Cats are able to jump from a high-rise without any sign of injury, which is attributed in large part to their impact-resistant paw pads. The biomechanical study of paw pads may therefore contribute to improving the impact resistance of specific biomimetic materials. The present study is aimed at investigating the mechanics of the paw pads, revealing their impact-resistant biomechanism from macro- and microscopic perspectives. Histological and micro-CT scanning methods were exploited to analyze the microstructure of the pads, and mechanical testing was conducted to observe the macroscopic mechanical properties at different loading frequencies. Numerical micromodels of the ellipsoidal and cylindrical adipose compartments were developed to evaluate the mechanical functionality as compressive actions. The results show that the stiffness of the pad increases roughly in proportion to strain and mechanical properties are almost impervious to strain rate. Furthermore, the adipose compartment, which comprises adipose tissue enclosed within collagen septa, in the subcutaneous tissue presents an ellipsoid-like structure, with a decreasing area from the middle to the two ends. Additionally, the finite element results show that the ellipsoidal structure has larger displacement in the early stage of impact, which can absorb more energy and prevent instability at touchdown, while the cylindrical structure is more resistant to deformation. Moreover, the Von Mises of the ellipsoidal compartment decrease gradually from both ends to the middle, making it change to a cylindrical shape, and this may be the reason why the macroscopic stiffness increases with increasing time after contact. This preliminary investigation represents the basis for biomechanical interpretation and can accordingly provide new inspirations of shock-absorbing composite materials in engineering.
Cats are generally acknowledged to have excellent athletic ability, especially in jumping, achieved through natural selection. When striking the ground, they can land smoothly, without any injury, though they are subjected to large impact forces, as high as several times their body weight [
In the past few decades, a large number of studies have been done on the mechanical properties of human heel pads, revealing the nonlinear, viscoelastic mechanical behavior [
Nevertheless, there have been few systematic studies on the biomechanical behaviour of cat paw pads. Alexander et al. [
As stated above, there is currently sufficient evidence to elucidate the important role of cat paw pads in energy absorption during impact. However, to our knowledge, there is a lack of comprehensive and comparative studies on cats’ paw pads and no quantitative investigation of the micromechanics of paw pads has been published. It is known that the paw pads are composite materials, and their observed mechanical properties are achieved by the interaction of the various components. Studies of micromechanics (the ways in which the components interact), based on finite element analysis, can thus provide comprehensive insight into the internal buffering mechanism of cat paw pad during impact. In previous studies, the microstructure of the paw pads was concentrated in the two-dimensional morphology, but the minimum three-dimensional structural unit of load-bearing was not proposed. As a result, it is not well established that this information is sufficient to provide representative interpretation of impact resistance in the cat’s paw pad.
The objective of this paper is therefore to study the comprehensive biomechanism of impact resistance in the cat’s paw pad. In this study, a mechanical testing system was used to observe the macroscopic mechanical properties at different vibration frequencies, and the microstructure were investigated using section staining technique and micro-CT scanning. Additionally, finite element models of ellipsoidal and cylindrical (for control) adipose compartments, which are considered to be small hydrostatic systems, were established to study internal buffering mechanism of cat paw pad, making it possible to visualize the events that occur during impact. The results of this study will help to interpret and understand the impact resistance biomechanism of cat paw pads. A more practical motivation for this study is to provide useful information for the future development of impact resistant biomaterials.
A total of five domestic cats (2.45 ± 0.29 years of age, 3.6 ± 0.35 kg) that had died of heart disease were included in the study. After their death, the metacarpal pads of the forelimbs were removed and preserved. All experimental procedures were approved by the Science and Ethics Committee of Beihang University.
The metacarpal pads of the left forelimbs of two cats were fixed in 10% formalin solution. Ten-micrometer-thick sections in the sagittal planes were obtained from the paraffin-embedded samples and stained with hematoxylin-eosin (HE), Verhoeff-van Gieson for elastic fibers, and Sirius red for histological examination. In particular, the subtypes of collagen were studied in the Sirius red staining sections using a polarized light microscope and recorded with a high-resolution digital camera able to differentiate type I collagen fibers, which appear orange to red, from the thinner type III collagen fibers, which appear yellow to green [
In order to accurately investigate the two-dimensional morphology and three-dimensional structure, the metacarpal pads of the left forelimbs of the remaining three cats were scanned by micro-CT (Skyscan1272, Skyscan, Belgium) at a spatial resolution of 8
The metacarpal pads of the right forelimbs were slowly thawed to room temperature and cut into cylindrical samples with a diameter of 7 mm by a corneal trephine. Then the five pad samples with heights of 5.2 mm, 5.4 mm, 5.5 mm, 5.7 mm and 5.9 mm, were subjected to dynamic compressive tests, using Instron E10000 testing machine. Figure
A diagram showing how the paw pads were mounted in the dynamic testing machine.
Before the mechanical testing, we read some typical articles on the mechanical behaviour of human and mammal heel (paw) pads [
Due to the irregularity of the reconstructed compartment structure, we idealized it as an ellipsoid in this paper. Meanwhile, in combination with previous studies [
In order to simulate the hydrodynamic effects, the shell models were filled with incompressible water. Furthermore, we applied the software Hypermesh 12.0 to mesh the models, as shown in Figure
Material properties of all components used for finite element modelling.
Ellipsoid shell | Cylindrical shell | Water | Top and ground plates | |
---|---|---|---|---|
Fluid Bulk Modulus (Mpa) | - | - | 2000 | - |
Young’s Modulus (Mpa) | 1 | 1 | - | 21300 |
Poisson’s Ratio | 0.3 | 0.3 | - | 0.3 |
Density (t/mm3) | 1.27e-009 | 1.27e-009 | 1e-009 | 1e-018 |
Viscosity (Mpa·s) | - | - | 1e-009 | - |
The ellipsoid and cylindrical models before and after mesh generation used for the finite element analysis.
It can be seen from the previous cat jumping experiments, there was a nearly linear growth in the ground reaction force on the paw pads. In order to simulate the value of the peak force acting on the pad during a 1-m jump down, the dimensions of the finite element models were compared with the actual sizes of the adipose compartments, obtained from micro-CT scanning and section staining results, to derive the conversion relationship between them. And the actual peak force was then converted into a suitable force that was linearly loaded onto the two models (making the total force on the top surface increase to 20 N in 2.25s), in accordance with this conversion relationship. Therefore, in the simulation process, we used the load control instead of the displacement control. Finally, the effective stresses (Von Mises), displacements and shape change of the two models in the whole fluid-solid coupling analysis step were recorded and analyzed.
The hysteresis loops of stress-strain at three frequencies are graphically presented in Figure
Means and SD of energy dissipation and elasticity modulus at particular loads, for different vibration frequencies.
Frequency (Hz) | Elasticity modulus (Mpa) at loads of | Energy dissipation (%) | |
---|---|---|---|
50N | 100N | ||
0.11 | 6.52 (1.38) | 14.83 (3.14) | 29.19 (4.13) |
1.1 | 7.96 (2.56) | 15.33 (2.83) | 31.28 (5.54) |
11 | 8.21 (2.87) | 16.18 (1.65) | 27.67 (3.87) |
Representative average Stress-Strain curves of tests at 0.11Hz, 1.1Hz, and 11Hz.
As is shown in Table
Histological examination and micro-CT scanning results of metacarpal pads from the left forelimbs are presented in Figures
Composition of fibers in the dermis layer and subcutaneous layer investigated.
Elastic fibers | Collagen I fibers | Collagen III fibers | Other components | |
---|---|---|---|---|
Dermis layer | 9% | 53% | 24% | 14% |
Subcutaneous layer | <1% | 67% | 22% | 11% |
Representative histological images of the paw pad, stained with hematoxylin-eosin stain (a, b), Verhoeff-van Gieson stain (c, d), and Sirius red stain (e, f). Scale bars in the images (a–f) represent 200
CT image (left) of the paw pad and idealized schematic diagram (right) of the spatial structure of an adipose compartment.
However, thus far, little is known about the three-dimensional structure of adipose compartments in subcutaneous tissue. Therefore, we scanned the pads using micro-CT, in order to investigate the spatial structure of adipose compartments for the first time, and the results suggest that the three-dimensional structure of each compartment is not exactly the same, which can also be inferred from the results of section staining that, for a given section, each closed area has a different shape. However, they have one thing in common, that is, the cross-sectional area decreases gradually from the middle to the two ends, which is similar to the structure of the ellipsoid. In a departure from the previous study which reduced their structures to cylinders [
The comparison between ellipsoidal and cylindrical models using the stress (Von Mises) vs strain curves is shown in Figure
The stress (Von Mises) versus strain curves of the ellipsoidal and cylindrical models.
Furthermore, the stress-strain curve of the cylindrical model is almost linear, while that of the ellipsoid has an increasing slope. We suspect that the reason for this result is the shape of the cylinder is always a cylinder during the compression process, only the height and width have changed, but the shape of the ellipsoid has changed a lot. Accordingly, we also analyzed the shape change of the ellipsoidal model during loading, as is shown in Figure
The shape change of the ellipsoidal model during loading.
In order to further investigate the stress distribution characteristics, the color nephograms of the Von Mises of the two models at different loading times were provided in Figure
The color nephograms of the Von Mises of the two models during loading.
By summarizing the results of mechanical testing, histological examination, micro-CT scanning and finite element analysis, we are able to examine the microstructure of the cat’s paw pad and to analyze the macroscopic and microscopic mechanical responses to impacts, gaining insight into the biomechanism of impact resistance in cat’s paw pad. Our results show that there are variable nonlinear and viscoelastic properties in cat’s paw pads, which is attributable to the changes in the shapes of the microscopic adipose compartments during impact. Notably, the pads were found to have multiple layers, which help dissipate the impact forces, and the ellipsoid-like structures of adipose compartments exert a dominant role in impact resistance. The results of this study can provide biological inspiration for impact resistant foot pad to reduce human lower limbs injuries during landing. It should be noted that, in this study, we ignored the interplay between the adipose compartments, while, in fact, the space arrangement of compartments would affect the energy absorption and shape change of pads during impact, so further study is warranted to establish the three-dimensional structure of multiple compartments simultaneously.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors are indebted to Jie Yao and Shouhui Wang for providing the experimental apparatuses, and we would also like to thank Zhiqiang Zhang for his help and advice. This project was funded by Defense Industrial Technology Development Program under Grants JCKY2018601B106 and JCKY2017205B032.