CHAPTER 2 MODELING OXYGEN TRANSPORT IN THE RETINA
2.3 AXISYMMETRIC MODEL OF THE MACULA AND SURROUNDING PERIPHERY . 28
2.3.2 MODELING AND OPTIMIZING THE DEVICE
An oxygen containing ring is placed around the macula at the edge of the perifovea. The ring is comprised of 120µm thick silicone shell with hollow interior set at a fixed concentration. The ring prevents occlusions along the optical path of the macula, and reduces the risk of damage to the fovea if the ring were to contact the retina. The ring also provides an even oxygen distribution within the region of the macula compared to a point source (Figure 2.15). First, this section will confirm the device can improve oxygen tension, and reduce VEGF upregulation in the inner macula. The device will be swept across all parameters to determine the distance from the retina and the device oxygen tension required to treat DR.
Figure 2.15: 9-layer model with 200mmHg device. Retina with 33µL/min blood flow.
Figure 2.16: Simulation with 33 µL/min and 200mmHg device (vitreous not plotted).
The AXSY model estimates three ratios with respect to a healthy retina: VEGF upregulation, moles of oxygen in the retina, and oxygen consumption in the retina. Animal models will be needed to validate the estimates, since these are just a starting point. The device’s oxygen tension and position were independently swept for these ratios. The device’s position was fixed at 10µm above the nerve fiber layer at the perifovea, and the oxygen tension swept values are shown in Figure 2.17. Note that oxygen’s diffusion path length is much shorter in the retina than in the vitreous due to the lower diffusion and solubility constants. Furthermore, consumption in the GCL and IPL increases the
amount of oxygen deposited in those layers before it can diffuse deeper into the retina. This second effect efficiently deposits oxygen that enters the hypoxic tissue of the GCL and the IPL, where it is most needed (Figure 2.11).
Figure 2.17: Ischemia model with varying device oxygen tension. Device placed 10µm from the perifovea and tested with a 15% reduction in retinal blood flow from the healthy 42.7µL/min.
In the AXSY model, oxygen from the device is not transported through the vasculature. The vasculature normally transports oxygen along the layer. In the AXSY model, the vasculature does not shuttle oxygen, consequently the model overestimates the oxygen requirements from the device.
Figure 2.18: Simulation VEGF upregulation for different device oxygen tension. VEGF upregulation with 33µL/min retinal blood flow rate (22.7% reduction from the healthy 42.7µL/min flow rate) and a device with varied 𝑝𝑂2.
The percentage of VEGF upregulation is plotted in Figure 2.18. VEGF upregulation starts to be suppressed at 100mmHg, and falls below 80% at 200mmHg. VEGF upregulation of 1.5× the healthy retina’s VEGF upregulation is considered unhealthy, considering that VEGF upregulation 1.4× that of healthy retinal VEGF was not observed to overexpress in the IPS layer in severe ischemia (refer
to the outer retina of Figure 2.6). Now that the device produces a favorable effect on the hypoxia in the inner retina, the device will be optimized for different severities of DR.
Three contour plots are used to optimize the distance between the device and the macula, and to the device’s oxygen tension: moles of oxygen in the inner macula (Figure 2.19), oxygen consumption in the inner macula (Figure 2.20), and VEGF upregulation ratios in the combined GCL and IPL (Figure 2.21).
For moles of oxygen and consumption in the inner macula, the positive slope of the contour line implies that reducing the oxygen tension from the device must also be followed with nearly linear reduction in distance between the device and the NFL. The values necessary for treatment depend on the level of ischemia. For a severe ischemia (30% reduction), which equates to PDR, either 175mmHg at 0µm from the NFL or 250mmHg at 500µm fall within the treatable range for moles of oxygen and for retinal consumption. Lower oxygen tension devices or devices farther away from the retina, such as 100mmHg with a 1000µm separation, are adequate to treat mild to moderate NPDR.
VEGF upregulation has an optimum distance around 200µm-400µm away from the NFL layer that is independent of oxygen tension. When the device is moved away from the retina, the thinner bottom membrane (the reason for thicker sidewalls can be found in section 6.3.1) has a more direct path length with tissue through vitreous, which is far more permeable than the retina. If the device is too close, oxygen is wasted oversupplying a smaller segment of the retina. As VEGF upregulation is more sensitive in the low oxygen tension, this effect is magnified in Figure 2.21. A 22.7% ischemia (moderate to severe non-proliferative DR) is best treated by a device of 150mmHg or greater oxygen tension at approximately 200µm. Since lower ischemia has a lower oxygen demand, such a device is adequate to treat those as well. PDR is best treated with a device of 250mmHg at 200µm from the nerve fiber layer.
Note that these simulations assume very little cell death in the inner retina’s tissue; if sufficient oxygen could be supplied, retinal consumption would be the same as healthy. Therefore, the model overestimates the oxygen. The percentage of cell death is not modeled, as it would be a free parameter that is difficult to estimate correctly. Instead, the model sets an upper bound. As is seen in section 7.3.2, the provided oxygen tension may be modulated as desired.
Figure 2.19: Contour map of the ratio between moles of oxygen in the inner macula (integration of concentration in the NFL, GCL, IPL, OPL) for treated ischemic tissue compared to the untreated healthy case. A value less that 1 (blue) means the oxygen concentration is less than the healthy case. A value greater than 1 (red) means the net oxygen tension is higher than the healthy case.
Figure 2.20: Contour map of oxygen consumption in the inner macula. Ratio oxygen consumption in the dark adapted inner macula between the treated ischemic and untreated healthy cases. A consumption of 1 or higher (orange to yellow) will be considered healthy.
Figure 2.21: Contour map of VEGF upregulation in the GCL an IPL. Ratio between treated ischemic and untreated healthy case, for the integrated VEGF Upregulation in the GCL and IPL for a dark-adapted macula. The goal would be to minimize the amount of VEGF production in tissue to near the healthy value.
Finally, this device requires approximately 0.25nmol/s of oxygen to achieve treatment (Table 2.6).
This requirement is only 3x the inner retinal deficit over the 6mm radius of the modeled retina (Table 2.4). This is an efficiency of at worst 36.4%. The flux has little variation between 200µm and 1mm separation from the retina, so the target maximum flux is accurate.
Table 2.6: Simulated oxygen flux from diffusor in nmol/s out of the device. The estimate was taken on the outer surface of the silicone wall. The top and bottom silicone walls are 120µm thick, and the device is 0.5mm from the NFL at perifovea.
Diffusor Oxygen Flux at 0.5mm from Dark Adapted Perifovea (nmol/s) Blood Flow (µm) 42.7 38.43 36.295 33 29.89
Device O2 Tension (mmHg)
25 0.004 0.008 0.012 0.017 0.020
50 0.023 0.028 0.031 0.037 0.040
100 0.063 0.067 0.069 0.075 0.080 150 0.102 0.105 0.108 0.113 0.119 200 0.140 0.143 0.146 0.150 0.156 250 0.178 0.181 0.183 0.187 0.193 300 0.215 0.218 0.220 0.223 0.228