The optic chiasm has been an object of interest for many centuries (1). Although the concept of hemidecussation is now universally accepted, there are still many unanswered 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), alteration 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, therefore, 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. We have used finite element modeling (FEM), a tool regularly used by engineers to investigate complex, 3-dimensional structures such as aircraft and engines (8) to model the chiasm and investigate this hypothesis (See Supplemental Digital Content, 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 anatomical structure and physical properties (e.g., elastic modulus 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 component parts. The number of cells is clearly critical—too few and the model will be too coarse to provide any useful information; 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.
Development of the Model
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 dimensions of the macroscopic model were derived from published data (13–16) but, for the sake of simplicity, the plane of the chiasm was assumed to be horizontal and perpendicular 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 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 μm (18). Crossing of fibers was assumed to occur at precisely 90°, whereas parallel fibers were assumed to be precisely parallel.
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 (ν) as shown in Table 1. Material 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 macroscopic model of the chiasm.
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 macroscopic 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 margin 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
* 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 limited 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).
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 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 position 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 differences between chiasms, variation in catheter position or elevation, or variation in transducer location. Nevertheless, the experimental values and trends are very similar to the values generated by the model.
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 experimentally by Kosmorsky et al (4). We previously performed a parametric study (26), which showed that varying the material properties resulted in quantitative, but not qualitative, 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 hemianopia 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 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 computational experiment that must be further investigated and validated 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 properties of the tissues can be described in simple linear terms, whereas most biological tissues are anisotropic and demonstrate 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 disruption 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. With further refinement of the model, it may be possible to calculate the thresholds for nerve damage in terms of loss of function vs irreversible axonal damage and to offer predictions based on analysis of magnetic resonance imaging of chiasmal compression. An increased understanding of the way the complicated nervous system structures behave when compressed should translate to other structures and may contribute to the management of various forms of injury to eye, optic nerve, brain, and spinal cord.
1. Glaser JS. Romancing the chiasm: vision, vocalization, and virtuosity. J Neuroophthalmol. 2008;28:131–143.
2. Hedges TR. Preservation of the upper nasal field in the chiasmal syndrome: an anatomic explanation. Trans Am Ophthalmol Soc. 1969;67:131–141.
3. Bergland R, Ray BS. The arterial supply of the human optic chiasm. J Neurosurg. 1969;31:327–334.
4. Kosmorsky GS, Dupps WJ Jr, Drake RL. Nonuniform pressure generation in the optic chiasm may explain bitemporal hemianopsia. Ophthalmology. 2008;115:560–565.
5. McIlwaine GG, Carrim ZI, Lueck CJ, Chrisp TM. A mechanical theory to account for bitemporal hemianopia from chiasmal compression. J Neuroophthalmol. 2005;25:40–43.
6. Danesh-Meyer HV, Papchenko T, Savino PJ, Law A, Evans J, Gamble GD. In vivo retinal nerve fiber layer thickness measured by optical coherence tomography predicts visual recovery after surgery for parachiasmal tumors. Invest Ophthalmol Vis Sci. 2008;49:1879–1885.
7. Moon CH, Hwang SC, Kim BT, Ohn YH, Park TK. Visual prognostic value of optical coherence tomography and photopic negative response in chiasmal compression. Invest Ophthalmol Vis Sci. 2011;52:8527–8533.
8. Amoo LM. On the design and structural analysis of jet engine fan blade structures. Prog Aerosp Sci. 2013;60:1–11.
9. Yang KH, King AI. A limited review of finite element models developed for brain injury biomechanics research. Int J of Vehicle Design. 2003;32:116–129.
10. Cirovic S, Bhola RM, Hose DR, Howard IC, Lawford PV, Marr JE, Parsons MA. Computer modelling study of the mechanism of optic nerve injury in blunt trauma. Br J Ophthalmol. 2006;90:778–783.
11. Norman RE, Flanagan JG, Sigal IA, Rausch SMK, Tertinegg I, Ethier CR. Finite element modeling of the human sclera: Influence on optic nerve head biomechanics and connections with glaucoma. Exp Eye Res. 2011;93:4–12.
12. Ausiello P, Apicella A, Davidson CL, Rengo S. 3D-finite element analyses of cusp movements in a human upper premolar, restored with adhesive resin-based composites. J Biomech. 2001;34:1269–1277.
13. Parravano JG, Toledo A, Kucharczyk W. Dimensions of the optic nerves, chiasm, and tracts: MR quantitative comparison between patients with optic atrophy and normals. J Comput Assist Tomogr. 1993;17:688–690.
14. Wagner AL, Murtagh FR, Hazlett KS, Arrington JA. Measurement of the normal optic chiasm on coronal MR images. AJNR Am J Neuroradiol. 1997;18:723–726.
15. Li X, Liu X, Li H. Measurement of optic chiasm and its adjacent structures. J Changzhi Med Coll. 2002;16:164–166.
16. Schmitz B, Schaefer T, Krick CM, Reith W, Backens M, Käsmann-Kellner B. Configuration of the optic chiasm in humans with albinism as revealed by magnetic resonance imaging. Invest Ophthalmol Vis Sci. 2003;44:16–21.
17. Sigal IA, Flanagan JG, Tertinegg I, Etbier CR. Finite elemenet modeling of optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2004;45:4378–4387.
18. Jonas JB, Müller-Bergh JA, Schlötzer-Schrehardt UM, Naumann GO. Histomorphometry of the human optic nerve. Invest Ophthalmol Vis Sci. 1990;31:736–744.
19. Zhivoderov NN, Zavalishin NN, Neniukov AK. Mechanical properties of the dura mater of the human brain [Article in Russian]. Sud Med Ekspert. 1983;26:36–37.
20. Miller K. Constitutive model of brain tissue suitable for finite element analysis of surgical procedures. J Biomech. 1999;32:531–537.
21. Kobayashi AS, Woo SL, Lawrence C, Schlegel WA. Analysis of the corneo-scleral shell by the method of direct stiffness. J Biomech. 1971;4:323–330.
22. Ueno K, Melvin JW, Li L, Lighthall JW. Development of tissue level brain injury criteria by finite element analysis. J Neurotraum. 1995;12:695–706.
23. Raul JS, Baumgartner D, Willinger R, Ludes B. Finite element modelling of human head injuries caused by a fall. Int J Legal Med. 2006;120:212–218.
24. Neveu MM, Jeffery G. Chiasm formation in man is fundamentally different from that in the mouse. Eye. 2007;21:1264–1270.
25. Bain A. In Vivo Mechanical Thresholds for Morphological and Functional Axonal Injury
[PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1998:109–153.
26. Wang X, Neely A, Lueck C, Tahtali M, McIlwaine G, Lillicrap T. Parametric studies of optic chiasmal compression biomechanics using finite element modelling. In: Kotousov A, Das R, Wildy S, eds. Proceedings of the 7th Australasian Congress on Applied Mechanics. Barton, Australia: Engineers Australia, 2012:341–350.