Vol. 10, No. 4, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Global sensitivity analysis in a mathematical model of the renal insterstitium

Mariel Bedell, Claire Yilin Lin, Emmie Román-Meléndez and Ioannis Sgouralis

Vol. 10 (2017), No. 4, 625–649
Abstract

The pressure in the renal interstitium is an important factor for normal kidney function. Here we develop a computational model of the rat kidney and use it to investigate the relationship between arterial blood pressure and interstitial fluid pressure. In addition, we investigate how tissue flexibility influences this relationship. Due to the complexity of the model, the large number of parameters, and the inherent uncertainty of the experimental data, we utilize Monte Carlo sampling to study the model’s behavior under a wide range of parameter values and to compute first- and total-order sensitivity indices. Characteristically, at elevated arterial blood pressure, the model predicts cases with increased or reduced interstitial pressure. The transition between the two cases is controlled mostly by the compliance of the blood vessels located before the afferent arterioles.

Keywords
mathematical model, sensitivity analysis, Monte Carlo, kidney, interstitium
Mathematical Subject Classification 2010
Primary: 49Q12, 65C05, 92C30, 93A30
Secondary: 92C50, 92C42
Milestones
Received: 29 September 2015
Revised: 26 April 2016
Accepted: 11 July 2016
Published: 7 March 2017

Communicated by Suzanne Lenhart
Authors
Mariel Bedell
Carnegie Mellon University
5000 Forbes Ave.
Pittsburgh, PA 15213
United States
Claire Yilin Lin
Emory University
201 Dowman Dr.
Atlanta, GA 30322
United States
Emmie Román-Meléndez
University of Puerto Rico Mayaguez
259 Blvd. Alfonso Valdez Cabian
Mayagüez 00680
Puerto Rico
Ioannis Sgouralis
National Institute for Mathematical and Biological Synthesis (NIMBioS)
University of Tennessee
1122 Volunteer Blvd., Suite 106
Knoxville, TN 37996
United States