Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

In vitro basal cytotoxicity assay applied to estimate acute oral systemic toxicity of grandisin and its major metabolite

Preclinical investigations can start with preliminary in vitro studies before using animal models. Following this approach, the number of animals used in preclinical acute toxicity testing can be reduced. In this study, we employed an in-house validated in vitro cytotoxicity test based on the Spielmann approach for toxicity evaluation of the lignan grandisin, a candidate anticancer agent, and its major metabolite. the 4-O-demethylgrandisin, by neutral red uptake (NRU) assay, on mouse fibroblasts Balb/c 3T3 cell line. Using different concentrations of grandisin and its major metabolite (2.31; 1.16; 0.58; 0.29; 0.14; 0.07; 0.04; 0.002 mu M) in Balb/c 3T3-A31 NRU cytotoxicity assay, after incubation for 48 h, we obtained IC(50) values for grandisin and its metabolite of 0.078 and 0.043 mu M, respectively. The computed LD(50) of grandisin and 4-O-demethylgrandisin were 617.72 and 429.95 mg/kg, respectively. Both were classified under the Globally Harmonized System as category 4. Since pharmacological and toxicological data are crucial in the developmental stages of drug discovery, using an in vitro assay we demonstrated that grandisin and its metabolite exhibit distinct toxicity profiles. Furthermore, results presented in this work can contribute to reduce the number of animals required in subsequent pharmacological/toxicological studies. (C) 2010 Elsevier GmbH. All rights reserved.