A Mathematical Model of Interstitial Fluid Flow and Retinal Tissue Deformation in Macular Edema

Abstract

Purpose: This study aims to develop a mathematical model to elucidate fluid circulation in the retina, focusing on the movement of interstitial fluid (comprising water and albumin) to understand the mechanisms underlying exudative macular edema (EME).

Methods: The model integrates physiological factors such as retinal pigment epithelium (RPE) pumping, osmotic pressure gradients, and tissue deformation. It accounts for spatial variability in hydraulic conductivity (HC) across the retina and incorporates the structural role of Müller cells (MCs) in maintaining retinal stability.

Results: The model predicts that tissue deformation is maximal at the center of the fovea despite fluid exudation from blood capillaries occurring elsewhere, aligning with clinical observations. Additionally, the model suggests that spatial variability in HC across the thickness of the retina plays a protective role against fluid accumulation in the fovea.

Conclusions: Despite inherent simplifications and uncertainties in parameter values, this study represents a step toward understanding the pathophysiology of EME. The findings provide insights into the mechanisms underlying fluid dynamics in the retina and fluid accumulation in the foveal region, showing that the specific conformation of Müller cells is likely to play a key role.

Figure 1.

(A) Sketch of Müller cell density in the retina. (B) Spatial arrangement of MCs. (C) Sketch of the regions considered in the model. The red region denotes the exudation zone during exudative macular edema (EME).

Figure 2.

Values of the HC K, assigned in the various regions of the domain.

Figure 3.

Pressure (A) and concentration (B) distributions and flow streamlines in physiological conditions.

Figure 4.

(A) OCT of the macular region in the presence of EME. (B) Pressure distribution. (C) Velocity field. (D) Concentration distribution. The white curves with arrows in (A–C) represent streamlines of the flow.

Figure 5.

(A) Mean pressure in the foveola as a function of the fluid exudation rate. (B) Mean pressure in the foveola versus the HC ratio K⁽¹⁾/K⁽²⁾ between the layer in which cells are straight and that in which they are inclined.

Figure 6.

ILM profiles after deformation due to the exudation for different values of the fluid exudation rate amplitude A_f.

Figure A1.

Sketch of the assumed arrangement of MCs for the calculation of the HC of the tissue and cross section of the micro-scale unit cells. In the top panel, MCs are perpendicular to the retinal plane. In the bottom panel, MCs are inclined at an angle α, and they get closer to each other.

Figure A2.

Dependency of the components of the hydraulic conductivity tensor K_ij on the angle of inclination of MCs. α = 0 refers to the case of cells orthogonal to the RPE plane.

Figure A3.

Bar chart displaying the relationship between hydraulic conductivity (m/s/Pa) and pressure jump (mm Hg) across the membrane for a water flux per unit surface of 1 × 10⁻⁸ m/s. Experimental measurements from Tsuboi (RPE–choroid complex), Moore et al. for young and old subjects (Bruch’s membrane and choroid), Fatt and Shantinath (whole retina), and Antcliff et al. The baseline bar refers to our choice and includes the contribution of the retina and the RPE–Bruch’s membrane complex.^,