Keywords

1 Introduction

Among injuries of lower extremities, the most widespread are those of distal part of lower leg and ankle, which, according to literature data, make up from 12.0 to 20.0% of all fractures of locomotor apparatus. In 12–39.8% of cases unsatisfactory results of treatment are observed, and the long-term disability lasts from 4 to 8 months. One of the most common injuries sustained by humans is damage to the ankle joint in sports, domestic, industrial exercises, and as a result of car accidents. Falling from heights with a landing on the feet, including parachuting, also often results in injuries to the ankle joint (AJ). Statistically, more than half of all lower limb injuries and about 40% of joint injuries are ankle injuries. We also know that 54% of ankle fractures and dislocations occur at a young age, when the ability to work is important. After an injury, there is a long process of treatment and rehabilitation, and after surgery, rehabilitation can be complicated by prolonged stiffness of the joint. In many countries, work is underway to develop devices and devices that allow for the post-traumatic rehabilitation of the individual using AJ passive mechanotherapy devices. This approach makes it possible to perform foot movements according to an individual rehabilitation program (IRP) set by the doctor. The FLEX-02, A3 Ankle CPM, Kinetec Breva ankle, and ARTROMOT SP3 are widespread [1,2,3].

At the same time, due to the influence of indefinitely variable parameters of the AJ muscular system, it is difficult to ensure the required accuracy of the patient’s foot movement along the trajectory set by the doctor, which reduces the effectiveness of the rehabilitation process. Therefore, the creation of such devices requires an in-depth study of the theory of human-device interaction, creation of man-machine interfaces, mathematical models, and control algorithms that provide the specified quality indicators. Thus, the issues of developing and creating robotic devices for post-traumatic ankle rehabilitation that provide a given movement of the foot under unpredictable changes in physiological parameters are relevant [4,5,6].

The aim of the study is to improve the effectiveness of the rehabilitation process with an active-passive mechanotherapy and rehabilitation device that provides a given precision through adaptive control of foot movement, taking into account the individual characteristics of the patient’s AJ.

2 Tasks of Ankle Rehabilitation

The main objectives of ankle rehabilitation during the recovery period:

  • reverse the processes of muscle atrophy and destructive changes in the vessels;

  • return mobility to the joint;

  • prevent stagnation of fluids in the reconstructed limb;

  • increase the motor activity of the joint.

In the early stages of rehabilitation, it is necessary to perform simple movements of the foot in small ranges at a slow pace. Movements such as plantar flexion and dorsiflexion as well as pronation and supination. The exercises are shown in Fig. 1. Once the rehabilitator has noticed an improvement in the ankle’s motor function, the range of motion can be gradually increased.

Fig. 1.
figure 1

Exercises for early rehabilitation.

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All therapeutic and rehabilitation measures are determined by the severity of the injury as well as the individual characteristics of the patient. After the cast is removed, it is important to put stress on the ankle joint gradually. The exercises are shown in Fig. 2.

Fig. 2.
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Exercises for the final stage of rehabilitation.

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In the final stage of recovery, you should start gradually combining these two movements by making circular movements with the foot. Also, continue to perform the operations described in the first phase, but with larger rotation angles until the ankle is able to perform the movements within the usual ranges of motion. The normal ranges of motion of the foot are shown in Fig. 3 [7, 8].

Fig. 3.
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Range of motion of the healthy ankle.

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3 The Circuit Diagram of the Active-Passive Mechanotherapy Device

The circuit diagram of the active-passive mechanotherapy device for the ankle, shown in Fig. 4, is a parallel manipulator equipped with linear actuators [9].

Fig. 4.
figure 4

Spatial kinematic diagram of the appliance.

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Figure 4 shows the following designations: 1 is the linear actuator 1 (l1); 2 is the linear actuator 2 (l2); 3 is the linear actuator 3 (l3); 4 is the controlled mobile platform; 5 is the patient’s foot; 6 is the platform in initial position; 7 is the virtual joint.

By changing the lengths of the actuators, it is possible to change the position of the controlled mobile platform (CMP) and consequently the patient’s foot. The structure of the device includes the patient’s foot, mobile platform, electric actuators, power frame sensors, control system. The electric actuators of the manipulator are connected to the body by means of joints A1, B1, C1. Actuators are connected to the platform by means of joints A, B, C. The joints A, B, C, A1, B1 are two-coordinate, while C1 is a single-coordinate joint, capable of changing its position in the sagittal plane [10, 11].

In order for the device to work correctly, the center of rotation of the CMP “virtual joint” O1, defined by the intersection of the joint axes (A, B, C), must be at the point O2 of the ankle joint center. During rehabilitation measures, point O2 remains stationary and all platform movements occur around this point. The radius vectors determining the position of points O1 and O2 must be equal \(\overline{r}_{o1} = \overline{r}_{o2}\). At the same time, under real-world conditions, there is a tolerance between the vectors, determined by the formula: \(\overline{r} = \overline{r}_{o1} - \overline{r}_{o2}\).

We will assume that the trajectories of the mobile platform points satisfying the condition \(\frac{{\left| {\Delta \overline{r}} \right|}}{{\left| {\overline{r}_{{O_{1} }} } \right|}} = \varepsilon \le 0.01\), are valid trajectories.

A parallel kinematics mechanism (PKM) [12, 13] is used to implement the “virtual hinge” of the platform and ensure the intersection of the mobile platform rotation axes in the center (tibia and talus contact zone) of the AJ, based on three linear actuators.

The ankle joint is formed by the tibia and talus bones. The articular surfaces of the lower leg bones and their ankles are encompassed by the Talus block in a fork-like fashion. The ankle joint is block-shaped. In this joint, flexion (movement towards the plantar surface of the foot) and extension (movement towards the rear surface of the foot) are possible around the transverse axis that runs through the talus block. The subtalar joint is responsible for pronation (rotation of the foot with the sole turning outwards) and supination (rotation of the foot with the sole turning inwards) of the foot. The human foot moves in three planes, the rotation around the vertical axis is caused by the rotation of the lower leg, therefore when working with active-passive mechanotherapy for ankle joint device (APMAJ) you should take this fact into account and not to fix the lower leg, otherwise you can get new injuries.

4 Diagrams for Measuring Leg and Platform Interaction Forces

The principle of operation of the force meter is based on monitoring the relative movement of the upper and lower module elements of the mobile platform at four points. The device has sensors that measure the force between the patient’s foot and the mobile platform at these points. In active mode the patient provides the foot movement and the APMAJ platform replicates this movement. Impedance control is used for this. The mobile platform is attached to the patient’s foot via a system of elastic connections, the drive platform is equipped with angle sensors and electrically controlled actuators and ensures a defined movement of the foot. When a relative movement of one platform with respect to the other occurs, a deformation of the elastic elements of the measuring device occurs, which is registered by the movement sensor [14,15,16].

During operation of the device, reaction forces from the platform arise between the patient’s foot and the platform. To account for these forces, it is necessary to introduce a model to describe the interactions between the foot and the platform [17].

The foot acts on the platform as a distributed load, so replace it with two concentrated forces. Assume that the foot is in contact with the platform by the heel and metatarsal bones, together they form a bony system, which is connected to the plantar side of the foot by muscular tissues. Figure 5 shows a diagram of the interaction of the foot and platform in the sagittal plane. The following symbols are included in the diagram: 1 is ankle joint; 2 is metatarsal bones; 3 is heel bone; 4 is tibia; 5 is platform; 6 is force-moment interaction sensors.

Fig. 5.
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Diagram of foot and platform interaction in the sagittal plane.

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Let’s write down the equation of moments for the patient’s foot in the sagittal plane:

$${J}_{bs}\ddot{\psi }={M}_{R}+M\left(G\right)-{M}_{C},$$
(1)

where: Jbs is the moment of inertia of the bone system;

MR is the moment created by the support reaction forces;

M(G) is the moment created by the gravity of the bone system;

MC is the resistance moment of leg muscles.

Let’s represent the muscle tissues as a Kelvin-Feugt model, with viscous and elastic components arranged in parallel. Given this, for sagittal plane, we will find forces R1, R2 by formulas:

$${R}_{1}={c}_{1}\left(\psi -{\psi }_{1}\right)+{\mu }_{1}\left(\dot{\psi }-{\dot{\psi }}_{1}\right),$$
(2)
$${R}_{2}={c}_{2}\left(\psi -{\psi }_{1}\right)+{\mu }_{2}\left(\dot{\psi }-{\dot{\psi }}_{1}\right),$$
(3)

where c is the reduced muscle stiffness coefficient;

μ is the reduced muscle viscosity coefficient;

\((\psi -{\psi }_{1})\) is the relative strain of muscle tissues;

\((\dot{\psi }-{\dot{\psi }}_{1})\) is the relative strain rate of the muscle tissues.

5 Functional Diagram of the Control System

The functional diagram of the APMAJ robotic device is shown in Fig. 6. The diagram consists of a hardware and software system, a physiological parameter monitoring unit, a rehabilitation program selection unit, a signal processing unit, a mobile platform, electric drives, amplifiers, a control unit, a sensor system for measuring linear and angular movements and reactions between the patient’s foot and the APMAJ mobile platform in the sagittal and frontal planes [18]. The choice of rehabilitation mode determines the program of movements of the patient’s foot, formalized in the form of parametric equations \( \overline{\lambda }(t)^{*} = (\phi (t)^{*} ,\theta (t)^{*} ,\psi (t)^{*} )^{T}\). If the conditions are met \(\overline{\lambda }(t)^{*} < \overline{\lambda }(t)_{0}^{*}\), where \(\overline{\lambda }(t)_{0}^{*}\) is the range of permissible rotation angles. The on-board computer (signal processing unit) solves the inverse kinematics task (IKT) and determines the length change laws of the linear actuators \( \bar{L}^{*} = (L^{*} _{1} ,{\text{L}}^{*} _{2} ,{\text{L}}^{*} _{3} )^{T} \).

Fig. 6.
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Functional diagram of the APMAJ robotic appliance.

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Further signals are proportional \( \overline{L}^{*} = (L^{*}_{1} {\text{, L}}^{*}_{2} {\text{, L}}^{*}_{3} )^{T}\) are fed to the appropriate comparison units (comparators), where they are compared with the real values \( \overline{L} = (L_{1} {\text{, L}}_{2} {\text{, L}}_{3} )^{T}\). The presence of feedbacks makes it possible to determine the deviation of the real position of the platform from the set position in the form of a vector Δλ and force interaction vector ΔP. The regulators receive an error value \( \Delta \bar{L} = (\Delta L_{1} ,\Delta L_{2} ,\Delta L_{3} )^{T} \) for each controlled variable. These values are converted by the control algorithm into control voltages \( \overline{U} = (U_{1} {\text{, U}}_{2} {\text{, U}}_{3} )^{T}\).

The force-moment sensing system makes it possible to evaluate changes in the reaction value over time and detect the moment of spastic effects, muscle contractures and automatically change the laws of foot movement in order to eliminate the patient’s trauma and pain syndrome. In accordance with the ACS diagram, the actuators are controlled to provide the specified movement of the patient’s foot. The feedback channels are the data recorded by the swing angle sensors on the respective axes, as well as the force-momentum sensor values. The LQR-optimization strategy is used to optimize the settings of the controllers to give the required quality performance of the APMAJ control system. If an abnormal situation occurs (reaction force limits are exceeded), the ACS algorithm allows you to change the exercise pace, perform the complex movements required for safe operation of the device and stop if necessary, thus ensuring safe patient rehabilitation [19].

6 Description of the Unit’s Operating Modes

The rehabilitation unit has several modes of operation. Before starting the rehabilitation procedure, the rehabilitation therapist must select the operating mode parameters, using a program on a personal computer. The operation of the device has been simulated in MATLAB/Simulink environment, information about the operation modes is presented below.

Plantar - Dorsiflexion. This robotic mode allows a rotational movement of the patient’s foot in the sagittal plane. The range of rotation angle is 42° ≤ ψ ≤ 23°. The results of the simulation mode are shown in Fig. 7.

Fig. 7.
figure 7

Mode of operation - plantar – dorsiflexion.

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Pronation - supination. This mode of operation allows a rotational movement of the patient’s foot in the frontal plane. The range of rotation angle is 40° ≤ φ ≤ 40°. The results of the simulation are shown in Fig. 8.

Fig. 8.
figure 8

Mode of operation - Pronation – supination.

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Any rehabilitation mode should be set according to the recommendations of the rehabilitation therapist. In this mode, the person’s foot can perform both combined and circular movements of the foot. The mode chosen by the user can include changing direction, speed of movement and number of repetitions (Fig. 9).

Fig. 9.
figure 9

User-configured operating mode.

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The effectiveness of rehabilitation interventions depends largely on factors such as gender, age, duration of disability, educational level, and occupational affiliation of the patient. The Barthel and Rankin scales record the condition without offering the patient understandable benchmarks for the dynamics of the rehabilitation process, do not allow for accessible formulation of rehabilitation goals and motivation of the patient. Thus, these scales are appropriate for a screening assessment of the overall rehabilitation process. RMI, HAI and the KX test are recognized as informative techniques that are sensitive to changes in the patient’s condition in relation to both muscle function and functioning. The clarity of objectives and graded assessment allows rehabilitation goals to be formulated in an accessible format, which increases patient motivation and satisfaction with treatment.

It is important to correctly determine the predicted end result of rehabilitation in each individual case, as this is the basis for the subsequent comprehensive assessment of the effectiveness of rehabilitation.

At the same time, objective and informative criteria for the effectiveness of medical rehabilitation in various forms of occupational diseases have not been sufficiently developed and put into practice today. Meanwhile, data from domestic and foreign sources show that the levels of rehabilitation indicators are closely interrelated with the indicators of disability, mortality, morbidity, organization and quality of medical care and are directly related to qualitative and quantitative criteria that characterize public health.

7 Conclusion

On the basis of the research carried out in the article, the following scientific and practical results have been obtained:

  • Computational schemes have been given, on the basis of which mathematical models describing kinematic and dynamic interactions of the device and the patient’s leg have been constructed.

  • The functional diagram of the device reflecting the structure of automatic control system is given and described.

  • The operating modes of the device are described.

A prototype device is under development.