Woodpecker can beat trees 20-25 times per second and lasts for several seconds, with a 1200 g deceleration, but it appears that they never get brain concussion. How does the stress wave propagate from the beak tip to brain and how does a woodpecker protect itself from brain damage? In this paper, we establish a finite element model of typical woodpecker head based on its X-ray tomography images and conduct the numerical analysis of the impact response of the woodpecker's head by using a viscoelasticity material model. Especially, the woodpecker head response to an impact speed of 7 m/s is investigated to explore the stress concentration zone and how the stress wave propagates in its head. The numerical results show that the stress wave in the head propagates from the upper beak to back skull and is reduced by the specific structure of hyoid and viscoelasticity of biomaterials. The maximum stresses in skull and brain are both below the safe level. The stress in skull almost disappears before the next impact. The stress in brain lasts for a little longer but shows smaller value with little variation. The stress is impossible to accumulate in the limited pecking time, so the brain damage can be avoided.
I. INTRODUCTION
Woodpeckers beat trees or drill holes into trees every day by using their hard beak to obtain enough food, get communications with others and attract the heterosexual's attention. The drumming (impacting) frequency of the woodpecker's head ranges from a few Hz up to 25 Hz.1,2 Besides, woodpeckers excavate cucurbit-like cavity nests in the trees with a horizontal entry using their long beak. How does woodpecker avoid brain concussion during the drilling, excavating and drumming process? It has been one of most interesting topic to many researchers for a long time.
Early in 1976, May et al.3 gave a detailed description of the woodpecker's drilling action. Using a high speed camera, they obtained the high-speed films of an acorn woodpecker pecking into a tree (the bird was unable to fly as a result of injuries from a broken wing, but lived in the office of a park ranger in California and would peck on a tree trunk in the office when it heard the tapping of typewriter keys). The analysis of images showed that the woodpecker's head moved forward in a straight trajectory, reaching the maximum speed up to 5-7 m/s and deceleration of about 600-1500 g on impacting within merely 0.5-1 ms.3 However, the brain of human beings can usually bear only 300 g deceleration during the same time interval,4 which is far below the woodpecker's level. Gibson5 compared the skull structure and impact resistant ability between the woodpeckers and human beings, proposed that the following three factors working together may give the woodpeckers an optimal ability to avoid brain injury: small sized skull, short impact duration and the large area between brain and skull.
Oda et al.6 also dissected the head part structure of a woodpecker and made 3D stereo lithography head model three-times larger than the woodpecker head. They measured the strain in each part of the lithography head model and compared the experimental results with numerical ones. In addition, they established two 2D analytical models to study the cerebrospinal fluid and hyoid bone's function. However, the simplification of the hyoid bone using the 2D model might be far from the actual head structure of woodpecker. Yoon et al.7 made a woodpecker-inspired shock isolation using a microgranular bed to protect micromachinary and electronic devices for high-g environment. The microgranular bed composing of close-packed microglass beads reduces the mechanical excitations.
More recently Wang et al.8 made experimental observation for the pecking process of a living woodpecker and obtained the pecking force of 8.1N and the pecking velocity of 7.6 m/s for foam. They set up an FEM model by micro-CT scanning and did an analysis of woodpecker's pecking on a rigid wall. In their analysis model, they discussed the effect of the length of the lower and upper beak on the stress in the skull, finally they gave the conclusion that the stress passed through the lower beak to avoid damage to the brain.
However, according to other people's research, the woodpecker's beaks were tightly closed during the pecking process,2 seemly the stress passed through the both beaks and may present another distribution. Also according to our measurement of the beak by nano-indentation, the modulus of the outer layer (stratum corneum) of the beak is much bigger than that of the inner bone and the stratum corneum is nearly grown on the surface of the bones which is hard to remove, so the structure of beaks may have a special effect on the stress propagation in the skull. In addition, the dura matter and hyoid in and around the skull should be considered.
To clarify the impact response of woodpecker's head structure, an effort is made in this paper to perform a numerical analysis for the stress distribution and stress wave propagation in the woodpecker's head based on the former work. We establish a 3D finite element (FE) model of the woodpecker's head using CT scanner and geometric reconstruction techniques.
II. FINITE ELEMENT MODEL
A. Geometrical model
Woodpeckers form their head structure and special function during the evolution process gradually. They have long and hard beaks, small head, big eyeball, little cerebrospinal fluid and tight connection between brain and skull which keeps the brain stable during oscillation.6 Hyoid bone is about four times the length of the beak, with its end fixed on the right nostril, bypasses the skull and stretches out from the mouth to reinforce the head.9 The muscles and ligaments in woodpecker's head help attaching the hyoid to the mandible tightly when impact happens.3 Muscle of the woodpecker's neck are quite tight when impact happens, it can reduce load-induced damage in a very short time period.3 All these factors should be considered in the computed model.
The woodpecker studied in this paper named Grey-headed Woodpecker is living in the northeast forests in China. An actual woodpecker's head consists of beaks, bones, muscles, skins and so on. The head configuration is composed of a series of complex curves, thus it is hard to establish an actual geometrical model of the woodpecker's head directly.
We take a series of CT scanning images of the woodpecker's head (Fig. 1(a)) after removing the excess skins and utilize them to form a 3D scatter-point diagram (Fig. 1(b)). Based on these scatter-point diagrams, we use the 3D image processing software (ProE) to cluster the small planes consisting of the scatter points and form integrated curves adapted to the actual object. At last, in order to get a 3D FE model, the curves above are transformed to solids by hypostatization (Fig. 1(c)), then refined FE mesh is made on the geometry model (Fig. 1(d)). From the beak sample, we observe that the woodpecker's upper beak was about 1 mm longer than the lower one, which is opposite to the assumption made in the study of Wang et al.8 Figure 1(e) is the close shot of the woodpecker's beaks which indicates that the upper beak may first contact with wood when pecking.
CT images, Geometrical model and FE model of woodpecker's head: (a) a representative section view of CT images, (b) 3D scatter point diagram consisting of the section images, (c) geometrical model diagram, (d) finite element model diagram and (e) actual picture of the end of the beaks.
CT images, Geometrical model and FE model of woodpecker's head: (a) a representative section view of CT images, (b) 3D scatter point diagram consisting of the section images, (c) geometrical model diagram, (d) finite element model diagram and (e) actual picture of the end of the beaks.
B. Material properties and the FE model
Accurate values of the material property parameters are important to the FE analysis. However, as woodpecker's bone is a kind of biomaterial, many factors may affect the real mechanical property, such as the blood in bone, the muscle around the bone and the different scales of porosity in the bone.
In this paper we divide the whole head simply to several material components, the outer layer (stratum corneum) of the beak, the hyoid, the dura matter, the brain and the bone which is the most important. In the former studies,6,7 people used the material parameters of human being's bone as the bone structure of woodpecker's head. Recently, Wang et al.10 have measured the elastic modulus of the woodpecker's skull bone and beak using a compression method. Zhou et al.9 have measured the hyoid property in their research early.
It's hard to measure the material property of the other components inside the woodpecker head. Here we assume that the mechanical properties of the woodpecker's brain and dura matter are the same as the human being's,11–15 the components except the beak and hyoid are linear-viscoelasticity. Simply the viscosity parameters of the dead brain and dura matter are referenced to the work of Sack et al.12 and the viscosity of bone is referenced to those of Lunde et al.16 and Matthew et al.17 The wood is considered as the spruce wood,18 which is a kind of the woodpecker's favorite trees. The material properties used in this paper are given in Table I.
Material properties.
| Component | Density [kg m−3] | Young's modulus [Pa] | Coefficient of viscosity [Pa·s] | References |
|---|---|---|---|---|
| Bone | 1200 | 3.1 × 108 | 0.086 | Wang et al.9 Lunde et al.11 |
| Beak | 1456 | 1.0 × 109 | — | Wang et al.9 |
| Hyoid | 1200 | 3.72 × 109 | — | Zhou et al. 200910 |
| Brain | 1040 | 3156 | 3.85 | Taylor et al.11 Sack et al.12 |
| Dura matter | 1040 | 3.7 × 108 | 3.85 | Iwaniuk et al.15 |
| Wood | 500 | 2 × 109 | — | Gindl et al.18 |
| Component | Density [kg m−3] | Young's modulus [Pa] | Coefficient of viscosity [Pa·s] | References |
|---|---|---|---|---|
| Bone | 1200 | 3.1 × 108 | 0.086 | Wang et al.9 Lunde et al.11 |
| Beak | 1456 | 1.0 × 109 | — | Wang et al.9 |
| Hyoid | 1200 | 3.72 × 109 | — | Zhou et al. 200910 |
| Brain | 1040 | 3156 | 3.85 | Taylor et al.11 Sack et al.12 |
| Dura matter | 1040 | 3.7 × 108 | 3.85 | Iwaniuk et al.15 |
| Wood | 500 | 2 × 109 | — | Gindl et al.18 |
A symmetrical FEmodel mainly composed of tetrahedral elements is set up based on the geometrical model, which contains more than 256,000 nodes and 1,192,000 elements, the components of the model are shown in Fig. 2. The following hypotheses are used in order to reduce the computational time and maintain the computation reasonable.
The woodpecker's head is almost bilateral symmetric, we consider it as a 3D symmetrical structure and establish the half head model.
The upper and lower beaks are tied together during impact analysis because woodpecker's beaks are occlusive closely when pecking the trees.2,19
The viscosity of material properties were considered as isotropic linear-viscoelasticity.
The woodpecker's hyoid is attached to the skull by muscles and ligaments and moved with the head together when pecking.3,9
The brain is regarded as almost incompressible with Poisson's ratio near 0.5. Because there is little cerebrospinal fluid between woodpeckers’ brain and skull, the brain is considered sticking on the dura matter.6
III. IMPACT ANALYSIS
When a woodpecker is drumming, the body is nearly parallel, but the beak is vertical to the trunk of the tree. The woodpecker can firmly grasp the trunk with its sharp claws and keep its body stable with the tail feathers when it whacks the trunk.2,7 Its head moves straightly to the target with a high speed ranging from 3.5 m/s to 7.5 m/s.2,3 The impact time is usually in millisecond scale. In this paper, we assume the impact speed is 7 m/s, which is the most common speed in woodpeckers.
As we all known, the woodpecker pecks the tree several times in one second. The continuous pecking process is composed of several single hit processes. Here we take a single impact process as an example to find out the stress distribution and propagation in woodpecker's head. The woodpecker's head is set near to the wood, given an initial velocity towards the wood, which is shown in Fig. 2.
ABAQUS software is used here to do dynamic explicit analysis for the whole model. In order to study the stress level in the skull and brain, we choose several monitored points at different positions as shown in Fig. 2. Points A, B, C, D are set to monitor the stress in the skull bone and points a, b, c, d, e are set in the brain.
A. Stress distribution and propagation in the skull bone
The impact process of woodpecker head to a tree is very short. Here we study the situation within 1 ms. Figure 3 shows the stress distribution during the impact time of 1 ms. We can see the stress wave propagates from beaks to the back skull in very short time and high-value stress mainly appears at the beak, hyoid and two sides of skull parietal. The stress state is divided into four cases during the whole process of impact. Next, we will analyze the results in detail.
At beginning of the impact (Fig. 3, impact start), the stress wave starts from the upper beak, propagates into the lower beak and the nostrils. When it passes through the beaks (impacting process), the stress wave disperses in different parts in the skull, such as the hyoid and two sides of the parietal behind the eyehole. From the view of Fig. 3, we can see that after the stress reaches the bottom of the upper beak (t = 0.3 ms) most of the stress goes into the hyoid bone around the skull. In this way the hyoid bone absorbs most of the impacting energy and protects the brain in the skull. From the bottom view in Fig. 3, it is observed that the special structure of skull helps dispersing the stress to the sides of skull parietal, which could avoid the stress focusing in one place.
Evidently the high-value stress occurs in the following zones: around the nostrils of the upper beak, the top skull bone and its two sides. The four monitored points (A, B, C and D, shown in Fig. 2) we have set before are in these interested zones, point A locates at the upper beak near the nostril and the others spread around the skull.
In order to understand the stress of monitored points, Figure 4 shows that the average stress on the beaks (points A and B) is larger than the one on the skull (points C and D). The maximum stress in point A is about 24MPa and reaches the minimum at time 0.6 ms, the moment when woodpecker's head departs from the wood. The stress of top and back skull also has the same propagation trend.
From the Fig. 4, we can see that the stress takes about 0.6 ms first to rise up from zero to the maximum (∼24MPa) and then reduces to about 1.5MPa. During this stress impact period, the woodpecker head touches the wood and departs from it. Then the stress wave goes into the second propagation period, between 0.6 ms and 0.8 ms. But the maximum stress in the second propagation is reduced by 60% compared with the maximum value in the first propagation period (0–0.6 ms). This indicates that the viscosity of material plays an important role in reducing the stress when the structure is in the status of free vibration after departing from the wood.
However, the stress at the lower beak (point B) appears later than the upper beak and is almost decreased to its minimum value at 0.4 ms, 0.6 ms and 0.75 ms, respectively. This indicates that the upper beak first bears the stress when subjected to an impacting force and the stress wave mainly propagates from the upper beak during the pecking process because the stress in lower beak reaches a minimum before the head departs from the wood.
The stress value at point C is below 6MPa, which is much lower than the upper beak. To our surprise, the stress value at point D is only about 10% of the stress at pint A (upper beak), which is very helpful for protecting the dead brain from damage. The stress all over the skull is less than 8MPa during the whole pecking process. According to the research work of Pithioux et al.,20 this stress is at the safe level with no possibility of the bone failure.
Due to special structure of the woodpecker head, the impacting stress wave propagates first through the beaks and front skull, and then becomes lower and lower, the farther the position from the impact area, the lower the stress in the skull. The reason for this is the combined function of the viscosity of head materials, special structure of the head, and hyoid around the head.
When the beak separates from the wood at 0.6 ms, the impacting process is over. The stress in the skull bone structure reduces to a low level about 3MPa and the stress wave propagates forwards and backwards in the head freely. It should be noticed that 0.6 ms is a very short time compared with a period 40 ms of pecking. During the returning time of the head from the pecking process, the stress in the skull will become lower and lower because of the structure damping. The stress would nearly disappear before the next impact coming.
B. Stress analysis in the brain
We have set five monitored points at the top, bottom, front, back and middle of the brain, individually named a, b, c, d, e (as shown in Fig. 2), to record the stress value occurring in the brain during the impact process.
Because the brain is a softer material than the skull, the stress is found three orders of magnitude smaller than the skull's. Figure 5 gives the stress curves of the five points. The maximum stresses at the monitored points and the whole brain at different time are given in Table II. The bold numbers in lines represent maximum stress of the five points and the right column shows the location and the value of maximum stress in the brain. It can be seen that during the whole impact process, the maximum stress occurs at the front of brain.
von-Mises stress of the monitored points in the brain.
| Time | a (top) | b (bottom) | c (front) | d (back) | e (middle) | Maximum stress Position | |
|---|---|---|---|---|---|---|---|
| (ms) | (kPa) | (kPa) | (kPa) | (kPa) | (kPa) | and Value (kPa) | |
| 0.10 | 0.02 | 0.00 | 0.10 | 0.00 | 0.00 | Near Top | 0.51 |
| 0.15 | 0.35 | 0.38 | 0.71 | 0.43 | 0.00 | Near Front | 3.24 |
| 0.20 | 0.77 | 2.45 | 1.52 | 1.48 | 0.00 | Near Bottom | 7.24 |
| 0.25 | 2.35 | 4.74 | 3.06 | 2.11 | 0.07 | Near Bottom | 11.05 |
| 0.30 | 4.68 | 7.12 | 5.11 | 2.59 | 0.47 | Near Front | 14.29 |
| 0.35 | 7.26 | 8.83 | 7.97 | 3.46 | 0.77 | Near Front | 18.00 |
| 0.40 | 8.69 | 8.15 | 11.46 | 3.71 | 0.95 | Near Front | 18.31 |
| 0.45 | 9.54 | 5.94 | 14.48 | 3.89 | 0.97 | Near Front | 17.21 |
| 0.50 | 7.76 | 3.02 | 14.32 | 3.84 | 1.20 | Near Front | 15.73 |
| 0.55 | 6.95 | 3.55 | 9.37 | 3.07 | 1.14 | Near Front | 26.04 |
| 0.60 | 5.64 | 7.65 | 9.03 | 3.81 | 1.00 | Near Front | 20.20 |
| 0.65 | 5.54 | 11.21 | 4.81 | 3.62 | 0.89 | Near Front | 20.72 |
| 0.70 | 5.84 | 11.68 | 7.76 | 1.63 | 0.71 | Near Front | 24.75 |
| 0.75 | 6.60 | 8.21 | 12.70 | 2.71 | 0.52 | Near Front | 28.56 |
| 0.80 | 7.38 | 4.25 | 20.18 | 4.89 | 0.96 | Near Front | 24.72 |
| 0.85 | 8.50 | 2.73 | 24.94 | 7.26 | 0.92 | Near Front | 39.78 |
| 0.90 | 6.76 | 4.25 | 23.47 | 6.41 | 0.67 | Near Front | 38.54 |
| 0.95 | 4.36 | 8.09 | 15.89 | 3.97 | 1.02 | Near Front | 32.78 |
| 1.00 | 2.21 | 5.51 | 11.72 | 2.63 | 1.18 | Near Front | 27.45 |
| Time | a (top) | b (bottom) | c (front) | d (back) | e (middle) | Maximum stress Position | |
|---|---|---|---|---|---|---|---|
| (ms) | (kPa) | (kPa) | (kPa) | (kPa) | (kPa) | and Value (kPa) | |
| 0.10 | 0.02 | 0.00 | 0.10 | 0.00 | 0.00 | Near Top | 0.51 |
| 0.15 | 0.35 | 0.38 | 0.71 | 0.43 | 0.00 | Near Front | 3.24 |
| 0.20 | 0.77 | 2.45 | 1.52 | 1.48 | 0.00 | Near Bottom | 7.24 |
| 0.25 | 2.35 | 4.74 | 3.06 | 2.11 | 0.07 | Near Bottom | 11.05 |
| 0.30 | 4.68 | 7.12 | 5.11 | 2.59 | 0.47 | Near Front | 14.29 |
| 0.35 | 7.26 | 8.83 | 7.97 | 3.46 | 0.77 | Near Front | 18.00 |
| 0.40 | 8.69 | 8.15 | 11.46 | 3.71 | 0.95 | Near Front | 18.31 |
| 0.45 | 9.54 | 5.94 | 14.48 | 3.89 | 0.97 | Near Front | 17.21 |
| 0.50 | 7.76 | 3.02 | 14.32 | 3.84 | 1.20 | Near Front | 15.73 |
| 0.55 | 6.95 | 3.55 | 9.37 | 3.07 | 1.14 | Near Front | 26.04 |
| 0.60 | 5.64 | 7.65 | 9.03 | 3.81 | 1.00 | Near Front | 20.20 |
| 0.65 | 5.54 | 11.21 | 4.81 | 3.62 | 0.89 | Near Front | 20.72 |
| 0.70 | 5.84 | 11.68 | 7.76 | 1.63 | 0.71 | Near Front | 24.75 |
| 0.75 | 6.60 | 8.21 | 12.70 | 2.71 | 0.52 | Near Front | 28.56 |
| 0.80 | 7.38 | 4.25 | 20.18 | 4.89 | 0.96 | Near Front | 24.72 |
| 0.85 | 8.50 | 2.73 | 24.94 | 7.26 | 0.92 | Near Front | 39.78 |
| 0.90 | 6.76 | 4.25 | 23.47 | 6.41 | 0.67 | Near Front | 38.54 |
| 0.95 | 4.36 | 8.09 | 15.89 | 3.97 | 1.02 | Near Front | 32.78 |
| 1.00 | 2.21 | 5.51 | 11.72 | 2.63 | 1.18 | Near Front | 27.45 |
Because the stress in the brain is mainly resulted from the deformation of the skull surrounded the brain, the stress distribution in the brain is a little similar to the skull, which is higher at the front, lower at the bottom and back. Except the front of the brain, the other region of the dead brain has a lower average stress. The center of the brain (point e in Fig. 5) has the lowest stress below 1kPa and the least stress changes during the impact process. This is because the outer area of the brain is easily affected by the skull vibration. But the stress versus time curves in front and back brain (curves c and d) do not decay like the others (curves a, b, e) because the stress wave propagates mainly in the front-back direction.
In Table II, the stress of five monitored points and the maximum stress in brain are listed. The maximum stress 40kPa in the front of brain does not appear during the impacting time 0–0.6 ms, but occurs at the departing time of 0.85 ms. This indicates that the brain reaches the maximum stress later than the skull. At the same time, the stress in the brain changes less than the skull, it has to last a longer time because of the damping function of the viscoelastic material.
IV. CONCLUSIONS
The woodpecker's head is a high effective shock absorbing system, due to the special structure and viscoelasticity of the biomaterials. This paper uses the CT scanning images to establish an FE model of a green woodpecker's head. Based on the existing material properties and the observation of the skull structures, we have performed the numerical analysis of the impact process. We found that the brain protecting mechanism is different from the previous report. The following conclusions can be made from our study:
Under the impact speed of 7 m/s, the maximum stress in the bone structure of the woodpecker's skull reaches 24MPa, but the maximum stress occurring in the brain is below 40kPa due to the special structure of the bird skull. The low level of stress occurring in the brain is the main reason protecting it from damage.
The dome structure of the woodpecker skull is suitable for spreading the stress wave into the two sides of the skull. It can change the stress wave propagation directions to protect the brain from suffering a large stress.
The hyoid around the skull plays an important role in absorbing the impacting energy. Most of the high-value stress wave goes into the hyoid bone from the upper beak during the impacting process.
The viscosity of biomaterials plays an important role in decreasing the stress value. The stress in the skull may disappear before the next impact occurs. Although the small stress in brain may last for a little longer time, the stress variation in the brain is very small.
There are still some issues to be further explored, for example, the detailed functions of the spongy bone in the front and bottom of skull and the neck muscles and skin's influence to the stress wave propagation and the stress distribution.
ACKNOWLEDGMENT
This work was supported by the National Natural Science Foundation of China (10972050, 90816025) and the doctoral education foundation of China Education Ministry (20110041110021)
