Three-dimensional finite element analysis of hyperbaric oxygen therapy on the optic nerve from a damaged orbit＊＊＊＊☆

Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi Province, China

lNTRODUCTlON

Visual function in a damaged optic nerve cannot be restored, even following treatment, because the damage is irreversible.However, the underlying mechanisms and treatment remain controversial[1-2].Some scholars have noted that elevated intraocular pressure compresses the optic nerve, thereby affecting axonal transport and leading to optic nerve atrophy[3-4].Present studies have primarily focused on the establishment of animal models with optic nerve damage and MRI examinations in a broader attempt to lay a foundation for optic nerve damage research[5-9].Animal models of nerve injury are generally characterized by transection or crush injury[5].Rosneret al[6]established animal models of optic nerve clamp injury; results helped to determine the optimal light intensity and frequency to avoid degradation following optic nerve injury.Another study[7]established an animal model of optic nerve axonal traverse injury, with the presence of intact blood vessels and continuous meninges; this model was an effective approach for neural regenerationin vivo.In addition, an animal model of optic nerve impact injury[8]was used to compare with normal optic nerve for retinal morphological differences, and optic nerve drag injury has been successfully established in the guinea pig[9].

The mechanism underlying optic nerve damage and regeneration has not been fully elucidated.In addition, clinical diagnosis and treatment of optic nerve damage lacks uniform standards and surgical treatments remain controversial[10-11].Several studies have established biomechanical models by measuring optic nerve geometric parameters[12-15].However, there are too few factors to ensure its accuracy.Another study reported that a small number of Chinese patients developed decreased vision and blindness during hyperbaric oxygen (HBO) treatment[16].However,the effects of optic nerve compression in patients with orbital damage following HBO treatment remain poorly understood.

Therefore, the present study conducted finite element analysis following HBO treatment to optic nerve in the damaged orbit.Analysis was based on human head CT scans and three-dimensional finite element model of the eyes and relevant tissues.

RESULTS

Three-dimensional finite element analysis following HBO therapy to the optic nerve in a damaged orbit

To compare optic nerve stress under varying degrees of skull strength in a damaged orbit, a three-dimensional finite element model of the eyes and relevant tissues was established, which included the optic nerve, orbit, eyeballs, orbital fat body, and brain tissue.Optic nerve stress in a HBO environment was simulated by changing the elastic modulus and external pressure of the skull at the damaged orbit.The elastic modulus (E) from the damaged side was characterized by three gradients of strength using finite element analysis software (ANSYS).Von Mises stress contours visualized stress distribution in the optic nerve.AsEat the damaged orbit reached 8 000 MPa, and the external environment was at atmospheric pressure, optic nerve stress was distributed between the damaged and complete side (Figure 1).Simulation analysis demonstrated that optic nerve stress was maximal at contact parts between the optic nerve and eyeballs in damaged and complete orbits.

Figure 1 Three-dimensional finite element model of optic nerve stress in damaged and intact orbits (E=8 000 MPa,P=0.1 MPa).(A) Damaged side; (B) intact side.Contour at E=1 000 and 100 MPa, P=0.1 MPa (supplementary Figure 1 online).E: Elastic modulus.

AsEat the damaged orbit reached 8 000, 1 000, and 100 MPa, and the external environment reached 1, 2,and 3 atmospheric pressures (external uniform pressures ofP=0.1, 0.2, 0.3 MPa), respectively, optic nerve stress was distributed between the damaged and intact sides (Table 1).

Table 1 Comparison of stress in the damaged and intact orbit in the three-dimensional finite element model (MPa)

Optic nerve stress at the damaged orbit significantly increased, stress at the intact side changed slightly, andEdecreased when external pressure remained unchanged.In addition, anterior optic nerve stress was greater than posterior optic nerve stress.WhenEremained unchanged, maximal optic nerve stress significantly increased with increased external pressure.

DlSCUSSlON

In the present study, three-dimensional geometric and finite element model of the eye and relevant tissues were established using MIMICS software (trial version) and ANSYS 10.0.The model consisted of optic nerve, orbit,eyeballs, orbital fat body, and brain tissues.Several reports on the optic nerve finite element model exist in China, although experimental data are rare and HBO treatment to the optic nerve has received little attention.The present study simulated optic nerve stress in a hyperbaric chamber, resulting in the following conclusions:

(1) Optic nerve stress in the damaged and intact orbits were maximized at contact regions between the optic nerve and the eyeballs.

(2) When external pressure remained unchanged, optic nerve stress in the damaged orbit increased along with decreasedE.Under a uniform pressure load,Ewas reduced from 8 000 to 1 000 MPa.In addition, maximal stress at the anterior and posterior ends of the optic nerve in the damage orbit increased by＜0.02 MPa, and the value was less than at anEof 8 000 MPa.WhenEwas reduced from 1 000 to 100 MPa, maximal stress at the anterior optic nerve increased by 0.062 64 MPa, while stress at the posterior end increased by 0.276 568 MPa.These experimental findings indicated that optic nerve stress significantly increased with decreasingE, suggesting that the skull protected the optic nerve against external damage.

(3) WhenEremained unchanged, maximal optic nerve stress sharply increased with increasing external pressure.These results suggested that the optic nerve was compressed by HBO treatment.Maximal optic nerve stress in the damaged orbit increased from 0.338 954 MPa at 1 atmospheric pressure to 0.547 926 MPa at 3 atmospheric pressures; maximal optic nerve stress in the intact orbit increased from 0.118 92 MPa at 1 atmospheric pressure to 0.276 852 MPa at 3 atmospheric pressures.Optic nerve stress at 3 atmospheric pressures was significantly greater than that at 1 atmospheric pressure.In the future, HBO therapy should take optic nerve compression into consideration.

(4) Simulation analysis showed that optic nerve stress on the damaged side was larger than that on the intact side.Maximal optic nerve stress in the damaged orbit was 0.338 954 MPa, but 0.118 92 MPa in the intact side,1 atmospheric pressure.Decreased vision in a damaged orbit following HBO therapy could be the result of a compressed optic nerve in the damaged side.In addition,maximal stress of the optic nerve was 0.277 964 MPa at 3 atmospheric pressures, which was less than in the damaged orbit at 1 atmospheric pressure(0.338 954 MPa).HBO therapy induced pain in the damaged orbit, and no pain was experienced in the intact orbit, which was consistent with the simulation results.Future trials should include the following:

(1) Human tissues should be viscoelastic and the linear replacement is available for a certain range of mechanics.To better simulate reality, more material models are needed to determine the material properties of eye tissues.

(2) In the present study, eye muscles were not considered, and it was hypothesized that there was no frictional contact between the eyeballs and the orbital fat body,which was different from the actual condition.Therefore,reasonable constraint conditions of the eyeballs should be a focus for future studies.

(3) The human body typically self-regulates intracranial and intraocular pressure during compression and decompression procedures of HBO therapy.However,there very little is known regarding intracranial and intraocular pressures.Future clinical and experimental studies should determine these changes with external pressure.

SUBJECTS AND METHODS

Design

A computer simulation experiment utilizing neuroimaging.

Time and setting

Experiments were conducted at the Biomechanics Laboratory, Taiyuan University of Technology and the Department of Radiology, Taiyuan Central Hospital,China from June 2009 to March 2010.

Subjects

A middle-aged male suffering from comminuted fracture of the right orbit due to a traffic accident was enrolled in the present study.There was no previous history of diseases prior to injury.Head CT images were scanned at the Department of Radiology, Taiyuan Central Hospital,China using a 64-slice spiral CT (Siemens AG, Munich,Germany).According toAdministrative Regulations on Medical Institutions, issued by the State Council of China[17], the patient was informed of the experimental design and risks prior to experimentation, and the patient provided informed consent.

Methods

Finite element model establishment of the eyes and relevant tissues

CT scan images were stored in Digital and Communications in Medicine (DICOM) format (Figure 2) and introduced into MIMICS software (trial version, Materialise interactive medical image control system; Materialise,the Netherlands) to extract the model outline, and a geometric model of the optic nerve was subsequently established.Simultaneously, four geometric models of the eyeballs, orbital fat body, orbit, and brain tissues were created as a subsidiary model of the optic nerve; all models together were considered to be the eyes and relevant tissues model (Figure 3).

Geometric models were stored as ＂.lis＂ files, which were input into a finite element software ANSYS10.0 (ANSYS Corporation, Canonsburg, PA, USA) to establish a three-dimensional finite element model of the eyes and relevant tissues[18], which included the optic nerve, orbit,eyeballs, orbital fat body, and brain tissues.The overall geometrical model of the eyes is shown in Figure 4.

Figure 2 CT image (A) of eyes and relevant tissues model (B) in MIMICS software.L: Left; R: right.

Figure 3 Geometric model of the eyes and relevant tissues.Green refers to damaged orbit, orange refers to eyeballs, and the surrounding area of the eyeballs is orbital fat body.The optic nerve is located posteriorly and is covered with orbital fat body and the eyeball.

Figure 4 Finite element models of optic nerve in damaged (A) and intact orbits (B) were created using ANSYS software.

Parameters of the finite element model

The present study defined the optic nerve as an elastic material.The orbital fat body plays a supporting role for the eye.For example, when increasing intraocular pressure alters eye shape, Poisson's ratio of orbital fat body is approximately 0.5, which is similar to water; in addition, Young's modulus is relatively small(≤ 0.047 MPa)[13].These results suggested that orbital fat body produced minimal stress, but maximal strain, under compression due to eyeball expansion.A smallEis not effective for keeping eyeball shape[13].However, eyeballs are limited by eye muscles (which includes four rectus muscles, two oblique muscles, and the levator muscle).Eof muscles was 20 MPa[13], which is harder than eyeballs.To take actual eyeball constraints into consideration, the present study utilized the orbital fat body to represent constraints to the eyeballs, and the material parameterEwas set to 1 MPa.

The orbits and eyeballs were defined as homogeneous,isotropic, linear, elastic materials, and the material parameters are listed in Table 2.

Table 2 Material parameters of the finite element model

Following comminuted facture in the right orbit,Ewas greatly reduced.However, there have been no reports on skull strength following fracture.In the present study,Eof the damaged orbit was defined as 8 000, 1 000, and 100 MPa, respectively, to establish a finite element model that included 46 189 nodes and 249 115 Solid 45 elements.The overall finite element model is shown in Figure 5.

Figure 5 Finite element model of the eyes and relevant tissues.

Contact conditions of the finite element models

Human orbital fat body covers the optic nerve and posterior eyeballs.It was hypothesized that frictionless surface-to-surface contact existed between the optic nerve and the orbital fat body, between the eyeballs and the orbital fat body, and between the orbit and the orbital fat body.

Boundary conditions of the finite element models

The orbit remains unchanged when upper and lower regions undergo slight stress.Therefore, upper and lower orbits served as fixed constraints in the present study.The human optic nerve is covered by cerebrospinal fluid, and the intraorbital segment and optic canal bear intracranial pressure.In addition, intraocular pressure exists within the eyes.Moreover, the inner surface of the skull is covered by a layer of cerebrospinal fluid[19].In the present model, cerebrospinal fluid pressure on the skull was achievedviaintracranial pressure of brain tissue.The optic nerve and brain tissues were exposed to loading pressure equal to normal intracranial pressure,and the eyeballs were loaded with normal intraocular pressure[20-21].The external environment was set to 1, 2,and 3 atmospheric pressures to calculate optic nerve stress, so the front of the orbit and the anterior eyeballs were exposed to external uniform pressures ofP=0.1,0.2, and 0.3 MPa.

Author contributions:Yuan Guo established a geometrical,finite element model, integrated data, and wrote the manuscript.Yanjun Li participated in parts of the establishment of the finite element model and data analysis.Weiyi Chen proposed ideas and validated the study and was also responsible for funding and research mentoring.Meiwen An was responsible for research design.

Conflicts of interest:None declared.

Funding:This study was financially sponsored by the National Natural Science Foundation of China (Key Program), No.11032008; the National Natural Science Foundation of China(General Program), No.10872140, 10702048; and the Natural Science Foundation of Shanxi Province, No.2010021004-1.

Ethical approval:This study was approved by the Ethics Committee, Taiyuan University of Technology in China.

Supplementary lnformation:Supplementary data associated with this article can be found, in the online version, by visiting www.nrronline.org, and entering Vol.6, No.29, 2011 after selecting the “NRR Current Issue” button on the page.

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