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.

Systemic delivery of adult stem cells improves cardiac function in spontaneously hypertensive rats

Heart regeneration after myocardial infarction (MI) can occur after cell therapy, but the mechanisms, cell types and delivery methods responsible for this improvement are still under investigation. In the present study, we evaluated the impact of systemic delivery of bone marrow cells (BMC) and cultivated mesenchymal stem cells (MSC) on cardiac morphology, function and mortality in spontaneously hypertensive rats (SHR) submitted to coronary occlusion. Female syngeneic adult SHR, submitted or not (control group; C) to MI, were treated with intravenous injection of MSC (MI + MSC) or BMC (MI + BM) from male rats and evaluated after 1, 15 and 30 days by echocardiography. Systolic blood pressure (SBP), functional capacity, histology, mortality rate and polymerase chain reaction for the Y chromosome were also analysed. Myocardial infarction induced a decrease in SBP and BMC, but not MSC, prevented this decrease. An improvement in functional capacity and ejection fraction (38 +/- 4, 39 +/- 3 and 58 +/- 2% for MI, MI + MSC and MI + BM, respectively; P < 0.05), as well as a reduction of the left ventricle infarcted area, were observed in rats from the MI + BM group compared with the other three groups. Treated animals had a significantly reduced lesion tissue score. The mortality rate in the C, MI + BM, MI + MSC and MI groups was 0, 0, 16.7 and 44.4%, respectively (P < 0.05 for the MI + MSC and MI groups compared with the C and MI + BM groups). The results of the present study suggest that systemic administration of BMC can improve left ventricular function, functional capacity and, consequently, reduce mortality in an animal model of MI associated with hypertension. We speculate that the cells transiently home to the myocardium, releasing paracrine factors that recruit host cells to repair the lesion.

Neuromuscular electrical stimulation improves GLUT-4 and morphological characteristics of skeletal muscle in rats with heart failure

Aim: Changes in skeletal muscle morphology and metabolism are associated with limited functional capacity in heart failure, which can be attenuated by neuromuscular electrical stimulation (ES). The purpose of the present study was to analyse the effects of ES upon GLUT-4 protein content, fibre structure and vessel density of the skeletal muscle in a rat model of HF subsequent to myocardial infarction. Methods: Forty-four male Wistar rats were assigned to one of four groups: sham (S), sham submitted to ES (S+ES), heart failure (HF) and heart failure submitted to ES (HF+ES). The rats in the ES groups were submitted to ES of the left leg during 20 days (2.5 kHz, once a day, 30 min, duty cycle 50%- 15 s contraction/15 s rest). After this period, the left tibialis anterior muscle was collected from all the rats for analysis. Results: HF+ES rats showed lower values of lung congestion when compared with HF rats (P = 0.0001). Although muscle weight was lower in HF rats than in the S group, thus indicating hypotrophy, 20 days of ES led to their recovery (P < 0.0001). In both groups submitted to ES, there was an increase in muscle vessel density (P < 0.04). Additionally, heart failure determined a 49% reduction in GLUT-4 protein content (P < 0.03), which was recovered by ES (P < 0.01). Conclusion: In heart failure, ES improves morphological changes and raises GLUT-4 content in skeletal muscle.