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.