Numerical Simulation of Mechanical Interaction

							Journal of Information & Computational Science 1: 1 (2004) 15– 19
Available at http://www.joics.com


         Numerical Simulation of Mechanical Interaction
          betweenLower-limb and Compression Stocking
              ,
X. Dai, Y. Li∗R. Liu, Y. L. Kwok
Institute of Textiles and Clothing, The Hong Kong Polytechnic University,
Hong Kong, China
Received 11 June 2004; revised 2 September 2004
Abstract Stocking compression exerted on lower limb is effective to prevent and manage various
venous diseases, such as varicose vein, oedema, and deep vein thrombosis. Different diseases and
different stage of a disease may require compression of different degrees. The purpose of this
study is to theoretically examine the pressure distribution on leg and the mechanical state of the
leg under stocking pressure. A FEM approach is used to simulate the dynamic put-on process of a
knee-length stocking. A biomechanical solid model consisting of soft tissue and bones is built for
the lower leg, and an orthotropic shell model is built for the stocking. With this approach, a
stocking simulation involving different materials, and a lower leg was carried out. Reasonable
pressure and stress distributions in the stocking and the lower leg are obtained. The comparison
between the simulated pressure values and the respective measured results confirms that this
approach is able to predict the pressure of stockings exerted on the legs.
Keywords: Biomechanical model; Pressure distribution; Compression stocking

1 Introduction
For over 150 years, compression stocking has been used as a treatment for venous and
lymphatic disorders, such as deep vein thrombosis(DVT), superficial phlebitis, as well as
in chronic conditions, such as leg ulcers, lymph-edema, and so on [3, 5]. Different
diseases and different stage of a disease may require compression of different degrees.
Compression stocking may be designed to apply graduated or uniform compression.
Graduated compression refers to the application of varying degrees of constant
compression to different segments of the leg, with pressure being greatest at the ankle and
gradually decreasing proximally. Graduated Compression Stockings(GCS) have been
reported that can enhance venous return, reduce stasis by providing graded compression
with the greater pressure applied more distally [3].
As a key factor in the compression therapy, the pressure itself has not been investigated
sufficiently. The pressure exerted by a GCS may vary among individuals, different levels
of a same leg, and even different regions at a same level. Although there are several
approaches that have been reported to model the soft tissue deformation under external
pressure [2, 1, 4], there is still few effective methods to evaluate the pressure exerted by
GCS, and the mechanism of the compression therapy is still not clear. Our aim is to
theoretically investigate the interaction between a leg and a GCS, to predict the pressure
accurately, and further to fundamentally un-derstand the mechanism of the compression
therapy exerted by stockings. For these purposes, we develop a contact model to simulate
the mechanical interaction between a stocking and a leg. A knee-length GCS is modelled
numerically to derive pressure distribution and compared with experimental
measurement.

2 Biomechanical Model
2.1 3-D geometric models of lower leg and stocking
The legging of a compression stocking is usually a round-knitted tube, after fitted to a leg,
it will take the shape of the leg surface. To obtain this 3-dimentional leg-fitted shape, and
also the actual mechanical state for the stocking, a common way is to simulate a dynamic
putting-on process. A simplified model including soft tissue and two bones(the medial
tibia and the lateral fibula) is used to model a lower leg during standing still. The
geometrical model of a lower leg is reconstructed from Magnetic Resonance
Imaging(MRI) coronal images. Fig. 1(a) shows the soft tissue layer of the lower leg.
(a) Lower leg (b) Legging of stocking Fig. 1 Geometrical models We use a kind of commercial
GCS with medical effect to prevent and manage varicose vein as a sample, and simulate
its dynamic wearing on the leg. The stocking size is chosen properly according to the
lower leg’s dimension. The legging of the stocking is of cylindrical shape. We build a
cylindrical tube shown in Fig. 1(b) as the initial geometry of the legging, and its size is
taken from the actual sample.

2.2 Material properties
We made an assumption that the medial tibia and the lateral fibula do not deform due to
wearing stocking, so the bones are assumed to be rigid. The soft tissue material is
assumed to be Part W(tonne/mm) E
1

(MPa) E
2

(MPa) G
12

(MPa)
υ
1

t(mm)
Ankle
2.1 × 10
− 10

0.098
0.147
0.052
0.113
0.8
Calf
2.10 × 10
− 10

0.093
0.059
0.029
0.369
0.76
homogeneous, isotropic and linear elastic. For the soft tissue, Young’s modulus, Poisson
ratio, and mass density are taken as 0.01MPa, 0.49, and 9.37 × 10− 10
tonne/mm
3

respectively [2, 6].
Since knitted fabrics often have significantly different mechanical properties in wale and
course
directions, the material property for stocking is defined as orthotropic and linearly elastic.
Two
kinds of knit stitches are used for the ankle part and the calf part of the legging of the
sample
stocking respectively as illustrated in Fig. 1(b). Hence the two parts have different
mechanical
properties. All the parameters used in the numerical analysis are listed in Table 1, where
E
1

and
E
2

denote the Young’s moduli in the course and wale directions respectively, G
12

and υ
1

are the
shear modulus and Poisson ratio, and t denotes the fabric thickness.

2.3 Finite element analysis
2.3.1 Model discretization
The model was elaborated using the ABAQUS 6.4 FE software package. Automatic
division
was used to generate meshes of 4-node linear tetrahedron solid elements for bone and soft
tissue
respectively with the global seed size of 8mm, as well as a mesh of 4-node quadrilateral
membrane
elements for the legging, whose global seed size is 3mm. Each node has three degrees of
freedom.
2.3.2 Contact constraints
The interface between a legging and a lower limb is considered as surface-to-surface
contact, the
surfaces can undergo finite sliding relative to each other. Finite sliding allows arbitrary
motion
of the surfaces forming the contact pair. A penalty method is employed to enforce a
kinematical
constraint that the slave surface nodes(inner surface of legging) do not penetrate the
master
surface(lower leg surface). Forces(pressures) that are a stiff linear function of the
penetration
distance(overclosure) are applied to the slave nodes to oppose the penetration into the
master
faces, while equal and opposite forces act on the master surface at the penetration point.
And
then the master surface contact forces are distributed to the nodes of the master faces
being
penetrated.
2.3.3 Boundary condition
We assumed that the medial tibia and the lateral fibula do not deform due to wearing
sock,
therefore the displacements of all the nodes on the two bones are constrained in all
directions as
boundary condition in the simulation. For the legging, along the lower leg length
direction, the
displacements of both the top and the bottom welts are defined while in the
cross-sectional plane
they can deform freely according to the shape of the lower leg.
2.3.4 Numerical solution
The geometric non-linearity due to the large deformation of the stocking, and the
boundary
non-linearity due to the discontinuous contact constraints make the mechanical simulation
com-
plicated. ABAQUS/Explicit, which is well suited for nonlinear analysis, is used to solve
the
dynamic system.

                                                                                   Page 4
18
X. Dai et al. /Journal of Information & Computational Science 1: 1 (2004) 15– 19

3 Experimental Results and Discussions
Fig. 2 shows two frames taken from the dynamic wearing simulation, the top frame is
during
the putting-on process, and the bottom one is the final completed state. From these figures
we
can notice that once the contact occurs, the interaction between the lower leg and the
stocking
stretches the stocking, meanwhile inducing pressure on the lower leg. As the contact area
in-
creases, the pressure also spreads. As the stocking becomes much more stretched, the
pressure
value increases. However, even at the final state, the pressure does not distribute
uniformly all
over the lower leg. Due to the complicated geometrical feature of the lower leg surface,
the legging
is not in contact with the underlying leg everywhere.
(a) Stress in Stocking
(b)Pressure on leg surface
Fig. 2 Dynamic wearing of a stocking on a leg
(a) Measurement position
(b) Pressure values
Fig. 3 Pressure exerted on leg
At the final wearing completed state, the ankle part shows significant higher stress than
that
at the calf part due to the difference of mechanical properties of the materials used for the
two
parts. It results in that the pressure value decreases as going up from the ankle to the calf.
This
pressure gradient is usually demanded in compression therapy.

                                                                                     Page 5
X. Dai et al. /Journal of Information & Computational Science 1: 1 (2004) 15– 19
19
To confirm the simulated results, the wear trial of the stocking on the subject whose leg is
scanned for the simulation is carried out, and the pressure in situ is measured. The
measurement
positions are illustrated in Fig. 3(a). Comparing the measured pressure values to the
respective
simulated results, good agreement is obtained as shown in Fig. 3 (b), where “ M” and “ S”
denote
measured pressure and simulated pressure respectively.

4 Conclusion
The dynamic putting-on simulation demonstrates that the pressure exerted on leg is
induced due
to the fabric stretch, and its value depends on fabric tension and the curvature of the leg
surface.
The comparison between the simulated results and the experimental measurements
confirms that
the model is able to assess the pressure with satisfied accuracy. With the stocking wearing
model,
the overall pressure distribution can be predicted in a quick and easy way. It will be
helpful in
the clinical practice and the design of compression stockings. Through this model, the
further
investigation on the internal mechanical state of the leg is expected to help us understand
the
mechanism of compression therapy.

Acknowledgment
We would like to thank the Hong Kong Polytechnic University for the funding of this
research
through the project G-YD31 entitled “ Biomechanical Sensory Functional Design of
Socks” .

References
[1] R. G. M. Breuls et al., A theoretical analysis of damage evolution in skeletal muscle tissue
with
reference to pressure ulcer development, J. Biomech. Eng 125 (12) (2003) 902-909.
[2] G. H. Dai, J. P. Gertler and R. D. Kamm, The effects of external compression on venous blood
flow and tissue deformation in the lower leg, J. Biomech. Eng 121 (12) (1999) 557-564.
[3] O. A. G. Hamilton and D. Baker, Graduated compression stockings in the prevention of
venous
thromboembolism, Br. J. Surg 86 (1999) 922-1004.
[4] C. W. J. Oomens et al., Can loaded interface characteristics influence strain distribution in
muscle
adjacent to bony promiences?, Comp. Meth. Biomech. Biomed Eng 6 (3) (2003) 171-180.
[5] A. A. Ramelet, Compression therapy, Dermatol. Surg 28 (2002) 6-10.
[6] Y. Xiu, Advances in Sports Biomechanics, National Defense Industry Press, Beijing, 1998,
215-240.