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Journal articles on the topic 'Stabilization of PDEs'

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Published: 14 September 2024

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1

Mokra, Daniela, and Juraj Mokry. "Phosphodiesterase Inhibitors in Acute Lung Injury: What Are the Perspectives?" International Journal of Molecular Sciences 22, no. 4 (February 16, 2021): 1929. http://dx.doi.org/10.3390/ijms22041929.

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Despite progress in understanding the pathophysiology of acute lung damage, currently approved treatment possibilities are limited to lung-protective ventilation, prone positioning, and supportive interventions. Various pharmacological approaches have also been tested, with neuromuscular blockers and corticosteroids considered as the most promising. However, inhibitors of phosphodiesterases (PDEs) also exert a broad spectrum of favorable effects potentially beneficial in acute lung damage. This article reviews pharmacological action and therapeutical potential of nonselective and selective PDE inhibitors and summarizes the results from available studies focused on the use of PDE inhibitors in animal models and clinical studies, including their adverse effects. The data suggest that xanthines as representatives of nonselective PDE inhibitors may reduce acute lung damage, and decrease mortality and length of hospital stay. Various (selective) PDE3, PDE4, and PDE5 inhibitors have also demonstrated stabilization of the pulmonary epithelial–endothelial barrier and reduction the sepsis- and inflammation-increased microvascular permeability, and suppression of the production of inflammatory mediators, which finally resulted in improved oxygenation and ventilatory parameters. However, the current lack of sufficient clinical evidence limits their recommendation for a broader use. A separate chapter focuses on involvement of cyclic adenosine monophosphate (cAMP) and PDE-related changes in its metabolism in association with coronavirus disease 2019 (COVID-19). The chapter illuminates perspectives of the use of PDE inhibitors as an add-on treatment based on actual experimental and clinical trials with preliminary data suggesting their potential benefit.

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2

Bernard, Pauline, and Miroslav Krstic. "Adaptive output-feedback stabilization of non-local hyperbolic PDEs." Automatica 50, no. 10 (October 2014): 2692–99. http://dx.doi.org/10.1016/j.automatica.2014.09.001.

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3

Li, Jian, and Yungang Liu. "Adaptive stabilization for ODE systems coupled with parabolic PDES." Journal of Systems Science and Complexity 29, no. 4 (May 27, 2016): 959–77. http://dx.doi.org/10.1007/s11424-016-5094-4.

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4

Bernard, Pauline, and Miroslav Krstic. "Adaptive Output-Feedback Stabilization of Non-Local Hyperbolic PDEs." IFAC Proceedings Volumes 47, no. 3 (2014): 7755–60. http://dx.doi.org/10.3182/20140824-6-za-1003.00108.

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5

Lhachemi, Hugo, and Christophe Prieur. "Global Output Feedback Stabilization of Semilinear Reaction-Diffusion PDEs." IFAC-PapersOnLine 55, no. 26 (2022): 53–58. http://dx.doi.org/10.1016/j.ifacol.2022.10.376.

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6

Krstic, Miroslav. "Systematization of approaches to adaptive boundary stabilization of PDEs." International Journal of Robust and Nonlinear Control 16, no. 16 (2006): 801–18. http://dx.doi.org/10.1002/rnc.1098.

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7

Yıldız, Hüseyin Alpaslan, and Leyla Gören-Sümer. "Stabilization of a class of underactuated Euler Lagrange system using an approximate model." Transactions of the Institute of Measurement and Control 44, no. 8 (December 7, 2021): 1569–78. http://dx.doi.org/10.1177/01423312211058556.

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The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the underactuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear and nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of underactuated EL systems. To develop this method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. Hence, the assignable potential energy function and the controlled inertia matrix both are constructed as a common solution of these PDEs. Subsequently, the gyroscopic and dissipative forces are determined as the solution for kinetic energy matching condition. Conclusively, the control rule is constructed by adding energy shaping rule and additional dissipation injection to provide asymptotic stability. The stability analysis of the closed-loop system which used the control rule derived with the proposed method is also provided. To demonstrate the success of the proposed method, the stability problem of the inverted pendulum on a cart is considered.

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Auriol, Jean, and Florent Di Meglio. "Two-Sided Boundary Stabilization of Heterodirectional Linear Coupled Hyperbolic PDEs." IEEE Transactions on Automatic Control 63, no. 8 (August 2018): 2421–36. http://dx.doi.org/10.1109/tac.2017.2763320.

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9

Elharfi, Abdelhadi. "Exponential stabilization of a class of 1-D hyperbolic PDEs." Journal of Evolution Equations 16, no. 3 (February 3, 2016): 665–79. http://dx.doi.org/10.1007/s00028-015-0317-z.

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10

Fornberg, Bengt, and Erik Lehto. "Stabilization of RBF-generated finite difference methods for convective PDEs." Journal of Computational Physics 230, no. 6 (March 2011): 2270–85. http://dx.doi.org/10.1016/j.jcp.2010.12.014.

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11

Lhachemi, Hugo, and Robert Shorten. "Boundary output feedback stabilization of state delayed reaction–diffusion PDEs." Automatica 156 (October 2023): 111188. http://dx.doi.org/10.1016/j.automatica.2023.111188.

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12

Auriol, Jean, and Florent Di Meglio. "Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs." Automatica 115 (May 2020): 108896. http://dx.doi.org/10.1016/j.automatica.2020.108896.

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13

Phan, Tuấn Đình, and Ha Ngoc Hoang. "NONLINEAR CONTROL OF TEMPERATURE PROFILE OF UNSTABLE HEAT CONDUCTION SYSTEMS: A PORT HAMILTONIAN APPROACH." Journal of Computer Science and Cybernetics 32, no. 1 (April 8, 2016): 61–74. http://dx.doi.org/10.15625/1813-9663/32/1/6401.

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This paper focuses on boundary control of distributed parameter systems (also called infinite dimensional systems). More precisely, a passivity based approach for the stabilization of temperature profile inside a well-insulated bar with heat conduction in a one-dimensional described by parabolic partial differential equations (PDEs) is developed. This approach is motivated by an appropriate model reduction schema using the finite difference approximation method. On this basis, it allows to discretize and then, write the original parabolic PDEs into a Port Hamiltonian (PH) representation. From this, the boundary control input is therefore synthesized using passive tools to stabilize the temperature at a desired reference profile asymptotically. The infinite dimensional nature of the original distributed parameter system in the PH framework is also discussed. Numerical simulations illustrate the application of the developments.

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14

Cristofaro, A., and F. Ferrante. "Boundary stabilization of systems of high order PDEs arising from flexible robotics." IFAC-PapersOnLine 53, no. 2 (2020): 7807–12. http://dx.doi.org/10.1016/j.ifacol.2020.12.1876.

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15

Wang, Jun-Min, Han-Wen Zhang, and Xiu-Fang Yu. "Input-to-state stabilization of coupled parabolic PDEs subject to external disturbances." IMA Journal of Mathematical Control and Information 39, no. 1 (December 31, 2021): 185–218. http://dx.doi.org/10.1093/imamci/dnab040.

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Abstract In this paper, we are concerned with the input-to-state stabilization of coupled parabolic partial differential equations, which is suffering the disturbances in all channels. By using the sliding mode control integrated with the backstepping approach, we design two boundary feedback controllers to reject the matched boundary disturbances, stabilize the whole coupled system in the absence of unmatched disturbances and achieve the input-to-state stability property of the closed-loop system with respect to the unmatched disturbances. We show the existence of the generalized solutions of the closed-loop system in the Hilbert energy space. Some numerical simulations are presented to illustrate the effectiveness of the proposed controllers.

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16

Zhang, Jin, Wen Kang, Emilia Fridman, and Alexandre Seuret. "Delayed stabilization of parabolic PDEs via augmented Lyapunov functionals and Legendre polynomials." Systems & Control Letters 156 (October 2021): 105003. http://dx.doi.org/10.1016/j.sysconle.2021.105003.

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17

Chen, Juan, Aleksei Tepljakov, Eduard Petlenkov, YangQuan Chen, and Bo Zhuang. "Stabilization and Stability Robustness of Coupled Non-Constant Parameter Time Fractional PDEs." IEEE Access 7 (2019): 163969–80. http://dx.doi.org/10.1109/access.2019.2951058.

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18

Kang, Wen, Emilia Fridman, and Chuan-Xin Liu. "Stabilization by switching of parabolic PDEs with spatially scheduled actuators and sensors." Automatica 147 (January 2023): 110668. http://dx.doi.org/10.1016/j.automatica.2022.110668.

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19

Lhachemi, Hugo, and Christophe Prieur. "Output feedback stabilization of reaction–diffusion PDEs with a non-collocated boundary condition." Systems & Control Letters 164 (June 2022): 105238. http://dx.doi.org/10.1016/j.sysconle.2022.105238.

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20

Vazquez, Rafael, and Miroslav Krstic. "Explicit integral operator feedback for local stabilization of nonlinear thermal convection loop PDEs." Systems & Control Letters 55, no. 8 (August 2006): 624–32. http://dx.doi.org/10.1016/j.sysconle.2005.09.019.

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21

Xu, Zaihua, and Yungang Liu. "Adaptive boundary stabilization for first-order hyperbolic PDEs with unknown spatially varying parameter." International Journal of Robust and Nonlinear Control 26, no. 3 (March 13, 2015): 613–28. http://dx.doi.org/10.1002/rnc.3331.

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22

Zhang, Jing, and Jie Qi. "Robust stabilization of 2 × 2 first-order hyperbolic PDEs with uncertain input delay." Automatica 157 (November 2023): 111235. http://dx.doi.org/10.1016/j.automatica.2023.111235.

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23

Kitsos, Constantinos, Rami Katz, and Emilia Fridman. "Internal stabilization of three interconnected semilinear reaction-diffusion PDEs with one actuated state." IFAC-PapersOnLine 56, no. 2 (2023): 8934–39. http://dx.doi.org/10.1016/j.ifacol.2023.10.101.

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24

Yu, Xin, Chao Xu, Huacheng Jiang, Arthi Ganesan, and Guojie Zheng. "Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/643640.

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This paper deals with the stabilization problem of first-order hyperbolic partial differential equations (PDEs) with spatial-temporal actuation over the full physical domains. We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differential equation (ODE). A Volterra integral transformation is used to convert the original system into a simple target system using the backstepping-like procedure. Unlike the classical backstepping techniques for boundary control problems of PDEs, the internal actuation can not eliminate the residual term that causes the instability of the open-loop system. Thus, an additional differential transformation is introduced to transfer the input from the interior of the domain onto the boundary. Then, a feedback control law is designed using the classic backstepping technique which can stabilize the first-order hyperbolic PDE system in a finite time, which can be proved by using the semigroup arguments. The effectiveness of the design is illustrated with some numerical simulations.

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25

Kang, Wen, Shan Li, and Da-Wei Ding. "Input-to-State Stabilization of Uncertain Parabolic PDEs Using an Observer-Based Fuzzy Control." IEEE Access 7 (2019): 3581–91. http://dx.doi.org/10.1109/access.2018.2889650.

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26

Lehrenfeld, Christoph, and Maxim Olshanskii. "An Eulerian finite element method for PDEs in time-dependent domains." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 2 (March 2019): 585–614. http://dx.doi.org/10.1051/m2an/2018068.

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The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in a triangulated computational domain and can overlap the time-independent background mesh in an arbitrary way. The numerical method is based on finite difference discretizations of time derivatives and a standard geometrically unfitted finite element method with an additional stabilization term in the spatial domain. The performance and analysis of the method rely on the fundamental extension result in Sobolev spaces for functions defined on bounded domains. This paper includes a complete stability and error analysis, which accounts for discretization errors resulting from finite difference and finite element approximations as well as for geometric errors coming from a possible approximate recovery of the physical domain. Several numerical examples illustrate the theory and demonstrate the practical efficiency of the method.

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27

Chehab, Jean-Paul. "Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs." Discrete & Continuous Dynamical Systems - S 14, no. 8 (2021): 2693. http://dx.doi.org/10.3934/dcdss.2021002.

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28

Anfinsen, Henrik, and Ole Morten Aamo. "Adaptive Output Feedback Stabilization of $n + m$ Coupled Linear Hyperbolic PDEs with Uncertain Boundary Conditions." SIAM Journal on Control and Optimization 55, no. 6 (January 2017): 3928–46. http://dx.doi.org/10.1137/16m1099662.

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29

Auriol, Jean, and Florent Di Meglio. "Corrigendum to “Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs” [Automatica 115]." Automatica 119 (September 2020): 109107. http://dx.doi.org/10.1016/j.automatica.2020.109107.

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30

Su, Lingling, Stephen Chen, Jun-Min Wang, and Miroslav Krstic. "Stabilization of a 2 × 2 system of hyperbolic PDEs with recirculation in the unactuated channel." Automatica 120 (October 2020): 109147. http://dx.doi.org/10.1016/j.automatica.2020.109147.

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31

Srivastava, Neeraj. "Optimization of Convergence of Mixed Finite Element Approximations Analysis." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9, no. 2 (December 30, 2018): 692–702. http://dx.doi.org/10.17762/turcomat.v9i2.13871.

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The numerical approximation of partial differential equations (PDEs) plays a vital role in many scientific and engineering applications. Mixed finite element methods have emerged as powerful techniques for solving a wide range of PDEs due to their ability to handle problems with mixed variables, such as fluid flow and elasticity. However, ensuring the convergence of mixed finite element approximations remains a challenging task. It presents a comprehensive analysis of the optimization strategies employed to enhance the convergence of mixed finite element approximations. We investigate the key factors that impact the convergence behaviour of these methods and propose various techniques to mitigate convergence issues. we discuss the importance of appropriate discretization strategies for mixed finite element approximations. We analyze the impact of element types, mesh refinement, and stabilization techniques on the convergence rates. By examining the properties of the underlying mixed variational formulations, we identify the optimal discretization choices that lead to improved convergence behaviour. We delve into the analysis of numerical stability and consistency in the context of mixed finite element methods. We explore the role of stabilization techniques, such as bubble functions and penalty terms, in mitigating instabilities and achieving optimal convergence rates. We investigate the effect of different stabilization parameters and establish guidelines for their selection to ensure both stability and convergence. We address the issue of error estimation and adaptivity in mixed finite element approximations. We review error indicators and adaptive mesh refinement strategies that enable the refinement of regions with high solution gradients, thus enhancing the convergence rates. We discuss the interplay between error estimation and adaptive refinement and present numerical examples illustrating their effectiveness. We highlight recent advancements in optimization algorithms specifically tailored for enhancing convergence in mixed finite element approximations. We explore strategies like multigrid methods, preconditioning techniques, and domain decomposition methods, which accelerate the convergence rates and enable the solution of large-scale problems. This paper provides a comprehensive analysis of the optimization of convergence for mixed finite element approximations. It serves as a valuable resource for researchers and practitioners seeking to improve the efficiency and accuracy of numerical solutions obtained through mixed finite element methods.

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32

Dong, Zhaonan, and Alexandre Ern. "Hybrid high-order method for singularly perturbed fourth-order problems on curved domains." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 6 (November 2021): 3091–114. http://dx.doi.org/10.1051/m2an/2021081.

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We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty technique to weakly enforce the boundary conditions and a scaling of the weighting parameter in the stabilization operator that compares the singular perturbation parameter to the square of the local mesh size. With these ideas in hand, we derive stability and optimal error estimates over the whole range of values for the singular perturbation parameter, including the zero value for which a second-order elliptic problem is recovered. Numerical experiments illustrate the theoretical analysis.

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33

Farahani, Hamed Shirinabadi, Heidar Ali Talebi, and Mohammad Baghermenhaj. "An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient." Archives of Control Sciences 27, no. 1 (March 1, 2017): 63–76. http://dx.doi.org/10.1515/acsc-2017-0004.

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Abstract The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.

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34

Bekiaris-Liberis, Nikolaos. "Hybrid boundary stabilization of linear first-order hyperbolic PDEs despite almost quantized measurements and control input." Systems & Control Letters 146 (December 2020): 104809. http://dx.doi.org/10.1016/j.sysconle.2020.104809.

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35

Karafyllis, Iasson, and Miroslav Krstic. "Small-Gain-Based Boundary Feedback Design for Global Exponential Stabilization of One-Dimensional Semilinear Parabolic PDEs." SIAM Journal on Control and Optimization 57, no. 3 (January 2019): 2016–36. http://dx.doi.org/10.1137/18m1213129.

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36

Di Meglio, Florent, Rafael Vazquez, and Miroslav Krstic. "Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input." IEEE Transactions on Automatic Control 58, no. 12 (December 2013): 3097–111. http://dx.doi.org/10.1109/tac.2013.2274723.

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37

DIAGNE, Mamadou, Peipei SHANG, and Zhiqiang WANG. "Feedback Stabilization of a Food Extrusion Process Described by 1D PDEs Defined on Coupled Time-Varying Spatial Domains." IFAC-PapersOnLine 48, no. 12 (2015): 51–56. http://dx.doi.org/10.1016/j.ifacol.2015.09.352.

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38

He, Cang, Fang Zhang, and Jinhui Jiang. "Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network." Shock and Vibration 2020 (November 16, 2020): 1–13. http://dx.doi.org/10.1155/2020/8261423.

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In this paper, nonlinear dynamical equations of the flexible manipulator with a lumped payload at the free end are derived from Hamilton's principle. The obtained model consists of both distributed parameters and lumped parameters, namely, partial differential equations (PDEs) governing the flexible motion of links and boundary conditions in the form of ordinary differential equations (ODEs). Considering the great nonlinear approximation ability of the radial basis function (RBF) neural network, we propose a combined control algorithm that includes two parts: one is a boundary controller to track the desired joint positions and suppress the vibration of flexible links; another is a RBF neural network designed to compensate for the parametric uncertainties. The iteration criterion of the RBF neural network weight matrix is derived from the extended Lyapunov function. Stabilization analysis is further carried out theoretically via LaSalle’s invariance principle. Finally, the results of the numerical simulation verify that the proposed control law can realize the asymptotic convergence of tracking error and suppression of the elastic vibration as well.

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39

Lhachemi, Hugo, Christophe Prieur, and Robert Shorten. "Robustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time- and spatially-varying input delays." Automatica 123 (January 2021): 109347. http://dx.doi.org/10.1016/j.automatica.2020.109347.

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40

Mavi, Anele, and Tiri Chinyoka. "Finite Volume Computational Analysis of the Heat Transfer Characteristic in a Double-Cylinder Counter-Flow Heat Exchanger with Viscoelastic Fluids." Defect and Diffusion Forum 424 (May 8, 2023): 19–43. http://dx.doi.org/10.4028/p-j482zy.

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This work presents a computational analysis of the heat-exchange characteristics in a double-cylinder (also known as a double-pipe) geometrical arrangement. The heat-exchange is from a hotter viscoelastic fluid flowing in the core (inner) cylinder to a cooler Newtonian fluid flowing in the shell (outer) annulus. For optimal heat-exchange characteristics, the core and shell fluid flow in opposite directions, the so-called counter-flow arrangement.The mathematical modelling of the given problem reduces to a system of nonlinear coupled Partial Differential Equations (PDEs). Specifically, the rheological behaviour of the core fluid is governed by the Giesekus viscoelastic constitutive model. The governing system of coupled nonlinear PDEs is intractable to analytic treatment and hence is solved numerically using Finite Volume Methods (FVM). The FVM numerical methodology is implemented via the open-source software package OpenFOAM. The numerical methods are stabilized, specifically to address numerical instabilities arising from the High Weissenberg Number Problem (HWNP), via a combination of the Discrete Elastic Viscous Stress Splitting (DEVSS) technique and the Log-Conformation Reformulation (LCR) methodology. The DEVSS and LCR stabilization techniques are integrated into the relevant viscoelastic fluid solvers. The novelties of the study center around the simulation and analysis of the optimal heat-exchange characteristics between the heated Giesekus fluid and the coolant Newtonian fluid within a double-pipe counter-flow arrangement. Existing studies in the literature have either focused exclusively on Newtonian fluids and/or on rectangular geometries. The existing OpenFOAM solvers have also largely focused on non-isothermal viscoelastic flows. The relevant OpenFOAM solvers are modified for the present purposes by incorporating the energy equation for viscoelastic fluid flow. The flow characteristics are presented qualitatively (graphically) via the fluid pressure, temperature, velocity, and the polymer-stress components as well as the related normal stress differences. The results illustrate the required decrease in the core fluid temperature in the longitudinal direction due to the cooling effects of the shell fluid, whose temperature predictably increases in the counter-flow direction.

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41

Guerrero-Sánchez, María-Eusebia, Omar Hernández-González, Rogelio Lozano, Carlos-D. García-Beltrán, Guillermo Valencia-Palomo, and Francisco-R. López-Estrada. "Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload." Mathematics 7, no. 11 (November 11, 2019): 1090. http://dx.doi.org/10.3390/math7111090.

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This paper presents the control of a quadrotor with a cable-suspended payload. The proposed control structure is a hierarchical scheme consisting of an energy-based control (EBC) to stabilize the vehicle translational dynamics and to attenuate the payload oscillation, together with a nonlinear state feedback controller based on an linear matrix inequality (LMI) to control the quadrotor rotational dynamics. The payload swing control is based on an energy approach and the passivity properties of the system’s translational dynamics. The main advantage of the proposed EBC strategy is that it does not require excessive computations and complex partial differential equations (PDEs) for implementing the control algorithm. We present a new methodology for using an LMI to synthesize the controller gains for Lipschitz nonlinear systems with larger Lipschitz constants than other classical techniques based on LMIs. This theoretical approach is applied to the quadrotor rotational dynamics. Stability proofs based on the Lyapunov theory for the controller design are presented. The designed control scheme allows for the stabilization of the system in all its states for the three-dimensional case. Numerical simulations demonstrating the effectiveness of the controller are provided.

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42

Kumari, Neeraj, Maya Ferrell, Carolina G. Garcia, and Cullen M. Taniguchi. "Abstract 1107: Exploring the hypoxia pathway for gastrointestinal radioprotection in human minigut model." Cancer Research 83, no. 7_Supplement (April 4, 2023): 1107. http://dx.doi.org/10.1158/1538-7445.am2023-1107.

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Abstract Introduction: When pancreatic cancer cannot be removed by surgery, radiation can be used to approximate a resection. Unfortunately, conventional radiation therapy cannot achieve ablative doses in the pancreas due to potential radiotoxicity to the nearby intestinal tissues. Thus, treatment-related gastrointestinal (GI) toxicity may be the most significant barrier to improving treatment responses for unresectable pancreatic cancer. There are no medications that can selectively protect the intestine from radiation damage, but we previously demonstrated that the genetic or pharmacologic inhibition of the EGLN prolyl hydroxylases protects murine intestines from radiation injury. To translate these findings to patients, we sought to test the EGLN inhibitor, FG-4592, and its mechanism of selective radioprotection in patient-derived intestinal organoids (also known as enteroids or mini-guts). Methods: The patient-derived enteroids (PDEs) were grown from duodenal tissue of non-oncologic patients, embedded in Matrigel, and cultured in media impregnated with essential growth factors. These PDEs have the capacity to recapitulate the full array of intestinal cells that are present in the crypt-villus axis. We first treated PDEs with FG-4592 then irradiation at 24 hours followed by RT-qPCR at 72 hrs post-exposure to gauge the effects of radiation on markers associated with intestinal stem cells (ISCs) and differentiated epithelial cells. Single cell RNA seq techniques were used to identify shifts in cellular populations FG-4592 and/or radiation treatment of human enteroids. Results: Irradiation produced a signature of enhanced Crypt Base Columnar (CBC) cells and +4 quiescent stem cells markers (Bmi1, Tert, Dclk1) suggesting these specialized cells awaken upon crypt damage and start to proliferate to restore the ISC pool. The +4 cell markers are further enhanced in FG-4592 treated irradiated group, suggesting EGLN inhibition leads to activation of these specialized cell population along with restoration of other intestinal cells like secretory progenitors and Paneth cells. Further, gene set enrichment analysis after FG-4592 treatment showed the activation of key pathways involved in proliferation, maintaining homeostasis, metabolism, and DNA repair that could lead to intestinal proliferation and recovery from radiation damage. Conclusion: Taken together, these preliminary data suggest that HIF stabilization by FG-4592 upregulates the normally quiescent +4 stem cells, a radioresistant stem population historically thought to become active upon radiation injury, along with activation of several other pathways required for normal proliferation and recovery from radiation injury. Our study justifies further exploration in clinical trials as a radioprotective or radio mitigative agent. Citation Format: Neeraj Kumari, Maya Ferrell, Carolina G. Garcia, Cullen M. Taniguchi. Exploring the hypoxia pathway for gastrointestinal radioprotection in human minigut model [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 1107.

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43

Dubljevic, Stevan. "Model predictive control of diffusion-reaction processes." Chemical Industry and Chemical Engineering Quarterly 11, no. 1 (2005): 10–18. http://dx.doi.org/10.2298/ciceq0501010d.

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Parabolic partial differential equations naturally arise as an adequate representation of a large class of spatially distributed systems, such as diffusion-reaction processes, where the interplay between diffusive and reaction forces introduces complexity in the characterization of the system, for the purpose of process parameter identification and subsequent control. In this work we introduce a model predictive control (MPC) framework for the control of input and state constrained parabolic partial differential equation (PDEs) systems. Model predictive control (MPC) is one of the most popular control formulations among chemical engineers, manly due to its ability to account for the actuator (input) constraints that inevitably exist due to finite actuator power and its ability to handle state constraints within an optimal control setting. In controller synthesis, the initially parabolic partial differential equation of the diffusion reaction type is transformed by the Galerkin method into a system of ordinary differential equations (ODEs) that capture the dominant dynamics of the PDE system. Systems obtained in such a way (ODEs) are used as the basis for the synthesis of the MPC controller that explicitly accounts for the input and state constraints. Namely, the modified MPC formulation includes a penalty term that is directly added to the objective function and through the appropriate structure of the controller state constraints accounts for the infinite dimensional nature of the state of the PDE system. The MPC controller design method is successively applied to control of the diffusion-reaction process described by linear parabolic PDE, by demonstrating stabilization of the non-dimensional temperature profile around a spatially uniform unstable steady-state under satisfaction of the input (actuator) constraints and allowable non-dimensional temperature (state) constraints.

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Priyanka, R., and S. Ramadevi. "A Hyperbolic PDE-ODE System with Delay-Robust Stabilization." International Journal of Trend in Scientific Research and Development Volume-2, Issue-5 (August 31, 2018): 1988–90. http://dx.doi.org/10.31142/ijtsrd17157.

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Chen, Jiyun, Brahmam Pujala, Ashu Gupta, Amantullah Ansaria, Farha Khana, Elbert Lee, and Sarvajit Chakravarty. "A novel orally bioavailable small molecular ENPP1 inhibitor (OC-1) for cancer immunotherapy." Journal of Clinical Oncology 41, no. 16_suppl (June 1, 2023): e15136-e15136. http://dx.doi.org/10.1200/jco.2023.41.16_suppl.e15136.

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e15136 Background: Ectonucleotide pyrophosphatase/phosphodiesterase I (ENPP1) is a type II transmembrane glycoprotein with nucleotide pyrophosphatase and phosphodiesterase enzymatic activities. Inhibiting ENPP1 activity has emerged as an attractive approach in cancer immunotherapy, based on two distinct mechanisms. One mechanism is the stabilization of cyclic GMP–AMP (2’3’-cGAMP), which binds to stimulator of IFN genes (STING) and functions as an endogenous second messenger to activate the innate immune system; the other is the lowering of adenosine concentrations in the tumor microenvironment. ENPP1 inhibitors have shown promising monotherapy activity and synergy with various targeted therapies in preclinical models. Methods: OC-1 was characterized, for activity and selectivity, in the following in vitro assays: a luminescence-based enzymatic assay; cell proliferation assays; selectivity assays against 15 phosphodiesterases (PDE) based on inhibition of enzymatic activity; and a cytokine release assay in human THP cells and mouse splenocytes looking at changes in IFN-β/CXCL10. Oral bioavailability of OC-1 in mice and rats was studied following oral gavage. Plasma exposures were quantified using standard LC/MS/MS methods. In vivo tumor growth inhibition (TGI) of OC-1 was evaluated in syngeneic mouse tumor models (CT26 and MC38), as monotherapy and in combination with an anti-PD1 antibody. OC-1 was dosed orally in all in-vivo models. Results: We have discovered a novel small molecule inhibitor of ENPP1, OC-1, with a Ki value less than 10 nM in an ENPP1 enzymatic assay. Increase in gene expression of IFN-β and CXCL10/IP10 was observed in OC-1-treated THP1 cells. No inhibition in cell proliferation in various cancer lines was seen up to the highest concentration tested (30 µM). OC-1 was also selective against 15 PDEs with IC50 > 30 µM. The mean oral bioavailability of OC-1 was 72% and 63% in mice and rats, respectively. OC-1 showed single agent activity (20 – 40% TGI) and combination activity of approximately 75% TGI when it was combined with an anti-PD-1 antibody in in vivo efficacy studies with no impact on body weight. Conclusions: In summary, OC-1 is an orally bioavailable ENPP1 inhibitor with promising anti-tumor activity in preclinical models. Its physicochemical properties make it a suitable candidate for clinical investigation.

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Cedervall, Peder, Ann Aulabaugh, Kieran F. Geoghegan, Thomas J. McLellan, and Jayvardhan Pandit. "Engineered stabilization and structural analysis of the autoinhibited conformation of PDE4." Proceedings of the National Academy of Sciences 112, no. 12 (March 9, 2015): E1414—E1422. http://dx.doi.org/10.1073/pnas.1419906112.

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Phosphodiesterase 4 (PDE4) is an essential contributor to intracellular signaling and an important drug target. The four members of this enzyme family (PDE4A to -D) are functional dimers in which each subunit contains two upstream conserved regions (UCR), UCR1 and -2, which precede the C-terminal catalytic domain. Alternative promoters, transcriptional start sites, and mRNA splicing lead to the existence of over 25 variants of PDE4, broadly classified as long, short, and supershort forms. We report the X-ray crystal structure of long form PDE4B containing UCR1, UCR2, and the catalytic domain, crystallized as a dimer in which a disulfide bond cross-links cysteines engineered into UCR2 and the catalytic domain. Biochemical and mass spectrometric analyses showed that the UCR2-catalytic domain interaction occurs in trans, and established that this interaction regulates the catalytic activity of PDE4. By elucidating the key structural determinants of dimerization, we show that only long forms of PDE4 can be regulated by this mechanism. The results also provide a structural basis for the long-standing observation of high- and low-affinity binding sites for the prototypic inhibitor rolipram.

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Temmesfeld-Wollbrück, Bettina, Bernhard Brell, Corinna zu Dohna, Martin Dorenberg, Andreas C. Hocke, Holger Martens, Jürgen Klar, Norbert Suttorp, and Stefan Hippenstiel. "Adrenomedullin reduces intestinal epithelial permeability in vivo and in vitro." American Journal of Physiology-Gastrointestinal and Liver Physiology 297, no. 1 (July 2009): G43—G51. http://dx.doi.org/10.1152/ajpgi.90532.2008.

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Leakage of the gut mucosal barrier in the critically ill patient may allow translocation of bacteria and their virulence factors, thereby perpetuating sepsis and inflammation. Present evidence suggests that adrenomedullin (AM) improves endothelial barrier function and stabilizes circulatory function in systemic inflammation. We tested the hypothesis that exogenously applied AM stabilizes gut epithelial barrier function. Infusion of Staphylococcus aureus α-toxin induced septic shock in rats. AM infusion in a therapeutic setting reduced translocation of labeled dextran from the gut into the systemic circulation in this model. AM also reduced α-toxin and hydrogen peroxide (H2O2)-related barrier disruption in Caco-2 cells in vitro and reduced H2O2-related rat colon barrier malfunction in Ussing chamber experiments. AM was shown to protect endothelial barrier function via cAMP elevation, but AM failed to induce cAMP accumulation in Caco-2 cells. cAMP is degraded via phosphodiesterases (PDE), and Caco-2 cells showed high activity of cAMP-degrading PDE3 and 4. However, AM failed to induce cAMP accumulation in Caco-2 cells even in the presence of sufficient PDE3/4 inhibition, whereas adenylyl cyclase activator forskolin induced strong cAMP elevation. Furthermore, PDE3/4 inhibition neither amplified AM-induced epithelial barrier stabilization nor affected AM cAMP-related rat colon short-circuit current, furthermore indicating that AM may act independently of cAMP in Caco-2 cells. Finally, experiments using chemical inhibitors indicated that PKC, phosphatidylinositide 3-kinase, p38, and ERK did not contribute to AM-related stabilization of barrier function in Caco-2 cells. In summary, during severe inflammation, elevated AM levels may substantially contribute to the stabilization of gut barrier function.

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Pecout, S., E. Baudin, A. Paoli, F. Maire, E. Terrebonne, E. Mitry, M. Pavel, P. Ruszniewski, G. Cadiot, and H. Brixi-Benmansour. "Efficacy and tolerance of chemotherapy with dacarbazine or temozolomide associated or not with 5-fluorouracil (5-FU) in endocrine carcinomas: A retrospective multicentric study from the Groupe des Tumeurs Endocrines (GTE)." Journal of Clinical Oncology 27, no. 15_suppl (May 20, 2009): e15523-e15523. http://dx.doi.org/10.1200/jco.2009.27.15_suppl.e15523.

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e15523 Background: Small studies have shown that therapy with dacarbazine and temozolomide give up to 34% tumoral response rates in endocrine carcinomas. The aim of this large retrospective multicentric study was to evaluate efficacy and tolerance of chemotherapy with dacarbazine or temozolomide associated or not with 5-FU in endocrine carcinomas. Methods: Patients were recruited in 6 French and 1 German centers. All patients with well (WDEC) or poorly-differentiated endocrine carcinoma (PDEC), whatever the primary, and who have been treated with dacarbazine or temozolomide associated or not with iv 5-FU or capecitabine, were included. Response rates were evaluated according to RECIST criteria by one of the investigator and toxicity according to National Cancer Institute Common criteria. Results: 86 patients were included : 36 women, median age 61.7 years (27.7 - 85.7), 67 WHO-PS 0–1. Primaries were : pancreas (n=34), digestive tract (n=23), thyroid (n=9), lung (n=6), other (n=6), unknown (n=8). 64 patients had WDEC and 11 PDEC (11 not determined). The number of previous systemic treatments (chemotherapy, chemoembolization, radionuclide therapy) was: 0 (n=16), 1 (n=25), 2 (n=25), 3 (n=14), 4 and more (n=6). Treatments received were : dacarbazine (n=3), temozolomide (n=19), dacarbazine + 5-FU (n=48), temozolomide + capecitabine (n=16). Evaluation was impossible in two patients. Tumoral response rates (partial and stabilization) were 61.2% in WDEC and 18.2% in PDEC. The best response rates in WDEC were : partial response (n=6; 9.7%), stabilization (n=32; 51.6%), progression (n=24; 38.7%) without significant differences between regimens and primary location. Response rates in WDEC were 88.9%, 71.4% and 64.7% in first, second and third line therapies, respectively. Median progression free survival in WDEC was 5.7 months (0.1–41.7). Grade 3–4 toxicities were hematologic (n=8), digestive (n=10), infection (n=3). Conclusions: Dacarbazine and temozolomide therapy showed high partial response and stabilization rates up to 3rd line therapy in well-differentiated endocrine carcinoma, with moderate toxicity. MGMT tumoral status is currently investigated. No significant financial relationships to disclose.

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de Oliveira, Ivan Pires, Caroline Honaiser Lescano, and Gilberto De Nucci. "In Silico Mapping of Essential Residues in the Catalytic Domain of PDE5 Responsible for Stabilization of Its Commercial Inhibitors." Scientia Pharmaceutica 87, no. 4 (November 1, 2019): 29. http://dx.doi.org/10.3390/scipharm87040029.

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Phosphodiesterase type 5 (PDE5) is an important enzyme associated with the hydrolysis of cyclic guanosine monophosphate (cGMP) to guanosine monophosphate (GMP). Due to the relevant role of second messenger cGMP as a mediator in many physiological processes, efforts have been converged to find a safe pharmacological approach, seeking a specific, selective and potent inhibitor of the PDE5 enzyme. There are five commercial drugs with potential for clinical use: tadalafil, sildenafil, avanafil, udenafil and vardenafil. Here, we applied molecular modeling to obtain different profiles of protein–ligand interactions by adopting distinct PDE5 structures, specifically PDBid:1XOZ and two extracted from molecular dynamics (MD) simulations. The results generated by molecular docking showed several possibilities for inhibitor interactions with the catalytic pocket. Tadalafil, sildenafil and vardenafil were clearly stabilized by Gln817 via a well-oriented hydrogen bond. Another set of different interactions, such as polar, hydrophobic, π-stacking, metal–ligand and electrostatic, were responsible for accommodating avanafil and udenafil. All of the ligands are discussed in detail with consideration of the distinct protein structures, and a profile of the probability of residue–ligand contact is suggested, with the most frequently observed being: Tyr612, His613, Ser661, Thr723, Asp724, Asp764, Leu765, Val782 and Phe786. The molecular interactions displayed herein confirm findings achieved by previous authors and also present new contacts. In addition, the discussion can help researchers obtain a molecular basis for planning new selective PDE5 inhibitors, as well as explain an inhibitor’s experimental assays by considering the specific interactions occurring at the catalytic site.

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Avalos, George. "The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics." Abstract and Applied Analysis 1, no. 2 (1996): 203–17. http://dx.doi.org/10.1155/s1085337596000103.

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We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE's which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domainΩ, coupled to a “parabolic–like” beam equation holding on∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity estimate for solutions of hyperbolic equations.

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