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Geometrical and material parameters to assess the macroscopic mechanical behaviour of fresh cranial bone samples
Journal of Biomechanics 47 (2014) 1180–1185
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Geometrical and material parameters to assess the macroscopic mechanical behaviour of fresh cranial bone samples Audrey Auperrin a,b,c, Rémi Delille c, Denis Lesueur c, Karine Bruyère a,n, Catherine Masson b, Pascal Drazétic c a
Université de Lyon, F-69622, Lyon, IFSTTAR, LBMC, UMR_T9406, Université Lyon 1, , France Aix-Marseille Univ, LBA, F-13015 Marseille, IFSTTAR, LBA, F-13015 Marseille, France c University of Valenciennes (UVHC), LAMIH UMR CNRS 8201, 59313 Valenciennes, France b
art ic l e i nf o
a b s t r a c t
Article history: Accepted 26 October 2013
The present study aims at providing quantitative data for the personalisation of geometrical and mechanical characteristics of the adult cranial bone to be applied to head FE models. A set of 351 cranial bone samples, harvested from 21 human skulls, were submitted to three-point bending tests at 10 mm/ min. For each of them, an apparent elastic modulus was calculated using the beam0 s theory and a density-dependant beam inertia. Thicknesses, apparent densities and percentage of ash weight were also measured. Distributions of characteristics among the different skull bones show their symmetry and their significant differences between skull areas. A data analysis was performed to analyse potential relationship between thicknesses, densities and the apparent elastic modulus. A specific regression was pointed out to estimate apparent elastic modulus from the product of thickness by apparent density. These results offer quantitative tools in view of personalising head FE models and thus improve definition of local injury criteria for this body part. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Cranial bone Three-point bending tests Density Geometry
1. Introduction In the field of road safety, preventing and limiting injuries and fatalities require a profound knowledge of the human body submitted to an impact. Research in impact biomechanics aims at characterising the behaviour of the human body, including kinematics, injury mechanisms, tolerance thresholds, and biological materials properties, thanks to experimental tests. In a crash environment, the injury risks are classically assessed by using anthropomorphic test dummies (ATD). These regulation tools are limited as they represent a little part of the population in terms of anthropometry. Moreover, ATDs measure global physical parameters, to be related to global injury criteria or specific injury risk curves (UN/ECE, 2005; UN/ECE, 2008). Compared to ATDs, finite element modelling has demonstrated promising potentialities. This method enables a personalisation of the geometry (Buhmann, 2003; Serre et al., 2006) and material properties can also be adjusted in order to represent a wider population in terms of age and gender. Moreover, local parameters are available to calculate local criteria related to specific injury mechanisms. Head injuries still represent the most serious traumatisms in terms of fatalities and injuries observed in traffic accidents n
Corresponding author. Tel.: + 33472142328. E-mail address: [email protected] (K. Bruyère).
0021-9290/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.10.060
(Amoros et al., 2008). Intracranial lesions are complex and strong improvements in the prediction of such injuries are expected with FE modelling and the availability of local injury criteria. Head models and their associated local injury criteria have already been published (Takkounts et al., 2003; Baumgartner and Willinger, 2005). However these models correspond to one subject geometry and the cranial bone is often considered has an isotropic homogeneous elasto-plastic material (Horgan and Gilchrist, 2004; Baumgartner and Willinger, 2005; Belingardi et al., 2005). At a macroscopic scale, the variability of the skull geometry may be represented by integrating the skull thickness distribution from standard in vivo CT-scan (Laurent et al., 2011). Yet, the spatial resolution of a standard in vivo CT-scan does not allow the extraction of the thicknesses of the respective cortical and diploe layers, which represent the structural variability of the human cranial bone. Concerning the material properties of head tissues, many studies have been performed to improve the modelling of intracranial tissues (see review in Cheng et al. (2008)). Considering the material properties of cranial bone, from the 1970s, several authors studied its mechanical properties in view of defining a substitute material for physical or numerical model of the head (McElhaney et al., 1970; Hubbard, 1971; Wood, 1971; Got et al., 1983; Schueler et al., 1994). McElhaney et al. proposed a distribution of cranial bone mechanical properties on the skull and statistical regressions for their estimation from the apparent
A. Auperrin et al. / Journal of Biomechanics 47 (2014) 1180–1185
density but they also noticed the skull to skull variability of cranial bone and diploe thicknesses (McElhaney et al., 1970). Schueler et al. integrated both geometrical data and densities from QCT in statistical prediction models of cranial bone properties under compression and shear tests (Schueler et al., 1994). More recently, new data have been published on the mechanical behaviour of both infant cranial bone (Margulies and Thibault., 2000) and adult cranial bone (Vershueren et al., 2006) (Motherway et al., 2009), under 3 point bending tests at various loading speeds. In Vershueren et al. (2006), and Motherway et al. (2009), tested samples were obtained from fresh-frozen or embalmed subjects. In the present study, we quantify the macroscopic thickness, the apparent density and an apparent elastic modulus on a large number of human fresh cranial bone samples. By analysing both the distribution of these characteristics among the different skull bones and the relationships between the cranial bone sample characteristics, this study also aims at providing tools for personalisation of geometrical and mechanical characteristics of the adult cranial bone to be applied to head FE models in order to improve the definition of local injury criteria.
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2.2. Density measurements The apparent density (ρapp) of each specimen was calculated from specimens0 weights in air and in water, using Archimedes0 principle (1)
ρapp ¼
M air ρwater M air M water
ð1Þ
the percentage of ash weight (%ash) was deduced from specimens0 weights after calcination (2). Specimens were calcinated in an oven 40 min at 6001. %ash ¼
M ash 100 M air
ð2Þ
2.3. Geometrical measurements The average width (b) and the average thickness (h) of each specimen were computed from 3 measurements per sample taken at the centre and at the level of the right and left 3-point bending supports. For the calculation of the inertia (I), each specimen was considered as a straight beam with a uniform apparent cross section (S) along its length, assuming that all the porosity of the sample was concentrated in a square area of size (a) computed from the percentage ash density (%ash) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ a ¼ Sð1 %ash Þ thus,
2. Materials and methods
3
I ¼ I %ash ¼ 2.1. Cranial bone material Twenty one skulls were obtained through the anatomy departments at the “Université Claude Bernard” in Lyon, and at the University Rene Descartes in Paris, thanks to local Body Donation Programs. The age of the donors ranges from 52 to 95 years at death (mean 74.8 years), and all donors were males. All skulls were kept fresh at 4 1C prior specimens0 preparation. Once soft tissues had been removed from the calvaria, seventeen rectangular specimens were harvested from each skull, over the parietal bones, the temporal bones, the frontal bone and the coronal suture (Fig. 1). The specimens0 dimensions were approximately 60 mm in length and 13 mm in width. At the end, 357 specimens were obtained and stored in a saline solution at a temperature of 4 1C. In order to assess the influence of the cranial sample position and orientation, the specimens were distributed into 5 different categories according to the sample location and defined as follows: -
Right Parietal (RP): EP 02, EP 04, EP 06 and EP 08 Left Parietal (LP): EP 01, EP 03, EP 05 and EP 07 Frontal (F): EP 09, EP 10, EP 11, EP 12 and EP 16 Right Temporal (RT): EP 18 Left Temporal (LT): EP 17 Sutures: EP 13 and EP 14
bh Sð1 %ash Þ 12 12
ð4Þ
2.4. Three-point bending tests All specimens were tested using a universal compression machine, equipped with a 5 kN load cell. The three-point bending apparatus was made of a loading pin and two outer support pins 40 mm apart. The pins were cylinder-shaped, 5 mm in diameter and 30 mm in length (Fig. 2). Three cycles of loading were performed at 10 mm/min in the elastic domain limited by a maximal deflection of specimens equal to 0.4 mm. To estimate an apparent elastic modulus (E) of cranial bone, a comparison between the Euler Bernoulli beam theory and the Timoshenko theory applied as in Motherway et al. (2009) was performed. Differences were inferior to 0.01% and we kept values form the Euler Bernouilli beam theory for the analysis, considering that each specimen was a straight beam with a uniform apparent cross section along its length (L). The inertia (I%ash) of this section was computed from the percentage ash density as described in §2.3. The slope of the load displacement curve (K) was taken in the linear part of the last cycle of loading. E¼
K L3 48 I %ash
ð5Þ
2.5. Statistical analysis The statistical analysis was performed using the Unistat 5.6 (Unistat s statistical package, Unistat Ltd.). Descriptive statistics were summarised by mean and standard deviation or by box plotting. As some studied parameters were not normally distributed, nonparametric analysis was performed. Paired comparisons were assessed by Wilcoxon tests. Relationships between parameters were assessed by Pearson correlation coefficients. The significance level for all analysis was set as po 0.05.
Fig. 1. The location of the specimens on the skull (superior view).
Fig. 2. Sample on the three-point-bending test device.
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A. Auperrin et al. / Journal of Biomechanics 47 (2014) 1180–1185
3. Results 3.1. Geometrical measurements and densities Mean and standard deviation of thickness for the 5 categories are illustrated on Fig. 3a. Thicknesses of left and right parietal bone samples are not statistically different (p¼ 0.87). The same observation is made for frontal bone (p ¼0.72) and temporal bone (p ¼0.86). The average thickness are 7.071.1 mm for frontal bone samples (F, n ¼147), 6.5 71.3 mm for parietal bone samples (P, n ¼166) and 4.7 71.0 mm for temporal bone samples (T, n ¼42) (Fig. 3b). These differences between the thicknesses of the different type of skull bones are significant (p o0.0001). Mean and standard deviation of apparent density for the 5 categories are illustrated on Fig. 4a. Apparent densities of left and right parietal bone samples are not statistically different (p¼ 0.42). The same observation is made for frontal bone (p¼0.37) and temporal bone (p¼0.32). The average apparent densities are 1710 7127 kg/m3 for frontal bone (F, n ¼147) 16847 124 kg/m3 for parietal bones (P, n ¼167) and 1782 7121 kg/m3 for temporal bones (T, n ¼42) (Fig. 4b). These differences between the apparent densities of the different type of skull bones are significant (po 0.05). Apparent density and percentage ash density are closely correlated (R²¼ 0.98, po0.001, n¼356). Linear relationship between these two
Fig. 4. Box and whisker plots for the apparent density of 356 samples, (a) distribution among right and left areas (LT/RT¼ left/right temporal bone, LP/ RP¼ left/right parietal bone, LF/RF ¼ left/right frontal bone, CF¼ centred frontal bone) and (b) Distribution among each bone type (n indicates significant differences, p o 0.05) The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
Fig. 5. Linear correlation between apparent density and percentage ash density (n ¼356).
densities (Fig. 5) is
ρapp ðg=cm3 Þ ¼ 0:042%ash 19:2;
Fig. 3. Box and whisker plots for the thickness of 355 samples (a) Distribution among right and left areas (LT/RT¼ left/right temporal bone, LP/RP ¼ left/right parietal bone, LF/RF ¼left/right frontal bone, CF¼ centred frontal bone) and (b) distribution among each bone type (n indicates significant differences, p o0.0001) The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
n ¼ 356
ð6Þ
3.2. Apparent elastic modulus Mean and standard deviation of apparent elastic modulus for the 5 categories are illustrated in Fig. 6a. Apparent elastic modulus of left and right parietal bone samples are not statistically different
A. Auperrin et al. / Journal of Biomechanics 47 (2014) 1180–1185
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between subjects is clearly shown and seems not linked to the age of the subjects.
3.3. Relationship between apparent elastic modulus, thickness and apparent density For whole samples from all skull areas, apparent elastic modulus is significantly correlated with the thickness and the apparent density (po0.01). Thickness and apparent density are also significantly correlated (po0.01). But for the correlation with the
Fig. 6. Box and whisker plots for the apparent elastic modulus of 342 samples (a) Distribution among right and left areas (LT/RT¼left/right temporal bone, LP/ RP ¼left/right parietal bone, LF/RF ¼ left/right frontal bone, CF¼ centred frontal bone), and (b) Distribution among each bone type (n indicates significant differences, p o 0.0001) The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
Fig. 7. Box and whisker plots for the apparent elastic modulus measured on the 21 subjects The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
(p ¼0.42). The same observation is made for frontal bone (p ¼0.37) and temporal bone (p ¼0.32). The average apparent elastic modulus are 3.8171.55 GPa for frontal bone (F, n¼ 147) 5.0073.12 GPa for parietal bones (P, n ¼167) and 9.7075.75 GPa for temporal bones (T, n¼ 42) (Fig. 6b). These differences between the apparent elastic modulus of the different type of skull bones are significant (po 0.0001). Mean and standard deviation of apparent elastic modulus are illustrated for the 21 subjects in Fig. 7. The variability of results
Fig. 8. (a) Exponential regression to estimate the apparent elastic modulus from thickness and apparent density of cranial bone samples (n¼ 341) and (b) predicted apparent elastic modulus compared to the measured one.
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A. Auperrin et al. / Journal of Biomechanics 47 (2014) 1180–1185
apparent density, Spearman coefficients are very low (0.13 with the apparent elastic modulus and 0.17 with the thickness). A stronger correlation is observed between apparent elastic modulus and thickness with r ¼ 0.84 (p o0.0001). The relationship between the apparent elastic modulus and thickness is improved when thickness is combined to apparent density, specifically for the thinner samples (Fig. 8a). Thus, to consider the estimation of the apparent elastic modulus from geometrical and density parameters, regression equations have been assessed using the product (thickness apparent density) (Fig. 8a and b). The best regression gives 4 E ðGPaÞ ¼ 63:3 exp 2:410 ½thicknessðmmÞρapp
2
r ¼ 0:65ðp o 0:01Þ
ðkg=m3 Þ
;
n ¼ 341; ð7Þ
and the Standard Error of Estimate (SEE) is equal to 2.02 GPa for estimated values between 0.12 GPa and 24.6 GPa.
mineralisation of the bone tissue. Got et al. suggested characterising the cortical/diploe proportion and the mineralisation of cranial bone but results were related to whole skull mechanical tolerance. Then, Schueler et al. presented significant correlation between density obtained from CT-scan and mechanical properties measured in compression and shear (Schueler et al., 1994). In our study, the relationship estimating the apparent elastic modulus was established from in vitro measurements of the cranial bone thickness and of the apparent density, but these input data can be obtained from a standard in vivo CT-scan of the head. Skull thickness can be measured from CT-scan with a high accuracy (Laurent et al., 2011) and relationships between bone density and grey levels have already been established for other sites (Keyak et al., 1994). Thus, the relationships established in this study, is a first tool to build a subject-specific model of the human adult skull from CTscan. Using such personalised models of skull for accident reconstructions could help in the definition of head injury criteria.
4. Discussion The analysis presented here included more than 300 samples taken off from 21 fresh subjects. This represents a large database compared to other recent studies (Delille et al., 2007; Motherway et al., 2009; Verschueren et al., 2006). Several parameters have been analysed: total thickness of cranial bone, apparent density and apparent elastic modulus obtained from 3 point-bending tests. This analysis showed that thickness and apparent density of cranial bone strongly depend on the location on the skull. The first observation is the sagittal symmetry of the thickness and apparent density distributions. Differences among skull areas are significant. The thickest is the frontal bone while the thinnest is the temporal bone and on the contrary, the apparent density is higher for the temporal bone and lowest for the parietal bone. For the assessment of the apparent elastic modulus, an original method has been carried out to take into account the porosity of each sample. We considered this porosity as centred in the sample section and we estimated its size from the sample ash density. This method represents a compromise solution between the hypothesis of an homogeneous dense cross section (Motherway et al., 2009) and the measurement of a real cross section that need a high resolution CT-scan of each sample (Vershueren et al., 2006), difficult to carry out on a large number of samples. By computing an apparent elastic modulus of the cranial bone by this way, we integrate both structural and material properties of this composite material. The average values of apparent elastic modulus among the different skull bones (3.81 GPa for frontal bone, 5.00 GPa for parietal bones and 9.70 GPa for temporal bones) are between those measured by Vershuren et al. under similar loading (1.7 GPa, number of samples unknown) (Vershuren et al., 2006) and those obtained by Motherway et al., on parietal and frontal bone samples submitted to higher loading rates (between 4.35 GPa and 10.3 GPa on 18 samples) (Motherway et al., 2009). The distribution of apparent elastic modulus also showed a sagittal symmetry and significant differences between different skull bones. Then, we proposed an estimation of the apparent elastic modulus of the human cranial bone from its apparent density and thickness. The strong correlation observed between the apparent elastic modulus and the thickness of samples shows that the whole thickness of the cranial bone is linked to its cortical/diploë proportion. This is clear that the temporal samples which are the thinnest are mainly made of cortical bone and that the frontal and parietal samples which are the thickest present a thick diploë. The apparent density and the ash densities also contain information on the cortical/diploë proportion, and moreover on the
Conflict of interest statement The authors hereby affirm that this study does not raise any conflict of interest.
Acknowledgements The present research work has been supported by IFSTTAR, GDR 2610 “Recherches en Biomécanique des chocs”, International Campus on Safety and Intermodality in Transportation (CISIT), the Région Nord Pas de Calais, the European Community, the Délégation Régionale à la Recherche et à la Technologie, the Ministère de l0 Enseignement Supérieur et de la Recherche, and the Centre National de la Recherche Scientifique: the authors gratefully acknowledge these institutions for their support and funding. The authors also wish to thank Pierre Lapelerie and Christophe Regnier for their helpful contribution to experiments. References Amoros, E., Martin, J.L., Lafont, S., Laumon, B., 2008. Actual incidences of road casualties, and their injury severity, modelled from police and hospital data, France. Eur. J. Public Health 18 (4), 360–365. Baumgartner, D., Willinger, R., 2005. Human head tolerance limits to specific injury mechanisms inferred from real world accident numerical reconstruction. Revue Européenne des Eléments Finis 14 (N 4–5), 421–443 Belingardi, G., Chiandussi, G., Gaviglio, I., 2005. Development and validation of a new FE model of human head.In: Proceeding of the 19th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Washington DC. June 6–9. Buhmann, M.D., 2003. Radial basis functions: theory and implementations, Applied Mathematical Sciences. Cambridge University Press p. 259. (Cambridge Monographs on Applied and Computational Mathematics N112) Cheng, S., Clarke, E.C., Bilston, L.E., 2008. Rheological properties of the tissues of the central nervous system: a review. Med. Eng. Phys. vol. 30 (10), 1318–1337. Delille, R., Lesueur, D., Potier, P., Drazetic, P., Markiewicz, E., 2007. Experimental study of the bone behaviour of the human skull bone for the development of a physical head model. Int. J. Crashworthiness 12 (2). Got C., Guillon F., Patel A., Mack P., Brun-cassan F., Fayon A., Tarrière C., Hureau J., 1983, Morphological and biomechanical study of 146 human skulls used in experimental impacts, in relation with the observed injuries. In: Proceedings of the 27th Stapp Car Crash Conference, pp. 241–259. Horgan, T.J., Gilchrist, M.D., 2004. Influence of FE model variability in predicting brain motion and intracranial pressure changes in head impact simulations. Int. J. Crashworthiness 9 (4), 401–418. Hubbard, R., 1971. Flexure of layered cranial bone. J. Biomech. 4, 251–263. Keyak, J.H., Lee, I.Y., Skinner, H.B., 1994. Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J. Biomed. Mater. Res. 28, 1329–1336. Laurent, C.P., Jolivet, E., Hodel, J., Decq, P., Skalli, W., 2011. New method for 3D reconstruction of the human cranial vault from CT-scan data. Med. Eng. Phys. 33, 1270–1275.
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McElhaney, J.M., Fogle, J.L., Melvin, J.W., Haynes, R.R., Roberts, V.L., Alem, N.M., 1970. Mechanical properties of cranial bone. J. Biomech. 3, 495–511. Margulies, S.S., Thibault, K.L., 2000. Infant skull and suture properties: measurements and implications for mechanicsms of pediatric brain injury. J. Biomech. Eng. 122, 364–371. Motherway, J.A., Verschueren, P., Van Der Perre, G., Vander Sloten, J., Gilchrist, M.D., 2009. The mechanical properties of cranial bone: The effect of loading rate and cranial sampling position. J. Biomech. 42, 2129–2135. Schueler, F., Zimmer, G., Min, J., Mattern, R., 1994. Assessment of mechanical properties of the human skull-cap through basic biomechanical tests and quantitative computed tomography (QCT). In: Proceedings of the IRCOBI Conference, pp. 23–37. Serre, T., Brunet, C., Bruyère, K., Verriest, J.P., Mitton, D., Bertrand, S., Skalli, W., Bekkour, T., Kayvantash, K., 2006. HUMOS (Human Model for Safety) Geometry:
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From one specimen to the 5th and 95th percentile, Digital Human Modeling for Design and Engineering Conference, Lyon, July 2006. SAE 2006 Transactions Journal of Passenger Cars – Mechanical Systems, Paper no. 2006-01-2324. Takkounts, E.G., Eppinger, R.H., Quinn Campbell, J., Tannous, R.E., Power, E.D., Shook, L.S., 2003. On the development of the SIMon finite element head model. Stapp Car Crash J. 47, 107–133. UN/ECE Regulation 95, 2005. Protection of the occupants against frontal collision. UN/ECE Regulation 94, 2008. Protection of the occupants against frontal collision. Verschueren, P., Delye, H., Berckmans, D., Verspoest, I., Goffin, J., Vander Sloten, J., Van der Perre, G., 2006. Analysis of fracture characteristics of cranial bone for FE modelling. In: Proceedings for the IRCOBI Conference, Madrid (Spain). Wood, J.L., 1971. Dynamic response of human cranial bone. J. Biomech. 4, 1–12.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Geometrical and material parameters to assess the macroscopic mechanical behaviour of fresh cranial bone samples Audrey Auperrin a,b,c, Rémi Delille c, Denis Lesueur c, Karine Bruyère a,n, Catherine Masson b, Pascal Drazétic c a
Université de Lyon, F-69622, Lyon, IFSTTAR, LBMC, UMR_T9406, Université Lyon 1, , France Aix-Marseille Univ, LBA, F-13015 Marseille, IFSTTAR, LBA, F-13015 Marseille, France c University of Valenciennes (UVHC), LAMIH UMR CNRS 8201, 59313 Valenciennes, France b
art ic l e i nf o
a b s t r a c t
Article history: Accepted 26 October 2013
The present study aims at providing quantitative data for the personalisation of geometrical and mechanical characteristics of the adult cranial bone to be applied to head FE models. A set of 351 cranial bone samples, harvested from 21 human skulls, were submitted to three-point bending tests at 10 mm/ min. For each of them, an apparent elastic modulus was calculated using the beam0 s theory and a density-dependant beam inertia. Thicknesses, apparent densities and percentage of ash weight were also measured. Distributions of characteristics among the different skull bones show their symmetry and their significant differences between skull areas. A data analysis was performed to analyse potential relationship between thicknesses, densities and the apparent elastic modulus. A specific regression was pointed out to estimate apparent elastic modulus from the product of thickness by apparent density. These results offer quantitative tools in view of personalising head FE models and thus improve definition of local injury criteria for this body part. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Cranial bone Three-point bending tests Density Geometry
1. Introduction In the field of road safety, preventing and limiting injuries and fatalities require a profound knowledge of the human body submitted to an impact. Research in impact biomechanics aims at characterising the behaviour of the human body, including kinematics, injury mechanisms, tolerance thresholds, and biological materials properties, thanks to experimental tests. In a crash environment, the injury risks are classically assessed by using anthropomorphic test dummies (ATD). These regulation tools are limited as they represent a little part of the population in terms of anthropometry. Moreover, ATDs measure global physical parameters, to be related to global injury criteria or specific injury risk curves (UN/ECE, 2005; UN/ECE, 2008). Compared to ATDs, finite element modelling has demonstrated promising potentialities. This method enables a personalisation of the geometry (Buhmann, 2003; Serre et al., 2006) and material properties can also be adjusted in order to represent a wider population in terms of age and gender. Moreover, local parameters are available to calculate local criteria related to specific injury mechanisms. Head injuries still represent the most serious traumatisms in terms of fatalities and injuries observed in traffic accidents n
Corresponding author. Tel.: + 33472142328. E-mail address: [email protected] (K. Bruyère).
0021-9290/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.10.060
(Amoros et al., 2008). Intracranial lesions are complex and strong improvements in the prediction of such injuries are expected with FE modelling and the availability of local injury criteria. Head models and their associated local injury criteria have already been published (Takkounts et al., 2003; Baumgartner and Willinger, 2005). However these models correspond to one subject geometry and the cranial bone is often considered has an isotropic homogeneous elasto-plastic material (Horgan and Gilchrist, 2004; Baumgartner and Willinger, 2005; Belingardi et al., 2005). At a macroscopic scale, the variability of the skull geometry may be represented by integrating the skull thickness distribution from standard in vivo CT-scan (Laurent et al., 2011). Yet, the spatial resolution of a standard in vivo CT-scan does not allow the extraction of the thicknesses of the respective cortical and diploe layers, which represent the structural variability of the human cranial bone. Concerning the material properties of head tissues, many studies have been performed to improve the modelling of intracranial tissues (see review in Cheng et al. (2008)). Considering the material properties of cranial bone, from the 1970s, several authors studied its mechanical properties in view of defining a substitute material for physical or numerical model of the head (McElhaney et al., 1970; Hubbard, 1971; Wood, 1971; Got et al., 1983; Schueler et al., 1994). McElhaney et al. proposed a distribution of cranial bone mechanical properties on the skull and statistical regressions for their estimation from the apparent
A. Auperrin et al. / Journal of Biomechanics 47 (2014) 1180–1185
density but they also noticed the skull to skull variability of cranial bone and diploe thicknesses (McElhaney et al., 1970). Schueler et al. integrated both geometrical data and densities from QCT in statistical prediction models of cranial bone properties under compression and shear tests (Schueler et al., 1994). More recently, new data have been published on the mechanical behaviour of both infant cranial bone (Margulies and Thibault., 2000) and adult cranial bone (Vershueren et al., 2006) (Motherway et al., 2009), under 3 point bending tests at various loading speeds. In Vershueren et al. (2006), and Motherway et al. (2009), tested samples were obtained from fresh-frozen or embalmed subjects. In the present study, we quantify the macroscopic thickness, the apparent density and an apparent elastic modulus on a large number of human fresh cranial bone samples. By analysing both the distribution of these characteristics among the different skull bones and the relationships between the cranial bone sample characteristics, this study also aims at providing tools for personalisation of geometrical and mechanical characteristics of the adult cranial bone to be applied to head FE models in order to improve the definition of local injury criteria.
1181
2.2. Density measurements The apparent density (ρapp) of each specimen was calculated from specimens0 weights in air and in water, using Archimedes0 principle (1)
ρapp ¼
M air ρwater M air M water
ð1Þ
the percentage of ash weight (%ash) was deduced from specimens0 weights after calcination (2). Specimens were calcinated in an oven 40 min at 6001. %ash ¼
M ash 100 M air
ð2Þ
2.3. Geometrical measurements The average width (b) and the average thickness (h) of each specimen were computed from 3 measurements per sample taken at the centre and at the level of the right and left 3-point bending supports. For the calculation of the inertia (I), each specimen was considered as a straight beam with a uniform apparent cross section (S) along its length, assuming that all the porosity of the sample was concentrated in a square area of size (a) computed from the percentage ash density (%ash) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ a ¼ Sð1 %ash Þ thus,
2. Materials and methods
3
I ¼ I %ash ¼ 2.1. Cranial bone material Twenty one skulls were obtained through the anatomy departments at the “Université Claude Bernard” in Lyon, and at the University Rene Descartes in Paris, thanks to local Body Donation Programs. The age of the donors ranges from 52 to 95 years at death (mean 74.8 years), and all donors were males. All skulls were kept fresh at 4 1C prior specimens0 preparation. Once soft tissues had been removed from the calvaria, seventeen rectangular specimens were harvested from each skull, over the parietal bones, the temporal bones, the frontal bone and the coronal suture (Fig. 1). The specimens0 dimensions were approximately 60 mm in length and 13 mm in width. At the end, 357 specimens were obtained and stored in a saline solution at a temperature of 4 1C. In order to assess the influence of the cranial sample position and orientation, the specimens were distributed into 5 different categories according to the sample location and defined as follows: -
Right Parietal (RP): EP 02, EP 04, EP 06 and EP 08 Left Parietal (LP): EP 01, EP 03, EP 05 and EP 07 Frontal (F): EP 09, EP 10, EP 11, EP 12 and EP 16 Right Temporal (RT): EP 18 Left Temporal (LT): EP 17 Sutures: EP 13 and EP 14
bh Sð1 %ash Þ 12 12
ð4Þ
2.4. Three-point bending tests All specimens were tested using a universal compression machine, equipped with a 5 kN load cell. The three-point bending apparatus was made of a loading pin and two outer support pins 40 mm apart. The pins were cylinder-shaped, 5 mm in diameter and 30 mm in length (Fig. 2). Three cycles of loading were performed at 10 mm/min in the elastic domain limited by a maximal deflection of specimens equal to 0.4 mm. To estimate an apparent elastic modulus (E) of cranial bone, a comparison between the Euler Bernoulli beam theory and the Timoshenko theory applied as in Motherway et al. (2009) was performed. Differences were inferior to 0.01% and we kept values form the Euler Bernouilli beam theory for the analysis, considering that each specimen was a straight beam with a uniform apparent cross section along its length (L). The inertia (I%ash) of this section was computed from the percentage ash density as described in §2.3. The slope of the load displacement curve (K) was taken in the linear part of the last cycle of loading. E¼
K L3 48 I %ash
ð5Þ
2.5. Statistical analysis The statistical analysis was performed using the Unistat 5.6 (Unistat s statistical package, Unistat Ltd.). Descriptive statistics were summarised by mean and standard deviation or by box plotting. As some studied parameters were not normally distributed, nonparametric analysis was performed. Paired comparisons were assessed by Wilcoxon tests. Relationships between parameters were assessed by Pearson correlation coefficients. The significance level for all analysis was set as po 0.05.
Fig. 1. The location of the specimens on the skull (superior view).
Fig. 2. Sample on the three-point-bending test device.
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3. Results 3.1. Geometrical measurements and densities Mean and standard deviation of thickness for the 5 categories are illustrated on Fig. 3a. Thicknesses of left and right parietal bone samples are not statistically different (p¼ 0.87). The same observation is made for frontal bone (p ¼0.72) and temporal bone (p ¼0.86). The average thickness are 7.071.1 mm for frontal bone samples (F, n ¼147), 6.5 71.3 mm for parietal bone samples (P, n ¼166) and 4.7 71.0 mm for temporal bone samples (T, n ¼42) (Fig. 3b). These differences between the thicknesses of the different type of skull bones are significant (p o0.0001). Mean and standard deviation of apparent density for the 5 categories are illustrated on Fig. 4a. Apparent densities of left and right parietal bone samples are not statistically different (p¼ 0.42). The same observation is made for frontal bone (p¼0.37) and temporal bone (p¼0.32). The average apparent densities are 1710 7127 kg/m3 for frontal bone (F, n ¼147) 16847 124 kg/m3 for parietal bones (P, n ¼167) and 1782 7121 kg/m3 for temporal bones (T, n ¼42) (Fig. 4b). These differences between the apparent densities of the different type of skull bones are significant (po 0.05). Apparent density and percentage ash density are closely correlated (R²¼ 0.98, po0.001, n¼356). Linear relationship between these two
Fig. 4. Box and whisker plots for the apparent density of 356 samples, (a) distribution among right and left areas (LT/RT¼ left/right temporal bone, LP/ RP¼ left/right parietal bone, LF/RF ¼ left/right frontal bone, CF¼ centred frontal bone) and (b) Distribution among each bone type (n indicates significant differences, p o 0.05) The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
Fig. 5. Linear correlation between apparent density and percentage ash density (n ¼356).
densities (Fig. 5) is
ρapp ðg=cm3 Þ ¼ 0:042%ash 19:2;
Fig. 3. Box and whisker plots for the thickness of 355 samples (a) Distribution among right and left areas (LT/RT¼ left/right temporal bone, LP/RP ¼ left/right parietal bone, LF/RF ¼left/right frontal bone, CF¼ centred frontal bone) and (b) distribution among each bone type (n indicates significant differences, p o0.0001) The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
n ¼ 356
ð6Þ
3.2. Apparent elastic modulus Mean and standard deviation of apparent elastic modulus for the 5 categories are illustrated in Fig. 6a. Apparent elastic modulus of left and right parietal bone samples are not statistically different
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between subjects is clearly shown and seems not linked to the age of the subjects.
3.3. Relationship between apparent elastic modulus, thickness and apparent density For whole samples from all skull areas, apparent elastic modulus is significantly correlated with the thickness and the apparent density (po0.01). Thickness and apparent density are also significantly correlated (po0.01). But for the correlation with the
Fig. 6. Box and whisker plots for the apparent elastic modulus of 342 samples (a) Distribution among right and left areas (LT/RT¼left/right temporal bone, LP/ RP ¼left/right parietal bone, LF/RF ¼ left/right frontal bone, CF¼ centred frontal bone), and (b) Distribution among each bone type (n indicates significant differences, p o 0.0001) The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
Fig. 7. Box and whisker plots for the apparent elastic modulus measured on the 21 subjects The box indicates the median value, the lower and upper quartiles, the whiskers indicate the lower and upper adjacent values.
(p ¼0.42). The same observation is made for frontal bone (p ¼0.37) and temporal bone (p ¼0.32). The average apparent elastic modulus are 3.8171.55 GPa for frontal bone (F, n¼ 147) 5.0073.12 GPa for parietal bones (P, n ¼167) and 9.7075.75 GPa for temporal bones (T, n¼ 42) (Fig. 6b). These differences between the apparent elastic modulus of the different type of skull bones are significant (po 0.0001). Mean and standard deviation of apparent elastic modulus are illustrated for the 21 subjects in Fig. 7. The variability of results
Fig. 8. (a) Exponential regression to estimate the apparent elastic modulus from thickness and apparent density of cranial bone samples (n¼ 341) and (b) predicted apparent elastic modulus compared to the measured one.
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apparent density, Spearman coefficients are very low (0.13 with the apparent elastic modulus and 0.17 with the thickness). A stronger correlation is observed between apparent elastic modulus and thickness with r ¼ 0.84 (p o0.0001). The relationship between the apparent elastic modulus and thickness is improved when thickness is combined to apparent density, specifically for the thinner samples (Fig. 8a). Thus, to consider the estimation of the apparent elastic modulus from geometrical and density parameters, regression equations have been assessed using the product (thickness apparent density) (Fig. 8a and b). The best regression gives 4 E ðGPaÞ ¼ 63:3 exp 2:410 ½thicknessðmmÞρapp
2
r ¼ 0:65ðp o 0:01Þ
ðkg=m3 Þ
;
n ¼ 341; ð7Þ
and the Standard Error of Estimate (SEE) is equal to 2.02 GPa for estimated values between 0.12 GPa and 24.6 GPa.
mineralisation of the bone tissue. Got et al. suggested characterising the cortical/diploe proportion and the mineralisation of cranial bone but results were related to whole skull mechanical tolerance. Then, Schueler et al. presented significant correlation between density obtained from CT-scan and mechanical properties measured in compression and shear (Schueler et al., 1994). In our study, the relationship estimating the apparent elastic modulus was established from in vitro measurements of the cranial bone thickness and of the apparent density, but these input data can be obtained from a standard in vivo CT-scan of the head. Skull thickness can be measured from CT-scan with a high accuracy (Laurent et al., 2011) and relationships between bone density and grey levels have already been established for other sites (Keyak et al., 1994). Thus, the relationships established in this study, is a first tool to build a subject-specific model of the human adult skull from CTscan. Using such personalised models of skull for accident reconstructions could help in the definition of head injury criteria.
4. Discussion The analysis presented here included more than 300 samples taken off from 21 fresh subjects. This represents a large database compared to other recent studies (Delille et al., 2007; Motherway et al., 2009; Verschueren et al., 2006). Several parameters have been analysed: total thickness of cranial bone, apparent density and apparent elastic modulus obtained from 3 point-bending tests. This analysis showed that thickness and apparent density of cranial bone strongly depend on the location on the skull. The first observation is the sagittal symmetry of the thickness and apparent density distributions. Differences among skull areas are significant. The thickest is the frontal bone while the thinnest is the temporal bone and on the contrary, the apparent density is higher for the temporal bone and lowest for the parietal bone. For the assessment of the apparent elastic modulus, an original method has been carried out to take into account the porosity of each sample. We considered this porosity as centred in the sample section and we estimated its size from the sample ash density. This method represents a compromise solution between the hypothesis of an homogeneous dense cross section (Motherway et al., 2009) and the measurement of a real cross section that need a high resolution CT-scan of each sample (Vershueren et al., 2006), difficult to carry out on a large number of samples. By computing an apparent elastic modulus of the cranial bone by this way, we integrate both structural and material properties of this composite material. The average values of apparent elastic modulus among the different skull bones (3.81 GPa for frontal bone, 5.00 GPa for parietal bones and 9.70 GPa for temporal bones) are between those measured by Vershuren et al. under similar loading (1.7 GPa, number of samples unknown) (Vershuren et al., 2006) and those obtained by Motherway et al., on parietal and frontal bone samples submitted to higher loading rates (between 4.35 GPa and 10.3 GPa on 18 samples) (Motherway et al., 2009). The distribution of apparent elastic modulus also showed a sagittal symmetry and significant differences between different skull bones. Then, we proposed an estimation of the apparent elastic modulus of the human cranial bone from its apparent density and thickness. The strong correlation observed between the apparent elastic modulus and the thickness of samples shows that the whole thickness of the cranial bone is linked to its cortical/diploë proportion. This is clear that the temporal samples which are the thinnest are mainly made of cortical bone and that the frontal and parietal samples which are the thickest present a thick diploë. The apparent density and the ash densities also contain information on the cortical/diploë proportion, and moreover on the
Conflict of interest statement The authors hereby affirm that this study does not raise any conflict of interest.
Acknowledgements The present research work has been supported by IFSTTAR, GDR 2610 “Recherches en Biomécanique des chocs”, International Campus on Safety and Intermodality in Transportation (CISIT), the Région Nord Pas de Calais, the European Community, the Délégation Régionale à la Recherche et à la Technologie, the Ministère de l0 Enseignement Supérieur et de la Recherche, and the Centre National de la Recherche Scientifique: the authors gratefully acknowledge these institutions for their support and funding. The authors also wish to thank Pierre Lapelerie and Christophe Regnier for their helpful contribution to experiments. References Amoros, E., Martin, J.L., Lafont, S., Laumon, B., 2008. Actual incidences of road casualties, and their injury severity, modelled from police and hospital data, France. Eur. J. Public Health 18 (4), 360–365. Baumgartner, D., Willinger, R., 2005. Human head tolerance limits to specific injury mechanisms inferred from real world accident numerical reconstruction. Revue Européenne des Eléments Finis 14 (N 4–5), 421–443 Belingardi, G., Chiandussi, G., Gaviglio, I., 2005. Development and validation of a new FE model of human head.In: Proceeding of the 19th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Washington DC. June 6–9. Buhmann, M.D., 2003. Radial basis functions: theory and implementations, Applied Mathematical Sciences. Cambridge University Press p. 259. (Cambridge Monographs on Applied and Computational Mathematics N112) Cheng, S., Clarke, E.C., Bilston, L.E., 2008. Rheological properties of the tissues of the central nervous system: a review. Med. Eng. Phys. vol. 30 (10), 1318–1337. Delille, R., Lesueur, D., Potier, P., Drazetic, P., Markiewicz, E., 2007. Experimental study of the bone behaviour of the human skull bone for the development of a physical head model. Int. J. Crashworthiness 12 (2). Got C., Guillon F., Patel A., Mack P., Brun-cassan F., Fayon A., Tarrière C., Hureau J., 1983, Morphological and biomechanical study of 146 human skulls used in experimental impacts, in relation with the observed injuries. In: Proceedings of the 27th Stapp Car Crash Conference, pp. 241–259. Horgan, T.J., Gilchrist, M.D., 2004. Influence of FE model variability in predicting brain motion and intracranial pressure changes in head impact simulations. Int. J. Crashworthiness 9 (4), 401–418. Hubbard, R., 1971. Flexure of layered cranial bone. J. Biomech. 4, 251–263. Keyak, J.H., Lee, I.Y., Skinner, H.B., 1994. Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J. Biomed. Mater. Res. 28, 1329–1336. Laurent, C.P., Jolivet, E., Hodel, J., Decq, P., Skalli, W., 2011. New method for 3D reconstruction of the human cranial vault from CT-scan data. Med. Eng. Phys. 33, 1270–1275.
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