Study of a Passive Orthosis for Reducing the Load Transfer in the Hip Joint

Abstract

There are several orthoses that allow for the assistance of movement on the lower limbs, mainly flexion–extension. However, there is still a lack of systems that allow, in addition to assisting movement, for transferring the load from weakened anatomical parts to physically healthy joints. A model of a passive and light orthosis that is capable of transferring part of the load from the hip joint directly to the body of the femur was developed and tested. This helps to attenuate the longitudinal component of the force, thus reducing pain and the patient’s discomfort. Computer-aided design (CAD) models and numerical studies were conducted using an offline model of the hip forces, and a proof-of-concept prototype was also developed for experimental validation. The model uses a rigid ergonomic structure and an elastic energy-accumulating device, in this case, a spring, whose preload can be regulated for controlling the assistance’s level. The numeric simulations demonstrated the adequacy of the model for a spring pre-load of 20% of the force applied to the femoral head, reducing the load in the hip joint. The hypothesis of the present study, that the orthosis can reduce the reaction load on the hip joint, was validated by the computational model developed and by the preliminary experimental results obtained with the concept prototype. The approached model represents a promising starting point for subsequent studies and progression for the practical and clinical field.

1. Introduction

Population ageing is one of the most critical challenges in the near future, characterized by a low birth rate and a long life expectation, especially in industrialized societies. In 40 years from now, nearly 35% of the European population will be over 60 years old, resulting in the urgency to provide solutions that allow our ageing society to remain active, creative, productive, and independent [1]. When the hip joint is damaged by arthritis, fractures, or other problems associated with ageing or an accident, some common daily activities, such as walking, sitting, or climbing stairs, become limited and quite painful for the patient. One of the ultimate solutions is an arthroplasty, which aims to replace, remodel, or realign this joint to relieve pain and restore mobility and functional capacity, and hip total arthroplasties are growing in Europe [2]. Nevertheless, with advancing age, bone osteolysis could incite a new joint replacement, which might be a risky procedure for elderly people [3].

Among all the existing assistive devices, wearable orthosis can be used to either augment, train, or supplement human motor function [4], being generally anthropomorphic and prepared to be comfortably worn by its user. Examples of such robots are exoskeleton upper limbs [5,6], bionic prostheses, exosuits, and body-worn collaborative robots [7,8].

These systems are mainly developed for four specific targeted ends. The first application focuses on rehabilitation, helping patients with mobility disorders in the rehabilitation of musculoskeletal strength and motor control [9,10]. The second application consists of human motor assistance, which is targeted for paralyzed patients who have lost (or never had) their motor and sensor functions [1,11]. The third is aimed at enhancing the physical abilities of able-bodied humans [12,13]. Lastly, in industrial production scenarios, the use of passive orthosis in a production line allows employees to adopt a healthy posture, thereby avoiding injuries resulting from repetitive actions and therefore reducing physical wear and tear and increasing production speed [14,15].

An active orthosis uses a source of electrical energy and, through a control system and actuators, converts it into mechanical energy in order to produce moments and, consequently, movement [16,17,18,19]. Current active actuators (electric, hydraulic, and pneumatic actuators) can cumulatively meet the requirements of orthoses, but individually, they have serious limitations that make orthoses bulky, rigid, and impractical as wearable devices [20].

On the other hand, passive orthosis does not use any source of electrical energy. Instead, they use elastic or viscous components and actuators, allowing for:

• Weight redistribution: several mechanisms, such as articulated springs with hard materials, for example, allow the load transfer between the user’s anatomical components or even to the ground, in order to mitigate the effect of the trunk and upper limbs’ gravity;
• Energy capture: spring-clutch and spring-dynamo systems allow for improving gait efficiency;
• Damping: systems with springs and dampers allow for reducing the vibrations due to radical activities;
• Fixation and support: some passive systems are developed to allow the user to maintain a certain working position and reduce their associated effort for long periods of time [21].

An elastic actuator is a flexible object capable of storing potential elastic energy. Typically, springs or other elastic materials are used to apply forces to passive exoskeletons, whereas springs in series with electric motors are used on enhanced semi-active exoskeletons [22,23].

The existing passive exoskeletons, which use elastic elements in parallel with the lower limbs, may allow for supporting part of the bodyweight to which the joints are subjected, storing and redistributing energy along the limb. Several passive models have been developed [24,25]. However, as to the best of our knowledge, one of the biggest practical gaps found in the literature, which inspired the purpose of this work, is the transfer of load at the hip joint. This problematic proves not to be the main objective in the development of current systems, as they seek more assistance to the movement or rehabilitation of muscular functions than to support body mass.

The present study aims to develop a new concept of passive orthosis that allows for a reduction in the hip joint loads. The concept was initially developed with a mathematical model of the orthosis and later validated with a physical prototype. The results show that it is possible to reduce the reaction of the hip joint, thus allowing for alleviation of the pain in the articulation suffering of a generic pathology.

2. Materials and Methods

2.1. Definition of Concept

According to Nikooyan et al. [26], the human body can be approached, in various daily activities, like a passive mass-spring-damper (MSD) model, as shown in Figure 1a). In this sense, it was intended to develop a system capable of complementing the simple hip model with an external spring system with an elastic constant k_ex that exerts a force F_e,ex. In the model proposed for the hip joint (Figure 1b), m represents the mass corresponding to the weight applied to the hip joint, which exerts a force F_h and undergoes a Z displacement, F_e corresponds to the force applied to the hip by the MSD model’s spring, where K_hip is the spring elastic constant, and F_d is the force applied by the MSD model’s damper, where C_hip is the shock absorber constant.

In this simple model, the knee joint is considered an extension of the ground, so it is therefore treated as a fixed border point. Thus, in the one-dimensional MSD model, it is described by:

$$F_{res}=F_h-F_e-F_d-F_{e,ex}$$

(1)

$$\iff m\ddot{z}=F_h-k_{hip}z-c_{hip}\dot{z}-k_{ex}z$$

(2)

$$\iff \ddot{z}=\frac{1}{m}\left[F_h-c_{hip}\dot{z}-(k_{ex}+k_{hip}\right)z]$$

(3)

Thus, we hypothesize that the addition of an external compensating elastic element, in this case the exoskeleton spring, will contribute to a reduction in the spring and dumping force of the simple MSD model of the hip joint.

In a two-dimensional model, we start by analysing the situation where the point of rotation of the exoskeleton is precisely over the hip joint. In this case, in the stance phase of the gait cycle, one can assume a capable and healthy knee joint as an extension of the ground and, as such, consider it a fixed point. Thus, the exoskeleton will be able to transfer part of the load from the hip joint to the knee joint with the application of an elastic force (preload) that counteracts the body weight (Figure 2a). On the other hand, in the swing phase, the foot is not in contact with the ground, and, therefore, the knee joint can no longer be considered a fixed point. Thereover, the direction of the force will reverse, as shown in Figure 2b.

Therefore, the system is aimed to present a dual behavior. In the stance phase, the spring is able to apply a force that counteracts the body weight, and, in the swing phase, the spring applies virtually zero force. This behavior can be achieved by placing the exoskeleton rotation point below the hip rotation point, although it will be always a difficult task to determine the hip joint center. In this situation, we also hypothesize that the radius of curvature of the exoskeleton would be smaller than the radius of rotation of the thigh, causing the spring to stretch in the swing phase and thus attenuate the applied force, as demonstrated in Figure 3. Determining the center of hip rotation will always be a difficult task in daily activities. One possibility is using a pelvic radiograph, as proposed [27], to identify the highest point of the iliac bone (upper pelvic line) and the distance to the center of the hip joint. Another approximate method would be to place the system on the patient and check when the spring has zero deformation. This point will be the center of rotation.

2.2. Mathematical Model

Taking into account the dual behavior of the system (Figure 2), it becomes necessary to calculate the spring elongation as a function of the angular displacement of the thigh, θ. Considering the center of rotation of the hip joint as the origin, we have the position of the center of rotation of the exoskeleton, C(0, h), and the arbitrary point in the radius of the circumference of the thigh rotation, P$\left(x,z\right)$: $y^2+z^2=L^2$.

Calculating the distance between C and P, we have:

$$d\left(y_p,z_p\right)=\sqrt{{\left(y_c-y_p\right)}^2+{\left(z_c-z_p\right)}^2}=\sqrt{y_p^2+{\left(h-z_p\right)}^2}$$

(4)

In polar coordinates, with the variable change

$$\{\begin{array}{c}{y}_p=L·sin\left(\theta \right)\\ z_p=L·cos\left(\theta \right)\end{array}$$

We obtain:

$$d\left(\theta \right)=\sqrt{L^2+h^2-2hL\cos \left(\theta \right)}$$

(5)

Therefore, it becomes possible to calculate the spring elongation as a function of the angular displacement of the thigh, ${\displaystyle \Delta }r\left(\theta \right)$:

$${\displaystyle \Delta }r\left(\theta \right)=\mathrm{d}\left(\theta \right)-\left(L-h\right)=\sqrt{L^2+h^2-2hL\cos \theta }-L+h$$

(6)

Then, the elastic force exerted by the spring can be calculated:

$$\overrightarrow{F_e}=\left[-\kappa \left(\sqrt{L^2+h^2-2hL\cos \theta -L+h}\right)+PL\right]·\widehat{e_d}$$

(7)

where k is the spring elastic constant, PL the applied preload, and $\widehat{e_d}$ is the longitudinal unit vector. Knowing that:

$$L·\cos \left(\theta \right)=\mathrm{d}\left(\theta \right)\cdot \cos (\varnothing )+h$$

(8)

$$\cos (\varnothing )=\frac{L·\cos \left(\theta \right)-h}{d\left(\theta \right)} ,$$

(9)

Equation (7) can be rewritten as:

$$\overrightarrow{F_{ez}}\left(\theta \right)=\left[-\kappa \left(\sqrt{L^2+h^2-2hL\cos \left(\theta \right)-L+h}\right)+PL\right]·\frac{L·\cos \left(\theta \right)-h}{d\left(\theta \right)} \widehat{e_z}$$

(10)

2.3. Numerical Model

Data from the OrthoLoad–Loading of Orthopaedic Implants provide the components of force $(F_x,F_y$, $F_z)$ applied to the hip joint of a 64-kg-body-mass individual, who underwent arthroplasty, during the gait cycle at a constant speed of 2 km/h. Then, it was possible to approximate the cosine of the instantaneous angular displacement of the thigh,$\cos \left(\theta \right)$, from the internal product of the projection of the force applied to the joint on the YoZ plane and the vector $\widehat{e_z}$:

$$\cos \left(\theta \right)=\frac{F_z}{\sqrt{F_y^2+F_z^2}}$$

(11)

In this sense, it is appropriate to study the effect of choosing the spring constant, k, and the distance between the hip joint and the point of rotation of the exoskeleton, h, in the gait cycle. Therefore, using the MATLAB^® R2018b software package and the hip force’s model given by Equations (10) and (11), the spring preload (PL) was defined at 20% of the triple of the body weight and the radius of rotation of the thigh (L) at 400 mm (thigh size). Then, in the first place, the distance h was defined as 100 mm, considering an exact point of rotation, and the behaviour of the system was studied for various values of k. The value of h was considered as a first approach for the preliminary study and was based on a suitable value to the human anatomy and the system requirements in order to attenuate the force applied to the hip. Second, the constant k was defined at 5 N/mm, and the behaviour of the system was studied for various values of h. The choice of the PL, k, and h values relied on an estimation of the force, spring constant, and distance that would be sufficient to attenuate a patient’s pain without added discomfort. Other value combinations may be further studied in the future.

2.4. CAD Experimental Model

In order to adapt the 2D sketch to human anatomy, a 3D CAD model of the exoskeleton system were developed as represented in Figure 4 in a Solidworks CAD design tool. It consists of a belt (7), a gaiter (5), and two pieces (3 and 8) sewn to the belt and gaiter. These can be screwed to two other parts (9 and 10), allowing for an adjustment of the height of both rotation points (1 and 6) of the exoskeleton. At that point (6), a threaded rod (4) is attached to guide the spring (2) of the exoskeleton as well as to regulate the preload applied to it. Finally, the terminal area of the spring (1), next to the gaiter, is a movable point, thus allowing for the extension of the spring in flexion and extension movements.

2.5. Experimental Model

A one-leg physical prototype for experimental validation was also developed (Figure 5). Hip and thigh parts were made by 3D printing in PLA (polylactic acid), and the support adjustable bars were machined in aluminium. Finally, the rest of the pieces are a threaded rod made of zinc-plated steel, a 60 mm-length spring, threads, and washers (not identified in Figure 4).

To evaluate the spring stiffness, tests in a 10 kN machine (Shimadzu AGS-X 10 kN) were performed at a speed of 1 mm/s up to 50% of the base spring length, and an elastic spring constant of $k=4.1\pm 0.1\mathrm{N}/\mathrm{mm}$ was measured after 10 trials.

A first experimental test was carried out using the developed prototype. A 91-kg-body-mass (BW), healthy male subject 183-cm-high wore the exoskeleton prototype and performed a normal gait along a straight path. By measuring the spring elongation using a displacement sensor (M12 ultrasonic sensor, model nano 15/CU, from Microsonic, Dortmund, Germany) and knowing its constant k, it was possible to measure the force exerted by the exoskeleton and, consequently, the model’s adequacy. The difficulty of determining the hip joint contact center was observed. To manage this drawback, some trials were carried out to determine the neutral position in rotation without spring force.

3. Results

The results of experimental and numerical models are presented and analysed in the next sections.

3.1. Numerical Model Results

The results of the numeric model (distance h was defined as 100 mm) show the behaviour of the studied system for various values of k. These are represented in Figure 6 for the different stiffnesses of the spring. The data are reported as averages across all gait cycles (solid line) with the correspondent point-to-point standard deviations (shaded area).

Based on the obtained graphics, it is possible to observe that the system effectively presents a dual behaviour, which severely depends on the spring constant k. For smaller values of k, 5 N/mm for instance, the results show a slightly minor decrease in the force applied by the exoskeleton to the hip joint on the swing phase. Although the system allows for a reduction in the force applied to the joint during the gait cycle, it starts to have a negative effect during the swing phase with a symmetrical force of around 0.2%BW. Nevertheless, for greater values of k, near 20 N/mm, an effective dual behaviour can be observed during the gait cycle owing to the effective reduction of the force applied by the exoskeleton on the swing phase, around 85% and 95% of the gait cycle, which leads the force applied to the hip joint to be similar to the case in which the orthosis is not worn, near 0.2%BW.

On the other hand, the results in which the constant k was defined at 5 N/mm and the behaviour of the system was studied for various values of h are shown in Figure 7. The data are also reported as averages across all gait cycles (solid line) with the correspondent point-to-point standard deviations (shaded area).

3.2. Experimental Results

Subsequently, the preliminary experimental results using the concept prototype, represented in Figure 8, validate the numerical model. By measuring the spring elongation, it was possible to infer the force exerted by the exoskeleton.

Therefore, it is possible to verify an oscillatory behaviour with a loss in the force exerted by the spring on the swing phase to values around 0.25%BW, which directly relates to a dual behaviour during the gait cycle in which the exoskeleton shall only have an effect during the stance phase.

4. Discussion

When the hip joint becomes damaged, some common daily activities might become limited and painful for the individual due to the application of heavy loads on the wrecked surfaces. For many of these cases, an arthroplasty is presented as a reliable solution, but the load on the hip joint is a key factor for hip joint arthroplasty success [28,29]; however, this procedure might be risky, mainly for revisions or on the elderly [3]. In this case, it is important to develop novel solutions that may be presented as an alternative to the procedure and allow for answering the problem of returning life standards to those people.

The presented model allows for a reduction in the load on the hip joint by transferring the load between the upper body and the knee joint, bypassing part of the upper body weight through a passive exoskeleton. For this purpose, a pre-load of PL is applied to the spring of the exoskeleton, allowing for the redistribution of the forces through the exoskeleton, thus easing the load applied in the hip joint.

Moreover, it was intended that the exoskeleton only presented influence and assistance during the stance phase of the gait cycle, when the higher longitudinal force, responsible for the subject’s discomfort, is observed. To settle this, we placed the exoskeleton’s rotation point below the hip’s rotation point, so the radius of curvature of the exoskeleton would be smaller than the radius of rotation of the thigh, causing the spring to stretch in the swing phase, then attenuating the force applied, as demonstrated in Figure 3.

In order to study the applicability and accuracy of the mathematical model regarding the choice and the influence of the spring constant, k, and the distance between the exoskeleton and hip rotation points, h, numerical studies were achieved. As seen in Figure 6, it can be concluded that the exoskeleton is capable of effectively reducing the maximum longitudinal force applied to the femoral head and presenting a dual behaviour along the gait cycle. This is because the spring constant allows for attenuating the action of the system essentially during the swing phase, when the spring elongates, and gives effective support during the stance phase, when the spring is fully loaded. Results show that, for different values of the spring constant and for a k that is too small, the spring elongation is not enough to cancel the elastic force, showing a small effect. On the other hand, for a k that is too high, the spring force begins to form an unstable equilibrium peak in the swing phase, although the peak of the force applied to the hip joint when using the exoskeleton is similar to the case in which the orthosis is not worn.

Moreover, confronting various values of the distance h from the interval that we consider anatomically adaptable, i.e., 0 mm to 150 mm, for the same k, it was possible to conclude that the distance h also allows for the regulation of the system’s action, essentially in the swing phase, although not as effectively as the variation in the spring constant, as demonstrated in Figure 7. For instance, with h = 0 and as expected, the exoskeleton is unable to present the intended dual behavior, since the radius of rotation of the thigh was theoretically the same. Therefore, for a smaller value of h, the spring effect was not sufficiently attenuated, whereas for a larger value, the spring force also begins to form an unstable equilibrium peak in the swing phase, though it demonstrated a greater attenuation.

Finally, the preliminary experimental study results, shown in Figure 8, validated the mathematical model, as it was possible to verify an oscillatory behaviour with a loss in the force exerted by the exoskeleton on the swing phase of the gait cycle, which directly relates to a dual behaviour during the gait cycle in which the exoskeleton shall only have an effect during the stance phase.

The existing passive exoskeletons allow for supporting the joints, storing and redistributing energy along the limbs, thus being conceived as a functional extension of the organism. Several passive models have been developed for this purpose, such as the models from Alamdari et al. [16], the passive lower limb exoskeleton from Van Dijk et al. [30] or the system from Yang et al. [31]. However, none of these systems offers a resolution to the presented problem, i.e., a reduction in the load on a pathological hip joint. This key problem proves not to be the main objective in the development of current systems, as they seek more movement assistance and rehabilitation of muscular functions that support body mass to reduce the discomfort and pain of more prone subjects. Therefore, in the present work, the approached model represents a promising starting point for an effective solution as a load-transfer daily wearable device.

5. Pending Studies and Future Work

Despite the obtained results of this preliminary study, the system and the model have shown their own drawbacks. First of all, in the transition between the stance and swing phases, the exoskeleton appears to have a clear hindrance effect on the wearer, i.e., the force exerted by the exoskeleton’s spring counteracts the force exerted by the muscles to generate movement. This is because the spring is being loaded during this transition as it regains its initial potential energy. As a matter of fact, this may only imply a greater metabolic cost for a healthy user; however, on a patient with a weakened hip joint or bone structure, this will create a larger joint reaction force and moment on the femoral neck and head. Moreover, the releasing of the spring during the transition of the stance to the swing phase may lead to an excessive distraction force in the hip joint.

In addition, the knee joint is considered to be an extension of the ground on a simple mass-spring-dumper model in which the center of rotation can be precisely located, and it is assumed that any force applied to this joint would be transmitted directly to a fixed border without any displacement, a healthy knee in this case. However, this approach may not be valid in all daily activities, and, moreover, this joint may be overloaded due to the pre-load applied to the spring, especially during the swing phase.

Finally, the gaiter used was not able to withstand the load applied to it since, within a short time of use of the exoskeleton, the friction between this one and the clothing was not enough to keep it fixed on the thigh.

Regarding the stated limitations, as future work, our group intends to develop a better physical prototype and to lead further experimental studies capable of measuring the experimental dependency of k and h values on a larger sample of subjects. Moreover, we also aim to study the feasibility of the model on individuals who rely on upper-body supports such as armrests, crutches, or grab bars, which also allow for a load transfer directly to the ground. Furthermore, we are also looking forward to evaluating the feasibility of applying active or series elastic actuators in the system to control its stability and balance, as well as to compensate for the unwanted moments generated by the spring in the transitions between gait phases. These adaptations will maintain the desired goal of supporting body mass with an exoskeleton while reducing the user’s metabolic effort and risk of fracture or displacement of the hip joint.

6. Conclusions

This study aimed to conceive an exoskeleton model for load transfer in the hip joint. In this sense, the development of this model was based on a mathematical study of its dual behaviour whose dependencies on the variables in question were studied. Furthermore, a design of a computational model, a 3D CAD model, and a prototype exoskeleton were developed. Numerical studies showed the sustainability of the model for a 20% reduction in the load applied to the hip joint in the stance phase of the gait cycle. Although preliminary experimental procedures validated the model, it was stated that the force exerted by the exoskeleton counteracts the movement in the transition between the stance and swing phases, which may imply greater metabolic cost to the user.