biology

Article Computational Modeling of Skull Bone Structures and Simulation of Skull Fractures Using the YEAHM Head Model

Alcino Barbosa 1,Fábio A. O. Fernandes 1,* , Ricardo J. Alves de Sousa 1 , Mariusz Ptak 2 and Johannes Wilhelm 2

1 TEMA: Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal; [email protected] (A.B.); [email protected] (R.J.A.d.S.) 2 Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, Łukasiewicza 7/9, 50-371 Wrocław, Poland; [email protected] (M.P.); [email protected] (J.W.) * Correspondence: [email protected]; Tel.: +351-234-370-830; Fax: +351-234-370-953



Received: 23 July 2020; Accepted: 2 September 2020; Published: 4 September 2020


Abstract: The human head is a complex multi-layered structure of hard and soft tissues, governed by complex materials laws and interactions. Computational models of the human head have been developed over the years, reaching high levels of detail, complexity, and precision. However, most of the attention has been devoted to the brain and other intracranial structures. The skull, despite playing a major role in direct head impacts, is often overlooked and simplified. In this work, a new skull model is developed for the authors’ head model, the YEAHM, based on the original outer geometry, but segmenting it with sutures, diploë, and cortical bone, having variable thickness across different head sections and based on medical craniometric data. These structures are modeled with constitutive models that consider the non-linear behavior of skull bones and also the nature of their failure. Several validations are performed, comparing the simulation results with experimental results available in the literature at several levels: (i) local material validation; (ii) blunt trauma from direct impact against stationary skull; (iii) three impacts at different velocities simulating falls; (iv) blunt ballistic temporoparietal head impacts. Accelerations, impact forces, and fracture patterns are used to validate the skull model.

Keywords: finite element method; skull; trabecular bone; cortical bone; biomechanics; head injury; sutures; skull fractures

1. Introduction Road traffic accidents are one of the leading causes of mortality in the world, resulting in approximately 1.35 million deaths [1]. Head injuries play a significant role, being also one of the main outcomes of work accidents [2]. Skull fractures may range from a simple nose fracture (one in the Abbreviated Injury Scale, AIS) to a five to six for depressed skull fractures that usually result in a subdural hematoma (SDH), with bones penetrating and tearing veins within the subdural space or, in the worst-case scenario, crushing the cranium. There are many types of cranial fractures but one major cause: an impact or a blow to the head, strong enough to fracture the bone. The type of fracture depends on the impact force, its pulse, the impacted location, and the shape of the impacting object. Cranial fractures can occur without evidence of brain damage [3]. Nevertheless, the incidence of intracranial hematomas is higher among patients with cranial fractures [4].

Biology 2020, 9, 267; doi:10.3390/biology9090267 www.mdpi.com/journal/biology Biology 2020, 9, 267 2 of 18

The skull is a layered structure comprised of a compact inner and an outer table separated by a porous diplöe layer. When a layered panel is transversely loaded, four types of mechanisms can lead to transverse deflection: membrane deformation, bending deformation, shear deformation, and local core compression and puncture of the skull [5]. The compact bone is a dense calcified tissue that forms the outer layer of all bones and surrounds the cancellous bone. Overall, a bone is neither ductile nor fragile, but a combination of both, presenting a quasi-brittle behavior. The mineral part is more unstable/brittle and the organic part (collagen) is more ductile [6]. The quasi-brittle behavior shows the gradual decrease of stress after reaching the yield stress or elastic limit of the material [7]. Lynnerup et al. [8] reported that neither trabecular skull thickness nor total skull thickness is significantly associated with an individual’s gender, weight, or height. Additionally, a statistically significant correlation between trabecular layer thickness and total skull thickness was found. Lillie et al. [9] reported interesting data regarding the thickness of both cortical and trabecular bones. The reported values of cortical thickness range between 1 and 2.6 mm, varying with age and gender (20 to 99 years old). The human skull consists of approximately twenty-two bones, mostly connected by ossified joints, the so-called sutures. Sutures are flexible joints that allow the bones to grow evenly as the brain grows and the skull expands. All skull bones are connected by cranial sutures, which are mainly composed of collagen. There are thirteen sutures in the human skull, four of which are considered the main ones: the coronal suture, the sagittal suture, the squamous suture, and the lambdoid suture. The literature lacks a consensus on the mechanical properties of cranial sutures. This is due to their different spatial distribution of collagen fibers, which results in different geometries and mechanical properties [10]. These properties vary significantly with age, for instance, the Young modulus of cranial sutures is reported to go from 50 to 200 MPa in infants [11–13] and 4 GPa in adults [14]. To better understand traumatic head injury, mechanical and mathematical models of the human head have been developed. Essential to the development of these models is the study of the mechanical behavior of the materials and structures which constitute the human head. The main building component of the bone tissue is mineralized collagen fibril (ossein) [10]. The collagen fibers at the outer and inner tables are arranged hierarchically. On the contrary, in the trabecular bone, collagen fibrils are oriented irregularly, and the structure is spongy. The position of fibers in the bone affects its mechanical properties. Many postmortem investigations have been conducted using human and animal heads, and also physical head and in vitro models. These experiments provided valuable data, which combined with the development of computational techniques, resulted in the development of numerical head models, mainly resorting to the finite element method (FEM) [4]. Although consisting of a numerical procedure to determine approximate solutions for physical or mathematical problems, it requires a precise representation of complex geometries, boundary conditions, and suitable constitutive laws. These models have been used in several fields, from the study of sports trauma to traffic accident reconstruction and forensic research [15–19]. FE models of the skull have also been used in the study of cranioplasty implant systems for the human skull [20,21]. One of the first attempts to model the behavior of the human head response through the FEM was made by Hardy and Marcal [22], who developed a 2D FE model of the skull, later enhanced by Shugar [23], who added an elastic brain firmly attached to the skull. Since then, many FEHMs have been developed, evolving towards more complex models constituted by more intracranial features and modeled with complex non-linear constitutive laws [24,25]. However, most of the attention has been devoted to the brain and other intracranial structures. The skull, despite playing a major role in direct head impacts, is often overlooked and simplified. Usually, at least one of the following simplificative assumptions can be found in the literature: constantly thick skulls, homogeneous skull material, linear elastic mechanical response, and sometimes a lack of validation against experiments regarding skull mechanical response under loading neither its fracture propagation. In the present work, the authors try to enhance the state-of-art by covering all of these points, including variable thicknesses, inclusion Biology 2020, 9, 267 3 of 18 of sutures, and segmentation of compact bone and diplöe (all modeled with hexahedral elements), damage models for crushing of trabecular bone and fracture propagation, and finally, a set of distinct validations from specific crushing of trabecular bone to depressed skull fractures. In the literature, there are a few studies where cadaveric experiments were simulated in order to validate the model, focusing on the skull response during dynamic experiments. For instance, Sahoo et al. [26] simulated the drop tests performed by Yoganandan et al. [27] aiming to validate the skull response under different impact velocities, representing different and possible impact energies in real-world falls. Later, Asgharpour et al. [28] used the same FEHM and simulated the frontal impact tests performed with cadaver heads in a two-pendulum apparatus by Verschueren et al. [29]. In another example, Cai et al. [30] developed a FEHM to simulate the skull fracture experiment from Yoganandan et al. [31], in which the skull is impacted by a hemispherical anvil, and also the lateral head drop experiments from Yoganandan et al. [27] and finally, the blunt ballistic temporoparietal impact experiment from Raymond et al. [32]. However, Cai et al. [30] modeled all the cranial structures as linear elastic materials, which negatively affect the model response, especially for the simulation and prediction of skull fractures. Other skull models have been developed for particular studies, studying very specific subjects, different from the works mentioned above that comprise the entire head structure. Chamrad et al. [33] reviewed different ways to model the human skull and concluded that the skull model must have both types of bone. Additionally, the case of cortical bone modeled with shell element-layers filled with solid elements that represent trabecular bone tissue, it was found to be less precise and feasible than modeling it with solid elements. Chamrad et al. [33] also compared different cortical thicknesses, 1 and 2 mm, and better results were achieved with the thinner cortical layers. Nevertheless, the response might have been influenced by the simply linear-elastic material models employed. In another study, Ptak et al. [10] investigated how dynamic loading affects the mechanics of cranial sutures and surrounding bones and concluded that the stiffness of cranial sutures plays an important role in stress distribution and energy absorption. Thus, it is possible to conclude that the modeling of cranial sutures is vital for realistic modeling and simulation of skull fractures. Nevertheless, this model was neither assembled nor validated and the intracranial components were missing. Recently, an advanced FE model of the human skull for a child was developed by Wilhelm et al. [34]. Nevertheless, the particular validation for the skull was not carried out due to the lack of experimental data for the validation of the child head models. A similar methodology was adopted in this study, re-modeling the skull of the YEt Another Head Model (YEAHM), which can be compared with experimental data available in the literature for adult subjects. This work introduces a new skull model to the YEAHM, substituting the linear elastic homogeneous skull developed in Fernandes et al. [35]. Since this model does not differentiate the types of skull bone, modeling it as a linear-elastic homogenous solid, in the present work, a new skull model is developed for the YEAHM. It is based on the original geometry and focuses on the differentiation and segmentation of compact and cancellous tissue and the inclusion of cranial sutures, having variable thickness across different sections and based on craniometric data. These structures are modeled with constitutive models that consider the non-linear behavior of skull bones and also the nature of their failure. Several validations are performed, comparing the simulation results with experimental results available in the literature at three levels: (i) local material validation [36]; (ii) blunt trauma from direct impact against a stationary skull [31]; (iii) three impacts at different velocities simulating falls [27]; (iv) blunt ballistic temporoparietal head impacts [37]. Accelerations, impact forces, and fracture pattern results are compared with experimental data from the literature in an attempt to validate the skull model.

2. Materials and Methods The YEAHM, as originally developed by Fernandes et al. [35], was constituted by the skull, brain, and cerebrospinal fluid (CSF), was further enhanced by Migueis et al. [38] adding the bridging veins and Biology 2020, 9, 267 4 of 18 the transverse and superior sagittal sinuses and by Costa et al. [39] pressurizing these hollow structures and validating them against experimental studies from Monea et al. [40] and Depreitere et al. [41], in order to accurately capture the onset of bridging veins rupture and SDH prediction. The model was also previously validated against the experiments of Nahum et al. [42] and Hardy et al. [35,43,44]. The Biology 2020, 9, x 4 of 18 latter model is employed as the base model in the present study. Since the development and validation theofYEAHM development can be and found validation in the literature,of YEAHM only can data be found referring in the to theliterature, skull model only data here referring developed to willthe skullbe addressed. model here Figure developed1 presents will the be majoraddressed. modeling Figure and 1 presents validation the stages, major whichmodeling will and be thoroughly validation stages,addressed which in thewill following be thoroughly sections. addressed in the following sections.

Figure 1. a b Figure 1. ModelingModeling and and validation validation stages: stages: (a () )YEAHM YEAHM original original skull skull model; model; ( (b)) trabecular trabecular bone bone structure; (c) trabecular bone covered by the cortical layers; (d) sutures inclusion; (e) adding of structure; (c) trabecular bone covered by the cortical layers; (d) sutures inclusion; (e) adding of intracranial contents; (f) trabecular bone compression; (g) blunt impact against stationary skull; intracranial contents; (f) trabecular bone compression; (g) blunt impact against stationary skull; (h) (h) simulation of falls—lateral impacts; (i) blunt ballistic temporo-parietal head impacts. simulation of falls—lateral impacts; (i) blunt ballistic temporo-parietal head impacts. 2.1. Skull Modeling 2.1. Skull Modeling The first step in the development was to segment the cranial bones. If properly carried out, cortical and trabecularThe first step bones in willthe havedevelopment distinct geometries was to segmen and materialt the cranial properties. bones. As If referred, properly cranial carried sutures out, corticalwere also and modeled. trabecular bones will have distinct geometries and material properties. As referred, cranialLinear sutures hexahedral were also finite modeled. elements are the selected choice, instead of the previously employed quadraticLinear (second-order)hexahedral finite tetrahedral elements elements.are the selected Tetrahedral choice, instead finite elements of the previously are easier employed to mesh quadraticconsidering (second-order) geometrical irregularities, tetrahedral butelements. first-order Tetrahedral ones are excessivelyfinite elements stiff, leadingare easier to numericalto mesh consideringpathologies suchgeometrical as volumetric irregularities, locking asbut reported first-order by Fernandes ones are excessively et al. [35] for stiff, the nearlyleading incompressible to numerical pathologiesbrain matter. such On theas othervolumetric hand, locking second-order as reported tetrahedral by Fernandes elements are et extremelyal. [35] for CPU the intensive. nearly incompressibleLinear hexahedral brain elements matter. haveOn the the other advantage hand, second-order of having fewer tetrahedral nodes while elements giving are as extremely accurate CPUresults intensive. as second-order Linear hexahedral tetras, reducing elements the have computation the advantage cost [of45 having]. Nevertheless, fewer nodes when while modeling giving ascomplex accurate geometries results as with second-order linear hexahedral tetras, reduci elements,ng the it iscomputation necessary to cost address [45]. their Nevertheless, sensibility when to the modelingcorner angle. complex geometries with linear hexahedral elements, it is necessary to address their sensibilitySince to the the skull corner is a layeredangle. structure, shell elements could be an option in some FEHMs to model the skullSince [the26]. skull However, is a layered in this structure, work, there shell are elemen mainlyts could three be reasons an option for in the some use ofFEHMs solid to elements model theinstead skull of [26]. shells However, for the cortical in this bone:work, there are mainly three reasons for the use of solid elements instead of shells for the cortical bone: 1. Construction of the model: with solid finite elements it is possible to quickly make geometrical

1. Constructionadjustments of to the model: model andwith adapt solid finite zones elements more easily it is thanpossible in the to casequickly of shells. make geometrical In addition, adjustmentssince the head to isthe also model a layered and adapt structure zones itself more (meninges, easily than skull, in scalp,the case etc.), of solid shells. elements In addition, make sinceit easier the tohead model is also additional a layered layers structure in future itself works. (meninges, skull, scalp, etc.), solid elements make it easier to model additional layers in future works. 2. Solids also have the advantages of handling double contact better and have a more accurate description of the stress gradient over the thickness, contrary to shells based on plane stress assumptions. Full 3D material laws can be employed without simplifying assumptions like in the case of shells. 3. Solid elements are more appropriate than shell elements to study the fracture phenomena of the skull. Biology 2020, 9, 267 5 of 18

Biology 2020, 9, x 5 of 18 2. Solids also have the advantages of handling double contact better and have a more accurate 2.1.1. descriptionGeometrical ofModeling the stress gradient over the thickness, contrary to shells based on plane stress assumptions. Full 3D material laws can be employed without simplifying assumptions like in the The YEAHM skull geometry is based on computer tomography (CT) scans, more specifically 460 case of shells. slices at 1.5 mm intervals images. The geometry generated in Fernandes et al. [35] was used as the base3. inSolid this elementsstudy. Meshmixer are more (Autodesk, appropriate San than Rafa shellel, CA, elements USA) was to study employed the fracture to obtain phenomena one internal of surfacethe and skull. one external surface of the skull. The original skull model was then separated into two distinct parts, defining the cut in the foramen magnum, a large opening through the occipital bone 2.1.1. Geometrical Modeling located in the center of the posterior fossa of the neurocranium. Following,The YEAHM an skull inward geometry thickness is based of 1.5 on mm computer was attributed tomography to each (CT) part scans, based more on specifically the range 460 of thicknessesslices at 1.5 reported mm intervals for the images. cortical The layer geometry (1 and 2 generated mm) [9], to in be Fernandes used as a et virtual al. [35 ]reference was used border as the betweenbase in this the study. two bone Meshmixer constituents. (Autodesk, The Sangeometry Rafael, was CA, then USA) imported was employed into SolidWorks to obtain one (Dassault internal Systèmes,surface and Vélizy-Villacoublay, one external surface France) of the skull.to create The a original solid part. skull The model FE mesh was then of the separated solid trabecular into two componentdistinct parts, was defining created the with cut the in themesh foramen generator magnum, algorithms a large from opening HyperMesh through (Altair, the occipital Troy, bone MI, USA).located in the center of the posterior fossa of the neurocranium. TheFollowing, mesh generation an inward was thickness controlled of 1.5 by mm setting was two attributed parameters, to each the part desired based element on the size range of of2 mmthicknesses and a minimum reported Jacobian for the cortical determinant layer of (1 0.3 and as 2 parameters, mm) [9], to to be ensure used as low-distortion, a virtual reference good borderaspect ratiobetween hexahedral the two elements. bone constituents. Those specific The paramete geometryrs was were then defined imported to ameliorate into SolidWorks convergence (Dassault and diminishSystèmes, the V éoveralllizy-Villacoublay, CPU cost on France) further to simulations. create a solid part. The FE mesh of the solid trabecular componentThe cortical was created layer was with created the mesh based generator on the algorithms trabecular from mesh HyperMesh by extruding (Altair, a 1.5 Troy, mm MI, layer USA). of hexahedralThe mesh elements generation sharing was nodes controlled with bythe setting trabec twoular parameters, core. Overall, the the desired mesh element element size quality of 2 mm is goodand a and minimum faithful Jacobian to the geometry. determinant Lastly, of 0.3the as two parameters, components to ensurewere segmented low-distortion, to create good a component aspect ratio ofhexahedral cranial sutures, elements. using Those reference specific images parameters from a were3D atlas. defined The toskull ameliorate hexahedr convergenceal mesh is then and imported diminish intothe overallthe Abaqus CPU solver cost on to further run the simulations. simulations, bearing in mind that the final part would be sectioned with theThe three cortical different layer components was created (trabecular, based on cortical, the trabecular and cranial mesh su bytures). extruding The final a 1.5model mm (Figure layer 2) of ishexahedral constituted elements by these sharing distinct nodes components: with the a trabecular trabecular core. component Overall, with the mesh92,300 element hexahedral quality elements, is good aand cortical faithful component to the geometry. with 133,045 Lastly, hexahedral the two componentselements, and were a cranial segmented sutures to component create a component with 12,271 of hexahedralcranial sutures, elements. using In reference addition, images the interfac from aes 3D between atlas. Thethe skullcomponents hexahedral have mesh shared is thennodes. imported into theAfter Abaqus creating solver the skull to run model, the simulations, the intracranial bearing components in mind that (namely the final the partbrain, would the CSF, be sectioned the BVs, andwith the the SSS) three from different the componentsexisting YEAHM (trabecular, model cortical, were assembled and cranial to sutures). the new The skull final model model in (Figure Abaqus2) (Figureis constituted 1e). For by this these purpose, distinct during components: the modeling a trabecular process component of the skull, with the 92,300 coordinate hexahedral system elements, and its origina cortical were component preserved. with Overall, 133,045 the hexahedral model contains elements, 1,202,015 and a elements, cranial sutures of which component 20% (237,616) with 12,271 form thehexahedral skull. elements. In addition, the interfaces between the components have shared nodes.

FigureFigure 2. 2. VisualizationVisualization of of the the final final complete complete model model in Abaqus in Abaqus with with trabecular trabecular bone, bone, cortical cortical bone bone (1.5 mm),(1.5 mm), and andcranial cranial sutures. sutures.

2.1.2. Material Modeling The geometries of the cortical and trabecular bones along with the cranial sutures were modeled resorting to material models available at the Abaqus material library. The trabecular or spongy bone was modeled as an elastic-plastic material since, from all the bones, this type behaves more like, as Biology 2020, 9, 267 6 of 18

After creating the skull model, the intracranial components (namely the brain, the CSF, the BVs, and the SSS) from the existing YEAHM model were assembled to the new skull model in Abaqus (Figure1e). For this purpose, during the modeling process of the skull, the coordinate system and its origin were preserved. Overall, the model contains 1,202,015 elements, of which 20% (237,616) form the skull.

2.1.2. Material Modeling The geometries of the cortical and trabecular bones along with the cranial sutures were modeled Biologyresorting 2020, to9, x material models available at the Abaqus material library. The trabecular or spongy6 of 18 bone was modeled as an elastic-plastic material since, from all the bones, this type behaves more thelike, name as the indicates, name indicates, a sponge abetween sponge the between cortical the bone cortical tables bone and tables without and exhibiting without exhibitingan S-shaped an stress–strainS-shaped stress–strain curve for higher curve fordeformations, higher deformations, typical of typicalcrushable of crushablefoams. This foams. model This is also model the ismost also usedthe most one on used the one FEHMs on the available FEHMs in available the literature in the [24]. literature The compression [24]. The compression tests performed tests by performed Boruah etby al.Boruah [36] were et al. used[36] to were fit the used model to fit in the Abaqus. model Figure in Abaqus. 3 shows Figure the 3stress-strain shows the stress-straincurve obtained curve by Boruahobtained et byal. Boruah[36] and et used al. [ 36in ]this and work used to in characterize this work to the characterize material behavior. the material Moreover, behavior. the Moreover, material wasthe materialconsidered was isotropic considered with isotropica density withof 1500 a density kg/m3, a of Poisson’s 1500 kg/ ratiom3, a of Poisson’s 0.05, and ratio a Young of 0.05, modulus and a ofYoung 1000 modulusMPa, values of 1000 found MPa, throughout values found the literature throughout [46]. the literature [46].

20

15

10

5 Stress (MPa) 0 024681012 Strain (%)

Figure 3. Stress–strain behavior of trabecular bone under compression loading [36]. Figure 3. Stress–strain behavior of trabecular bone under compression loading [36]. Based on the information found in the literature regarding the cortical bone and sutures, knowing thatBased these typeson the of information tissues present found a quasi-brittle in the literatur mechanicale regarding behavior, the acortical material bone model and capable sutures, of knowingsimulating that brittle these fracture types of is tissues necessary. present Abaqus a quas providesi-brittle suchmechanical a material behavior, law to a model material the model brittle capablebehavior of of simulating materials brittle such as fractu ceramics,re is necessary. concrete, andAbaqus even provides glass [47 ].such The a removalmaterial oflaw elements to model based the brittleon a brittle behavior failure of materials criterion such is also as employed.ceramics, conc Therete, mechanical and even behavior glass [47]. described The removal by this of elements model is baseddriven on by a twobrittle stages: failure prior criterion to and is afteralso employed cracking.. Prior The mechanical to cracking, behavior a linear elasticdescribed isotropic by this material model ismodel driven defines by two its stages: mechanical prior to behavior, and after as cracking. described Prior by the to classicalcracking, Hooke’s a linear Law.elastic The isotropic elastic material behavior modelvalues chosendefines forits bothmechanical cortical bonebehavior, and cranialas descri suturesbed by can the be seenclassical in Table Hooke’s1. Law. The elastic behavior values chosen for both cortical bone and cranial sutures can be seen in Table 1. Table 1. Cortical bone and sutures elastic material properties.

Tissue TypeTable 1. DensityCortical (kgbone/m and3) suturesYoung elastic Modulus material (MPa) properties. Poisson’s Ratio TissueCortical Type Density 1900(kg/m3) Young Modulus 20,000 (MPa) Poisson’s 0.21 Ratio CorticalSutures 1900 2100 20,000 15,000 0.30.21 Sutures 2100 15,000 0.3 To define crack initiation and the behavior of bone tissue after cracking, three modules must be To define crack initiation and the behavior of bone tissue after cracking, three modules must be defined: a post-failure stress–strain relation, a shear retention model, and a brittle failure criterion defined: a post-failure stress–strain relation, a shear retention model, and a brittleI failure criterion (Figure4). The post-failure stress–strain relation defines the post-failure stress, σt , as a function of I (Figure 4). The post-failure stress–strainck relation defines the post-failure stress, σt , as a function of the the strain across the crack, ε nn, modeling it after its initiation. Figure5 shows the values used for strain across the crack, εcknn, modeling it after its initiation. Figure 5 shows the values used for both tissues. both tissues.

Figure 4. Cracking modeling—strain softening and strain hardening under uniaxial tensile loading. Biology 2020, 9, x 6 of 18

the name indicates, a sponge between the cortical bone tables and without exhibiting an S-shaped stress–strain curve for higher deformations, typical of crushable foams. This model is also the most used one on the FEHMs available in the literature [24]. The compression tests performed by Boruah et al. [36] were used to fit the model in Abaqus. Figure 3 shows the stress-strain curve obtained by Boruah et al. [36] and used in this work to characterize the material behavior. Moreover, the material was considered isotropic with a density of 1500 kg/m3, a Poisson’s ratio of 0.05, and a Young modulus of 1000 MPa, values found throughout the literature [46].

20

15

10

5 Stress (MPa) 0 024681012 Strain (%)

Figure 3. Stress–strain behavior of trabecular bone under compression loading [36].

Based on the information found in the literature regarding the cortical bone and sutures, knowing that these types of tissues present a quasi-brittle mechanical behavior, a material model capable of simulating brittle fracture is necessary. Abaqus provides such a material law to model the brittle behavior of materials such as ceramics, concrete, and even glass [47]. The removal of elements based on a brittle failure criterion is also employed. The mechanical behavior described by this model is driven by two stages: prior to and after cracking. Prior to cracking, a linear elastic isotropic material model defines its mechanical behavior, as described by the classical Hooke’s Law. The elastic behavior values chosen for both cortical bone and cranial sutures can be seen in Table 1.

Table 1. Cortical bone and sutures elastic material properties.

Tissue Type Density (kg/m3) Young Modulus (MPa) Poisson’s Ratio Cortical 1900 20,000 0.21 Sutures 2100 15,000 0.3

To define crack initiation and the behavior of bone tissue after cracking, three modules must be defined: a post-failure stress–strain relation, a shear retention model, and a brittle failure criterion Biology(Figure2020, 9 ,4). 267 The post-failure stress–strain relation defines the post-failure stress, σtI, as a function of the7 of 18 strain across the crack, εcknn, modeling it after its initiation. Figure 5 shows the values used for both tissues.

Biology 2020, 9, x 7 of 18

800 700 600 Cortic al 500 400 300 Stress (MPa) 200 Biology 2020, 9, x 7 of 18 FigureFigure 4. Cracking 4. Cracking modeling—strain100 modeling—strain softening softening and strain strain hardening hardening under under uniaxial uniaxial tensile tensile loading. loading. 8000 700 0 0.00005 0.0001 0.00015 0.0002 0.00025 600 Strain Cortic al 500 Figure 5. Post-failure stress–strain curve for both cortical and sutures tissues. 400 Regarding the shear300 retention model, it requires the definition of the post-cracked shear stiffness as a function of the openingStress (MPa) strain across the crack. This relation is defined by: 200 100 =ω(ε) (1) where ε is the strain0 after cracking, ω is the shear retention factor and Gc is the cracked shear modulus. The last one reduces0 as 0.00005 the crack 0.0001 opens. Figure 0.00015 6 shows 0.0002 the relation 0.00025 employed for the specific case of both cortical and sutures tissues. Strain The material cracking is defined by an often-used criterion to predict the failure of brittle Figure 5. Post-failure stress–strain curve for both cortical and sutures tissues. materials, the RankineFigure 5. Post-failurecriterion, which stress–strain is based curve on for the both maximum cortical and normal sutures stresstissues. and determines the crackRegarding initiation, the deleting shear retentionthe corresponding model, it element. requires The the brittle definition failure of thecriterion post-cracked allows the shear definition stiffness Regarding the shear retention model, it requires the definition of the post-cracked shear stiffness asof a functionthe number of the of local opening direct strain cracking across strain the crack.components This relation (maximum is defined three) by:at a material point and as a function of the opening strain across the crack. This relation is defined by: the failure strain to cause element failure. When the material point fails, all the stress components are =ω(εck) (1) set to zero. If all the material points in an Gelementc = ω( εfail,nn) Gthe element is removed from the mesh. The (1) number of material points required for element failure can be defined. In this case, for the cortical where ε is the strain after cracking, ω is the shear retention factor and Gc is the cracked shear ck wherebone,modulus.εnn oneis thematerialThe strainlast onepoint after reduces was cracking, set as as the ωthe iscrack requirement the shearopens. retention Figure for element 6 factorshows failure andthe Grelation withc is the a directemployed cracked cracking shear for the modulus.failure Thestrainspecific last oneof case 0.0006. reduces of both Similarly, ascort theical crack forand the sutures opens. cranial tissues. Figure sutures, 6 shows one material the relation point employed was set as for the the requirement specific case for of bothelement corticalThe failure material and but sutures cracking with tissues.a reduced is defined direct by crackingan often-us failureed criterion strain ofto 0.0004. predict the failure of brittle materials, the Rankine criterion, which is based on the maximum normal stress and determines the crack initiation, deleting the corresponding element. The brittle failure criterion allows the definition of the number of local direct cracking strain components (maximum three) at a material point and the failure strain to cause element failure. When the material point fails, all the stress components are set to zero. If all the material points in an element fail, the element is removed from the mesh. The number of material points required for element failure can be defined. In this case, for the cortical bone, one material point was set as the requirement for element failure with a direct cracking failure strain of 0.0006. Similarly, for the cranial sutures, one material point was set as the requirement for element failure but with a reduced direct cracking failure strain of 0.0004.

FigureFigure 6. 6.Shear Shear retentionretention modelmodel values for for both both cortical cortical and and sutures sutures tissues. tissues.

2.2.The Skull material Model Validation cracking is defined by an often-used criterion to predict the failure of brittle materials, the RankineThe selection criterion, of which the experimental is based on studies the maximum to perform normal the validations stress and determines is based on thecommonly crack initiation, used deletingtests in the the corresponding literature and the element. necessity The for brittle specific failure validations criterion such allows as the the trabecular definition bone of the [36]. number After of validating the compression of this type of bone, simulations can be performed covering the entire skull eliminating the diplöe as a variable. Additionally, in the literature, no study was found

Figure 6. Shear retention model values for both cortical and sutures tissues.

2.2. Skull Model Validation The selection of the experimental studies to perform the validations is based on commonly used tests in the literature and the necessity for specific validations such as the trabecular bone [36]. After validating the compression of this type of bone, simulations can be performed covering the entire skull eliminating the diplöe as a variable. Additionally, in the literature, no study was found Biology 2020, 9, 267 8 of 18 local direct cracking strain components (maximum three) at a material point and the failure strain to cause element failure. When the material point fails, all the stress components are set to zero. If all the material points in an element fail, the element is removed from the mesh. The number of material points required for element failure can be defined. In this case, for the cortical bone, one material point was set as the requirement for element failure with a direct cracking failure strain of 0.0006. Similarly, for the cranial sutures, one material point was set as the requirement for element failure but with a reduced direct cracking failure strain of 0.0004.

2.2. Skull Model Validation The selection of the experimental studies to perform the validations is based on commonly used tests in the literature and the necessity for specific validations such as the trabecular bone [36]. After validating the compression of this type of bone, simulations can be performed covering the entire skull eliminating the diplöe as a variable. Additionally, in the literature, no study was found addressing experimental testing solely on sutures without the influence of cortical tissue, and vice-versa. Therefore, after trabecular bone validation, the skull model was validated by simulating head blunt trauma and head impacts resulting from falls [27,31]. Additionally, to validate the behavior of the damage/failure models, another experimental study needed to be simulated in order to compare the fracture patterns [37]. Given the kinematics of the analyzed problems, all the simulations performed used the dynamic explicit solver. No mass scaling technique was employed. The interaction between the parts was considered as frictionless general contact, in order to reduce CPU cost and also given the lack of information on the friction coefficients for most of the experiments. Additionally, the majority of the contacts happened against metallic components with low roughness and in a linear fashion, with minimal tangential displacements.

2.2.1. Trabecular Bone Compression—Local Material Validation For the trabecular bone validation, the uniaxial compression tests conducted by Boruah et al. [36] were simulated. Boruah et al. [36] tested a total of ten adult male post-mortem human surrogates, representing the 50th percentile adult male with an upper age limit of 70 years. A skull CT was used to identify ten anatomical locations on the right half of the calvarium for harvesting cores with the locations chosen to avoid sutures. The scalp was removed, and cylindrical-shaped samples were harvested on the right side of the calvarium. The process was guided by a clinical CT to precisely remove the samples for each human surrogate on the desired locations and avoid specific anomalies such as deformation and table curvature. A total of 84 cores with a diameter of 18.24 mm were obtained from the right calvaria of the ten subjects. Table2 indicates the mean thickness of each layer and the corresponding standard deviation. The samples were potted in a minimal amount of polyester resin to provide two flat and parallel surfaces for mounting the specimen on the uniaxial test rig.

Table 2. Micro CT measurements [36].

Bone Structure Thickness (mm) Standard Deviation (mm) Outer Table 0.76 0.29 ± Inner Table 0.35 0.15 ± Trabeculae 5.08 2.01 ±

To simulate the compression of trabecular bone and to validate the constitutive strategy and material properties employed for trabecular bone, a cylindrical sample was developed based on the average measurements for outer and inner tables and trabeculae, as obtained in Boruah et al. [36], reducing the probability of errors due to geometrical deviations. Biology 2020, 9, 267 9 of 18

For this reason, for numerical simulation purposes, the mean dimensions presented in Table2 were adopted. The compressibility test setup consisted of the core specimens being loaded with a ramp displacement applied to the outer table at a target rate of 15 mm/s, with the outer table facing the actuator. Figure1f shows the numerical setup, which consists of two rigid parts, the bottom one fully constrained, and the top one with one degree of freedom. The velocity of 15 mm/s was prescribed to the latter. The cylindrical samples were modeled with hexahedral elements, analyzing the element size, the type of integration, and the influence of the damage model.

2.2.2. Skull Vertex Impact Experiment—Blunt Trauma from Direct Impact against a Stationary Skull In Yoganandan et al. [31], 21 specimens were loaded at quasi-static and dynamic rates. From these tests, a specific test, specimen number 7, was chosen to be recreated on a simulation. This particular test consisted of a dynamic rate test where a hemispherical anvil with 96 mm of diameter and a mass of 1.213 kg impacted on the vertex of the cranium (on the sagittal sutures) at 7.2 m/s. This one was chosen because the impact location contained for the most part sutures and also because force–deflection curves were provided in Yoganandan et al. [31]. Additionally, the specimen was from a 65-year-old man, having similar conditions to the specimen from whose medical images were used to create YEAHM, e.g., the craniometric data [35]. The specimens were prepared with a fixation device designed to achieve rigid boundary conditions at the distal end. Therefore, the skull model was properly constrained to represent the experimental boundary conditions. The bottom of the model was fully constrained as in the experiments [31]. Figure1g presents the numerical setup, showing the constrained area of the skull and the rigid hemispherical impactor. In this simulation, an initial velocity of 7.2 m/s was set to a 1.213 kg rigid hemispherical anvil with a diameter of 96 mm and with an initial speed of 7.2 m/s, which impacted against the vertex of the skull.

2.2.3. Lateral Head Impact Experiment—Three Impacts at Different Velocities Simulating Falls In Yoganandan et al. [27], post-mortem human subjects were subjected to impacts on the lateral side of the cranium. Three linear accelerometers at each site/region were rigidly fixed onto a metal cube that was then rigidly mounted to a contoured plate. This plate was attached to the cranium using screws at each corner. The specimens were impacted with successively increasing input energies until fracture. The stopping criterion was a decrease in force occurring with increasing impact velocity, or the impact force being closer to the rated limit of the load cell. A 40-durometer padding (50 mm thickness) material served as a stationary object onto which the head impacted. The dynamic loading was accomplished using free-fall (drop) techniques where the specimen was completely unconstrained. The FEHM can be validated by comparing the accelerations at the three regions where accelerometers were placed in the experiment. The resultant accelerations from the experiments were filtered at 1000 Hz with the SAE recommended filtered. The same protocol is employed to filter the numerical results. Figure1h presents the numerical setup, where the head model was positioned laterally to the surface of the pad. Velocities of 6, 4.9, and 3.5 m/s were given to the head so that it would impact against a 40-durometer neoprene padding (50 mm thickness) material laying on a rigid structure [27,48]. Yoganandan et al. [27] did not give any reference to the material nor its mechanical properties, only stating that it was a 40-durometer layer. Therefore, data from ElGawady et al. [49] and Sahoo et al. [26] were used to model the pad. From ElGawady et al. [49], compression data from the tests performed on a 40 durometer neoprene pad, and in the second [26], the density and Poisson’s ratio used in Yoganandan et al. [27] were revealed. The pad was modeled as a Hyperfoam material with a density of 4320 kg/mm3, a Poisson’s ratio of 0.43, and the uniaxial compression test curve is shown in Figure7. Biology 2020, 9, x 9 of 18

from a 65-year-old man, having similar conditions to the specimen from whose medical images were used to create YEAHM, e.g., the craniometric data [35]. The specimens were prepared with a fixation device designed to achieve rigid boundary conditions at the distal end. Therefore, the skull model was properly constrained to represent the experimental boundary conditions. The bottom of the model was fully constrained as in the experiments [31]. Figure 1g presents the numerical setup, showing the constrained area of the skull and the rigid hemispherical impactor. In this simulation, an initial velocity of 7.2 m/s was set to a 1.213 kg rigid hemispherical anvil with a diameter of 96 mm and with an initial speed of 7.2 m/s, which impacted against the vertex of the skull.

2.2.3. Lateral Head Impact Experiment—Three Impacts at Different Velocities Simulating Falls In Yoganandan et al. [27], post-mortem human subjects were subjected to impacts on the lateral side of the cranium. Three linear accelerometers at each site/region were rigidly fixed onto a metal cube that was then rigidly mounted to a contoured plate. This plate was attached to the cranium Biologyusing2020 screws, 9, 267 at each corner. 10 of 18 The specimens were impacted with successively increasing input energies until fracture. The stopping criterion was a decrease in force occurring with increasing impact velocity, or the impact 2.2.4. Blunt Ballistic Temporo-Parietal Head Impacts force being closer to the rated limit of the load cell. A 40-durometer padding (50 mm thickness) materialHuang served et al. as [37 a] performedstationary object two blunt onto ballisticwhich temporoparietalthe head impacted. head The impacts dynamic carried loading out onwas a post-mortemaccomplished human using free-fall subject. (drop) A rigid, techniques flat-faced where 38.1 mmthe specimen diameter was projectile completely with aunconstrained. mass of 0.1 kg was usedThe for allFEHM impacts. can The be impactorvalidated was by aligned comparing so the th contacte accelerations face struck at the the specimen three regions normal where to the skinaccelerometers surface. Two were impact placed conditions in the experiment. were performed, The resultant one to eachaccelerations of the two from bilateral the experiments temporoparietal were regions.filtered at Condition 1000 Hz Awith was the performed SAE recommended at a target velocityfiltered. ofThe 20 same m/s to protocol the right is sideemployed while conditionto filter the B wasnumerical targeted results. for an impact velocity of 35 m/s to the left side. ToFigure validate 1h presents the model, the numerica both conditionsl setup, werewhere simulated, the head model especially was conditionpositioned B laterally since fracture to the patternssurface of were the provided pad. Velocities for this case.of 6, 4.9, This and experiment 3.5 m/s provideswere given data to from the head temporoparietal so that it would head impacts impact ofagainst post-mortem a 40-durometer human neopre subjectsne padding necessary (50 to mm validate thickness) FE modelsmaterial as laying a prediction on a rigid tool structure for localized [27,48]. depressedYoganandan skull et fractures.al. [27] did not give any reference to the material nor its mechanical properties, only statingFor that this it simulation,was a 40-durometer a 0.1 kg cylindricallayer. Therefore, impactor datawith from 38.1 ElGawady mm of diameteret al. [49] and was Sahoo modeled. et al. Two [26] impactswere used were to model performed, the pad. one From at 35 ElGawady m/s and another et al. [49], at 20compression m/s. The anvildata from impacts the thetests head performed on the temporoparietalon a 40 durometer region, neoprene with a pad, targeted and impactin the pointsecond (25 [26], mm the anterior density to theand external Poisson’s acoustic ratio used meatus in andYoganandan 35 mm superior et al. [27] to were the Frankfurt revealed. Plane).The pad Similar was modeled to the experiment, as a Hyperfoam the head material model with was a density free to moveof 4320 without kg/mm restrictions.3, a Poisson’s Figure ratio1 ofi depicts 0.43, and the the numerical uniaxial setup, compression with a rigidtest curve projectile is shown positioned in Figure on the7. temporoparietal region, following the experiments.

FigureFigure 7.7. Stress–strain curve of the neopreneneoprene fromfrom uniaxialuniaxial compressioncompression teststests [[49].49]. 3. Results 2.2.4. Blunt Ballistic Temporo-Parietal Head Impacts 3.1. TrabecularHuang et. Bone al [37] Compression—Local performed two Materialblunt ballistic Validation temporoparietal head impacts carried out on a post-mortemSimilarly human to the experiment,subject. A rigid, measurements flat-faced 38.1 of themm skull diameter numerical projectile model, with in a what mass would of 0.1 kg be was the sameused skullfor all locations impacts. asThe in impactor the experiment, was aligned were madeso the to contact find out face what struck parts the of specimen the skull havenormal a higher to the degree of geometrical similarity with the computational model. Figure8 shows the locations in the YEAHM skull. Locations 1, 4, and 7 had the best fit regarding the samples’ average thickness of 6.19 mm, as can be seen in Table3. Therefore, the stress–strain curves obtained for the three samples were the ones primarily used for the model validation. A finite element formulation comparison was made to find the best compromise between accuracy and efficiency. Linear hexahedral elements from Abaqus finite element library with reduced integration and hourglass stabilization (C3D8R), full integration (C3D8), and incompatible modes (C3D8I) were compared. For each type of element, a mesh density analysis was performed with element sizes of 0.2, 0.5, 1, and 2 mm. This mesh sensitivity analysis makes it possible to ensure that the average element size for the trabeculae in the skull model is in good fit with the experiments. It was found that the C3D8R prevailed with the best compromise. Stress–strain curves were obtained to compare the results between simulations and experiments. These results can be seen, altogether, in Figure9. Biology 2020, 9, x 10 of 18

skin surface. Two impact conditions were performed, one to each of the two bilateral temporoparietal regions. Condition A was performed at a target velocity of 20 m/s to the right side while condition B was targeted for an impact velocity of 35 m/s to the left side. To validate the model, both conditions were simulated, especially condition B since fracture patterns were provided for this case. This experiment provides data from temporoparietal head impacts of post-mortem human subjects necessary to validate FE models as a prediction tool for localized depressed skull fractures. For this simulation, a 0.1 kg cylindrical impactor with 38.1 mm of diameter was modeled. Two impacts were performed, one at 35 m/s and another at 20 m/s. The anvil impacts the head on the temporoparietal region, with a targeted impact point (25 mm anterior to the external acoustic meatus and 35 mm superior to the Frankfurt Plane). Similar to the experiment, the head model was free to move without restrictions. Figure 1i depicts the numerical setup, with a rigid projectile positioned on the temporoparietal region, following the experiments.

3. Results

3.1. Trabecular Bone Compression—Local Material Validation Similarly to the experiment, measurements of the skull numerical model, in what would be the same skull locations as in the experiment, were made to find out what parts of the skull have a higher degree of geometrical similarity with the computational model. Figure 8 shows the locations in the YEAHM skull. Locations 1, 4, and 7 had the best fit regarding the samples’ average thickness of 6.19 mm, as can be seen in Table 3. Therefore, the stress–strain curves obtained for the three samples were the ones primarily used for the model validation.

Table 3. Model thickness measurements in different skull locations.

Location 1 2 3 4 5 6 7 8 9 10 Biology 2020, 9, 267 Skull Thickness (mm) 6.1 7.1 5.7 6.3 7.3 7.8 6.3 7.3 6.9 5 11 of 18 Deviation from the Average (mm) 0.1 0.9 0.5 0.1 1.1 1.6 0.1 1.1 0.7 1.2

FigureFigure 8. Locations 8. Locations of the of samplesthe samples numbered numbered 1–10 1–10 and and highlighted highlighted inin grey.grey. MeasurementsMeasurements were were carried carried to find the closest thickness between the numerical model and the samples. to find the closest thickness between the numerical model and the samples. A finite element formulation comparison was made to find the best compromise between Table 3. Model thickness measurements in different skull locations. accuracy and efficiency. Linear hexahedral elements from Abaqus finite element library with reduced Biology 2020, 9, x 11 of 18 integration and Locationhourglass stabilization (C3D8R), 1 full 2 integration 3 4 (C3D8), 5 and 6 incompatible 7 8 modes 9 10 (C3D8I) were compared. For each type of element, a mesh density analysis was performed with Skull Thickness (mm) 6.1 7.1 5.7 6.3 7.3 7.8 6.3 7.3 6.9 5 found elementthat the sizesC3D8R of 0.2, prevailed 0.5, 1, and with 2 mm. the Thisbest mesh compromise. sensitivity Stress–strain analysis makes curves it possible were to obtained ensure that to compare the resultsthe averageDeviation between element fromsimulations thesize Average for the and trabeculae (mm) experiments. in the0.1 skul Thes 0.9l modele results 0.5 is in 0.1 cangood be 1.1 fit seen, with 1.6 the altogether, experiments. 0.1 1.1 in Figure0.7It was 1.2 9.

Figure 9. ElementElement type type and and mesh mesh density density results results in in compar comparisonison with with the the experiments experiments for for three three locations. locations.

Another analysis was made to analyze the inclusioninclusion of a damagedamage model,model, by comparing the trabeculae material with damage, without damage, and with unloading and damage for the 2 mmmm C3D8R case. The material properties properties are are the the ones ones referred referred previously coupled with with a a damage damage model. model. 1 For that, a ductile damage model was used with a fracturefracture strainstrain ofof 0.1,0.1, aa strainstrain raterate ofof 1.171.17 ss−–1 [36],[36], and aa displacementdisplacement at at failure failure of 0.1.of 0.1. Both Both fracture fracture strain strain and displacement and displacement at failure at werefailure found were through found iteration.through iteration. The results The of results this comparison of this comparison are plotted are in Figureplotted 10 in. InFigure conclusion, 10. In theconclusion, compression the behaviorcompression of the behavior trabeculae of the is trabeculae deemed validated, is deemed and validated, the material and the model material with model the C3D8R with the elements C3D8R withoutelements damage without will damage be the will one be used the inon alle used the remainingin all the remaining simulations. simulations.

Figure 10. Damage model influence, with and without unloading in comparison with the experiments from all the locations. Biology 2020, 9, x 11 of 18

found that the C3D8R prevailed with the best compromise. Stress–strain curves were obtained to compare the results between simulations and experiments. These results can be seen, altogether, in Figure 9.

Figure 9. Element type and mesh density results in comparison with the experiments for three locations.

Another analysis was made to analyze the inclusion of a damage model, by comparing the trabeculae material with damage, without damage, and with unloading and damage for the 2 mm C3D8R case. The material properties are the ones referred previously coupled with a damage model. For that, a ductile damage model was used with a fracture strain of 0.1, a strain rate of 1.17 s–1 [36], and a displacement at failure of 0.1. Both fracture strain and displacement at failure were found through iteration. The results of this comparison are plotted in Figure 10. In conclusion, the Biology 2020compression, 9, 267 behavior of the trabeculae is deemed validated, and the material model with the C3D8R 12 of 18 elements without damage will be the one used in all the remaining simulations.

Figure 10.FigureDamage 10. Damage model model influence, influence, with with and and withoutwithout un unloadingloading in comparison in comparison with the with experiments the experiments fromBiology all from2020 the, locations.9all, x the locations. 12 of 18 Biology 2020, 9, x 12 of 18 3.2. Skull3.2. Vertex Skull Vertex Impact Impact Experiment—Blunt Experiment—Blunt TraumaTrauma from from Direct Direct Impact Impact against against Stationary Stationary Skull Skull 3.2. Skull Vertex Impact Experiment—Blunt Trauma from Direct Impact against Stationary Skull A preliminaryA preliminary analysis analysis was was made made to to determine determine the theproper proper element element type for typethe cortical for the bone cortical and bone the sutures.A preliminary Figure analysis11 compares was made these to simulationdetermine sthe with proper the elementexperiment. type forOverall, the cortical there boneis not and a and thesignificantthe sutures. sutures. difference FigureFigure betw1111 comparescompareseen the different these these simulationtypes, simulations concludings with withthatthe theexperiment. the C3D8R experiment. would Overall, best Overall,theresuit the is modelnot there a is not a significantsincesignificant its di behaviorff differenceerence is betweenin betw bettereen accordance the the different different with types, the types, concludingmaximum concluding forcethat the found thatC3D8R in the the would C3D8Rexperiments. best suit would theFigure model best 12 suit the modelpresents since its its thebehavior behavior results is (force–deflection in is better in better accordance accordancecurve) with of the the simulation withmaximum the compared maximumforce found with in force thethe experiment.experiments. found in the Figure experiments. 12 Figure 12presents presents the results the results (force–deflection (force–deflection curve) of the curve) simulation of the compared simulation with comparedthe experiment. with the experiment.

Figure 11. Comparison between element types for the cortical bone and sutures. FigureFigure 11. Comparison 11. Comparison between between elementelement types types fo forr the the cortical cortical bone bone and sutures. and sutures.

FigureFigure 12. Results12. Results of of the the simulation simulation compared compared with with the theexperiment experiment results. results. Figure 12. Results of the simulation compared with the experiment results. 3.3. Lateral Head Impact Experiment—Three Impacts at Different Velocities Simulating Falls 3.3. Lateral Head Impact Experiment—Three Impacts at Different Velocities Simulating Falls Comparisons between results will be done using the acceleration history of three different locations,Comparisons by taking betweenthe average results result will of 10be nodes done fr usingom each the location acceleration (anterior, history posterior, of three and different contra- lateral).locations, They by takingare depicted the average in Figure result 13, of where10 nodes the fr blackom each continuous location (anterior,curves represent posterior, the and averaged contra- accelerationlateral). They values, are depicted the dashed in Figure curves 13, represent where the the black standard continuous deviation curves from represent the mean the results averaged and theacceleration red curves values, represent the dashedthe results curves from represent the simulations. the standard deviation from the mean results and the redThe curves agreement represent tends the to results be much from better the simulations.for impacts with higher velocities but deteriorates for lowerThe impact agreement energies. tends A plausible to be much reason better might for beimpacts related with to the higher pad material velocities model but deteriorates since there arefor somelower uncertainties impact energies. regarding A plausible the material reason usedmight in be the related experiments. to the pad For material instance, model this material since there might are besome strain uncertainties rate dependent, regarding and the the mechanical material used properti in thees experiments. are based in theFor literature,instance, thiswithout material strain might rate dependency,be strain rate whichdependent, can possibly and the mechanicalbe a match forproperti 6 m/ses impact, are based but in not the the literature, case of withoutthe lowest strain impact rate energy.dependency, Since therewhich is can not possiblyenough informationbe a match forin the 6 m/s literature impact, regarding but not the this case point, of itthe will lowest be assumed impact energy. Since there is not enough information in the literature regarding this point, it will be assumed Biology 2020, 9, 267 13 of 18

3.3. Lateral Head Impact Experiment—Three Impacts at Different Velocities Simulating Falls Comparisons between results will be done using the acceleration history of three different locations, by takingBiology the 2020 average, 9, x result of 10 nodes from each location (anterior, posterior, and contra-lateral).13 of 18 They are depicted in Figure 13, where the black continuous curves represent the averaged acceleration that the material model of the pad is the major factor for the discrepancies between the simulations values,and the the dashed experiment curves results. represent the standard deviation from the mean results and the red curves represent the results from the simulations.

Contra-Lateral Anterior Posterior

Figure 13. Comparison between the experimental acceleration response expressed as mean one Figure 13. Comparison between the experimental acceleration response expressed as mean ± one± standardstandard deviation deviation and theand resultsthe results from from the the simulations simulations for for allall the nine nine cases: cases: impact impact velocities: velocities: 6 m/s, 6 m/s, 4.9 m/s,4.9 and m/s, 3.5 and m 3.5/s; m/s; location: location: anterior, anterior, posterior, posterior, and and contra-lateral). contra-lateral).

The agreementAdditionally, tends in terms to be of much impact better location, for the impacts posterior with one higher showed velocities the higher but deviations. deteriorates One for lowerpossible impact energies.cause of the A deviations plausible for reason the posterior might becases related might tobe thethe ex padistence material of significant model sincedifferences there are some uncertaintiesbetween the craniometry regarding theof the material specimens used and in thethe experiments.YEAHM skull. ForHowever, instance, it is this not materialpossible mightto be strainconfirm rate dependent,it or refuse andthis hypothesis the mechanical since propertiesYoganandan are et based al. [27] in only the literature,reported one without craniometry strain rate dependency,measurement, which the can head possibly breadth. be YEAHM’s a match forskull 6 has m/s a impact,head breadth but notof 145 the mm, case which of the is only lowest higher impact energy.than Since two there of the is notten specimens enough information of Yoganandan in the et literatureal. [27], where regarding the lowest this point, and the it willlargest be assumedhead breadths are 140 and 178 mm, respectively. that the material model of the pad is the major factor for the discrepancies between the simulations Typically, oscillations such as the ones observed in the simulations results of Figure 13, might and the experiment results. reflect numerical instabilities, coming from the contact algorithm or even from the complex material Additionally,laws employed. in termsHowever, of impacta deeper location, investigation the posterior allowed the one authors showed to the conclude higher that deviations. the One possibleacceleration cause on the of thechosen deviations nodes (10 for nodes, the which posterior acceleration cases might runs were be theaveraged existence eventually) of significant can differencesbe amplified between by thestress-waves craniometry on the of impacted the specimens skull. Inand the experiment, the YEAHM the skull. accelerometers However, always it is not possiblehave to confirmsome inertia, it or unlike refuse in this a numerical hypothesis approach since Yoganandan where the nodes et al. have [27] only the reported material one distributed craniometry measurement,mass. Moreover, the head the breadth. presumed YEAHM’s filtering in skullthe experi hasment a head resulted breadth in smoother of 145 mm, acceleration which is runs only than higher than twoin FE of simulations. the ten specimens Additionally, of Yoganandan in the explicit et al. analyses, [27], where no mass-scaling the lowest techniques and the largest were heademployed. breadths are 140Nevertheless, and 178 mm, the respectively. use of mass-scaling would ease the instabilities observed. Overall, the extracted curves are still valuable outputs that can be compared against the experiments, with the trend Typically, oscillations such as the ones observed in the simulations results of Figure 13, might behavior clearly observed. reflect numerical instabilities, coming from the contact algorithm or even from the complex material laws employed. However, a deeper investigation allowed the authors to conclude that the acceleration on the chosen nodes (10 nodes, which acceleration runs were averaged eventually) can be amplified by Biology 2020, 9, 267 14 of 18 stress-waves on the impacted skull. In the experiment, the accelerometers always have some inertia, unlike in a numerical approach where the nodes have only the material distributed mass. Moreover, the presumed filtering in the experiment resulted in smoother acceleration runs than in FE simulations. Additionally, in the explicit analyses, no mass-scaling techniques were employed. Nevertheless, the use of mass-scaling would ease the instabilities observed. Overall, the extracted curves are still valuable outputs that can be compared against the experiments, with the trend behavior clearly observed. Biology 2020, 9, x 14 of 18 3.4. Blunt Ballistic Temporo-Parietal Head Impacts 3.4. Blunt Ballistic Temporo-Parietal Head Impacts In the experiments, the impact at 35 m/s caused a circular depressed fracture, contrary to the In the experiments, the impact at 35 m/s caused a circular depressed fracture, contrary to the 20 20 m/m/ss impact. impact. Damage Damage toto thethe bone wa wass only only observed observed in inthe the higher higher energy energy impact. impact. Figure Figure 14 compares 14 compares YEAHM’sYEAHM’s fracture fracture pattern pattern with with both both experimental experimental and numerical numerical results results obtained obtained by Huang by Huang et al. et[37]. al. [37]. As canAs be can seen, be seen, the resultsthe results obtained obtained using using the the YEAHM YEAHM model model updatedupdated with with the the new new skull skull was was able able to predictto predict a similar a similar depressed depressed fracture fracture to Huang’s to Huang’s study, study, with with a dimension a dimension of 43 of mm43 mm vertically vertically and and48 mm horizontally.48 mm horizontally. The results The with results this modelwith this were model closer were to closer the experiments to the experiments than the than numerical the numerical model of Huangmodel et al. of [37Huang], considering et al. [37], theconsidering two reported the two dimensions, reported dimensions, fitting perfectly fitting perfectly one of the one dimensions of the of thedimensions depressed of fractures,the depressed and fractures, achieving and another achievin closerg another to thecloser experiment. to the experiment. However, However, in the in latter the latter (horizontally), the difference was still significant. (horizontally), the difference was still significant.

(a) (b)

(c) (d)

Figure 14. Comparisons of depressed skull fracture pattern obtained with YEAHM and in both Huang’s Figure 14. Comparisons of depressed skull fracture pattern obtained with YEAHM and in both experimentHuang’s and experiment simulation: and (simulation:a) fracture ( patterna) fracture from pattern the 35 from m/s the simulation; 35 m/s simulation; (b) fracture (b) patternfracture from the 35pattern m/s experiment from the 35 (adapted m/s experiment from [37 (adapted]); (c) fracture from [37]); pattern (c) fromfracture the pattern 35 m/ sfrom simulation the 35 withm/s the modelsimulation from Huang with the et al. model [37] from (adapted Huang from et al. [ 37[37]]); (adapted (d) fracture from pattern [37]); (d from) fracture the pattern 20 m/s from simulation. the 20 m/s simulation. In the experiments carried out by Huang et al. [37], the impactor face struck the specimen normal to the skinIn surface. the experiments This might carried be oneout by possible Huang causeet al. [37] of, the the discrepancyimpactor face instruck the horizontalthe specimen measurement. normal Sinceto the the model skin doessurface. not This have might skin, be it isone much possible harder cause to position of the discrepancy the impactor in accuratelythe horizontal once the measurement. Since the model does not have skin, it is much harder to position the impactor accurately once the reference in the model is the skull surface. Additionally, in the lower energy impact, a tiny fracture was predicted. A possible reason may be also related to the absence of the scalp, so the impact is more concentrated on those specific locations, and the first structure to absorb Biology 2020, 9, 267 15 of 18 reference in the model is the skull surface. Additionally, in the lower energy impact, a tiny fracture was predicted. A possible reason may be also related to the absence of the scalp, so the impact is more concentrated on those specific locations, and the first structure to absorb the impact energy and physically contact a striking object is the skull. This reason is very relevant since the study of Trotta et al. [50] showed that scalp tissue affects head impact biomechanics in a significant way, reducing the linear/rotational acceleration and in some cases causing an important change in the impact kinematics.

4. Conclusions Apart from a few deviations that can be linked to subjects’ variability and uncertain material properties from some experiments, one can state that the validations were performed with success. First, the compression of trabecular bone was validated, achieving a good agreement between numerical and experimental results. The entire skull structure response was validated thanks to blunt impacts with an anvil striking the head and another test method, where the head falls onto the covered ground. These are important to validate the remaining structures of the skull. A good agreement was found between YEAHM’s response and the experimental data. Nevertheless, in the simulation of the experiments resembling falls, significant deviations were found between numerical results and the experiments. The main justification for this deviation is the covering layer of the stationary anvil. The author of the study does not provide the material properties of it, nor a reference, which makes it necessary to assume some of the properties, with some being based on other validation studies from the literature. Nevertheless, the 6 and 4.9 m/s impacts were well simulated, where the main difference is in the lower energy impact, which makes it possible to question the strain rate dependency of the material. Additional validation was performed to confirm the model’s ability to predict depressed skull fractures. The experiment from Huang et al. [37] was reproduced, and a similar fracture pattern was observed. A better prediction was achieved than the model developed by Huang et al. [37]. Although a better prediction was achieved, there was still a significant deviation in one of the dimensions, and a small fracture was predicted in a non-fracture case. The main justification for this issue is the absence of a scalp structure in the model. Recently, Trotta et al. [50] showed how scalp tissue affects the head impact response. The research work carried out presents an update in the YEAHM model, focusing on the enhancement and development of a new skull model, a part usually overlooked and simplified in finite element modeling of the human head. Although most of the attention has been devoted to the brain and other intracranial structures, the authors consider the accurate skull modeling of significant importance as well as other structures, such as the scalp in Trotta et al. [50], which will be addressed in future research works. In this sense, the YEAHM head model can now be employed in a wider range of injury assessments, conjugating the previous developments in terms of SDH predictions with the new capacity to predict skull fractures. The model developed in this study can be used to optimize headgear (e.g., helmets, headbands, etc.) based on the model response and injury prediction based on reported head injury criteria. The model is also an excellent support tool in the design of products or components where there is a high chance of direct head impact. It can also be a useful tool in forensics science, for instance, in the reconstruction of road accidents or assaults involving head trauma as an outcome from blunt impacts on the head. This model makes it also possible to study some of the deformation mechanisms of the skull and to understand how certain parameters influence its response under an impact. Overall, once properly validated, such a tool allows the evaluation of injuries that may be a possible outcome from head impact scenarios.

Author Contributions: Conceptualization, F.A.O.F. and R.J.A.d.S.; methodology, F.A.O.F., R.J.A.d.S., M.P., and J.W.; software, A.B., F.A.O.F., M.P., and J.W.; validation, A.B., F.A.O.F., and R.J.A.d.S.; formal analysis, F.A.O.F. and R.J.A.d.S.; investigation, A.B., F.A.O.F., R.J.A.d.S., M.P., and J.W.; resources, M.P., R.J.A.d.S., and F.A.O.F; Biology 2020, 9, 267 16 of 18 data curation, A.B., F.A.O.F., and R.J.A.d.S.; writing—original draft preparation, A.B., F.A.O.F., and R.J.A.d.S.; writing—review and editing, A.B., F.A.O.F., R.J.A.d.S., M.P., and J.W.; visualization, M.P. and J.W.; supervision, F.A.O.F. and R.J.A.d.S.; project administration, F.A.O.F. and R.J.A.d.S.; funding acquisition, F.A.O.F., R.J.A.d.S., and M.P. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the projects UIDB/00481/2020 and UIDP/00481/2020—FCT—Fundação para a Ciência e a Tecnologia, and CENTRO-01-0145-FEDER-022083—Centro Portugal Regional Operational Programme (Centro2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund. The researcher under grant (CEECIND/01192/2017) would like to acknowledge the support given by Fundação para a Ciência e a Tecnologia (FCT). Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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