Hinged External Fixators for Knee Rehabilitation

Kinematic Concept of a Two Degree-of-Freedom System

Gianluca Gatti

, Shadi Shweiki

, Giorgia Lupinacci

, Gionata Fragomeni

and Guido Danieli

Dept. of Mechanical, Energy and Management Engineering, University of Calabria, V. Bucci, 87036 Rende (CS), Italy

Dept. of Medical and Surgical Sciences, University of Magna Graecia, V. Europa, 88100 Catanzaro (CZ), Italy

Keywords: Knee Kinematics, Passive Knee, Hinged External Fixator, Knee Dislocation.

Abstract: Hinged external fixators are used in knee dislocation treatment, where they have shown their effectiveness.

They are proposed as a technique to protect ligament reconstructions while allowing early postoperative

rehabilitation. A hinged external fixator usually consists of two rigid links connected to each other by a

revolute joint. Each link is then fixed to the femur and tibia, via direct pin fixation. A single-axis hinged

external fixator thus well accommodates the main knee movement, i.e. the flexion and extension. This paper

presents an investigation on the conceptual idea of a double-axis hinged external fixator for the human knee,

which accommodates for both flexion-extension and longitudinal internal-external rotation of the tibia

respect to the femur. The potential advantage of such a design is foreseen in the increasing range of motion

in postoperative knee rehabilitation and a better accommodation of natural knee motion.

1 INTRODUCTION

Injuries and trauma that may occur in the human

knee often lead to difficulties in having a fast and

complete rehabilitation. Among these trauma,

dislocation is one of the most severe injuries.

Clinical outcomes after knee dislocations are

frequently unsatisfactory, and pain, instability and

arthrofibrosis are the most frequent complications

(Stannard et al., 2003; Stayner and Coen, 2000). The

instability basically lies in the injury of ligaments,

and in some cases, even after repair, there is

insufficient stability for early rehabilitation. This is

the reason why preliminary reports on such

treatment focused on achieving stability of the

ligaments by means prolonged immobilisation

during the postoperative period, although this would

lead to stiffness of the joint (Noyes and Barber-

Westin, 1997; Shapiro and Freedman, 1995).

In more recent studies, authors intensely

advocate early and aggressive mobility despite the

risk of ligament repair or reconstruction failing

(Cole and Harner, 1999; Yeh et al., 1999), and this

led to the concept of the fixator with motion

capabilities (Deszczynski et al., 2000; Fitzpatrick et

al., 2005). A hinged external fixator usually consists

of two rigid links connected to each other by a

revolute joint. Each link is fixed to the femur and

tibia through direct pin fixation. Previous

biomechanical studies showed that a single-axis

hinged external fixator is able to reproduce and

accommodate the normal knee kinematics in a

limited portion of the range of motion without

harmfully loading the structures (Sommers et al.,

2004; Wroble et al., 1997). Such external hinge, set

to an approximate rotational axis of the articular

joint, neutralises the displacing forces during the

movement, and control the natural repair mechanism

of the ligament apparatus. The fixator will thus

allow patient mobility without the risk of loading the

injured area during treatment and rehabilitation.

The main difficulty in the application of hinged

external fixators is the implantation and, in

particular, the location of the articular joint axis of

rotation. Commonly, this axis is manually identified

by means of radiographs on the base of bony

landmarks (Fragomeni et al., 2006; Richter and

Lobenhoffer, 1998) and then the mechanical hinge

of the fixator is aligned through screw adjustments.

This technique may be prone to errors and the

approximation in enforcing an articular joint to an

unnatural mechanical behaviour may lead to

unwanted outcomes in post-traumatic knee

kinematics. This latter is, in fact, a result of a

224

Gatti G., Shweiki S., Lupinacci G., Fragomeni G. and Danieli G..

Hinged External Fixators for Knee Rehabilitation - Kinematic Concept of a Two Degree-of-Freedom System.

DOI: 10.5220/0004904002240229

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2014), pages 224-229

ISBN: 978-989-758-013-0

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

complex interaction of bones, ligaments and

muscles, which may be completely described by six

degrees of motion during dynamic activities

(Palastanga et al., 1989; Lafortune et al., 1992).

Only as a first approximation, such kinematics may

be modelled as a simple flexion-extension

movement, which is indeed coupled to the

longitudinal rotation of the tibia (Piazza and

Cavanagh, 2000), making knee kinematics three-

dimensional.

In this paper, we present the conceptual idea of a

two degree-of-freedom (DOF) system from the

kinematic point of view, which may cope with both

the two dominant movements of the knee, i.e. the

flexion-extension (FE) and the longitudinal internal-

external rotation (LR). The aim of the paper is

mainly to show the most relevant kinematic issues

involved in such a design. As such, some of the

forthcoming issues related to the materials selection,

and to the specific fastening and assembling

considerations are not treated in the following

sections.

Such a device design would potentially allow for

a better rehabilitation, while retaining the main

advantages of articulated external fixation. And this

would be due to the fact that an additional degree of

mobility, respect to traditional hinged fixators,

would allow the articular knee joint to better

accomplish its natural movement

2 MATERIALS & METHODS

2.1 Knee Joint Axes Identification

Design and implant of hinged external fixators

requires a good understanding ok knee kinematics

and accurate measurements. Among the different

techniques effectively used for joints kinematics

detection, relying on electromagnetic, imaging or

ultrasound systems (Kinzel and Gutkowski, 1983;

Bull and Amis, 1998), instrumented spatial linkages

(ISLs) are perhaps some of the most commonly used

6-DOF measuring devices for anatomical joints

motion description. An application of an ISL in

place on a MITA Endo Leg system and on a virtual

knee model is reported in Figure1(a) and (b).

An ISL consists of a series of seven rigid links

connected to each other by six rotational sensors.

The end segments of the ISL are attached to the two

bones whose relative motion is to be measured, and

this motion can be estimated by the geometry of the

linkage and the transducers reading. The use of ISLs

to measure three-dimensional human joints motion

were effectively applied for either in vitro or in vivo

studies (Lewandowski et al., 1997; Van Sint Jan et

al., 2002), and also effectively used whenever direct

fixation to bones is required (Gardner et al., 1996;

Danieli et al., 2005a; Ishii et al., 1997), as an

alternative approach to active robotic systems

(Danieli et al., 2005b). Requirements for adequate

measurements involve advanced calibration of the

devices (Liu and Panjabi, 1996; Gatti et al., 2010;

Gatti and Danieli, 2008; Sholukha et al., 2004; Gatti

and Danieli, 2007).

(a)

(b)

Figure 1: An application of an ISL to measure knee

kinematics of (a) a MITA Endo Leg System and (b) a

virtual knee model.

Several authors (Hollister et al., 1993; Roland et

al., 2010; Gatti, 2012), presented and validated

techniques to estimate and identify both the

functional FE axis and the LR axis of the human

knee. Experimental clinical outcomes based on

literature, e.g. Smith et al. (2003) and Williams and

Logan (2004), may be also used as a guide to

correctly identify the location of knee axes and help

in correctly setting the external fixator implant.

With reference to Figure 2, for instance, the

HingedExternalFixatorsforKneeRehabilitation-KinematicConceptofaTwoDegree-of-FreedomSystem

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technique presented in (Gatti, 2012) let one define

the FE axis by identifying the components of its unit

vector u

and the coordinates of a point O

in an

orthogonal reference frame (x

) attached to the

femur. In a similar way, the LR axis is defined by

identifying the components of its unit vector u

and

the coordinates of a point O

in an orthogonal

reference frame (x

) attached to the tibia. These

geometrical features are easily identified when using

an ISL with its end fixtures attached rigidly to the

proximal and distal bones.

Figure 2: Identification of the dominant axes of the knee

joint according to the procedure described in (Gatti, 2012).

Although these techniques appear to be applied

to virtual models, and clinical applications to

cadaveric knee specimens seems not to be reported

yet, they seem to be potentially applicable in

experimental campaigns on in-vitro fresh-frozen

cadaveric specimens to clinically identify the

approximate location of the two dominant axes with

respect to specific bony landmarks.

2.2 External Fixator Kinematics

Once the approximate FE axis and the LR axis are

identified, an articulated hinged external fixator with

two degrees of freedom, i.e. having two rotational

hinges, may be designed having its mechanical

hinge joints aligned to the functional knee axes, in a

similar manner than that currently suggested in the

recommended technique and instructions by

manufacturers of single-axis hinged external fixators

(e.g. Compass Universal Hinge, Smith&Nephew).

In order to allow for an accurate alignment, the

kinematic structure of the 2-DOF external fixator

should be designed properly, such to have the

capability to set the correct position and orientation

of each functional axis respect to the relative bone.

This can be assured by the use of a multi-DOF

adjustable kinematic structure which is attached at

one end to the fixation pins of the correspondent

bone, and at the other end is aligned to the

correspondent functional axis. The kinematic

structure reported in the schematics of Figure 3,

illustrates these requirements. In this figure,

different mechanical joints are identified by different

letters, where R stands for ‘rotational’ joint, which

allows only a relative rotation to its joined links

around its axis of rotation, and C stands for

‘cylindrical’ joint, which allows for simultaneous

independent rotation and translation of its joined

links around and along its axis of motion. As a

whole, the kinematic chain reported in Figure 3, has

three rotational joints each allowing for one relative

DOF and two cylindrical joints, each allowing for

two relative DOF – it then has a total of one DOF

which is uses to adjust the kinematic structure

according to the bone segment.

Figure 3: Schematics of the multi-DOF kinematic

structure to allow for alignment of the functional FE axis.

An equivalent structure is used, respect to the tibia, to

allow for alignment of the functional LR axis.

Once each functional axis is identified in its

correspondent reference frame, the multi-DOF

structure, as sketched in Figure 3, may be used to set

the correct alignment both in position and

orientation.

The coupling between the two structures is then

realized by designing a two DOF mechanism which

allows for free independent rotations around the two

functional axes of the knee joint. This is illustrated

in the sketch of Figure 4.

Figure 4: Schematics of the 2-DOF mechanism to allow

for independent rotations around the two functional axes

of the knee joint.

The mechanism is realized by assembling three

cylindrical joints to assure a fixed orientation

between the two functional knee joint axes.

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The mechanical assembly sketched in Figure 3 may

be realized by connecting standard fixator

components. A virtual CAD model of the proposed

multi-DOF structure is illustrated in Figure 5(a),

while a photograph of the correspondent standard

component assembly is shown in Figure 5(b).

(a)

(b)

Figure 5: Multi-DOF structure used to assure correct

position and orientation of functional joint axis respect to

the correspondent bone: (a) virtual CAD model and (b)

photograph of an assembly using standard fixator

components.

From the mechanical point of view, the 2-DOF

mechanism sketched in Figure 4 presents an issue

related to the fact that it is not possible to align a

mechanical joint to the LR axis since it is located

internally to the shank. This is overcome by

designing an equivalent mechanism, whose virtual

CAD model is shown in Figure 6. In this assembly

the DOF associated to the FE rotation is realized by

the use of a hinge joint located externally to the

knee, while the DOF associated to the LR rotation is

realized by the use of a circular ring coupled to a

mating feature which realizes an equivalent

rotational motion without the need of physically

locating a mechanical hinge on the LR axis. The full

virtual assembly of the external fixator, with the

multi-DOF structures connected to the 2-DOF

mechanism is illustrated in Figure 7.

The 2-DOF hinged external fixator is then

designed so that it may be correctly implanted once

the relative location and orientation of the two

Figure 6: Virtual CAD model of the 2-DOF mechanism

used to assure free independent rotations around the two

functional axis of the knee joint.

(a)

(b)

Figure 7: Virtual CAD model of the whole 2-DOF hinged

external fixator implanted to a virtual knee model: (a)

assembly in the full extended configuration with no LR

rotation, and (b) assembly in a configuration such that the

angle of flexion is about 45° relative to the configuration

in (a), and the angle of longitudinal rotation is

approximately 5° relative to the configuration in (a).

functional knee joint axes are identified by the use of

an ISL. The fixation pins on each bone segment

assure that both the ISL and the external fixator have

a unique reference frame association, so that errors

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may be reduced at source. The multi-DOF structures

are cinematically designed so has to allow for a

proper degree of mobility in order to set the

clamping fixture on the fixation pins according to

the specific thigh/shank conformation. Once each

multi-DOF structure is adjusted to correctly match

the correspondent functional axis, each joint of the

structure is locked using the screw connections

adopted in standard fixators, as shown in Figure

5(b). This assures that the relative position and

orientation of the functional axes remain constant

throughout the knee joint motion.

Simulations are finally performed on a virtual

model of the knee as illustrated in Figure 7,

assuming fixed axis of FE and fixed axis of LR. To

account for a more general case, the functional axes

are chosen neither to be orthogonal nor to intersect

each other. More specifically, a simulation is run by

assuming, with reference to Figure 2, the following

location for the functional FE axis

= (190, 80, -

10) mm,

= (0.1219, 0.9775, 0.1724) and the

following location for the functional LR axis

(16.068, -107.57, 139.52) mm,

= (0.0733,

0.9779, 0.1956), where the superscript on the left-

hand side denotes the frame of reference respect to

which coordinates are given. The angle of flexion

and longitudinal rotation are varied according to the

plot in Figure 8. The simulations performed

confirmed the validity of the kinematic solution

proposed in the paper.

Figure 8: Angles of flexion-extension and longitudinal

rotation imposed in simulation.

3 CONCLUSIONS

The conceptual idea of a double-axis hinged

articulated external fixator with two degrees of

freedom is illustrated in this paper. Such a system is

based on clinical findings which shows that, in the

human knee motion, the flexion extension

movement is coupled with a longitudinal internal-

external rotation of the tibia. In knee dislocations

treatments, where aggressive mobility and

rehabilitation is advocated, such a biomechanical

devices could potentially improve the motion

capabilities currently provided by available single-

axis external fixators, and hopefully improve

postoperative outcomes for patients. The current

work limited the presentation to the kinematic

design and conceptualization of the fixator. As such,

the mobility of the device, its degree of adjustment

according to patient, and its main kinematic issues

have been addressed. Kinematic simulations have

been performed to assess the validity of the design.

The main fixator components are those used in other

standard fixators, so that the design of specific

features is only limited to the innovative parts

achieving the double-axis movement. Comparative

analyses with other fixators is foreseen, and

extensions of the present work will include also an

insight into the manufacturing issues, strength

requirements and material selection. A preliminary

prototype of the proposed external fixator is planned

to be realized and applied to a physical model of the

knee joint available in laboratory, once its functional

axes have been estimated by the use of the available

ISL using the procedures described in the literature.

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