Journal of Limb Lengthening & Reconstruction

ORIGINAL ARTICLE
Year
: 2020  |  Volume : 6  |  Issue : 2  |  Page : 107--115

Curved “K” wires: The covert villain in circular external fixators


Charles Brian Howard1, Eitay Farkash2,  
1 Department of Orthopaedic, Hadassah University Hospital, Jerusalem, Israel
2 CEO Mark Industries, Beer-Sheva, Israel

Correspondence Address:
Prof. Charles Brian Howard
1, Sigalon Street, Omer, 8496500
Israel

Abstract

Context: Complications associated with “K” wires used in circular external fixators include intraoperative nerve and vessel damage, loss of tension, high rates of pin tract infection, and wire breakage. Aims: To investigate if insertion of “K” wire with a curvature is responsible, in part, for these complications. Settings and Design: This paper is a theoretical analysis of the forces and consequences of a tensioned curved wire on the bone, experimental measurement of the heat produced on inserting a curved compared to a straight (with a guide) wire into a bovine rib bone. Subjects and Methods: 1.8 mm K wires were drilled into two bovine rib bones using a battery-powered hand drill. The temperatures reached were recorded with a thermal camera. Statistical Analysis Used: Student's t-test. Results: (1) A tensioned curved wire would cut through the bone. (2) higher temperatures were reached when inserting a K wire in a curved manner than with a guide. (3) Drilling a curved wire initiates metal fatigue. It is theoretically possible to reach the forces needed to correct the curvature on the wire by “pinching” the wire near its insertion into the bone with the index and thumb of the non-drilling hand, but these forces far exceed the pressure pain threshold. In addition, the constantly changing force and direction would make the necessary proprioceptive changes almost impossible to follow. Conclusions: Theoretically and experimentally a curve on a K wire will increase vessel/nerve damage, thermal necrosis, pin tract infection, loosening, and loss of wire tension. Present-day method of “pinching” the end of the K wire to prevent curvature is probably inefficient and K wires should be inserted using a guide.



How to cite this article:
Howard CB, Farkash E. Curved “K” wires: The covert villain in circular external fixators.J Limb Lengthen Reconstr 2020;6:107-115


How to cite this URL:
Howard CB, Farkash E. Curved “K” wires: The covert villain in circular external fixators. J Limb Lengthen Reconstr [serial online] 2020 [cited 2021 May 16 ];6:107-115
Available from: https://www.jlimblengthrecon.org/text.asp?2020/6/2/107/306108


Full Text



 Introduction



It is not surprising that complications, obstacles, and problems frequently occur during the difficult complicated cases treated by the Ilizarov concept. First, the K wire may be bent as it is inserted which will lead to the wire deviating from the surgeon's desired course, with consequent increase risk of vessel and nerve damage [Video 1]. In addition, drilling a flexed wire will increase the amount of energy needed to insert it, leading to increased thermal bone and skin necrosis, pin tract infection, loosening, and loss of tension and late wire breakage (due to initiation of metal fatigue). Second, a permanent curve on the wire may be introduced when attaching it to the ring. When such a wire is tensioned, a static cutting force is applied to the bone, producing widening of the pin tract, loss of tension, and loss of frame stability. We analyzed the forces involved, carried out some thermal drilling experiments to test the theoretical background to our hypothesis.

 Subjects and Methods



Mechanical and theoretical considerations

In the fully assembled apparatus, during the post-operative period, curved, tensioned wires can cut through the bone and straighten. Thus the tension in the wire is lost. [Figure 1] shows the proportion of tension in the wire converted into a cutting force with increasing curve, making the following assumptions:{Figure 1}

Tension in wire, F = 1200 N

Width of each cortex, c = 5 mm

Diameter of wire, d = 1.8 mm

Angle between ring and wire = θ [Figure 2] {Figure 2}

Force on bone = F sinθ N

[INLINE:1]

The distance between points of connection of the wire to the ring is longer if the wire has a curve on it than if the wire is straight. At least part of this is compensated by the stretch produced by the tension. The amount the wire is stretched [INSIDE:1] is found from:

[INLINE:2]

[INLINE:3]

Where

L0 = original length of wire (180 mm)

A = cross section area of the wire = πr2 ≅ 2.5 mm2

E ≅ 200 Gpa for 316L steel

i.e. the wire will stretch by Δ L = 0.4 mm. Thus, even an extremely small reduction in the wire's longer, curved path to a shorter, straighter one, will result in marked loss of tension.

Experiments

Heat production during drilling of K wires into a bovine rib bone.

Methods

Ten 1.8 mm trochar tipped K wires were drilled into a bovine rib bone, using an electric battery-powered drill (Bosch GER 10,8 2-li). The drilling speed was kept constant at 1300 RPM. Each wire was inserted through 1 cortex, once without a guide and a deliberate curve of about 25–30°, and once with an overguide [Figure 3] (We were unable to find a guide suitable for circular external fixators, so we designed and manufactured one-”EasyFix” guide) which prevented curving of the wires. In clinical practice, the wire is probably bent <25–30, but we chose this angle to increase visualization of the problem that occurs even at lower angles. 10 wires were used four times, twice without and twice with a guide, 20 insertions with a guide and 20 without a guide. When inserting the wires with the guide, the insertion point was chosen to be as close to an insertion point of a wire without a guide as possible. This experiment was repeated on a separate occasion with a different rib bone and new set of wires. There were 35 insertions with a guide and 35 without a guide. The results of the two series (without and with a guide) were compared using one tail Student's t-test.{Figure 3}

The insertions were filmed with a thermal camera (Seek thermal Compact Pro). The thermal videos were examined and the highest temperature reached during the insertion of the wire was recorded. In two cases of insertion without a guide, the drill/drilling hand blocked the lens of the camera and these were discarded leaving 33 insertions without a guide for analysis.

Google image analysis

A Google Image search, entitled “radiographs + tibia + Ilizarov,” produced radiographs of 28 tibiae treated with an Ilizarov apparatus. From these, 108 wires were identified.

 Results



The maximum temperatures reached are shown in [Table 1]. In the first series, the average maximum temperature without a guide was 91°C and with a guide 76°C, a difference of 15°C (P < 0.01). In the second series, in two of the insertions without a guide, the drill blocked the camera leaving 33 insertions for analysis. The average maximum temperature was 66°C without a guide and 46°C with a guide, a difference of 20°C (P < 0.01). A typical picture from one of the videos is shown in [Figure 4].{Table 1}{Figure 4}

During the drilling without a guide, two of the wires broke. To demonstrate this phenomenon, a wire was videoed as it was drilled into a bone with a curve. A wave like motion could be seen developing at the curved part of the wire and shortly after this the wire broke; the broken surface having the characteristics of a fatigue fracture [[Figure 5] and Video 2 “breaking wire”].{Figure 5}

Google image search

Of the 108 wires present on the radiographs, 67 (62%) were noted to have a curve on them.

Possible solutions

1. Reducing heat production at the bone/pin interface.

Piska et al.[1] showed that under laboratory conditions, changing the configuration of the K wire tip, reduced the temperatures produced during insertion (129°C ± 6°C [trochar tipped], 98°C ± 7°C [diamond tipped], 66°C ± 2°C [fluted tip]), but this does not seem to have entered clinical practice to any great degree.

A commonly used method is to hold the K wire as near to the end as possible with a gauze swab soaked in ice cold saline. While widely believed, this method does not appear to be able to carry away much heat, as the following calculation shows:

Specific heat of 316L steel = 0.42 joules per gram per 'K

Thermal conductivity of 316L steel K = 16.2 joules/s/m/'K

Density of 316L steel = 8 g/cc

Wt of last 0.5 cm of K wire = volume × density = 0.5 x πxr2 x 8 =0.1 gm

∴Heat (joules) to raise last 5 mm (tip) of k wire k wire per 1°C

= 0.42 × 0.1 = 0.04 joules

Assuming temp at tip = 100°C and temp at 3 cm from tip = 0°C due to ice cold saline swab.

Heat flux (flow of heat from tip to saline swab) = K × area (m2) × δt = 16.2 × 3.14 × 0.0009 × 0.0009 × 100 = 0.004 joules/s

Hence, even when there is a large temperature gradient (100°C), the amount of heat that can be removed by a gauze swab soaked on ice cold saline is only 0.004 joules/s. It would take 10 seconds to lower the temperature by 1°C replying solely on this method. During this time, heat is dissipated into bone and soft tissue in contact with the pin tip.

2. Holding (pinching) the wire near the bone entry point.

It is a common clinical practice to hold or pinch the wire near its entry to the bone, at position ([INSIDE:2]), in order to counteract the bending force and the bending moment of the wire, thus returning the end of the wire to its original x-axis [Figure 6].{Figure 6}

However, there are two problems with this method, making this solution difficult. First, the movement of the drilling hand varies, thus changing the offset from the desired axis, varying the flexion and position of the wire in space and time. In addition, the amount of pushing pressure on the drill/wire also varies. Compensating for all these factors would require a very high proprioceptive ability of the gripping fingers.

Second, as we show below from analysis of the forces involved, it is unlikely that the “pinch” on the wire can produce a full correction.

Consider a K wire of diameter d and length l where l >>d that is positioned horizontally to a flat surface, along the x axis. Under an axial compressive force P applied by an unsupported drilling hand the wire can (a) flex and (b) deviate from that axis [Figure 6] with deflection profile ω(x). Assuming the deflections are small compared with the K wire length (ω<<l), the deformation of the K wire can be described as an elastic beam. Therefore, the deflection of the K wire is the solution to

ωiv + k2ω” = 0 (0.1)

where k2 = P/EI, E is Young's modulus, I = πd4/64 is the second moment of area of a cylinderical beam, and derivatives are with respect to the position x with the origin at the bone end. The K wire is under simple support at the bone end x = 0 and can have some nonzero angle α and displacement Δ at the other end x = 1 Since the insertion of the K wire is a manual process, we assume that either α or Δ or both are nonzero. We do not discuss the less-likely case α = Δ = 0, where the K wire should remain parallel to the X axis and buckle only above a critical force. In addition, we account for an intermediate support at distance x = xf (the site at which the finger pinch force is applied) where zero deflection and zero slope are applied. Therefore, the explicit boundary conditions are

ω = 0, ω” = 0, on x = 0, (0.2a)

ω = 0, ω' = 0, on x = xf, (0.2b)

ω = 0, ω” = 0, on x = x1, (0.2c)

To apply these boundary conditions, we model the beam in two sections (0 ≤ x ≤ xf and xf ≤ x ≤ x1), each obeys (0.1). This requires two additional boundary conditions, representing continuity of ω and ω' at [INSIDE:3]. The solution implies that the vertical shear force [INSIDE:4] and bending moment [INSIDE:5] applied at the intermediate support [INSIDE:6] are as follows.

[INLINE:4]

[INLINE:5]

where [INSIDE:7]. This implies that the force and moment that should be applied at xf to keep the K wire perpendicular to the bone can vary substantially with the angle and the displacement at the edge and with the position of the support relatively to the edge [Figure 7]. Specifically, pinching the K wire near its end may require substantially larger force than supporting at intermediate positions [INSIDE:8] [Figure 8]. The corresponding necessary moment is also relatively large when supporting near the end, but when the angle at the loaded edge is nonzero, the moment could also be large at intermediate supporting positions [Figure 9].{Figure 7}{Figure 8}{Figure 9}

Example:

For a K wire of diameter d = 1.8 mm, length x1 = 16 cm, with a Young's modulus of 200 GPa, applying an axial (drilling) force equivalent to 4 kg (P = 39.2 N) and “pinching” the wire 3 cm from the bone (xf = 3 cm) will result in k of approximately 19.5 m 1 and ξ of approximately 2.15. The resulting deflection profiles for several boundary conditions are shown in [Figure 7]. The corresponding force at this position of [INSIDE:9] can vary substantially [Figure 7], between V ≈ 0.9 N (for ∝ = 5° and Δ = 1 cm) to the 30 times larger V ≈ 27.3 N (for ∝ = 05° and Δ = 3 cm). The corresponding bending moments at the support vary from −0.3 Nm to −2 Nm, respectively, for these two boundary conditions [Figure 9].

These forces are smaller than the maximum force that can be developed between the whole of the pulp of the distal phalanges of the index finger and thumb.[2],[3] However, these forces applied across the lateral aspect of the distal phalanx of the index finger (about 1 cm) [Figure 10] by a wire of 1.8 mm diameter would produce a pressure of 1516 KPa for the shear force correction and 1110 KPa for the bending moment. The reported pressure pain thresholds for these sites are much lower, being from 500 Kpa to 850 Kpa.[4],[5],[6]{Figure 10}

The use of the “pinching” method is a well establish practice that has stood the test of time. However, it requires a great deal of skill to assess the changes in the wire's flexion with changes in pressure and movement of the drilling hand, particularly through a saline gauze and surgical gloves. Even in the most experienced hands, this method cannot be relied upon to produce a perfect straight wire every time. Use of a guide, on the other hand, is simple, requires much less skill, and guarantees a perfectly straight inserted wire consistently.

The guide prevents a curved insertion with its associated problems of increased heat production, static cutting force on the bone with consequent vicious cycle of increase width of the pin tract, loss of tension, loosening, and pin tract infections.

Only clinical studies can provide proof one way or the other of the various claims made above. This study provides the theoretical basis for such studies.

 Discussion



The introduction of the Ilizarov method and apparatus has revolutionized the treatment of limb deformities, leg length discrepancies, difficult fractures, and non-unions. However, the method is prone to a high complication rate.[7],[8] Intrinsic to the Ilizarov method is placing thin wires under tension,[9],[10],[11],[12],[13],[14] which markedly increases the rigidity and stability of the construct,[9],[12],[15],[16] but this tension is lost fairly rapidly.[15],[17],[18] Loss of tension has been ascribed to slippage at the screw/wire interface and/or plastic deformation in the wire.[10],[14],[15],[18],[19],[20],[21],[22] Half pins, which are also not without problems, have become increasing popular as an alternative, possible due to these problems. Solving or greatly reducing K wire complications may allow a return to Ilizarov's original concept of tensioned K wires.

The cases treated are often complicated and difficult; thus, it is not surprising that these procedures are fraught with complications during the months of long treatment.

This paper concerns four of these complications, viz., intraoperative nerve/vessel damage, pin tract infection, loosening and loss of tension in the wire, and wire breakage. Of these, only intraoperative nerve/vessel damage is considered a true complication. The other three are categorized as problems or, if further surgeries are required, obstacles.[23] They are considered as almost inevitable unavoidable incidents which occur during the long treatment period to be dealt with as they occur.[24] However, whatever they are called, prevention is more desirable than cure. We have investigated a possible common factor in the causation of the above four problems/obstacles/complications and come to the conclusion that insertion of the “K” wires with a curve in either/both the transverse or sagittal planes is an important etiological factor in all these problems.

A wire may be inserted curved because:

The wire is not perfectly straight to start withEye-hand inaccuracy in placement of the wire, with incomplete correction with spacing washersFlexing of wire during insertion.

The first is caused by either manufacturing inaccuracies or post manufacturing damage. Other than to state it can occur, illustrate it [Figure 11] and note how even a small deformity of the wire can lead to large discrepancies between ring and wire [Figure 2], it will not be considered further in this paper.{Figure 11}

The last two depend on the surgeon applying the apparatus.

It is very difficult to accurately insert wires and screws unaided.[25],[26],[27],[28],[29] Cortical screws, spinal screws, ligament reconstruction anchors, and even Steinmann pins used with circular fixators are all directed by guides. Yet, for some reason, the long flexible K wires are inserted freehand. This curvature leads to a number of problems. First, it may cause deviation from the path designated by the surgeon. Even assuming the best possible scenario in that the surgeon applies pressure on the wire exactly in the axial direction, wires can buckle and flex. The slightest hand movement outside this exact line adds to this tendency to bend the wire. Once the curve has formed and the wire enters the bone, it will continue on this offset course [[Figure 12], [Figure 13] and Video 1 drilling curved wire] and may lead to nerve or vessel damage. Second, any deviation from a direction normal to the bone, converts part of the “pushing” force into a tangential component. We used a deviation of 25–30° which, while being extreme, is not unusually during the insertion into hard bone if a lot of pressure is applied to the drill. This part of the force is wasted, generating extra heat. The energy needed to insert a wire depends on several factors: the quality and thickness of the bone, the speed of the drill, and drill tip.[30],[31],[32] As shown in [Figure 14], the effective force inserting the wire into the bone is F cos θ and the “wasted” energy is F sin θ. The more the bend, the greater the tangential component [Figure 15]. Third, when a curved wire is tensioned, part of that tension is converted into a “cutting force” [Figure 16]. Once the bone has been so cut, the pin tract enlarges leading to loosening. In addition, there will be a contraction in the length of the wire, leading to loss of tension. This, in addition to slippage at the screw/nut connection, is a cause of wire tension loss. {Figure 12}{Figure 13}{Figure 14}{Figure 15}{Figure 16}

The combination of the static, cutting force on the bone, bone resorption, loss of tension in the wire, loss of frame stability, pin loosening, and bone necrosis in turn increases the likelihood of pin tract infection. Infections contribute to a vicious circle of even more bone resorption and further wire loosening and further loss of frame stability.

Fourth, as a curved wire rotates during insertion, there is cycling of tension on the convex surface and compression on the concave side. Just as bending a spoon up and down eventually breaks the spoon from metal fatigue, so drilling a curved wire fatigues the wire. Rarely, if ever, is the time taken to insert the wire sufficient to break the wire. However, the process, which starts with a microcrack, does weaken the wire. This, in turn, may lead to breakage at a later stage. Although wire breakage may not be a common occurrence, it does occur and may entail further operative procedures to replace the broken wire/wires. Madhusufhan el al.[33] reported that 31% of their patients (7 out of 22) had wire fractures and Adair[8] a 1% wire fracture rate. What is certain is that drilling a K wire in a curved condition (which is inevitable considering the flexibility and length of the wire) damages and weakens the wire.

The question arises, “Do curved wires occur in clinical practice?”

The high percentage (62%) of curved wires seen on the radiographic search is a reasonable indication that curved wires are, in fact, a common occurrence. The experimental data clearly showed that more heat was produced when the wire was introduced with a curve, but there was a very wide spread of maximum temperatures within each rib bone and between the two ribs. One of the problems was the inhomogeneity of the cortical bone width and density along the ribs, but this problem is shared with all bones. Unfortunately, there is no artificial material which can satisfactorily take the place of bone. Thus, while the conclusion of the experiments is that there is a reduction in heat produced when using a guide, we cannot make any quantitative comments as to how big an effect this would be in clinical practice.

Pin tract infection is reported to occur from to 0% to 100%. A review by Lobst and Liu of 150 articles found an overall infection rate of 29.5% in circular frames.[34] K-wires are notorious for producing thermal necrosis on insertion. Piska et al. found temperatures of 100°C–140°C[1] after ten seconds drilling and Van Egmond[35] recorded temperatures up to 190°C. The amount of heat generated depends on the thickness and density of the bone, drill speed, the pressure applied to the wire, drilling time, wire diameter, and configuration of the wire tip. However, temperatures above 47°C cause osteocyte death.[36],[37],[38] Osteocytes inhibit osteoclasts and the absence of osteocytes thus activates bone resorption and consequent implant loosening.[36],[38],[39],[40],[41] Although it will need experimental or clinical proof, it is reasonable to assume decreasing the heat at the wire/bone interface will decrease bone death and may decrease both osteoclastic bone resorption and infections. While the majority of pin tract infections can be treated with proper pin site care and possibly antibiotic therapy, at the very least, they cause pain, malaise, and discomfort to the patient and increased medical costs from extra nursing, clinic visits, antibiotics, etc.[42] At worst, they can be very serious and lead to osteomyelitis,[43],[44] bacteremia, bacterial endocarditis, and septic shock.[45]

Mechanical studies ascribe wire tension loss to slippage at the screw/wire interface and/or plastic deformation in the wire.[10],[14],[15],[18],[19],[20],[21],[22] There are no studies showing that tension loss can be due to the cutting through the cortices by a curved wire, but we believe this does happen in clinical practice. Presumably, in mechanical studies, the wires have been inserted without a curve, by use of an overguide, which is standard engineering drilling practice.

In conclusion, one possible solution is a small change in operative practice, i.e., use of a guide to introduce K wires has the potential to reduce pin tract infection, loosening of the construct, loss of tension, and wire breakage.

Acknowledgment

Dr. Roiy Sayag was instrumental in the developing the mathematical model of the forces required to correct a curvature on the wire by holding it a distances along its length.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.

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