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Biomechanical Assessment of Radial Optic Neurotomy
Biomechanical Assessment of Radial Optic Neurotomy Thomas R. Friberg, MS, MD,1 Patrick Smolinski, PhD,2 Sarajane Hill, BS,2 Shree K. Kurup, MD1 Purpose: A biomechanical model was constructed to simulate the potential therapeutic effect that the surgical procedure radial optic neurotomy (RON) would have on an eye with a central retinal vein occlusion. Design: Experimental study. Controls: Model eyes undergoing RON were compared to control eyes under the same baseline conditions. Intervention: Radial optic neurotomy. We modeled the optic nerve, lamina cribrosa, and the sclera separately and then reassembled the components. Material properties of the sclera and lamina cribrosa were extracted from the literature and both stiff and more elastic values were used for the optic nerve. Intraocular and arterial pressures were varied across a wide range in the analysis. Main Outcome Measure: Change in central retinal vein lumen size. Results: Over a clinically relevant range of boundary conditions, the increase in the lumen area of the central retinal vein lumen after RON remained trivial, ranging from 1% to a maximum of 5%. Conclusions: The biomechanical effect of RON is negligible, and is unlikely to be a procedure that could mechanically ameliorate the clinical sequelae of a central vein occlusion. Ophthalmology 2008;115:174 –180 © 2008 by the American Academy of Ophthalmology.
When retinal venous drainage is compromised, visual loss commonly occurs.1,2 Central retinal vein occlusion (CRVO) is the most visually devastating because venostasis after occlusion results in retinal thickening and macular edema, severely impairing retinal function. Treatment is often frustrating, partly because the etiology and pathophysiology of CRVO are not well understood.1,3 The Central Vein Occlusion Study revealed that there is a high degree of correlation between the initial and final visual acuity in affected eyes.1 Visual acuity reflects existing blood flow, with more ischemic eyes having a poorer initial vision as well as a poorer prognosis.1,2 Furthermore, 40% to 50% of ischemic eyes develop complications such as iris and anterior chamber angle neovascularization and secondary glaucoma.1 Clinicians have used several therapeutic options for CRVO with limited success.2– 4 Some strategies target the thrombus in the occluded vein. Such thrombus formation Originally received: September 27, 2006. Final revision: March 2, 2007. Accepted: March 6, 2007. Available online: June 4, 2007. Manuscript no. 2006-1092. 1 Department of Ophthalmology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania. 2 Mechanical Engineering Department, University of Pittsburgh School of Engineering, Pittsburgh, Pennsylvania. Presented in part at: Retina Society annual meeting, September 2004, Baltimore, Maryland. Supported in part by Research to Prevent Blindness, Inc., New York, New York. Correspondence to Thomas R. Friberg, MS, MD, Professor of Ophthalmology and Professor of Bioengineering, University of Pittsburgh, UPMC Eye Center, 203 Lothrop Street, Room 824, Pittsburgh PA 15213. E-mail: [email protected].
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occurs commonly, but whether it is a primary or secondary event is unclear.3 How such thrombi develop and conditions that increase risk have also been explored.5,6 The location of the typical thrombus formation along the vein is controversial,3,7 but in a substantial percentage of cases, the thrombus is located well away from the lamina cribrosa. Pharmacologic strategies for the treatment of CRVO include the injection of thrombolytic agents to dissolve or dislodge the thrombus, and the use of corticosteroids or other antiinflammatory drugs to address the associated macular edema.2,8,9 Alternate therapeutic approaches aim to bypass the thrombus by creating collateral blood flow.10 Relatively recently, Opremcak et al11 proposed that a scleral compartment or outlet syndrome exists in CRVO analogous to the “thoracic syndrome.” They described a surgical technique to decompress the central retinal vein by a single radial incision (radial optic neurotomy [RON]) placed at the edge of the optic nerve head.11 The rationale for RON as published is that it decompresses the venular flow resistance by relieving pressure in the compartment.12 The merits of such an approach have been challenged in the literature3,13,14 and from the podium (Friberg, Retina Society annual meeting, September 2004, Baltimore, Maryland). However, some suggest that RON could work by increasing collateral vessel formation or improving the hemodynamics within the affected vein.15,16 A randomized study of RON for CRVO would be difficult to execute and may well be inappropriate. Alternatively, we tested the basic physical hypothesis implicit in the RON procedure by modeling the biomechanical effects RON in a virtual eye, using a computer simulation technique—namely, finite element analysis.17 Finite element analysis is widely used to assist in the ISSN 0161-6420/08/$–see front matter doi:10.1016/j.ophtha.2007.03.013
Friberg et al 䡠 Biomechanical Assessment of Radial Optic Neurotomy design of aircraft and shell structures, and models the deformation of a structure subjected to load. The structure of interest is subdivided into a virtual meshwork of tiny 3-dimensional elements (volumes), each of which is subject to its own boundary conditions. A computer algorithm then performs thousands of calculations to determine stresses and strains at key points or nodes. This type of analysis has been used previously in biological structures,18 and in particular, in the evaluation of stress in aneurysms.19,20 Recently, finite element analysis has been applied to biomechanics of the lamina cribrosa of the eye.21 Implicit in finite element investigations, boundary conditions must be set that are consistent with the dimensional and elastic properties of the elements. The individual elements are characterized by equations to define the stiffness properties of each element, and these elements are then combined piece by piece to determine the stiffness properties of the entire structure as well as the deformations under loading conditions.17 Stiffness in biomechanical terms is expressed by a material’s modulus of elasticity or E, which is given in units of force per unit area. E relates how a material of length (L) changes in dimension if a force (F) is applied perpendicular to its cross-section. Force (F) divided by the cross-sectional area of the material or stress (force/ unit area) is related to the deformation of the material or strain (change in length/original length) by the modulus of elasticity (E). In biomechanical terms, E equals stress divided by strain. Very elastic materials are those with a smaller modulus. The structures of interest in our model are the sclera, cribriform plate, optic nerve sheath, and optic nerve. The physical properties, pressure loads on the tissues, and inherent elastic parameters were each assumed to encompass a range in values. This then simulated a diversity of clinical conditions, and demonstrated how the eye might change under these perturbations. We analyzed RON in this context.
Materials and Methods The globe, optic nerve head, and optic nerve were divided into small regions or elements and, by approximating the displacements in each element, a stiffness matrix was derived computationally. The stiffness matrices for all elements and given loads (pressures) were assembled, and equations were derived and solved to calculate the displacements at the vertices of the elements (nodes). The strains and stresses were determined from these displacements. We used ALGOR V19 software (Algor Inc, Pittsburgh, PA) to perform the computations for the human eye.
0.3 mm and the thickness of the lamina cribrosa was set at 0.5 mm. The length of the optic nerve segment as modeled was 1.25 mm, as the entire length of the nerve has decreasing influence the further away it is from its insertion into the posterior globe. The optic cup diameter and depth were modeled at 0.9 mm and 0.25 mm, respectively (Fig 1C). The width and depth of the RON incision were each taken to be 0.8 mm. These parameters were chosen to make the nerve head compliant and thus more amenable to the potential effects of radial optic neuropathy.
Material Properties The material properties of all tissues were assumed to be linearly elastic, isotropic, and almost incompressible with Poisson’s ratio equal to 0.49. Based on these assumptions, the only parameter necessary to further describe the stiffness of each tissue was the modulus of elasticity (Young’s modulus). The modulus for scleral tissue Es was taken to be Es ⫽ 2.5 MPa based on our earlier work.22,23 Although there is some uncertainty regarding the exact mechanical properties of the lamina cribrosa,21 we used a modulus of elasticity of Elc ⫽ 0.25 MPa, which is approximately the mean value for human tissue. Because there are also limited data regarding the material properties of the optic nerve, values for both a stiff and compliant tissue were assigned in the analysis. For the stiff neural tissue, the modulus En was assumed to be 4 times that of the sclera (En ⫽ 4Es) and the compliant modulus was assumed to be one tenth of the sclera value (En ⫽ 0.1Es).
Loads and Boundary Conditions A uniform intraocular pressure (IOP) was assumed to be present on all internal surfaces of the eye, and a uniform and constant venous pressure was applied to the inner walls of the vein as shown in Figure 1B. The external surfaces of all tissues were estimated to be subject to 0 mmHg pressure, again to favor RON efficacy. The physiologic ranges of values used for the IOP were 10, 25, and 35 mmHg; 50 and 75 mmHg were used for the central retinal venous pressures. Different constraints on displacements were modeled. In the model before RON was virtually applied, all the nodes on the cut plane (plane of symmetry) were constrained in the x direction. That is, the nodes were not allowed to displace out of this plane. For models that had undergone a virtual RON procedure, the nodes in the area of the RON incision (on the plane of symmetry) were not constrained to the y–z plane, allowing them to move up out of the plane of symmetry (toward or away from the center of the eye). Figure 1C shows the position of the incision with respect to the optic nerve head. The interfaces between the other different tissues were taken to be completely bonded and thus were not allowed to develop any separations.
Results Geometric Assumptions Our model eye was virtually constructed to contain the globe itself, a segment of the optic nerve, and the lamina cribrosa. The geometries are 3-dimensional; but, because of symmetry, only one half of each structure generally needed to be modeled for computational purposes. We assumed that the globe was a hemispherical shell with an inner diameter of 20 mm and an outer diameter of 22 mm (scleral thickness ⫽ 1 mm). The diameter of the optic nerve was assigned to be 1.5 mm and the central opening for the vein passing through the nerve was assumed to be 0.3 mm (Fig 1A). The central venous lumen diameter was assumed to be just under
Our model showed that the lumen shape of the central retinal vein before RON under changing boundary conditions was always circular, as expected because of symmetry of the globe and nerve head. However, after RON, the tissue has been relaxed more in one direction than the other, and hence, the lumen becomes slightly elliptical in shape. The quantitative results showing the effect of RON for the various pressures and material properties are shown graphically in Figure 2. These curves give the ratio of the diameter of the lumen of the vein after RON to the diameter without RON in the stated direction, and the data vary with respect to the applied IOP. The 4 curves in the graph correspond to different values of
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Figure 1. A, Model geometry of the optic nerve head showing the dimensional assumptions at baseline. B, The intraocular and venous pressures impinging upon the model elements are assumed to be applied as shown. C, The model as it appears from inside the virtual vitreous cavity. The radial optic neurotomy (RON) incision has been modeled to straddle the peripheral edge of the optic nerve head and is assumed to be 0.8 mm long (along the y axis). The plane of symmetry, for analysis sake, is shown by the vertical dotted line. Deformations of the tissue at the RON incision location are allowed in the x and y directions, as well as perpendicular to the nerve head or z direction (toward or away from the virtual center of the vitreous cavity).
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Figure 2. A, Ratio of the central lumen diameter after radial optic neurotomy (RON) to the central lumen diameter before RON in the x direction (per Fig 1C) at the optic nerve insertion. The plot is a function of the intraocular pressure (IOP) for different nerve moduli of elasticities and venous pressures within the central retinal vein (VPs; Fig 1B); Es is the scleral modulus and En is the modulus of the nerve tissue. A higher modulus indicates a stiffer material. B, Ratio of central lumen diameter after RON to central lumen diameter before RON in the y direction at the nerve head as a function of IOP for different nerve moduli and intraocular and intravenous pressures. The flatter slopes of the curve (compared with A) illustrate that only a very small change in dimension occurs in the radial (y) direction compared to the circumferential (x) direction.
nerve elastic modulus (En ⫽ 4Es and En ⫽ 0.1Es and venous pressure of 50 and 75 mmHg). Figure 2A gives the normalized x-direction inner diameter and Figure 2B gives the normalized y-direction inner diameter of the lumen where the central retinal vein enters the nerve. Figure 3 shows the overall geometry of our assembled finite element model as well as a magnified view of the optic nerve at its scleral insertion. Figure 4 shows the geometric deformation of nerve tissue at the bottom of the optic cup (Fig 1) before and after RON for the case of En ⫽ 4Es and IOP and central venous pressure ⫽ 50 mmHg.
Discussion Although RON has been advocated as an effective treatment for visual loss from CRVO, we critically evaluated the potential biomechanical effect of RON on the optic nerve head and major vessels in the region. To our knowledge, RON has always been performed as part of a vitreoretinal procedure that includes pars plana vitrectomy. We focused, however, on only the mechanical
effect of the procedure, because the presence or absence of vitreous gel makes no real difference to our approach. (It could, however, alter the clinical results of the RON procedure by, for instance, altering the oxygenation within the vitreous cavity.) We found that the average RON-induced decompression (maximum increase in the central retinal vein lumen diameter) was a paltry 4%. That is, the diameter of the central venous lumen under the best of conditions could only increase 4% (y-direction). This is accompanied by only a very small increase (1.4%) in the perpendicular direction (x) in the central lumen diameter. We find it extremely unlikely then that any meaningful physiologic mechanical advantage can be gained by the radial cut itself. Only if the sclera was both extremely elastic (low modulus of elasticity) and extremely thin would we expect a possible potential benefit from severing a “fibrous ring.” However, on the contrary, the sclera is tough and rather thick and it does not readily change diameter with changes in IOP.22,23 Furthermore, the
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Figure 3. Full finite-element model of the globe and optic nerve inserting within it. The grid lines show the individual elements. The optic nerve region is shown in more detail below. Each element is treated separately.
expansion of the sclera at the optic nerve is confined by the relatively solid architecture of the optic nerve itself.24 The cribriform plate is relatively stiff, but on the other hand, it contains a meshwork of holes. Some argue that such a meshwork thus allows for expansion of the plate after the RON procedure. However, any expansion of this meshwork is mechanically constrained by the material that fills the holes. In vivo, ganglion cell axons pass through the cribriform plate on their way to the geniculate ganglion. Because the axons are composed of rather incompressible biological material, we argue that the meshwork would not freely expand. Some authors have speculated that the apparent selective clinical success of RON depends on the presurgical state of the retinal vasculature and that RON favors eyes that are less ischemic.3 Another hypothesis is that RON promotes alternative collateral flow by creating choroidal anastomoses4 to the central retinal vein. However, such collaterals do
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not necessarily form at a rate significantly higher than in the natural course of the disease.3,4 The location and depth of the RON incision25 have also been discussed as influencing efficacy. From a biomechanical perspective, we suggest that the location and depth are unimportant, because the effect of RON on lumen size is minuscule. Although our model did not specifically consider the late effects of healing and fibrosis at the site of the RON incision, our model indicates that the chance of these late changes affecting lumen size is remote. Our study raises serious questions about the potential efficacy of this invasive technique. Furthermore, the associated complications are not trivial and have been extensively documented. These include arterial occlusions, retinal detachments, loss of visual field, choroidal neovascularization, and a further decrease in venous blood flow.4,26 –29 Moreover, the risk of interruption of the optic nerve head arterial circle must be balanced against historically claimed success.3
Friberg et al 䡠 Biomechanical Assessment of Radial Optic Neurotomy
Figure 4. Top, Color-coded finite element plot of deformations of the optic nerve tissue in the composite model without the radial optic neurotomy (RON) incision, assuming modulus of the nerve tissue (En) ⫽ 4Es (scleral modulus) and that the intraocular pressure (IOP) and central venous pressure equal 50, parameters which would favor the mechanical effect of RON. Only the nerve tissue is shown here, for clarity. The upper surface represents the bottom of the optic cup, where the canal for the retinal vein begins. The deformations are secondary to the baseline IOP as well as other pressures on the optic nerve inserted into the globe. Note the circumferential symmetry. Bottom, Plot of the deformed geometry of the optic nerve after the RON incision at the same location within the eye and under the same conditions as above. The change in the lumen diameter is negligible.
Such success may in turn be primarily a reflection of better residual blood flow in certain eyes before RON. Unfortunately, it is not always possible to distinguish between the ischemic and nonischemic forms of CRVO, although the presence of cotton wool spots, a substantial afferent papillary defect, or angiographic abnormalities can be helpful.3,8 Other investigators have also raised questions about the use of RON for CRVO. In a recently published clinical study, Horio and Horiguchi30 performed RON on 7 consecutive patients with CRVO and measured retinal blood flow before and 6 months after surgery. They found no significant alterations of blood flow after RON despite the fact that all eyes developed chorioretinal anastomoses. They suggested that vitreous removal alone rather than RON might account for any decrease in macular edema after the procedure, although this decrease could also represent the natural course of events after CRVO. Their results slightly differ from those from an earlier study by Nomoto et al,16 who also measured blood flow before and after RON using retinal circulation times (T50). Some degree of improvement in T50 occurred in about half of the patient eyes undergoing RON, and this result appeared to be related
to the development of chorioretinal anastomoses. Based on their results, they concluded that RON may not decompress the central retinal vein within the scleral outlet. Finally, in a comprehensive review article, Shahid et al31 found little evidence to support any therapeutic benefit from RON, optic nerve decompression, or sheathotomy alone applied to retinal venous occlusions. While the effects of RON were being studied, other surgeons took an alternative surgical approach to treat eyes with CRVO. D’Amico et al14 initially speculated that by puncturing the optic nerve head adjacent to the central retinal vein, the vein could decompress into the newly created space, possibly dislodging the thrombosis and promoting clinical resolution of the venous occlusion. Although this technique, called lamina puncture, in our opinion makes more biomechanical sense than does RON, it presumes an anterior location of the thrombus within the central retinal vein. In their paper, they found that the procedure did not reliably restore visual acuity in a pilot study of 20 patients who underwent lamina puncture. Furthermore, complications were not trivial.14 These authors also presented a review of published RON studies that
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Ophthalmology Volume 115, Number 1, January 2008 they found in the literature. From these data, they also concluded that RON for CRVO “is not an effective treatment for visual restoration.” Our study, focusing only on the biomechanical ramifications of RON, fully and firmly supports this conclusion. In conclusion, the underlying rationale for RON, that the procedure ameliorates the effects of CRVOs because of mechanical decompression of the vein, is seriously flawed. If this procedure results in a therapeutic benefit, we disagree that the effects are secondary to any mechanical considerations.
References 1. Baseline and early natural history report: the Central Vein Occlusion Study. Arch Ophthalmol 1993;111:1087–95. 2. Elman MJ. Thrombolytic therapy for central retinal vein occlusion: results of a pilot study. Trans Am Ophthalmol Soc 1996;94:471–504. 3. Hayreh SS. Radial optic neurotomy for central retinal vein occlusion. Retina 2002;22:374 –7. 4. Martinez-Jardon CS, Meza-de Regil A, Dalma-Weiszhausz J, et al. Radial optic neurotomy for ischaemic central vein occlusion. Br J Ophthalmol 2005;89:558 – 61. 5. Pe’er J, Folberg R, Itin A, et al. Vascular endothelial growth factor upregulation in human central retinal vein occlusion. Ophthalmology 1998;105:412– 6. 6. Guven D, Sayinalp N, Kalayci D, et al. Risk factors in central retinal vein occlusion and activated protein C resistance. Eur J Ophthalmol 1999;9:43– 8. 7. Green WR, Chan CC, Hutchins GM, Terry JM. Central retinal vein occlusion: a prospective histopathologic study of 29 eyes in 28 cases. 1981. Retina 2005;25(suppl):27–55. 8. Ip MS, Gottlieb JL, Kahana A, et al. Intravitreal triamcinolone for the treatment of macular edema associated with central retinal vein occlusion. Arch Ophthalmol 2004;122:1131– 6. 9. Hattenbach LO, Steinkamp G, Scharrer I, Ohrloff C. Fibrinolytic therapy with low-dose recombinant tissue plasminogen activator in retinal vein occlusion. Ophthalmologica 1998; 212:394 – 8. 10. Chen CH, Lai CH, Kuo HK. Laser chorioretinal venous anastomosis for progressive nonischemic central retinal vein occlusion. Chang Gung Med J 2005;28:866 –71. 11. Opremcak EM, Bruce RA, Lomeo MD, et al. Radial optic neurotomy for central retinal vein occlusion: a retrospective pilot study of 11 consecutive cases. Retina 2001;21:408 –15. 12. Opremcak EM, Bruce RA, Lomeo MD, et al. Radial optic neurotomy for central retinal vein occlusion: reply. Retina 2002;22:377–9. 13. Hayreh SS. Radial optic neurotomy for nonischemic central retinal vein occlusion [letter]. Arch Ophthalmol 2004;122: 1572–3. 14. D’Amico DJ, Lit ES, Viola F. Lamina puncture for central retinal vein occlusion: results of a pilot trial. Arch Ophthalmol 2006;124:972–7.
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15. Garciia-Arumii J, Boixadera A, Martinez-Castillo V, et al. Chorioretinal anastomosis after radial optic neurotomy for central retinal vein occlusion. Arch Ophthalmol 2003;121: 1385–91. 16. Nomoto H, Shiraga F, Yamaji H, et al. Evaluation of radial optic neurotomy for central retinal vein occlusion by indocyanine green videoangiography and image analysis. Am J Ophthalmol 2004;138:612–9. 17. Vonesh MJ, Cho CH, Pinto JV Jr, et al. Regional vascular mechanical properties by 3-D intravascular ultrasound with finite-element analysis. Am J Physiol 1997;272:H425–37. 18. Belli S, Eskitascioglu G, Eraslan O, et al. Effect of hybrid layer on stress distribution in a premolar tooth restored with composite or ceramic inlay: an FEM study. J Biomed Mater Res B Appl Biomater 2005;74:665– 8. 19. Mower WR, Baraff LJ, Sneyd J. Stress distributions in vascular aneurysms: factors affecting risk of aneurysm rupture. J Surg Res 1993;55:155– 61. 20. Stringfellow MM, Lawrence PF, Stringfellow RG. The influence of aorta-aneurysm geometry upon stress in the aneurysm wall. J Surg Res 1987;42:425–33. 21. Edwards ME, Good TA. Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation. Curr Eye Res 2001;23:215–25. 22. Friberg TR, Lace JW. A comparison of the elastic properties of human choroid and sclera. Exp Eye Res 1988;47:429 –36. 23. Friberg TR. The etiology of choroidal folds: a biomechanical explanation. Graefes Arch Clin Exp Ophthalmol 1989;227: 459 – 64. 24. Tao Y, Jiang YR, Li XX, et al. Fundus and histopathological study of radial optic neurotomy in the normal miniature pig eye. Arch Ophthalmol 2005;123:1097–101. 25. Wrede J, Varadi G, Volcker HE, Dithmar S. Radial optic neurotomy for central retinal vein occlusion— how deep should it be? [in German]. Ophthalmologe 2006;103:321– 4. 26. Schneider U, Inhoffen W, Grisanti S, et al. Chorioretinal neovascularization after radial optic neurotomy for central retinal vein occlusion. Ophthalmic Surg Lasers Imaging 2005; 36:508 –11. 27. Yamamoto S, Takatsuna Y, Sato E, Mizunoya S. Central retinal artery occlusion after radial optic neurotomy in a patient with central retinal vein occlusion. Am J Ophthalmol 2005;139:206 –7. 28. Samuel MA, Desai UR, Gandolfo CB. Peripapillary retinal detachment after radial optic neurotomy for central retinal vein occlusion. Retina 2003;23:580 –3. 29. Horio N, Horiguchi M. Central retinal vein occlusion with further reduction of retinal blood flow one year after radial optic neurotomy. Am J Ophthalmol 2005;139:926 –7. 30. Horio N, Horiguchi M. Retinal blood flow and macular edema after radial optic neurotomy for central retinal vein occlusion. Am J Ophthalmol 2006;141:31– 4. 31. Shahid H, Hossain P, Amoaku WM. The management of retinal vein occlusion: is interventional ophthalmology the way forward? Br J Ophthalmol 2006;90:627–39.
When retinal venous drainage is compromised, visual loss commonly occurs.1,2 Central retinal vein occlusion (CRVO) is the most visually devastating because venostasis after occlusion results in retinal thickening and macular edema, severely impairing retinal function. Treatment is often frustrating, partly because the etiology and pathophysiology of CRVO are not well understood.1,3 The Central Vein Occlusion Study revealed that there is a high degree of correlation between the initial and final visual acuity in affected eyes.1 Visual acuity reflects existing blood flow, with more ischemic eyes having a poorer initial vision as well as a poorer prognosis.1,2 Furthermore, 40% to 50% of ischemic eyes develop complications such as iris and anterior chamber angle neovascularization and secondary glaucoma.1 Clinicians have used several therapeutic options for CRVO with limited success.2– 4 Some strategies target the thrombus in the occluded vein. Such thrombus formation Originally received: September 27, 2006. Final revision: March 2, 2007. Accepted: March 6, 2007. Available online: June 4, 2007. Manuscript no. 2006-1092. 1 Department of Ophthalmology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania. 2 Mechanical Engineering Department, University of Pittsburgh School of Engineering, Pittsburgh, Pennsylvania. Presented in part at: Retina Society annual meeting, September 2004, Baltimore, Maryland. Supported in part by Research to Prevent Blindness, Inc., New York, New York. Correspondence to Thomas R. Friberg, MS, MD, Professor of Ophthalmology and Professor of Bioengineering, University of Pittsburgh, UPMC Eye Center, 203 Lothrop Street, Room 824, Pittsburgh PA 15213. E-mail: [email protected].
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occurs commonly, but whether it is a primary or secondary event is unclear.3 How such thrombi develop and conditions that increase risk have also been explored.5,6 The location of the typical thrombus formation along the vein is controversial,3,7 but in a substantial percentage of cases, the thrombus is located well away from the lamina cribrosa. Pharmacologic strategies for the treatment of CRVO include the injection of thrombolytic agents to dissolve or dislodge the thrombus, and the use of corticosteroids or other antiinflammatory drugs to address the associated macular edema.2,8,9 Alternate therapeutic approaches aim to bypass the thrombus by creating collateral blood flow.10 Relatively recently, Opremcak et al11 proposed that a scleral compartment or outlet syndrome exists in CRVO analogous to the “thoracic syndrome.” They described a surgical technique to decompress the central retinal vein by a single radial incision (radial optic neurotomy [RON]) placed at the edge of the optic nerve head.11 The rationale for RON as published is that it decompresses the venular flow resistance by relieving pressure in the compartment.12 The merits of such an approach have been challenged in the literature3,13,14 and from the podium (Friberg, Retina Society annual meeting, September 2004, Baltimore, Maryland). However, some suggest that RON could work by increasing collateral vessel formation or improving the hemodynamics within the affected vein.15,16 A randomized study of RON for CRVO would be difficult to execute and may well be inappropriate. Alternatively, we tested the basic physical hypothesis implicit in the RON procedure by modeling the biomechanical effects RON in a virtual eye, using a computer simulation technique—namely, finite element analysis.17 Finite element analysis is widely used to assist in the ISSN 0161-6420/08/$–see front matter doi:10.1016/j.ophtha.2007.03.013
Friberg et al 䡠 Biomechanical Assessment of Radial Optic Neurotomy design of aircraft and shell structures, and models the deformation of a structure subjected to load. The structure of interest is subdivided into a virtual meshwork of tiny 3-dimensional elements (volumes), each of which is subject to its own boundary conditions. A computer algorithm then performs thousands of calculations to determine stresses and strains at key points or nodes. This type of analysis has been used previously in biological structures,18 and in particular, in the evaluation of stress in aneurysms.19,20 Recently, finite element analysis has been applied to biomechanics of the lamina cribrosa of the eye.21 Implicit in finite element investigations, boundary conditions must be set that are consistent with the dimensional and elastic properties of the elements. The individual elements are characterized by equations to define the stiffness properties of each element, and these elements are then combined piece by piece to determine the stiffness properties of the entire structure as well as the deformations under loading conditions.17 Stiffness in biomechanical terms is expressed by a material’s modulus of elasticity or E, which is given in units of force per unit area. E relates how a material of length (L) changes in dimension if a force (F) is applied perpendicular to its cross-section. Force (F) divided by the cross-sectional area of the material or stress (force/ unit area) is related to the deformation of the material or strain (change in length/original length) by the modulus of elasticity (E). In biomechanical terms, E equals stress divided by strain. Very elastic materials are those with a smaller modulus. The structures of interest in our model are the sclera, cribriform plate, optic nerve sheath, and optic nerve. The physical properties, pressure loads on the tissues, and inherent elastic parameters were each assumed to encompass a range in values. This then simulated a diversity of clinical conditions, and demonstrated how the eye might change under these perturbations. We analyzed RON in this context.
Materials and Methods The globe, optic nerve head, and optic nerve were divided into small regions or elements and, by approximating the displacements in each element, a stiffness matrix was derived computationally. The stiffness matrices for all elements and given loads (pressures) were assembled, and equations were derived and solved to calculate the displacements at the vertices of the elements (nodes). The strains and stresses were determined from these displacements. We used ALGOR V19 software (Algor Inc, Pittsburgh, PA) to perform the computations for the human eye.
0.3 mm and the thickness of the lamina cribrosa was set at 0.5 mm. The length of the optic nerve segment as modeled was 1.25 mm, as the entire length of the nerve has decreasing influence the further away it is from its insertion into the posterior globe. The optic cup diameter and depth were modeled at 0.9 mm and 0.25 mm, respectively (Fig 1C). The width and depth of the RON incision were each taken to be 0.8 mm. These parameters were chosen to make the nerve head compliant and thus more amenable to the potential effects of radial optic neuropathy.
Material Properties The material properties of all tissues were assumed to be linearly elastic, isotropic, and almost incompressible with Poisson’s ratio equal to 0.49. Based on these assumptions, the only parameter necessary to further describe the stiffness of each tissue was the modulus of elasticity (Young’s modulus). The modulus for scleral tissue Es was taken to be Es ⫽ 2.5 MPa based on our earlier work.22,23 Although there is some uncertainty regarding the exact mechanical properties of the lamina cribrosa,21 we used a modulus of elasticity of Elc ⫽ 0.25 MPa, which is approximately the mean value for human tissue. Because there are also limited data regarding the material properties of the optic nerve, values for both a stiff and compliant tissue were assigned in the analysis. For the stiff neural tissue, the modulus En was assumed to be 4 times that of the sclera (En ⫽ 4Es) and the compliant modulus was assumed to be one tenth of the sclera value (En ⫽ 0.1Es).
Loads and Boundary Conditions A uniform intraocular pressure (IOP) was assumed to be present on all internal surfaces of the eye, and a uniform and constant venous pressure was applied to the inner walls of the vein as shown in Figure 1B. The external surfaces of all tissues were estimated to be subject to 0 mmHg pressure, again to favor RON efficacy. The physiologic ranges of values used for the IOP were 10, 25, and 35 mmHg; 50 and 75 mmHg were used for the central retinal venous pressures. Different constraints on displacements were modeled. In the model before RON was virtually applied, all the nodes on the cut plane (plane of symmetry) were constrained in the x direction. That is, the nodes were not allowed to displace out of this plane. For models that had undergone a virtual RON procedure, the nodes in the area of the RON incision (on the plane of symmetry) were not constrained to the y–z plane, allowing them to move up out of the plane of symmetry (toward or away from the center of the eye). Figure 1C shows the position of the incision with respect to the optic nerve head. The interfaces between the other different tissues were taken to be completely bonded and thus were not allowed to develop any separations.
Results Geometric Assumptions Our model eye was virtually constructed to contain the globe itself, a segment of the optic nerve, and the lamina cribrosa. The geometries are 3-dimensional; but, because of symmetry, only one half of each structure generally needed to be modeled for computational purposes. We assumed that the globe was a hemispherical shell with an inner diameter of 20 mm and an outer diameter of 22 mm (scleral thickness ⫽ 1 mm). The diameter of the optic nerve was assigned to be 1.5 mm and the central opening for the vein passing through the nerve was assumed to be 0.3 mm (Fig 1A). The central venous lumen diameter was assumed to be just under
Our model showed that the lumen shape of the central retinal vein before RON under changing boundary conditions was always circular, as expected because of symmetry of the globe and nerve head. However, after RON, the tissue has been relaxed more in one direction than the other, and hence, the lumen becomes slightly elliptical in shape. The quantitative results showing the effect of RON for the various pressures and material properties are shown graphically in Figure 2. These curves give the ratio of the diameter of the lumen of the vein after RON to the diameter without RON in the stated direction, and the data vary with respect to the applied IOP. The 4 curves in the graph correspond to different values of
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Figure 1. A, Model geometry of the optic nerve head showing the dimensional assumptions at baseline. B, The intraocular and venous pressures impinging upon the model elements are assumed to be applied as shown. C, The model as it appears from inside the virtual vitreous cavity. The radial optic neurotomy (RON) incision has been modeled to straddle the peripheral edge of the optic nerve head and is assumed to be 0.8 mm long (along the y axis). The plane of symmetry, for analysis sake, is shown by the vertical dotted line. Deformations of the tissue at the RON incision location are allowed in the x and y directions, as well as perpendicular to the nerve head or z direction (toward or away from the virtual center of the vitreous cavity).
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Figure 2. A, Ratio of the central lumen diameter after radial optic neurotomy (RON) to the central lumen diameter before RON in the x direction (per Fig 1C) at the optic nerve insertion. The plot is a function of the intraocular pressure (IOP) for different nerve moduli of elasticities and venous pressures within the central retinal vein (VPs; Fig 1B); Es is the scleral modulus and En is the modulus of the nerve tissue. A higher modulus indicates a stiffer material. B, Ratio of central lumen diameter after RON to central lumen diameter before RON in the y direction at the nerve head as a function of IOP for different nerve moduli and intraocular and intravenous pressures. The flatter slopes of the curve (compared with A) illustrate that only a very small change in dimension occurs in the radial (y) direction compared to the circumferential (x) direction.
nerve elastic modulus (En ⫽ 4Es and En ⫽ 0.1Es and venous pressure of 50 and 75 mmHg). Figure 2A gives the normalized x-direction inner diameter and Figure 2B gives the normalized y-direction inner diameter of the lumen where the central retinal vein enters the nerve. Figure 3 shows the overall geometry of our assembled finite element model as well as a magnified view of the optic nerve at its scleral insertion. Figure 4 shows the geometric deformation of nerve tissue at the bottom of the optic cup (Fig 1) before and after RON for the case of En ⫽ 4Es and IOP and central venous pressure ⫽ 50 mmHg.
Discussion Although RON has been advocated as an effective treatment for visual loss from CRVO, we critically evaluated the potential biomechanical effect of RON on the optic nerve head and major vessels in the region. To our knowledge, RON has always been performed as part of a vitreoretinal procedure that includes pars plana vitrectomy. We focused, however, on only the mechanical
effect of the procedure, because the presence or absence of vitreous gel makes no real difference to our approach. (It could, however, alter the clinical results of the RON procedure by, for instance, altering the oxygenation within the vitreous cavity.) We found that the average RON-induced decompression (maximum increase in the central retinal vein lumen diameter) was a paltry 4%. That is, the diameter of the central venous lumen under the best of conditions could only increase 4% (y-direction). This is accompanied by only a very small increase (1.4%) in the perpendicular direction (x) in the central lumen diameter. We find it extremely unlikely then that any meaningful physiologic mechanical advantage can be gained by the radial cut itself. Only if the sclera was both extremely elastic (low modulus of elasticity) and extremely thin would we expect a possible potential benefit from severing a “fibrous ring.” However, on the contrary, the sclera is tough and rather thick and it does not readily change diameter with changes in IOP.22,23 Furthermore, the
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Figure 3. Full finite-element model of the globe and optic nerve inserting within it. The grid lines show the individual elements. The optic nerve region is shown in more detail below. Each element is treated separately.
expansion of the sclera at the optic nerve is confined by the relatively solid architecture of the optic nerve itself.24 The cribriform plate is relatively stiff, but on the other hand, it contains a meshwork of holes. Some argue that such a meshwork thus allows for expansion of the plate after the RON procedure. However, any expansion of this meshwork is mechanically constrained by the material that fills the holes. In vivo, ganglion cell axons pass through the cribriform plate on their way to the geniculate ganglion. Because the axons are composed of rather incompressible biological material, we argue that the meshwork would not freely expand. Some authors have speculated that the apparent selective clinical success of RON depends on the presurgical state of the retinal vasculature and that RON favors eyes that are less ischemic.3 Another hypothesis is that RON promotes alternative collateral flow by creating choroidal anastomoses4 to the central retinal vein. However, such collaterals do
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not necessarily form at a rate significantly higher than in the natural course of the disease.3,4 The location and depth of the RON incision25 have also been discussed as influencing efficacy. From a biomechanical perspective, we suggest that the location and depth are unimportant, because the effect of RON on lumen size is minuscule. Although our model did not specifically consider the late effects of healing and fibrosis at the site of the RON incision, our model indicates that the chance of these late changes affecting lumen size is remote. Our study raises serious questions about the potential efficacy of this invasive technique. Furthermore, the associated complications are not trivial and have been extensively documented. These include arterial occlusions, retinal detachments, loss of visual field, choroidal neovascularization, and a further decrease in venous blood flow.4,26 –29 Moreover, the risk of interruption of the optic nerve head arterial circle must be balanced against historically claimed success.3
Friberg et al 䡠 Biomechanical Assessment of Radial Optic Neurotomy
Figure 4. Top, Color-coded finite element plot of deformations of the optic nerve tissue in the composite model without the radial optic neurotomy (RON) incision, assuming modulus of the nerve tissue (En) ⫽ 4Es (scleral modulus) and that the intraocular pressure (IOP) and central venous pressure equal 50, parameters which would favor the mechanical effect of RON. Only the nerve tissue is shown here, for clarity. The upper surface represents the bottom of the optic cup, where the canal for the retinal vein begins. The deformations are secondary to the baseline IOP as well as other pressures on the optic nerve inserted into the globe. Note the circumferential symmetry. Bottom, Plot of the deformed geometry of the optic nerve after the RON incision at the same location within the eye and under the same conditions as above. The change in the lumen diameter is negligible.
Such success may in turn be primarily a reflection of better residual blood flow in certain eyes before RON. Unfortunately, it is not always possible to distinguish between the ischemic and nonischemic forms of CRVO, although the presence of cotton wool spots, a substantial afferent papillary defect, or angiographic abnormalities can be helpful.3,8 Other investigators have also raised questions about the use of RON for CRVO. In a recently published clinical study, Horio and Horiguchi30 performed RON on 7 consecutive patients with CRVO and measured retinal blood flow before and 6 months after surgery. They found no significant alterations of blood flow after RON despite the fact that all eyes developed chorioretinal anastomoses. They suggested that vitreous removal alone rather than RON might account for any decrease in macular edema after the procedure, although this decrease could also represent the natural course of events after CRVO. Their results slightly differ from those from an earlier study by Nomoto et al,16 who also measured blood flow before and after RON using retinal circulation times (T50). Some degree of improvement in T50 occurred in about half of the patient eyes undergoing RON, and this result appeared to be related
to the development of chorioretinal anastomoses. Based on their results, they concluded that RON may not decompress the central retinal vein within the scleral outlet. Finally, in a comprehensive review article, Shahid et al31 found little evidence to support any therapeutic benefit from RON, optic nerve decompression, or sheathotomy alone applied to retinal venous occlusions. While the effects of RON were being studied, other surgeons took an alternative surgical approach to treat eyes with CRVO. D’Amico et al14 initially speculated that by puncturing the optic nerve head adjacent to the central retinal vein, the vein could decompress into the newly created space, possibly dislodging the thrombosis and promoting clinical resolution of the venous occlusion. Although this technique, called lamina puncture, in our opinion makes more biomechanical sense than does RON, it presumes an anterior location of the thrombus within the central retinal vein. In their paper, they found that the procedure did not reliably restore visual acuity in a pilot study of 20 patients who underwent lamina puncture. Furthermore, complications were not trivial.14 These authors also presented a review of published RON studies that
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Ophthalmology Volume 115, Number 1, January 2008 they found in the literature. From these data, they also concluded that RON for CRVO “is not an effective treatment for visual restoration.” Our study, focusing only on the biomechanical ramifications of RON, fully and firmly supports this conclusion. In conclusion, the underlying rationale for RON, that the procedure ameliorates the effects of CRVOs because of mechanical decompression of the vein, is seriously flawed. If this procedure results in a therapeutic benefit, we disagree that the effects are secondary to any mechanical considerations.
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