Page 50 - Advances in Biomechanics and Tissue Regeneration

44 3. DESIGN, SIMULATION, AND EXPERIMENTATION OF COLONIC STENTS

BEHAVIOR EQUATIONS
6EIδ 2M 12EIδ
Bending moment: M ¼ L 2 ; shear force: V ¼ L ¼ L 3
The relationship between the pressure and the diameter of the stent may be written as:
12EIπΔD
cosα
p ¼ 3
nL D
where tanα¼πD/2nh.
Gianturco, Song, Choo, Cook, and Symphony stents correspond to this mechanism, with some variants. Therefore,
on the one hand, some of them present sliding knots among modules (Gianturco, Song, and Choo), while others pre-
sent rigid knots (Cook and Symphony); on the other hand, the knots in the different modules of the stents can be cor-
responding (Symphony) or not corresponding (Gianturco, Song, Choo, and Cook). Finally, Gianturco, Song, and Cook
stents have straight arms, while Choo and Symphony stents have curved trusses.

3.2.3.1.3 RADIAL MULTIPLE ARCS SPRING
The Ultraflex Tracheobronchial Stent (Boston Scientific) is based on the radial spring with multiple arcs and
sliding knots between wires (Fig. 3.12A), with design parameters: pitch (h), diameter (D), wire diameter (d),
number of arcs along the circumference (n), arc radius (r), arc angle with respect to the stent axis (α), and arc
semiangle (θ 0 ).
The behavior of this mechanism is much more complex, including multiple deformations at different levels.
However, the theory of slender arcs can be used to obtain a simplified model, depending on the bending defor-
mations of the smaller arcs, which are the most significant. According to Fig. 3.12B, considering the bending defor-
mations for an arc induced by pressure, the relationship between the pressure and the deformed shape of the stent
may be obtained.
Therefore we can write:

KINEMATICS RELATIONS
Undeformed circumference length: L 0 ¼π D
Deformed circumference length: L¼π (D+ΔD)
Increasing circumference length: ΔL¼πΔD¼nδ h
Increase in step: Δp¼δ v cosα

STATIC EQUILIBRIUM
Balancing forces in half spring (Fig. 3.12A), we have:
D + ΔD
2
Axial force: T ¼ p 0 p Δpð Þ
BEHAVIOR EQUATIONS
2Tr 2 1 3
4
2
Horizontal displacement: δ h ¼ EI θ 0 + cos2θ 0 sin2θ 0
Tr 2 1 θ 3
EI 2 0 sin2θ 0 cos2θ 0
4
Vertical displacement: δ v ¼

FIG. 3.12 Radial multiple arcs spring: (A) design parameters; (B) free-body diagram.

I. BIOMECHANICS