Drug dispersion for single- and multi-lumen catheters

doi:10.4236/jbise.2013.611127

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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

Email: [email protected]

Received 12 September 2013; revised 15 October 2013; accepted 25 October 2013

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.

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

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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:

iii

tx k







  (1)

Conservation of momentum:

2 1,2,3

jj j

iii

uu u

txx

 

 













 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





 (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

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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.

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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

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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.

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