- Email: [email protected]
Finite element model of ocular injury in abusive head trauma
Finite element model of ocular injury in abusive head trauma Nagarajan Rangarajan, PhD,a Sarath B. Kamalakkannan, MSME,a Vikas Hasija, MSME,a Tariq Shams, PhD,a Carole Jenny, MD, MBA,b Irina Serbanescu, BA,c Jamie Ho,c Matthew Rusinek,c and Alex V. Levin, MD, MHScc PURPOSE METHODS
To develop a finite element analysis of the eye and orbit that can be subjected to virtual shaking forces. LS-DYNA computer software was used to design a finite element model of the human infant eye, including orbit, fat, sclera, retina, vitreous, and muscles. The orbit was modeled as a rigid solid; the sclera and retina as elastic shells; the vitreous as viscoelastic solid or Newtonian fluid; and fat as elastic or viscoelastic solid. Muscles were modeled as spring-damper systems. Orbit-fat, fat-sclera, sclera-retina, and vitreous nodes-retina interfaces were defined with the use of the tied surface-surface function in LS-DYNA. The model was subjected to angular acceleration pulses obtained from shaking tests of a biofidelic doll (Aprica 2.5 kg dummy). Parametric studies were conducted to evaluate the effect of varying the material properties of vitreous/fat on maximum stress and stress distribution.
RESULTS
With the vitreous modeled as a Newtonian fluid, the repeated acceleration-deceleration oscillatory motion characteristic of abusive head trauma (AHT) causes cumulative increases in the forces experienced at the vitreoretinal interface. Under these vitreous conditions, retinal stress maximums occur at the posterior pole and peripheral retina, where AHT retinal hemorrhage is most often found.
CONCLUSIONS
Our model offers an improvement on dummy and animal models in allowing analysis of the effect of shaking on ocular tissues. It can be used under certain material conditions to demonstrate progressive ‘‘stacking’’ of intraocular stresses in locations corresponding to typical AHT injury patterns, allowing a better understanding of the mechanisms of retinal hemorrhage patterns. ( J AAPOS 2009;13:364-369)
A
busive head trauma (AHT) is a form of inflicted head trauma in infants, usually less than 3 years of age, resulting in characteristic injury to the central nervous system, skeleton, and eyes, particularly when the victim is submitted to repetitive acceleration-deceleration, with or without blunt head trauma (also known as See editorial on page 332.
Author affiliations: aGESAC Inc., Boonsboro Maryland; bBrown Medical School, Hasbro Children’s Hospital, Providence, Rhode Island; and cThe Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada Alex V. Levin, MD, MHSc, FRCSC, is now the Chief of Pediatric Ophthalmology and Ocular Genetics, Wills Eye Hospital, Philadelphia, Pennsylvania. Presented at the 34th Annual Meeting of the American Association for Pediatric Ophthalmology and Strabismus, Washington, DC, April 2-6, 2008. Presented in part at the Pediatric Academic Society Meeting, May 2007. Funded in part by Brandan’s Eye research Fund and APRICA, Inc. GESAC, Inc (SBK, VH, TS, NR) has a proprietary interest in the development of this model. Submitted April 4, 2008. Revision accepted November 7, 2008. Published online May 29, 2009. Reprint requests: Alex V. Levin, MD, MHSc, FRCSC, Pediatric Ophthalmology and Ocular Genetics, Wills Eye Hospital, 840 Walnut St., Philadelphia, PA 19107-5109 (email: [email protected]). Copyright Ó 2009 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/2009/$36.00 1 0 doi:10.1016/j.jaapos.2008.11.006
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shaken baby syndrome). Retinal hemorrhage is observed in approximately 85% of child victims of AHT.1,2 In approximately two-thirds of children with retinal hemorrhages the retinopathy is severe, with multilayered involvement extending out to the ora serrata, with or without macular retinoschisis.1 Although it is generally accepted that the major mechanism by which retinal hemorrhage occurs is related to vitreoretinal traction that occurs during repetitive acceleration-deceleration (eg, shaking with or without blunt head impact), other proposed theories include a role for increased intrathoracic pressure, increased intracranial pressure, hypoxia, and orbital injury.3 A reliable knowledge of the pathophysiology is important for maximizing the diagnostic specificity and sensitivity of hemorrhagic retinopathy as an indicator that a child has been abused, in particular because a history or witnessing of the abusive event is rarely offered at presentation. In an effort to better understand the mechanisms by which retinal hemorrhages are generated in the setting of abusive head injury, researchers have used clinical and autopsy data, animal models, and dummy models. Clinical and autopsy data are limited by a lack of knowledge of the exact events and mechanisms associated with the abuse.
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Volume 13 Number 4 / August 2009 Although animal models allow for the application of known forces, ethical concerns may preclude the development of models based on larger mammals with ocular and orbital configurations comparable with human infants. Dummy models are valuable but limited in terms of biofidelity and by an inability to model precise tissue characteristics. Taken together, these studies have allowed for remarkable progress in our understanding of AHT, but increasing the precision of AHT diagnosis remains an important goal. Finite element analysis is relatively inexpensive compared with animal and dummy modeling and allows for the application of forces to a computational model with analysis of the resultant predicted tissue stresses and strains. The basic procedure is to divide all the parts into very small pieces, where each piece can be shaped like a brick (solid elements) or like a thin plate (shell elements). The stresses and strains of each part are then computed based on external loading conditions. Other authors have developed finite element analysis models applicable to AHT,4,5 and models also have been developed for use in the analysis of blunt impact ocular trauma and other aspects of eye and orbital disease.6-12 We endeavored to develop a new finite element analysis of the eye and orbit that could be subjected to virtual forces experienced by a biofidelic infant dummy subjected to shaking by a human adult. This model has the potential to further our understanding of the unique mechanisms of retinal injury and to help our efforts to accurately diagnose AHT and to prevent it.
Methods Research ethics board review was not required for this study. The finite element analysis was developed with the use of input from a wide variety of literature sources reporting tissue properties related to the eye and orbit (e-Supplement 1, available at jaapos. org). Efforts were made to gather data applicable to a full-term human newborn. Where such data were not available, we either extrapolated backward from adult or older childhood data (using linear or nonlinear curves as seemed appropriate based on the available data), used data from similar nonocular tissues or, as a last resort, used data from animal studies. We did not conduct any direct tissue property analysis. Retrospective analysis of anonymized 3-dimensional computed tomography scan reconstructions of the orbits in the axial plane from 6 normal infants ages 4-7 months undergoing computed tomography scanning for other concerns that proved not to be present, on file at the center of the senior author (AVL), was conducted to obtain an average measurement of the shortest distance between the back of the globe and the optic nerve foramen at the apex of the orbit. Measurements of the right and left orbits of each patient’s scan at a cut through the optic nerve-scleral junction were averaged together and then the average of all 6 patients was calculated.
Description of the Finite Element Model An LS-DYNA computer software program was used to create a finite element model to study the effects of angular acceleration of the infant head on the eye. The model includes representation of
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Table 1. Characteristics of the mesh model Eye model component
Number of elements
Number of nodes
Orbit Fat Sclera Retina Vitreous
2025 6500 486 150 875
4112 7776 986 152 976
the orbit, cornea, sclera, retina, and vitreous. The geometrical dimensions of the globe, retina, and vitreous were scaled from the values presented by Stitzel and colleagues.11 Their dimension of 25 mm for the adult globe was scaled to 20 mm in the current model to represent a typical infant eye,13 and the other structures were also scaled correspondingly. The lens, iris, ciliary body, and optic nerve were not included. The extraocular muscles were modeled as 8 mm wide, 50 mm long,13 with an elastic stiffness of 0.1 N/mm and a damping coefficient of 5 104 N/(mm/s). Dimensions of the other model components are provided in e-Supplement 2 (available at jaapos.org) and their material properties are listed in e-Supplement 3 (available at jaapos.org). The model is depicted in e-Supplement 4 (available at jaapos.org). The sclera and cornea were modeled as continuous homogenous thin spherical shells with elements of uniform thickness. The retina is a thin shell. Fat is represented as solid elements filling the space between the orbit and the eye, and the orbital bone is modeled with solid elements. The vitreous was modeled as a sphere. Table 1 details the mesh model properties. The 4 rectus muscles are modeled as parallel spring-damper systems, with uniform length and thickness. Each rectus muscle was modeled with 4 springs and 4 dampers to distribute the action of the muscle across its width at its insertion point. Each muscle had separate attachment points on the sclera and one common attachment point at the apex of the orbit. The superior oblique muscle also was modeled with 4 parallel spring-dampers. Its attachment points on the sclera are all behind the equator. There is one common attachment point at the apex of the orbit. The inferior oblique muscle is modeled with four parallel springdampers. The 4 attachment points on the sclera are behind the equator. There are 4 different attachment points for each spring-damper on the orbit. Positions of attachment points are based on a three-dimensional eye model and anatomy. Figure 1 shows the locations of the spring-dampers (i.e., muscle models). Contacts between orbit and fat, fat and sclera, and sclera and retina are defined with the use of tied surface-to-surface function in LS-DYNA. In this type of contact, mating nodes move together. Contact between retina and vitreous is defined using tied node-to-surface function in LS-DYNA. In this contact case, specific nodes of the retina are tied to the adjacent nodes on the vitreous and will move together, leaving other parts of the retina to move separately. The contact between the vitreous and the retina is limited to the macula area and a strip anterior to the equator of width approximately equal to the vitreous base attachment of a newborn infant. The macula is represented by one element, with 4 nodes attaching the vitreous to the retina. The contact between the vitreous and the retina is shown in e-Supplement 5 (available at jaapos.org). Note that this contact
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Volume 13 Number 4 / August 2009 certainty in the measured values, and the aim was to evaluate dependence of response to this key input parameter. Simulations were started with material properties calculated from values provided by Stitzel and colleagues11 using equations 1, 2, and 3 (to follow). This starting simulation is referred to as Case 1. In Cases 2 through 6, fat was treated as a viscoelastic material with the same elastic modulus as in Case 1. Bulk modulus and shear modulus of the vitreous were calculated using the following formulas: K5
E 3ð1 2nÞ
[1]
where K is bulk modulus, n is Poisson ratio, and E is Young’s modulus. G5 FIG 1. Eye model with muscles from an oblique view.
definition only applies when using material types other than Fluid for the vitreous. If material type Fluid is used for the vitreous, then all nodes in the vitreous must be constrained. Node numbers are detailed in Table 1. The contacts between the vitreous and the optic nerve and between the vitreous and the lens were not included in this initial phase of our investigation. During early testing of the model, simulation runs were conducted with different mesh sizes and number of elements/nodes. These early models included 3 layers: the sclera/choroid, the retina, and the vitreous. The number of elements was varied from about 1,400 to 16,000. It was found that the change in the peak von Mises stress or time to peak was less than 20%. Because this work was exploratory, and some material properties were not known with this accuracy, a decision was made to use lower mesh density to keep simulation times at reasonable values (Table 1).
Parametric Tests The model was exercised with the use of a pulse shown in e-Supplement 6 (available at jaapos.org): a 5-Hz rotation about the center of gravity of orbit around the lateral axis that was used as the input for the simulations. The peak value of rotation is about 50 rad/s. The pulse was obtained from shaking experiments conducted with the Aprica 2.5 kg biofidelic dummy (data not shown).14 Once the model proved to be stable, parametric runs were made to evaluate the effect of variations in material properties. The vitreous was modeled as a viscoelastic material and as a fluid. Fat was modeled as an elastic and viscoelastic material. Key parameters used to define these materials are listed in e-Supplement 7 (available at jaapos.org). These 2 components are large structures that might have considerable effect on the kinematics of the system and it was thought advisable to vary their properties over a reasonably large range to study the effects of such changes on the motion of the eye. Fat was chosen because it controls the motion of the globe relative to the orbit, and vitreous was chosen as its deformation during rotation would tend to drag attached retinal nodes and thus lead to maximum relative displacement of retinal nodes. A factor-of-ten variation in the material properties of vitreous was considered reasonable for this exercise, because there was un-
E 2ð11vÞ
[2]
where G is shear modulus. The shear relaxation behavior in a viscoelastic material is described as, GðtÞ 5 GN 1ðG0 GN Þebt
[3]
Results The effect of material properties on the maximum stress on the retina is shown in e-Supplement 8 (available at jaapos. org). Peak maximal stress was experienced in Cases 4 and 5, where the fat was modeled as a viscoelastic and the vitreous as fluid. The stresses on different elements of the retina were examined, and the peak stresses usually were found along the set of elements along the ora serrata, where the nodes of the retina were tied to the nodes of the vitreous. The von Mises stress was used as the response variable. This stress is a useful measure of the stress because it depends on all 3 principal stress components and is dependent only on the deformation of an element. For the case in which viscoelastic material was used for both vitreous and fat (Case 2), the time history of the von Mises stresses is shown in Figure 2A. The time history of the stress shows increasing values during the first several shaking cycles until stress reaches an approximately constant value by the sixth cycle. Changing the material type of fat to elastic (Case 1) did not show much effect on the maximum stress. When the bulk modulus of the vitreous was increased by 10 times (Case 3), the von Mises stress on the retina decreased by 50%, and the stress build-up effect over multiple shaking cycles also decreased. The stress time history for the case is shown in Figure 2B. When the vitreous was modeled as a fluid with a viscous coefficient (VC) of 0.5 (Case 4), there were noticeable differences in maximum stress, stress distribution, and stress build-up effect, when compared with the case where it was modeled as viscoelastic (Case 2). Von Mises stress increased 10-fold, and there was a marked stress build-up effect. Maximum stress occurs around the junction of the retina and the vitreous. The stress time history is given in
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0.016
von Mises stress (MPa)
0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000
0.0
0.2
0.4
A
0.6
0.8
1.0
1.2
1.4
Time (sec) 0.0035
von Mises stress (MPa)
0.0030
0.0020 0.0015 0.0010 0.0005
0.0
0.2
0.4
B
0.6
0.8
1.0
1.2
1.4
Time (sec) 0.14 0.12
von Mises stress (MPa)
there was a small reduction in maximum stress, but the simulation also stopped prematurely, probably because the VC was at the recommended limit provided by the software manufacturer. For the viscoelastic model, peak contact forces between the orbit and fat as well as between fat and sclera are in the range of 0.09-0.10 N (and vary between the global X direction and Z direction as the globe undergoes rotation). For the fluid model, the corresponding peak forces are in the range of 0.08-0.09 N. The contact forces between sclera and retina and retina and vitreous are in the range of 0.05-0.06 N for both models. The time variation is also different for the 2 models, with contact forces for the fluid model showing a reduction in peak values for every cycle and contact forces in the viscoelastic model showing a more constant behavior. Stress Distribution on the Sclera, Retina, and Vitreous Simulation results indicate that stress distributions for the sclera, retina, and vitreous for Cases 2 and 3 are similar to those estimated in Case 1, whereas stress distributions for the sclera, retina, and vitreous in Cases 4 and 6 are very similar to those in Case 5. Figures 3A and 3B show that the stress distribution and the location of maximum stress depend on the choice of material model for the eye components. When the vitreous is modeled using viscoelastic material, the areas with maximum stress on the retina, the sclera, and the vitreous are located mostly in front of the equator. However, when the vitreous is modeled using fluid material, the areas with maximum stress are found behind the equator, and the most heavily stressed parts of the vitreous are at the posterior pole (Figure 3B) and at the front pole (not shown).
0.0025
0.0000
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0.10
Discussion
0.08 0.06 0.04 0.02 0.00 0.0
0.2
C
0.4
0.6
0.8
1.0
1.2
1.4
Time (sec)
FIG 2. A, von Mises stresses on element no. 29 of retina (Case 2, viscoelastic vitreous and fat, K 5 0.7); B, element no. 75 of retina (Case 3, viscoelastic vitreous, K 5 7.0); C, element no. 17 of retina (Case 4, Newtonian fluid vitreous, VC 5 0.5).
Figure 2C, which shows that the peak stress increases through all cycles that were simulated. When the VC is reduced by 40% to 0.3, the peak stress, stress distribution, and stress build-up effect do not change significantly. When the VC was further reduced to 0.1,
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A finite element model of the eye has been developed and exercised with a 5-Hz, 50 rad/s peak pulse. The pulse was obtained from shaking tests by Japanese adult males of average weight and height conducted on the Aprica 2.5 kg biofidelic infant dummy. Parametric tests were conducted to evaluate the effect of changing material properties of fat and vitreous on retinal stress. We found that changing the material type of fatty tissue from elastic to viscoelastic did not show much effect on the maximum stress and the stress distribution. The assigned properties of the vitreous had significant effects on the maximum stress and the stress distribution. When the bulk modulus of the vitreous was increased (by 10 times), the maximum stress on the retina decreased by approximately 50%. In the meantime, the stress buildup effect was significantly reduced. Changing the material type of vitreous from viscoelastic to fluid had a significant effect on the maximum stress, stress distribution, and the stress buildup; however, when the viscosity coefficient of the fluid was changed, there was not much effect. The difference is likely attributable to the different constraint between the nodes in the
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FIG 3. von Mises stress (MPa) distribution on retina: A, Case 1, vitreous as viscoelastic; B, Case 5, vitreous as Newtonian fluid. Red indicates area of greatest stress. Tangent lines indicate stress from superior oblique (SO).
retina and the vitreous. In the viscoelastic model, the retina is attached at a selected number of nodes to the vitreous, whereas in the fluid model all of the retinal nodes are attached to the vitreous surface. Further investigation is necessary to quantify the influence of the relative number of constrained nodes to the rate of stress buildup. The contact forces between orbit and fat and fat and sclera are reduced by 15% to 25% when the vitreous material is changed from viscoelastic to fluid. The motion of the globe is constrained by the contact forces between orbit and fat and between fat and sclera. However, there is very little change in the contact forces between sclera and retina and between retina and vitreous when the vitreous material is changed. Maximum stress occurs around the retina-vitreous connection area, correlating with the clinical manifestation of hemorrhagic retinopathy observed in AHT, wherein there is a predilection for hemorrhage to occur at the ora and the posterior pole.1,2,15-18 Traumatic macular retinoschisis is a cardinal finding in AHT: it has been shown clinically, histologically, and electrophysiologically to represent a result of vitreoretinal traction at the posterior pole, where the vitreous of infants is uniquely and firmly attached to the retina3,19 (see also e-Supplement 1). It should be noted that we did not ‘‘instruct’’ our model to mimic the clinical reality of AHT; rather, we simply relied on the known anatomic relationships between the retina and vitreous. It may be that our results would be different if we included the lens and optic nerve head to which the vitreous also has adhesion. As a result, the vitreous would be further stabilized at this anterior point. The fixation of the vitreous at the optic nerve may not change our observations given its close proximity, if not contiguous relationship, with the macular vitreo-retinal attachments; however, we hope to refine our model to include anterior segment structures and an optic nerve.
We observed that stress on the retina and sclera accumulates as the shaking continues for certain material models for vitreous (eg, viscoelastic or fluid). When modeling vitreous as a viscoelastic material, assigning smaller bulk modulus to the material showed a clear stress accumulation effect. The rate of change of stress was more evident in this case. When the vitreous is modeled as a fluid, varying the viscosity coefficient did not show significant effects on maximum stress, stress accumulation, and stress distribution; nonetheless, the maximum stress on the retina builds up to a bigger number when the vitreous is modeled as a fluid. On the basis of perpetrator confessions, clinical observations and animal models,20 it is apparent that repetitive acceleration-deceleration is what characterizes this form of abusive head injury as opposed to single impact mechanisms. This stress accumulation effect is a critical component of AHT, a fact that helps to explain why biomechanical calculations that are limited to attempts to predict the effects of a single acceleration-deceleration cycle will by definition not apply to the scenario of this form of AHT. The cumulative increase in force would also help to explain the marked disparity between accidental and abusive injuries, in particular hemorrhagic retinopathy, even when one considers severe single acceleration-deceleration accidental mechanisms such as some motor vehicle accidents.18,21,22 There are several limitations to our study, including of course the incomplete nature of our model. Because we are not testing actual human tissue, globes, or infants, the interpretation of results, although based on the extensive literature on this subject, remains a theoretical application to the abused human infant. The current model does not include several important structures, such as the lens, choroid, ciliary body, and cornea. The fat distribution and orbit geometry were approximated. Cirovic and colleagues4,23 noted the importance of a suction type attachment between orbital fat and
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Volume 13 Number 4 / August 2009 sclera, which we have not yet modeled. Material property data were scaled and the appropriateness of scaling is yet to be evaluated. All the material data in this study are currently available in the LS-DYNA material library. It may be necessary to develop new material models to fully describe the materials used in this model. Ultimately, direct testing of the biomechanical properties of neonatal tissues (eg, vitreous) will be required to optimize the accuracy of our input data. Because of the uncertainty regarding material properties of the important tissues involved in the eye, especially under dynamic loading, and as viscoelastic materials sometimes show dynamic stiffening with increased rates of loading, the variation by an order of 10 in the material properties was to evaluate the change in response (as defined by maximum stress values) with such a change in input parameters. A more accurate simulation must await more accurate experiments to obtain these properties at the loading rates of interest. The convergence of the model and optimum mesh size will have to be established for the complete model. Also, the variation of response as a function of uncertainty in material properties will have to be evaluated. Input motion was purely rotational at the center of the orbit unlike the multidirectional movements experienced by the infant head during AHT. The effect of variation of mesh size, integration intervals, and integration procedure has not yet been fully evaluated. At the time of the simulations, location of head center of gravity relative to orbit landmarks was not known. Because this work was exploratory, the input of the angular motion directly at the center of the orbit was the simplest and also most conservative, since any additional arm length would increase linear velocities at the region of the eye. Future simulations could be altered to reflect alternate center of gravity points. Our model is far from complete. This is a preliminary study to provide a qualitative picture of what happens within the infant eye under repeated acceleration-deceleration motion at rates and forces similar to that which an adult male can apply to a 2.5 kg neonate as measured using a biofidelic dummy. Although our results should be interpreted with caution, the correlations between our findings and the clinical reality offer promise that finite element analysis may be an applicable method of experimental investigation to better understand the eye abnormalities observed in AHT.
Acknowledgments We acknowledge the invaluable assistance of our Research Assistants Erica Bell and Charmaine DeSouza. We are grateful for access to normal CT scans provided by Dr. Christopher Forrest and assistance with the measurements taken from the CT scans from Stephanie Holowka. We are also grateful for the support of APRICA Inc. and in particular Chairman Kenzo Kassai, Mr. Shin Shimomaki and their Pediatric Research Advisor, Dr. Robert Bigge. References 1. Morad Y, Kim Y, Armstrong D, Huyer D, Mian M, Levin A. Correlation between retinal abnormalities and intracranial abnormali-
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ties in the shaken baby syndrome. Am J Ophthalmol 2002;134: 354-9. Kivlin J, Simons K, Lazoritz S, Ruttum M. Shaken baby syndrome. Ophthalmology 2000;107:1246-54. Levin A. Retinal haemorrhage and child abuse. In: David T, editor. Recent advances in paediatrics. Vol 18. London: Churchill Livingstone; 2000. p. 151-219. Cirovic S, Bhola RM, Hose DR, Howard IC, Lawford PV, Parsons MA. A computational study of the passive mechanisms of eye restraint during head impact trauma. Comput Methods Biomech Biomed Engin 2005;8:1-6. Roth S, Raul JS, Ludes B, Willinger R. Finite element analysis of impact and shaking inflicted to a child. Int J Legal Med 2007; 121:223-8. Uchio E, Ohno S, Kudoh J, Aoki K, Kisielewicz LT. Simulation model of an eyeball based on finite element analysis on a supercomputer. Br J Ophthalmol 1999;83:1106-11. Uchio E, Kadonosono K, Matsuoka Y, Goto S. Simulation of air-bag impact on an eye with transsclerally fixated posterior chamber intraocular lens using finite element analysis. J Cataract Refract Surg 2004;30:483-90. Scott J. A finite element model of heat transport in the human eye. Phys Med Biol 1988;33:227-41. Stay MS, Xu J, Randolph TW, Barocas VH. Computer simulation of convective and diffusive transport of controlled-release drugs in the vitreous humor. Pharm Res 2003;20:96-102. Vinger PF. Understanding eye trauma through computer modeling. Arch Ophthalmol 2005;123:833-4. Stitzel JD, Hansen GA, Herring IP, Duma SM. Blunt trauma of the aging eye: Injury mechanisms and increasing lens stiffness. Arch Ophthalmol 2005;123:789-94. Schutte S, van den Bedem SP, van Keulen F, van der Helm FC, Simonsz HJ. A finite-element analysis model of orbital biomechanics. Vision Res 2006;46:1724-31. Swan KC, Wilkins JH. Extraocular muscle surgery in early infancy-anatomical factors. J Pediatr Ophthalmol Strabismus 1984; 21:44-9. Wang Y, Ranagarajan N, Shams T, Fukuda T, Yamada T, Jenny C. Design of a biofidelic instrumented 3.4 kg infant dummy. Paper presented at: Proceedings 19th International Technical Conference on the Enhanced Safety of Vehicles, 2005; Washington, DC. Gilliland M, Luckenbach M, Chenier T. Systemic and ocular findings in 169 prospectively studied child deaths: Retinal hemorrhages usually mean child abuse. Forensic Sci Int 1994;68:117-32. Greenwald M. The Shaken Baby syndrome. Sem Ophthalmol 1990;5: 202-15. Marshall D, Brownstein S, Dorey M, Addison D, Carpenter B. The spectrum of postmortem ocular findings in victims of shaken baby syndrome. Can J Ophthalmol 2001;36:377-84. Bechtel K, Stoessel K, Leventhal JM, Ogle E, Teague B, Lavietes S, et al. Characteristics that distinguish accidental from abusive injury in hospitalized young children with head trauma. Pediatrics 2004; 114:165-8. Greenwald M, Weiss A, Oesterle C, Friendly D. Traumatic retinoschisis in battered babies. Ophthalmology 1986;93:618-25. Raghupathi R, Mehr MF, Helfaer MA, Margulies SS. Traumatic axonal injury is exacerbated following repetitive closed head injury in the neonatal pig. J Neurotrauma 2004;21:307-16. Vinchon M, Defoort-Dhellemmes S, Desurmont M, Dhellemmes P. Accidental and nonaccidental head injuries in infants: A prospective study. J Neurosurg 2005;102(4 Suppl):380-84. Vinchon M, Noizet O, Defoort-Dhellemmes S, Soto-Ares G, Dhellemmes P. Infantile subdural hematoma due to traffic accidents. Pediatr Neurosurg 2002;37:245-53. Cirovic S, Bhola RM, Hose DR, Howard IC, Lawford PV, Parsons MA. Mechanistic hypothesis for eye injury in infant shaking: An experimental and computational study. Foren Sci Med Pathol 2005;1:53-9.
To develop a finite element analysis of the eye and orbit that can be subjected to virtual shaking forces. LS-DYNA computer software was used to design a finite element model of the human infant eye, including orbit, fat, sclera, retina, vitreous, and muscles. The orbit was modeled as a rigid solid; the sclera and retina as elastic shells; the vitreous as viscoelastic solid or Newtonian fluid; and fat as elastic or viscoelastic solid. Muscles were modeled as spring-damper systems. Orbit-fat, fat-sclera, sclera-retina, and vitreous nodes-retina interfaces were defined with the use of the tied surface-surface function in LS-DYNA. The model was subjected to angular acceleration pulses obtained from shaking tests of a biofidelic doll (Aprica 2.5 kg dummy). Parametric studies were conducted to evaluate the effect of varying the material properties of vitreous/fat on maximum stress and stress distribution.
RESULTS
With the vitreous modeled as a Newtonian fluid, the repeated acceleration-deceleration oscillatory motion characteristic of abusive head trauma (AHT) causes cumulative increases in the forces experienced at the vitreoretinal interface. Under these vitreous conditions, retinal stress maximums occur at the posterior pole and peripheral retina, where AHT retinal hemorrhage is most often found.
CONCLUSIONS
Our model offers an improvement on dummy and animal models in allowing analysis of the effect of shaking on ocular tissues. It can be used under certain material conditions to demonstrate progressive ‘‘stacking’’ of intraocular stresses in locations corresponding to typical AHT injury patterns, allowing a better understanding of the mechanisms of retinal hemorrhage patterns. ( J AAPOS 2009;13:364-369)
A
busive head trauma (AHT) is a form of inflicted head trauma in infants, usually less than 3 years of age, resulting in characteristic injury to the central nervous system, skeleton, and eyes, particularly when the victim is submitted to repetitive acceleration-deceleration, with or without blunt head trauma (also known as See editorial on page 332.
Author affiliations: aGESAC Inc., Boonsboro Maryland; bBrown Medical School, Hasbro Children’s Hospital, Providence, Rhode Island; and cThe Hospital for Sick Children, University of Toronto, Toronto, Ontario, Canada Alex V. Levin, MD, MHSc, FRCSC, is now the Chief of Pediatric Ophthalmology and Ocular Genetics, Wills Eye Hospital, Philadelphia, Pennsylvania. Presented at the 34th Annual Meeting of the American Association for Pediatric Ophthalmology and Strabismus, Washington, DC, April 2-6, 2008. Presented in part at the Pediatric Academic Society Meeting, May 2007. Funded in part by Brandan’s Eye research Fund and APRICA, Inc. GESAC, Inc (SBK, VH, TS, NR) has a proprietary interest in the development of this model. Submitted April 4, 2008. Revision accepted November 7, 2008. Published online May 29, 2009. Reprint requests: Alex V. Levin, MD, MHSc, FRCSC, Pediatric Ophthalmology and Ocular Genetics, Wills Eye Hospital, 840 Walnut St., Philadelphia, PA 19107-5109 (email: [email protected]). Copyright Ó 2009 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/2009/$36.00 1 0 doi:10.1016/j.jaapos.2008.11.006
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shaken baby syndrome). Retinal hemorrhage is observed in approximately 85% of child victims of AHT.1,2 In approximately two-thirds of children with retinal hemorrhages the retinopathy is severe, with multilayered involvement extending out to the ora serrata, with or without macular retinoschisis.1 Although it is generally accepted that the major mechanism by which retinal hemorrhage occurs is related to vitreoretinal traction that occurs during repetitive acceleration-deceleration (eg, shaking with or without blunt head impact), other proposed theories include a role for increased intrathoracic pressure, increased intracranial pressure, hypoxia, and orbital injury.3 A reliable knowledge of the pathophysiology is important for maximizing the diagnostic specificity and sensitivity of hemorrhagic retinopathy as an indicator that a child has been abused, in particular because a history or witnessing of the abusive event is rarely offered at presentation. In an effort to better understand the mechanisms by which retinal hemorrhages are generated in the setting of abusive head injury, researchers have used clinical and autopsy data, animal models, and dummy models. Clinical and autopsy data are limited by a lack of knowledge of the exact events and mechanisms associated with the abuse.
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Volume 13 Number 4 / August 2009 Although animal models allow for the application of known forces, ethical concerns may preclude the development of models based on larger mammals with ocular and orbital configurations comparable with human infants. Dummy models are valuable but limited in terms of biofidelity and by an inability to model precise tissue characteristics. Taken together, these studies have allowed for remarkable progress in our understanding of AHT, but increasing the precision of AHT diagnosis remains an important goal. Finite element analysis is relatively inexpensive compared with animal and dummy modeling and allows for the application of forces to a computational model with analysis of the resultant predicted tissue stresses and strains. The basic procedure is to divide all the parts into very small pieces, where each piece can be shaped like a brick (solid elements) or like a thin plate (shell elements). The stresses and strains of each part are then computed based on external loading conditions. Other authors have developed finite element analysis models applicable to AHT,4,5 and models also have been developed for use in the analysis of blunt impact ocular trauma and other aspects of eye and orbital disease.6-12 We endeavored to develop a new finite element analysis of the eye and orbit that could be subjected to virtual forces experienced by a biofidelic infant dummy subjected to shaking by a human adult. This model has the potential to further our understanding of the unique mechanisms of retinal injury and to help our efforts to accurately diagnose AHT and to prevent it.
Methods Research ethics board review was not required for this study. The finite element analysis was developed with the use of input from a wide variety of literature sources reporting tissue properties related to the eye and orbit (e-Supplement 1, available at jaapos. org). Efforts were made to gather data applicable to a full-term human newborn. Where such data were not available, we either extrapolated backward from adult or older childhood data (using linear or nonlinear curves as seemed appropriate based on the available data), used data from similar nonocular tissues or, as a last resort, used data from animal studies. We did not conduct any direct tissue property analysis. Retrospective analysis of anonymized 3-dimensional computed tomography scan reconstructions of the orbits in the axial plane from 6 normal infants ages 4-7 months undergoing computed tomography scanning for other concerns that proved not to be present, on file at the center of the senior author (AVL), was conducted to obtain an average measurement of the shortest distance between the back of the globe and the optic nerve foramen at the apex of the orbit. Measurements of the right and left orbits of each patient’s scan at a cut through the optic nerve-scleral junction were averaged together and then the average of all 6 patients was calculated.
Description of the Finite Element Model An LS-DYNA computer software program was used to create a finite element model to study the effects of angular acceleration of the infant head on the eye. The model includes representation of
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Table 1. Characteristics of the mesh model Eye model component
Number of elements
Number of nodes
Orbit Fat Sclera Retina Vitreous
2025 6500 486 150 875
4112 7776 986 152 976
the orbit, cornea, sclera, retina, and vitreous. The geometrical dimensions of the globe, retina, and vitreous were scaled from the values presented by Stitzel and colleagues.11 Their dimension of 25 mm for the adult globe was scaled to 20 mm in the current model to represent a typical infant eye,13 and the other structures were also scaled correspondingly. The lens, iris, ciliary body, and optic nerve were not included. The extraocular muscles were modeled as 8 mm wide, 50 mm long,13 with an elastic stiffness of 0.1 N/mm and a damping coefficient of 5 104 N/(mm/s). Dimensions of the other model components are provided in e-Supplement 2 (available at jaapos.org) and their material properties are listed in e-Supplement 3 (available at jaapos.org). The model is depicted in e-Supplement 4 (available at jaapos.org). The sclera and cornea were modeled as continuous homogenous thin spherical shells with elements of uniform thickness. The retina is a thin shell. Fat is represented as solid elements filling the space between the orbit and the eye, and the orbital bone is modeled with solid elements. The vitreous was modeled as a sphere. Table 1 details the mesh model properties. The 4 rectus muscles are modeled as parallel spring-damper systems, with uniform length and thickness. Each rectus muscle was modeled with 4 springs and 4 dampers to distribute the action of the muscle across its width at its insertion point. Each muscle had separate attachment points on the sclera and one common attachment point at the apex of the orbit. The superior oblique muscle also was modeled with 4 parallel spring-dampers. Its attachment points on the sclera are all behind the equator. There is one common attachment point at the apex of the orbit. The inferior oblique muscle is modeled with four parallel springdampers. The 4 attachment points on the sclera are behind the equator. There are 4 different attachment points for each spring-damper on the orbit. Positions of attachment points are based on a three-dimensional eye model and anatomy. Figure 1 shows the locations of the spring-dampers (i.e., muscle models). Contacts between orbit and fat, fat and sclera, and sclera and retina are defined with the use of tied surface-to-surface function in LS-DYNA. In this type of contact, mating nodes move together. Contact between retina and vitreous is defined using tied node-to-surface function in LS-DYNA. In this contact case, specific nodes of the retina are tied to the adjacent nodes on the vitreous and will move together, leaving other parts of the retina to move separately. The contact between the vitreous and the retina is limited to the macula area and a strip anterior to the equator of width approximately equal to the vitreous base attachment of a newborn infant. The macula is represented by one element, with 4 nodes attaching the vitreous to the retina. The contact between the vitreous and the retina is shown in e-Supplement 5 (available at jaapos.org). Note that this contact
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Volume 13 Number 4 / August 2009 certainty in the measured values, and the aim was to evaluate dependence of response to this key input parameter. Simulations were started with material properties calculated from values provided by Stitzel and colleagues11 using equations 1, 2, and 3 (to follow). This starting simulation is referred to as Case 1. In Cases 2 through 6, fat was treated as a viscoelastic material with the same elastic modulus as in Case 1. Bulk modulus and shear modulus of the vitreous were calculated using the following formulas: K5
E 3ð1 2nÞ
[1]
where K is bulk modulus, n is Poisson ratio, and E is Young’s modulus. G5 FIG 1. Eye model with muscles from an oblique view.
definition only applies when using material types other than Fluid for the vitreous. If material type Fluid is used for the vitreous, then all nodes in the vitreous must be constrained. Node numbers are detailed in Table 1. The contacts between the vitreous and the optic nerve and between the vitreous and the lens were not included in this initial phase of our investigation. During early testing of the model, simulation runs were conducted with different mesh sizes and number of elements/nodes. These early models included 3 layers: the sclera/choroid, the retina, and the vitreous. The number of elements was varied from about 1,400 to 16,000. It was found that the change in the peak von Mises stress or time to peak was less than 20%. Because this work was exploratory, and some material properties were not known with this accuracy, a decision was made to use lower mesh density to keep simulation times at reasonable values (Table 1).
Parametric Tests The model was exercised with the use of a pulse shown in e-Supplement 6 (available at jaapos.org): a 5-Hz rotation about the center of gravity of orbit around the lateral axis that was used as the input for the simulations. The peak value of rotation is about 50 rad/s. The pulse was obtained from shaking experiments conducted with the Aprica 2.5 kg biofidelic dummy (data not shown).14 Once the model proved to be stable, parametric runs were made to evaluate the effect of variations in material properties. The vitreous was modeled as a viscoelastic material and as a fluid. Fat was modeled as an elastic and viscoelastic material. Key parameters used to define these materials are listed in e-Supplement 7 (available at jaapos.org). These 2 components are large structures that might have considerable effect on the kinematics of the system and it was thought advisable to vary their properties over a reasonably large range to study the effects of such changes on the motion of the eye. Fat was chosen because it controls the motion of the globe relative to the orbit, and vitreous was chosen as its deformation during rotation would tend to drag attached retinal nodes and thus lead to maximum relative displacement of retinal nodes. A factor-of-ten variation in the material properties of vitreous was considered reasonable for this exercise, because there was un-
E 2ð11vÞ
[2]
where G is shear modulus. The shear relaxation behavior in a viscoelastic material is described as, GðtÞ 5 GN 1ðG0 GN Þebt
[3]
Results The effect of material properties on the maximum stress on the retina is shown in e-Supplement 8 (available at jaapos. org). Peak maximal stress was experienced in Cases 4 and 5, where the fat was modeled as a viscoelastic and the vitreous as fluid. The stresses on different elements of the retina were examined, and the peak stresses usually were found along the set of elements along the ora serrata, where the nodes of the retina were tied to the nodes of the vitreous. The von Mises stress was used as the response variable. This stress is a useful measure of the stress because it depends on all 3 principal stress components and is dependent only on the deformation of an element. For the case in which viscoelastic material was used for both vitreous and fat (Case 2), the time history of the von Mises stresses is shown in Figure 2A. The time history of the stress shows increasing values during the first several shaking cycles until stress reaches an approximately constant value by the sixth cycle. Changing the material type of fat to elastic (Case 1) did not show much effect on the maximum stress. When the bulk modulus of the vitreous was increased by 10 times (Case 3), the von Mises stress on the retina decreased by 50%, and the stress build-up effect over multiple shaking cycles also decreased. The stress time history for the case is shown in Figure 2B. When the vitreous was modeled as a fluid with a viscous coefficient (VC) of 0.5 (Case 4), there were noticeable differences in maximum stress, stress distribution, and stress build-up effect, when compared with the case where it was modeled as viscoelastic (Case 2). Von Mises stress increased 10-fold, and there was a marked stress build-up effect. Maximum stress occurs around the junction of the retina and the vitreous. The stress time history is given in
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0.016
von Mises stress (MPa)
0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000
0.0
0.2
0.4
A
0.6
0.8
1.0
1.2
1.4
Time (sec) 0.0035
von Mises stress (MPa)
0.0030
0.0020 0.0015 0.0010 0.0005
0.0
0.2
0.4
B
0.6
0.8
1.0
1.2
1.4
Time (sec) 0.14 0.12
von Mises stress (MPa)
there was a small reduction in maximum stress, but the simulation also stopped prematurely, probably because the VC was at the recommended limit provided by the software manufacturer. For the viscoelastic model, peak contact forces between the orbit and fat as well as between fat and sclera are in the range of 0.09-0.10 N (and vary between the global X direction and Z direction as the globe undergoes rotation). For the fluid model, the corresponding peak forces are in the range of 0.08-0.09 N. The contact forces between sclera and retina and retina and vitreous are in the range of 0.05-0.06 N for both models. The time variation is also different for the 2 models, with contact forces for the fluid model showing a reduction in peak values for every cycle and contact forces in the viscoelastic model showing a more constant behavior. Stress Distribution on the Sclera, Retina, and Vitreous Simulation results indicate that stress distributions for the sclera, retina, and vitreous for Cases 2 and 3 are similar to those estimated in Case 1, whereas stress distributions for the sclera, retina, and vitreous in Cases 4 and 6 are very similar to those in Case 5. Figures 3A and 3B show that the stress distribution and the location of maximum stress depend on the choice of material model for the eye components. When the vitreous is modeled using viscoelastic material, the areas with maximum stress on the retina, the sclera, and the vitreous are located mostly in front of the equator. However, when the vitreous is modeled using fluid material, the areas with maximum stress are found behind the equator, and the most heavily stressed parts of the vitreous are at the posterior pole (Figure 3B) and at the front pole (not shown).
0.0025
0.0000
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0.10
Discussion
0.08 0.06 0.04 0.02 0.00 0.0
0.2
C
0.4
0.6
0.8
1.0
1.2
1.4
Time (sec)
FIG 2. A, von Mises stresses on element no. 29 of retina (Case 2, viscoelastic vitreous and fat, K 5 0.7); B, element no. 75 of retina (Case 3, viscoelastic vitreous, K 5 7.0); C, element no. 17 of retina (Case 4, Newtonian fluid vitreous, VC 5 0.5).
Figure 2C, which shows that the peak stress increases through all cycles that were simulated. When the VC is reduced by 40% to 0.3, the peak stress, stress distribution, and stress build-up effect do not change significantly. When the VC was further reduced to 0.1,
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A finite element model of the eye has been developed and exercised with a 5-Hz, 50 rad/s peak pulse. The pulse was obtained from shaking tests by Japanese adult males of average weight and height conducted on the Aprica 2.5 kg biofidelic infant dummy. Parametric tests were conducted to evaluate the effect of changing material properties of fat and vitreous on retinal stress. We found that changing the material type of fatty tissue from elastic to viscoelastic did not show much effect on the maximum stress and the stress distribution. The assigned properties of the vitreous had significant effects on the maximum stress and the stress distribution. When the bulk modulus of the vitreous was increased (by 10 times), the maximum stress on the retina decreased by approximately 50%. In the meantime, the stress buildup effect was significantly reduced. Changing the material type of vitreous from viscoelastic to fluid had a significant effect on the maximum stress, stress distribution, and the stress buildup; however, when the viscosity coefficient of the fluid was changed, there was not much effect. The difference is likely attributable to the different constraint between the nodes in the
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FIG 3. von Mises stress (MPa) distribution on retina: A, Case 1, vitreous as viscoelastic; B, Case 5, vitreous as Newtonian fluid. Red indicates area of greatest stress. Tangent lines indicate stress from superior oblique (SO).
retina and the vitreous. In the viscoelastic model, the retina is attached at a selected number of nodes to the vitreous, whereas in the fluid model all of the retinal nodes are attached to the vitreous surface. Further investigation is necessary to quantify the influence of the relative number of constrained nodes to the rate of stress buildup. The contact forces between orbit and fat and fat and sclera are reduced by 15% to 25% when the vitreous material is changed from viscoelastic to fluid. The motion of the globe is constrained by the contact forces between orbit and fat and between fat and sclera. However, there is very little change in the contact forces between sclera and retina and between retina and vitreous when the vitreous material is changed. Maximum stress occurs around the retina-vitreous connection area, correlating with the clinical manifestation of hemorrhagic retinopathy observed in AHT, wherein there is a predilection for hemorrhage to occur at the ora and the posterior pole.1,2,15-18 Traumatic macular retinoschisis is a cardinal finding in AHT: it has been shown clinically, histologically, and electrophysiologically to represent a result of vitreoretinal traction at the posterior pole, where the vitreous of infants is uniquely and firmly attached to the retina3,19 (see also e-Supplement 1). It should be noted that we did not ‘‘instruct’’ our model to mimic the clinical reality of AHT; rather, we simply relied on the known anatomic relationships between the retina and vitreous. It may be that our results would be different if we included the lens and optic nerve head to which the vitreous also has adhesion. As a result, the vitreous would be further stabilized at this anterior point. The fixation of the vitreous at the optic nerve may not change our observations given its close proximity, if not contiguous relationship, with the macular vitreo-retinal attachments; however, we hope to refine our model to include anterior segment structures and an optic nerve.
We observed that stress on the retina and sclera accumulates as the shaking continues for certain material models for vitreous (eg, viscoelastic or fluid). When modeling vitreous as a viscoelastic material, assigning smaller bulk modulus to the material showed a clear stress accumulation effect. The rate of change of stress was more evident in this case. When the vitreous is modeled as a fluid, varying the viscosity coefficient did not show significant effects on maximum stress, stress accumulation, and stress distribution; nonetheless, the maximum stress on the retina builds up to a bigger number when the vitreous is modeled as a fluid. On the basis of perpetrator confessions, clinical observations and animal models,20 it is apparent that repetitive acceleration-deceleration is what characterizes this form of abusive head injury as opposed to single impact mechanisms. This stress accumulation effect is a critical component of AHT, a fact that helps to explain why biomechanical calculations that are limited to attempts to predict the effects of a single acceleration-deceleration cycle will by definition not apply to the scenario of this form of AHT. The cumulative increase in force would also help to explain the marked disparity between accidental and abusive injuries, in particular hemorrhagic retinopathy, even when one considers severe single acceleration-deceleration accidental mechanisms such as some motor vehicle accidents.18,21,22 There are several limitations to our study, including of course the incomplete nature of our model. Because we are not testing actual human tissue, globes, or infants, the interpretation of results, although based on the extensive literature on this subject, remains a theoretical application to the abused human infant. The current model does not include several important structures, such as the lens, choroid, ciliary body, and cornea. The fat distribution and orbit geometry were approximated. Cirovic and colleagues4,23 noted the importance of a suction type attachment between orbital fat and
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Volume 13 Number 4 / August 2009 sclera, which we have not yet modeled. Material property data were scaled and the appropriateness of scaling is yet to be evaluated. All the material data in this study are currently available in the LS-DYNA material library. It may be necessary to develop new material models to fully describe the materials used in this model. Ultimately, direct testing of the biomechanical properties of neonatal tissues (eg, vitreous) will be required to optimize the accuracy of our input data. Because of the uncertainty regarding material properties of the important tissues involved in the eye, especially under dynamic loading, and as viscoelastic materials sometimes show dynamic stiffening with increased rates of loading, the variation by an order of 10 in the material properties was to evaluate the change in response (as defined by maximum stress values) with such a change in input parameters. A more accurate simulation must await more accurate experiments to obtain these properties at the loading rates of interest. The convergence of the model and optimum mesh size will have to be established for the complete model. Also, the variation of response as a function of uncertainty in material properties will have to be evaluated. Input motion was purely rotational at the center of the orbit unlike the multidirectional movements experienced by the infant head during AHT. The effect of variation of mesh size, integration intervals, and integration procedure has not yet been fully evaluated. At the time of the simulations, location of head center of gravity relative to orbit landmarks was not known. Because this work was exploratory, the input of the angular motion directly at the center of the orbit was the simplest and also most conservative, since any additional arm length would increase linear velocities at the region of the eye. Future simulations could be altered to reflect alternate center of gravity points. Our model is far from complete. This is a preliminary study to provide a qualitative picture of what happens within the infant eye under repeated acceleration-deceleration motion at rates and forces similar to that which an adult male can apply to a 2.5 kg neonate as measured using a biofidelic dummy. Although our results should be interpreted with caution, the correlations between our findings and the clinical reality offer promise that finite element analysis may be an applicable method of experimental investigation to better understand the eye abnormalities observed in AHT.
Acknowledgments We acknowledge the invaluable assistance of our Research Assistants Erica Bell and Charmaine DeSouza. We are grateful for access to normal CT scans provided by Dr. Christopher Forrest and assistance with the measurements taken from the CT scans from Stephanie Holowka. We are also grateful for the support of APRICA Inc. and in particular Chairman Kenzo Kassai, Mr. Shin Shimomaki and their Pediatric Research Advisor, Dr. Robert Bigge. References 1. Morad Y, Kim Y, Armstrong D, Huyer D, Mian M, Levin A. Correlation between retinal abnormalities and intracranial abnormali-
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