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 Table of Contents  
ORIGINAL ARTICLE
Year : 2017  |  Volume : 3  |  Issue : 1  |  Page : 45-51

Analysis of strut-to-bone lengthening ratio for hexapod frames using mathematical modeling


1 Texas Scottish Rite Hospital, Dallas, TX, Nemours Children's Hospital, Orlando, FL, USA
2 Department of Orthopedic Surgery, Nationwide Children's Hospital, Columbus, OH, USA

Date of Web Publication15-Mar-2017

Correspondence Address:
Christopher A Iobst
Department of Orthopedic Surgery, Nationwide Children's Hospital, 700 Children's Drive Suite A2630, Columbus, OH 43205-2696
USA
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/jllr.jllr_29_16

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  Abstract 

Background: Hexapod external fixators often incorporate bone lengthening as part of a multi-planar deformity correction plan. The hexapod struts, however, do not distract in the direction of bone lengthening. Their oblique orientation to the ring creates a vector that is the summation of multiple individual strut adjustments. We demonstrate that a 1 mm lengthening of each of all six struts always created more than 1 mm of lengthening at the bone. Methods: The amount of lengthening was analyzed with the Taylor Spatial Frame™ (Smith and Nephew, Memphis, TN, USA) software using two different methods. Results: As the strut lengths got longer the ratio got closer to one but it never reached 1.0. Conclusions: This information is critical when using very short struts or very large rings. In these two scenarios, the Δ frame height relative to the Δ strut length becomes much greater than one. Clinical Relevance: A strut length much greater than one will cause the bone to lengthen much faster than the surgeon desires. It may also lead to unhealthy regenerate bone formation and could create delays in bone healing.

Keywords: External fixation, multiplanar deformity, strut adjustment


How to cite this article:
Cherkashin A, Samchukov M, Iobst CA. Analysis of strut-to-bone lengthening ratio for hexapod frames using mathematical modeling. J Limb Lengthen Reconstr 2017;3:45-51

How to cite this URL:
Cherkashin A, Samchukov M, Iobst CA. Analysis of strut-to-bone lengthening ratio for hexapod frames using mathematical modeling. J Limb Lengthen Reconstr [serial online] 2017 [cited 2020 Sep 20];3:45-51. Available from: http://www.jlimblengthrecon.org/text.asp?2017/3/1/45/202213


  Introduction Top


External fixators are the most commonly used devices for limb lengthening. They create gradual distraction between the two bone segments, providing the scaffold necessary for distraction osteogenesis. Rail uniplanar external fixators and Ilizarov circular fixators perform lengthening along a straight line in the axial plane using threaded rods or worm gear mechanisms [Figure 1]. Because these fixators apply pure axial distraction as they are elongated, every increment of external lengthening is replicated as internal lengthening at the bone. In other words, 1 mm of lengthening along the threaded rod of the fixator should also create 1 mm of lengthening at the osteoplasty site.
Figure 1: Example of a circular fixator which performs lengthening along a straight line in the direction of threaded rods

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Hexapod circular external fixators were introduced in the mid-1990s. This fixator design utilizes six telescopic struts that are connected obliquely between two rings using multiaxial hinges [Figure 2]. Because of this unique design, these fixators have proven to be excellent devices for correcting multiplanar deformities with or without limb lengthening. Hexapod fixators are sometimes used to perform pure limb lengthening, because if a secondary deformity develops during the lengthening process, it can be easily corrected with strut adjustments.
Figure 2: Example of a hexapod fixator, where six struts are not parallel to the lengthening axis

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The standard reported limb lengthening rate for a long bone is 1 mm/day. With threaded rods or worm gear distractors, this is easy to calculate and execute because the distraction is occurring along a straight line. When using hexapod fixators for limb lengthening, however, the lengthening process is not as simple. Because the struts are oriented obliquely to the rings, a 1-mm adjustment to the strut may not produce the same length adjustment of the bone fragments. Computer software that is paired with the hexapod external fixator helps calculate the proper strut adjustments. However, the strut adjustments in the software are rounded to the smallest available strut change increment, which is 1 mm for the Taylor spatial frame (TSF), and it does not show the corresponding change in bone length.

The question of how much lengthening is actually occurring with each strut adjustment has clinical ramifications. The literature has demonstrated that delayed consolidation of the regenerate bone is possible when using hexapod external fixators.[1],[2],[3] Fractures of the regenerate bone have been reported which can indicate poor regenerate bone formation.[4],[5] The purpose of this study was to determine how the hexapod external fixator height changes when each of the struts is lengthened 1 mm. Our null hypothesis is that 1 mm of lengthening performed to the strut will produce a different change in frame height.


  Materials and Methods Top


The amount of lengthening was analyzed with the TSF™ (Smith and Nephew, Memphis, TN, USA) software using two different methods. First, the TSF software was used to calculate frame height changes for each 1 mm increase in strut length. Using the chronic mode, frames with 155 mm full rings were chosen. The deformity parameters were all left at zero, except for the axial plane. This was entered as 1 mm short. The mounting parameters were all set to zero, indicating the bone was centered in the rings in all planes. All allowable neutral strut lengths (from 75 to 311 mm) were entered on the Strut Settings page of the software with 1 mm increments. For each strut length, neutral frame height was calculated by the software and recorded [Figure 3]. The dependent variable was the frame height. The following data points determined by the software were then recorded for each strut length: strut length before, strut length after, previous frame height, neutral frame height, the frame length change (previous height − current height). The last parameter (Δ frame height) represents the amount of frame height increase for a 1-mm strut length increase for each particular neutral frame height [Table 1].
Figure 3: Taylor spatial frame software screen shot where the final frame height is calculated based on the given strut length

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Table 1: Frame height increase per 1 mm strut length increase for each particular neutral frame height as calculated by the Taylor spatial frame software

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The second software simulation created frames that had an identical final frame height of 150 mm. In this case, the ring sizes were the dependent variable ranging from 80 to 300 mm diameter. The deformity parameters were all set to zero, except for the axial plane being 5 mm short. All of the mounting parameters were again set to zero. For a 5-mm change in frame height, the following data points were recorded for each ring size: initial strut setting, final strut setting, Δ strut setting, ratio calculating 5 mm frame height change/Δ strut setting.

As a method of comparison, a third test was performed using two 155 mm rings connected with six extra-short Fast Fx struts (Smith and Nephew, Memphis, TN, USA). The struts were all set to their minimum length setting (91 mm). The height of the frame was measured from the inner surface of each ring with a ruler and recorded. Each strut was then expanded to its maximal length setting (121 mm). The height of the frame was again measured from the inner surface of each ring with a ruler and recorded. The difference in the frame heights (final height − initial height) was calculated.


  Results Top


For the frame using 155 mm rings, increasing each strut by 1 mm produced >1 mm of length regardless of the initial strut setting [Table 1]. As the initial strut settings got shorter, the amount of Δ frame height increased dramatically [Figure 4]. For example, by increasing each strut 1 mm from an initial strut setting of 75, the frame height increased 5.8 mm. As the initial strut settings got larger, the frame length change began to approach 1 mm but never reached exactly 1 mm (1.02 mm at initial strut length 305).
Figure 4: Graphic representation of the strut-to-frame lengthening ratio, depending on the initial frame height. Note that the ratio is greater the smaller the distance between the rings

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When different ring sizes were tested using a final frame height of 150 mm, the ratio 5 mm frame height change/Δ strut setting equaled 1.0 for only the smallest ring sizes (80 mm and 105 mm). As the ring sizes increased, the ratio increased up to 1.67 [Table 2]. Note that software was rounding the frame height to the nearest whole number. Furthermore, the strut settings were rounded to the allowable 1 mm increments. Therefore, the initial ratio of 1 for the ring sizes 80 mm and 105 mm is calculated using rounded numbers and is actually slightly higher than 1.
Table 2: Frame-to-strut lengthening ratio for each ring size with final frame height 150 mm

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The initial height of the frame using 155 mm rings and extra-short Fast Fx struts at the minimum setting (91 mm) measured 75 mm between the inner surfaces of each ring [Figure 5]. After increasing each strut to its maximal length (121 mm), the height of the frame was 120 mm between the inner surfaces of each ring [Figure 6]. This was a 45-mm increase in height. The struts were increased by 30 mm. The Δ frame height/Δ strut length = 45/30 or 1.5.
Figure 5: The initial height of the frame using 155 mm rings and extra-short Fast Fx Taylor spatial frame struts at the minimum setting (91 mm) measured 75 mm between the inner surfaces of each ring

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Figure 6: The final frame height measured 120 mm between the inner surfaces of each ring after lengthening each strut to its maximal length (121 mm)

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Software simulation with different horizontal or vertical reference ring offset parameters produce the same results. When the mounting parameters were changed from zero, the ratios of Δ frame height/Δ strut length did not change.


  Discussion Top


Hexapod external fixators are designed to perform multiplanar deformity corrections. The frame consists of two rings connected by six obliquely oriented telescopic struts [Figure 2]. The struts are connected to the rings through multiaxial joints at each end. This design allows the frame to move freely with six degrees of freedom. Using a hexapod external fixator, the surgeon can correct limb deformity in the coronal, sagittal, and axial planes simultaneously.

Axial plane deformity (lengthening or shortening) correction is often necessary to fully restore the patient's limb alignment. Hexapod external fixators can incorporate lengthening of a bone as part of a multiplanar deformity correction plan. They can also be used to perform isolated limb lengthening with axial distraction as the primary purpose. Hexapod external fixators are sometimes selected for limb lengthening because secondary deformities that occur during the lengthening process can be corrected using the struts' multiplanar capabilities.

The literature, however, has demonstrated that lengthening with hexapod external fixators may not always be ideal. Kristiansen compared two groups of mostly skeletally mature patients undergoing a tibial lengthening, one using an Ilizarov fixator (27 patients) and one using the TSF (20 patients).[1] In the Ilizarov group, the healing index was 1.7 months/cm compared to an index of 4.0 for the TSF group. When they separated out only the patients with lengthening between 2.4 and 6 cm, the index was 1.8 for the Ilizarov group and 2.4 for the TSF group. In addition, 20% of the TSF patients had reduced callus formation requiring bone grafting, compared to 3.7% of the Ilizarov patients. Iobst compared two groups of pediatric patients undergoing limb lengthening: Group 1 used TSF rings connected by four Ilizarov clickers and Group 2 used TSF rings connected by six TSF struts.[2] In the group using Ilizarov clickers (six patients), the lengthening index was 1.33 months/cm. In the group using the TSF struts (15 patients), the lengthening index was 1.79 months/cm. Ganger examined the correction of posttraumatic lower limb deformities using the TSF.[3] They found that 6/25 (24%) of their cases had delayed ossification.

These data indicate that there must be something different about the process of lengthening using hexapod struts compared to lengthening with threaded rods or worm gear mechanisms. The threaded rods or worm gear mechanisms are distracting along a straight line. Therefore, as they are adjusted, the incremental length changes should be replicated at the osteoplasty site. In bone models, there is a one-to-one ratio of lengthening at the fixator and at the bone.

The hexapod struts, however, do not distract in the direction of bone lengthening. Their oblique orientation to the ring creates a vector, that is, the summation of multiple individual strut adjustments. The amount of movement in each direction depends on the orientation of the strut to the ring. Ring size and strut length can affect the orientation angle of the strut to the ring. For each 1 mm adjustment of the struts, different amounts of lengthening may occur at the bone depending on the combination of these variables.

This study demonstrated that a 1-mm lengthening of each of all six struts always created more than 1 mm of lengthening at the bone. In our model using 155 mm rings, none of the strut lengths created a one-to-one ratio of strut lengthening to bone lengthening. As the strut lengths got longer, the ratio got closer to, never reached, 1.0. In the short strut lengths, the ratio was substantially >1.0. In the most extreme case (performing a 1-mm adjustment of each strut from a starting length of 75), almost 6 mm of bone length occurred. Lengthening at such an enormous rate would definitely be detrimental to regenerate bone formation. For strut lengths 178 and higher, however, the ratios of bone to strut length all measured <1.1. This may explain why the clinical results with hexapod external fixators are not dramatically different than other external fixator designs. In the majority of cases, surgeons are obtaining a nearly one-to-one ratio between strut lengthening and bone lengthening. The delayed healing seen in the literature may reflect the fact this ratio is not exactly 1.0. It is also extremely important in smaller limbs, such as with pediatric patients, where the initial height of the external fixator is 150 mm or less. Lengthening with hexapod frames in these cases may cause dangerous amounts of distraction to the regenerate bone with each strut adjustment.

The second part of the study also had similar findings. When keeping the final frame height at 150 mm but varying the ring sizes, the ratio of Δ frame height/Δ strut length increased to 1.67 for rings 230 mm and larger. The smallest ring sizes (80 mm and 105 mm) maintained a one-to-one ratio of frame height to strut length. However, the middle ring sizes (130–205 mm) had a ratio of 1.25 and the largest rings had a ratio of 1.67. In other words, for every 1 mm increase in strut length, the frame height increased 1.67 mm.

Our final test, using a ruler to measure the actual change in frame height, also demonstrated that there was not a one-to-one ratio present. Our 155 mm ring frame height increased 45 mm while the strut lengths only increased 30 mm. This means that on average for every 1 mm increase in strut length, there is a corresponding 1.5 mm increase in frame height.

Why is the lengthening ratio >1 to 1? Intuitively, looking at the frame, it seems that lengthening the strut 1 mm should create less than 1 mm of frame height increase. This is true when considering the lengthening of just one individual strut. However, when all six struts are adjusted simultaneously, the resulting bone length increase is greater than the individual strut. When the question about the relationship between struts to bone lengthening ratio was posed to more than 100 surgeons in an informal survey, the unanimous response was that the frame height would increase <1 mm for every 1 mm lengthening of the struts. The real answer, however, is related to the geometry of the hexapod design. The oblique orientation of the strut to the ring creates a series of right triangles [Figure 7]. The side of the triangle that represents the amount of frame height change is the hypotenuse of the triangle. The strut length increase represents the cathetus of the triangle. The Pythagorean theorem is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Based on this theorem, the amount of frame height increase will always be greater than the same amount of strut length increase.
Figure 7: Diagram of the lengthening in a hexapod frame. The oblique orientation of struts to the ring creates a series of right triangles. The side of the triangle that represents the amount of frame height change (ΔB – amount of bone lengthening) is the hypotenuse of the triangle. The strut length increase(ΔS) represents the cathetus of the triangle

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Clinically, this information is critical when using very short struts or very large rings. In these two scenarios, the Δ frame height relative to the Δ strut length becomes much >1. This will cause the bone to lengthen much faster than the surgeon desires. It may also lead to unhealthy regenerate bone formation and can create delays in bone healing. In addition, it is important to take into consideration that the majority of hexapod frame systems only allow a minimum of 1 mm length change on each strut. With such a setting, the software cannot recommend smaller than 1 mm strut length increases and it compensates by inserting the adjustments with 0 mm length changes [Figure 8]. In such a scenario, the regenerate is intermittently stretched too much with periods of “catching up” in which no lengthening occurs. This cannot be healthy for the distraction regenerate bone formation.
Figure 8: Taylor spatial frame software screen shot with a prescription for 25 mm lengthening using 155 mm rings with initial 42 mm frame height. Note that struts are adjusted every 3rd or 4th day to catch up with larger frame lengthening per each minimal strut lengthening of 1 mm

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There are several alternative methods for lengthening if a surgeon wants to avoid the possibility of distracting more than 1 mm per day. If a straight lengthening is necessary, it may be better to perform it using threaded rods with hexapod rings. This will ensure a one-to-one lengthening ratio during distraction. If the lengthening process creates any deformity in the regenerate bone, the threaded rods can be exchanged to struts. The struts can then be used to correct the residual deformity. A second alternative would be to use a hexapod frame system that allows smaller than 1 mm increments of strut adjustment. Smaller incremental adjustments would allow the surgeon to have better control over the changes in the lengthening ratio that are present when using struts.


  Conclusion Top


The surgeon needs to be aware that lengthening a strut 1 mm will always result in >1 mm of bone lengthening when using with a hexapod frame system. The disparity between the amount of lengthening at the strut and at the bone becomes increasingly dramatic with hexapods using very short strut lengths or large ring sizes.

Financial support and sponsorship

Nil.

Conflicts of interest

Christopher Iobst is an educational consultant for Nuvasive, Orthofix, and on the speaker's bureau for Smith and Nephew.

 
  References Top

1.
Kristiansen LP, Steen H, Reikerås O. No difference in tibial lengthening index by use of Taylor spatial frame or Ilizarov external fixator. Acta Orthop 2006;77:772-7.  Back to cited text no. 1
    
2.
Iobst C. Limb lengthening combined with deformity correction in children with the Taylor Spatial Frame. J Pediatr Orthop B 2010;19:529-34.  Back to cited text no. 2
    
3.
Ganger R, Radler C, Speigner B, Grill F. Correction of post-traumatic lower limb deformities using the Taylor spatial frame. Int Orthop 2010;34:723-30.  Back to cited text no. 3
    
4.
Blondel B, Launay F, Glard Y, Jacopin S, Jouve J, Bollini G. Limb lengthening and deformity correction in children using hexapodal external fixation: Preliminary results for 36 cases. Orthop Traumatol Surg Res 2009;95:425-30.  Back to cited text no. 4
    
5.
Eidelman M, Bialik V, Katzman A. Correction of deformities in children using the Taylor spatial frame. J Pediatr Orthop B 2006;15:387-95.  Back to cited text no. 5
    


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]
 
 
    Tables

  [Table 1], [Table 2]


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