Browsing by Author "Acosta, Sebastian"
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Item Inverse Source Problems for Time-Dependent Radiative Transport(2014-05) Acosta, SebastianIn the first part of this thesis, I develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of the transport field with finite steering time. Absorbing and scattering effects, modeled by coefficients with low regularity, are incorporated in the formulation of these problems. This time reversal approach leads to a convergent iterative procedure to reconstruct the initial condition provided that the scattering coefficient is sufficiently small. Then, using duality arguments, I show that the solvability of the inverse problem leads to exact controllability of the transport field. The solution approach to both of these problems may have applications in areas such as optical imaging and optimization of radiation delivery. The second portion of the work is dedicated to the simultaneous recovery of a source term f(x) and an isotropic initial condition u0(x), using the single measurement induced by these data. This result is part of an effort to reconstruct optical properties using unknown illumination embedded in the unknown medium. More precisely, based on exact boundary controllability, I derive a system of equations for the unknown terms f and u0. The system is shown to be of Fredholm type if s satisfies a certain positivity condition. This condition requires that the radiation visits the region over which f is to be recovered. I show that for generic terms and weakly absorbing media, the inverse problem is well-posed.Item Numerical method of characteristics for one-dimensional blood flow(Elsevier, 2015) Acosta, Sebastian; Puelz, Charles; Riviére, Béatrice; Penny, Daniel J.; Rusin, Craig G.Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.Item Stratification of Pediatric COVID-19 Cases Using Inflammatory Biomarker Profiling and Machine Learning(MDPI, 2023) Subramanian, Devika; Vittala, Aadith; Chen, Xinpu; Julien, Christopher; Acosta, Sebastian; Rusin, Craig; Allen, Carl; Rider, Nicholas; Starosolski, Zbigniew; Annapragada, Ananth; Devaraj, SrideviWhile pediatric COVID-19 is rarely severe, a small fraction of children infected with SARS-CoV-2 go on to develop multisystem inflammatory syndrome (MIS-C), with substantial morbidity. An objective method with high specificity and high sensitivity to identify current or imminent MIS-C in children infected with SARS-CoV-2 is highly desirable. The aim was to learn about an interpretable novel cytokine/chemokine assay panel providing such an objective classification. This retrospective study was conducted on four groups of pediatric patients seen at multiple sites of Texas Children’s Hospital, Houston, TX who consented to provide blood samples to our COVID-19 Biorepository. Standard laboratory markers of inflammation and a novel cytokine/chemokine array were measured in blood samples of all patients. Group 1 consisted of 72 COVID-19, 70 MIS-C and 63 uninfected control patients seen between May 2020 and January 2021 and predominantly infected with pre-alpha variants. Group 2 consisted of 29 COVID-19 and 43 MIS-C patients seen between January and May 2021 infected predominantly with the alpha variant. Group 3 consisted of 30 COVID-19 and 32 MIS-C patients seen between August and October 2021 infected with alpha and/or delta variants. Group 4 consisted of 20 COVID-19 and 46 MIS-C patients seen between October 2021 andJanuary 2022 infected with delta and/or omicron variants. Group 1 was used to train an L1-regularized logistic regression model which was tested using five-fold cross validation, and then separately validated against the remaining naïve groups. The area under receiver operating curve (AUROC) and F1-score were used to quantify the performance of the cytokine/chemokine assay-based classifier. Standard laboratory markers predict MIS-C with a five-fold cross-validated AUROC of 0.86 ± 0.05 and an F1 score of 0.78 ± 0.07, while the cytokine/chemokine panel predicted MIS-C with a five-fold cross-validated AUROC of 0.95 ± 0.02 and an F1 score of 0.91 ± 0.04, with only sixteen of the forty-five cytokines/chemokines sufficient to achieve this performance. Tested on Group 2 the cytokine/chemokine panel yielded AUROC = 0.98 and F1 = 0.93, on Group 3 it yielded AUROC = 0.89 and F1 = 0.89, and on Group 4 AUROC = 0.99 and F1 = 0.97. Adding standard laboratory markers to the cytokine/chemokine panel did not improve performance. A top-10 subset of these 16 cytokines achieves equivalent performance on the validation data sets. Our findings demonstrate that a sixteen-cytokine/chemokine panel as well as the top ten subset provides a highly sensitive, and specific method to identify MIS-C in patients infected with SARS-CoV-2 of all the major variants identified to date.