To study the development of contractures of the finger joints of the fingers, we created a mathematical model for the operation of the proximal interphalangeal (PIP) joint of the finger of the hand.
The purpose of the work: to build a mathematical model of the work of the PIP joint, based on the law of conservation of energy, to determine the external work needed to overcome resistance in the joint for various types of contractures.
Materials and methods. The mathematical model is implemented in the MS Excel software product, for which a system of equations of static equilibrium of the system is created. The model is based on the law of conservation of energy. Different types of limitation of mobility in the hinge, simulating the interphalangeal joint, are modeled by a change in the stiffness parameters.
Results. The model connects the main parameters of the work of the PIP joint, reflects the relationship between these parameters and allows us to investigate physical patterns. The model includes active and passive forces, so it allows modeling the effect of external fixation devices in the treatment of contractures. Also, the model includes the rigidity of the tendon, the coefficient of friction of the tendon in the canal, the elasticity of the skin, the stiffness of the joint, which allows modeling various types of stiffness of the interphalangeal joint.
Conclusions. With the help of the constructed mathematical model of the operation of the joints based on the law of conservation of energy, it is possible to determine the necessary effort to overcome some degree of stiffness. By measuring the force Fa (internal force), it is possible to calculate the corresponding external force Ff of the external mechanical device necessary for the movement of phalanges of the finger in various types of stiffness at any angle of flexion of the phalanx in the PIP joint.