D. G. Shombert Division of Physical Sciences, Office of Science and Technology, Center For Devices and Radiological Health, Food and Drug Administration, Rockville, MD 20857
Measurement of Steady-Flow Instability and Turbulence Levels in Dacron Vascular Grafts Fluid dynamic properties of Dacron vascular grafts were studied under controlled steady-flow conditions over a Reynolds number range of 800 to 4500. Knitted and woven grafts having nominal diameters of 6 mm and 10 mm were studied. Thermal anemometry was used to measure centerline velocity at the downstream end of the graft; pressure drop across the graft was also measured. Transition from laminar flow to turbulent flow was observed, and turbulence intensity and turbulent stresses (Reynolds normal stresses) were measured in the turbulent regime. Knitted grafts were found to have greater pressure drop than the woven grafts, and one sample was found to have a critical Reynolds number (Rc) of less than one-half the value of' Rc for a smooth-walled tube.
Introduction The use of a prosthetic device to replace a failing part of the arterial system is a common surgical procedure. Perhaps the most familiar example is coronary bypass surgery, in which new vessels are grafted into place to direct flow around occluded sections of the coronary arteries. Other vessels for which vascular grafts are used as replacements include the aorta and the femoral, iliac, and brachial arteries. Depending on the application, the prosthesis may be a section of autogenous vein, it may be derived from animal tissue, or it may be made of a synthetic material. The history of vascular grafts dates back to the early part of this century (Carrel, 1910). The earliest versions of these devices used glass and aluminum tubes with a paraffin lining. Since that time, a wide variety of materials and designs have been used, including animal tissue, human tissue, polytetrafluoroethylene (PTFE), and fabric (e.g., Darcon). All of these materials have been found to be less than ideal in one or more respects. A study conducted by the Utah Biomedical Test Laboratory (1981) identified the following as common failure modes for vascular grafts: thrombosis, anastomotic hyperplasia, mechanical failure (stiffening, kinking, etc.), and seroma. Thrombosis was estimated to occur in as many as ten percent of all implants. The details of graft failure are not fully understood. The relationship between general fluid dynamic parameters (particularly shear stress) and pathologic events has been studied extensively in recent years (Giddens et al., 1990; Rittgers et al., 1978; Friedman et al., 1981), but the exact role of fluid dynamics in graft failure (e.g., in thrombogenesis and intimal hyperplasia) remains unclear. The mechanical properties of most grafts differ significantly from those of the host vessel, and the resulting compliance mismatch at the anastomoses has Contributed by the Bioengineering Division for publication in the JOURNAL OF BioMECHANicAi ENQINEBEING. Manuscript received by the Bioengineering Division October 27, 1991; revised manuscript received February 28, 1992. Associate Technical Editor: J. M. Tarbell.
been implicated by several investigators as an important factor (Abbott et al., 1987; Stewart and Lyman, 1992), but the extent to which this contributes to graft failure is also unclear. Studies of the effects of mechanical properties (e.g., burst strength) have been possible because the mechanical properties themselves, as well as the methods for determining them, have been well documented. At present, one domestic standard has been published (AAMI, 1986) and an international standard is being drafted by the International Organization for Standardization (ISO). Both of these standards specify detailed methods for determining the mechanical properties of vascular grafts. The fluid dynamic behavior of these devices has received much less attention. A preliminary study of transition to turbulence in Dacron grafts indicated that the critical Reynolds number could be much lower than that for a smooth-walled tube (Shombert, 1989). Measurement of pressure drop and transition to turbulence in tapered grafts has also been reported recently (Black and How, 1989). However, much remains to be done to fully characterize the flow characteristics of all the different types of grafts currently in use. This study addresses the fluid dynamics of Dacron grafts. These have a corrugated wall structure that suggests an extreme case of wall roughness, a known cause of flow instability and increased pressure drop. The magnitude of the corrugations is decreased by stretching the graft; since this varies with surgical technique, flow characterization at more than one degree qf stretching is desirable . This paper reports the results of an experimental study of pressure drop and transition to turbulence in steady flow through Dacron grafts at two different amounts of stretching. Results are presented for grafts of two different sizes and several different fabric configurations. Comparison is made to the results of the same measurements in a smooth-walled tube. Flow System Description The steady-flow system, shown in Fig. 1, operates as follows: NOVEMBER 1992, Vol. 114 / 521
Journal of Biomechanical Engineering
Copyright © 1992 by ASME Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Fig. 1
Steady-flow system
PRESSURE TAP
'
Fig. 2
luctance transducer, with interchangeable diaphragms to allow selection of the appropriate measurement range. Calibration is accomplished by connecting the transducer to a water column of known height. Velocity is measured by a hot-film probe that is inserted at the 90 degree bend and positioned on the centerline of the flow at the downstream end of the graft. Hot-film anemometry is an established technique that has been successfully applied to physiological flow (Nerem et al., 1972; Klanchar and Tarbell, 1989). Our system consists of a flow analyzer (TSI Inc. model IFA-100) which controls the probe operating parameters, a digitizer (TSI Inc. model IFA-200), and PC-based software (TSI model DAP-4). The software controls data acquisition and corrects for temperature changes during the experiment if necessary; subsequently, it calculates the mean, variance, and higher order statistics of the velocity data, as well as the turbulence intensity and Reynolds stresses. The turbulence intensity is a parameter that characterizes the level of turbulence in the flow. The TSI software uses a common definition,
PRESSURE TAP
(2) I=(u'T /U where u' is the fluctuating component of the velocity and U is the mean velocity. The Reynolds stress is a physical stress that is present in the fluid because of the turbulent fluctuations. Its components are defined as (Schlichting, 1979) Reynolds normal stress:
Graft sealing chamber
The constant head upper reservoir supplies the flow through a smooth inlet to a Lucite tube 150 cm long. The flow passes through the graft, through a short section of Lucite tube and a 90 degree turn, then through a turbine flowmeter (Flow Technology, Inc. Series II FTO), a control valve, and into the lower reservoir. Return flow is provided by a variable speed pump (Cole-Parmer model 7144-04). The turbine flowmeter measures the volume flow rate Q, from which the Reynolds number is calculated: R = Ud/v where U = average velocity = Q/A A = tube cross-sectional area d = tube diameter v = fluid kinematic viscosity
(1)
Main flow tubes were fabricated for this system in both 6 mm and 10 mm internal diameters, two nominal sizes in which Dacron grafts are manufactured. The graft connections are made by clamping the graft onto thin-walled stainless steel fittings that protrude from the ends of the Lucite tubes; the tubes and fittings are machined for a smooth interior fit to prevent any disturbance of the flow. The fluid used in these experiments is distilled, degassed water. Fluid temperature in the lower reservoir is monitored by a thermocouple probe (YSI Inc. model 46 TUC). Dacron grafts are porous, so much so that they require preclotting at the time of implant (Sheehan et al., 1989). For in vitro studies, it is necessary to somehow prevent or contain the flow through the walls. This was accomplished by enclosing the graft in a sealed chamber as shown in Fig. 2. The initial flow through the graft wall fills the chamber to the vent, which is then capped. This contains the leakage through the wall but does not affect the flow through the graft; a hot-film probe temporarily inserted through the chamber wall showed no motion of the fluid inside the chamber. The seals between the chamber and the flow tube tube are movable, so that the graft sample may be accurately stretched to the desired length after it is mounted. Pressure drop across the graft is measured by connecting a differential pressure transducer (Validyne Engineering model P305) to the pressure taps as shown. This is a variable re5 2 2 / V o l . 114, NOVEMBER 1992
(TR)ii = PUi'2
(3)
Reynolds shear stress: (TR)ij = pUiUj
(4)
where p is the fluid density and u, , Uj are the velocity fluctuations in the /, j directions. The Reynolds shear stress component has been linked to several adverse physiological phenomena such as red blood cell lysis (Sutera and Mehrjardi, 1975) and thrombus formation (Stein and Sabbah, 1974). Since it is defined as a correlation, its measurement requires simultaneous velocity measurement in two orthogonal directions, and this has been done extensively by other workers using laser Doppler anemometry (Yoganathan et al., 1986; Tiederman et al., 1986). Hot-film anemometry is also capable of this measurement, but the size of the two-sensor probes precluded their use in this study. The normal component of the Reynolds stress can be measured with a onesensor probe, which is considerably smaller, and thus is reported here. Experimental results reported by others indicate that the Reynolds normal stress has the same order of magnitude as the maximum value of the Reynolds shear stress (Yoganathan et al., 1979). The hot-film probes used for these measurements, also manufactured by TSI, have a sensor cross-sectional area of the order of 10" 3 mm 2 . The sensor is located at the upstream tip of the probe so that it will be unaffected by any perturbation of the flow by the probe body. The probes are calibrated in a water probe calibrator (TSI Inc. model 10180), which provides a uniform jet of known velocity over a selected range; in this case the probes were calibrated at fifteen points from zero to 150 cm/s, which covers the range of velocities encountered in the experiments. The TSI software includes a calibration package which fits the calibration data to a fourth-order polynomial; the latter is then used for velocity calculation during an experiment.
Experimental Procedures The six different graft samples that were studied are listed by size and type in Table 1. All were made by the same manufacturer. In each size, two types of woven grafts were availTransactions of the ASME
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Table 1 Sizes and fabric configurations of the graft samples. Type A and type B grafts differ in the structure of the weave. Sample number Fabric configuration Diameter (mm) 1 2 3 4 5 6
Woven, type A Woven, type B Knitted Woven, type A Woven, type B Knitted
10 10 10 6 6 6
12 - Sample 4
v
10 V
8 -
d
Measurement of Steady-Flow Instability and Turbulence Levels in Dacron Vascular Grafts Fluid dynamic properties of Dacron vascular grafts were studied under controlled steady-flow conditions over a Reynolds number range of 800 to 4500. Knitted and woven grafts having nominal diameters of 6 mm and 10 mm were studied. Thermal anemometry was used to measure centerline velocity at the downstream end of the graft; pressure drop across the graft was also measured. Transition from laminar flow to turbulent flow was observed, and turbulence intensity and turbulent stresses (Reynolds normal stresses) were measured in the turbulent regime. Knitted grafts were found to have greater pressure drop than the woven grafts, and one sample was found to have a critical Reynolds number (Rc) of less than one-half the value of' Rc for a smooth-walled tube.
Introduction The use of a prosthetic device to replace a failing part of the arterial system is a common surgical procedure. Perhaps the most familiar example is coronary bypass surgery, in which new vessels are grafted into place to direct flow around occluded sections of the coronary arteries. Other vessels for which vascular grafts are used as replacements include the aorta and the femoral, iliac, and brachial arteries. Depending on the application, the prosthesis may be a section of autogenous vein, it may be derived from animal tissue, or it may be made of a synthetic material. The history of vascular grafts dates back to the early part of this century (Carrel, 1910). The earliest versions of these devices used glass and aluminum tubes with a paraffin lining. Since that time, a wide variety of materials and designs have been used, including animal tissue, human tissue, polytetrafluoroethylene (PTFE), and fabric (e.g., Darcon). All of these materials have been found to be less than ideal in one or more respects. A study conducted by the Utah Biomedical Test Laboratory (1981) identified the following as common failure modes for vascular grafts: thrombosis, anastomotic hyperplasia, mechanical failure (stiffening, kinking, etc.), and seroma. Thrombosis was estimated to occur in as many as ten percent of all implants. The details of graft failure are not fully understood. The relationship between general fluid dynamic parameters (particularly shear stress) and pathologic events has been studied extensively in recent years (Giddens et al., 1990; Rittgers et al., 1978; Friedman et al., 1981), but the exact role of fluid dynamics in graft failure (e.g., in thrombogenesis and intimal hyperplasia) remains unclear. The mechanical properties of most grafts differ significantly from those of the host vessel, and the resulting compliance mismatch at the anastomoses has Contributed by the Bioengineering Division for publication in the JOURNAL OF BioMECHANicAi ENQINEBEING. Manuscript received by the Bioengineering Division October 27, 1991; revised manuscript received February 28, 1992. Associate Technical Editor: J. M. Tarbell.
been implicated by several investigators as an important factor (Abbott et al., 1987; Stewart and Lyman, 1992), but the extent to which this contributes to graft failure is also unclear. Studies of the effects of mechanical properties (e.g., burst strength) have been possible because the mechanical properties themselves, as well as the methods for determining them, have been well documented. At present, one domestic standard has been published (AAMI, 1986) and an international standard is being drafted by the International Organization for Standardization (ISO). Both of these standards specify detailed methods for determining the mechanical properties of vascular grafts. The fluid dynamic behavior of these devices has received much less attention. A preliminary study of transition to turbulence in Dacron grafts indicated that the critical Reynolds number could be much lower than that for a smooth-walled tube (Shombert, 1989). Measurement of pressure drop and transition to turbulence in tapered grafts has also been reported recently (Black and How, 1989). However, much remains to be done to fully characterize the flow characteristics of all the different types of grafts currently in use. This study addresses the fluid dynamics of Dacron grafts. These have a corrugated wall structure that suggests an extreme case of wall roughness, a known cause of flow instability and increased pressure drop. The magnitude of the corrugations is decreased by stretching the graft; since this varies with surgical technique, flow characterization at more than one degree qf stretching is desirable . This paper reports the results of an experimental study of pressure drop and transition to turbulence in steady flow through Dacron grafts at two different amounts of stretching. Results are presented for grafts of two different sizes and several different fabric configurations. Comparison is made to the results of the same measurements in a smooth-walled tube. Flow System Description The steady-flow system, shown in Fig. 1, operates as follows: NOVEMBER 1992, Vol. 114 / 521
Journal of Biomechanical Engineering
Copyright © 1992 by ASME Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Fig. 1
Steady-flow system
PRESSURE TAP
'
Fig. 2
luctance transducer, with interchangeable diaphragms to allow selection of the appropriate measurement range. Calibration is accomplished by connecting the transducer to a water column of known height. Velocity is measured by a hot-film probe that is inserted at the 90 degree bend and positioned on the centerline of the flow at the downstream end of the graft. Hot-film anemometry is an established technique that has been successfully applied to physiological flow (Nerem et al., 1972; Klanchar and Tarbell, 1989). Our system consists of a flow analyzer (TSI Inc. model IFA-100) which controls the probe operating parameters, a digitizer (TSI Inc. model IFA-200), and PC-based software (TSI model DAP-4). The software controls data acquisition and corrects for temperature changes during the experiment if necessary; subsequently, it calculates the mean, variance, and higher order statistics of the velocity data, as well as the turbulence intensity and Reynolds stresses. The turbulence intensity is a parameter that characterizes the level of turbulence in the flow. The TSI software uses a common definition,
PRESSURE TAP
(2) I=(u'T /U where u' is the fluctuating component of the velocity and U is the mean velocity. The Reynolds stress is a physical stress that is present in the fluid because of the turbulent fluctuations. Its components are defined as (Schlichting, 1979) Reynolds normal stress:
Graft sealing chamber
The constant head upper reservoir supplies the flow through a smooth inlet to a Lucite tube 150 cm long. The flow passes through the graft, through a short section of Lucite tube and a 90 degree turn, then through a turbine flowmeter (Flow Technology, Inc. Series II FTO), a control valve, and into the lower reservoir. Return flow is provided by a variable speed pump (Cole-Parmer model 7144-04). The turbine flowmeter measures the volume flow rate Q, from which the Reynolds number is calculated: R = Ud/v where U = average velocity = Q/A A = tube cross-sectional area d = tube diameter v = fluid kinematic viscosity
(1)
Main flow tubes were fabricated for this system in both 6 mm and 10 mm internal diameters, two nominal sizes in which Dacron grafts are manufactured. The graft connections are made by clamping the graft onto thin-walled stainless steel fittings that protrude from the ends of the Lucite tubes; the tubes and fittings are machined for a smooth interior fit to prevent any disturbance of the flow. The fluid used in these experiments is distilled, degassed water. Fluid temperature in the lower reservoir is monitored by a thermocouple probe (YSI Inc. model 46 TUC). Dacron grafts are porous, so much so that they require preclotting at the time of implant (Sheehan et al., 1989). For in vitro studies, it is necessary to somehow prevent or contain the flow through the walls. This was accomplished by enclosing the graft in a sealed chamber as shown in Fig. 2. The initial flow through the graft wall fills the chamber to the vent, which is then capped. This contains the leakage through the wall but does not affect the flow through the graft; a hot-film probe temporarily inserted through the chamber wall showed no motion of the fluid inside the chamber. The seals between the chamber and the flow tube tube are movable, so that the graft sample may be accurately stretched to the desired length after it is mounted. Pressure drop across the graft is measured by connecting a differential pressure transducer (Validyne Engineering model P305) to the pressure taps as shown. This is a variable re5 2 2 / V o l . 114, NOVEMBER 1992
(TR)ii = PUi'2
(3)
Reynolds shear stress: (TR)ij = pUiUj
(4)
where p is the fluid density and u, , Uj are the velocity fluctuations in the /, j directions. The Reynolds shear stress component has been linked to several adverse physiological phenomena such as red blood cell lysis (Sutera and Mehrjardi, 1975) and thrombus formation (Stein and Sabbah, 1974). Since it is defined as a correlation, its measurement requires simultaneous velocity measurement in two orthogonal directions, and this has been done extensively by other workers using laser Doppler anemometry (Yoganathan et al., 1986; Tiederman et al., 1986). Hot-film anemometry is also capable of this measurement, but the size of the two-sensor probes precluded their use in this study. The normal component of the Reynolds stress can be measured with a onesensor probe, which is considerably smaller, and thus is reported here. Experimental results reported by others indicate that the Reynolds normal stress has the same order of magnitude as the maximum value of the Reynolds shear stress (Yoganathan et al., 1979). The hot-film probes used for these measurements, also manufactured by TSI, have a sensor cross-sectional area of the order of 10" 3 mm 2 . The sensor is located at the upstream tip of the probe so that it will be unaffected by any perturbation of the flow by the probe body. The probes are calibrated in a water probe calibrator (TSI Inc. model 10180), which provides a uniform jet of known velocity over a selected range; in this case the probes were calibrated at fifteen points from zero to 150 cm/s, which covers the range of velocities encountered in the experiments. The TSI software includes a calibration package which fits the calibration data to a fourth-order polynomial; the latter is then used for velocity calculation during an experiment.
Experimental Procedures The six different graft samples that were studied are listed by size and type in Table 1. All were made by the same manufacturer. In each size, two types of woven grafts were availTransactions of the ASME
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Table 1 Sizes and fabric configurations of the graft samples. Type A and type B grafts differ in the structure of the weave. Sample number Fabric configuration Diameter (mm) 1 2 3 4 5 6
Woven, type A Woven, type B Knitted Woven, type A Woven, type B Knitted
10 10 10 6 6 6
12 - Sample 4
v
10 V
8 -
d
