Abstract
Purpose:
To identify and rank the lamina cribrosa (LC) morphologic factors that influence LC microcapillary hemodynamics and oxygen concentrations using computational fluid dynamics (CFD).
Methods:
We generated 12,000 ‘artificial' LC microcapillary networks and predicted blood flow velocities and oxygen concentrations within the microcapillaries using CFD. Across models, we varied the average pore size of the LC (5500 ± 2400 μm2), the microcapillary arrangement (radial, isotropic, or circumferential), the LC diameter (1.9 ± 0.3 mm), the inferior–superior curvature (340 ± 116 m−1), and the nasal–temporal curvature (−78 ± 130 m−1). We assumed that blood flow originated from the Circle of Zinn-Haller, fed the LC uniformly at its periphery, and was drained into the central retinal vein. Arterial (50 ± 6 mm Hg) and venous (17.7 ± 6 mm Hg) pressures were applied as boundary conditions and were also varied within our simulations. Finally, we performed linear regression analysis to rank the influence of each factor on LC hemodynamics and oxygen concentrations.
Results:
The factors influencing LC hemodynamics and oxygen concentrations the most were: LC diameter, arterial pressure, and venous pressure, and to a lesser extent: the microcapillary arrangement (anisotropy) and nasal–temporal curvature. Lamina cribrosa pore size and superior–inferior curvature had almost no impact. Specifically, we found that LCs with a smaller diameter, a radial arrangement of the microcapillaries, an elevated arterial pressure and a decreased venous pressure had higher oxygen concentrations across their networks.
Conclusion:
This study described LC hemodynamics using a computational modeling approach. Our study may provide clinically relevant information for the understanding of ischemia-induced neuronal cell death in optic neuropathies.
Open angle glaucoma (OAG) is an optic neuropathy disease, characterized by a progressive loss of retinal ganglion cells (RGC), and permanent vision loss. A well-known risk factor for OAG is an elevated IOP and it is currently considered the only treatable factor. However, the link between the pathogenesis of OAG and elevated IOP is not firmly established.
1 Up to one-third of glaucoma patients do not have elevated IOP
2 and a significant number of people with elevated IOP never develop glaucoma.
3
Intraocular pressure is known to deform the posterior structures of the eyes, particularly the structurally weak lamina cribrosa (LC)
4,5—a major site of RGC damage in glaucoma. The LC is a sieve-like network of collagenous connective tissue beams located in the optic nerve head (ONH) containing a comprehensive network of capillaries that provides nutritional and oxygen support to the RGCs.
6 The LC undergoes morphologic changes (e.g., ‘cupping') and significant remodeling during OAG development
7–10 and these changes have become the focus of many studies that have attempted to link changes in IOP to RGC death. A prominent hypothesis suggests that IOP-induced ONH strains damage the RGCs either directly
11 or indirectly through a mechanical disruption of axonal transport in RGCs, thus depriving RGCs from essential trophic factors.
12–14 An alternative hypothesis suggests that ONH strains can alter hemodynamics within the LC, which will in turn reduce the diffusion of nutrients to astrocytes and/or induce ischemia, thus resulting in RGC death.
To date, there is evidence to support the latter vascular hypothesis. Several studies have reported a correlation between poor ocular hemodynamics and glaucoma
15–17; for instance, Kanakamedal et al.
18 have suggested that people of African descent had a much higher prevalence of OAG compared with those of European descent due to their relatively weaker vascular components. The study also revealed a significant correlation between changes in blood flow and ONH morphology. Unfortunately, accurate measurement of blood circulation in vivo, especially at the level of the LC, has remained extremely challenging. This represents a barrier to establish impaired ocular hemodynamics as a contributing cause of OAG.
In view of the technical limitations, computational fluid dynamics (CFD) is a powerful alternative to understand how deep ocular blood flow could be involved in the development and progression of OAG. A CFD study by Carichino et al.
19 revealed that IOP-induced LC deformation could reduce the lumen size of the central retinal artery (CRA), and thus the overall ocular blood flow volume. A computational study by Causin et al.
20 also suggested that an increase in IOP could disrupt LC hemodynamics through biomechanical interactions. However, no CFD studies have yet modeled the LC as a detailed capillary network and studied how changes in ONH morphology could affect hemodynamics and oxygen concentrations within such a capillary network. We believe it is of critical importance to understand how ONH morphologic changes impact the LC blood flow at the microscale, because this could be a major reason for RGC death in OAG pathophysiology.
The goal of this study was to provide a modeling study of LC hemodynamics and oxygen concentration at the microscale. Specifically, we aimed to identify the main LC morphologic parameters that could affect LC blood flow and oxygen distribution. Because a majority of these morphologic parameters can now be measured in vivo with optical coherence tomography (OCT), our study may be relevant for the clinical management of glaucoma.
LC Network Generator Algorithm.
LC Pore Size.
LC Anisotropy.
LC Diameter.
LC Curvature.
Blood Flow Equations.
Oxygen Diffusion and Consumption Equations.
Influence of the LC Parameters on Oxygen Concentration, Flow Velocity, and Hypoxic Area
In this study, we developed a novel method to generate LC microcapillary networks that were incorporated into a CFD model for blood flow analysis. We were able to finely control the important LC morphologic parameters (pore size, anisotropy, diameter, and curvature) and study their effects on LC hemodynamics and oxygen concentration. Our models predicted that LC hemodynamics was highly influenced by the LC diameter, the arterial pressure, and the venous pressure. Notably, LCs with large diameters (>2.0 mm) had significantly poorer oxygen concentrations. Other parameters, such as pore size, anisotropy, and curvature had much less influence on LC hemodynamics.
We found that the regional variations in both the flow velocity and oxygen concentration were significant along the radial direction, but not in the circumferential N-T-S-I direction (
Fig. 4d). On average, oxygen concentrations decreased significantly from 64 mm Hg O
2 in the peripheral region to 25 mm Hg O
2 in the central region. While there is no literature to date that measured human ONH oxygen concentrations in vivo, our range of values is consistent with that observed in mice and porcine models.
40,41 The absolute velocity values obtained from our simulations also expand our knowledge of ocular blood flow in the human LC, because conventional techniques (e.g., laser speckle flowgraphy) yield only relative velocities and cannot provide deep flow measurements within the LC.
42
Lamina cribosa diameter was found to be the most influential parameter affecting both oxygen concentration and hemodynamics. Lamina cribosas with large diameters were found to exhibit a lower average oxygen concentration, a lower average flow velocity and a higher percentage of hypoxic area (up to 80% for LCs larger than 2.0 mm). Previous studies have reported an increase in optic disc diameter in glaucoma patients.
43,44 Combined with our findings, this suggests a plausible mechanism for RGC axonal death in glaucoma: elevated IOP could result in an increase in LC diameter (acutely and chronically),
45–47 which may in turn result in lower blood flow velocities and oxygen concentrations within the LC, starving RGC axons of oxygen, and possibly other nutrients. Further research needs to be done on the role of optic disc enlargement as a triggering cause for glaucoma. Our finding may also explain why certain races have a greater predisposition to OAG.
18 For instance, people of African descent have been shown to exhibit significantly larger optic discs
48 and poorer vascular components compared with those of European descent.
18
Not surprisingly, arterial and venous blood pressures were the other two most significant parameters that affected oxygen concentration and flow velocity. A decrease in arterial pressure and an increase in venous pressure both resulted in lower average oxygen concentration and flow velocity. This result is reasonable, as the aforementioned changes in pressure will reduce the overall perfusion pressure of the LC. It has also been shown that both an increase in central venous pressure and a decrease in arterial pressure are risk factors for the development of OAG,
49–52 and our result suggests that changes in blood pressure can significantly impact LC hemodynamics and potentially contribute to OAG progression.
We found LC pore size to have a significantly smaller influence on LC hemodynamics when compared with other factors. Changes in pore size had almost no effect on the oxygen concentration, while larger pores slightly increased the average blood flow velocity. Several monkey model studies have shown that there are no significant differences in pore size between normal and glaucomatous eyes.
53,54 A histologic study by Roberts et al.
8 found an increase in connective tissue beams in experimental glaucoma eyes, but the connective tissue volume fraction (analogous to pore area) remained relatively constant. Our findings further suggest that changes in collagenous beams and the LC microcapillary pore size may not significantly impact LC hemodynamics.
Anisotropy of the microcapillary network was shown to have greater impact on average oxygen concentration than pore size. Lamina cribosas with radially oriented capillaries at the peripheral region had higher average oxygen concentration than those with isotropic or circumferential configurations. Note that human LCs naturally exhibit a radial arrangement of the microcapillaries at the periphery
31 and any deviations from such an arrangement (possible through focal defects
55) may contribute to the development of OAG.
We found that an increase in curvature along the N-T direction (K1) resulted in both lower average oxygen concentration and blood flow velocity, whereas changes in S-I curvature (K2) had almost no impact on the two output parameters. The increase in N-T curvature corresponds to an increase in LC ‘cupping' and LC depth,
21 which are well-known to be associated with glaucoma development.
56,57 It was notable in our study that K1 was significantly more influential than K2. This difference may arise from the heterogeneity in LC capillary density. The N-T region has a greater density of microcapillaries than the S-I region (due to smaller pore area). This may mean that changes to curvature along the N-T direction have a greater influence on microcapillary morphology and hemodynamics.
It should be mentioned that a computational study on LC hemodynamics was previously conducted by Causin et al.
20 The authors used a poroelastic model, whereby blood capillaries were modeled as homogeneous pores in an elastic matrix. The work accounted for the biomechanical action of IOP, retrolaminar tissue pressure, and scleral tension on hemodynamics, but it did not take into account complex capillary networks and oxygen transport. On the other hand, our work took those latter into account, but ignored the effects of mechanical stress. We believe both works should be regarded as complementary and contribute to the current understanding of LC hemodynamics.
The followings are the main limitations of our study. First, we modelled the LC as a surface. This is not biologically accurate as the LC has a thickness of approximately 270 μm.
58 Considering that the LC may exhibit highly heterogeneous stresses (induced by IOP, the retrolaminar pressure, or during eye movements
59), it would be logical to observe variations in LC hemodynamics and oxygen concentrations through the thickness of the LC, as predicted by Causin et al.
20 LC thickness has also been shown to change with glaucoma progression, which may in turn compromise blood flow further in glaucoma subjects.
8 While using ‘surface-like' LCs (as performed herein) should provide a first degree of understanding of LC hemodynamics, future improvements to our models should prioritize on incorporating LC thickness and interactions with LC stresses.
Another limitation is that we simplified the study by reducing our 3D models into 1D ‘line' models in which only the average blood flow velocity and oxygen concentration were solved for each cross section of the capillary. According to our 3D preliminary work (
Supplementary Material), the average oxygen concentration inside the capillary segment was found representative of the surrounding neural tissue's oxygenation state, because the oxygen concentration dropped at most by 10% from the capillary to the adjacent LC nervous tissue. However, this assumption undermined the effect of very large pores in our findings as there could be a significant drop in oxygen concentration in the middle of the pore that was not taken into account in our models. Further models, which include nervous tissue between the LC pores, should be built, to better understand the effect of pore size.
We also imposed several constraints on the CFD simulation. The constraints associated with blood flow equations and oxygen diffusion in tissue are mostly justified based on similar computational studies conducted on capillary blood flow.
35,36 However, the blood viscosity, especially in microcirculation, may not be constant as we assumed. Blood becomes more particulate in small capillaries and its bulk viscosity can be a function of hematocrit, flow velocity, and capillary diameter.
60 One could try to account for this particulate nature by increasing the bulk viscosity of blood by 30% as proposed by several studies.
61,62 Interestingly, we found that increasing the viscosity did not considerably change the linear regression coefficients of all parameters (coefficients values changed by 5% at most when the viscosity was increased by 30% to 5.2 × 10
−3 Pa/s) and the ranking of factors remained the same. Changes in average flow velocity and oxygen concentration were observed but remained relatively small (20% and 12%, respectively). However, increasing viscosity may not necessarily make our models more biofidelic as blood viscosity in the microcapillary is determined by many factors, including the hematocrit. Furthermore, variations in viscosity could also happen locally in each capillary segment.
In addition, our assumption of constant capillary diameter may not be biologically accurate. A computational study by Causin et al.
20 also suggested that an increases in IOP could induce changes in the capillaries' diameter, which could compromise the lamina's perfusion. Autoregulation process can dynamically change the LC capillary diameter and autoregulation impairment at the ONH has been considered as a possible cause for glaucoma.
63,64 Unfortunately, no studies have yet provided a comprehensive map of capillary size within the LC. It is plausible that capillary radius could change regionally, and this may be further influenced by autoregulation, and IOP-induced LC stresses (these latter being highly heterogeneous). Note that all our other parameters were derived from experimental and clinical observations. Due to a lack of information, we have considered not to vary capillary radius in our models. Further studies are necessary to quantify the size of capillaries in the human LC. Such information could considerably enhance our models.
Our findings suggest that the central region of the LC may be more susceptible to ischemia than other regions. This is in contrast with other studies, which indicate that glaucomatous axonal loss starts from the peripheral region.
65 Also, an hour-glass pattern of axonal loss, in which S-I nerve fibers are selectively more damaged than the N-T nerve fibers,
65 was not evident from this study. These discrepancies may arise from the inhomogeneity of both the microcapillary characteristics (diameter, autoregulation capabilities, breakage, etc.) and nerve fiber density in each region of the LC. It is also possible that mechanical insult plays a greater role than hemodynamics in creating these damage patterns. Further studies that include the regional variations of both nerve fibers and microcapillaries may reconcile the observed axonal loss pattern and our hemodynamics result.
Lastly, accurate in vivo measurement of oxygen concentration and blood flow velocity are not yet possible with current techniques. This makes the validation of our model difficult. Nevertheless, our output lies within normal biological values in capillary networks of comparable size.
In summary, our study revealed, for the first time, the relationship between clinically relevant LC parameters and the hemodynamics and oxygen distribution of the LC. The clear ranking of each parameter's importance presented in the study has the potential to be clinically useful in glaucoma management, diagnosis, and risk profiling. Finally, our approach could serve as a numerical testbed for hypotheses related to LC hemodynamics.
Supported by grants from the Ministry of Education, Academic Research Funds, Tier 1 (MJAG; R-397-000-181-112; Singapore) and from an NUS Young Investigator Award (MJAG; NUSYIA_FY13_P03, R-397-000-174-133; Singapore).
Disclosure: T. Chuangsuwanich, None; K.E. Birgersson, None; A. Thiery, None; S.G. Thakku, None; H.L. Leo, None; M.J.A. Girard, None