Theoretical Analysis of the Mechanical Performance of Implantable Devices Used in the Treatment of Vertebral Compression Fractures (Kyphoplasty, SpineJack, Tri-Blade) and a Proposal of a Two-Arm Device with Increased Performance

Abstract

In this study, an analysis of the behavior of the vertebra during the use of KP and SJ was carried out to understand the kinematics of the movement of the fragments of the vertebra during action and the forces generated in the use of the two methods. For this analysis, the results published by various authors were used. Only the principle of the mechanical actuation of the vertebra fragments was analyzed, without addressing other aspects such as the method of cement introduction, the type of cement used, PMMA hardening times, the duration of the operation, the patient’s recovery time, etc. In addition to the analysis, the authors propose a device that eliminates the inconveniences observed in the two analyzed devices and promises to significantly improve the restoration of the vertebra’s height and, consequently, the patient’s symptoms. The observations show that the type of mechanism articulated at one end has both robustness and greater efficiency in this type of actuation. It is further shown that from this category, the mechanism with two arms (Two-Arm Device) proposed by the authors is superior to the existing ones in terms of robustness and efficiency. The perspectives of TAD are represented by the improvement of the vertebral statics and, consequently, the symptoms of the patients.

1. Introduction

A vertebral compression fracture (VCF) is a subsidence of a vertebra, a subsidence that occurs in the anterior part of the vertebral body. Radiologically, the vertebrae take on a cuneiform appearance.

Since two-thirds of the anterior column of the spine supports three-quarters of the body’s weight, a compression fracture of the vertebra involves the compression of the anterior body with the preservation of the posterior vertebral wall and the posterior elements of the vertebra.

Fractures predominantly occur at the T12–L1 level and, to a lesser extent, at the T7–T8 vertebrae. The risk of subsequent fracture increases by 5–10 times once the first osteoporotic fracture occurs.

Most compression fractures of the spine result from primary (age-related) or secondary (drug-related) osteoporosis (a reduction in bone mass and a deterioration of the micro-architecture of bone tissue that increases its fragility).

For these patients with osteoporosis, low-intensity stress on the spine generated by daily activities, minor trauma, can lead to a vertebral compression fracture [1]. Also, some malignant diseases (cancer) can be another cause of this type of fracture, as well as some traumas.

The treatment of VCFs has seen rapid progress in recent years. Starting from conservative, noninvasive methods (based on prescribed drug treatment, bed rest, medical recovery procedures, etc.), we switched to minimally invasive, percutaneous methods, of which their primary action is the injection of cement into the body of the vertebra (vertebroplasty, 1984 and kyphoplasty, 1998). In the last 15 years, combined treatment methods using implants and cement have appeared for the treatment of VCFs.

The percutaneous treatment of VCFs began with Pierre Galibert’s method of treating vertebral angiomas [1]. These results led to using vertebroplasty to treat this type of fracture. After some time, a new method appeared, namely, kyphoplasty [1,2], with derived variants [3]. The results were compared to those of the previous percutaneous treatment method, vertebroplasty. After another period, combined treatment methods appeared [4], which included implants and cement, such as SpineJack (SJ) [5], the Osseofix^® Spinal System [6], and the Kiva VCF System [7]. These new methods’ performances were also compared against the performance of the previous one, namely, kyphoplasty (KP) [8,9,10,11,12]. Until now, both KP and SJ have proven their effectiveness in treating VCFs both in terms of restoring vertebral height and of alleviating patient symptoms.

Given the spread of their use and the demonstrated results, the KP and SJ methods can be considered references in VCF treatment. Thus, it is natural that any new method that may appear should have its results measured against those of these reference methods.

Below are brief descriptions of the two methods:

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Kyphoplasty consists of inserting a balloon into the body of the vertebra, inflating it, and creating a cavity by moving the bone fragments to their original position or by yielding the cancellous bone tissue (especially if the cause of the fracture is osteoporosis); the cavity is formed in a somewhat random fashion, following the principle of least resistance against the pressure inside the balloon. The resulting cavity is filled with cement [1];

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the procedure using the SpineJack system promises to restore the height of the vertebra “like never before” by inserting an expandable implant into the body of the vertebra (very similar to a car jack), which in turn creates a cavity, following the expansion action of the two arms for pushing the two bony plates of the vertebra to the initial position; this time, the cavity is created as a result of the mechanical action, in a controlled direction (up–down), given the orientation of the implant [5].

2. Materials and Methods

For the analysis, the information presented in various studies carried out by different authors, at various time intervals, in different places, and obviously on different patients with spinal disorders at various levels was used. Results from cadaver or animal studies were also used.

The figures with the radiological images from the specialized papers were analyzed for the treated vertebras. They were presented as evidence of the research of the authors of the respective articles.

The deformation of the SpineJack implant used for repositioning bone fragments was then analyzed.

Additionally, the shapes of the cavities created using the kyphoplasty method were examined when attempting to reposition bone fragments or reinforce the vertebral body.

3. Results

How bone fragments move when using the KP or the SJ system has been examined.

Subsequently, an analysis was conducted on how another system, distinct from SJ but with two potential variants, operates. A comparative study was performed for these two variants, highlighting certain advantages of one of them.

3.1. Analysis of the Mode of Action of the SJ and KP

Suppose it is only desired to strengthen the weakened (demineralized) structure of the vertebra without moving the bone fragments. In the case of using the SJ system, it can be observed that the pushing soles of the implant remain approximately parallel.

If, however, an attempt is made to restore the height of the vertebra, it is observed that, after the introduction of the expansion element (SpineJack or balloon) and its operation, to create the cavity to restore this height, a cavity is produced in the body of the vertebra (as seen from the sagittal view) with a quite pronounced conical shape. These cavities were created both due to the damage to the internal bone structure (under the mechanical action of the balloon or the implant) and due to the displacement of the upper and lower plates of the vertebra. In analyzing the shapes of the cavities obtained, it can be seen that they have larger openings toward the anterior part of the vertebra.

In the case of SJ, it can be seen from the moment that the device is opened that its soles tend to act uniformly on the fragment from the top and the bottom due to the constructive parallelism. However, in the end, these soles lose their parallelism and end up in inclined positions with a pronounced conical shape, as shown in Figure 1. This aspect is easily observable in works [13,14,15,16,17,18].

The same is observed in the case of KP, as shown in Figure 2. Since there is pneumatic action, the pressure in the balloon is constant, generating equal pushing forces through the balloon’s walls in all directions.

When only the reinforcement of the vertebra is desired (for cases of a nonmobile fracture), the shape of the balloon is approximately symmetrical along its length. Thus, the resulting cavity has a relatively constant height when viewed from the side, as shown in Figure 2.

Sometimes, bone fragment displacement is desired in mobile fractures. In the end, the creation of a cavity with a variable opening can also be observed.

In other words, under the action of a relatively evenly distributed force toward the surfaces of the two plates (upper and lower) of the fractured vertebra, they do not move linearly but (as expected) have a rotational movement (the opposite of the one produced at the time of fracture). This can be observed in works [19,20,21,22,23,24,25].

Kinematically, it seems that during the restoration of its shape (height), the vertebra behaves like a joint with free ends toward the anterior part and the point of rotation somewhere in the posterior area of the vertebral body. This explains the more significant displacement in the anterior part of the vertebral plates.

In both cases (SJ or KP), part of the energy (the force developed by the system) is dissipated in the entrance area of the SJ or the balloon. In this portion, where the cavity created has a shape with small dimensions, close to the diameter of the hole made to access the body of the vertebra, practically, the pushing forces, no matter how great, do not produce significant displacements from a geometric point of view or with an anatomical effect. Thus, we conclude that the strength requirement is in the anterior part of the vertebra, namely, in the collapsed area, not in the posterior, intact area. However, both systems act both on the areas affected by the fracture that must be moved and on the unbroken (non-fractured) area that does not require movement.

This fact suggests that to effectively use the energy used to push the two plateaus of the fractured vertebra in the cranio–caudal direction, it is helpful to use a method to move them in the portion near the anterior edges, as far as it is acceptable from the “rotation point”.

A solution would be to use a mechanism made up of jointed arms that have little or no movement at one end (the one from the back, at the entrance to the hole made for inserting the implant) and maximum movement (16 mm) at the opposite end, toward the front, as indicated in Figure 3.

3.2. Analysis of the Actions of Some Mechanisms Articulated at One End on the Vertebral Fragments

Starting from specific proposals, namely, those used for the implantation of a mechanism with arms that can be extended only at one end, we carried out a comparative analysis between a solution that involves using an extensible mechanism made up of three arms that can be extended at one end and jointed at the other (named Tri-blade and presented schematically in Figure 4) [26] and another solution that involves using a mechanism with two jointed arms at one end and that is extendable at the other, the Two-Arm Device (TAD) illustrated in Figure 5.

In both situations, the arms are obtained by dividing the circular crown into three and two sectors, respectively. In the version with three arms, they can be divided identically or with different sections by varying the angle at the center. In the version with two arms, they are obtained by dividing the circular crown from which they originate equally.

In the following, an analysis of the loads of the two mechanisms will be presented in the first part, followed by an analysis of the most sensitive element of the mechanism and a method of improving the performance of this type of mechanism.

3.2.1. Comparative Analysis of the Loads of the Three- and Two-Arm Mechanisms Jointed at One End

Loads of the Three-Arm Mechanism

The three arms can be arranged symmetrically or asymmetrically relative to the axis.

We are not currently discussing aspects related to the practical possibilities of orienting the implant for its correct positioning in the vertebra’s body. We only analyzed the mechanism’s mechanical and kinematic elements.

We will start with a simplified scheme to understand what happens during the mechanism’s operation, as shown in Figure 6.

After inserting the implant, it can be oriented in two characteristic positions:

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The situation in which one of the three arms is in contact with one of the plates (den) of the vertebra and the other two will also be (both) in contact with the other plate (den) of the vertebra so that the entire force used is developed by the mechanism, as presented in Figure 6a;

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the situation in which not all three arms are in contact with the plates (den) of the vertebra, but one is in contact with a plate, and of the two remaining, only one pushes into the other plate, with the other relaxing and pushing to the side, depending on the angle between the arms, as shown in Figure 6b.

The second situation, where all three arms do not work, is undesirable and considered an incorrect operation. Thus, it was not analyzed (the reasons are obvious: instability during expansion, risk of damage to the vertebra through lateral thrust, etc.).

The first situation involves applying the three arms according to the loading scheme presented in Figure 7. For the simplicity of the analysis, the ideal situation is considered when the device is positioned symmetrically with respect to the cranio–caudal axis.

In using F to denote the force required to move the bone fragments through the associated plate, the force F acts on arm 1. The force F is transmitted to the two arms through the other plate. Due to the calculation assumption (that of the considered symmetry), each arm that comes into contact with this plate receives force F/2. As can be seen, one of the arms is subjected to the full force F, making it the most vulnerable in terms of loading. This is subjected to the bending request generated by force F. At the same time, for the other two arms, although they are each loaded with only half of the force to be developed, due to the action of this force at a certain angle on the arm, in addition to the bending request, these two arms are also subjected to a torsional moment, namely a compound request for each of them.

Obviously, the demand of each arm becomes more complex if all existing demands specific to the assembly are considered (interaction with the other elements, friction between the components of the mechanism, friction with the tissue, etc.).

The resistance of the entire mechanism is given by the resistance of the weakest element (the one that gives way first). This is why a solution can be obtained constructively and/or kinematically to balance the stress on the three arms.

Loads of Two-Arm Mechanism

The loading scheme for only two arms existing is shown in Figure 8. The two arms are identical. Only the situation in which the mechanism is correctly positioned is considered, when each arm comes into contact with one plate and acts in the (cranio–caudal) direction.

It is observed that each arm is subjected to the same force value, F. In considering the direction of the force, it is noted that both arms are subjected to bending.

First Key Finding

In comparing the two solutions and analyzing the arms subjected to a stress of force F, it can be seen that the arm in the solution with two arms has a more robust structure, and therefore, the value of the stress to which it can be subjected will be higher, as shown in Figure 9.

3.2.2. Analysis of Arm Action (Lever Loading)

Since the lever from Figure 10 is the element in the system on which both the external load (F) and the actuation transmitted through the piston act, the loading of this lever was analyzed in particular.

For this, a lever is isolated; it will be loaded with the stresses to which it is subjected, and both the forces that will be transmitted to the rod and the one that acts along the lever, i.e., the force that stresses the lever in compression, are determined.

The arm tilt angle $\beta$ in the initial position is 0, as depicted in Figure 11.

The upper end of a lever is considered to be acted upon by the force required by the mechanism denoted by F (the load). We noted the reactions in the two joints with $R_1$ and $R_2$. Let $F_{\mathrm{as}}$ be the axial force that will act on the rod and that is distributed evenly on the two levers. This results in $F_{\mathrm{as}}$/2. We use l to denote the calculated length of the lever and $\alpha$, the angle made by the lever with the horizontal axis.

Writing the equilibrium equations for the lever, we have

$$R_1=\frac{F_{\mathrm{as}}}{2}$$

(1)

$$R_2=F$$

(2)

$$F · l ·cos\left(\alpha \right)=R_1 · l ·sin\left(\alpha \right)$$

(3)

Also, by solving the above system, we obtain

$$F · l ·cos\left(\alpha \right)=\frac{F_{\mathrm{as}}}{2} · l ·sin\left(\alpha \right)\Rightarrow 2 · F ·cos\left(\alpha \right)=F_{\mathrm{as}} ·sin\left(\alpha \right)\Rightarrow F_{\mathrm{as}}=\frac{2 · F ·cos\left(\alpha \right)}{sin\left(\alpha \right)}$$

(4)

or:

$$F_{\mathrm{as}}=2 \times F \times cot\left(\alpha \right)$$

(5)

It is observed that for a value of the angle $\alpha ={90}^{\circ }$, $cos\left(\alpha \right)=0$. That is, $F_{\mathrm{as}}$ = 0. This means that the rod is no longer stressed axially.

If $\alpha \to 0$, then $sin\left(\alpha \right)\to 0$ and $F_{\mathrm{as}}\to \infty$.

If $\alpha ={45}^{\circ }$, it turns out that $F_{\mathrm{as}}=2\times F$.

Interpreting the above, we say that the axial force in the rod varies from zero to infinity, corresponding to the variation in the position of the lever from its vertical position to its horizontal position.

In the closed position (the position in which the mechanism is implanted), the levers are close to horizontal, and therefore, we have high values from the cotangent function. Thus, the initial value of the angle $\alpha$ is significant.

Regarding the axial force in the lever $F_{\mathrm{ap}}$, it is determined from the equilibrium equations corresponding to Figure 11b that

$$F_{\mathrm{ap}}=\frac{F_{\mathrm{as}}}{2} ·cos\left(\alpha \right)+R_2 ·sin\left(\alpha \right)$$

(6)

Substituting, we obtain

$$F_{\mathrm{ap}}=\frac{2 · F}{2} · \frac{cos\left(\alpha \right)}{sin\left(\alpha \right)} · cos\left(\alpha \right)+\frac{2 · F}{2} ·sin\left(\alpha \right)\Rightarrow F_{\mathrm{ap}}=\frac{F}{sin\left(\alpha \right)} · (cos{\left(\alpha \right)}^2+sin{\left(\alpha \right)}^2)\Rightarrow F_{\mathrm{ap}}=\frac{F}{sin\left(\alpha \right)}$$

(7)

This is the force that will apply to the lever during compression.

Second Key Finding

It is observed that both for the pushing force (actuation force) and for the tension in the lever, the highest values are at the beginning of the mechanism actuation when the device is in the closed position. This implies that to have as small values as possible for the axial force acting on the levers (and indirectly for the actuation force of the mechanism), the angle $\alpha$ must have as large of a value as possible. This will lead to lower demands for other components of the assembly.

3.2.3. The Method of Improving the Performance of the Merchandise Articulated at One End

From a technical point of view, three constructive variants for the articulation of the levers at the piston at the end of the rod were considered in order to study the initial value of the angle $\alpha$ corresponding to the closed position of the device (${\alpha }_{\mathrm{initial}}$).

The three variants presented in Figure 12 are the following:

(a) The joints of the two levers are located apart and on the other side of the axis of the rod, but each is in the same half-plane as the joint at the other end of each lever. This situation offers the advantage of using the same configuration for both levers. The major disadvantage, however, is the tiny angle—${\alpha }_1^{\circ }$ (there is a danger of being equal to zero), and therefore, very large forces exist that push the rod into the other elements of the system.

(b) The joints of the two levers coincide (and are placed on the axis of the rod). The initial value of the starting angle ${\alpha }_2^{\circ }$ in this case is significantly higher than in the previous case. In this situation, the two levers will have different shapes.

(c) The joints of the two levers are located apart and on the other side of the axis of the rod, but each in the half-plane opposite to the joint at the other end.

This last variant constructively offers the largest initial angle (${\alpha }_3^{\circ }$), so that the starting force is at the lowest values.

The starting force must be as low as possible, implying a lower actuation force. This is important not only from the point of view of the device’s mechanical strength calculations.

The action is performed from outside the patient’s body. The operator (surgeon) still performs this actuation manually, which must be sufficiently strong and delicate at the same time. The less physical effort required by the doctor, the more they can focus on the finesse of the action.

Third Key Finding

The advantage offered by solution (c) is very difficult to capitalize on using the three-arm variant, but it is accessible to the two-arm mechanism variant.

4. Discussion

A. In principle, in relation to the SJ system, the conical opening system allows the use of a lower force for restoration.

Also, the conical opening system avoids the pressure stress on the integral part of the vertebra. Since the required force is a significant limitation in constructing a mechanism of such small dimensions, the conical opening system offers a greater variety of constructive solutions that will lead to an optimized solution over time.

Even the SJ system can be adapted to have such kinematics that the opening of the arms is no longer plane-parallel but angular, in order to reduce the force required to push the bone fragments.

B. One of the arguments that recommends such a configuration (with three arms) is that of system stability.

Regarding the aspect of stability, it should be noted that inside the vertebra, there is bone tissue of a certain consistency. It is indeed of a much-rarefied consistency in relation to the wall of the vertebra and is even damaged through osteoporosis. But whether we are talking about SJ or other mechanisms, after the expansion of the arms, they will damage the spongy bone tissue themselves. In moving the arms, they flatten the tissue. This will generate cavities in the form of channels (trenches) that deepen to a certain point according to the direction of the force action. The walls of these channels will also prevent the deviation from the desired direction of the arms moving toward the upper and lower plateaus of the vertebral body

From the documentation with research data on the use of the SJ system, it does not appear that a mechanism with a two-way action would be unstable under these specific conditions of use. In other words, an alleged instability cannot be an argument for increasing the number of arms.

In referring to the behavior of the SpineJack system inside the vertebra, the deformations that appear in radiological images are not due to the system’s instability but to the uneven distribution of the force acting on the blades (arms), as previously presented.

C. Comparing the two solutions with a conical opening (the one with three arms and the one with two arms), we observed that the version with two arms provides the possibility of obtaining constructive solutions of more robust mechanisms that can withstand greater forces.

Another advantage of the two-arm system is that it develops equal and symmetrical stresses on each vertebral plate thanks to the constructive symmetry and the kinematics.

At the same time, geometrically, the version with two arms has a larger opening (a stroke) of the arms, which allows a more significant displacement of the vertebral plates, as shown in Figure 13. At the same time, inside the vertebra, the positioning of the device with two arms is less restrictive so that even for slight deviations, both arms will continue to have the same load and the same behavior, which provides greater stability to the system, compared to the one with more arms.

5. Conclusions

This study aimed to open new research perspectives based on the observed aspects that can be improved. In highlighting and analyzing these aspects, improvements in existing methods and the emergence of new solutions can be achieved.

In this work, the kinematics of the displacement of the vertebral fragments was highlighted after an appropriate analysis.

Following these observations, it was theoretically demonstrated that the type of mechanism articulated at one end can be much more useful.

From the category of this family of devices, the authors demonstrated that a mechanism articulated at one end but with only two arms—the TAD from Figure 5—can be superior to the one with three arms (TB).

The superiority of the Two-Arm Device consists of the following facts:

(a)

It is more robust than a multi-arm mechanism;

(b)

It acts more efficiently on the bone fragments both from the point of view of the functioning of the device (place of force action, way of moving the fragments, etc.) and from the point of view of the required force (less force is required than with the SpineJack).

On the one hand, the lower force required will result in an easier actuation of the mechanism. Since less actuation force is required, the emphasis will be on the smoothness of movement. On the other hand, due to its robustness, hopefully, a more efficient restoration of vertebral height will be achieved and, consequently, an improvement of the patient’s symptoms.