The design and performance of an experimental external fixator with variable axial stiffness and a compressive force transducer
Introduction
The use of external fixation to fix fractures, and so control the fracture site loads and movements, is far from new; Malgaigne's work, published in 1847[1], has been cited as the first to use true external fixation. The advantage of external fixation to the researchers into the effects of movement on fracture healing is that the main structural components of the device are external to the body and accessible. Consequently, they can be easily manipulated and different types of transducers and actuators can be incorporated within them with little difficulty2, 3, 4, 5, 6, 7.
It was for these reasons that a unilateral external fixator was used to investigate the effects of the biomechanical environment on fracture healing. It was felt that an appropriate system would control and monitor the biomechanical environment. Since such a system was not available commercially, it was decided to design and manufacture a bespoke system for these experiments; this system is described here.
This fixator allows axial movement at the experimental fracture site as a controlled response to normal physiological loads and not movements applied by some externally powered device. The axial movement is controlled by a spring of prescribable stiffness. The displacements, other than axial, are kept to a minimum by using stainless steel linear bearings with preloaded recirculating balls within the main fixator bar. These allow the fixator to be stiff in all directions except along the axis of the bar.
Section snippets
Design aim
The aim of this work was to design and manufacture a unilateral external fixator which could hold a diaphyseal osteotomy of the right tibia of the sheep, while allowing controlled axial movement in response to the compressive forces it experienced, and while minimising displacements to all other components of load.
General description
This external fixation system is based on a prototype system which has been published previously[7]. It is a unilateral device that is designed to stabilise an ovine tibia which has undergone a diaphyseal transverse osteotomy, the level of which is slightly distal to the midpoint of the bone, at about 65% of its length, which avoids the first branch of the nutrient artery. The bar is 175 mm in length with outer pins 145 mm apart; this allows 60 mm between the inner two pins for the spring and load
Spring design
The spring section of the module is composed of a block of silicone rubber, which functions as the spring (Cosmesil, Cosmedica Ltd, UK), and an epoxy resin spacer to which it is glued. The stiffness of this section can be varied by changing the relative thickness of these two materials. This combination of materials was found: to show no viscoelastic effects when subjected to cyclic loading at frequencies below 72 Hz, as can be seen in the transfer function shown in Fig. 3; to be linearly
Transducer design
A novel design of transducer has been used, based on a single sensing beam which is loaded by two knife edges at points equidistant from the ends, at a quarter of its length from each end. This is shown in the schematic diagram of the assembly in Fig. 5. The bending moment at the midpoint of the beam is measured using electrical resistance strain gauges arranged in pairs above and below the sensing beam and wired into a full Wheatstone bridge.
It is expected that no tensile loads would be
Instrumented treadmill design
The custom-built treadmill with its forceplate allows the vertical component of the ground reaction force under the involved limb to be measured at the same time as the measurement of the fixator force. Using a treadmill for these tests allowed the signal to be relayed to the recording computer via a flying lead. A motor controller allowed the speed of the treadmill to be easily varied, and a slow walking speed of 1 m s−1 was chosen for these experiments. The system is designed so that, during a
Calibration
Two forms of calibration were performed before each experiment: the calibration of the compressive force transducer and the measurement of the axial stiffness of the whole fixator/spring system. Both were performed in similar ways.
The fixator bar was mounted, with the spring and transducer module in place, onto a bone substitute made of a 25 mm diameter cylinder of beech wood with a 5 mm gap at the level of the osteotomy; the pins were located into predrilled holes to ensure accurate placement;
Transducer characteristics
The description of errors follows the Type A specification given in British Standard BS 4889:1990 Method for specifying the performance of electrical and electronic equipment. That is: the limits of errors are quoted as the maximum positive and negative errors that have been measured; the limits of the intrinsic errors have been investigated over the full range of the relevant parameters; the limits of the variations are quoted with respect to the influence quantity and the range over which the
Surgical procedure
With the animal under general anaesthesia, the right limb was shaved, sprayed with antiseptic and draped for the application of the fixator to the anteromedial aspect of the tibia. The joint centres at each end of the tibia were palpated and marked. The distance between these marks was measured and the site of the osteotomy was marked at a point slightly distal to the midpoint of the tibia, at 65% of its measured length.
The pins, numbered from one at the proximal end to six at the distal end,
Measurement procedure
Before the operation, the animals were walked upon the treadmill as a form of training. During the 24 h before surgery the mass of the animal was measured and a preoperative walking test was performed.
After the operation, walking tests were performed at intervals of seven days. Before each of these tests the tightening torque of each pin was measured, as shown in Fig. 6, and the pins tightened if necessary. Each postoperative test began with a `no-load' test; this was performed with the animal
Preliminary data
The fixator was applied to a 3-year-old blackface ewe with a preoperative mass of 54 kg. Fig. 7 shows the result recorded during a typical step. The curves show a characteristic shape of an inverted `U', which has been previously reported[8], with the maximum occurring at or just before the midpoint of the step. This shape was consistent through all the walking tests performed. Both the fixator and the ground forces have similar shapes; the correlation coefficient is r2=0.940. Fig. 8 shows the
Discussion
The error limits quoted in Table 1, Table 2 are pessimistic; adding all the limits assumes that all errors will be in the same direction and at the same time, which is unlikely. In addition, the measurement of friction was made by forcing a fixator through its full stroke at the end of a six-week experiment, by which time the travel had been limited by the bone which had united; consequently, the fixator was forced to travel through dirt which had built up, but which was not present at the
Acknowledgements
This work was made possible by funding from Action Research, project number A/L/0256. The early stages of this work were carried out in the Bioengineering Centre, Princess Margaret Rose Orthopaedic Hospital, Edinburgh.
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