Radial Compliance of Natural and Mock Arteries: How This Property Defines the Cyclic Loading of Deployed Vascular Stents
Biomedical Science Instrumentation, 38, pp. 163-172, (2002)

CONTI, JC1, Strope, ER

Dynatek Dalta Scientific Instruments, 105 E. 4th, Galena, Missouri

1 Department of Physics and Astronomy, Southwest Missouri State University

Keywords:

compliance, artery, mock, frequency, durability, fatigue, stents, vascular

Abstract

There have been a disturbing number of unexpected mechanical failures in deployed vascular stents and stent grafts. An analysis of the mechanical properties of mock arteries used to carry out standard durability testing on the aforementioned medical products suggests that some of the problems might be related to a frequency dependent change in the properties of these recipient vessels. This could lead to a lower than expected level of loading and an attendant reduction in severity of testing.

A clear understanding of how a pulsating artery cyclically loads a deployed stent is important before a mock artery can be designed to carry out biologically relevant in vitro durability testing. In addition, knowledge of the time dependent response of both the vessel and the stent/stent graft is critical before any accelerated testing protocol can be properly designed.

This paper will present an analysis of the loading on a stent versus pressure and diameter of the recipient vessel and how this varies with frequency. Actual compliance versus frequency data will be used from silicone mock arteries.

Introduction

Properly designed in vitro testing can be an important aid in the evaluation of the safety and efficacy of medical products. Not only is it usually more cost effective than using experimental animals, but it is possible to increase the testing frequency so as to reduce the time needed for testing. Unfortunately, failure to consider the effect of testing frequency on the mechanical properties of the devices or experimental apparatus can lead to experiments that are not predictory of clinical outcomes. This particular problem has been especially troubling in the area of vascular stent testing because there are several controversial issues associated with important experimental parameters, for example, the criteria to use to choose the stent size.

To make things more complex, some of the experimental parameters vary so widely that it renders proper choice of these values difficult (1-19). As an example, there are hundreds of literature references referring to the compliance or diameter / pressure relationship of natural arteries, reporting values from about 1% to 50% per 100mm Hg increase in pressure.

Over the past ten years or so, a great deal has been learned about which parameters are important and which instrument design characteristics can best yield reliable in vitro studies. One critically important parameter for testing implantable stents is the diameter of the recipient vessel into which the stent will be deployed. Although this may seem to be relatively straightforward, there are several different diameters that are commonly used when matching up stent and natural or mock artery. As an example, it is most convenient to fabricate, purchase, and mechanically measure the diameter of unpressurized tubes. This is the way many testing facilities choose the tubing to use to test the durability of vascular stents.

Another approach is to evaluate the diameter of the tube when held at a normal diastolic pressure. This becomes a little more problematic in that these numbers vary with the rate of pulsation of the pressure. However, if the artery is pulsed from 0 to 80mm Hg at 72bpm, one will get a relatively valid understanding of the diameter of that tube at 80mm Hg systolic pressure at the biologically relevant 72bpm. A third way of evaluating the diameter of a tube or artery to be used in an experiment or for stent deployment is to look at the diameter when the blood pressure reaches 120mm Hg. Finally, the choice of the experimental tube could be based upon what is currently considered the target systolic number for near worst case in vitro testing. This is 160mm Hg.

To complicate matters further, manufacturers often recommend "oversizing" the stent. That is, it is common for the device manufacturer to recommend that cardiologists or vascular surgeons choose a stent that is 10% larger than the recipient vessel, without always specifying the internal pressure of the recipient vessel. It could refer to oversizing based upon the diameter at 0, 80, 120, or 160mm Hg or even at the mean blood pressure of the particular patient receiving the stent. Although it would seem that the choice of diameter may not be as important for in vitro studies as it would be in choosing the proper size stent for clinical application, it does in fact have a large impact on certain characteristics of the testing loads that will be applied to the stent.

Compliance is another critically important variable in the design and implementation of in vitro testing. Healthy arteries are probably in the range of 3-4% per 100mm Hg compliant while diseased ones are usually less compliant. At present, industry, testing administrators and regulators have focused on the region of 5-7% per 100mm Hg as replicating an idealized artery. Although it is difficult to be certain that this is the perfect number to use, it probably does represent a near worst case scenario in testing programs. This is because higher compliance tubing has more wall movement per pulse than a tube of lower compliance, and, as a general rule, more flexure of a metal leads to greater fatigue. One of the very difficult issues related to the compliance of the tube is that these vessels, as well as natural vessels, have frequency dependant mechanical properties (20-25). Since the mechanical properties of the recipient tube have a direct effect on the nature and magnitude of the loading that the deployed stent will experience, it is critically important that we have an understanding of the conditions and loading that the stent will actually experience in vivo .

In this paper, we try to present a better understanding of the specifics of vascular wall mechanics that affect the actual motion and loading that occur in vivo . We then try to best replicate these observations during in vitro testing.

Materials and Methods

Several 3mm ID tubes were produced by dipping precisely machined mandrels into a platinum catalyzed, two component, polydimethylsiloxane mixture dissolved in xylene. These mandrels were dipped with wall thicknesses that varied from 5 to 15 thousandths of an inch. After dipping, the mandrels were subjected to a two-step curing process that resulted in unchanged mechanical properties with any further curing. This included a forty-five minute pre-cure at 170°F followed by two hours and fifteen minutes at 300°F.

Each tube was then subjected to internal liquid pressurization at various frequencies while its length and internal pressure were monitored. All testing was carried out at 37° C and phosphate buffered saline. From these data and the initial geometric information on the inside dimensions of the tube, a compliance or percent change in diameter or radius per 100mm Hg internal pressurization was calculated. Tubes were then chosen that had 6% per 100mm Hg internal compliance. From this information, calculations were made to relate the actual inside diameter of the tubes to various pressures. These tubes were tested at various frequencies but the comparisons in this paper will use the data from testing at 72bpm and 1500bpm. The 1500bpm target is one that many manufacturers would like to attain in their testing programs and so 1500bpm was chosen for that reason. In addition, the dramatic decrease in compliance when going from 72 to 1500bpm was felt to more clearly delineate the problems associated with high speed testing on these vessels.

Results

Table 1 shows a summary of the pressure versus diameter data at two different testing. As stated above, the results at 72bpm are from a tube with 6% per 100mm Hg radial compliance. The results at 1500bpm reflects the fact that the radial compliance of the tube has dropped to 2.4%. This increase in stiffness at higher speeds is a common characteristic of viscoelastic tubes and is the driving force for the changes in experimental results. The middle section of Table 1 shows a calculation of diameter in the region of a stent if the stent were oversized by 10% at each pressure noted. For example, the diameter of a 3mm tube at 120mm Hg internal pressurization is 3.216. If the 10% oversize stent directive is applied using the diameter at 120mm Hg as the reference or starting point, then the inside diameter of the tube after stent deployment would be 3.216x110% = 3.538mm. The right hand side of the chart shows the equivalent pressure that would be necessary to expand the tube by that same 10% oversize. For example, the diameter at 120mm Hg at 1500bpm is 3.086. A 10% oversizing produces a diameter of 3.395. This would require 555mm Hg pressure to achieve this diameter at 1500bpm, a direct result of the tubing compliance reduction seen at higher speeds. There are several ways of looking at this situation. It represents the internal pressure needed to release the stent from the inside of the tube. It represents the amount of compressive force pushing back on the stent by the expanded tube. Finally, it represents the effective pressure being delivered by a stent to the inside of the tube as it effects a 10% increase in diameter.

Table 1
Pressure - Diameter Characteristics

Internal Pressure (mm Hg)	Diameter (mm)			10% Stent Oversize (mm)			Pressure Equivalent to 10% Oversize (mm Hg)
	72bpm	1500bpm	72bpm		1500bpm	72bpm		1500bpm
0	3.000	3.000	3.300		3.300	167		416
80	3.144	3.058	3.458		3.364	254		514
120	3.216	3.086	3.538		3.395	299		555
160	3.288	3.115	3.617		3.427	343		593

This compressive force that is being applied to the stent increases when the testing speed is increased from 72 to 1500bpm. This is a variable that needs to be considered when doing this experimentation.

Tables 2 through 5 are summaries of computations evaluating diameters, compressive loads and cyclic loads at different testing speeds. In each table, the diameter at a different pressure was used as the reference point for the "10% oversize" directive. For example, Table 2 represents the pressure - diameter characteristics of the tubes as the pressures were pulsed from 0 up to the target internal pressure (80, 120, 160 or 167mm Hg) at 72 and 1500bpm. The diameter of the tube is oversized by 10% based upon the diameter at 0mm Hg pressure as the starting point. The varying compressive force on the stent as the pressure inside the tube increases is also given. That is, at 0mm Hg internal pressure, the stent would feel a compressive force of 167mm Hg. When the tube is internally pressurized to 80mm Hg, the stent only feels a compressive force of 87mm Hg (167minus 80). Note that this compressive force is that force being applied directly to the stent by the tube. This does not address the phenomena that occur at the end of the stent. Finally, the magnitude of the change in load (pulsing load) is also given.

Table 2
10% Oversize Stent from 3.00mm to 3.300mm (0mm Hg)

Internal Pressure (mm Hg)	Unstented Diameter (mm)		Stented Diameter (mm)	Compressive Force on Stent at 72bpm		Pulsing Load From 80mm Hg
	72bpm	1500bpm		psi	mm Hg	psi	mm Hg
0	3.000	3.000	3.300	3.23	167	na	na
80	3.144	3.058	3.300	1.68	87	0	0
120	3.216	3.086	3.300	0.909	47	0.771	40
160	3.288	3.115	3.300	0.135	7	1.545	80
167	3.300		3.300	0	0	1.682	87

Table 3 shows the data obtained when the 10% oversize number is calculated based upon a reference diameter at 80mm Hg. Table 4 shows the data based upon a tube oversized 10% from its diameter at120mm Hg, and Table 5 shows the data obtained when the tube is oversized 10% based upon the diameter at 160mm Hg.

Table 3
10% Oversize Stent from 3.144mm to 3.458mm (80mm Hg)

Internal Pressure (mm Hg)	Unstented Diameter (mm)		Stented Diameter (mm)	Compressive Force on Stent at 72bpm		Pulsing Load From 80mm Hg
	72bpm	1500bpm		psi	mm Hg	psi	mm Hg
0	3.000	3.00	3.458	4.91	2.54	na	na
80	3.144	3.058	3.458	3.36	1.74	0	0
120	3.216	3.086	3.458	2.59	1.34	.771	40
160	3.288	3.115	3.458	1.82	94	1.545	80
254	3.458	3.183	3.458	0	0	3.365	174

Table 4
10% Oversize Stent from 3.216mm to 3.538mm (120mm Hg)

Internal Pressure (mm Hg)	Unstented Diameter (mm)		Stented Diameter (mm)	Compressive Force on Stent at 72bpm		Pulsing Load From 80mm Hg
	72bpm	1500bpm		psi	mm Hg	psi	mm Hg
0	3.000	3.00	3.538	5.78	299	na	na
80	3.144	3.058	3.538	4.23	219	0	0
120	3.216	3.086	3.538	3.46	179	.771	40
160	3.288	3.115	3.538	2.69	139	1.545	80
299	3.538	3.215	3.538	0	0	4.215	218

Table 5
10% Oversize Stent from 3.288mm to 3.617mm (160mm Hg)

Internal Pressure (mm Hg)	Unstented Diameter (mm)		Stented Diameter (mm)	Compressive Force on Stent at 72bpm		Pulsing Load From 80mm Hg
	72bpm	1500bpm		psi	mm Hg	psi	mm Hg
0	3.000	3.00	3.617	6.63	343	na	na
80	3.144	3.058	3.617	5.08	263	0	0
120	3.216	3.086	3.617	4.31	223	.771	40
160	3.288	3.115	3.617	3.54	183	1.545	80
343	3.617	3.247	3.617	0	0	5.086	263

Table 6 is a summary of the change in diameter that occurs with each pulse when going from 80mm Hg up to targeted pressures of 120 or 160mm Hg. This set of measurements is associated with the inside diameter of the tube in the non-stented region.

Table 6
Pulsing Diameter from 80mm Hg

Internal Pressure (mm Hg)	72bpm (mm)	1500bpm (mm)
120	0.072	0.028
160	0.144	0.057

Discussion

In evaluating the various diameter and loading characteristics that one obtains, it becomes clear that experimenters need to pay careful attention to diameter, frequency, and compliance issues if they expect their in vitro testing to be reliable.

A review of Table 1 shows the oversizing of the stent to go into this tube, based upon the four pressure criteria that were mentioned earlier. As an example, the diameter of the tube at 80mm Hg and 72bpm is 3.144mm. If 80mm Hg is used as the base for oversizing, then the stented diameter would be 3.458mm, with a compressive force of 254mm Hg. The result is that the stent experiences much greater compressive forces (514mm Hg) if oversizing is based upon diameters generated at 1500bpm. Clearly, this characteristic alone should be of a concern to test administrators.

Reviewing Tables 2 through 5, two things become evident. Number one, as might easily be expected, the ?P or the ? loading on these stents when going from 80 to 120mm Hg or 80 to 160mm Hg during the cyclic testing does not vary with the frequency of the tests nor does it vary with the criteria that is used to determine which diameter will be used to calculate the oversize of the stent. Note, however, that these loading numbers are those compressive loads directly on the stent and are not associated with the more flexing type loads that will occur at the end of a stent

By reviewing the data located on Table 6, you will see that the amount of flexing motion in the unstented portion that occurs when pressurizing from 80 to 120 or from 80 to 160mm Hg varies rather substantially when increasing the speed of the test from 72 up to 1500bpm. There is a reduction of 62% when flexing from 80 to 120mm Hg and 61% when flexing from 80 to 160mm Hg. This type of motion is that which is experienced mostly by the end of the stent and represents the change in diameter that occurs in tubing that is not stented. See Figure 1.



Figure 1

Figure 1 shows a schematic diagram of the inside dimensions of stented and unstented regions of a tube during pressurization. This figure depicts a rigid stent.

Conclusion

We have seen that there are three important criteria that must be considered when designing an in vitro fatigue/durability test for implantable vascular stents or stent grafts: diameter, compliance, and test frequency. A consideration of the diameter of the tubing necessary turns out to be less straightforward than might appear at first. The choice of the specific diameter of the tubing has a rather major impact on the amount of compressive force that the stent will experience after deployment. This compressive force on the stent will also be a function of the compliance of the tube that is chosen as well as the frequency that the fatigue or durability test will be carried out. This latter characteristic is primarily a function of changing viscoelastic properties of the tube with frequency. Although none of the characteristics that we varied had an impact on the magnitude of the differential pressure delivered during each pulse, the absolute value of the compressive forces upon which this differential is occurring is dramatically affected.

Lastly, the frequency at which the pulsatile pressures are delivered to the tubing do have an impact on the magnitude of flexure of the non-stented tube that is directly adjacent to the end of the region that is stented. This variable works through a mechanism that results in an apparent reduction in compliance of the tube due to time dependant properties that inhibit the tubes response time to high speed pressurization.

In addition to the varying flexural motion and baseline compressive forces that are applied as a function of frequency, it is also important to note that many stents, because of their design, do have time dependant responses to loading. Although a departure from engineering studies that are usually done on metals, some stents have very complicated geometry and fabrication processes that result in surprising frequency dependant characteristics.

Diameter, compliance and testing speed comes together to influence the loading characteristics that a stent experiences during fatigue or durability testing. A careful consideration of these variables is vital to the generation of reliable in vitro testing with the net reduction in wasted animal experiments and unexpected clinical failures.

This paper has addressed pressure controlled experiments and relationships only. Tube displacement or stent strain-controlled experiments have their own experimental parameter issues, but usually require even higher loading to overcome the reduction in compliance due to elevated test frequency effects.

References

1. Kinley, C. E., and Marble, A. E., Compliance. J. Cardiovasc. Surg., 21,
    163-170 (1980).

2. Clark , R. E., Apostolou, S., and Kardos, J. L., Mismatch of Mechanical
    Properties as a Cause of Arterial Prosthesis Thrombosis. Surg. Forum, 27,
    208-217 (1976).

3. Gonza, E. R., Mason, W. F., Marble, A. E., and others, Necessity for
    Elastic Properties in Synthetic Arterial Grafts. Can. J. Surg., 17, 176-179 (1974).

4. Lyman, D. J., Fazzio, F. J., Voorhees, H., and others, Compliance as a
    Factor Effecting the Patency of Copolyurethane Vascular Grafts. J.
    Biomed. Master. Res., 12, 337-339 (1978).

5. Abbott, W. M., and Bouchier-Hayes, D. J., The Role of Mechanical Properties
    in Graft Design. In: Graft Materials in Vascular Surgery. Edited by H. Dardik.
    Miami: Symposia Specialists, Inc., 59 (1978).

6. Baird, R. N., Kidson, I. G., L'Italien, J. G., and Abbott, M. W., Dynamic
    Compliance of Arterial Grafts. Am. J. Physiol., 2, 568-572 (1977).

7. Bergel, D. H., The Static Elastic Properties of the Arterial Wall. J. Physiol.
    (London), 156, 445 (1961).

8. Bergel, D. H., The Dynamic Elastic Properties of the Arterial Wall. J. Physiol.
    (London), 156, 448 (1961).

9. Patel, D. J., De Freitan, F. M., Freenfield, J. R., and Fry, D. L., Relation of
    Radius to Pressure Along the Aorta in Living Dogs. J. Appl. Physiol, 18,
    1111 (1963).

10. Paterson, L. H. Jensen, R. E. and Parnell, J., Mechanical Properties of Arteries
      In Vivo. Circulation Res., 8, 622 (1960).

11. Walden , R., L'Italien , G. J., M egerman , J., and Abbott , W. M., Matched
      Elastic Properties and Successful Arterial Grafting. Arch. Surg., 115,
      1166-1169 (1980).

12. Gow, B. S., and Taylor , G., Measurement of Viscoelastic Properties of Arteries
      in the Living Dog, Circulatory Research, 23, 111 (1968).

13. Gow, B. S., An Electrical Caliper for the Measurement of Pulsatile
      Arterial Diameter In Vivo. J. Appl. Physiol, 21, 1122 (1960).

14. Gotoh, F., Muramatsu, F., Fukuuchi, Y., Okaysu, H., Tanaka, K., Suzuki, N.,
      and Kobari, M., Video Camera Method for Simultaneous Measurement of
      Blood Flow Velocity and Pial Vessel Diameter. J. Cereb. Blood Flow Metab.,
      2, 421-428 (1982).

15. Assmann, R. and Henrich, H., A Video-Angiometer for Simultaneous
      and Continuous Measurement of Inner and Outer Vessel Diameters.
      Pflugers Arch., 376, 263-266 (1978).

16. Halpern, W., Mongeon, S. A., and Root, D. T., Stress, Tension and
      Myogenic Aspects of Small Isolated Extraparenchymal Rat Arteries. In:
      Smooth Muscle Contraction, edited by N.L. Stephens. New York : Dekker,
      427-456 (1984).

17. Intaglietta, M. and Tompkins, W. R., On-Line Measurement of
      Microvascular Dimensions by Television Microscopy. J. Appl. Physiol., 32,
      546-551 (1972).

18. Wiederhielm, C. A., Continuous Recording of Arteriolar Dimensions with
      a Television Microscope. J. Appl. Physiol., 18, 1041-1042 (1963).

19. Halpern, W., Osol, G., Coy, G. S., Mechanical Behavior of Pressurized In
      Vitro Prearteriolar Vessels Determined with a Video System. Annals of
      Biomedical Engineering, 12, 463-479 (1984).

20. Conti, J. C., Strope, E. R., Rohde, D. R. and Greisler, H. P., A New Technique
      to Determine Vascular Compliance In Vivo, National Heart Lung and
      Blood Institute Contractors Meeting. Louisville, KY, 1989.

21. Bozzi, R., Conti, J. C., Soldani, G., Spence, L., Strope, E., and Withrow,
      D., Relating the Frequency Dependent Radial Compliance to the Tensile
      Modulus of Polyurethane and Latex Vascular Grafts. Transactions 5th
      World Biomaterials Congress, 434, U2 (1996).

22. Conti, J. C., Strope, E. R., Rohde, D. J., and Spence, L. D., Frequency
      Dependent Radial Compliance of Latex Tubing. Biomedical
      Sciences Instrumentation, 33, 524-529 (1997).

23. Conti, J. C., Strope, E. R., and Price, K. S., Sources of Error in Monitoring
      High Speed Testing of Vascular Grafts, Biomedical Sciences Instrumentation,
      34, 240-245 (1998).

24. Conti, J. C., Strope, E. R., Price, K. S., and Goldenberg, L. M, The
      High Frequency Testing of Vascular Grafts and Vascular Stents: Influence
      of Sample Dimensions on Maximum Allowable Frequency. Biomedical
      Sciences Instrumentation, 35, 339-346 (1999).

25. Conti, J. C., Strope, E. R., and Price, K. S., High Frequency Testing of Grafts
      and Mock Arteries for Stents: Influence of Testing Frequency on
      Durability, Transactions Society of Biomaterials, 403 (1999).