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Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications ab
Stefan Tabacu a
Department of Automotive, Faculty of Mechanics and Technology, University of Pitesti, 1, Târgu din Vale str., Pitesti, Romania b
Alseca Engineering, 64, Gheorghe Ionescu Sisesti str., Bucharest, Romania Published online: 25 Oct 2013.
Click for updates To cite this article: Stefan Tabacu (2015) Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications, Computer Methods in Biomechanics and Biomedical Engineering, 18:7, 769-781, DOI: 10.1080/10255842.2013.847092 To link to this article: http://dx.doi.org/10.1080/10255842.2013.847092
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Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 7, 769– 781, http://dx.doi.org/10.1080/10255842.2013.847092
Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications Stefan Tabacua,b* a
Department of Automotive, Faculty of Mechanics and Technology, University of Pitesti, 1, Taˆrgu din Vale str., Pitesti, Romania; bAlseca Engineering, 64, Gheorghe Ionescu Sisesti str., Bucharest, Romania
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(Received 17 April 2012; accepted 17 September 2013) In this paper, a methodology for the development and validation of a numerical model of the human head using generic procedures is presented. All steps required, starting with the model generation, model validation and applications will be discussed. The proposed model may be considered as a dual one due to its capabilities to switch from deformable to a rigid body according to the application’s requirements. The first step is to generate the numerical model of the human head using geometry files or medical images. The required stiffness and damping for the elastic connection used for the rigid body model are identified by performing a natural frequency analysis. The presented applications for model validation are related to impact analysis. The first case is related to Nahum’s (Nahum and Smith 1970) experiments pressure data being evaluated and a pressure map generated using the results from discrete elements. For the second case, the relative displacement between the brain and the skull is evaluated according to Hardy’s (Hardy WH, Foster CD, Mason, MJ, Yang KH, King A, Tashman S. 2001.Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray. Stapp Car Crash J. 45:337– 368, SAE Paper 2001-22-0016) experiments. The main objective is to validate the rigid model as a quick and versatile tool for acquiring the input data for specific brain analyses. Keywords: human head model; model generation; deformable model; rigid body model; model validation; impact applications
1. Introduction There is an increased interest in the analysis of the human head and brain motion during various trauma generation events. It is very difficult to carry out physical (in vivo) investigation and therefore an accurate numerical model of the human head may be a valuable tool for research. A review of the numerical models for injury biomechanics, celebrating Stapp Car Crash Conference at a 50 years anniversary (Yang et al. 2006) , outlines the developments in the field. Early and current numerical models of the human head are listed and presented. Together with the model features (model, structures modelled, number of nodes and elements), material models and mechanical properties are presented. The purpose of these models is to provide useful information related to traumatic brain injury in order to be used as tools for the development of safety devices. Among the most detailed numerical models of the human head are those developed by Zhang et al. (2001; WSUBIM), Kleiven and Hardy (2002), Takhounts et al. (2003; SIMON), Horgan and Gilchrist (2003; UCDBTM) and Willinger and Baumgartner (2003; ULP-FE). These models include detailed anatomical features, lately the influence of brain topology and bridging veins being investigated using updated version of these models. Numerical models developed using finite elements are used as injury-prediction tools (Gilchrist et al. 2001;
*Emails: [email protected]; [email protected] q 2013 Taylor & Francis
Canaple et al. 2003; Marjoux et al. 2008), and for safety equipment development (Ghajari et al. 2009; Panzer et al. 2012; Jazi et al. 2013), for paediatric injury prediction and evaluation (Rotha et al. 2010) and trauma criteria (Sabet et al. 2009). Detailed analyses of the brain injury can be performed (Ho and Kleiven 2009; Chen and OstojaStarzewski 2010) and neurosurgical procedures evaluated (Jones et al. 2010; Wittek et al. 2010). Simple lumped mass model marked the beginning of the development of numerical models. Those models were mainly used to analyse the motion of the skull – brain coupled system in the sagittal plane. Also these models were used for the investigation of the frequency response (Willinger et al. 1995) and the analysis of the relative motion between the brain and the skull (Hardy et al. 2001, 2007; Kleiven and Von Holst 2002; Zou, Kleiven, et al. 2007; Zou, Schmiedeler, et al. 2007; Weaver et al. 2012) and for the global evaluation of the head motion as well (Zou, Schmiedeler, et al. 2007; Yoganandan et al. 2008). Resuming the presentation of the finite elements of the human head, although some of them provide reliable results, the computer time required to solve the models may be an issue, probably just at this time, for extending the applications. Coupling finite elements models of the human head with rigid articulated models is currently investigated and used to analyse impact scenarios. It is also
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supposed that a 3D lumped model may be beneficial as it may be used for early or trial runs in order to calibrate the models. The model is designed for the analysis using finite elements codes or multibody (rigid body – lumped mass) methods. This model can be characterised as a dual model due to the relative minimal changes required for switching from deformable to rigid body model (RBM). The input for the model can be a geometry file (Horgan and Gilchrist 2003; Zhang and Bajaj 2006; in this case a.ply file) or computer-generated medical images (CT – computer tomography of magnetic resonance; Zhang et al. 2005; Pahr and Zysset 2009; Ji et al. 2011). These models are analysed according to Nahum experiments (Nahum and Smith 1970) and the brain pressures are evaluated. The spring force can be easily converted to a pressure applied on the brain, since the model is uniformly defined in terms of element size. The stiffness of the elastic connections is determined by identifying the natural frequencies of the head and comparing them with the literature. Damping is subsequently evaluated by comparing the sets of results with available experimental data. The relative displacement between the brain and the skull was investigated experimentally by Hardy et al. (2001) using Neutral Density Target (NDT) and high speed X-ray imaging technology. A number of experiments were performed using an inverted head in frontal and occipital impact cases. The most notable case, referenced by literature, is case C383. The human head is stuck in the frontal area and the parameters were recorded. 2. Generation of the finite elements numerical model 2.1 Hexahedral finite elements mesh generation method The method used to generate the all hexahedral finite elements model of the structure consists in a number of procedures used for reading the geometrical model, definition of the intersection planes and intersection contours, definition of the contour grid based quadrilateral mesh, definition of the section mesh, definition of the hexahedral finite elements and export of the numerical model (Teo et al. 2007; Shepherd and Johnson 2009; Lievers and Kent 2012; Mao et al. 2012). These procedures were implemented in a custom written code using Matlab. The geometrical model is converted to.ply (polygon) file format using an ASCII output. A.ply file consists of a header followed by a list of vertices and then a list of polygons. The header specifies how many vertices and polygons are in the file, and also states what properties are associated with each vertex, such as ðx; y; zÞ coordinates, normal and colour. The polygon faces are simply lists of indices into the vertex list, and each face begins with a count of the number of elements in each
list. The vertices are identified and the patches are constructed. Using the grid map and the defined finite elements size, the hexahedral finite elements are generated and saved in the output file. The resultant finite elements model and the associated final grid map are presented in Figure 1. The final finite elements model is generated using the same procedure. The novelty of the method resides in the overlapping procedure of the individual grid maps. Therefore, there are not required any specialised algorithms that must identify the relative position of the contours (Ho and Kleiven 2009). Using the method described earlier, a number of finite elements models were generated. Figure 2 presents the finite element models of the skull for different element sizes. 2.2 Hexahedral finite elements from CT images There are a number of available DICOM file viewer that can provide various tolls including file export, measuring, removal of personal information, area selection, etc. Resulting files (bitmap) are provided as rectangular grids. In Figure 3(a), the area with the brain was selected and the image is used as input for the numerical model generation (Zhang et al. 2005; Wittek et al. 2010). These images can be processed in order to obtain a lower numbers of colours (from 256 grey shades to 4 grey shades). A procedure that reads the exported DICOM images and resamples to 4 grey shades was implemented using Matlab. Also, a method to compress the files was developed and it has embedded the procedures for colour re-sampling (Figure 3). Using the measuring tools, anatomic details can be measured and the size of the finite element can be defined. 2.3
Numerical model
This method for generating the numerical model is general. It can be used for the generation of numerical model that accounts for small anatomical details or it can be used for volumes definition. A numerical model with an element size of 4 mm was developed using this method. From the numerical model of the skull, the brain was extracted using a volume defined using CT images (Figure 4). As the model is developed also for rigid body application, only few anatomical structures are represented: skull, cerebrospinal fluid (CSF) and the brain. The numerical models were solved using LS-Dyna (www.lstc.com) that has extended capabilities for implicit and explicit calculations. 3.
Generation of the rigid body model
A number of Matlab codes were developed and used to convert the deformable model into the RBM with elastic
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Figure 1.
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Generation of the finite elements model.
Figure 2. Finite element models of the skull. (a) CAD model (.ply file from www.biomedtown.org – LHDL project); (b) finite elements model (size 10 mm); (c) finite elements model (size 5 mm) and (d) finite elements model (size 2 mm).
Figure 3.
Applications of the meshing method.
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finite elements’ dimensions. For each element sharing nodes with CSF part and skull part, an extra node (*CONSTRAINED_EXTRA_NODES_NODE), defined as the geometrical centre, is generated and the data are saved in output files. Based on a minimum distance search algorithm, the closest extra nodes of the skull and CSF are selected and connection elements generated. The spring connections are collected in three additional parts depending on their direction (OX, OY, OZ). The results are saved in output files. Finally, the procedure completes by separating the CSF part from the skull. The material models used for the deformable model are updated in order to be suitable for the RBM, and rigid bodies sharing common nodes are merged together using *CONSTRAINED_RIGID_BODIES (e.g. CSF and the brain). Figure 5 presents the RBM and the spring connections between the CSF part and the skull.
Figure 4.
Numerical model.
connection. From the current deformable model of the human head, the RBM is constructed. All the procedures were implemented in custom written Matlab codes. Using as a reference part the elements associated with the CSF layer, the elements from the skull that are in the neighbourhood are selected based on the user-specified
Figure 5.
4. Natural frequencies analysis In their study, Khalil and Viano (1982) stated that a proper identification and evaluation of the natural frequencies are mandatory for the development of accurate numerical models of the human head for dynamic analysis. Moreover, an accurate identification of the natural frequencies of the human head is a critical issue for developing a reliable numerical model that can be used for simulations (Willinger et al. 1995). Two finite element numerical models (Figure 6) are used: the model developed using the meshing method presented in the paper and the model developed by Horgan and Gilchrist (2003). The study debuts with identification of the natural frequencies of the human skull. Experiments carried out by Khalil et al. (1979) identified for a skull corresponding to a 50th percentile male the first natural frequency to be at 1385 Hz. A study of the human skull in vivo performed by
RBM. Left – elastic connections between the skull and the CSF; right – model.
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Figure 6.
experimental values identified by Khalil et al. (1979) when similar mechanical properties were assigned. The results obtained using the numerical models are listed in Table 1. The brain was also individually investigated and a number of materials, reported by the literature, were assigned to the current and benchmark model (BM). Results and reference data are listed in Table 2. The BM is a more detailed representation of the human head and includes anatomical details (falx, trentorium, dura and pia mater). Therefore, for cases B IV and B V, these structures were excluded and subsequently included in the model and results compared. As expected, the inclusion of these structures stiffens the brain model and higher values for the natural frequencies are obtained. When available results from the literature are listed. It also worth mentioning that for the brain models without any structures, the responses are in good agreement. The current model (CM) does not include any other structures as it is designed as a fast model for both deformable and RBMs. In rigid body dynamics, the brain, falx, trentorium, dura and pia mater are merged together. These steps were performed in order to evaluate and identify the contribution of the structures to the head
Numerical models (a) CM and (b) BM/UCBDTM.
Ha˚kansson et al. (1994) identified the lowest (averaged) two resonance frequencies to be at 972 and 1230 Hz. The study also points that the variations between measured values can be explained by the skull geometry, skull thickness and bone structure, yet a direct relation between the skull size and the first natural frequency could not be identified. An analytical solution of the skull was developed by Charalambopoulos et al. (1996) and the natural frequencies calculated using the proposed model matched the Table 1.
Natural frequencies’ analysis of the skull.
CM (Hz) SI
Benchmark (Hz) – skull (face removed)
1770, 1990, 2175, 2389, 2664
n.a.
n.a.
1800, 2098, 2497, 2518, 2746
Table 2.
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Ref.
Model data
1994, 2121, 2472, 2731, 2749; Claessens et al. (1997)
Composite skull, elastic, E ¼ 6000 MPa (averaged), y ¼ 0.20, r ¼ 2070 kg/m3 Ward (1982) and Claessens et al. (1997) Scalp, elastic, E ¼ 16.7 MPa, y ¼ 0.42, r ¼ 1000 kg/m3; cortical bone, elastic, E ¼ 15,000 MPa, y ¼ 0.22, r ¼ 2000 kg/m3; trabecular bone, elastic, E ¼ 1000 MPa, y ¼ 0.24, r ¼ 1300 kg/m3 Horgan and Gilchrist (2003)
Natural frequencies’ analysis of the brain. CM (Hz)
Benchmark (Hz)
Ref. model
Material data
BI
74, 88, 102, 105, 113
71, 82, 96, 98, 101
B II
55, 65, 76, 78, 84
53,61, 71, 73, 75
B III
58, 69, 90, 82, 89
56, 64, 75, 77, 79
79, 81, 85, 103, 104; Claessens et al. (1997) 47, 65, 67, 92, 97; Gilchrist et al. (2001) n.a.; Willinger et al. (1999)
B IV
93, 110, 129, 132, 142
90, 104, 121, 123, 128
Elastic, E ¼ 1.0 MPa, y ¼ 0.480, r ¼ 1040 kg/m3. Elastic, E ¼ 558 kPa, y ¼ 0.480, r ¼ 1040 kg/m3. Elastic, E ¼ 675 kPa, y ¼ 0.480, r ¼ 1140 kg/m3. Viscoelastic, E ¼ 2190 MPa, G0 ¼ 528 kPa, G1 ¼ 168 kPa, b ¼ 35 s21.
BV
27, 33, 39, 40, 43
104*, 114*, 121*, 124*, 134* 27, 28, 32 37, 39 57*, 58*, 59*, 63*, 67*
n.a.; Shuck and Advani (1972), Willinger et al. (1999), Canaple et al. (2003) and Jazi et al. (2013) n.a.; Willinger and Baumgartner (2003)
Note: Values marked with *are for the model including falx, trentorium and dura mater.
Viscoelastic, E ¼ 1125 MPa, G0 ¼ 49 kPa, G1 ¼ 16 kPa, b ¼ 145 s21.
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Table 3.
HI H II H III
Natural frequencies’ analysis of head.
CM (Hz)
Benchmark (Hz)
Ref. (Hz)
Material data
232, 242 135, 139 72, 75 81*, 93*
219, 243 144, 167 78, 94
n.a. 126, 128, 140, 167, 177 100– 150 Hz for the sagittal plane, Willinger et al. (1995)
Shuck and Advani (1972) Gilchrist et al. (2001) Willinger and Baumgartner (2003)
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Note: Values marked with *are for the model including a simplified representation of falx and trentorium.
response for a natural frequency analysis. For the head model, the frequencies associated to decoupling phenomena in axial and sagittal plane are reported and listed in Table 3. For a stiff material model assigned to the brain, results show that the influence of falx and trentorium over the structural response of the head is limited. On the other hand, for the case H III, it can be noticed that there are some differences between computed values. The difference is significant for the value recorded in the sagittal plane as the result obtained using the BM is close to the value reported in the literature. As a consequence, in order to complete the evaluation of the CM, elements initially assigned to the brain were selected and a new part with the mechanical properties of falx and trentorium was created. Results obtained for case H III are presented in Figure 7 (axial plane) and Figure 8 (sagittal plane). The natural frequencies were investigated in order to identify the influence of the geometry and the material over the results. It was found that for the stiff material model, the geometry has a little influence over the structural response and while the stiffness of the brain material is decreased the geometrical features plays a
significant role. Also this analysis validates the CM to be used for further analyses. For the rigid body head model, multiple analyses were performed in order to identify the required stiffness of the elastic connection elements between the skull and the brain (Figure 9). From a value of 100 to 180 N/mm, the resulting natural frequencies of the rigid model were evaluated. Based on these values and using as a reference the values computed using the deformable model, the required stiffness for the spring elements is identified. The value that will be further assigned to the stiffness of the elastic elements is 0.155 kN/mm (Figure 10). Results obtained using the numerical models (deformable and rigid) are summarised in Table 4. In order to add a viscoelastic behavior for the brain, to the spring elements, connecting the CSF part with the skull of the RBM, damping elements were added (Table 5). The damping coefficient was determined by comparing the results using RBM with experimental data for Nahum and Smith (1970) and Hardy et al. (2001) and existing RBMs (Zou, Kleiven, et al. 2007).
Figure 7.
Displacement. Axial plane. (a) CM – 81 Hz and (b) BM – 78 Hz.
Figure 8.
Displacement. Sagittal plane. (a) CM – 93 Hz and (b) BM – 94 Hz.
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Figure 9.
Figure 10.
RBM. (a) Axial plane and (b) sagittal plane.
Identification of the spring stiffness.
Table 4. Results of the natural frequencies’ analysis. Model
CM
BM
RBM
Axial plane Sagittal plane
81 93
78 94
91 93
Table 5.
RBM model. Values for stiffness and damping.
Element Stiffness coefficient Damping coefficient
5.
775
RBM 0.155 kN=mm 0.001 kNs=mm (,1/(80– 100) stiffness, Zou, Kleiven, et al. (2007)
Model applications
The first case is an application for the evaluation of the model responses to Nahum and Smith (1970) experiments, while for the second case the relative displacement between the brain and the skull is evaluated. The mechanical properties of the materials used for the finite elements models are listed in Table 6.
5.1 Model response: Nahum’s experiments The studies performed by Nahum and Smith (1970) concerned the evaluation of the dynamic response of the brain in case of head impact. A number of seated, stationary cadavers were impacted on the frontal bone in the midsaggital plane, by a rigid mass with a constant velocity. The heads were inclined by 458 forward with respect to the Frankfort anatomical plane. In order to increase the impact duration in their experiments, Nahum et al. used various padding materials on the rigid mass. In this paper, the calculated impact force from the experiments was directly applied to the skull using a rigid element (Figure 11). For the multibody model, an extra node with the same coordinates as the centre of the rigid element used for the deformable model was added. An explicit analysis was performed using LsDyna. The analyses were performed for the CM (Figure 6 (a)), BM (Figure 6(b)) and RBM (Figure 5). For the RBM, the pressure is computed from the recorded springs forces divided by the elements’ faces areas. The impact force is presented in Figure 12. As mentioned, this load was applied to the centre node of the rigid body or the extra node attached to the rigid skull.
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Table 6.
S. Tabacu Mechanical and physical properties of the materials.
Structure
CM
Scalp, elastic, E ¼ 16.7 MPa, y ¼ 0.42, r ¼ 1000 kg/m3 Facial bone, elastic, E ¼ 5000 MPa, y ¼ 0.23, r ¼ 2100 kg/m3 Trabecular bone, elastic, E ¼ 1000 MPa, y ¼ 0.24, r ¼ 1130 kg/m3 Cortical bone, elastic, E ¼ 15,000 MPa, y ¼ 0.22, r ¼ 2000 kg/m3 Composite skull, elastic, E ¼ 6000 MPa, y ¼ 0.20, r ¼ 2070 kg/m3 CSF, elastic, E ¼ 0.148 MPa, y ¼ 0.499, r ¼ 1040 kg/m3 Brain, viscoelastic, E ¼ 1125 MPa, G0 ¼ 49 kPa, G1 ¼ 16 kPa, b ¼ 145 s21 Pia mater, elastic, E ¼ 11.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3 Dura mater, elastic, E ¼ 31.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3 Falx, elastic, E ¼ 31.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3 Trentorium, elastic, E ¼ 31.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3
n.a. n.a. n.a. n.a. p p p
n.a. n.a. n.a. n.a.
Figure 11.
Head model. Nahum et al. experiments. (a) Numerical model and (b) applied load.
Figure 12.
Experiment vs. numerical model. (a) Frontal pressure data and (b) psoterior fossa pressure data.
Referenced work presents the results (experiment 37) in term of measured head acceleration, frontal pressure, parietal pressure, occipital pressure and posterior fossa pressure. In this paper, the results obtained for the frontal pressure (Figure 12(a)) and posterior fossa pressure (Figure 12(b)) were evaluated. There is a good agreement between the results obtained using the proposed models and the experimental result for the head acceleration. For the posterior
BM p p p p n.a. p p p p p p
fossa, the positive value (, 0.04 kPa) of the pressure after 6 ms could not be recorded and discussion regarding this can be found in the literature (Kleiven and Hardy 2002; Horgan and Gilchrist 2003; Yan and Pangestu 2011). A Matlab code was developed, and using the forces recorded by the spring and damper elements from the RBM a pressure map may be constructed. The resulting pressure data are presented in Figure 13.
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Computer Methods in Biomechanics and Biomedical Engineering
Figure 13.
Pressure data obtained using RBM.
Figure 14.
Applied accelerations. (a) Linear acceleration and (b) angular acceleration.
5.2
Model response: Hardy’s experiments
The studies performed by Hardy et al. (2001) concerned the evaluation relative displacement between the brain and the skull. For an experimental case (C383), the RBM
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was positioned and loaded according to the literature data (Figure 14) (Hardy et al. 2001; Kleiven and Hardy 2002). The numerical model is presented in Figure 15(a) and the tracked nodes are presented in Figure 15(b) (neighbour
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Numerical model. (a) Model set-up and (b) tracked nodes.
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Figure 15.
S. Tabacu
Figure 16. Results. (a) X relative displacement: NDT a1, a2 and a6; (b) Z relative displacement: NDT a1, a2 and a6. (c) X relative displacement: NDT p1, p2 and p6 and (d) Z relative displacement: NDT p1, p2 and p6.
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Figure 17.
NDT trajectories.
Figure 18.
NDT trajectories (damping coefficient 0.0001 kNs=mm).
elements were selected in order to improve the displayed information). The results are presented in Figures 16 and 17. Experimental results for NDT a1 and NDT p1 display a relative displacement for the time interval 0– 50 ms of 2 5 mm while the maximum displacement recorded using
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the present model is of 2 1.1 mm. The recorded values for relative X and Z displacement are due to the definition of the brain as a rigid body. In order to evaluate the influence of damping, Figure 18 presents the NDTs paths for a small value of the damping coefficient (0.0001 kNs=mm). In this case, the relative
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displacement has a magnitude of 2.5 mm. As experimental data may be obtained in different conditions, the results obtained using RBM show that there is a combination between stiffness and damping coefficient that may provide good results. These results may validate RBM as a tool for relative brain –skull displacement with respect to model detail level and computational requirements. Future applications can be developed (Zou, Kleiven, et al. 2007; Zou, Schmiedeler, et al. 2007; Zou and Schmiedeler 2008).
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6.
Conclusions
In this paper, a methodology for the development and validation of a numerical model of the human head is presented. The numerical model is defined as a dual mode that can be used for finite elements and for rigid body applications. The paper presented all steps required, starting with the model generation, model validation and applications. The procedure, although exemplified for the numerical model presented in the paper (CM), can be extrapolated and applied for any numerical models (e.g. BM) given the nodes correspondence and nodes sharing between the structures of the head. The required stiffness for the spring connection used for the RBM was identified by performing a natural frequency analysis. The damping coefficient for the model was determined by comparing the results with the literature data. The applications presented are related to impact analysis. Two cases were presented: Nahum’s and Hardy’s experiments. For the first case, the frontal and posterior fossa pressures were evaluated and results compared with the experimental data. Using a custom code, a pressure map of the brain was constructed and results displayed. For the second case, the relative displacement between the brain and the skull was evaluated and reasonable agreement with literature data was found. The main objective was to validate the rigid model as a quick and versatile tool for acquiring the input data for specific brain analyses. The RBM presented in the paper may be used for 3D lumped mass models. The stiffness and damping of the connection can be easily adapted according to the anthropometric size as a linear function of the body (head) mass. The RBM may provide accurate results for different impact situation and it may also provide input data for detailed brain analyses (pressure map derived for the elastic connection force data).
References Canaple B, Rungen G, Drazetic P, Markiewicz E, Cesari D. 2003. Towards a finite element head model used as a head injury predictive tool. Int J Crashworthiness. 8(1):41 – 52.
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Computer Methods in Biomechanics and Biomedical Engineering using feature-based multi-block approach. Comput Methods Biomech Biomed Eng. 16(3):271– 279. Marjoux D, Baumgartner D, Deck C, Willinger R. 2008. Head injury prediction capability of the HIC, HIP, SIMon and ULP criteria. Accid Anal Prev. 40(3):1135– 1148. Nahum AM, Smith R. 1970. Intracranial pressure dynamics during head impact, SAE Techical Paper 770922, Society of Automotive Engineers, Warrendale, PA. Pahr DH, Zysset PK. 2009. From high-resolution CT data to finite element models: development of an integrated modular framework. Comput Methods Biomech Biomed Eng. 12(1): 45 – 57. Panzer MB, Myers BS, Capehart BP, Bass CR. 2012. Development of a finite element model for blast brain injury and the effects of CSF cavitation. Ann Biomed Eng. 40(7):1530– 1544. Rotha S, Raula JS, Willinger R. 2010. Finite element modelling of paediatric head impact: global validation against experimental data. Comput Methods Programs Biomed. 99(1):25– 33. Sabet AA, Christoforou E, Zatlin B, Genin GM, Bayly PV. 2009. Deformation of the human brain induced by mild angular head acceleration. J Biomech. 41(2):307– 315. Shepherd JF, Johnson CR. 2009. Hexahedral mesh generation for biomedical models in SCIRun. Eng Comput. 25(1):97 –114. Shuck LZ, Advani SH. 1972. Rheological response of human brain tissue in shearing. J Basic Eng. 94(4):905–911. Takhounts EG, Eppinger RH, Campbell JQ, Tannous RE, Power ED, Shook LS. 2003. On the development of the SIMon finite element head model. Stapp Car Crash J. 47:107– 133. Teo JCM, Chui CK, Wang ZL, Ong SH, Yan CH, Wang SC, Wong HK, Teoh SH. 2007. Heterogeneous meshing and biomechanical modeling of human spine. Med Eng Phys. 29 (2):277 – 290. Ward CC. 1982. Finite element models of the head and their use in brain injury research, Proceedings of the twenty-sixth Stapp Car Crash Conference, 71 – 86, Ann Arbor, Michigan, SAE Technical Paper 821154. Weaver AA, Danelson KA, Stitzel JD. 2012. Modeling brain injury response for rotational velocities of varying directions and magnitudes. Ann Biomed Eng. 40(9):2005– 2018. Willinger R, Baumgartner D. 2003. Human head tolerance limits to specific injury mechanisms. Int J Crashworthiness. 8(6): 605– 617.
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Computer Methods in Biomechanics and Biomedical Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gcmb20
Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications ab
Stefan Tabacu a
Department of Automotive, Faculty of Mechanics and Technology, University of Pitesti, 1, Târgu din Vale str., Pitesti, Romania b
Alseca Engineering, 64, Gheorghe Ionescu Sisesti str., Bucharest, Romania Published online: 25 Oct 2013.
Click for updates To cite this article: Stefan Tabacu (2015) Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications, Computer Methods in Biomechanics and Biomedical Engineering, 18:7, 769-781, DOI: 10.1080/10255842.2013.847092 To link to this article: http://dx.doi.org/10.1080/10255842.2013.847092
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Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 7, 769– 781, http://dx.doi.org/10.1080/10255842.2013.847092
Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications Stefan Tabacua,b* a
Department of Automotive, Faculty of Mechanics and Technology, University of Pitesti, 1, Taˆrgu din Vale str., Pitesti, Romania; bAlseca Engineering, 64, Gheorghe Ionescu Sisesti str., Bucharest, Romania
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(Received 17 April 2012; accepted 17 September 2013) In this paper, a methodology for the development and validation of a numerical model of the human head using generic procedures is presented. All steps required, starting with the model generation, model validation and applications will be discussed. The proposed model may be considered as a dual one due to its capabilities to switch from deformable to a rigid body according to the application’s requirements. The first step is to generate the numerical model of the human head using geometry files or medical images. The required stiffness and damping for the elastic connection used for the rigid body model are identified by performing a natural frequency analysis. The presented applications for model validation are related to impact analysis. The first case is related to Nahum’s (Nahum and Smith 1970) experiments pressure data being evaluated and a pressure map generated using the results from discrete elements. For the second case, the relative displacement between the brain and the skull is evaluated according to Hardy’s (Hardy WH, Foster CD, Mason, MJ, Yang KH, King A, Tashman S. 2001.Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray. Stapp Car Crash J. 45:337– 368, SAE Paper 2001-22-0016) experiments. The main objective is to validate the rigid model as a quick and versatile tool for acquiring the input data for specific brain analyses. Keywords: human head model; model generation; deformable model; rigid body model; model validation; impact applications
1. Introduction There is an increased interest in the analysis of the human head and brain motion during various trauma generation events. It is very difficult to carry out physical (in vivo) investigation and therefore an accurate numerical model of the human head may be a valuable tool for research. A review of the numerical models for injury biomechanics, celebrating Stapp Car Crash Conference at a 50 years anniversary (Yang et al. 2006) , outlines the developments in the field. Early and current numerical models of the human head are listed and presented. Together with the model features (model, structures modelled, number of nodes and elements), material models and mechanical properties are presented. The purpose of these models is to provide useful information related to traumatic brain injury in order to be used as tools for the development of safety devices. Among the most detailed numerical models of the human head are those developed by Zhang et al. (2001; WSUBIM), Kleiven and Hardy (2002), Takhounts et al. (2003; SIMON), Horgan and Gilchrist (2003; UCDBTM) and Willinger and Baumgartner (2003; ULP-FE). These models include detailed anatomical features, lately the influence of brain topology and bridging veins being investigated using updated version of these models. Numerical models developed using finite elements are used as injury-prediction tools (Gilchrist et al. 2001;
*Emails: [email protected]; [email protected] q 2013 Taylor & Francis
Canaple et al. 2003; Marjoux et al. 2008), and for safety equipment development (Ghajari et al. 2009; Panzer et al. 2012; Jazi et al. 2013), for paediatric injury prediction and evaluation (Rotha et al. 2010) and trauma criteria (Sabet et al. 2009). Detailed analyses of the brain injury can be performed (Ho and Kleiven 2009; Chen and OstojaStarzewski 2010) and neurosurgical procedures evaluated (Jones et al. 2010; Wittek et al. 2010). Simple lumped mass model marked the beginning of the development of numerical models. Those models were mainly used to analyse the motion of the skull – brain coupled system in the sagittal plane. Also these models were used for the investigation of the frequency response (Willinger et al. 1995) and the analysis of the relative motion between the brain and the skull (Hardy et al. 2001, 2007; Kleiven and Von Holst 2002; Zou, Kleiven, et al. 2007; Zou, Schmiedeler, et al. 2007; Weaver et al. 2012) and for the global evaluation of the head motion as well (Zou, Schmiedeler, et al. 2007; Yoganandan et al. 2008). Resuming the presentation of the finite elements of the human head, although some of them provide reliable results, the computer time required to solve the models may be an issue, probably just at this time, for extending the applications. Coupling finite elements models of the human head with rigid articulated models is currently investigated and used to analyse impact scenarios. It is also
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supposed that a 3D lumped model may be beneficial as it may be used for early or trial runs in order to calibrate the models. The model is designed for the analysis using finite elements codes or multibody (rigid body – lumped mass) methods. This model can be characterised as a dual model due to the relative minimal changes required for switching from deformable to rigid body model (RBM). The input for the model can be a geometry file (Horgan and Gilchrist 2003; Zhang and Bajaj 2006; in this case a.ply file) or computer-generated medical images (CT – computer tomography of magnetic resonance; Zhang et al. 2005; Pahr and Zysset 2009; Ji et al. 2011). These models are analysed according to Nahum experiments (Nahum and Smith 1970) and the brain pressures are evaluated. The spring force can be easily converted to a pressure applied on the brain, since the model is uniformly defined in terms of element size. The stiffness of the elastic connections is determined by identifying the natural frequencies of the head and comparing them with the literature. Damping is subsequently evaluated by comparing the sets of results with available experimental data. The relative displacement between the brain and the skull was investigated experimentally by Hardy et al. (2001) using Neutral Density Target (NDT) and high speed X-ray imaging technology. A number of experiments were performed using an inverted head in frontal and occipital impact cases. The most notable case, referenced by literature, is case C383. The human head is stuck in the frontal area and the parameters were recorded. 2. Generation of the finite elements numerical model 2.1 Hexahedral finite elements mesh generation method The method used to generate the all hexahedral finite elements model of the structure consists in a number of procedures used for reading the geometrical model, definition of the intersection planes and intersection contours, definition of the contour grid based quadrilateral mesh, definition of the section mesh, definition of the hexahedral finite elements and export of the numerical model (Teo et al. 2007; Shepherd and Johnson 2009; Lievers and Kent 2012; Mao et al. 2012). These procedures were implemented in a custom written code using Matlab. The geometrical model is converted to.ply (polygon) file format using an ASCII output. A.ply file consists of a header followed by a list of vertices and then a list of polygons. The header specifies how many vertices and polygons are in the file, and also states what properties are associated with each vertex, such as ðx; y; zÞ coordinates, normal and colour. The polygon faces are simply lists of indices into the vertex list, and each face begins with a count of the number of elements in each
list. The vertices are identified and the patches are constructed. Using the grid map and the defined finite elements size, the hexahedral finite elements are generated and saved in the output file. The resultant finite elements model and the associated final grid map are presented in Figure 1. The final finite elements model is generated using the same procedure. The novelty of the method resides in the overlapping procedure of the individual grid maps. Therefore, there are not required any specialised algorithms that must identify the relative position of the contours (Ho and Kleiven 2009). Using the method described earlier, a number of finite elements models were generated. Figure 2 presents the finite element models of the skull for different element sizes. 2.2 Hexahedral finite elements from CT images There are a number of available DICOM file viewer that can provide various tolls including file export, measuring, removal of personal information, area selection, etc. Resulting files (bitmap) are provided as rectangular grids. In Figure 3(a), the area with the brain was selected and the image is used as input for the numerical model generation (Zhang et al. 2005; Wittek et al. 2010). These images can be processed in order to obtain a lower numbers of colours (from 256 grey shades to 4 grey shades). A procedure that reads the exported DICOM images and resamples to 4 grey shades was implemented using Matlab. Also, a method to compress the files was developed and it has embedded the procedures for colour re-sampling (Figure 3). Using the measuring tools, anatomic details can be measured and the size of the finite element can be defined. 2.3
Numerical model
This method for generating the numerical model is general. It can be used for the generation of numerical model that accounts for small anatomical details or it can be used for volumes definition. A numerical model with an element size of 4 mm was developed using this method. From the numerical model of the skull, the brain was extracted using a volume defined using CT images (Figure 4). As the model is developed also for rigid body application, only few anatomical structures are represented: skull, cerebrospinal fluid (CSF) and the brain. The numerical models were solved using LS-Dyna (www.lstc.com) that has extended capabilities for implicit and explicit calculations. 3.
Generation of the rigid body model
A number of Matlab codes were developed and used to convert the deformable model into the RBM with elastic
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Computer Methods in Biomechanics and Biomedical Engineering
Figure 1.
771
Generation of the finite elements model.
Figure 2. Finite element models of the skull. (a) CAD model (.ply file from www.biomedtown.org – LHDL project); (b) finite elements model (size 10 mm); (c) finite elements model (size 5 mm) and (d) finite elements model (size 2 mm).
Figure 3.
Applications of the meshing method.
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finite elements’ dimensions. For each element sharing nodes with CSF part and skull part, an extra node (*CONSTRAINED_EXTRA_NODES_NODE), defined as the geometrical centre, is generated and the data are saved in output files. Based on a minimum distance search algorithm, the closest extra nodes of the skull and CSF are selected and connection elements generated. The spring connections are collected in three additional parts depending on their direction (OX, OY, OZ). The results are saved in output files. Finally, the procedure completes by separating the CSF part from the skull. The material models used for the deformable model are updated in order to be suitable for the RBM, and rigid bodies sharing common nodes are merged together using *CONSTRAINED_RIGID_BODIES (e.g. CSF and the brain). Figure 5 presents the RBM and the spring connections between the CSF part and the skull.
Figure 4.
Numerical model.
connection. From the current deformable model of the human head, the RBM is constructed. All the procedures were implemented in custom written Matlab codes. Using as a reference part the elements associated with the CSF layer, the elements from the skull that are in the neighbourhood are selected based on the user-specified
Figure 5.
4. Natural frequencies analysis In their study, Khalil and Viano (1982) stated that a proper identification and evaluation of the natural frequencies are mandatory for the development of accurate numerical models of the human head for dynamic analysis. Moreover, an accurate identification of the natural frequencies of the human head is a critical issue for developing a reliable numerical model that can be used for simulations (Willinger et al. 1995). Two finite element numerical models (Figure 6) are used: the model developed using the meshing method presented in the paper and the model developed by Horgan and Gilchrist (2003). The study debuts with identification of the natural frequencies of the human skull. Experiments carried out by Khalil et al. (1979) identified for a skull corresponding to a 50th percentile male the first natural frequency to be at 1385 Hz. A study of the human skull in vivo performed by
RBM. Left – elastic connections between the skull and the CSF; right – model.
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Figure 6.
experimental values identified by Khalil et al. (1979) when similar mechanical properties were assigned. The results obtained using the numerical models are listed in Table 1. The brain was also individually investigated and a number of materials, reported by the literature, were assigned to the current and benchmark model (BM). Results and reference data are listed in Table 2. The BM is a more detailed representation of the human head and includes anatomical details (falx, trentorium, dura and pia mater). Therefore, for cases B IV and B V, these structures were excluded and subsequently included in the model and results compared. As expected, the inclusion of these structures stiffens the brain model and higher values for the natural frequencies are obtained. When available results from the literature are listed. It also worth mentioning that for the brain models without any structures, the responses are in good agreement. The current model (CM) does not include any other structures as it is designed as a fast model for both deformable and RBMs. In rigid body dynamics, the brain, falx, trentorium, dura and pia mater are merged together. These steps were performed in order to evaluate and identify the contribution of the structures to the head
Numerical models (a) CM and (b) BM/UCBDTM.
Ha˚kansson et al. (1994) identified the lowest (averaged) two resonance frequencies to be at 972 and 1230 Hz. The study also points that the variations between measured values can be explained by the skull geometry, skull thickness and bone structure, yet a direct relation between the skull size and the first natural frequency could not be identified. An analytical solution of the skull was developed by Charalambopoulos et al. (1996) and the natural frequencies calculated using the proposed model matched the Table 1.
Natural frequencies’ analysis of the skull.
CM (Hz) SI
Benchmark (Hz) – skull (face removed)
1770, 1990, 2175, 2389, 2664
n.a.
n.a.
1800, 2098, 2497, 2518, 2746
Table 2.
773
Ref.
Model data
1994, 2121, 2472, 2731, 2749; Claessens et al. (1997)
Composite skull, elastic, E ¼ 6000 MPa (averaged), y ¼ 0.20, r ¼ 2070 kg/m3 Ward (1982) and Claessens et al. (1997) Scalp, elastic, E ¼ 16.7 MPa, y ¼ 0.42, r ¼ 1000 kg/m3; cortical bone, elastic, E ¼ 15,000 MPa, y ¼ 0.22, r ¼ 2000 kg/m3; trabecular bone, elastic, E ¼ 1000 MPa, y ¼ 0.24, r ¼ 1300 kg/m3 Horgan and Gilchrist (2003)
Natural frequencies’ analysis of the brain. CM (Hz)
Benchmark (Hz)
Ref. model
Material data
BI
74, 88, 102, 105, 113
71, 82, 96, 98, 101
B II
55, 65, 76, 78, 84
53,61, 71, 73, 75
B III
58, 69, 90, 82, 89
56, 64, 75, 77, 79
79, 81, 85, 103, 104; Claessens et al. (1997) 47, 65, 67, 92, 97; Gilchrist et al. (2001) n.a.; Willinger et al. (1999)
B IV
93, 110, 129, 132, 142
90, 104, 121, 123, 128
Elastic, E ¼ 1.0 MPa, y ¼ 0.480, r ¼ 1040 kg/m3. Elastic, E ¼ 558 kPa, y ¼ 0.480, r ¼ 1040 kg/m3. Elastic, E ¼ 675 kPa, y ¼ 0.480, r ¼ 1140 kg/m3. Viscoelastic, E ¼ 2190 MPa, G0 ¼ 528 kPa, G1 ¼ 168 kPa, b ¼ 35 s21.
BV
27, 33, 39, 40, 43
104*, 114*, 121*, 124*, 134* 27, 28, 32 37, 39 57*, 58*, 59*, 63*, 67*
n.a.; Shuck and Advani (1972), Willinger et al. (1999), Canaple et al. (2003) and Jazi et al. (2013) n.a.; Willinger and Baumgartner (2003)
Note: Values marked with *are for the model including falx, trentorium and dura mater.
Viscoelastic, E ¼ 1125 MPa, G0 ¼ 49 kPa, G1 ¼ 16 kPa, b ¼ 145 s21.
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Table 3.
HI H II H III
Natural frequencies’ analysis of head.
CM (Hz)
Benchmark (Hz)
Ref. (Hz)
Material data
232, 242 135, 139 72, 75 81*, 93*
219, 243 144, 167 78, 94
n.a. 126, 128, 140, 167, 177 100– 150 Hz for the sagittal plane, Willinger et al. (1995)
Shuck and Advani (1972) Gilchrist et al. (2001) Willinger and Baumgartner (2003)
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Note: Values marked with *are for the model including a simplified representation of falx and trentorium.
response for a natural frequency analysis. For the head model, the frequencies associated to decoupling phenomena in axial and sagittal plane are reported and listed in Table 3. For a stiff material model assigned to the brain, results show that the influence of falx and trentorium over the structural response of the head is limited. On the other hand, for the case H III, it can be noticed that there are some differences between computed values. The difference is significant for the value recorded in the sagittal plane as the result obtained using the BM is close to the value reported in the literature. As a consequence, in order to complete the evaluation of the CM, elements initially assigned to the brain were selected and a new part with the mechanical properties of falx and trentorium was created. Results obtained for case H III are presented in Figure 7 (axial plane) and Figure 8 (sagittal plane). The natural frequencies were investigated in order to identify the influence of the geometry and the material over the results. It was found that for the stiff material model, the geometry has a little influence over the structural response and while the stiffness of the brain material is decreased the geometrical features plays a
significant role. Also this analysis validates the CM to be used for further analyses. For the rigid body head model, multiple analyses were performed in order to identify the required stiffness of the elastic connection elements between the skull and the brain (Figure 9). From a value of 100 to 180 N/mm, the resulting natural frequencies of the rigid model were evaluated. Based on these values and using as a reference the values computed using the deformable model, the required stiffness for the spring elements is identified. The value that will be further assigned to the stiffness of the elastic elements is 0.155 kN/mm (Figure 10). Results obtained using the numerical models (deformable and rigid) are summarised in Table 4. In order to add a viscoelastic behavior for the brain, to the spring elements, connecting the CSF part with the skull of the RBM, damping elements were added (Table 5). The damping coefficient was determined by comparing the results using RBM with experimental data for Nahum and Smith (1970) and Hardy et al. (2001) and existing RBMs (Zou, Kleiven, et al. 2007).
Figure 7.
Displacement. Axial plane. (a) CM – 81 Hz and (b) BM – 78 Hz.
Figure 8.
Displacement. Sagittal plane. (a) CM – 93 Hz and (b) BM – 94 Hz.
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Figure 9.
Figure 10.
RBM. (a) Axial plane and (b) sagittal plane.
Identification of the spring stiffness.
Table 4. Results of the natural frequencies’ analysis. Model
CM
BM
RBM
Axial plane Sagittal plane
81 93
78 94
91 93
Table 5.
RBM model. Values for stiffness and damping.
Element Stiffness coefficient Damping coefficient
5.
775
RBM 0.155 kN=mm 0.001 kNs=mm (,1/(80– 100) stiffness, Zou, Kleiven, et al. (2007)
Model applications
The first case is an application for the evaluation of the model responses to Nahum and Smith (1970) experiments, while for the second case the relative displacement between the brain and the skull is evaluated. The mechanical properties of the materials used for the finite elements models are listed in Table 6.
5.1 Model response: Nahum’s experiments The studies performed by Nahum and Smith (1970) concerned the evaluation of the dynamic response of the brain in case of head impact. A number of seated, stationary cadavers were impacted on the frontal bone in the midsaggital plane, by a rigid mass with a constant velocity. The heads were inclined by 458 forward with respect to the Frankfort anatomical plane. In order to increase the impact duration in their experiments, Nahum et al. used various padding materials on the rigid mass. In this paper, the calculated impact force from the experiments was directly applied to the skull using a rigid element (Figure 11). For the multibody model, an extra node with the same coordinates as the centre of the rigid element used for the deformable model was added. An explicit analysis was performed using LsDyna. The analyses were performed for the CM (Figure 6 (a)), BM (Figure 6(b)) and RBM (Figure 5). For the RBM, the pressure is computed from the recorded springs forces divided by the elements’ faces areas. The impact force is presented in Figure 12. As mentioned, this load was applied to the centre node of the rigid body or the extra node attached to the rigid skull.
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Table 6.
S. Tabacu Mechanical and physical properties of the materials.
Structure
CM
Scalp, elastic, E ¼ 16.7 MPa, y ¼ 0.42, r ¼ 1000 kg/m3 Facial bone, elastic, E ¼ 5000 MPa, y ¼ 0.23, r ¼ 2100 kg/m3 Trabecular bone, elastic, E ¼ 1000 MPa, y ¼ 0.24, r ¼ 1130 kg/m3 Cortical bone, elastic, E ¼ 15,000 MPa, y ¼ 0.22, r ¼ 2000 kg/m3 Composite skull, elastic, E ¼ 6000 MPa, y ¼ 0.20, r ¼ 2070 kg/m3 CSF, elastic, E ¼ 0.148 MPa, y ¼ 0.499, r ¼ 1040 kg/m3 Brain, viscoelastic, E ¼ 1125 MPa, G0 ¼ 49 kPa, G1 ¼ 16 kPa, b ¼ 145 s21 Pia mater, elastic, E ¼ 11.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3 Dura mater, elastic, E ¼ 31.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3 Falx, elastic, E ¼ 31.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3 Trentorium, elastic, E ¼ 31.5 MPa, y ¼ 0.45, r ¼ 1130 kg/m3
n.a. n.a. n.a. n.a. p p p
n.a. n.a. n.a. n.a.
Figure 11.
Head model. Nahum et al. experiments. (a) Numerical model and (b) applied load.
Figure 12.
Experiment vs. numerical model. (a) Frontal pressure data and (b) psoterior fossa pressure data.
Referenced work presents the results (experiment 37) in term of measured head acceleration, frontal pressure, parietal pressure, occipital pressure and posterior fossa pressure. In this paper, the results obtained for the frontal pressure (Figure 12(a)) and posterior fossa pressure (Figure 12(b)) were evaluated. There is a good agreement between the results obtained using the proposed models and the experimental result for the head acceleration. For the posterior
BM p p p p n.a. p p p p p p
fossa, the positive value (, 0.04 kPa) of the pressure after 6 ms could not be recorded and discussion regarding this can be found in the literature (Kleiven and Hardy 2002; Horgan and Gilchrist 2003; Yan and Pangestu 2011). A Matlab code was developed, and using the forces recorded by the spring and damper elements from the RBM a pressure map may be constructed. The resulting pressure data are presented in Figure 13.
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Computer Methods in Biomechanics and Biomedical Engineering
Figure 13.
Pressure data obtained using RBM.
Figure 14.
Applied accelerations. (a) Linear acceleration and (b) angular acceleration.
5.2
Model response: Hardy’s experiments
The studies performed by Hardy et al. (2001) concerned the evaluation relative displacement between the brain and the skull. For an experimental case (C383), the RBM
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was positioned and loaded according to the literature data (Figure 14) (Hardy et al. 2001; Kleiven and Hardy 2002). The numerical model is presented in Figure 15(a) and the tracked nodes are presented in Figure 15(b) (neighbour
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Numerical model. (a) Model set-up and (b) tracked nodes.
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Figure 15.
S. Tabacu
Figure 16. Results. (a) X relative displacement: NDT a1, a2 and a6; (b) Z relative displacement: NDT a1, a2 and a6. (c) X relative displacement: NDT p1, p2 and p6 and (d) Z relative displacement: NDT p1, p2 and p6.
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Computer Methods in Biomechanics and Biomedical Engineering
Figure 17.
NDT trajectories.
Figure 18.
NDT trajectories (damping coefficient 0.0001 kNs=mm).
elements were selected in order to improve the displayed information). The results are presented in Figures 16 and 17. Experimental results for NDT a1 and NDT p1 display a relative displacement for the time interval 0– 50 ms of 2 5 mm while the maximum displacement recorded using
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the present model is of 2 1.1 mm. The recorded values for relative X and Z displacement are due to the definition of the brain as a rigid body. In order to evaluate the influence of damping, Figure 18 presents the NDTs paths for a small value of the damping coefficient (0.0001 kNs=mm). In this case, the relative
780
S. Tabacu
displacement has a magnitude of 2.5 mm. As experimental data may be obtained in different conditions, the results obtained using RBM show that there is a combination between stiffness and damping coefficient that may provide good results. These results may validate RBM as a tool for relative brain –skull displacement with respect to model detail level and computational requirements. Future applications can be developed (Zou, Kleiven, et al. 2007; Zou, Schmiedeler, et al. 2007; Zou and Schmiedeler 2008).
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6.
Conclusions
In this paper, a methodology for the development and validation of a numerical model of the human head is presented. The numerical model is defined as a dual mode that can be used for finite elements and for rigid body applications. The paper presented all steps required, starting with the model generation, model validation and applications. The procedure, although exemplified for the numerical model presented in the paper (CM), can be extrapolated and applied for any numerical models (e.g. BM) given the nodes correspondence and nodes sharing between the structures of the head. The required stiffness for the spring connection used for the RBM was identified by performing a natural frequency analysis. The damping coefficient for the model was determined by comparing the results with the literature data. The applications presented are related to impact analysis. Two cases were presented: Nahum’s and Hardy’s experiments. For the first case, the frontal and posterior fossa pressures were evaluated and results compared with the experimental data. Using a custom code, a pressure map of the brain was constructed and results displayed. For the second case, the relative displacement between the brain and the skull was evaluated and reasonable agreement with literature data was found. The main objective was to validate the rigid model as a quick and versatile tool for acquiring the input data for specific brain analyses. The RBM presented in the paper may be used for 3D lumped mass models. The stiffness and damping of the connection can be easily adapted according to the anthropometric size as a linear function of the body (head) mass. The RBM may provide accurate results for different impact situation and it may also provide input data for detailed brain analyses (pressure map derived for the elastic connection force data).
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