Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation

Abstract

Impaired blood flow and oxygenation contribute to many ocular pathologies, including glaucoma. Here, a mathematical model is presented that combines an image-based heterogeneous representation of retinal arterioles with a compartmental description of capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. Every terminal arteriole is connected in series to compartments for capillaries and venules, yielding a hybrid model for predicting blood flow and oxygenation throughout the retinal microcirculation. A metabolic wall signal is calculated in each vessel according to blood and tissue oxygen levels. As expected, a higher average metabolic signal is generated in pathways with a lower average oxygen level. The model also predicts a wide range of metabolic signals dependent on oxygen levels and specific network location. For example, for high oxygen demand, a threefold range in metabolic signal is predicted despite nearly identical PO2 levels. This whole-network approach, including a spatially nonuniform structure, is needed to describe the metabolic status of the retina. This model provides the geometric and hemodynamic framework necessary to predict ocular blood flow regulation and will ultimately facilitate early detection and treatment of ischemic and metabolic disorders of the eye.

Keywords: blood flow; glaucoma; heterogeneous vascular network; mathematical model; metabolic signaling; microcirculation; oxygen transport; retina.

Figure 1.

(A) Heterogeneous mouse arteriolar network obtained using position, length, and diameter data from [8,9], as described in [7]. (B) Heterogeneous human arteriolar network developed by modifying the mouse model in panel (A) in the following ways: reducing the number of main branches from six to four, rotating the four main branches according to oximetry images, and increasing vessel diameters and lengths by a scaling factor of 3.6 and 5.9, respectively.

Figure 2.

Schematic representation of the hybrid model. The circle shows an enlarged portion of the network where a series of compartments for the capillaries (C), small venules (SV), and large venules (LV) are attached to each terminal arteriole in the heterogenous model.

Figure 3.

Flowchart of the hybrid model programmed in C++ (blue) and MATLAB (purple). The heterogeneous arteriolar model is programmed in C++ and the compartmental capillary and venular model is in MATLAB. The two programming languages will be dynamically linked to exchange information repeatedly until a steady state of blood flow and diameter activation is achieved (future work, shaded gray).

Figure 4.

Contour plots (panels (A–C)) and histograms (panels (D–F)) of tissue PO₂ in the arteriolar network for varying levels of oxygen demand (M₀) prior to the calculation of the conducted metabolic response. Three levels of oxygen demand were simulated: low (M₀ = 1 cm³ O₂/100 cm³/min, panels (A,D)), moderate (M₀ = 2 cm³ O₂/100 cm³/min, panels (B,E)), and high (M₀ = 4 cm³ O₂/100 cm³/min, panels (C,F)). As M₀ is increased, a nonuniform decrease in tissue PO₂ was predicted.

Figure 5.

Mean PO₂ (panel (A)) and standard deviation of PO₂ (panel (B)) at the upstream (blue) and downstream (green) end of the capillary compartment as oxygen demand is varied from M₀ = 0.5 to 4 O₂/100 cm³/min. Mean (panel (C)) and standard deviation (panel (D)) of the metabolic signal (S_meta) calculated at the upstream end of the capillaries as oxygen demand is varied.

Figure 6.

Panels (A,C,E): Histograms giving the percent distribution of the metabolic signal (S_meta) in every arteriole for M₀ = 1, 2, and 4 cm³ O₂/100 cm³/min, respectively. Panels (B,D,F): Metabolic signal calculated at each point in the capillaries (C, blue), small venules (SV, brown), and large venules (LV, green) for M₀ = 1, 2, and 4 cm³ O₂/100 cm³/min, respectively.

Figure 7.

Metabolic signal (S_meta) calculated at the upstream end of the capillaries as a function of flow (panel (A)) or partial pressure of oxygen (panel (B)) at the upstream end of the capillaries for three levels of oxygen demand: M₀ = 1 (blue), 2 (red), and 4 (green) cm³ O₂/100 cm³/min.