Research Papers

A Model of Strain-Dependent Glomerular Basement Membrane Maintenance and Its Potential Ramifications in Health and Disease

[+] Author and Article Information
Victor H. Barocas

Department of Biomedical Engineering,  University of Minnesota, Minneapolis, MN 55455

Kevin D. Dorfman

Department of Chemical Engineering and Materials Science,  University of Minnesota, Minneapolis, MN 55455

Yoav Segal

Division of Renal Diseases and Hypertension, Department of Medicine,  University of Minnesota, Minneapolis, MN 55455; Minneapolis VA Health Care System, Minneapolis, MN 55417

J Biomech Eng 134(8), 081006 (Aug 06, 2012) (8 pages) doi:10.1115/1.4007098 History: Received February 08, 2012; Revised April 12, 2012; Posted July 06, 2012; Published August 06, 2012; Online August 06, 2012

A model is developed and analyzed for type IV collagen turnover in the kidney glomerular basement membrane (GBM), which is the primary structural element in the glomerular capillary wall. The model incorporates strain dependence in both deposition and removal of the GBM, leading to an equilibrium tissue strain at which deposition and removal are balanced. The GBM thickening decreases tissue strain per unit of transcapillary pressure drop according to the law of Laplace, but increases the transcapillary pressure drop required to maintain glomerular filtration. The model results are in agreement with the observed GBM alterations in Alport syndrome and thin basement membrane disease, and the model-predicted linear relation between the inverse capillary radius and inverse capillary thickness at equilibrium is consistent with published data on different mammals. In addition, the model predicts a minimum achievable strain in the GBM based on the geometry, properties, and mechanical environment; that is, an infinitely thick GBM would still experience a finite strain. Although the model assumptions would be invalid for an extremely thick GBM, the minimum achievable strain could be significant in diseases, such as Alport syndrome, characterized by focal GBM thickening. Finally, an examination of reasonable values for the model parameters suggests that the oncotic pressure drop—the osmotic pressure difference between the plasma and the filtrate due to large molecules—plays an important role in setting the GBM strain and, thus, leakage of protein into the urine may be protective against some GBM damage.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Glomerular capillary wall. Fluid filters from the blood through the fenestrated endothelium (E), the glomerular basement membrane (GBM), and the pores between the foot processes (FP) of the podocytes. The filtrate forms the primary urine.

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Figure 2

Schematic of the model. The GBM thickness is controlled by deposition and removal, which are both mediated by strain. Thickening of the GBM makes it strain less for the same transcapillary pressure but also increases the transcapillary pressure because of increased filtration resistance.

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Figure 3

Relation between the GBM thickness and strain. The plot, based on the values in Table 1, shows how the strain decreases with the increasing thickness. The limiting value (thickness ∞) is 0.34% strain.

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Figure 4

Allometry of the mammalian glomerular capillary. Data for human (H [19-22]), cat (C [23]), rhesus monkey (RM [24]), Wistar rat (WR [25]), Sprague-Dawley rat (SDR [26-27]), and mouse (M [28]) are plotted as inverse radius versus inverse thickness. The best-fit line gives an intercept of 1/r = 0.173 μm−1 , corresponding to a diameter of 11.6 μm.



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