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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
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  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 themechanism of bitemporal hemianopia by studying thebiomechanics of chiasmal compression caused by a pitui-tary tumor growing below the optic chiasm. Methods:  Chiasmal compression and nerve  󿬁 ber interactionin the chiasm were simulated numerically using  󿬁 niteelement modeling software. Detailed mechanical straindistributions in the chiasm were obtained to help understandthe mechanical behavior of the optic chiasm. Nerve  󿬁 ber models were built to determine the relative difference instrain experienced by crossed and uncrossed nerve  󿬁 bers. Results:  The central aspect of the chiasm always experi-enced higher strains than the peripheral aspect when thechiasm was loaded centrally from beneath. Strains in thenasal (crossed) nerve  󿬁 bers were dramatically higher than intemporal (uncrossed) nerve  󿬁 bers. Conclusions:  The simulation results of the macroscopicchiasmal model are in agreement with the limited experimentalresults available, suggesting that the  󿬁 nite element method isan appropriate tool for analyzing chiasmal compression.Although the microscopic nerve  󿬁 ber model was unvalidatedbecauseoflackofexperimentaldata,itprovidedusefulinsightsinto a possible mechanism of bitemporal hemianopia. Specif-ically, it showed that the strain difference between crossed anduncrossed nerve  󿬁 bers may account for the selective nervedamage, which gives rise to bitemporal hemianopia. Journal of Neuro-Ophthalmology 2014;0:1 – 7doi: 10.1097/WNO.0000000000000145© 2014 by North American Neuro-Ophthalmology Society T  he 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 lesionsuch as a pituitary adenoma can give rise to varying degreesof a   “ bitemporal ”  pattern of visual loss, but the question of  why this should be so has yet to be satisfactorily answered.To produce bitemporal  󿬁 eld loss, there must be selectivedamage to the crossing   󿬁 bers, but why crossing   󿬁 bers areselectively vulnerable remains an unanswered question. Todate, 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 thatthe crossing   󿬁 bers 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 willproduce a gradation across the chiasm: the magnitude will begreatest in the center and gradually decline towards the edges.This should result in a graded visual  󿬁 eld abnormality fromnasal to temporal  󿬁 elds, not an absolute vertical cutoff, or  “ step, ”  as occurs in a complete bitemporal hemianopia.McIlwaine et al (5) pointed out that crossing   󿬁 bers would potentially be more vulnerable than  󿬁 bers running in parallel simply because they cross. Crossing results ina much smaller contact area between neurons and, there-fore, a much greater stress on the crossing   󿬁 bers for any given compressive force applied to the chiasm (5). Recentstudies have looked at factors that can predict outcome after treatment, such as the degree of nerve  󿬁 ber loss at the opticdisc (6,7). A better understanding of the exact mechanisminvolved has signi 󿬁 cant implications for management and prognosis and may have more wide-reaching implicationsfor other forms of neural compression involving nerve  󿬁 berstraveling in different directions (e.g., in the spinal cord).Unfortunately, technical and ethical constraints mean that itis not possible to test this  “ crossing hypothesis ”  directly in vivo.However, it is possible to use computerized models to improveour 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, UnitedKingdom; Belfast Health and Social Care Trust (GGM), Belfast, UnitedKingdom; Department of Neurology, The Canberra Hospital (TPL,CJL), Canberra, Australia; and Medical School, Australian NationalUniversity (TPL, CJL), Canberra, Australia.The authors report no con 󿬂 icts of interest.Supplemental digital content is available for this article. Direct URLcitations 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, AustralianDefence Force Academy, Northcott Drive, Canberra ACT 2612, Australia; E-mail: Xiaofei87@live.com  Wang et al:  J Neuro-Ophthalmol 2014  ; 0: 1-7  1 Original Contribution Copyright     North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited.   We have used   󿬁 nite 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 isincreasingly being used in different areas of clinical medicineas an adjunct to other forms of clinical research (9 – 11).FEM involves breaking down a 3-dimensional structureinto a very large number of component units or cells. Theindividual 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 largenumber of simultaneous equations, it is possible to calculatethe 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 becauseof the computing time involved. Simplifying assumptions areusually necessary to achieve an appropriate compromise. Of course, any model must be validated against  “ real ”  data tocon 󿬁 rm that it offers an accurate representation of reality. We describe a FEM model of the optic chiasm and thendescribe limited validation using clinical information in theliterature. Implications of the model are discussed, along  with avenues for future testing. METHODS Development of the Model   Anatomy  Two models were constructed. The  󿬁 rst was a simpli 󿬁 ed macroscopic representation of the optic chiasm withadjacent pituitary tumor (Fig. 1A), and the second wasa microscopic representation of crossed and uncrossed nerve 󿬁 bers 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, theplane of the chiasm was assumed to be horizontal and per-pendicular to tumor growth. Optic nerves and tracts weremodeled as elliptical in cross-section with major radii of 3.0 mm and minor radii of 1.75 mm. The chiasm wasassumed to be 14.0 mm wide, 3.5 mm high, and 8.0 mmin anteroposterior extent, and the angles between the 2optic 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 wasmodeled as a hollow hemisphere with an external diameter of 20 mm with an outer layer of 0.5 mm thickness. Thesedimensions were chosen to conform to the details of theFoley 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 thetext; symmetry constraints allowed reduction in computa-tional time by the use of a quarter model, as illustrated inthe  top left corner  .  C . Uncrossed and crossed nerve  󿬁 bers inthe microscopic model; the bottom faces and cross sec-tions (indicated by   white arrows ) were constrained by fric-tionless supports. The horizontal displacement of thevertical centerline of the microscopic model was con-strained. OC, optic chiasm; ON, optic nerve; OT, optic tract. 2  Wang et al:  J Neuro-Ophthalmol 2014  ; 0: 1-7 Original Contribution Copyright     North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited.  enabling them to use balloon in 󿬂 ation 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 wereestablished, 1 for nasal (crossed)  󿬁 bers, the other for temporal(uncrossed)  󿬁 bers (Fig. 1C, analogous to McIlwaine et al (5)).The variation in nerve  󿬁 ber diameter in the chiasm wasignored for the sake of simplicity and nerve  󿬁 ber diameter  was set at 1  m m (18). Crossing of   󿬁 bers was assumed to occur at precisely 90°, whereas parallel  󿬁 bers were assumed to beprecisely parallel. Physical Properties  Accurate data about the mechanical properties of living biological tissues are scarce because of the practical dif  󿬁 cultiesinvolved 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 wereassumed to be isotropic to have a density of 1000 kg/m 3 and to have linear elastic material properties characterized by elasticmoduli (E) and Poisson ratios ( n ) as shown in Table 1. Mate-rial properties of individual nerve  󿬁 bers are not available in theliterature, so, although optic nerve  󿬁 bers are myelinated and therefore surrounded by a sheath, we considered nerves to behomogeneous 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 microscopicmodels were discretized into hexahedron-dominant meshes with 47,112 and 19,880 quadratic elements, respectively.Preliminary studies demonstrated that this mesh density wassuf  󿬁 cient to provide mesh-independent results. Because themodel of the chiasm was symmetrical in 2 planes,computational time was reduced by restricting calculationsto one-fourth of the entire chiasm (Fig. 1B).The boundary conditions of the simulation were asfollows: the distal faces of the optic nerves and tracts were 󿬁 xed to represent connections to the optic canals and brain,respectively. The tumor was  󿬁 xed 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 in 󿬂 ating thetumor from below. Pressure was applied in 5 discretesteps up to 0.145 MPa, resulting in elevation of the chiasmby 0.11h, 0.26h, 0.40h, 0.63h, and 0.94h (where h wasthe height of the chiasm, i.e., 3.5 mm). These values werechosen with a view to subsequent validation because they  were biologically plausible and similar to the elevationsseen in the video accompanying the experiment by Kosmorsky et al (4).Local pressure values derived from the macroscopicmodel along path A (Fig. 1B) were then applied to the 2microscopic nerve  󿬁 ber models to investigate the strain inthe nerve  󿬁 bers as a function of whether the nerves werecrossed or uncrossed. The loading transition was one-way inthis 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 takesaccount 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 geometriccenter (paths A and B, respectively, in Fig. 1B).Output of the microscopic model was initially calculated along path A for both crossed and uncrossed   󿬁 bers for thecondition of maximum elevation (i.e., 0.94h). The detailed nerve  󿬁 ber distribution in the optic chiasm is still unclear. Itis generally believed that the nasal nerve  󿬁 bers cross in thecentral part of the chiasm, whereas the temporal  󿬁 bers arerouted 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   󿬁 bers), whereas the output of the parallel model was applied to the lateral half (assumed tocontain the temporal, uncrossed   󿬁 bers).The output of the microscopic model was compared withthe  󿬁 ndings of a study on guinea pig optic nerves (25), which was able to de 󿬁 ne 3 strain thresholds of axonal injury: ã  the level below which no axon would be injured (T C ), ã  the level above which all axons would be injured (T L ),and  TABLE 1.  Assumed mechanical properties of tissues used in the  󿬁 nite element modeling simulations TissueTissue on WhichModel BasedElastic Modulus(E) (MPa) Poisson ’ s Ratio ( n ) ReferencesSheath 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)  Wang et al:  J Neuro-Ophthalmol 2014  ; 0: 1-7  3 Original Contribution Copyright     North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited.  ã  the level which provided the best discriminationbetween injured and uninjured axons (T B ). Validation of the Model   As stated, very few published experiments have looked atchiasmal compression from a mechanical perspective. Wecould only   󿬁 nd 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 themeasured pressures from the study by Kosmorsky et al(4). Unfortunately, these authors did not state the preciselocations of their transducers. The central transducer wasassumed to be at the center of the chiasm, whereas theperipheral transducer was assumed to be at 4.6 mm fromthe 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 chiasmas a result of increasing in 󿬂 ation pressure in the tumor along  with contours of von Mises strain distribution. The degreeof displacement refers to the elevation of the base of thechiasm as a function of the baseline height of the chiasm(h = 3.5 mm). The output of the model is also shown asa short animated sequence (See  Supplemental DigitalContent  , Video, http://links.lww.com/WNO/A106).Figure 3A, B show the von Mises strain distributionalong paths A and B (Fig. 1B) of the macroscopic modelbecause 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 fromthe 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 5steps (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). 4  Wang et al:  J Neuro-Ophthalmol 2014  ; 0: 1-7 Original Contribution Copyright     North American Neuro-Ophthalmology Society. Unauthorized reproduction of this article is prohibited.
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