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A global multiscale mathematical model for the human circulation with emphasis on the venous system
Author(s) -
Müller Lucas O.,
Toro Eleuterio F.
Publication year - 2014
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2622
Subject(s) - computer science , boundary value problem , human head , circulation (fluid dynamics) , mathematics , engineering , mathematical analysis , physics , mechanics , finite element method , structural engineering
SUMMARY We present a global, closed‐loop, multiscale mathematical model for the human circulation including the arterial system, the venous system, the heart, the pulmonary circulation and the microcirculation. A distinctive feature of our model is the detailed description of the venous system, particularly for intracranial and extracranial veins. Medium to large vessels are described by one‐dimensional hyperbolic systems while the rest of the components are described by zero‐dimensional models represented by differential‐algebraic equations. Robust, high‐order accurate numerical methodology is implemented for solving the hyperbolic equations, which are adopted from a recent reformulation that includes variable material properties. Because of the large intersubject variability of the venous system, we perform a patient‐specific characterization of major veins of the head and neck using MRI data. Computational results are carefully validated using published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient‐specific phase‐contrast MRI flow quantification data. A merit of our model is its global, closed‐loop character; the imposition of highly artificial boundary conditions is avoided. Applications in mind include a vast range of medical conditions. Of particular interest is the study of some neurodegenerative diseases, whose venous haemodynamic connection has recently been identified by medical researchers. Copyright © 2014 John Wiley & Sons, Ltd.