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Show Finite Element Modeling of Optic Chiasmal Compression Xiaofei Wang, MSc, Andrew J. Neely, PhD, Gawn G. McIlwaine, MB, FRCOphth, Murat Tahtali, PhD, Thomas P. Lillicrap, BSc, Christian J. Lueck, PhD, FRACP Background: The precise mechanism of bitemporal hemi-anopia is still not clear. Our study investigated the mechanism of bitemporal hemianopia by studying the biomechanics of chiasmal compression caused by a pitui-tary tumor growing below the optic chiasm. Methods: Chiasmal compression and nerve fiber interaction in the chiasm were simulated numerically using finite element modeling software. Detailed mechanical strain distributions in the chiasm were obtained to help understand the mechanical behavior of the optic chiasm. Nerve fiber models were built to determine the relative difference in strain experienced by crossed and uncrossed nerve fibers. Results: The central aspect of the chiasm always experi-enced higher strains than the peripheral aspect when the chiasm was loaded centrally from beneath. Strains in the nasal (crossed) nerve fibers were dramatically higher than in temporal (uncrossed) nerve fibers. Conclusions: The simulation results of the macroscopic chiasmal model are in agreement with the limited experimental results available, suggesting that the finite element method is an appropriate tool for analyzing chiasmal compression. Although the microscopic nerve fiber model was unvalidated because of lack of experimental data, it provided useful insights into a possible mechanism of bitemporal hemianopia. Specif-ically, it showed that the strain difference between crossed and uncrossed nerve fibers may account for the selective nerve damage, which gives rise to bitemporal hemianopia. Journal of Neuro-Ophthalmology 2014;34:324-330 doi: 10.1097/WNO.0000000000000145 © 2014 by North American Neuro-Ophthalmology Society The optic chiasm has been an object of interest for many centuries (1). Although the concept of hemidecussa-tion is now universally accepted, there are still many unan-swered questions. All neuro-ophthalmologists are familiar with the concept that compression of the chiasm by a lesion such as a pituitary adenoma can give rise to varying degrees of a "bitemporal" pattern of visual loss, but the question of why this should be so has yet to be satisfactorily answered. To produce bitemporal field loss, there must be selective damage to the crossing fibers, but why crossing fibers are selectively vulnerable remains an unanswered question. To date, several studies have investigated this variously suggesting that the causative factor is stretching of the chiasm (2), alter-ation in its blood supply (3), or a direct effect of pressure (4). All these explanations rely on anatomy, that is, the fact that the crossing fibers pass through the center of the chiasm, which would bear the brunt of any of these abnormalities. Any or all of these factors could contribute, but all will produce a gradation across the chiasm: the magnitude will be greatest in the center and gradually decline towards the edges. This should result in a graded visual field abnormality from nasal to temporal fields, not an absolute vertical cutoff, or "step," as occurs in a complete bitemporal hemianopia. McIlwaine et al (5) pointed out that crossing fibers would potentially be more vulnerable than fibers running in parallel simply because they cross. Crossing results in a much smaller contact area between neurons and, there-fore, a much greater stress on the crossing fibers for any given compressive force applied to the chiasm (5). Recent studies have looked at factors that can predict outcome after treatment, such as the degree of nerve fiber loss at the optic disc (6,7). A better understanding of the exact mechanism involved has significant implications for management and prognosis and may have more wide-reaching implications for other forms of neural compression involving nerve fibers traveling in different directions (e.g., in the spinal cord). Unfortunately, technical and ethical constraints mean that it is not possible to test this "crossing hypothesis" directly in vivo. However, it is possible to use computerized models to improve our understanding and devise clinically feasible experiments. School of Engineering and Information Technology (XW, AJN, MT, TPL), University of New South Wales, Canberra, Australia; Department of Ophthalmology, Queen's University Belfast (GGM), Belfast, United Kingdom; Belfast Health and Social Care Trust (GGM), Belfast, United Kingdom; Department of Neurology, The Canberra Hospital (TPL, CJL), Canberra, Australia; and Medical School, Australian National University (TPL, CJL), Canberra, Australia. The authors report no conflicts of interest. Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the full text and PDF versions of this article on the journal's Web site (www. jneuro-ophthalmology.com). Address correspondence to Xiaofei Wang, MSc, School of Engi-neering and Information Technology, UNSW Canberra, Australian Defence Force Academy, Northcott Drive, Canberra ACT 2612, Australia; E-mail: Xiaofei87@live.com 324 Wang et al: J Neuro-Ophthalmol 2014; 34: 324-330 Original Contribution Copyright © North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited. We have used finite element modeling (FEM), a tool regularly used by engineers to investigate complex, 3-dimensional struc-tures such as aircraft and engines (8) to model the chiasm and investigate this hypothesis (See Supplemental Digital Con-tent, Text, http://links.lww.com/WNO/A105). FEM is increasingly being used in different areas of clinical medicine as an adjunct to other forms of clinical research (9-11). FEM involves breaking down a 3-dimensional structure into a very large number of component units or cells. The individual units are "populated" by information about ana-tomical structure and physical properties (e.g., elastic modu-lus and Poisson ratio) (12). By means of solving a very large number of simultaneous equations, it is possible to calculate the theoretical response to an external disturbance (e.g., change in temperature or pressure), which can be studied looking at of the entire structure or, alternatively, its compo-nent parts. The number of cells is clearly critical-too few and the model will be too coarse to provide any useful infor-mation; too many and the model becomes insoluble because of the computing time involved. Simplifying assumptions are usually necessary to achieve an appropriate compromise. Of course, any model must be validated against "real" data to confirm that it offers an accurate representation of reality. We describe a FEM model of the optic chiasm and then describe limited validation using clinical information in the literature. Implications of the model are discussed, along with avenues for future testing. METHODS Development of the Model Anatomy Two models were constructed. The first was a simplified macroscopic representation of the optic chiasm with adjacent pituitary tumor (Fig. 1A), and the second was a microscopic representation of crossed and uncrossed nerve fibers within the chiasm (Fig. 1C). The shape and dimen-sions of the macroscopic model were derived from pub-lished data (13-16) but, for the sake of simplicity, the plane of the chiasm was assumed to be horizontal and per-pendicular to tumor growth. Optic nerves and tracts were modeled as elliptical in cross-section with major radii of 3.0 mm and minor radii of 1.75 mm. The chiasm was assumed to be 14.0 mm wide, 3.5 mm high, and 8.0 mm in anteroposterior extent, and the angles between the 2 optic nerves and the 2 optic tracts were both set at 75°. All structures were assumed to be covered by a layer of pia mater with 0.06 mm thickness (17). The pituitary tumor was modeled as a hollow hemisphere with an external diameter of 20 mm with an outer layer of 0.5 mm thickness. These dimensions were chosen to conform to the details of the Foley catheter balloon used in the experiment by Kosmorsky et al (4). Kosmorsky et al dissected autopsy specimens and inserted a Foley catheter directly under the chiasm, thereby FIG. 1. A. The macroscopic model of the optic chiasm; (B) demonstration of paths A and B, as referred to in the text; symmetry constraints allowed reduction in computa-tional time by the use of a quarter model, as illustrated in the top left corner. C. Uncrossed and crossed nerve fibers in the microscopic model; the bottom faces and cross sec-tions (indicated by white arrows) were constrained by fric-tionless supports. The horizontal displacement of the vertical centerline of the microscopic model was con-strained. OC, optic chiasm; ON, optic nerve; OT, optic tract. Wang et al: J Neuro-Ophthalmol 2014; 34: 324-330 325 Original Contribution Copyright © North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited. enabling them to use balloon inflation to simulate a growing pituitary tumor. This study was used for the purposes of validating the model. At a microscopic level, 2 additional FEM models were established, 1 for nasal (crossed) fibers, the other for temporal (uncrossed) fibers (Fig. 1C, analogous to McIlwaine et al (5)). The variation in nerve fiber diameter in the chiasm was ignored for the sake of simplicity and nerve fiber diameter was set at 1 mm (18). Crossing of fibers was assumed to occur at precisely 90°, whereas parallel fibers were assumed to be precisely parallel. Physical Properties Accurate data about the mechanical properties of living biological tissues are scarce because of the practical difficulties involved in their measurement. For the purposes of this study, material properties at both macroscopic and microscopic levels were derived from the literature (17,19-21). All materials were assumed to be isotropic to have a density of 1000 kg/m3 and to have linear elastic material properties characterized by elastic moduli (E) and Poisson ratios (n) as shown in Table 1. Mate-rial properties of individual nerve fibers are not available in the literature, so, although optic nerve fibers are myelinated and therefore surrounded by a sheath, we considered nerves to be homogeneous for the purposes of the microscopic model. Accordingly, the same properties were used as in the macro-scopic model of the chiasm. Simulations The model was created, meshed, and postprocessed using commercial FEM software (ANSYS 13.0; Ansys, Inc., Canonsburg, PA). The macroscopic and microscopic models were discretized into hexahedron-dominant meshes with 47,112 and 19,880 quadratic elements, respectively. Preliminary studies demonstrated that this mesh density was sufficient to provide mesh-independent results. Because the model of the chiasm was symmetrical in 2 planes, computational time was reduced by restricting calculations to one-fourth of the entire chiasm (Fig. 1B). The boundary conditions of the simulation were as follows: the distal faces of the optic nerves and tracts were fixed to represent connections to the optic canals and brain, respectively. The tumor was fixed at its inferior surface. Contact between the tumor and the chiasm was considered to be frictionless but the core tissues of the optic nerve, chiasm, and tract were bonded to their pial sheath. Compressive pressure was applied by inflating the tumor from below. Pressure was applied in 5 discrete steps up to 0.145 MPa, resulting in elevation of the chiasm by 0.11h, 0.26h, 0.40h, 0.63h, and 0.94h (where h was the height of the chiasm, i.e., 3.5 mm). These values were chosen with a view to subsequent validation because they were biologically plausible and similar to the elevations seen in the video accompanying the experiment by Kosmorsky et al (4). Local pressure values derived from the macroscopic model along path A (Fig. 1B) were then applied to the 2 microscopic nerve fiber models to investigate the strain in the nerve fibers as a function of whether the nerves were crossed or uncrossed. The loading transition was one-way in this initial study, that is, only the outputs of the macro-scopic model were applied to the microscopic model. Output of the Model Numerical values were given in units of von Mises strain. This unit is a widely-used measure (22,23), which takes account of both absolute magnitude and orientation of strain as a single value. Pressure (22) was also calculated for the sake of validation (see "Validation of the Model"). The strain values were plotted along 2 lines, one running from the geometric center of the chiasm to its lateral mar-gin and the other running vertically through the geometric center (paths A and B, respectively, in Fig. 1B). Output of the microscopic model was initially calculated along path A for both crossed and uncrossed fibers for the condition of maximum elevation (i.e., 0.94h). The detailed nerve fiber distribution in the optic chiasm is still unclear. It is generally believed that the nasal nerve fibers cross in the central part of the chiasm, whereas the temporal fibers are routed in a roughly parallel manner in the peripheral part of the chiasm (24). Accordingly, the output of the crossed model was applied to the central half of path A (assumed to contain the nasal, crossed fibers), whereas the output of the parallel model was applied to the lateral half (assumed to contain the temporal, uncrossed fibers). The output of the microscopic model was compared with the findings of a study on guinea pig optic nerves (25), which was able to define 3 strain thresholds of axonal injury: • the level below which no axon would be injured (TC), • the level above which all axons would be injured (TL), and TABLE 1. Assumed mechanical properties of tissues used in the finite element modeling simulations Tissue Tissue on Which Model Based Elastic Modulus (E) (MPa) Poisson's Ratio (n) References Sheath Human pia mater 3.0 0.49 Sigal et al (17); Zhivoderov et al (19) Optic nerve Porcine brain 0.03 0.49 Miller (20) Tumor Human sclera 5.5 0.47 Kobayashi et al (21) 326 Wang et al: J Neuro-Ophthalmol 2014; 34: 324-330 Original Contribution Copyright © North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited. • the level which provided the best discrimination between injured and uninjured axons (TB). Validation of the Model As stated, very few published experiments have looked at chiasmal compression from a mechanical perspective. We could only find one such study (4), which provided lim-ited measured data against which the current model could be validated. Pressure values were obtained and compared with the measured pressures from the study by Kosmorsky et al (4). Unfortunately, these authors did not state the precise locations of their transducers. The central transducer was assumed to be at the center of the chiasm, whereas the peripheral transducer was assumed to be at 4.6 mm from the center (See Supplemental Digital Content, Video, http://links.lww.com/WNO/A106). RESULTS Output of the Model Figure 2 shows the macroscopic deformation of the chiasm as a result of increasing inflation pressure in the tumor along with contours of von Mises strain distribution. The degree of displacement refers to the elevation of the base of the chiasm as a function of the baseline height of the chiasm (h = 3.5 mm). The output of the model is also shown as a short animated sequence (See Supplemental Digital Content, Video, http://links.lww.com/WNO/A106). Figure 3A, B show the von Mises strain distribution along paths A and B (Fig. 1B) of the macroscopic model because the chiasm was elevated by the growing tumor. Strain was always highest in the center of the chiasm and gradually decreased with increasing horizontal distance from the center; but, as tumor size increased, the point of FIG. 2. A-E. The von Mises strain distribution in the deformed 1/4 chiasm (Fig. 1B) as a result of increasing tumor size in 5 steps (see text for details). The location of the undeformed chiasm is shown as a frame of black lines and the scale is given in (F). h, height of chiasm (3.5 mm). Wang et al: J Neuro-Ophthalmol 2014; 34: 324-330 327 Original Contribution Copyright © North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited. maximum strain moved upwards along path B. Assuming that nasal (crossed) fibers were located in the central half of path A, the strain in the region of the crossed fibers was greater than that in the uncrossed fibers at any level of chiasmal elevation. However, the transition was always gradual with no clear step. Figure 3C shows the results of the microscopic model calculated at maximal chiasmal elevation (0.94h). The von Mises strain is plotted for both crossed and uncrossed nerve fibers along path A. Crossed nerve fibers clearly experienced higher strain levels than uncrossed nerve fibers at any posi-tion along path A. Figure 4A plots the output of the microscopic model (Fig. 3C) along with the 3 thresholds of reduced nerve function reported by Bain (25) in her experiment on guinea pig optic nerves. To account for the demarcation between the response of the nasal and temporal fibers, the bold line illustrates the effect of passing from crossed (i.e., nasal) fibers to uncrossed (i.e., temporal) fibers while moving from the center of the chiasm towards the periphery. Thus, the influence of fiber-crossing angle on strain as determined from the microscopic model is superimposed on the spatial distribution of strain from the macroscopic model. At the indicated level of TB, there is a clear difference between the strain experienced by crossed and uncrossed fibers that could explain the sharp vertical cutoff of vision loss in bitemporal hemianopia. Validation of the Model Figure 4B shows the calculated values of pressure along path A derived from the model along with the individual pressure measurements reported by Kosmorsky et al (4). There is a certain variability in the experimental results, which may reflect anatomical or material property differ-ences between chiasms, variation in catheter position or elevation, or variation in transducer location. Neverthe-less, the experimental values and trends are very similar to the values generated by the model. DISCUSSION In this study, FEM was used to simulate chiasmal compression to estimate the strain distribution across the chiasm and so gain a clearer understanding of the strains experienced by individual nerve fibers. To our knowledge, this is the first attempt to develop a 3-dimensional model of chiasmal compression to investigate the strain progression and distribution in detail. The results show that strain is higher in the center of the chiasm where the nasal (crossed) fibers are situated and, moreover, that the calculated pressures obtained from the model are consistent with the pressures measured experi-mentally by Kosmorsky et al (4). We previously performed a parametric study (26), which showed that varying the material properties resulted in quantitative, but not qualita-tive, changes of the results in the chiasmal model. The gradual upwards progression of strain distribution with increasing pressure would explain why upper visual fields are typically affected first (Fig. 3B), but this pressure alone cannot induce the step needed to explain bitemporal hemi-anopia because there is a gradual falloff of pressure towards the periphery. However, the model's results demonstrate that strain is higher if nerve fibers cross each other than if they run in parallel, and this difference may explain the FIG. 3. Strain values along path A (A) and path B (B) when the chiasm was elevated to various levels; (C) calculated maximum cross-sectional strain for uncrossed and crossed nerve fibers along path A. h, height of chiasm (3.5 mm). 328 Wang et al: J Neuro-Ophthalmol 2014; 34: 324-330 Original Contribution Copyright © North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited. observed step or spatial discontinuity in vision loss. These FEM results would be extremely difficult (or impossible) to obtain by in vivo experimental approaches, highlighting the potential benefits of using FEM. It is important to point out that because the models could not be validated, they cannot yet be used to predict strain in the chiasm or the nerve fibers. The presented strain estimates can only serve as a computa-tional experiment that must be further investigated and val-idated using experimental measures to provide certainty. The degree to which a model represents "real life" is critically dependent on accurate information about anatomy and physical properties; for this sort of model, limited knowledge of the physical properties of living biological tissue(s) is usually the greatest barrier. This model is based on a number of assumptions, both anatomical and physical. We have assumed that nerve fiber size is uniform, that crossing fibers are restricted to the center of the chiasm, that nerves travel individually, that nerve-fiber crossings occur at 90°, and that the maximal pressure is located at the geometric center of the chiasm. Similarly, we have used mechanical properties extrapolated from other studies, assumed that all chiasmal tumors have the same mechanical properties, and that the elastic prop-erties of the tissues can be described in simple linear terms, whereas most biological tissues are anisotropic and demon-strate viscoelastic or hyperelastic properties. This model does not address the precise mechanism of interruption of nerve impulse conduction at an axonal level for which there are several possible mechanisms including disrup-tion of ion channels, demyelination, and/or frank axonal transection. Further refinement of the model may allow increased understanding of which of these mechanisms could be occurring in a particular patient, which would have potential implications for prognosis and, potentially, management. In summary, this model has shown that it is possible to simulate the effects of chiasmal compression in a way that seems to be clinically valid. It has shown that the differential effects of pressure on crossed and uncrossed fibers can explain the phenomenon of bitemporal hemianopia. 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