Mechanical Properties of Abnormal Human Aortic and Mitral Valves

Paranjothi, K.; Saravanan, U.; Krishnakumar, R.; Balakrishnan, K.R.

doi:10.1007/978-1-4614-0219-0_8

Cited by 2 publications

(3 citation statements)

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“…sup (18) we have to decompose the vector u into the basis formed by the vectors {y,-aj^.^j. This is a potentially dangerous situation, since the basis is, in general, not orthonormal and, consequently, the magnitude of the projected vectors can be very large (see Theorem 3 (Norm of oblique projection in R"j.…”

Section: \Lf(a)-df(a)\=mentioning

confidence: 99%

“…In many cases, such as inflation tests on arteries,^ deformations of a beating heart, and uniaxial or biaxial deformations of a slab of inhomogeneous tissue, like those that comprise heart valves (see Ref. [18]), the underlying form of the inhomogeneous deformation field is not known. With some exceptions [5,16,[19][20][21], invariably, a homogeneous deformation (linear deformation field) is assumed for a small subpart of the body and the corresponding principal stretch/strain invariants are computed.…”

Section: Introductionmentioning

confidence: 99%

“…Reports of such determination of the deformation field, especially for soft tissues, abound (see, for example, Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). In many cases, such as inflation tests on arteries,^ deformations of a beating heart, and uniaxial or biaxial deformations of a slab of inhomogeneous tissue, like those that comprise heart valves (see Ref.…”

Section: Introductionmentioning

confidence: 99%

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Fidelity of the Estimation of the Deformation Gradient From Data Deduced From the Motion of Markers Placed on a Body That is Subject to an Inhomogeneous Deformation Field

Průša

Rajagopal

Saravanan

2013

Journal of Biomechanical Engineering

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Practically all experimental measurements related to the response of nonlinear bodies that are made within a purely mechanical context are concerned with inhomogeneous deformations, though, in many experiments, much effort is taken to engender homogeneous deformation fields. However, in experiments that are carried out in vivo, one cannot control the nature of the deformation. The quantity of interest is the deformation gradient and/or its invariants. The deformation gradient is estimated by tracking positions of a finite number of markers placed in the body. Any experimental data-reduction procedure based on tracking a finite number of markers will, for a general inhomogeneous deformation, introduce an error in the determination of the deformation gradient, even in the idealized case, when the positions of the markers are measured with no error. In our study, we are interested in a quantitative description of the difference between the true gradient and its estimate obtained by tracking the markers, that is, in the quantitative description of the induced error due to the data reduction. We derive a rigorous upper bound on the error, and we discuss what factors influence the error bound and the actual error itself. Finally, we illustrate the results by studying a practically interesting model problem. We show that different choices of the tracked markers can lead to substantially different estimates of the deformation gradient and its invariants. It is alarming that even qualitative features of the material under consideration, such as the incompressibility of the body, can be evaluated differently with different choices of the tracked markers. We also demonstrate that the derived error estimate can be used as a tool for choosing the appropriate marker set that leads to the deformation gradient estimate with the least guaranteed error.

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Section: \Lf(a)-df(a)\=mentioning

confidence: 99%