ELIZA

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26) Furthermore, our effective shear modulus is determined directly as a function of deformation, rather than as the slope of a fitted curve.

--- ABSTRACT ---

PMID:24071531 DOI:10.1093/imammb/dqt020

2015 Mathematical medicine and biology : a journal of the IMA

* The invalidity of the Laplace law for biological vessels and of estimating elastic modulus from total stress vs. strain: a new practical method.

- There are strong medical motivations to measure changes in material properties of tubular organs, in vivo and in vitro. The current approach estimates hoop stress from intraluminal pressure using the Laplace law and identifies 'elastic modulus' as the slope of a curve fitted hoop stress plotted against strain data. We show that this procedure is fundamentally flawed because muscle and other soft tissue are closely incompressible, so that the total stress includes a volume-preserving material-dependent hydrostatic response that invalidates the method. Furthermore, we show that the Laplace law incorrectly estimates total stress in biological vessels. However, the great need to estimate elastic modulus leads us to develop an alternative practical method, based on shear stress-strain, i.e. insensitive to nonelastic response from incompressibility, but that uses the same measurement data as the current (incorrect) method. The individual material parameters in the underlying (unknown) constitutive relation combine into an effective shear modulus that is a true measure of elastic response, unaffected by incompressibility and without reference to the Laplace law. Furthermore, our effective shear modulus is determined directly as a function of deformation, rather than as the slope of a fitted curve. We validate our method by comparing effective shear moduli against exact shear moduli for four theoretical materials with different degrees of nonlinearity and numbers of material parameters. To further demonstrate applicability, we reanalyse an in vivo study with our new method and show that it resolves an inconsistent change in modulus with the current method.

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(1)94 of	(10)7 with	(19)3 for	(28)2 leading
(2)74 null	(11)5 during	(20)3 has	(29)2 mutations
(3)53 and	(12)5 tests	(21)3 over	(30)2 on
(4)47 in	(13)5 that	(22)3 relationships	(31)2 or
(5)17 was	(14)4 among	(23)2 at	(32)2 physical
(6)12 as	(15)4 to	(24)2 but	(33)2 relationship
(7)12 is	(16)4 which	(25)2 can	(34)2 remains
(8)7 Index	(17)3 after	(26)2 could	(35)2 using
(9)7 were	(18)3 by	(27)2 grades

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--- WordNet output for function --- =>1.機能, 関数, 役割, 働き, 2.機能する, 作用する, 働く, 役目を果たす, 3.社交的会合, パーティー, 儀式 Overview of noun function The noun function has 7 senses (first 3 from tagged texts) 1. (43) function, mathematical function, single-valued function, map, mapping -- ((mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)) 2. (24) function, purpose, role, use -- (what something is used for; "the function of an auger is to bore holes"; "ballet is beautiful but what use is it?") 3. (7) function, office, part, role -- (the actions and activities assigned to or required or expected of a person or group; "the function of a teacher"; "the government must do its part"; "play its role") 4. function -- (a relation such that one thing is dependent on another; "height is a function of age"; "price is a function of supply and demand") 5. function -- (a formal or official social gathering or ceremony; "it was a black-tie function") 6. affair, occasion, social occasion, function, social function -- (a vaguely specified social event; "the party was quite an affair"; "an occasion arranged to honor the president"; "a seemingly endless round of social functions") 7. routine, subroutine, subprogram, procedure, function -- (a set sequence of steps, part of larger computer program) Overview of verb function The verb function has 3 senses (first 3 from tagged texts) 1. (9) function, work, operate, go, run -- (perform as expected when applied; "The washing machine won't go unless it's plugged in"; "Does this old car still run well?"; "This old radio doesn't work anymore") 2. (3) serve, function -- (serve a purpose, role, or function; "The tree stump serves as a table"; "The female students served as a control group"; "This table would serve very well"; "His freedom served him well"; "The table functions as a desk") 3. (1) officiate, function -- (perform duties attached to a particular office or place or function; "His wife officiated as his private secretary") --- WordNet end ---