Mock Artery Distension: Comparison of Optical, Mechanical and Theoretical Results

Biomedical Science Instrumentation, 43, pp. 46-53, (2007)

Ramesh Rajesh1, Conti JC2, Strope ER1

1 Dynatek dalta Scientific Instruments, 105 E Fourth St, Galena, MO 65656

2 Department of Physics, Astronomy and Material Sciences, Missouri State University, Springfield, MO 65803

Abstract

The relationship between the pressure inside a cylindrical mock vessel and the change in radius is called radial compliance.  It has been postulated that it is the internal change in radius with pressure that has a significant effect on blood flow disturbance or the interaction of a graft or synthetic tube with an indwelling stent or catheter. [1, 2] A variety of techniques are widely used in determining this parameter. Some are direct measurements of the internal diameter and some methods measure the outer diameter along with the use of theoretical calculations in determining this parameter. It is essential to understand and evaluate all the techniques widely used in the cardiovascular industry. This research work is an effort towards making this comparison.

Keywords

mock artery, compliance, laser, high speed photography, conversion, linear elastic mechanics, vascular stents, durability

Introduction

The effectiveness of in vitro experiments on medical devices like stents or grafts depends significantly on the distension of the mock arteries into which they are deployed. It is this parameter that determines the load being applied to the medical device. Radial distension of a mock artery depends on the radius of the artery and also on the internal pressure to which it is pulsed. [3-6] There are three common approaches, optical, mechanical and theoretical which are widely used in the cardiovascular industry in determining internal diameter. The most commonly used practice in the industry is to measure the change in internal diameter directly. Another method is to calculate the change in internal diameter by monitoring the change in outer diameter and using it along with theoretical equations from linear elastic mechanics.  In this study, a single silicone mock artery was tested at 72 bpm and its distension was measured using four commonly used techniques.  High speed photography and laser micrometry were used in the optical approach, dynamic internal compliance testing (DCT2) was used in the mechanical approach, and equations relating to the inner and outer diameter based on linear elastic mechanics were used in the theoretical approach.

Methods

A silicone mock artery (OD=24.87mm, ID=21.10mm, length=10cm) was selected for this experiment and was retested three times.  In each case, internal and external diameters were either measured or calculated at 0mm Hg and then  140mm Hg. Initial external and internal diameter and wall thickness were measured using a LaserMike 183 (LaserMike, Dayton, OH). Two points were marked on both the inner (16.36mm apart) and outer (16.57mm apart) diameters of this mock artery to assist in tracking. The silicone mock artery was tested in a DCT2 (Dynamic Compliance Tester DCT2, Dynatek Dalta Scientific Instruments, Galena, MO) for radial compliance. [1,2] Simultaneously, a Laser Micrometer LS7600 (Keyence Corp, Woodcliff Lake, NJ) was used to monitor the change in external diameter, while a high speed photographic camera (Fast Cam PCI 1280 Camera with Photron Motion Tools Software Version 1.05, Motion Engineering, Indianapolis, IN) was used to monitor both changes in internal and external diameter. The various techniques and devices used, and the information obtained from each are summarized below.

Table 1: Summary of Methods Used

Technique Device Result
Mechanical Dynamic Internal
Compliance Tester
Change in
Internal diameter
Optical High Speed Photography Change in Internal
and External Diameter
Optical Laser Micrometer Change in External Diameter
Theoretical Use of external diameter values
from optical technique plus
linear elastic mechanics equations
Change in Internal Diameter


Method Using Dynamic Compliance Tester (DCT2):

The DCT2 is equipped with a speed controlled DC motor.  This motor turns a shaft which is in conjunction with an adjustable eccentric coupler. This coupler along with a crank arm converts the rotational motion into linear motion. This linear motion is used to move a drive rod, which in turn compresses a bellows. During the test setup, the mock artery is fixed in the DCT2 machine such that one end is attached to the discharge end of the bellows and the other end is fixed to a manifold to which a pressure transducer is attached.

The basic principle for compliance measurement using a DCT2 machine is as follows: A highly sensitive linear voltage to displacement transducer (LVDT) monitors the position of the drive rod, which in turn is interpreted in terms of the amount of fluid injected from the bellows. Pressure is monitored by the pressure transducer and length change is monitored but neglected since the mock artery is fixed under slight tension between the two ports. All test data are acquired and recorded on a computer using a LabView (National Instruments, Austin, TX) data acquisition system. Data obtained from the DCT2 (pressure and change in volume) are used to plot a graph of loading and unloading curves. A second order polynomial curve is used to define a curve of best fit. To determine the radial compliance of the tube (mock artery), the initial length (Li) and initial radius (Ri) of the tube is measured, resulting in the initial volume (Vi) of the tube as follows: [7]

Vi = Π ×Ri2 ×Li

Where Vi is the volume at 0 mm Hg pressure.

If the tube is then inflated to a new pressure P2 with the length being fixed (there is no change in length Li), a new set of dimensions results for the tube depending on its compliance. Let ∆V be the change in volume.  Therefore the final volume Vf of the tube at pressure P2 is given by:

Vf = Vi +∆ V

Vf = Π × Rf2×Li   (where Rf is the radius at pressure P2)

Rf = sqrt (Vf / (Π ×Li))

% radial compliance (per 100mm Hg) is given by ((Rf-Ri) / (Ri × ∆P)) × 104

where ∆ P is change in pressure expressed in mm Hg.

Method using high speed photography [8-10]: A high speed photographic camera was used to determine the distension of the mock artery. Its associated tracking software has the capability of analyzing the fast motion within the captured image. The basic principle for distension measurements using high speed photography is as follows: The high speed camera will track the markings placed on the diameter of the mock arteries. The relative distance between these markings changes as the tube expands. The percent change in the chord length will be the same percentage change that occurs in the diameter and circumference.

Let us assume the cross section of the mock artery to be a circle of radius ri with center O.

Fig 1: Schematic Representation of Mock Artery Cross Section

Select two points Ai and Bi on the circle such that the arc AiBi subtends an angle Θ at the center of the circle as shown in the Fig 1. Let ci be the initial length of the chord AiBi.

So:

Ci = 2 sin (Θ/2) ri

As the mock artery is being pulsed from lower pressure to higher pressure, let Af and Bf be the final positions of points Ai and Bi respectively and rf be the final radius. Let the distance between Af and Bf be cf. The % strain (%Є) in the chord length is given by change in the chord length divided by the original chord length.

% Є = ((cf-ci)100)/ci

But cf = 2 sin (Θ/2) rf

Therefore, % Є =(rf – ri)/ ri

Method using laser micrometer:

A laser micrometer was used for measuring external distension of the mock artery due to change in pressure. The LS7600 Digital Micrometer used for this experiment has a measurement accuracy of ±3µm and high sampling rate of 2400 scans per second.  The basic principle of distension measurement using a laser micrometer is as follows:  Let Di be the external diameter of the mock artery measured at 0 mm Hg pressure.  The mock artery is then inflated to a new pressure P2 with the length being fixed, and Df is the diameter at the inflated pressure. Then the % distension of the mock artery is given by: ((Df – Di)/ Di) ×100

Method using theoretical calculations:

The relationship between the inner and outer tube diameters based on linear elastic mechanics is used in calculating the one when the other is measured.  The equation used in this research work is:

Di2= {b+ [(1+a2/b2)- ν (1-a2/b2 + 2ν)]  [b Δa/a]} [7]
2(1-ν2)

where: Di2 is the pressurized inner diameter;

ν  is Poisson’s ratio (for silicone= 0.41)

a is the initial outer diameter (in mm)

b is the initial inner diameter (21.10mm)

Δa  is the change in outer diameter due to change in pressure

In this equation the values for the change in outer diameter Δa was obtained from both high speed photography and laser micrometer measurements.

Results

The DCT2 measured the change in internal diameter with change in internal pressure. Thus compliance and, in turn, distension of the silicone mock artery was calculated and tabulated in Table 2.

Table 2: Compliance and Distension Measured by Dynamic Compliance Tester

Frequency
(Hz)
Peak Pressure(mmHg) Initial Inner Diameter (mm) Final Inner Diameter(mm) % Compliance % Distension
72 140 21.10 22.63 5.17 7.24
72 139 21.10 22.72 5.51 7.66
72 141 21.10 22.69 5.35 7.54

The two markings on both inner and outer diameters of the mock artery were tracked using the automated tracking function provided by the camera software and the data points were exported to a spreadsheet. Strain in the chord length was measured and percentage of distension was calculated for both inside and outside of the mock artery as shown in Table 3. The percentage distension was used in calculating the final inner and outer diameter of the mock artery.

Table 3: Inside and Outside Distension Measured by High Speed Photography

Frequency Peak
Pressure
% Inside
Distension
Final Inner
Diameter (mm)
% Outside
Distension
Final Outer
Diameter (mm)
72 140 6.73 22.52 5.19 26.15
72 139 7.13 22.60 5.3 26.19
72 141 6.82 22.54 5.02 26.12

 

The camera outer diameter measurement was used along with the linear elastic mechanics equation in calculating the pressurized inner diameter of the mock artery and tabulated as shown in Table 4.

Table 4: Final Inner Diameter as Calculated from Camera Final Outer Diameter

Peak
Pressure
(mm Hg)
Initial
Outer
Diameter
(mm)
Change in
Δ a (mm)
Outer
Diameter
Final Inner
Diameter
Using
Calculations
(mm)
Initial
Inner
Diameter
(mm)
% Inner
Distension
140.00 24.87 1.29 22.56 21.10 6.90
139.00 24.87 1.32 22.59 21.10 7.05
141.00 24.87 1.25 22.51 21.10 6.68

The change in external diameter due to a change in internal pressure was monitored by the laser micrometer. The external distension was then calculated and tabulated as shown in Table 5.

Table 5: Laser Micrometer Measurements

Frequency
(Hz)
Peak
Pressure
(mm Hg)
Final
Outer
Diameter
(mm)
Initial
Outer
Diameter
(mm)
% Outside
Distension
72 140 26.35 24.86 5.99
72 139 26.35 24.87 5.97
72 141 26.35 24.87 5.97

The outer diameter measurement was used along with the linear elastic mechanics equation in calculating the pressurized inner diameter of the mock artery and tabulated as shown in Table 6.

Table 6: Final Inner Diameter as Calculated from Final Laser Outer Diameter

Peak
Pressure
(mm Hg)
Initial
Outer
Diameter
(mm)
Change
Δa (mm)
in Outer
Diameter
Final
Inner
Diameter
Using
Calculations
(mm)
Initial
Inner
Diameter
(mm)
% Inner
Distension
140.00 24.86 1.49 22.78 21.10 7.96
139.00 24.87 1.48 22.77 21.10 7.93
141.00 24.87 1.49 22.78 21.10 7.94

 

Discussion

In this study, the high speed photographic camera is the only device capable of measuring distension both on the inside and outside of the mock arteries. From Table 3, which shows the measurements from the camera, it can be seen that outer distension is always lower than inner distension. Considering Table 3 and Table 5, it can be seen that percent outer distension as measured by the high speed camera is 0.8% less than that measured by the laser micrometer. Table 7 gives a summary of measured and calculated values of both final inner diameter and inner distension using various techniques. The magnitude of the variations between techniques can partially be explained by the differing levels of resolution or precision in each method. The dynamic compliance tester has the best precision with respect to instrumentation, but is an indirect measurement of the wall distension. The camera and laser micrometer have lower resolution. In our hands, we have become very confident in the data from the dynamic compliance tester, but in some cases would prefer to use the laser or camera techniques. Figure 2 shows the graphical representation of the variation in inner distension using the various techniques. Considering the repeatability error and other performance specifications of the measuring devices, the percentage of inner distension measured by all the devices using various techniques are comparable if the variability that was found is acceptable in any specific situation. If greater agreement between the dynamic compliance tester results and the laser- or camera-driven results using the equations of linear elastic mechanics is needed, then a closer correlation could be found empirically through a reconsideration of the Poisson’s ratio used in the equations. However, this does not address the next question: Does the medical device experience the same distension as the mock artery? To answer this question, further experiments and analyses are ongoing using the high speed photographic camera, which can monitor the motion of the device as well as the wall.

Table 7: Summary of Test Results Using Various Techniques

Dynamic Compliance
Tester
Internal Camera
Measurements
Final Inner
Diameter (mm)
% Inner
Distension
Final Inner
Diameter (mm)
% Inner
Distension
22.63 7.24 22.52 6.73
22.72 7.66 22.60 7.13
22.69 7.54 22.54 6.82
22.68 ± 0.05 7.48 ± 0.22 22.55 ± 0.04 6.89 ± 0.21

 

External Camera
Measurement

Laser Micrometer
Measurement

and Linear
Mechanics Equation

and Linear
Mechanics Equation

Final Inner
Diameter (mm)
% Inner
Distension
Final Inner
Diameter (mm)
% Inner
Distension
22.56 6.90 22.78 7.96
22.59 7.05 22.77 7.93
22.51 6.68 22.78 7.94
22.55 ± 0.04 6.88 ± 0.18 22.78 ± 0.00 7.94 ± 0.01

Fig 2: Variation of Inner Distension using Different Techniques


Acknowledgement

Special thanks to all employees of Dynatek dalta Scientific Instruments.

References

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