Bionic Joint
When my mother developed a debilitating disease in her finger joints, I became determined to devise products to help restore her to health and eliminate her suffering.
I was inspired by a video showing an artificial limb that imitates the biological structure of the human leg, and so decided to work out an artificial joint that could be substituted for the irrevocably damaged finger joints of my mother and patients like her. Such implants would both restore mobility and mitigate pain.
For an artificial joint to function well in the human body, the joint should resemble the human joint in geometrical and physical properties. Investigating current iterations of artificial joints used in the medical field, I discovered that most of the artificial finger joints do not possess the characteristic porous structure of human bones. I decided to produce a model of a joint incorporating a bionic porous structure with the same properties present in human bones.
For specific information:
1. Research on Geometrical Modeling and Physical Properties of Porous Structure of Human Bone
Research
Process
Finding out a structure that fits in the requirement for an artificial human joint, which requires the same mechanical properties as human joints do, I discovered that human joints possess some unique mechanical properties.
1. The human joints possess higher specific strength than mechanic joints commonly used on nowadays machines.
2. Due to capillary action, lipids are stored in the pores of human joints, which provides self-lubrication properties, letting the joints sustain great abrasive resistance. Therefore, the joints can function well for decades of years in normal conditions.
According to my further research, these advanced mechanical properties come from the porous structure on human joints. Additionally, the mechanical properties come from the geometrical properties of the porous structure. If I want to work out a bionic structure of the same mechanical properties as human joints do, my structure of the artificial human joints should retain the same geometrical properties as human joints do.
From the CT image of the cross section of a human joint, I found that the pores on the porous structures of human joints are irregular and random in shape -- the geometrical property of the pores cannot be explained through the traditional Euclidean geometrical function. I needed to work out special ways of imitating the geometrical properties of these pores.
Figure 1: CT image of the cross section of a human joint
Finding out solutions, I learned an algorithm called Sobel edge detection that can binarize images for emphasizing contours of the pores, enabling the calculation of parameters required to reach fractal dimensions. To implement the Sobel edge detection, I found a software called ImageJ that can transfer the CT images into the binary images of the pores, thus emphasizing the contours of the pores and reaching the parameters required.
I selected four pores from a CT image of the porous structure of a human joint and adopted the Sobel edge detection method by using ImageJ to binarize the image of those pores. From the contours of the four pores emphasized, I gained parameters of the pores from ImageJ. I inputted them into the Slit Island Method to work out the fractal dimensions of the pores.
Figure 2: CT image of the cross section of a human joint
After that, I calculated the fractal dimensions of these four contours of pores through the Slit Island Method. The results were similar, indicating they had similar fractal dimensions. The calculation results are shown below:
Figure 3: calculation results of the fractal dimensions of proes
In this diagram, Log (box size) represents logarithm of areas of pores, log (count) represents logarithm of perimeters of pores, D is calculated through the formula of Slit Island Method: 𝑙𝑔𝑃(𝜀)=𝐷𝑙𝑔𝛼(𝜀)+𝐷/2 𝑙𝑔𝐴(𝜀), where 𝑙𝑔𝑃(𝜀) and 𝑙𝑔𝐴(𝜀) represent the logarithm of perimeters (log (count)) and areas (Log (box size)) of pores measured with constant length (𝜀), 𝐴(𝜀) represents a constant.
Under the premise of the above-mentioned similar fractal dimensions, I adopted four pores to express random and irregular shapes of all the pores on porous structure of human bones.
I then started doing research on computer graphics to find out ways of imitating the four pores selected. In this way, I learned that B-spline is a mathematical model based on cubic equations, enabling it to imitate irregular closed shapes. Setting up knots and control points according to the contours of pores with a MATLAB program, I worked out B-splines imitating the shapes of the four pores, reflected through the graph shown below:
Figure 4: B-splines generated to imitate the four pores selected
In this graph, the blue lines are the B-splines generated to imitate the pores on human joints. Points on the red line are knots. Points on the green line are control points.
After generating B-spline models to imitate the pores, I need to establish a distribution method to randomly distribute these imitated pores like the pores on real human joints do. After searching and studying the algorithms related to random distribution, I found that the available algorithms usually have very high computational loads. Accordingly, I chose C++ as the programming language to ensure high computation speeds of the random distribution algorithms.
After further learning, I generated an algorithm that can distribute the B-spline models in random size and direction within a specific area. I also established a control panel that enables me to adjust the abundance of B-splines, thus controlling the porosity ratio of the bionic porous structure that I generated. Till then, I completed the imitation of the porous structure on human joints.
Figure 5: bionic porous structures with porosity 30% and 70%
To verify if the geometrical properties of the bionic porous structure I generated are similar to those of the porous structures in human joints, I calculated the fractal dimension of the bionic porous structure using the Slit Island Method. According to the results, the value of the fractal dimension of the bionic porous structure generated is 1.7842, which is like the calculated fractal dimension (D) of pores on human joints in value.
Therefore, I can successfully show that the bionic porous structure possesses the same geometrical property as porous structures in human joints.
Finding out whether my bionic structure really possesses advanced engineering quality than traditional ones, I decided to take my bionic porous structure into practical use. I then thought of using the structure on the joints of a snake-like robot. In order to achieve that, I used Rhino 7 to work out a spherical joint fitting in the snake-like robot. I then merged the bionic porous structure I generated with the spherical joint and manufactured it out with titanium alloy.
inner bionic porous structure of the spherical joint
spherical joint made of titanium alloy
Through utilizing the bionic joint on a snake-like robot, I compared the mechanical properties of the bionic joint with those of the original Hooke joints on the snake-like robot. The results are as listed:
Accordingly, the bionic joint possesses better mechanical properties than the original Hooke joints do.
While the bionic joint functioned well with the snake-like robot, I wondered if I can further improve its mechanical properties, especially for its self-lubrication property. According to Jurin’s law, the less the radii of the pores on the spherical joint, the higher the inner lubricating oil will rise, enabling the pores to store lubricating oil. Therefore, I needed to generate the pores with low radii as possible, so that the spherical joint with the porous structure I worked out would occupy the same oil storage capability as human joints do, letting the spherical joint possess self-lubrication property.
the bionic joint functions well with the snake-like robot