J. Biomedical Science and Engineering, 2013, 6, 1021-1028 JBiSE
http://dx.doi.org/10.4236/jbise.2013.611127 Published Online November 2013 (http://www.scirp.org/journal/jbise/)
Drug dispersion for single- and multi-lumen catheters
Dillon B. Schwalbach1, Brian D. Plourde1, John P. Abraham1, Robert E. Kohler2
1School of Engineering, University of St. Thomas, St. Paul, USA
2Translational Research Institute, Gilbert, USA
Received 12 September 2013; revised 15 October 2013; accepted 25 October 2013
Copyright © 2013 Dillon B. Schwalbach et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
This study presents a comparison of the drug disper-
sion capability of various catheters which can be used
to inject medication or stem cells into the arterial sys-
tem. The study was carried out by the use of numeri-
cal simulation so that various geometric and physical
operating parameters could be investigated. The blood
was modeled with a power-law viscosity and the me-
dication had two levels of viscosity to represent upper
and lower bounds expected in practice. Two different
medication flowrates were also incorporated into the
study. Finally, the impact of an inflated balloon up-
stream of the injection was studied. The artery was
simply modeled as a straight circular tube with the
catheters concentrically positioned. It was found that
in some cases, dispersion was improved by use of a
multi-lumen device, particularly when an upstream
balloon was employed to regulate blood flow and drug
residence time. In other cases, the dispersion from the
single-lumen device was su perior. Another finding was
that the multi-lumen device had a reduced hydraulic
resistance to blood flow, compared to the single-lu-
men device when an upstream balloon was inflated.
Keywords: Catheter Injection; Catheter Hemodynamics;
Intracoronary Injections; Stem Cell Treatment of
Infarction; Heart Disease; ND Infusion Catheter
1. INTRODUCTION
Numerous medical situations call for direct injection or
infusion of medication or other fluids that can be used
for patient treatment. Some examples include the intraco-
ronary injection of Adenosine or Nitroglycerin for tran-
sient occlusions or spasm or the infusion of stem cells for
regenerative therapy following myocardial infarction (MI).
For any case of intravascular infusion, it is important to
characterize the distribution of the injectant across the
cross section of the artery. Well-distributed injectant is
more capable of contacting the artery lumen and entering
into the tissue for therapy. As an example of this area of
active investigation, comparisons of direct injection and
intracoronary injections of stem cells are well represent-
ed in the literature, for instance [1-9]. Some of these stu-
dies compared various injection methods [4,6,8]; others
were overviews of the emerging technology of stem cell
use for treating MI (for instance [2,3]); while others com-
pared the impact of injection on the hemodynamics of
the neighboring arteries in bench-top tests (but not on di-
stribution of medication or cells within the artery) [9].
Figure 1 has been prepared to describe the qualitative
difference between a rapid and slowly dispersing injec-
tant. In the upper part of the figure, the injectant, shown
in grey, is seen to rapidly spread across the artery cross
section. In the second part of the figure, the injectant is
confined to a small central region that transits a signifi-
cant distance in the artery before dispersion. The figure
is intended to be illustrative rather than quantitative.
2. NUMERICAL MODELING
The numerical model was laminar, justified by the low-
Figure 1. Schematic of injecting catheters with a rapid
and slowly dispersing injectant.

D. B. Schwalbach et al. / J. Biomedical Science and Engineering 6 (2013) 1021-1028 1022
Reynolds numbers in the system. Blood velocities were
based on a cardiac-cycle average flowrate. The equations
of motion are listed below.
Conservation of mass of species k:
2
2
kk
iii
CC
uD
tx k
C
x



  (1)
Conservation of momentum:
2
2 1,2,3
jj j
iii
i
uu u
p
u
txx
x
 
 






 j
(2)
In these expressions, k designates the species, j indi-
cates Cartesian direction, and i is a tensor variable. The
term D is the diffusivity of the binary fluid mixture. All
equations are expressed in transient form to reflect the
solution strategy of the software (CFX Version 14.0) that
was used to complete the calculations; the ultimate solu-
tions are steady state, a situation which is achieved when
the flow field is no longer changing in time.
The artery is straight with a diameter of 3.5 mm for all
cases. A total of 16 cases were simulated, as listed in Ta-
ble 1. The fluid densities were 1060 and 1000 kg/m3, re-
spectively, for the medication and blood.
As seen from the table, a number of key parameters
are investigated. The first is the single/multiple lumen in-
jection catheter. Next, is the presence of a balloon up-
stream of the injection location which partially blocks
the artery passageway. The third issue listed in the table
is the inlet condition for the blood. For no balloon cases,
the inlet condition is a pre-specified blood flowrate (60
cc/min) coronary artery blood flow of the anterior des-
cending artery, which leads to an average blood velocity
of 0.1039 m/s. For the cases with upstream balloons, the
flowrate was not known apriori so an inlet pressure was
applied that matched the inlet pressure for the no-balloon
case. In this regard, an equivalent overall pressure drop
was enforced.
The fourth item is the viscosity of the injectant which
takes on high and low values that are expected to be up-
per and lower bounds on the actual medication viscosity
used in the therapy. Finally, the medication flowrates are
listed.
Blood was modeled as a non-Newtonian fluid with an
Ostwald-de Waele constitutive model [10] that is
n
K

  (5)
Here, K = 0.0147 (kg/m-s1.22) and n = 0.78 [11]. The
blood model is similar to that described in [12].
Simulated Geometry
To facilitate the discussion of the modeling effort, atten-
tion is next turned to the geometric details. Figure 2 has
been prepared to provide some dimensional detail. The
figure shows a single-lumen catheter positioned in an
artery. The figure is illustrative, in reality, the catheter is
circular as is the artery. The image can be interpreted as
a cut-view along the bisecting symmetry plane. The fig-
ure contains annotations which show key features, in-
cluding the location of blood and medication inlets. The
diameter of the artery is 3.5 mm and the length of the
model is 11 cm so it was necessary to use cut lines to
indicate the length of the model. The solution domain
extends 3 cm upstream of the location where the medica-
tion exits the catheter and enters the bloodstream. The
rationale for this was that such an extension allows natu-
ral development of the flow prior to the injection loca-
tion.
Table 1. List of cases for simulation.
No Lumens Balloon Inlet Cond.
Visc. (mPa*s) Medic. Flow (ml/min)
1 single no Flowrate 1.4 5
2 single yes Pressure 1.4 5
3 single no Flowrate 4.7 5
4 single yes Pressure 4.7 5
5 single no Flowrate 1.4 10
6 single yes Pressure 1.4 10
7 single no Flowrate 4.7 10
8 single yes Pressure 4.7 10
9 multiple no Flowrate 1.4 5
10 multiple yes Pressure 1.4 5
11 multiple no Flowrate 4.7 5
12 multiple yes Pressure 4.7 5
13 multiple no Flowrate 1.4 10
14 multiple yes Pressure 1.4 10
15 multiple no Flowrate 4.7 10
16 multiple yes Pressure 4.7 10

D. B. Schwalbach et al. / J. Biomedical Science and Engineering 6 (2013) 1021-1028 1023
Figure 2. The single-lumen catheter with boundaries and dimensions annotated.
For the case with an inflated balloon, the bounding di-
mensions are maintained however a balloon is positioned
upstream of the injection location. The balloon is sym-
metrically arranged around the catheter, as seen in Fig-
ure 3.
A multi-lumen catheter was modeled after the ND In-
fusion Catheter (Translational Research Institute, Gilbert,
AZ). Instead of a single port for medication to enter the
blood stream, as commonly found in a single-lumen ca-
ther, the ND Infusion Catheter has six ports. The injec-
tion plane of the catheter is shown in Figure 4. There,
the injection ports can be seen near the periphery of the
cross section.
Upstream of this injection plane, the multi-lumen ca-
theter has a complex fluid flow pathway with multiple
mixing regions and collection chambers. Figure 5 has
been prepared to show the medication passageway in an
oblique view. As with the single lumen case, the solution
domain is extended upstream from the injection plane so
that flow development can occur naturally.
From the figures, it is seen that the multi-lumen simu-
lation encompasses a far more complex flow geometry
than that of the single-lumen device. For instance, a sin-
gle channel empties into a mixing chamber which then
serves as a manifold for the six multiple injection lu-
mens.
3. COMPUTATIONAL MESH
The completion of the simulation requires subdivision of
the fluid space into regularly shaped computational ele-
ments. The quality and deployment of the computational
elements are crucial for a successful and accurate solu-
tion. Inasmuch as the flow in this problem is deeply la-
minar, it is not necessary to expend extra elements in the
near wall region to refine the boundary layer. On the
other hand, experience suggests that such near-wall ele-
ments will aid in the predictions of flow separation.
Consequently, the mesh shown in Figure 6 was used for
Figure 3. An inflated balloon positioned upstream of the injec-
tion location.
Figure 4. The injection plane of the multi-lumen ca-
theter with multiple ports indicated.
the single-lumen case. The figure shows a series of mag-
nifications which reveal the details of the mesh. It is seen
that very near the wall, there are thin layers of elements
which were described in the preceding text. Those thin
elements follow the contour of the lumen and balloon, as
evident in the lower part of the figure.
Similarly, the multi-lumen geometry was subdivided
into elements and that deployment is displayed in Figure
7. As with Figure 6, this image shows a succession of in-
creasing magnifications that allows identification of ar-
eas of fine mesh deployment.

D. B. Schwalbach et al. / J. Biomedical Science and Engineering 6 (2013) 1021-1028 1024
Figure 5. Oblique view of the medication passageway for the
multi-lumen device.
Figure 6. Computational mesh for single-lumen geometry.
Figure 7. Computational mesh for multi-lumen geometry.
Both the single- and multi-lumen cases were solved
with increasing numbers of elements so the impact of the
mesh on results could be determined. This succession
continued until the results no longer depended on the
mesh. In this manner, mesh independency was achieved.
The final meshes from this process are those displayed in
Figures 6 and 7 which contain more than 7 million ele-
ments. These meshes were far finer than that needed for
mesh independency.
4. RESULTS AND DISCUSSION
The primary results of interest are the distributions of the
medication across the cross section of the artery. To help
visualize the concentration results, Figure 8 has been
prepared. This figure shows two instances after the medi-
cation injectant has emerged from the catheter. The top
portion shows the medication shortly after emergence
and the bottom shows the injectant at a later time. The
bolus shown in the image is defined as the space which
has medication concentrations greater than some arbitra-
rily selected threshold (1%, 10%, etc.) by volume. Areas
outside the bolus have lower than the threshold concen-
tration. The metric which will be used to characterize the
performance of the devices is the percentage of a down-
stream cross section area that is occupied by volumetric
concentrations that are greater than 1% or 10%. With the
illustration of Figure 8 for context, attention will now be
turned to quantification of the concentrations.
The following results will be focused on the region
distal to the injectant port, within approximately 25 mm
of that location. It is important to recall that the results to
be presented here correspond to steady state conditions
after the bolus has reached the outlet and results are no
longer changing in time.
4.1. Single-Lumen Concentration Results
A global view of the injectant dispersion is provided by
Figure 9. That figure, which corresponds to Case 1, is
provided as a typical dispersion pattern. The top contour
image shows the injectant along the entire length of the
solution domain. The (b) and (c) parts are focused on the
region near the injectant location. The (b) part is color
coded to the legend on the left whereas (c) has two color
regions which reflect zones that have <1% and >1%
medication concentration. The last part of the figure, (d),
shows the 1% region at the exit of the domain. It is seen
that the injectant occupies the center of the artery.
Figure 8. Emergence of injectant bolus from catheter.

D. B. Schwalbach et al. / J. Biomedical Science and Engineering 6 (2013) 1021-1028 1025
Figure 9. Concentration contours on the symmetry plane and outlet for Case 1.
Another feature of the flow is that the medication is
constrained in the center portion of the artery by the
blood flow which insulates it from the artery wall. The
blood serves as a buffer against penetration to the wall.
Much of the spreading occurs in the very near proximity
to the injection ports; further downstream, the dispersion
is gradual.
4.1.1. Impact of Kinem ati c Di ff usi vit y Values
The first set of quantitative results shows the insensitiv-
ity of the results to the value of the kinematic diffusivity.
Four variants of Case 1 were completed with values of
kinematic diffusivity that were 0, 1e−12, 1e−9, and 2e−9
m2/s. These values represent a range of diffusivity values
that might be encountered with two liquid species. It was
found that the results are virtually identical, as displayed
in Figure 10. In fact, aside from the largest diffusion
case, the results are indistinguishable. This finding con-
firms our expectations that the dispersion is primarily
driven by advection rather than diffusion processes. As a
consequence, the remaining results will all be presented
for kinematic diffusivity values of 0 m2/s without loss of
generality.
Figure 10. Comparison of dispersion for four different values
of the kinematic diffusivity. The plotted values are volumetric
concentrations.
4.1.2. Effects of Viscosity, Medication Flowrate, and
Balloon
The next presentation will be for the distribution of in-
jectant from the single-lumen catheter. The metric for
evaluating performance will be the percent of down-
stream area that is occupied by fluid that is more than 1%
injectant and more than 10% injectant by volume. The
first image, Figure 11, shows the single-lumen situation,
with no upstream balloon. Two sets of results are shown
which correspond to Cases 1 and 3. It is quickly seen that
the viscosity of the medication has very little impact on
the dispersion rate of the medication. The results in the
figure are representative of other comparisons that show
insensitivity of viscosity.
Figure 11. Injectant concentrations downstream of single-lu-
men catheter Cases 1 and 3.
impact, the presence of the balloon is more apparent.
Figure 12 shows the development of medication in the
streamwise direction for Cases 3 and 4 which differ only
by the presence of the balloon. For both the 1% and 10% While the medication viscosity is seen to have a small

D. B. Schwalbach et al. / J. Biomedical Science and Engineering 6 (2013) 1021-1028 1026
Figure 12. Effect of balloon on dispersion from single-lumen
catheter, Cases 3 and 4.
regions, the presence of the balloon reduces the cross
sectional coverage.
The last comparison to be made for the single-lumen
case is for the injectant flowrate. For this comparison,
Figure 13 has been prepared which shows that there is
an impact on the dispersion by a doubling of the injectant
flow. In the region very near the injectant port, the lower
flowrate (Case 3) spreads slightly faster than the higher
flowrate case (Case 7). On the other hand, further down-
stream, the situation reverses and the higher medication
flowrate spreads significantly faster. Since there is more
medication entering the stream, it is clear why the larger
medication flowrate spreads faster. The very slight re-
duction in spreading near the injectant port is likely due
to the stronger jet coherence as the medication emerges
into the co-flowing blood stream. Nevertheless, the diffe-
rences in this region are very small. Similar findings
would be seen if other cases were compared, Cases 3 and
7 are representative samples.
4.2. Multi-Lumen Results
Medication that emerges from the multi-port injection
lumen has a distinct dispersion pattern that is best illus-
trated qualitatively. Figure 14 has been prepared which
shows an isosurface that demarks the surface on which
medication concentrations of 10% exist. It can be seen
that the medication emerges from the injection ports off-
center and predisposed to the artery wall, compared to
the symmetric emergence of medication from the single-
lumen case.
More quantitative information is available by plotting
the axial evolution of the dispersion of medication, in
particular, counterparts of Figures 12 and 13. To this end,
Figures 15 and 16 have been prepared. The first of the
figures shows the effect of the balloon on medication
dispersion. In contrast to the single-lumen case, it is seen
that the presence of the balloon actually increases the
Figure 13. Impact of injectant flowrate on dispersion from
single-lumen catheter, Cases 3 and 7.
Figure 14. Emergence of the medication plume from the multi-
lumen ports, flow is off-center, predisposed to the artery sur-
face. The emerging surface demarks a 10% medication concen-
tration zone.
Figure 15. Effect of balloon on dispersion from a multi-lumen
catheter, Cases 11 and 12.

D. B. Schwalbach et al. / J. Biomedical Science and Engineering 6 (2013) 1021-1028 1027
Figure 16. Impact of injectant flowrate on dispersion from
single-lumen catheter, Cases 11 and 15.
dispersion of the medication slightly. This is believed to
be due to the fact that the multiple injection ports are
located near the periphery of the catheter where flow
disturbances from the upstream balloon promote mixing
of the two fluids.
With respect to the effect of mass flowrate, it is seen
that the larger medication flowrates result in significantly
more widespread dispersion of the medication across the
artery cross section, as displayed in Figure 16. In fact,
the impact of the larger medication flowrate for the
multi-lumen geometry is very similar to that of the sin-
gle-lumen case which was displayed in Figure 13.
The last issue to be addressed is the dispersion rates
between the two geometries. It is seen that for some
cases, the single-lumen device results in faster dispersion
while in other cases, the situation reverses. In particular,
it is interesting to compare the dispersion rates of the two
devices in the presence of the upstream balloon. This
situation is particularly relevant because the balloon im-
pacted the two devices differently. Axial dispersion re-
sults are shown in Figure 17.
While this dispersion advantage of the multi-lumen
device is not universal, in some situations the single-
lumen dispersion rate is faster, it suggests that for injec-
tion of therapeutic cells into arteries in the presence of
balloons, enhancement is achieved with multiple lumens.
It also should be noted that while the axial patterns of
medication dispersion are similar, the cross sectional
distributions differ. As exhibited in Figures 9 and 14, the
distribution from the multi-lumen geometry lies closer to
the artery wall and thereby enhances blood-artery wall
mass transfer. This enhancement is important for mass
transfer into arterial tissue [13-20].
Another enhancement with the multi-lumen device is
that the hydraulic resistance for blood flow is reduced. In
the presence of an inflated balloon, the flow resistance
was notably smaller than that for the single lumen device.
Figure 17. Comparison of single- and multi-lumen dispersion
rates in the presence of an upstream balloon.
The differences were in the 8% - 12% range over the
length of the flow region, as depicted in Figure 2.
It is also clear that further improvements of dispersion
could be achieved by spreading the positions of the mul-
ti-lumen ports at the injection plane, or by creating some
radial flow direction at the port location. Not only would
such an arrangement increase dispersion, but it would re-
sult in medication being projected toward the arterial
wall.
5. CONCLUDING REMARKS
A detailed numerical study of the dispersion processes
associated with injection lumina was performed. To the
best knowledge of the authors, this is the first study of its
kind. The study encompassed single-lumen and multi-
lumen catheters and modeled a binary fluid mixture
(blood and medication). The simulation incorporated a
range of medication viscosities, flowrates, catheter ge-
ometries, and the presence or absence of an upstream
balloon. It was found that viscosity had little impact on
the dispersion, however, the presence of a balloon reduc-
ed dispersion for the single-lumen device and increased
dispersion for the multi-lumen device.
For both devices, increased medication flowrates im-
proved the spread of medication throughout the artery
cross section. Further, it was found that in some instanc-
es, the multi-lumen device led to increased dispersion of
medication and in other instances, the performance was
reversed. Finally, the multi-lumen device was found to
reduce hydraulic resistance to blood flow by approxi-
mately 8% - 12% when an upstream balloon was em-
ployed.
It is expected that further dispersion could be achieved
by the utilization of a radial velocity component at the
injection ports.

D. B. Schwalbach et al. / J. Biomedical Science and Engineering 6 (2013) 1021-1028 1028
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