Multispectral Imaging for Hemoglobin Estimation by PCA.

Tissular blood perfusion is helpful to assess the health condition of a subject and even monitor superficial lesions. Current state of the art is focused on developing non-invasive, quantitative and accessible methods for blood flow monitoring in large areas. This paper presents an approach based on multispectral images on the VIS-NIR range to quantify blood perfusion. Our goal is to estimate the changes in deoxygenated hemoglobin. To do so, we employ principal component analysis followed by a linear regression model. The proposal was evaluated using in-vivo data from a vascular occlusion protocol, and the results were validated against photoplethysmography measurements. Although the number of subjects in the protocol was limited, our model made a prediction with an average similarity of 91.53% with a mean R-squared adjusted of 0.8104.

Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach.

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.

Blind deconvolution estimation of fluorescence measurements through quadratic programming.

Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.

Estimation of the number of fluorescent end-members for quantitative analysis of multispectral FLIM data.

Multispectral fluorescence lifetime imaging (m-FLIM) can potentially allow identifying the endogenous fluorophores present in biological tissue. Quantitative description of such data requires estimating the number of components in the sample, their characteristic fluorescent decays, and their relative contributions or abundances. Unfortunately, this inverse problem usually requires prior knowledge about the data, which is seldom available in biomedical applications. This work presents a new methodology to estimate the number of potential endogenous fluorophores present in biological tissue samples from time-domain m-FLIM data. Furthermore, a completely blind linear unmixing algorithm is proposed. The method was validated using both synthetic and experimental m-FLIM data. The experimental m-FLIM data include in-vivo measurements from healthy and cancerous hamster cheek-pouch epithelial tissue, and ex-vivo measurements from human coronary atherosclerotic plaques. The analysis of m-FLIM data from in-vivo hamster oral mucosa identified healthy from precancerous lesions, based on the relative concentration of their characteristic fluorophores. The algorithm also provided a better description of atherosclerotic plaques in term of their endogenous fluorophores. These results demonstrate the potential of this methodology to provide quantitative description of tissue biochemical composition.

Blind end-member and abundance extraction for multispectral fluorescence lifetime imaging microscopy data.

This paper proposes a new blind end-member and abundance extraction (BEAE) method for multispectral fluorescence lifetime imaging microscopy (m-FLIM) data. The chemometrical analysis relies on an iterative estimation of the fluorescence decay end-members and their abundances. The proposed method is based on a linear mixture model with positivity and sum-to-one restrictions on the abundances and end-members to compensate for signature variability. The synthesis procedure depends on a quadratic optimization problem, which is solved by an alternating least-squares structure over convex sets. The BEAE strategy only assumes that the number of components in the analyzed sample is known a spriori. The proposed method is first validated by using synthetic m-FLIM datasets at 15, 20, and 25 dB signal-to-noise ratios. The samples simulate the mixed response of tissue containing multiple fluorescent intensity decays. Furthermore, the results were also validated with six m-FLIM datasets from fresh postmortem human coronary atherosclerotic plaques. A quantitative evaluation of the BEAE was made against two popular techniques: minimum volume constrained nonnegative matrix factorization (MVC-NMF) and multivariate curve resolution-alternating least-squares (MCR-ALS). Our proposed method (BEAE) was able to provide more accurate estimations of the end-members: 0.32% minimum relative error and 13.82% worst-case scenario, despite different initial conditions in the iterative optimization procedure and noise effect. Meanwhile, MVC-NMF and MCR-ALS presented more variability in estimating the end-members: 0.35% and 0.34% for minimum errors and 15.31% and 13.25% in the worst-case scenarios, respectively. This tendency was also maintained for the abundances, where BEAE obtained 0.05 as the minimum absolute error and 0.12 in the worst-case scenario; MCR-ALS and MVC-NMF achieved 0.04 and 0.06 for the minimum absolute errors, and 0.15 and 0.17 under the worst-case conditions, respectively. In addition, the average computation time was evaluated for the synthetic datasets, where MVC-NMF achieved the fastest time, followed by BEAE and finally MCR-ALS. Consequently, BEAE improved MVC-NMF in convergence to a local optimal solution and robustness against signal variability, and it is roughly 3.6 time faster than MCR-ALS.

A fully constrained optimization method for time-resolved multispectral fluorescence lifetime imaging microscopy data unmixing.

This paper presents a new unmixing methodology of multispectral fluorescence lifetime imaging microscopy (m-FLIM) data, in which the spectrum is defined as the combination of time-domain fluorescence decays at multiple emission wavelengths. The method is based on a quadratic constrained optimization (CO) algorithm that provides a closed-form solution under equality and inequality restrictions. In this paper, it is assumed that the time-resolved fluorescence spectrum profiles of the constituent components are linearly independent and known a priori. For comparison purposes, the standard least squares (LS) solution and two constrained versions nonnegativity constrained least squares (NCLS) and fully constrained least squares (FCLS) (Heinz and Chang, 2001) are also tested. Their performance was evaluated by using synthetic simulations, as well as imaged samples from fluorescent dyes and ex vivo tissue. In all the synthetic evaluations, the CO obtained the best accuracy in the estimations of the proportional contributions. CO could achieve an improvement ranging between 41% and 59% in the relative error compared to LS, NCLS, and FCLS at different signal-to-noise ratios. A liquid mixture of fluorescent dyes was also prepared and imaged in order to provide a controlled scenario with real data, where CO and FCLS obtained the best performance. The CO and FCLS were also tested with 20 ex vivo samples of human coronary arteries, where the expected concentrations are qualitatively known. A certainty measure was employed to assess the confidence in the estimations made by each algorithm. The experiments confirmed a better performance of CO, since this method is optimal with respect to equality and inequality restrictions in the linear unmixing formulation. Thus, the evaluation showed that CO achieves an accurate characterization of the samples. Furthermore, CO is a computational efficient alternative to estimate the abundance of components in m-FLIM data, since a global optimal solution is always guaranteed in a closed form.