**Purpose.**:
To test the hypothesis that blunt trauma shockwave propagation may cause macular and peripheral retinal lesions, regardless of the presence of vitreous. The study was prompted by the observation of macular hole after an inadvertent BB shot in a previously vitrectomized eye.

**Methods.**:
The computational model was generated from generic eye geometry. Numeric simulations were performed with explicit finite element code. Simple constitutive modeling for soft tissues was used, and model parameters were calibrated on available experimental data by means of a reverse-engineering approach. Pressure, strain, and strain rates were calculated in vitreous- and aqueous-filled eyes. The paired *t*-test was used for statistical analysis with a 0.05 significance level.

**Results.**:
Pressure at the retinal surface ranged between −1 and +1.8 MPa at the macula. Vitreous-filled eyes showed significantly lower pressures at the macula during the compression phase (*P* < 0.0001) and at the vitreous base during the rebound phase (*P* = 0.04). Multiaxial strain reached 20% and 25% at the macula and vitreous base, whereas the strain rate reached 40,000 and 50,000 seconds^{−1}, respectively. Both strain and strain rates at the macula, vitreous base, and equator reached lower values in the vitreous- compared with the aqueous-filled eyes (*P* < 0.001). Calculated pressures, strain, and strain rate levels were several orders of magnitude higher than the retina tensile strength and load-carrying capability reported in the literature.

**Conclusions.**:
Vitreous traction may not be responsible for blunt trauma–associated retinal lesions and can actually damp shockwaves significantly. Negative pressures associated with multiaxial strain and high strain rates can tear and detach the retina. Differential retinal elasticity may explain the higher tendency toward tearing the macula and vitreous base.

^{ 1 }They account for more than 60%

^{ 2 }of the estimated 2.4 million eye injuries per year in the United States alone.

^{ 3 }Retinal sequelae of blunt trauma span a variety of well-known conditions, including commotio retinas (Berlin's edema),

^{ 4 }choroidal rupture,

^{ 5 }retinal tears, retinal detachment, dialyses,

^{ 6 }and macular hole (MH).

^{ 7 }

^{ 8 }The most accepted theory postulates that vitreous traction is the main cause of retinal damage,

^{ 9 }whereas alternative explanations suggest other mechanisms, such as differential globe layer deformation and increased internal limiting membrane (ILM) stiffness.

^{ 10 }

^{ 11 }the cornea,

^{ 12 }and the whole eyeball.

^{ 13 }

^{ 14 }gun. The right eye had had successful surgery 3 years earlier for primary pars plana vitrectomy and gas exchange by one of us (TR), due to rhegmatogenous retinal detachment, and had a best corrected visual acuity of 20/25 at his latest follow-up visit, 4 months earlier.

^{ 15 }(Fig. 2A) and surface geometry, and thickness data were combined to generate an FE mesh modeler (Truegrid; XYZ Scientific Application, Inc., Livermore, CA). A finite element model using eight-node brick elements was been built for the cornea, sclera, crystalline lens, vitreous, and retina (Figs. 2B, 2C). All parts of the eye have been assumed to be connected. Half of the globe has been modeled assuming symmetry around the visual axis. The BB was modeled as a rigid solid half sphere with 4.5-mm diameter and 0.345/2 g weight, impacting the cornea at a speed of 62.5 m/s perpendicular to the corneal apex, according to the experimental conditions described by Delori et al.

^{ 9 }

Material | Constitutive Model | Young Modulus (MPa) | Shear Modulus (MPa) | Poisson Modulus | Bulk Modulus (MPa) | Density (kg/m^{3}) |
---|---|---|---|---|---|---|

Sclera | Linear elastic | 28.0 | — | 0.49 | — | 1200 |

Cornea | Linear EOS + shear modulus | 1.5 | 0.5 | — | 300 | 1143 |

Lens | Linear EOS | — | — | — | 1000 | 1100 |

Retina | Linear EOS + shear modulus | — | 0.035 | — | 1000 | 1100 |

Aqueous | Linear EOS | — | — | — | 2200 | 1000 |

Material | Constitutive Model | G _{0} (MPa) | G _{∞} (MPa) | Viscosity η_{0} (MPa) | Decay Constant | Bulk Modulus (MPa) | Density (kg/m_{3}) |
---|---|---|---|---|---|---|---|

Vitreous | Linear EOS + linear shear viscoelastic | 10e^{−6} | 2e^{−6} | 5e^{−6} | 0.01 | 2000 | 950 |

*and ε′*

_{ij}*are the deviatoric stress and strain tensors,*

_{ij}*G*

_{∞}is the saturated shear module,

*G*

_{∞}is the initial shear module, η

_{0}is the viscoelastic constant, and β is the decay constant (Table 1).

^{3}factor (Table 2), an inverse-engineering approach was adopted to overcome the uncertainty pertinent to the equation of state, the dynamic constitutive response, and the triaxial response to the stress of biological tissues.

Cornea | Sclera | Retina | Vitreous |
---|---|---|---|

0.05–0.4^{16} | 0.15–0.83^{16} | 0.02^{17} | 2.8^{18} |

0.07–0.29^{19} | 0.2–0.5^{20} | 7.0^{18} | |

0.2–2^{21} | 2.6^{22} | ||

0.3–50^{22} | 2.9^{23} | ||

2.87–19^{24} | 358^{19} | ||

124^{25} | |||

1300^{26} |

^{ 9 }by running multiple simulations and varying one modulus value at a time. Parametric analyses of bulk moduli were conducted by cross-matching simulation curves with Delori's results of corneal indentation (Fig. 3) and BB pellet rebound speed (Figs. 4, 5).

*t*

_{0}) were calculated, with special regard to the areas where damage is clinically more evident: the macula and vitreous base. The retinal equator location was also calculated as a reference.

*l*is the incremental elongation and

*l*

_{0}is the initial reference length. True strain of solid elements is commonly reported as principal strain along three orthogonal axes (max, mid, and min), whereas the net result of the three vectors composition at each given time point is reported as the algebraic sum and referred to as the “trace of the elastic strain tensor,” which can also be regarded as the percentage of volume variation for each tridimensional tissue element.

^{ 27 }to control 0 energy deformation modes and to avoid overstiffening of the element.

^{ 9 }thereafter.

*t*= 0) up to the time at which the BB pellet is arrested (

*V*= 0; which occurs at 0.28 ms after

*t*

_{0}), and a rebound phase (from 0.28 to 1 ms). Beyond this time point, the analysis was interrupted due to subsequent interaction and reverberation of reflected stress waves.

*t*-tests to compare pressure and strain values in vitreous- and aqueous-filled eyes. Significance was set at 0.05.

*t*

_{0}; Fig. 3A). Force at impact was 217 N and energy delivered was 0.68 J. BB pellet speed reached 0 at 0.28 ms after

*t*

_{0}. Rebound maximum speed was −11.4 m/s, and the amount of energy dissipated by the impact was 94.6%.

^{ 9 }Snapshots of FEM simulations taken every 0.1 ms from corneal contact (

*t*

_{0}) are reported in Figure 6. Pressure variations at the macula, vitreous base, and retinal equator in vitreous- and aqueous-filled eyes are reported in Figure 7. Paired

*t*-test analysis showed a significant pressure difference between the vitreous- and aqueous-filled eyes at the macula during the compression phase only (

*P*< 0.0001), whereas no significant differences were found at any examined location during the entire rebound phase. It should be noted, however, that peak negative pressure at the vitreous base was reached at 0.35 ms (Table 3), thus the “rebound” phase at the vitreous base seems to lag behind the corneal rebound and starts at this very moment. Of note, when the paired

*t*-test was run for the time-frame between 0.36 and 1 ms, the difference between vitreous- and aqueous-filled eyes pressures at the vitreous base yield statistically significant results (

*P*= 0.04).

Macula | Equator | Vitreous Base | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Vitreous | Aqueous | Vitreous | Aqueous | Vitreous | Aqueous | |||||||

MPa | t − t _{0} | Mpa | t − t _{0} | Mpa | t − t _{0} | Mpa | t − t _{0} | Mpa | t − t _{0} | Mpa | t − t _{0} | |

Peak negative pressure | −0.6 | 0.03 | −0.6 | 0.53 | −0.2 | 0.97 | −0.6 | 0.46 | −0.8 | 0.35 | −1 | 0.35 |

Peak positive pressure | 1.3 | 0.25 | 1.8 | 0.86 | 0.4 | 0.44 | 0.8 | 0.52 | 0.5 | 0.08 | 0.5 | 0.07 |

*t*-tests returned significantly higher strain values for aqueous-filled eyes at the macula, equator, and vitreous base for each calculated axis (in all cases

*P*< 0.001). The trace of the elastic strain tensor is shown in Figure 9. The difference between vitreous- and aqueous-filled eyes was not significant at the macula, equator, or vitreous base (

*P*= 0.23,

*P*= 0.11, and

*P*= 0.18, respectively).

^{−1}at the vitreous base, 57,000 seconds

^{−1}at the equator, and 40,000 seconds

^{−1}at the macula, with significantly higher values for aqueous-filled eyes at each investigated location (

*P*< 0.0001 in all cases). Calculated displacement velocity varied between 5,000 and 10,000 mm/s.

^{ 28,29 }and intrinsic complexity. While mesh geometry of an ideal eye can be drawn with relative ease, in fact, constitutive response data often derive from in vitro experiments of isolated tissues, and some are simply missing.

^{ 16,23,30 }

^{ 31 –33 }

^{ 9 }by using a reverse-engineering approach, to reproduce their results. Once properly calibrated, the constitutive model was used to investigate the response in both vitreous- and aqueous-filled eyes, to calculate pressure and strain variations.

^{ 9 }there is no reason to believe that the calculated values should differ from those obtained in the experimental setting.

^{ 17,19,34 }The clinical relevance of high positive pressure for less than 1 ms remains a matter of speculation, although it seems reasonable to assume that mechanical deformation, ischemia, and axon flux interference can all contribute to retinal and choroidal damage. Such damage, being mediated by physiologic factors (i.e., ischemia, axonal transport, and perfusion) would most likely take time to become patent and is probably responsible for the subacute and chronic manifestation of blunt trauma: retinal ischemia and RPE mottling.

^{ 35,36 }measured retinal stress at a failure of 9 kPa at 0.03 mm/s, which rose to 11 kPa when load rate increased to 1.65 mm/s, whereas the strain of isolated retinal strips reduced from 80% to 50%. Wu et al.

^{ 37 }calculated a reference Young's modulus in simple uniaxial elongation of 5 kPa, whereas Friberg

^{ 16 }determined values of stress at failure for isolated choroid strips of 300 kPa. Similar results, although difficult to compare due to significant mismatch of the respective experimental settings, are several orders of magnitude lower than the pressures we calculated. We therefore propose that negative pressure can conceivably both tear and detach the retina.

^{−1}for the macula and over 50,000 seconds

^{−1}for the vitreous base (Fig. 9) and a displacement velocity between 5,000 and 10,000 mm/s. The question of whether those values are capable of ripping the retina is a difficult one. Wollensak et al.

^{ 35,36 }reported a much higher strain at failure of 51% at 1.6 mm/s, whereas Wu et al.

^{ 37 }measured extension ratios of isolated animal retina strips between 1.7 and 1.9, calculated at extremely low displacement velocity varying between 0.36 and 3.60 mm/sec. Jones et al.

^{ 23 }calculated a Young's modulus of 20 kPa for the isolated retina. Because of inconsistency in the methods, these data also are hardly comparable and may be not be representative of the eye response. Extrapolating data from isolated tissues, in fact, warrants extreme caution, especially because the retina, choroid and sclera all show nonlinear, anisotropic, and inhomogeneous mechanical characteristics

^{ 25,29 }and living, perfused organs can behave in a significantly different way. It must be noted, however, that the strain rates and displacement velocity that we measured along multiple axes (Figs. 9, 10) are more than 10

^{3}times higher than most reported experimental data. Several classes of materials show a strain rate effect on the constitutive response (i.e., an increased stress value at the same strain level for higher strain rates), but the same cannot be inferred for strain-to-failure values that may either increase or decrease as a function of the strain rate. In any case, we were able to measure a high level of stress multiaxiality (measured by the ratio of the hydrostatic and the deviatoric part of the stress tensor), which is known to reduce drastically the material strain to failure.

^{ 38 }We therefore propose that multiaxial strain also participates in the pathogenesis of anterior and posterior retinal lesions.

^{ 37 }and Chen et al.

^{ 25 }found that isolated retinal strips containing retinal vessels are significantly stiffer than strips with no visible vessels, possibly due to the presence of the elastic tunica. The fovea is avascular, and the vitreous base contains very few vessels; the retina can therefore be regarded as a series of elements whose differential stiffness may force the most elastic ones (vitreous base and macula) to deform more and possibly reach the breaking point earlier when stress is applied. We also showed that both positive and negative pressures were higher at the macula and vitreous base than at the equator (Fig. 6, Table 3), and this could add a further reason for localizing damage in such areas. Based on this assumption, strain does not seem to explain the preferential location of retinal damage at the vitreous base and macula, since peak values did not differ significantly. Multiaxial strain patterns over the time and the trace of the elastic tensor (Figs. 8, 9), instead, differed overtly, although we are unable to assign a clinical significance to such behavior.

^{ 18,20,31 }reduces pressures and therefore strain and perhaps, damage. Whether this statistically significant difference translates into a real-life clinical protective effect, especially when impacts generating such high pressures are considered, remains unclear and is probably true only for much lower pressures at which the vitreous damping role is intended to function.

^{ 27 }at least to some extent. However, as discussed in the paper, due to the lack of information about the effective response of these materials under complex stress states, dynamic pressure, and deformation (strain rate sensitivity), it seemed reasonable to approach the problem by limiting the number of unknown constitutive parameters, to ensure that the optimized set found by reverse engineering of the Delori experiment was unique and the best suited. Further research is warranted in the field of applying FEM to biological systems. We believe the refinement of mathematical models will undoubtedly participate in a substantial improvement of our knowledge of eye trauma.