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Issues in the one-dimensional dynami...

Cain, John Wesley.

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Issues in the one-dimensional dynamics of a paced cardiac fiber.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Issues in the one-dimensional dynamics of a paced cardiac fiber./
Author:	Cain, John Wesley.
Description:	110 p.
Notes:	Source: Dissertation Abstracts International, Volume: 66-06, Section: B, page: 3159.
Contained By:	Dissertation Abstracts International66-06B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3179221
ISBN:	0542191822

Issues in the one-dimensional dynamics of a paced cardiac fiber.
Cain, John Wesley.

Issues in the one-dimensional dynamics of a paced cardiac fiber. - 110 p.

Source: Dissertation Abstracts International, Volume: 66-06, Section: B, page: 3159.

Thesis (Ph.D.)--Duke University, 2005.

Consider a typical experimental protocol in which a one-dimensional fiber of cardiac tissue is periodically stimulated, or paced, resulting in a train of propagating action potentials. There is evidence that a sudden change in the pacing period, say from Bold to B new, can initiate abnormal cardiac rhythms. In this dissertation, we analyze how the fiber responds to such a change in a regime without arrhythmias.

ISBN: 0542191822Subjects--Topical Terms:

515831
Mathematics.

Issues in the one-dimensional dynamics of a paced cardiac fiber.
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100 1 $a Cain, John Wesley. $3 1908824
245 1 0 $a Issues in the one-dimensional dynamics of a paced cardiac fiber.
300 $a 110 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-06, Section: B, page: 3159.
500 $a Supervisor: David G. Schaeffer.
502 $a Thesis (Ph.D.)--Duke University, 2005.
520 $a Consider a typical experimental protocol in which a one-dimensional fiber of cardiac tissue is periodically stimulated, or paced, resulting in a train of propagating action potentials. There is evidence that a sudden change in the pacing period, say from Bold to B new, can initiate abnormal cardiac rhythms. In this dissertation, we analyze how the fiber responds to such a change in a regime without arrhythmias.
520 $a More quantitatively, suppose that a fiber of length L is paced at x = 0, where the length variable x denotes the distance from the pacing site. Changing the pacing period from Bold to Bnew introduces spatial variation in action potential duration (APD). Provided that B new is sufficiently large, long-term pacing with the new period leads to a steady-state response in which APD is constant, say A*, along the entire fiber. The convergence to steady-state can be monitored by measuring An(x), the APD following the nth stimulus applied with period Bnew. Mathematically, our problem can be formulated as follows: Givenanyh >0,determineN=N h,Lsuch that Anx -A*<h, ∀x∈0,L, ∀n>N.
520 $a To address this problem, we derive an infinite sequence of linear integral equations from a standard kinematic model of fiber dynamics. These integral equations can be solved exactly to yield approximations of the functions An(x) in terms of generalized Laguerre polynomials. We then estimate N using an asymptotic approximation for generalized Laguerre polynomials. We find that, for lengths L characteristic of cardiac tissue, it is often the case that N exhibits no dependence on L. In particular, there is a critical fiber length L* such that, if L < L*, the convergence to steady-state is slowest at the x = 0 boundary. Moreover, we shall see that L* → infinity as the slope of the restitution curve increases to 1.
590 $a School code: 0066.
650 4 $a Mathematics. $3 515831
650 4 $a Biology, Animal Physiology. $3 1017835
650 4 $a Engineering, Biomedical. $3 1017684
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710 2 0 $a Duke University. $3 569686
773 0 $t Dissertation Abstracts International $g 66-06B.
790 1 0 $a Schaeffer, David G., $e advisor
790 $a 0066
791 $a Ph.D.
792 $a 2005
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