RESUMO
In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure-volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches.
RESUMO
Introduction: Chronic kidney disease of uncertain etiology (CKDu) is a leading cause of death of adults in Sri Lanka's dry region. Methods: We initiated the Kidney Progression Project (KiPP) to prospectively follow 292 persons with Chronic Kidney Disease Epidemiology Collaboration estimated glomerular filtration rate (eGFR) 20 to 60 ml/min per 1.73 m2 living in a CKDu endemic area. Using data from 3-year follow-up, we assessed kidney function decline (>30% from baseline eGFR), and the composite outcome of >30% eGFR decline, eGFR <15 ml/min or death, and explored the association of the 2 outcomes with baseline demographic, residential, and clinical parameters accounting for baseline eGFR. Results: Median eGFR at enrollment was 28 ml/min among 71 women; 30 ml/min among 221 men; 91% to 99% had trace or no proteinuria during follow-up. At enrollment, median serum sodium, uric acid, and potassium were 143 mmol/l, 6.3 mg/dl, 4.5 meq/l, respectively among women; and 143 mmol/l, 6.9 mg/dl, 4.3 meq/l among men. Mean slope of eGFR decline was -0.5 (SD 4.9) ml/min/yr. In exploratory analyses, men with greater years of education and those living in northern region of the study area experienced lower likelihood of disease progression (hazard ratios [HR] 0.87 [0.77-0.98] per additional year and 0.33 [0.12-0.89] for northern versus other subregions, respectively). There was a suggestion that men drinking well water had higher likelihood and men living further away from reservoirs had lower likelihood of >30% decline in eGFR (HR 2.07 [0.95-4.49] for drinking well water versus not, and HR 0.58 [0.32-1.05] per kilometer distance, respectively). Conclusions: The overall rate of kidney function decline was slow in this CKDu cohort, similar to other nonalbuminuric CKD, and event rates were similar among men and women. Further etiologic investigations could focus on specific residence locale and water use.
