Frank B. Sachse's Computational Cardiology: Modeling of Anatomy, PDF

By Frank B. Sachse

ISBN-10: 0976654504

ISBN-13: 9780976654506

This e-book is dedicated to computer-based modeling in cardiology, via taking an academic perspective, and via summarizing wisdom from numerous, typically thought of delimited parts of cardiac examine in a constant way.

First, the rules and numerical thoughts from arithmetic are supplied, with a selected concentrate on the finite aspect and finite adjustments equipment. Then, the speculation of electrical fields and continuum mechanics is brought with recognize to numerical calculations in anisotropic organic media. as well as the presentation of electronic photograph processing concepts, the next chapters care for specific elements of cardiac modeling: cardiac anatomy, cardiac electro body structure, cardiac mechanics, modeling of cardiac electro mechanics.

This ebook used to be written for researchers in modeling and cardiology, for medical cardiologists, and for complicated students.

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Extra info for Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics

Sample text

Hereby, four node variables specify the solution function u. The cubic approach leads to the shape-functions (Fig. 7 c): 1 H0 (x) = − (x − 1)(3x − 2)(3x − 1) 2 9 H1 (x) = (x − 1)x(3x − 2) 2 9 H2 (x) = − (x − 1)x(3x − 1) 2 1 H3 (x) = x(3x − 2)(3x − 1) 2 Alternatively, an element can be defined with two node points, where at each point a node variable fixes the value of the function u and a secondary node variable defines the derivative of the function u: H0 (x) = (1 − x)2 (1 + 2x) H1 (x) = x(1 − x)2 H2 (x) = x2 (3 − 2x) H3 (x) = −x2 (1 − x) The usage of this element type is recommended if the continuity of the first derivative at the node points is required.

The derivatives in a two-dimensional domain Ω can be derived straightforwardly from the one-dimensional derivatives. In a rectangular, equidistant mesh, the first order derivatives at the node point xi,j are approximated by: ∂u ui+1,j − ui−1,j (xi,j ) ≈ ∂x1 2∆x1 ∂u ui,j+1 − ui,j−1 (xi,j ) ≈ ∂x2 2∆x2 with the distance between the node points ∆x1 and ∆x2 in x1 and x2 direction, respectively. The node variables ui+1,j , ui−1,j , ui,j+1 and ui,j−1 correspond to the node points xi+1,j , xi−1,j , xi,j+1 and xi,j−1, respectively (Fig.

With direct methods, to deter(0) (0) mine the coarse correction v h−1 . The correction v h−1 is transferred to the fine discretized domain by a prolongation operator resulting in the correction (0) v h . Each of the following operators represented by the matrices P2×2×2 and P3×3×3 can be used to perform the transfer, which can be understood as interpolation starting from a coarse domain into a fine domain. 125 The expense of a prolongation operator is determined by type and sparcity of (0) the transfer matrix.

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Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics by Frank B. Sachse


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