Ocular trauma is one of the most common types of combat injuries resulting from the exposure of military personnel with improvised explosive devices. The injury mechanism associated with the primary blast wave is poorly understood. We employed a three-dimensional computational model, which included the main internal ocular structures of the eye, spatially varying thickness of the cornea-scleral shell, and nonlinear tissue properties, to calculate the intraocular pressure and stress state of the eye wall and internal ocular structure caused by the blast. The intraocular pressure and stress magnitudes were applied to estimate the injury risk using existing models for blunt impact and blast loading. The simulation results demonstrated that blast loading can induce significant stresses in the different components of the eyes that correlate with observed primary blast injuries in animal studies. Different injury models produced widely different injury risk predictions, which highlights the need for experimental studies evaluating mechanical and functional damage to the ocular structures caused by the blast loading.

## Introduction

The increasing use of explosive weaponry in military conflicts and terrorist attacks has led to an increase in the incidence of combat-related blast injuries sustained by soldiers and civilians. The ratio of ocular traumatic injuries to all injuries during Operation Desert Storm was nearly six times larger than in World War II [14] and made ocular trauma the fourth most common injury related to military deployment [5]. Blast injuries can be separated into four categories: primary from the blast overpressure, secondary from propelled fragments, tertiary from blunt impact, and quaternary from burns and other effects [6]. While secondary, tertiary, and quaternary injury mechanisms can be identified within the military's casualty care system, mechanisms unique to primary blast injuries are still poorly understood [7]. Computational modeling studies and animal studies show that the risk of ocular blast injury correlates with the high-pressure shock front, referred to as the positive phase, and the subsequent lower subatmospheric pressure, referred to as the negative phase of the blast wave [8], as well as reflections of the blast wave from the orbit [9] and facial features surrounding the eye [10]. There is, however, a dearth of clinical data that could verify these findings and establish the mechanism of the injury. Measuring and assessing the influence of these factors are difficult because survivable primary blast injuries are likely accompanied by injuries from fragments and blunt force trauma and are thus more difficult to distinguish and enumerate. Moreover, the severity of the blast injuries and the distance of the care facility from the injury site mean that often patients are unable to recount the injury event, and witnesses are unavailable. There has been an ongoing effort to identify the mechanism of injuries in recent years. Hines-Beard et al. [11] tested the effects of blast overpressure on mice, by firing short bursts of pressurized air through paintball gun barrels, which inflicted closed-eye injuries with features similar to those seen in patients with ocular blast trauma. Alphonse et al. [12] performed an experiment to investigate the effect of low-pressure blasts from fireworks and gunpowder charges on human cadaver eyes. They reported minor corneal abrasion caused by propelled fragmented and found a low risk of severe ocular damage. Sherwood et al. [13] studied the tissue damage in enucleated porcine eyes caused by a blast wave generated by a shock tube and reported angle recession, internal scleral delamination, cyclodialysis, and peripheral chorioretinal detachments. Bhardwaj et al. [10] demonstrated, through a computational modeling study, the strong influence of facial features on blast pressure loading to the eye and the internal ocular structures on the biomechanical response. Due to the importance of the facial feature and the internal ocular structures on the biomechanical response, and challenges to performing the experimental studies in full scale, computational modeling can improve the understanding of the mechanism of the primary injuries.

Experimental studies of blunt impact have developed statistical models correlating injury risks to the kinetic energy, velocity, mass, and normalized energy of the projectile [2326]. Compared to experimental studies, computational studies can quantify the global responses (i.e., intraocular pressure) of the globe and the local stress and deformation state of the intraocular tissues with more detail [27]. Validated computational models of the eye have been used to analyze the risk of injuries from eye impacts of projectiles with different mass, velocity, and size [15,27,28]. Weaver et al. [27] used a large number of experimental eye impact tests collected from literature to construct a model and analyzed the global and localized responses of the eye to a variety of blunt projectile impacts and evaluated the risk of eye injuries. Alphonse et al. [12] used a correlation between the intraocular pressure (IOP) and normalized energy based on the assumption that the projected area of an unprotected eye is equivalent to a 11.16 mm diameter of a projectile. The authors used the IOP as a metric to calculate the risk of injuries from firework overpressure [10]. Sherwood et al. [13] developed a score-based system using terminology consistent with the Birmingham Eye Trauma Terminology (BETT) [29] based on the specific impulse which was calculated by timewise integration of the positive blast pressure waveform.

The goal of this study is to understand the mechanism of primary ocular injury based on stress analysis and also compare the probability of the injury based on three injury risk models. We extended the computational model of Bhardwaj et al. [10] to include the sclera, cornea, limbus, aqueous, lens, ciliary zonule, ciliary muscle, vitreous, retina, choroid, lamina cribrosa (LC), prelaminar neural tissue (PLNT), and extraocular tissue. We compared the injury risks predicted by Kennedy–Duma [30] and Weaver et al. [20] which used IOP and the maximum principal stress and the injury risk developed by Sherwood et al. [13] which used specific impulse of the positive blast phase.

## Materials and Methods

We developed a three-dimensional computational model composed of a deformable globe with internal ocular structures, rigid skull, and fluid domain. A finite difference compressible flow solver was used to simulate the propagation of the blast wave in the fluid domain [10], while a finite element elastodynamic solver was used to calculate the large deformation and stress response of tissue components of the globe. A sharp-interface immersed boundary method was used to describe the fluid–structure interaction at the interface of the solid and fluid domains [31].

Figure 1 shows a schematic of the computational domain. We considered a 2.0 kg TNT charge mass located Lex = 2.5 m in front of the face and applied the initial boundary condition at Lin = 1.8 m from the charge. The charge mass and location were obtained from the conditions of field blast tests performed by the Army Test Center [32], and these conditions were also used in our previous computational modeling study on the effect of facial features on blast wave reflections around the eye [10]. The rigid skull is meshed using bilinear triangular surface elements, while the deformable eye has trilinear hexahedral elements.

Fig. 1
Fig. 1
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### Finite Element Models of the Head and Eye.

The model of the rigid skull was described in detail by Bhardwaj et al. [10]. The deformable model for the globe was positioned inside the orbit of the rigid skull model, such that the lateral protrusion (LP = 12.0 mm) of lateral distance (LD = 19.0 mm) of the globe (Fig. 2) was representative of the averaged measurements for a 21-yr-old male [33,34]. The deformable model for the globe was created using CUBIT©, a geometry and mesh generation toolkit developed at Sandia National Laboratories, and meshed using eight-node hexahedral elements. The model included the important intraocular components, including the sclera, limbus, cornea, aqueous humor, lens, ciliary zonule, ciliary muscles, vitreous humor, retina, choroid, LC, PLNT, and the surrounding orbital/fatty tissue (Fig. 2). The surrounding orbital tissue was described as a sphere of a space-filling, homogeneous material, and the attachment location to orbital tissue to the globe was determined from the measurements for a 25-yr-old female, reported by Schutte et al. [35]. The extraocular orbital tissue was assumed to be perfectly bonded to the globe and to the orbit of the rigid skull. The latter was accomplished by fixing the nodes on the outer surface of the extraocular tissue adjacent to the rigid skull model. The finite element model for the individual intraocular components is described below in detail.

Fig. 2
Fig. 2
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Fig. 3
Fig. 3
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Cornea and Sclera: The corneoscleral shell is the stiff outer layer of the eye wall that protects the intraocular components from external loading. The sclera and cornea were described as spherical shells with outer radii of 12.0 mm and 7.8 mm, respectively. The center of the sphere representing the cornea was positioned 5.0 mm [15] anterior to the center of the sclera. The thickness of the corneoscleral shell was varied continuously from the cornea to the limbus. The corneal thickness was assumed to increase linearly from 0.52 mm at the apex to 0.66 mm at the limbus [15]. The thickness of the limbus also increased linearly from 0.66 to 0.8 mm [15].

The thickness of the sclera was represented using the micro-MRI measurements of Norman et al. [36] for 11 human eyes. In the experimental study [36], the eyes were sectioned into 15 equal-width slices along the anterior–posterior axis. We used the same method to divide the model of the sclera into 12 sections corresponding to the first 12 slices as in the study of Norman et al. [36]. In order to accommodate the eccentric position of the optic nerve head (ONH), the sectioning planes were rotated such that the anterior-most plane coincided with the plane of the posterior surface of the limbus and the posterior-most plane coincided with the plane of the anterior surface of LC. Intermediate planes were rotated through angles obtained by linear interpolation between the angles of the terminal planes. The nodes of the internal surface of the spherical shell model of the sclera were moved along the normal direction to obtain the average thickness among 11 specimens measured for the given section and quadrant [36]. The nodes on the exterior surface of the scleral shell were fixed, and the internal nodes were moved along the radial direction to achieve the local thickness measured in experiments while maintaining the uniform spacing of the nodes along the radial direction. It should be noted that the model was constructed for a left eye, while the results presented by Norman et al. [36] were for a right eye. Thus, the thickness variation in the model is a mirror image of the measured variation (Fig. 3).

Retina and Choroid: In our model, the retina was extended anteriorly up to the ora serrata, while the choroid was extended up to the ciliary body. We assumed a uniform thickness of 0.24 mm for the retina from the measurements of Wagner-Schuman et al. [37] for Caucasian males and 0.35 mm for the choroid based on measurements of mean subfoveal choroidal thickness for healthy, Japanese individuals by Ikuno et al. [38].

Lens and Zonule: We approximated the geometry of the lens measurements from a young, normal accommodated lens [39]. The lens included two components: the outer cortex and the inner nucleus. Both structures were assumed to be axisymmetric about the optical axis (Fig. 4(a)). A fifth-order polynomial ($y=ax5+bx4+cx3+dx2+f$) with coefficients a = −0.00153, b = 0.01191, c = −0.02032, d = −0.07692, and f = 2.04, for anterior, and a = 0.00375, b = −0.03036, c = 0.06955, d = 0.0943, and f = −2.09, for posterior, was used to define the cortex outline from the central axis to the designated points with 0.39 mm distance from circular end cap, shown in Fig. 4(a). The periphery of the lens was approximated by a circular end cap [39]. The lens nucleus was assumed to have the same shape as the cortex. The thickness of nucleus was scaled to 62% of the thickness of the lens [40]. Finally, the position of the horizontal axis of the nucleus was offset from that of the outer cortex by 0.51 mm [39].

Fig. 4
Fig. 4
Close modal

Ciliary Body and Zonule Fibers: In this study, we approximated the zonule fibers as one structure. The anterior attachment location of the zonule fibers to the lens was set to 1.5 mm from the lens periphery [41] (Fig. 4(b)). We also approximated the ciliary body, which includes the ciliary muscle and ciliary processes, as a single structure. The geometry, location, and variation in the thickness of the ciliary body from anterior to posterior were taken from the study of Kao et al. [42]. The ciliary body was attached directly into the choroid, approximately 3 mm anterior to the ora serrata (Fig. 4(b)).

Optic Nerve Head: The dimensions of the ONH were obtained from the literature [43,44] (Fig. 4(c)). The LC and the connective tissue that supports the optic nerve axons as they leave the intraocular space were considered in this study as a disk with an anterior radius of 0.95 mm, a curvature of 0.2 mm [43], and a thickness of 0.4 mm [44]. The shape of the ONH cup was simplified from Ref. [43] to increase mesh size for computational time purposes.

#### Material Properties.

A quasi-incompressible neo-Hookean hyperelastic model was applied to describe the mechanical behavior of all the tissue components of the globe and orbital tissues. The neo-Hookean strain energy function is defined as [45]
$ψ(C)=μ2(I1̂−3)+κ2(I3−ln(I3)−1)$
(1)

where I1, I2, and I3 are the three invariants of the Cauchy–Green deformation tensor, and $I1̂=I3−13I1$ is the deviatoric part of the first invariant. The parameters μ and κ are the shear and bulk moduli.

Table 1 lists the material properties used for each tissue component. Few studies have measured the mechanical behavior of ocular tissues under high-rate conditions representative of the blast. The majority of the mechanical properties in Table 1 were obtained from quasi-static measurements. The shear modulus for the sclera was obtained from the dynamic inflation experiments of Bisplinghoff et al. [49]. We assumed the bulk modulus of the retina to be the same as that of water. The shear modulus of the retina was obtained from contact angle measurement of Grant et al. [52]. In this study, the properties of the limbus were assumed to be the same as the cornea, and the material parameters for choroid were assumed as those for the retina. The shear modulus of aqueous was considered the same as the vitreous. The density and bulk modulus of the ciliary zonule and ciliary muscle assumed the same values as those reported for the lens. The shear modulus for the LC was estimated from the Young's modulus used by Norman et al. [54], assuming a Poisson's ratio of 0.47 [43]. The density of the PLNT was considered the same as the density of the retina. The Young's modulus and Poisson's ratio of the PLNT are obtained based on the mean value of the ranges prescribed by Sigal [53].

Table 1

Material properties used for the various ocular components (w—assumed equal to that of water, r—assumed equal to that of retina, s—assumed equal to that of sclera, and l—assumed equal to that of lens)

Componentρ (kg m−3)K (MPa)μ (kPa)
Sclera1400 [15]3571 [47]1000 [49]
Limbus1150 [21]3020 [48]1660 [21]
Cornea1150 [21]3020 [48]1660 [21]
Aqueous1003 [46]2266 [46]0.007 [50]
Nucleus lens1100 [21]2950 [48]0.039 [21]
Cortex lens1100 [21]2950 [48]0.0983 [21]
Ciliary zonule1000 (l)2950 (l)0.119 [51]
Ciliary muscle1100 (l)2950 (l)0.119 (c)
Vitreous1009 [46]2353 [46]0.007 [50]
Retina1100 [21]2200 (w)3.51 [52]
Choroid1100 [21]2200 (w)3.51 [52]
PLNT1100 (r)3571 (s)17.3 [53]
LC1400 (s)3571 (s)102 [54]
Extraocular tissue1100 (w)2200 (w)500 [55]
Componentρ (kg m−3)K (MPa)μ (kPa)
Sclera1400 [15]3571 [47]1000 [49]
Limbus1150 [21]3020 [48]1660 [21]
Cornea1150 [21]3020 [48]1660 [21]
Aqueous1003 [46]2266 [46]0.007 [50]
Nucleus lens1100 [21]2950 [48]0.039 [21]
Cortex lens1100 [21]2950 [48]0.0983 [21]
Ciliary zonule1000 (l)2950 (l)0.119 [51]
Ciliary muscle1100 (l)2950 (l)0.119 (c)
Vitreous1009 [46]2353 [46]0.007 [50]
Retina1100 [21]2200 (w)3.51 [52]
Choroid1100 [21]2200 (w)3.51 [52]
PLNT1100 (r)3571 (s)17.3 [53]
LC1400 (s)3571 (s)102 [54]
Extraocular tissue1100 (w)2200 (w)500 [55]

### Injury Risk.

We applied three different models of an ocular injury risk to analyze the biomechanical outcomes of the blast simulations. Two of the models were constructed from the data for blunt impact tests using either the IOP or the maximum principal stress of the corneal-scleral shell as the dependent variable. The third was developed by Sherwood et al. [13] based on specific impulse of the positive blast phase.

Kennedy–Duma model: Kennedy et al. [30] used a database contains 251 individual eye impact tests reported in the literature to develop injury criteria for hyphema, lens damage, and retinal damage. A survival analysis using maximum likelihood method was performed on the data to generate the following parametric risk functions:
$RB=[1−e−xβαβ]100%$
(2)

where x is the area normalized energy of the projectile (kJ/m2), β is a dimensionless parameter that depends on the injury type, and the parameter α is expressed in terms of m2/kJ. The values of α and β were obtained from the maximum likelihood parameter estimation method for hyphema, lens damage, and retinal damage [30]. The coefficients of the risk function predicting the corneal abrasions were obtained from logistic regression [30]. To determine the risk of injury, we first determined the maximum IOP from the blast simulation to determine the area-normalized kinetic energy of the projectile using the correlation provided by Duma et al. [56] for an aluminum projectile of 11.16 mm.

VT-WFU CIB Model: Weaver et al. [20] developed an injury risk function for globe rupture using 79 computationally validated models for different types of projectiles [27]. The risk of globe rupture was estimated for maximum stress and maximum IOP for different types of projectiles, and the corresponding normalized energy was calculated based on the globe rupture risk [30]. The normalized energy was then used to estimate the risk of injuries for hyphema, lens dislocation, and retinal damage by using Eq. (2). In the Kennedy–Duma model, the area of the projectile is assumed to be 11 mm to calculate normalized energy. In contrast, the VT-WFU CIB model uses the IOP measured in the simulation to calculate a globe rupture risk and then back calculate the normalized energy and risk of the other injuries.

Sherwood Model: Sherwood et al. [13] developed an injury risk function using the ordinal logistic regression which predicts the risk of trauma level for a given tissue using the Cumulative Injury Scale Score (CIS) based on the specific impulses (Eq. (4)). The specific impulse of the positive blast phase was calculated by timewise integration of the positive phase of the pressure waveform. The CIS score 1 indicated that the eye has some damage, but should heal fully on its own. The CIS score 2 indicated that the eye has damage that will require surgery to repair, leaving chronic pathology. The CIS 3 indicated that the eye has damage that might be repairable with surgery, with severe visual loss. The CIS 4 indicated that the eye is likely damaged beyond meaningful functional repair [13]
(3)

where logit is the inverse of the sigmoidal logistic function, RS is the probability of occurrence of the particular CIS category, j is the individual injury grade, J is the number corresponding to the type of injury, α is the respective intercept, and β is the respective slope.

## Results

The IOP, computed as the average of the three principal stresses, was maximum at a posterior location in the vitreous near the ONH (Fig. 5) throughout the simulation. The time history of the maximum IOP oscillated about an increasing mean. The oscillation was caused by wave reflections, while the overall increase in IOP was caused by the increasing blast overpressure of the positive phase duration. The structures of the posterior eye wall (e.g., sclera, retina, macula, and optic nerve head) experienced the highest maximum principal stress and the highest amplitude oscillations. In contrast, the anterior structures, including the lens, cornea, limbus, ciliary zonule, and ciliary muscle, showed significantly smaller amplitude. The maximum principal stress of the anterior structures increased rapidly to a peak, and then slowly decayed with time, which agrees qualitatively with results reported by Rossi et al. [6]. The maximum principal stress of the sclera initially occurred at a posterior location close to the ONH, while the maximum principal stress of the retina occurred at a location in the fovea. At 1.4 ms, which is 0.5 ms after the initial impact of the blast wave, the location of the maximum principal stress of the sclera shifted to a temporal location where the sclera attached to the extraorbital tissues. The reflection of the blast wave off the facial features produced an asymmetric pressure loading on the eye. This pushed the globe away from the nasal site and caused large stresses to develop at the attachment to the orbital tissue (Fig. 5(a)). This effect can be observed as a rapid increase in the maximum principal stress in the sclera (Fig. 6(b)), cornea, limbus, and ciliary body (Fig. 6(c)) at 1.4 ms. The von Mises stress, which is a distortional stress measure, also experienced a sharp increase in these at this time. The value at 1.7 ms is more than double that at 1.4 ms in the sclera, limbus, choroid, and ciliary body. In contrast, the von Mises stress of the posterior structures, such as the LC, decreased at 1.4 ms. The von Mises stress level in the retina, PLNT, and LC is lower than the other ocular components, and this can be due to the presence of the extraocular tissue which protects the PLNT, LC, and retina from excessive distortion.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

### Implications to the Eye Injury.

We applied the three injury risk models (Sec. 2.2) to estimate the likelihood of the occurrence of different types of injuries. The calculated percentages of injury risks of the VT-WFU CIB model based on maximum IOP value of 0.29 MPa were approximately 1.16%, 78%, 53%, and 48%, for globe rupture, hyphema, lens damage, and retinal damage, respectively. The calculated injuries risk of the Kennedy–Duma model, which was also based on the maximum IOP but assumed a projectile area of 11 mm2, was 8%, 0.01%, 11%, 0%, and 0%, for corneal abrasions, globe rupture, hyphema, lens damage, and retinal damage, respectively. We also calculated the injury risk of the VT-WFU CIB model based on the maximum principal stress of the cornea-scleral shell and found a 0%, 1%, <1%, and <1% risk of injury for globe rupture, hyphema, lens dislocation, and retinal damage, respectively. The summary of the injury risk evaluated using both models is provided in Table 2.

Table 2

Injury risks calculated for model with uniform thickness (uniform) and model with nonuniform thickness (nonuniform) based on maximum IOP (MPa)

Risk of injuryType of injuriesUniform (%)Nonuniform (%)
VT-WFU CIB risk of injury (IOP)Globe rupture0.941.16
Hyphema76.0478.39
Lens dislocation47.9653
Retinal damage43.8148.27
VT-WFU CIB risk of injury (maximum S1)Globe rupture00
Hyphema0.591.05
Lens dislocation00.002
Retinal damage0.0010.004
Kennedy–Duma risk of injury (IOP) [30]Globe rupture0.01620.016
Hyphema11.3711.07
Lens damage00
Retinal damage00
Corneal abrasions6.637.72
Maximum IOP (MPa)0.270.29
Maximum cornea-scleral S1 (MPa)0.440.61
Risk of injuryType of injuriesUniform (%)Nonuniform (%)
VT-WFU CIB risk of injury (IOP)Globe rupture0.941.16
Hyphema76.0478.39
Lens dislocation47.9653
Retinal damage43.8148.27
VT-WFU CIB risk of injury (maximum S1)Globe rupture00
Hyphema0.591.05
Lens dislocation00.002
Retinal damage0.0010.004
Kennedy–Duma risk of injury (IOP) [30]Globe rupture0.01620.016
Hyphema11.3711.07
Lens damage00
Retinal damage00
Corneal abrasions6.637.72
Maximum IOP (MPa)0.270.29
Maximum cornea-scleral S1 (MPa)0.440.61

The Sherwood model for the risk of injury was used to calculate the probability of achieving a CIS injury level based on the specific impulse of the positive blast phase. The results for the probability of achieving a CIS level for angle recession, damage to anterior chamber, choroid, optic nerve head, retina, and sclera are summarized in Fig. 7. The probability of occurrence was greater than 55% for all CIS level 1 injury and greater than 15% for the most severe CIS level 4 injuries. The largest decrease in the injury risk with the CIS level was calculated for the anterior chamber, while the injury risk exceeded 98% for all CIS levels for sclera injury. The highest risk of injury was to the sclera, which experienced the highest maximum principal tensile stress and von Mises distortional stress at the location of attachment to the orbital tissues. There was also a high risk of injury to the ONH because of the high stresses that developed in the posterior location in the early stages of blast loading.

Fig. 7
Fig. 7
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### Sensitivity of the Model to Sclera Thickness.

In this section, we compared the model with nonuniform sclera thickness (baseline model) and model with uniform sclera thickness to show the effect of the variation of the cornea-scleral shell thickness on the risk of injuries and stress distribution. The maximum thickness of the sclera (1 mm) was chosen for the model with uniform thickness. The IOP and stresses of both models showed the same trend and nearly identical magnitudes up to 1.4 ms, when the maximum stress in the sclera shifted from a posterior location near the ONH to a temporal location near the extraocular attachment. After 1.4 ms, the model with nonuniform thickness showed a 6% larger maximum IOP (at 1.63 ms), 34% larger maximum principal stress in the sclera (at 1.75 ms), and 15% larger von Mises stress in the sclera compared to the uniform thickness model (Fig. 8). The scleral thickness at the site of maximum stress was 0.7 mm, which was 80% smaller than for the uniform thickness model.

Fig. 8
Fig. 8
Close modal

The von Mises stress in the adjacent tissues of the limbus, choroid, and ciliary muscle was also significantly higher in the nonuniform thickness model (Fig. 9), while there was less than a 5% difference in the von Mises stresses of the two models in the more posterior tissues, such as the PLNT and the LC. The IOP and maximum principal stress of all ocular components for both models showed the same trend and nearly identical magnitudes up to 1.4 ms and after which the model with nonuniform thickness showed higher stress in the sclera and higher IOP in comparison to the model with uniform thickness. These differences between maximum values of the maximum principal stress of the sclera and the IOP lead to the underestimation of risk of injuries based on the VT-WFU CIB risk model and the Kennedy–Duma risk model using the model with uniform thickness (Table 2).

Fig. 9
Fig. 9
Close modal

## Discussion

The maximum IOP reached a peak of 0.29 MPa (2175 mm Hg) at 1.63 ms, which is two orders of magnitude larger than the 15 mm Hg physiologic IOP for a healthy eye. Cockerham et al. [57] reported closed-eye injuries such as corneal abrasions, vitreous hemorrhage, retinal detachment, and optic nerve atrophy in 43% out of 46 documented blast-induced traumatic brain injury patients. The blast simulations indicated high tensile (maximum principal) and distortion (von Mises) stresses in the cornea, limbus, sclera, choroid, and ciliary zonule, which were consistent with the observed injuries in the study of Cockerham et al. [57] and ex vivo study of Sherwood et al. [13]. The maximum von Mises stress in the sclera, choroid, and ciliary zonule shows the possibility of internal scleral delamination [13], chorioretinal detachments [6,13], and lens dislocation [15] (Fig. 6(d)). The high maximum principal stress at the extraocular attachment is consistent with the findings of rat studies showing torn extraocular muscles in animals exposed to blast loadings [11]. We evaluated the injury risk to the ocular components using three different injury models. The VT-WFU CIB injury risk model using the maximum IOP generally estimated a higher risk of injury than the Kennedy–Duma model. The injury risks evaluated from VT-WFU CIB model based on the maximum principal stresses were smaller than those evaluated based on the IOP. The deformation and stress state of the ocular tissues under blast loading are different from blunt impact because the pressure rate and spatial distribution are different. The discrepancy in the injury risks evaluated based on different biomechanical outcomes indicated that injury risk models based on blunt impact may not be appropriate for blast conditions. Both the VT-WFU CIB and Kennedy–Duma models showed that the probability of hyphema was higher than the other types of injuries. Moreover, all models based on the maximum IOP and maximum principal stress showed that risk of globe rupture was less than 2%, which was consistent with the experimental observations that exposure to the blast overpressure mainly produced closed globe injuries.

Each model for injury risk had its own inherent limitations. The Kennedy–Duma and VT-WFU CIB models were constructed using the data from blunt impact. The Sherwood model was developed from ex vivo experiments on porcine eyes and did not take into account the wave reflections from facial features, which amplify the blast overpressure loading on the eye. Porcine eyes may have higher mechanical strength than human eyes [58], which may lead to an underestimation of the injury risks. Furthermore, we showed the effect of the variation of the corneal-scleral shell thickness on the risk of injuries and stress distribution in ocular components. The model with uniform thickness underestimated the probability of occurrence of a different type of injuries (Table 2). These findings verified the initial hypothesis that the regional thickness variation of the cornea-scleral shell can amplify the stress distribution in the sclera.

The computational model contained a number of limitations. The injury risks were evaluated for a single blast condition with a 2 kg TNT charge mass detonated at a standoff distance of 2.5 m and position in front of the face. Further studies are needed to determine the effect of blast conditions on the injury risks. However, this study determined the distribution of stresses in the intraocular tissues caused by the primary blast wave and provided qualitative information on which ocular components are more susceptible to the damage based on the three different injury models.

The tissues of the cornea and sclera were assumed to be isotropic, spatially homogeneous, and described by a neo-Hookean hyperelastic material model. This neglects the effect of anisotropy and strain stiffening, which can be significant in collagenous tissues of the eye wall, including the cornea, sclera, lamina cribrosa, and choroid. We have extended the constitutive models to include anisotropy and strain stiffening. We are currently evaluating their effects on the tissue stress state and injury risks. We used existing measurements in the literature for the material properties of the ocular components. However, the measurements were performed under quasi-static conditions, and the quasi-static stress response is typically more compliant than the high-rate response elicited under blast conditions. Moreover, the properties vary significantly in the literature for many ocular tissues, such as the cornea, sclera, and choroid. Thus, the material properties are a significant source of uncertainty in the injury risk predictions. We are currently performing a design of experiments to determine the sensitivity of the injury risk predictions to the uncertainty in the material properties. Finally, we did not consider the viscoelastic behavior of ocular tissue, which can influence the stress magnitudes and IOP.

We estimated the risk of ocular injuries using three eye injury models. However, two of those, the Kennedy–Duma model and VT-WFU CIB model, were constructed from the blunt impact test data using either the IOP or the maximum principal stress of the corneal-scleral shell as the dependent variable. The injury risk functions used in Kennedy–Duma model and VT-WFU CIB are high-level correlations of injury risk based upon apparent insult, but are not obtained based on blast experiments. Blunt impact and blast loading have different time scales and mechanics which may result in a different distribution of stresses in the cornea and sclera and IOP. The Sherwood model was constructed based on the shock-tube experiments that subjected enucleated porcine eyes potted in gelatin to a shock wave. The injury model used the specific impulse of the positive phase duration as the dependent variable rather than a biomechanical outcome, such as the IOP or the maximum principal stress of the eye wall. Thus, the Sherwood model does not account for the focusing effects of facial features, which can significantly amplify the blast overpressure [10]. Moreover, postmortem degradation of the enucleated eyes may make the tissues more susceptible to damage from the shock wave. All three models produced widely different injury risk predictions, with the blast-specific Sherwood model providing the most severe predictions. These findings indicate that more realistic blast experiments are needed to evaluate the ocular injury risks. Furthermore, the experiments should be more tightly integrated with computational models to connect the blast conditions (e.g., specific impulse) to the intraocular biomechanical environment (e.g., IOP and tissue-level stress levels) and the injury outcomes.

## Conclusion

We presented a computational model to study the propagation of the blast wave through a deforming human eye. The model included detailed descriptions of a skull with the typical features of a 21-yr-old male, the internal ocular structures, spatially varying thickness, and isotropic, finite deformation behavior of the tissue. The stress analyses in our study correlate with the observed primary blast injuries in animal studies and ex vivo blast experiments on the choroid, retina, lens, sclera, ciliary zonules, and ONH. In addition, our sensitivity analyses showed that the effect of considering variational thickness in the cornea-scleral shell has a noticeable effect on the calculated risk of injuries. The findings of our simulations support the experimental observations of injury to the choroid, retina, lens, sclera, ciliary zonules, and ONH.

## Acknowledgment

This research was supported by US Army Medical Research, Vision Research Program under Grant No. W81XWH10-1-0766. We thank the support from the Department of Defense Science, Mathematics and Research for Transformation (DoD SMART) Scholarship for Service Program. Meshes of the skull were provided by WMRD, US Army Research Laboratory, Aberdeen, MD. We thank Professor R. Mittal for helpful discussions.

## Funding Data

• Congressionally Directed Medical Research Programs (W81XWH10-1-0766)

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