Int J Legal Med (2013) 127:111–118 DOI 10.1007/s00414-011-0627-9

ORIGINAL ARTICLE

Effects of fall conditions and biological variability on the mechanism of skull fractures caused by falls Anissa Hamel & Maxime Llari & Marie-Dominique Piercecchi-Marti & Pascal Adalian & Georges Leonetti & Lionel Thollon

Received: 1 June 2011 / Accepted: 26 September 2011 / Published online: 9 October 2011 # Springer-Verlag 2011

Abstract In a forensic investigation, there is considerable difficulty in distinguishing between different mechanisms that could explain the head injury sustained. The key question is often whether the injury was the consequence of a fall, a blow, or a fall caused by a blow. Better understanding of the parameters influencing the mechanism of skull fracture could be of use when attempting to distinguish between different causes of injury. Numerous parameters concerning fall conditions and biological variability are reported in the literature to influence the mechanism of skull fracture. At the current time, there are no studies that investigate both the effect of a fall and biological parameters. The aim of this paper is to study the influence of these parameters on the mechanism of skull fracture using a numerical approach. We focused on accidental falls from a standing height. A multibody model was used to estimate head impact velocities and a finite element model was used to investigate the effect of the fall conditions and of biological variability on skull fracture. The results show that the mechanism of skull fractures is A. Hamel : M. Llari : L. Thollon (*) Laboratoire de Biomécanique Appliquée, Faculté de Médecine secteur Nord, boulevard Pierre Dramard, 13916 Marseille Cedex 20, France e-mail: [email protected] M.-D. Piercecchi-Marti : P. Adalian : G. Leonetti Service de Médecine Légale et Droit de la Santé, CHU Timone Faculté de Médecine, 27 boulevard Jean Moulin, 13385 Marseille Cedex 5, France A. Hamel : M.-D. Piercecchi-Marti : P. Adalian : G. Leonetti Laboratoire d’Anthropologie, UMR 6578, Faculté de Médecine secteur Nord, 27 boulevard Jean Moulin, 13385 Marseille Cedex 5, France

influenced by a combination of at least four parameters: impact velocity, impact surface, cortical thickness and cortical density. Keywords Skull fractures . Falls . Multibody dynamics . Finite element modeling . Forensic investigations

Introduction Despite rapid advances in knowledge and techniques, everyday forensic practice holds considerable difficulties, especially when accidental as well as criminal causes may be involved. In a forensic investigation, there is considerable difficulty in making a distinction between the different mechanisms that could explain the head injury sustained. The key question is often whether the head injury was the consequence of a fall, a blow, or a fall caused by a blow. At the present time, the medical expert evaluates only the compatibility between the head injury sustained and a given mechanism of injury. Nevertheless, understanding of the parameters influencing the mechanism of skull fracture could serve as an aid when attempting to distinguish between different causes of injury. Numerous fall parameters affect the type of injuries sustained during a fall. One of these is the height of the fall, which influences impact velocity: impact velocity increases as fall height increases [1]. Fall height also influences the risk of injury: risk is greatest for children falling from a height of more than 150 cm [2–5]. The impact surface also influences the head injuries sustained: a more resilient surface can absorb more kinetic energy than a rigid surface, and thus causes less damage [1, 4–6]. The last parameter that influences injury risk is impact position, with a frontal impact carrying the greatest risk [6].

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The mechanism of skull fracture also depends on the biological parameters of the skull, including its geometry and anthropometry, the nature of the material, presence of sutures, and maximum stress to failure of cortical bone [7, 8]. However, the influence of these parameters has not yet been studied in depth. The influencing factor that has previously been studied is variation in skull thickness [8]. The results suggested that the thicker the skull, the less energy absorbed, and so the less the skull deformation. Information on head injury mechanisms originates from various sources including experiments on human cadavers, anesthetized animals or anthropomorphic dummies. Such experiments are adequate for measuring several parameters (forces, acceleration, displacements, etc.) and for relating them to head tolerance limits and type of injury. However, these methods involve inaccuracy due to the experimental material used [1, 9, 10]. An alternative to experiments is numerical modeling. With rapid advances in computer technology, numerical modeling appears to be an interesting tool in investigating the mechanism of head injury [7, 9, 11–15]. Numerical modeling involves various simplifying assumptions [10, 16] but nevertheless its main advantages are the repeatability and reproducibility of simulations [6, 17] and the ability to perform variability studies by varying the chosen parameters [18]. The first model that is frequently used is multibody modeling [6, 19–21] that is a good representation of the body's motion during a fall. This method was used by O'Riordain et al. [20] to evaluate the effect of altering initial velocities. It was also used by Rueda and Gilchrist [6] to understand the effect of impact surface and impact posture on head injuries. The second method, the finite element approach, makes it possible to model skull fractures [11–13]. This method was used in 2006 by Raul et al. [11] to reconstruct the fall of a 63-yearold man who had been given a slight push resulting in a parietooccipital fracture. The results showed an anatomical distribution of the deleted elements that was similar to the fracture observed at autopsy. At the present time, there are no studies that investigate the effect of both fall conditions and biological parameters on the mechanism of skull fractures in an attempt to distinguish between different causes of injury. In this paper, we focused on accidental falls. We examined the effect of fall conditions and biological variability on skull fractures using a numerical approach. The case studied was that of a backward fall from a standing height, without initial velocity, resulting in a parietooccipital impact. The effect of fall conditions was investigated taking into account impact velocity, impact surface and angle of impact between the ground and the head. The thickness, rigidity and density of cortical bone were the parameters studied to investigate the effect of biological variability. Accidental falls were modeled using a two-step approach. A multibody model was employed to recreate the

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overall movement of the body during the fall and to estimate the head impact velocities. A 3D finite element model of the head was then used to examine the effect on skull fracture of altering the parameters studied.

Material and methods Multibody modeling A multibody model consists of a rigid body interconnected by kinematic joints. Relative motion of the body is allowed by the degrees of freedom in translation and rotation defined for each kinematic joint. We used this model to infer head impact velocities by simulating the dynamic behavior of the body during the fall. To assess impact velocities, we took into account variability of body height and weight. The fall heights considered were a range of standing heights from 1.60 m to 1.80 m and the values chosen for weight were 50 kg and 75 kg. The model employed was a pedestrian model developed by Faurecia [22] and the University of Chalmers [23]. It was validated in collaboration with the Laboratory of Biomechanics and Applications [24]. The original model represented a human body similar to a 50th percentile male (1.75 m, 78 kg). From this model, we made scale models with the chosen heights and weights. All simulations were carried out with the same impulse load conditions: a model placed in the standing position (Fig. 1) with no initial velocity. As the behavior of the body during a fall is not exactly known, we performed the simulations firstly with all possible degrees of freedom for each joint (termed “free fall”). Secondly, the runs were made with zero degrees of freedom for each joint (termed “blocked fall”). This approach made it possible to take into account the widest range of possible impact velocities. We made twelve runs using MADYMO® V7.1 software (Tass Safe, Eindhoven, The Netherlands). This step provided impact velocity outputs used as inputs in the finite element model. A Spearman partial correlation test was used to measure the degree of association between height and impact velocity given the weight, and between weight and impact velocity given the height. The null hypothesis is that there is no relationship between height and impact velocity or between weight and impact velocity. The significance level (α error) of the test is 5%. The Spearman partial correlation was conducted using R® software (http://www.r-project.org). Finite element modeling A finite element model is based on idealized geometry, material properties, initial and boundary conditions, and it includes simplifications of the applied modeling loads. The

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Fig. 1 Fall sequences of the multibody model. a Free fall sequence, 1.80 m, 75 kg. b Free fall sequence, 1.60 m, 75 kg. c Free fall sequencee, 1.60 m, 50 kg. d Blocked fall sequence, 1.60 m, 50 kg

first stage of model development is geometry acquisition followed by the model meshing and modeling phases. Finally, the model is validated against experimental tests. Skull geometry was developed from the computed tomography scans of a 30-year-old male with 1-mm slices using MIMICS 12.3® software (Materialise, Leuven, Belgium). The main anatomical features (scalp, subarachnoid space and brain) were added during the meshing phase. The model was continuously meshed using Hypermesh® software (Altair Engineering, Inc., Detroit, MI, USA) and was developed with the Radioss® code (Altair Engineering, Inc., Detroit, MI, USA). The average dimension of an element is 2 mm. The skull was simulated by three layers representing compact and spongious bone. Compact bone was modeled with three-node shell elements and spongious bone was modeled with tetrahedral elements. The brain was modeled with tetrahedral elements and the subarachnoid space, displayed between the brain and the skull to simulate the cerebral spinal fluid, was modeled by a layer of tetrahedral elements. The scalp was partially modeled with two layers of brick elements. Globally, the finite element human head model consisted of 497,000 elements made up of 435,000 tetrahedrons, 8,000 bricks and 54,000 shells (Fig. 2). Its total mass was 4,200 kg. The mechanical parameters assigned to each anatomical feature were based on the literature data review [15, 25–27] and reported in Table 1. Once the model was developed, it was validated using the experimental test of Yoganandan et al. [28]. In this test, the human head was impacted by a hemispherical anvil at a

dynamic rate with an impact angle of 35°. In order to reproduce the experimental impact conditions, the anatomical plane of the model was inclined about 35°. Validation was performed with the Radioss® code and was based on maximum load, deflection and fracture shape (Table 2). Variability study The first experiment was carried out in order to identify the effect of three fall parameters: & & &

Impact velocities: from 3.5 to 6.5 ms−1, Impact surface: the ground or the curb of a sidewalk, and Angle of inclination to the ground : 45° or 90°.

Fig. 2 3D human head model including the different parts of the head

1.25 – –

0.49 0.42 –0.01

0.21

0.012 6 – 4,500

6,000

1,225

–

Linear velocity (m/s)

Force (N)

Deflection (mm)

Parietal bone Parietal bone

7.3

10,009

9.74

7.3

9,320

100 –

0.0167

–

–

80

7 40

– – – – – – 35 – – 145 – – –

– – 0.049 – – –

Ultimate stress (MPa) Yield stress (MPa) Decay factor β (ms−1) Long term shear modulus G∞ (MPa) Short term shear modulus GO (MPa) Bulk modulus K (MPa) Poisson's coefficient ν Young's modulus E (MPa)

1,800 Elastoplastic Inner and outer tables

1.5 or 3

1,200 1,200 1,200 1,500 Linear elastic Linear elastic Viscoelastic Elastoplastic CSF Scalp Brain Diploë

2 5 – Min=9 Max=13 Mean=11

Density ρ (kg m−3)

Impact area

Yoganandan's experiment Numerical modeling

10.3

Injury

Circular fracture Circular fracture

The simulations were performed by fixing the biological parameters (i.e., density 1,800 kg m−3, thickness 1.5 mm and rigidity 6,000 MPa) and by varying the fall parameters. The effect of the biological parameters was then investigated using the following values: Cortical density: 1,500, 1,800 or 2,100 kg m−3, Cortical thickness: 1.5 mm or 3 mm, and Young's modulus representing the rigidity of cortical bone: 6,000, 10,000 or 15,000 MPa.

The simulations were performed by fixing the fall parameters (i.e., a ground impact velocity of 6 ms−1 and with an angle of impact between the ground and the head of 90°) and by varying the biological parameters. Thirty simulations were finally carried out. All simulations were performed with the Radioss® code. The impact surface was assumed to be nondeformable. The head was assumed to be free in its six degrees of freedom because the neck does not influence the mechanics of the head during the first 30 ms [29].

Results Multibody models

Law

Thickness (mm)

Table 2 Validation of the finite element model by comparing the results of the experimental and the numerical tests

& & &

Anatomical component

Table 1 Material properties of the anatomical components of the finite element model

– – –

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The behavior of the body during the fall was analyzed by comparing four cases (cases A, C, G, and K). For each case, the fall conditions (height, weight and degree of freedom) are given in Table 3. Each case is represented by photographs taken at three different times: the standing position (t=0 ms), the position during the fall at t=1.28 ms and the position at the end of the fall at t=1.64 ms (Fig. 1). The first three cases (cases K, C and A in Fig. 1a–c) concern free falls. Figure 1a shows case K (1.80 m, 75 kg). During the fall, the knees bend slightly. The buttocks impact the ground first and the head impacts the ground last. Figure 1b shows case C (1.60 m, 75 kg). Despite the difference in height, we observed that the body's motion during the fall is similar to case K. Figure 1c shows case A (1.60 m, 50 kg). The knees are more bent and the trunk is perpendicular to

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Table 3 Results of multibody modeling Cases

Height (m)

Weight (kg)

Degree of freedom

A B C D E F G H I J K L

1.60

50

All 0 All 0 All 0 All 0 All 0 All 0

75 1.70

50 75

1.80

50 75

Table 4 Results of fall parameters Impact velocity (m s−1)

Maximum velocity (m s−1)

5.97 3.71 4.82 4.93 6.15 4.39 4.62 4.98 6.33 4.36 4.71 5.02

5.97 5.73 5.69 5.74 6.15 5.90 6.57 5.91 6.33 6.06 7.20 6.07

the legs compared with case C. However, the body position at impact is the same as in case C. Figure 1d represents a blocked fall for a height of 1.60 m and a weight of 50 kg (case B). The pattern is completely different from all the other cases because the model is completely rigid. The head, back, buttocks and legs impact the ground at the same time. The results in terms of impact velocities are presented in Table 3. In free falls, the greatest impact velocity is 6.33 m s−1 (case I) and the smallest is 4.62 ms−1 (case G). Whatever the height, impact velocities are greatest for a weight of 50 kg. For a weight of 75 kg, impact velocity is greater for a height of 1.60 m than for 1.80 m. For a weight of 50 kg, impact velocity is greater for 1.80 m than for 1.60 m and greater for 1.60 m than 1.70 m. In blocked falls, the greatest impact velocity is 5.02 ms−1 (case L) and the lowest is 3.71 ms−1 (case B). In all simulations, impact velocity is lower than maximum velocity. This is probably because other parts of the body struck the ground before the head, thus reducing head impact velocity. The degree of association between impact velocity and body height and weight was measured with a Spearman partial correlation test. No association was found between height and impact velocity (p value=0.649) or between weight and impact velocity (p value=0.573). Finite element model All the results obtained with the finite element model are summarized in Tables 4 and 5 and some of these results are illustrated in Fig. 3. Each figure compares two cases, presented in Tables 4 and 5, by varying only one parameter. Fracture is shown by element deletion (related to maximal strain deformation).

Cases

Impact surface

Head inclination angle (°)

1 2 3 4 5 6 7 8 9 10 11 12

Ground Ground Ground Ground Ground Ground Curb Curb Curb Curb Curb Curb

90 90 90 45 45 45 90 90 90 45 45 45

Head impact velocity (m s−1)

3.5 5 6.5 3.5 5 6.5 3.5 5 6.5 3.5 5 6.5

Skull fracture

Load (N)

No No Yes No No Yes Yes Yes Yes Yes Yes Yes

14,300 24,500 37,000 14,800 24,600 35,100 8,800 8,900 9,000 8,800 12,300 12,200

Figure 3a and b focuses on the fall parameters. Figure 3a compares an impact on the curb and on the ground (cases 5 and 11). Fracture occurs when the head impacts the curb of a sidewalk. No fracture is observed when the head impacts the ground. Figure 3b compares an impact at 5 ms−1 and 6.5 ms−1 (cases 5 and 6). Fracture occurs at maximum velocity, not at a velocity of 5 ms−1. In Table 4, it can be seen that fracture occurs systematically when the head impacts the curb of a sidewalk. When the head impacts the Table 5 Results of biological parameters Cases

Density (kg m−3)

Young's modulus (MPa)

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

1,500 1,500 1,500 1,500 1,500 1,500 1,800 1,800 1,800 1,800 1,800 1,800 2,100 2,100 2,100 2,100

6,000 6,000 10,000 10,000 15,000 15,000 6,000 6,000 10,000 10,000 15,000 15,000 6,000 6,000 10,000 10,000

29 30

2,100 2,100

15,000 15,000

Cortical thickness (mm)

Skull fracture

Load (N)

1.5 3.0 1.5 3.0 1.5 3.0 1.5 3.0 1.5 3.0 1.5 3.0 1.5 3.0 1.5 3.0

No No Yes No Yes No No No Yes No Yes Yes No No Yes Yes

31,500 37,700 31,800 39,200 32,300 40,150 32,400 39,400 32,600 40,900 33,150 40,900 33,200 41,000 33,500 41,600

1.5 3.0

Yes Yes

33,900 42,000

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Fig 3 Effect of the fall and biological parameters on skull fracture. a Effect of cortical thickness. b Effect of cortical density. c Effect of impact surface. d Effect of impact velocity

ground, fracture occurs only at a velocity of 6.5 ms−1. At other velocities, no fracture was observed when we modified the angle of impact between the ground and the head. Figure 3c and d focuses on the biological parameters. Figure 3c compares a cortical thickness of 1.5 mm and 3 mm (cases 15 and 16). Fracture occurs with a cortical thickness of 1.5 mm but not with a thickness of 3 mm. Figure 3d compares a cortical density of 1,500 kg m −3 and 2,100 kg m−3 (cases 16 and 28). Fracture occurs with a cortical density of 2,100 kg m−3 but not with a cortical density of 1,500 kg m−3. In Table 5, it can be seen that fracture never occurs for a Young's modulus of 6,000 MPa. When Young's modulus is greater than 6,000 MPa, fracture always occurs with a cortical thickness of 1.5 mm and a density of 2,100 kg m−3.

Discussion In forensic science, the mechanism of fatal head injuries caused by falls is difficult to assess. Many studies have focused on head impacts in childhood falls, because falls may be wrongly considered as the mechanism of injury in child abuse cases. However, there are few published studies on fall injuries in adults. With the development of numerical modeling, it is now easier to compare the mechanisms of head injury caused by a fall. Each numerical method carries

various limitations such as relevance to in vivo conditions, material properties, and identification of initial and boundary conditions. Nevertheless, use of these methods in complement with other techniques could increase the accuracy of the results, as suggested by Doorly and Gilchrist [20]. Our approach showed that the mechanism of skull fracture caused by a fall from standing height is influenced by a combination of at least two fall parameters: impact velocity (determined with the multibody model) and impact surface, and two biological parameters: cortical thickness and cortical rigidity (observed with the finite element model). Multibody model The multibody approach made it possible to investigate parameters that could influence impact velocity. The results in terms of the body's movement suggest that the behavior of the body in a blocked fall seems improbable; the conditions of free falls appear more like real-life falls. However, the results in terms of impact velocities for free falls as well as blocked falls agree with previously published data [11, 21, 30]. The two anthropometric parameters investigated were height and weight. –

The results obtained suggest that height has no influence on either the behavior of the body or impact

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–

velocity. Indeed, for a same weight but different heights, the behavior of the body during a free fall is the same (Fig. 1a and b). For a weight of 75 kg, there is a relation between velocity and height: velocity increases with decreasing height. However, the difference between maximum (case C) and minimum (case G) velocity is very small (0.20 ms−1). For a weight of 50 kg, there is no relation between velocity and height. Nevertheless, the impact velocities are very close. Hence, the difference between maximum (case I) and minimum (case A) velocity is also very slight (0.36 ms−1). The Spearman partial correlation test agrees with the results. Height does not influence impact velocity, probably because close values of height were chosen. Concerning weight, we observed that it has an effect on both the behavior of the body and on impact velocity. For the same height but different weights, the behavior of the body during a free fall is slightly different. The results in terms of velocity show increasing velocity with decreasing weight for the same height. The difference between the maximum and minimum velocity is a large one: 1.15 ms−1 for a height of 1.60 m, 1.53 ms−1 for 1.70 m and 1.62 ms−1 for 1.80 m. However, the result of the Spearman partial correlation test does not confirm this hypothesis. This is probably because the statistical test is not strong enough to detect a correlation. It could be useful to increase sample size for the multibody model with the aim of performing a statistical test stronger than the Spearman partial correlation test and that could detect a correlation between weight and impact velocity.

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influence the mechanism, because changing the value of the angle does not change the result. This is probably because the model has a uniform cortical thickness. As pointed out by Raul et al., a model that takes local variations in skull thickness into account could predict skull fracture with greater accuracy [11, 12]. Young's modulus, which represents cortical rigidity, could influence the mechanism. With low rigidity (6,000 MPa) fracture never occurs, whereas fracture may occur with a greater Young's modulus, depending on the other biological parameters. A skull with low rigidity is more flexible than a skull with high rigidity. This could explain why fracture never occurs in cases of low rigidity. However, this result needs to be evaluated in greater depth. The biological parameters that influence the mechanism are cortical thickness and cortical density. In some cases, fracture occurs no matter what the cortical thickness (cases 23, 24, 27, 28, 29, and 30 in Table 5), and in other cases fracture occurs only for a cortical thickness of 1.5 mm (cases 15, 16, 17, 18, 21, and 22 in Table 5). In agreement with Ruan and Prasad [8], risk of injury is greater for a cortical thickness of 1.5 mm than for a thickness of 3 mm. In the same way, fracture occurs for a density of 1,800 kg m−3 (case 24) whereas it does not occur for a density of 1,500 kg m−3 (case 18). In case 28, fracture occurs for the greatest density whereas it does not occur for a density of 1,500 or 1,800 kg m−3 (cases 16 and 22). This result suggests that risk of injury is greater for a high cortical density than for a low cortical density. It could be useful to evaluate the influence of this parameter in depth as it has never yet been studied.

Finite element model

Conclusion

The results obtained with the finite element model make it possible to understand the influence of the fall conditions and biological variability on a given mechanism of skull fracture. The results presented in Tables 4 and 5 and illustrated in Fig. 3 suggest that the mechanism of skull fracture is influenced by several fall and biological parameters. The impact surface could influence the mechanism because fracture always occurs when the head impacts the curb of a sidewalk. Thus, the risk of injury is greater when the head impacts a surface such as the curb of a sidewalk than when the impact occurs on to a flat surface such as the ground. When the head impacts the ground, the mechanism is influenced by impact velocity. Fracture never occurs when the impact velocity is 3.5 ms−1 or 5 ms−1. Risk of injury is greater for a velocity of 6.5 ms−1. The angle of impact between the ground and the head does not seem to

Our results show that the mechanism of skull fracture in a case of a backward fall from standing height is influenced by a combination of fall parameters and biological parameters. To distinguish the head injuries caused by a fall and those caused by a blow, it would be interesting to carry out the same study with head injuries caused by a blow. Comparison of the results could allow identification of the parameters that can discriminate between the two possible mechanisms. The finite element model developed in this paper may be relevant for investigating skull injuries. In forensic medicine, it could contribute to objective evaluation of the different mechanisms involved in head injuries caused by a fall. Acknowledgments The authors thank Mme Berengère Saliba-Serre of the physical anthropology laboratory for assistance and support with all the statistical aspects of this work.

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