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Flow perturbations in a mathematical...

Oldson, Darren Randall.

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Flow perturbations in a mathematical model of the tubuloglomerular feedback system.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Flow perturbations in a mathematical model of the tubuloglomerular feedback system./
Author:	Oldson, Darren Randall.
Description:	198 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3854.
Contained By:	Dissertation Abstracts International64-08B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3102250
ISBN:	0496498207

Flow perturbations in a mathematical model of the tubuloglomerular feedback system.
Oldson, Darren Randall.

Flow perturbations in a mathematical model of the tubuloglomerular feedback system. - 198 p.

Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3854.

Thesis (Ph.D.)--Duke University, 2003.

A previously-formulated mathematical model predicts that limit-cycle oscillations (LCO) in nephron flow are mediated by tubuloglomerular feedback (TGF) and that the LCO arise from a bifurcation that depends heavily on the feedback gain magnitude gamma and on its relationship to a theoretically determined critical value of gain, gammac (H. E. Layton, E. B. Pitman, L. C. Moore, Am. J. Physiol. 261: F904--F919, 1991). In this study that model is used to show how sustained perturbations in proximal tubule flow, which can be introduced by a common experimental maneuver, can initiate or terminate LCO by changing the values of gamma and gammac and thus changing the sign of gamma - gammac. This result may help explain experiments in which intratubular pressure oscillations were initiated by the sustained introduction or removal of fluid from the proximal tubule (P. P. Leyssac and L. Baumbach, Acta Physiol. Scand. 117: 415--419, 1983). In addition, this model predicts that, for a range of TGF sensitivities, sustained perturbations that initiate or terminate LCO can yield substantial and abrupt changes in both distal NaCl delivery and NaCl delivery feedback compensation, changes that may play an important role in the response to physiological challenge.

ISBN: 0496498207Subjects--Topical Terms:

515831
Mathematics.

Flow perturbations in a mathematical model of the tubuloglomerular feedback system.
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035 $a (UnM)AAI3102250
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100 1 $a Oldson, Darren Randall. $3 1932079
245 1 0 $a Flow perturbations in a mathematical model of the tubuloglomerular feedback system.
300 $a 198 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3854.
500 $a Supervisor: Harold E. Layton.
502 $a Thesis (Ph.D.)--Duke University, 2003.
520 $a A previously-formulated mathematical model predicts that limit-cycle oscillations (LCO) in nephron flow are mediated by tubuloglomerular feedback (TGF) and that the LCO arise from a bifurcation that depends heavily on the feedback gain magnitude gamma and on its relationship to a theoretically determined critical value of gain, gammac (H. E. Layton, E. B. Pitman, L. C. Moore, Am. J. Physiol. 261: F904--F919, 1991). In this study that model is used to show how sustained perturbations in proximal tubule flow, which can be introduced by a common experimental maneuver, can initiate or terminate LCO by changing the values of gamma and gammac and thus changing the sign of gamma - gammac. This result may help explain experiments in which intratubular pressure oscillations were initiated by the sustained introduction or removal of fluid from the proximal tubule (P. P. Leyssac and L. Baumbach, Acta Physiol. Scand. 117: 415--419, 1983). In addition, this model predicts that, for a range of TGF sensitivities, sustained perturbations that initiate or terminate LCO can yield substantial and abrupt changes in both distal NaCl delivery and NaCl delivery feedback compensation, changes that may play an important role in the response to physiological challenge.
520 $a This study also presents a rigorous analysis of the linear discrete-delay TGF model introduced by Layton et al. Existence of a unique solution is established by integrating along characteristics and applying the method of steps. Continuous dependence on the initial data (initial history) follows from Gronwall's lemma, if one interprets the linear model as an abstract delay differential equation (ADDS) on L1[0, 1]. The mild solution of the ADDE yields a strongly continuous semigroup on the history space C([-tau, 0]; L 1[0,1]). The mild solution semigroup is eventually compact, so the semigroup exhibits spectrum-determined growth: the stability of the solution w &equiv; 0 of the linear TGF model is determined by the spectral bound of the solution semigroup generator Aw. The spectral values of Aw are given by the roots of a characteristic equation that is essentially the same as that derived by the nonrigorous methods of Layton et al. Therefore, the present analysis justifies the use of the previously derived characteristic equation. In particular, one can reasonably expect the sign of gamma - gamma c to correspond to the sign of the spectral bound of Aw.
590 $a School code: 0066.
650 4 $a Mathematics. $3 515831
650 4 $a Biology, Animal Physiology. $3 1017835
690 $a 0405
690 $a 0433
710 2 0 $a Duke University. $3 569686
773 0 $t Dissertation Abstracts International $g 64-08B.
790 1 0 $a Layton, Harold E., $e advisor
790 $a 0066
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3102250