Development of a method and algorithm for determining the reaction forces of the joints of the patient's lower extremities

Abstract

This paper proposes a method and algorithm for determining the reaction forces occurring in the hip and knee joints, as well as the interaction forces between the musculoskeletal system and the external environment, using mathematical modeling. This allows for the assessment of movement dynamics and load distribution across the joints, muscles, and bone structures of the musculoskeletal system to analyze the patient's functional state and subsequently restore lower extremity motor function.

The diagnostic and rehabilitation device is presented in this work as a crank-slider mechanism equipped with a linear drive, ensuring linear motion of the patient's heel. The mathematical model of the patient's lower limb motion in this device is based on the solution of a direct kinematics and dynamics problem and is represented as Newtonian and Lagrange differential equations of the second kind for a constrained mechanical system. These equations allow for the active and reactive forces acting on the thigh, lower leg, and heel, depending on the driving force generated by the electric drive.

The aim of the study is to develop a method and algorithm for determining reaction forces in the hip and knee joints to assess the dynamics of movements and diagnose the condition of the patient's joints, as well as to analyze the distribution of loads on the elements of the musculoskeletal system when it interacts with the external environment.

Graphs were constructed showing the dependence of forces occurring in the hip and knee joints, heel pressure on the support surface, and frictional forces (over time) on the hip rotation angle. It was established that rheological parameters μ_i of the lower limb muscular system significantly influence the force responses in the hip and knee joints: their increase leads to increased joint loads.

Monitoring the duration of the muscle contraction phase and the nature of limb control provides an objective assessment of the effectiveness of rehabilitation measures, which allows for the optimization of recovery programs for patients with affected joints.