ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

elease and absorption of the heparin. According to [10], the diffusivity of the drug in
the arterial wall Dw and in the lumen Dl are set equal to 7.7x10 -6 mm 2 /s and 1.5x10 -4
mm 2 /s. Concerning the interaction involving drug and ligand/receptor we apply a model
from [11] where the binding reaction constants are kon =10 2 s -1 and koff=10 -2 s -1 and the
average concentration of receptors in the tissue is set to bw,0 =5 (we recall that all data
refer to non-dimensional concentrations with respect to the reference value ĉ, which is
the drug saturation level in water). For the modeling of the stent struts we assume a
circular section radius equal to Rs =0.052 mm which represents the equivalent radius
accounting for the stent thickness. We assume that the initial drug charge, cs, is 10 times
ĉ. In order to evaluate the drug delivery to the arterial wall, we define the dose which is
the time-averaged drug concentration at each point of the arterial wall defined as
T
d (x) = T w −1 ∫ c (t,x)dt eq. (1)
w
0
where cw(t,x) represents the total drug concentration within the arterial tissue given by
the sum of free aw(t,x) and bound drug (bw,0-bw(t,x)) and its mean value
dw(V) = V −1 M (d w ,V) where V represents the control volume. All data refer to the time T
when the drug in the stent coating has been released (T= 6h 20').
The results are evaluated over four different regions of the coronary bifurcation (Fig. 2):
the whole volume of the bifurcation (V-TOT), the proximal part of the MB (V-MBP),
the distal part of the MB (V-MBD) and the SB region (V-SB).
Figure 2: Regions of the coronary bifurcation: whole region (grey), proximal main
branch (V-MBP), distal main branch (V-MBD) and side branch region (V-SB).
In order to evaluate the drug waste due to either the incomplete stent apposition or the
stent struts overlapping in the case of multiple stent implantation, we consider for both
the procedures an idealized configuration in which all the stent struts are perfectly
apposed to the arterial wall.
4. RESULTS AND CONCLUSIONS
For each stenting procedure, we report the total amount of drug delivered to V-TOT, V-
MBP, V-MBD and V-SB.
The delivered drug is quantified by means of bars for both the realistic and idealized
cases. The concentration scale refers to non-dimensional concentration units relative to
the saturation level of dissolved drug in water.
First, comparing the two configurations we observe that the drug dose is higher in all
the four regions when the two-stent technique is performed. Moreover, the analysis of
drug dosage over the four different regions (Fig. 3) gives rise to interesting
considerations.