Metatarsal Osteotomy Using Double-Threaded Screws - Biomechanical Analysis

METATARSAL OSTEOTOMY USING DOUBLE-THREADED SCREWS:

BIOMECHANICAL ANALYSIS

Anna ZIĘBOWICZ, Anita KAJZER, Wojciech KAJZER, and Jan MARCINIAK

Silesian University of Technology, Institute of Engineering Materials and Biomaterials, ul. Konarskiego 18a,

44-100 Gliwice, Poland

email: [email protected]

Abstract: The fundamental purpose of this research was to determine the biomechanical characteristics of the

first metatarsal bone – double-threaded screws system made of stainless steel (Cr-Ni-Mo) and an assessment of

its stability. To define the biomechanical characteristics of the system, the finite element method and

experimental method were applied. Geometric models of metatarsal bone and double-threaded screws, were

discretized by means of SOLID 95 element. Appropriate boundary conditions imitating phenomena in the real

system with appropriate accuracy were established. The aim of biomechanical analysis was calculation of

displacements and stresses in the bone and the stabilizers in a function of the applied loading. The experimental

method was carried out to calculate displacements of the analyzed system. The obtained results can be applied to

determine the construction features of the stabilizer and to select mechanical properties of metallic biomaterial

(selection of degree of strain hardening).

1. INTRODUCTION

The human foot combines mechanical complexity and structural strength. The ankle serves

as a foundation, shock absorber and propulsion engine. The foot can sustain enormous

pressure (several tons over the course of a one-mile run) and provides flexibility and

resilience. Structurally, the foot has three main parts: the forefoot, the midfoot, and the

hindfoot.

The foot and ankle contain: 26 bones that can be divided into the tarsal bones, the

metatarsal bones and the phalanges – Fig.1. The tarsal bones are the larger bones that form the

back section of foot, with the calcaneum being the largest. There are five metatarsal bones and

these are given names from the first to the fifth. The first metatarsal bone is the largest and is

the bone that joins to the big toe. It also has a lack of interconnecting ligaments between itself

and the second metatarsal. This allows for independent motion.

Fig.1. Top view of foot bones [1]

The foot also contains: 33 joints; more than 100 muscles, tendons (fibrous tissues that

connect muscles to bones), ligaments (fibrous tissues that connect bones to other bones) and

a network of blood vessels, nerves, skin and soft tissue.

These components work together to provide the body with support, balance and mobility.

A structural flaw or malfunction in any one part can result in the development of problems

elsewhere in the body. Abnormalities in other parts of the body can lead to problems in the

feet [2,3].

The metatarsal bones are some of the most commonly fractured (broken) bones in the foot.

There are two main types of metatarsal fractures:

acute fractures – due to a sudden injury to the foot (commonly dropping a heavy

object onto the foot, a fall or a sporting injury) [4]

stress fractures – due to overuse, or repetitive, injury to a normal metatarsal bone [5].

The kind of fracture should be characterized and treatment initiated. Metatarsal fractures

are divided into three sections – 1st, 5

th and 2

nd – 4

th [6,7]. Due to the head of the first

metatarsal being thought to bear one third of our body weight, any evidence of instability

requires operative fixation [8]. The present-day alternative of small-bones reconstructions in

orthopaedics is the double-threaded screws, that indicate many favorable features especially

with reference to minimization of tissue traumas. The matter of these solutions is application

of two threads of diverse diameter, that assure stabilization of bone fragments with the use of

physiological effects [9].

2. MATERIALS AND METHODS

The main aim of the work was the determination of the biomechanical characteristics of the

first metatarsal bone – double-threaded screws fixation. On the basis of technical

documentation, the geometrical model of screws was carried out in ANSYS v.10 – Fig. 2. In

order to carry out the numerical analysis, the following material properties were as follows:

bone: E=18600 MPa, =0.3

Cr-Ni-Mo steel: E=200000 MPa, =0.33 [10,11,12].

The geometrical model of metatarsal bone – the double-threaded screws system takes into

consideration the operation technique was presented in Fig. 3.

Fig.2. Geometrical model of double-threaded screw

On the basis of the geometrical models a finite element mesh was generated with the

use of SOLID95 finite elements. In order to carry out calculations, it was necessary to

evaluate and establish initial and boundary conditions which imitate phenomena in the real

system with appropriate accuracy [13,14,15]. The following assumptions were established:

lower part of the metatarsal bone was immobilized (all degrees of freedom of nodes on

external surfaces of condyles were taken away)

there was three stages of solution performed: 1 – displacement 1 mm was established at

the basis of metatarsal bone, 2 – force F=500 N was applied at the basis of metatarsal

bone, 3 – force F=3000 N was applied according to bending and compression tests.

L

L1 3,5

D2

D1

2,0

Fig.3. Geometrical model of : a – human foot, experimental and geometrical model of:

b – metatarsal bone “I”– double-threaded screws system

The scope of the analysis included the determination of displacements and stresses in

elements of the metatarsal bone “I” – double-threaded screws made of stainless steel.

Stresses and strains obtained in the analysis are reduced values according to the Huber –

Misses hypothesis.

In the experimental research of the metatarsal bone – double-threaded screws system

(anatomical fracture simulated) the universal testing machine Zwick/Roell Z100/SN5A was

applied. The experimental model was placed between cross-beams in order to do

a compressing test. Measurement of the displacement values were done on the z axis direction

– Fig. 4a. Measurement of the displacement values during the bending test were registered in

the direction of the y axis – Fig. 4b.

Fig. 4. Experimental model and a – compressing test, b – bending test

a) b)

3.RESULTS

The obtained results for the given boundary condition were presented in Table 1 as well as

in graphic form – Fig.5 and 6.

Table 1.

Results of the numerical analysis of the metatarsal bone "I" – double-threaded screws system

Load steps

Displacement, mm

Strain ,

%

Stress ,

MPa

x y z

1 Displacement

1 mm

System 0.300 0.030 0.160 1.069 0.32 4762

Double-threaded

screws 1389

2 Force

F = 500 N

System 0.006 0.005 0.05 0.529 0.44 4525

Double-threaded

screws 541

3 Force

F = 3000 N

Compression 0.004 0.005 0.05 0.529 0.46 4707

Bending 0.152 0.012 0.016 0.020 0.43 4890

Double-threaded

screws 690

Maximum stresses in the screws were localized in the transition zone between threads for the

displacement equal to 1 mm. For the stainless steel screws and for the applied boundary

conditions, maximum stresses were equal to 1389 MPa. However, the stresses on the whole

surface for the applied force 500 N and the displacement equal to 1 mm, did not exceed 500

MPa.

Fig. 5. Displacement distribution in bone – double-threaded screws system: a) axis OX, b) axis OY, c) axis OZ,

d) displacement vector sum, load step 1

a) b)

c) d)

Fig. 6. Displacement distribution in bone – double-threaded screws system: a) axis OX, b) axis OY, c) axis OZ,

d) displacement vector sum, load step 2

On the basis of the performed analyses, it can be stated that the displacement

characteristics of the first metatarsal bone – double-threaded screws system in the

experimental and numerical conditions were similar – Fig. 7.

Fig. 7. Comparison of displacements for experimental and numerical analysis

Observations of the experimental model after the compression test revealed that one of the

compression screws was broken.

Damage localization corresponded with the maximum values of stresses obtained from the

numerical analysis – Fig. 8.

a) b)

c) d)

Fig. 8. The place of screw damage reduced stresses distribution, MPa – a,

displacement distribution in bone, mm – b

Analogous, stress analysis of the numerical model revealed that the maximum values

of stresses obtained from the bending loads were localized in the place of screw narrowing –

Fig. 9.

Fig. 9. The place of the maximal screw effort reduced stresses distribution, MPa – a,

displacement distribution in bone, mm – b

On the basis of the analysis, it was concluded that maximum equivalent stresses were

localized the fixation site of the model and at the point of the applied loading.

The obtained displacements for the metatarsal bone – compression screws system for both

tests: compression and bending revealed, that maximum values did not exceed 0.22 mm and

0.15 mm respectively whereas displacements obtained from the experimental analysis were

equal to 0.23 mm for the compression and 0.19 mm for the bending test.

b) a)

a) b)

4. CONCLUSIONS

The work presents results of biomechanical analysis of the first metatarsal bone – double-

threaded screws system. The analyses were carried out with the use of finite element method

and experimental method.

Proposed numerical solutions were followed by biomechanical analysis which allows the

determination of characteristics connected with displacements in a function of applied

loading. This fact is of great importance in risk assessment of the operation and the

rehabilitation as well.

Knowledge of overloading causes dysfunctions as a consequence of instability determine

further therapeutic management – both operative and rehabilitation. Of the back of the

postoperative effects like decreased first metatarsophalangeal joint motion, shortening of the

first metatarsal, dorsal displacement of the capital fragment deformation causes – generally

functional disorders and dysfunctions of the foot – can be observed.

Displacements and stresses in the systems’ elements were calculated. In the work

presented, the most often using metallic biomaterial - Cr-Ni-Mo steel. Susceptibility of the

system to displacement caused by the applied loading is the important parameter influencing

the effectiveness of the proposed stabilization. Therefore, the numerical analysis of the

metatarsal bone – double-threaded screws system for the applied metallic biomaterial

indicated dangerous areas of the screws and is a starting point for the geometry optimization.

The analysis of the obtained results showed that for the given way of loading, the damage of

the screws is highly probable in the most vulnerable area i.e. the transition zone between

threads. Experimental research of double-threaded screws was focused on stability tests in

order to verify the results of the numerical analysis.

On the basis of the obtained results, it can be stated that:

the displacement characteristics of the first metatarsal bone – double-threaded screws

system received with the use of the experimental method showed good correlation

with the numerical results

the maximum values of the screw stresses obtained from the numerical method

confirm the damage localization of the canullated compression screw observed during

the experimental analysis

the obtained results are the basis for the selection of the structure and mechanical

properties of the metallic biomaterial and geometrical features of the implant, it can

also be applied in the selection of stabilization methods of metatarsal fractures.

ACKNOWLEDGEMENTS

The work was supported by the research and development project no. R0801601 founded

by the Ministry of Science and Higher Education.

BIBLIOGRAPHY

1. Anatomical Chart Company (2005) Anatomy and injuries of the foot and ankle.

Lippincott Williams & Wilkins.

2. Foster A., Edmonds M. (2007) A colour atlas of foot and ankle disorders. Churchil

Livingstone, first edition.

3. Arndt A., Ekenman I., Westblad P., Lundberg A. (2002) Effects of fatigue and load

variation of metatarsal deformation measured in vivo during barefoot walking. Journal

of Biomechanics 35: 621-628.

4. Rosenberg G.A., Sferra J.J. (2000) Treatment strategies for acute fractures and

nonunions of the proximal fifth metatarsal. Journal of the American Academy of

Orthopaedic Surgeons 8(5): 332-338.

5. Buckwalter J.A., Brander E.A. (1997): Stress and insufficiency fractures. American

Academy of Family Physician 56: 175-182.

6. Beck M., Mittlmeier T. (2008) Metatarsal fractures. Der Unfallchirurg.111(10): 829-

839 (in German).

7. Rammelt S., Heineck J., Zwipp H. (2004) Metatarsal fractures. Injury 35 Suppl 2:

SB77-86.

8. Sorensen M.D., Hyer C.F. (2009) Metatarsus primus varus correction: the osteotomies.

Clinics in Podiatric Medicine and Surgery 26(3): 409-425.

9. Stryker Leibinger GmbH & Co. KG (2004) TwinFix cannulated compression screw,

Leibinger solutions for hand surgery. Procedural Guide.

10. Marciniak J. (2000) Austenitic steel – the basic implantation material used in

orthopaedic surgery. Orthopaedy, Traumatology, Rehabilitation 3: 52-58. (in Polish)

11. Marciniak J. (2002) Biomaterials, Edit by Silesian University of Technology, Gliwice:

238-252 (in Polish).

12. ISO 5832-1 (2007) Implants for surgery metallic materials -- Part 1 -- Wrought

stainless steel.

13. Walke W., Marciniak J., Paszenda Z., Kaczmarek M., Cieplak J. (2008) Biomechanical

behaviour of double threaded screw in tibia fixation. Information Technologies in

Biomedicine. Advances in Soft Computing Springer-Verlag 47, Berlin Heidelberg:

521-528.

14. Ziębowicz A., Kajzer A., Kajzer W., Marciniak J. (2009) Biomechanical analysis of

the 1st metatarsal - compression screws system. Engineering of Biomaterials.

15. Kajzer W., Kajzer A., Marciniak J. (2009) FEM analysis of compression screws used

for small bone treatment. Journal of Achievements in Materials and Manufacturing

Engineering 33(2): 189-196.