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. 2016 Feb 1;310(3):F222-9.
doi: 10.1152/ajprenal.00182.2015. Epub 2015 Oct 14.

A computational model of flow and species transport in the mesangium

Sarah E Hunt  1 , Kevin D Dorfman  2 , Yoav Segal  3 , Victor H Barocas  4
Affiliations

A computational model of flow and species transport in the mesangium

Sarah E Hunt et al. Am J Physiol Renal Physiol. .

Abstract

A variety of macromolecules accumulate in the glomerular mesangium in many different diseases, but the physics of the transport of these molecules within the mesangial matrix has not been extensively studied. We present a computational model of convection and diffusion within the porous mesangial matrix and apply this model to the specific instance of immunoglobulin A (IgA) transport in IgA nephropathy. We examine the influence of physiological factors including glomerular basement membrane (GBM) thickness and mesangial matrix density on the total accumulation of IgA. Our results suggest that IgA accumulation can be understood by relating convection and diffusion, thus demonstrating the importance of intrinsic glomerular factors.

Keywords: IgA; IgA nephropathy; convection; diffusion; glomerulus; mesangial cells; mesangium.

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Figures

Fig. 1.
Fig. 1.
A: A sketch of glomerular capillaries with the adjacent mesangium. The simulation region is highlighted by dark black lines. The glomerular capillary was considered as a boundary condition. Only the mesangial matrix domain is shown in the figures. The perimesangial filtration barrier (PFB) was considered as the combination of the glomerular basement membrane and the podocytes. B: sketch of the simulation domain showing the pressure boundary conditions.
Fig. 2.
Fig. 2.
Albumin boundary conditions showing capillary concentrations on the left, with symmetry conditions on the right as well as front and rear faces. Albumin flux across the top (PFB) is defined to be zero.
Fig. 3.
Fig. 3.
Results for the base case with a filtration barrier thickness of 0.4 µm, volume fraction ϕm = 0.05, and rIgA = 75 Å. A: contour lines for the pressure in mmHg. The highest pressures are found at the capillary boundary, with the pressure quickly dropping as fluid is lost across the filtration barrier. B: streamlines of plasma flow in the mesangial matrix. The symmetry boundary condition on the right-hand side causes a sharp turn in plasma flow. C: Albumin concentration within the matrix. Albumin is very close to the plasma level throughout the mesangium. D: immunoglobulin A (IgA) concentration within the mesangial matrix. Because of its larger size, IgA diffuses more slowly and therefore concentrates more than albumin, rising 20% above its capillary concentration. E: oncotic pressure due to albumin in the mesangial matrix. This pressure significantly reduces the driving force of filtration.
Fig. 4.
Fig. 4.
A: as the filtration barrier becomes thinner, mesangial flux increases. Mesangial flux values are normalized by the value in the reference case. B: mesangial matrix fiber volume fraction has only a small effect for thicker filtration barriers (0.2–0.4 µm). For a filtration barrier thickness of 0.1 µm, however, changing the mesangial matrix volume fraction has a noticeable effect.
Fig. 5.
Fig. 5.
Excess mesangial accumulation vs. filtration barrier thickness (A) and mesangial matrix fiber volume fraction (B). Excess mesangial IgA is the IgA in the mesangial matrix above the concentration in the capillary. The reference case is again marked with the large black square.
Fig. 6.
Fig. 6.
As the radius of IgA increases, the accumulation of IgA in the mesangium also increases. Results shown here are for IgA having a radius of 1×, 1.25×, and 1.75× the actual radius of IgA. These results are with a filtration barrier thickness of 0.4 µm, and mesangial matrix volume fractions of 0.05, 0.08, and 0.1.
Fig. 7.
Fig. 7.
When a cell surface reaction is added to the model accumulation decreases. The magnitude of the decrease depends on the reaction rate, with faster reactions leading to less accumulation or even eliminating it altogether.
Fig. 8.
Fig. 8.
The accumulation of IgA in the mesangium for the cases plotted earlier but vs. the Péclet number. They form a smooth line, suggesting that accumulation depends significantly on Péclet number rather than the specific parameters of the simulation.
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