Discovery of transport and reaction properties in distributed systems

Abstract

in Wiley InterScience (www.interscience.wiley.com).In distributed systems, transport phenomena coupled with chemical or metabolic reactions are functions of space. A computational method is outlined to acquire unknown system properties in distributed systems by problem inversion. Physical and chemical properties are estimated simultaneously. The finite-volume discretization method formulated in generalized curvilinear coordinates applied to inversion problem of arbitrarily complex geometries. The direct solution approach of the reacting transport problem through inexpensive acquisition of sensitivity information is presented. An inexact trust region method improves the convergence rate of the large-scale transport and kinetic inversion problem (TKIP). The case studies demonstrate a novel computational approach for quantifying unknown transport properties, as well as reaction or metabolic constants. Solutions to technological challenges is presented in computational fluid mechanics and biotransport using mathematical programming techniques for inversion of distributed systems.

Cerebral Microcirculation and Oxygen Tension in the Human Secondary Cortex

“…(1) which we implemented with non-linear constrained optimization algorithms developed by our group. 69,79,80 The resulting network is an acyclic binary graph composed of cylindrical elements, where N is the number of segments belonging to the tree.…”

Computational methods for predicting drug transport in anisotropic and heterogeneous brain tissue

“…(4-6) into a discrete set of nonlinear algebraic equations. The set of discretized transport equations along with the proper boundary conditions-given in Appendix B-can be solved directly with inexact Newton-Krylov subspace iteration methods (Zhang et al, 2007). Our simulation results were validated with commercial CFD software (Fluent, Ansys Inc.).…”

“…Diffusion coefficients for certain trophic factors and therapeutic proteins have been determined via rigorous experimental studies (Nicholson, 2001;Saltzman and Radomsky, 1991;Saltzman et al, 1994;Stroh et al, 2003;Sykova et al, 1994;Tao and Nicholson, 1996;Thorne et al, 2004). Unknown transport and kinetic properties can also be determined by problem inversion of in-vivo drug distribution data Zhang et al, 2007). Finally, property estimation techniques such as the Polson semi-empirical equation provide initial guesses for diffusivity as a function of their molecular weights (Geankpolis, 2003;Polson, 1950).…”

“…We also determined the hydraulic conductivity in rat tissue with inversion techniques to find values in the order of, K e ¼ 15 Â 10 À12 m 4 /N/s (Zhang et al, 2007).…”

Current status of intratumoral therapy for glioblastoma

“…millimeter sized) bubbles may redirect flow away from the catheter tip in unpredictable ways. Thus, optimization of devices and of various protocols constitute an extremely important part of improving the efficacy of CED [29][30][31][32]. Future CED efforts will benefit from the expanded use of reliable computer modeling, and real-time monitoring of catheter placement and the infusion process [33,34].…”