optical Radiation Bioeffects Branch, Air Force Research Lab, JBSA Fort Sam Houston, Texas, 78234, USA
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