1. Biomechanics Vol. 23, No. 10, pp. 9855989, 1990. Printed in Chat Britain
0
@x2-9290/90 s3.00+ .I0 1990 Pergamon Pnap plc
BIOMECHANICS OF THE VENOUS WALL UNDER SIMULATED ARTERIAL CONDITIONS SCOTT A. BERCELI,DAVID P. SHOWALTER,RICHARDA. SHEPPECK,WILLIAM A. MANDARINOand HARVEYS. BOROVETZ* Department of Surgery, University of Pittsburgh, Pittsburgh, PA 15261,U.S.A. Ahatrm%-The failure of vein graft conduits implanted in the arterial circulation has been hypothesized to occur in part due to the exposure of the graft to altered biomechanical and fluid shearing forces. In the present study, these forces are characterized for canine internal jugular veins (IJV) exposed to realistic arterial flow dynamica. Freshly excised vein segments were mounted into a pulsatile perfusion apparatus and exposed to arterial flow conditions (P = 115/75 mm Hg and Q = 110 ml min - ’ ) for 2 h. Dynamic measurements of intraluminal pressure and flow rate and vessel wall radial distension were acquired to accurately qua&ate the incremental modulus of elasticity; hoop, axial and radial wall stresses; and fluid shearing forces within the vessel. Identical measurements were performed on canine carotid arteries (CCA) to serve as a comparison. Under arterial conditions, IJV segments demonstrated a significant elevation (p ~0.05) over the CCA in the incremental elasticity modulus, along with a corresponding elevation in hoop and axial wall stresses. Additionally the average wall shearing rate to which the IJV endothelial surface was exposed was a factor of six less than that observed in the CCA. These results are discussed in relationship to the clinical situation of vein graft adaptation to arterial hemodynamics.
EXPERIMENTAL
JNTRODUCTION The interposition of a venous conduit in the arterial circulation is routinely performed in aortocoronary and femoral-popliteal bypass grafting. While these veins are almost always disease-free at the time of operation, vein graft thickening and late atherosclerosis is a common finding (Stanley et al., 1973; Szilagyi et al., 1973). These biologic changes are believed to be associated with the response of the vein to acute and chronic injury inflicted during operation and the subsequent exposure to arterial flow conditions (Brody et al., 1972). Regarding the latter, Zwolak et al. (1987) proposed that mean tangential stress and fluid shearing stress may be involved in vein graft remodelling. However, there is a paucity of experimental data characterizing venous wall biomechanics under pulsatile, arterial conditions. The focus of the present work is to obtain such information in freshly excised canine internal jugular veins exposed to realistic arterial flow hemodynamics. A pulse duplicator apparatus (PDA) is utilized to simulate the pulsatile arterial waveforms in vitro. From dynamic measurements of transmural pressure, flow rate, and the radial displacement of the venous wall, calculations are made of the incremental modulus of elasticity; hoop, axial and radial venous wall stresses; and fluid shearing stress. These data are compared to companion measures previously obtained for canine carotid arteries (Brant et al., 1988; Johnson et al., 1989). The relationship of this biomechanical information to vein graft adaptation to arterial flow is discussed.
Receiwd inpnal form 9 February 1990. * Author to whom correspondence should be addressed.
Animal model
Only adult mongrel dogs (25 kg) intended for sacrifice served as the vessel donors. The animals were anesthetized with sodium pentobarbital(30 mg kg-‘) and a ventral midline neck incision was made. One internal jugular vein (IJV) was then carefully exposed, cannulated, flushed in situ with normothermic canine serum and a 10 cm segment excised at natural length and distension using a specially designed pair of noncrushing vascular clamps. The clamps were not removed until the vessel was secured in its natural orientation in the PDA. The second IJV was harvested as described but utilized in a separate, unrelated study. All animal procedures were performed in accordance with NIH and University guidelines for the care and use of laboratory animals. Perfusion apparatus
The pulse duplicator apparatus (PDA) used to simulate the arterial flow conditions has been described in detail elsewhere (Brant et al., 1986). Briefly, this system simulates the natural environment of an intact vascular segment, providing pulsatile pressures and flows and physiologic pH, PO,, pCOz and temperature. The excised IJV were secured (with suture material) in their natural orientation in the tissue housing chamber of the perfusion apparatus. A 30 cm length of straight, stainless steel tubing led to (and away from) the tissue housing chamber. This length was selected based upon the calculations of entrance and exit length requirements for the fully established flow through test blood vessels (Bird et al., 1960). Instrumentation associated with the PDA allowed dynamic measurements to be made of proximal and distal intraluminal pressures; transmural pressure;
985
S. A. BERCELIet al.
986
flow rate; and radial excursion of the wall of the IJV. Details of these protocols have recently been reported (Brant et al., 1987). Calculations of vessel wall stress
Incremental modulus of elasticity; hoop, axial and radial wall stresses; and fluid shearing stress were derived from the present experimental data following protocols described elsewhere (Brant et al., 1988; Johnson ef al., 1989; Rodgers et a1.,1987). Briefly, we based our calculations of elasticity modulus on the classical work of Bergel (1961) and Pate1 and Fry (1969) and have utilized an incremental modulus, Elnc, for calculation of longitudinal and hoop stress: Ei*o=
TP, - TP, R,,-R,,
2 (1 -a) R& R,, ’
R,Z-R;
(1)
.
Here TP refers to the transmural pressure, u= Poisson’s ratio (assumed = OS), R = radius, and the subscripts i, o, 1, 2, 3 represent inside, outside, minimum (diastolic) value, mean value and maximum (systolic) value of the parameter over the 1 Hz cardiac cycle. The model of arterial wall stress used in this analysis is adapted from the elastic tube model of Kuchar and Ostrach (1966). With the assumptions that the venous wall is elastic, axisymmetric, semi-infinite in length, straight with circular cross-section, constrained from motion longitudinally, and that the radial displacement of the vein wall during each cycle is small in comparison to the mean radius, the general form of the equations for the radial (S,), axial (T-J, and hoop (T,) stresses shown in Fig. 1 are:
%=[T-P;],.,,,
(2)
fJE*nc tl
Txx=(l’-o*) 41
(3)
E in0
rl
E~noh* tl
-a*) Te”=r-‘-+
R,,
12 R;, (1 -a*) ’
STRESSES
ACTING ON SMALL ELEMENT ARTERIAL WALL
(4)
OF
Fig. 1. Close-up of small element of vesselwall showing the stresses acting on it. T,, and Tss are the longitudinal and circumferential wall stresses, respectively. S,, and S,, are the normal and fluid shear stresses, respectively.
Here: r = radial coordinate; v = radial fluid velocity component; fl =dynamic fluid viscosity; v = experimentally measured radial displacement of the vein wall; h = vein wall thickness. Other nomenclature follows that of Equation (1). The mathematical model originally developed by Tsai and Hung (1984) and adapted by Johnson et al. (1989) is employed to determine the dynamic wall shear rate (WSR) acting on the perfused LTV.Using a finite difference numerical scheme, the Navier-Stokes equations for pulsatile flow in a straight deformable vessel are solved using pressure drop, flow rate, vessel wall radius, and radial wall motion as input. The assumptions of uniform vessel geometry, laminar flow, axisymmetry, and uniform pressure drop are incorporated in the model equation and boundary conditions (Johnson et al., 1989). Identical measurements were performed previously on companion canine carotid arteries (Brant et al., 1988; Johnson et al., 1989), and serve as a comparison. Statistical differences in the aforementioned biomechanic and hemodynamic parameters between the IJV and companion canine carotid artery (CCA) were assessed using the Student’s t-test. RESULTS
Four canine IJV were exposed for two hours to intraluminal perfusion pressures of 115/75 mm Hg and mean flow rates of 110 mlmin-I. No vessel leakage or aneurysmal behavior was observed during these brief perfusion periods. Hemodynamic signals were obtained immediately prior to the conclusion of each study. Typical experimentally derived tracings of pressure drop, flow rate, inner radius, and radial wall velocity are illustrated in Fig. 2. These signals served as input to both the biomechanic and hemodynamic models. Table 1 summarizes the biomechanical response of the wall of the IJV to arterial flows. The inner radius of the IJV (3.4-3.9mm) is twice that (1.7mm) of the companion canine carotid artery @ ~0.001). A striking increase in the incremental modulus (E,,,) for the IJV vs the CCA (p
0
@x2-9290/90 s3.00+ .I0 1990 Pergamon Pnap plc
BIOMECHANICS OF THE VENOUS WALL UNDER SIMULATED ARTERIAL CONDITIONS SCOTT A. BERCELI,DAVID P. SHOWALTER,RICHARDA. SHEPPECK,WILLIAM A. MANDARINOand HARVEYS. BOROVETZ* Department of Surgery, University of Pittsburgh, Pittsburgh, PA 15261,U.S.A. Ahatrm%-The failure of vein graft conduits implanted in the arterial circulation has been hypothesized to occur in part due to the exposure of the graft to altered biomechanical and fluid shearing forces. In the present study, these forces are characterized for canine internal jugular veins (IJV) exposed to realistic arterial flow dynamica. Freshly excised vein segments were mounted into a pulsatile perfusion apparatus and exposed to arterial flow conditions (P = 115/75 mm Hg and Q = 110 ml min - ’ ) for 2 h. Dynamic measurements of intraluminal pressure and flow rate and vessel wall radial distension were acquired to accurately qua&ate the incremental modulus of elasticity; hoop, axial and radial wall stresses; and fluid shearing forces within the vessel. Identical measurements were performed on canine carotid arteries (CCA) to serve as a comparison. Under arterial conditions, IJV segments demonstrated a significant elevation (p ~0.05) over the CCA in the incremental elasticity modulus, along with a corresponding elevation in hoop and axial wall stresses. Additionally the average wall shearing rate to which the IJV endothelial surface was exposed was a factor of six less than that observed in the CCA. These results are discussed in relationship to the clinical situation of vein graft adaptation to arterial hemodynamics.
EXPERIMENTAL
JNTRODUCTION The interposition of a venous conduit in the arterial circulation is routinely performed in aortocoronary and femoral-popliteal bypass grafting. While these veins are almost always disease-free at the time of operation, vein graft thickening and late atherosclerosis is a common finding (Stanley et al., 1973; Szilagyi et al., 1973). These biologic changes are believed to be associated with the response of the vein to acute and chronic injury inflicted during operation and the subsequent exposure to arterial flow conditions (Brody et al., 1972). Regarding the latter, Zwolak et al. (1987) proposed that mean tangential stress and fluid shearing stress may be involved in vein graft remodelling. However, there is a paucity of experimental data characterizing venous wall biomechanics under pulsatile, arterial conditions. The focus of the present work is to obtain such information in freshly excised canine internal jugular veins exposed to realistic arterial flow hemodynamics. A pulse duplicator apparatus (PDA) is utilized to simulate the pulsatile arterial waveforms in vitro. From dynamic measurements of transmural pressure, flow rate, and the radial displacement of the venous wall, calculations are made of the incremental modulus of elasticity; hoop, axial and radial venous wall stresses; and fluid shearing stress. These data are compared to companion measures previously obtained for canine carotid arteries (Brant et al., 1988; Johnson et al., 1989). The relationship of this biomechanical information to vein graft adaptation to arterial flow is discussed.
Receiwd inpnal form 9 February 1990. * Author to whom correspondence should be addressed.
Animal model
Only adult mongrel dogs (25 kg) intended for sacrifice served as the vessel donors. The animals were anesthetized with sodium pentobarbital(30 mg kg-‘) and a ventral midline neck incision was made. One internal jugular vein (IJV) was then carefully exposed, cannulated, flushed in situ with normothermic canine serum and a 10 cm segment excised at natural length and distension using a specially designed pair of noncrushing vascular clamps. The clamps were not removed until the vessel was secured in its natural orientation in the PDA. The second IJV was harvested as described but utilized in a separate, unrelated study. All animal procedures were performed in accordance with NIH and University guidelines for the care and use of laboratory animals. Perfusion apparatus
The pulse duplicator apparatus (PDA) used to simulate the arterial flow conditions has been described in detail elsewhere (Brant et al., 1986). Briefly, this system simulates the natural environment of an intact vascular segment, providing pulsatile pressures and flows and physiologic pH, PO,, pCOz and temperature. The excised IJV were secured (with suture material) in their natural orientation in the tissue housing chamber of the perfusion apparatus. A 30 cm length of straight, stainless steel tubing led to (and away from) the tissue housing chamber. This length was selected based upon the calculations of entrance and exit length requirements for the fully established flow through test blood vessels (Bird et al., 1960). Instrumentation associated with the PDA allowed dynamic measurements to be made of proximal and distal intraluminal pressures; transmural pressure;
985
S. A. BERCELIet al.
986
flow rate; and radial excursion of the wall of the IJV. Details of these protocols have recently been reported (Brant et al., 1987). Calculations of vessel wall stress
Incremental modulus of elasticity; hoop, axial and radial wall stresses; and fluid shearing stress were derived from the present experimental data following protocols described elsewhere (Brant et al., 1988; Johnson ef al., 1989; Rodgers et a1.,1987). Briefly, we based our calculations of elasticity modulus on the classical work of Bergel (1961) and Pate1 and Fry (1969) and have utilized an incremental modulus, Elnc, for calculation of longitudinal and hoop stress: Ei*o=
TP, - TP, R,,-R,,
2 (1 -a) R& R,, ’
R,Z-R;
(1)
.
Here TP refers to the transmural pressure, u= Poisson’s ratio (assumed = OS), R = radius, and the subscripts i, o, 1, 2, 3 represent inside, outside, minimum (diastolic) value, mean value and maximum (systolic) value of the parameter over the 1 Hz cardiac cycle. The model of arterial wall stress used in this analysis is adapted from the elastic tube model of Kuchar and Ostrach (1966). With the assumptions that the venous wall is elastic, axisymmetric, semi-infinite in length, straight with circular cross-section, constrained from motion longitudinally, and that the radial displacement of the vein wall during each cycle is small in comparison to the mean radius, the general form of the equations for the radial (S,), axial (T-J, and hoop (T,) stresses shown in Fig. 1 are:
%=[T-P;],.,,,
(2)
fJE*nc tl
Txx=(l’-o*) 41
(3)
E in0
rl
E~noh* tl
-a*) Te”=r-‘-+
R,,
12 R;, (1 -a*) ’
STRESSES
ACTING ON SMALL ELEMENT ARTERIAL WALL
(4)
OF
Fig. 1. Close-up of small element of vesselwall showing the stresses acting on it. T,, and Tss are the longitudinal and circumferential wall stresses, respectively. S,, and S,, are the normal and fluid shear stresses, respectively.
Here: r = radial coordinate; v = radial fluid velocity component; fl =dynamic fluid viscosity; v = experimentally measured radial displacement of the vein wall; h = vein wall thickness. Other nomenclature follows that of Equation (1). The mathematical model originally developed by Tsai and Hung (1984) and adapted by Johnson et al. (1989) is employed to determine the dynamic wall shear rate (WSR) acting on the perfused LTV.Using a finite difference numerical scheme, the Navier-Stokes equations for pulsatile flow in a straight deformable vessel are solved using pressure drop, flow rate, vessel wall radius, and radial wall motion as input. The assumptions of uniform vessel geometry, laminar flow, axisymmetry, and uniform pressure drop are incorporated in the model equation and boundary conditions (Johnson et al., 1989). Identical measurements were performed previously on companion canine carotid arteries (Brant et al., 1988; Johnson et al., 1989), and serve as a comparison. Statistical differences in the aforementioned biomechanic and hemodynamic parameters between the IJV and companion canine carotid artery (CCA) were assessed using the Student’s t-test. RESULTS
Four canine IJV were exposed for two hours to intraluminal perfusion pressures of 115/75 mm Hg and mean flow rates of 110 mlmin-I. No vessel leakage or aneurysmal behavior was observed during these brief perfusion periods. Hemodynamic signals were obtained immediately prior to the conclusion of each study. Typical experimentally derived tracings of pressure drop, flow rate, inner radius, and radial wall velocity are illustrated in Fig. 2. These signals served as input to both the biomechanic and hemodynamic models. Table 1 summarizes the biomechanical response of the wall of the IJV to arterial flows. The inner radius of the IJV (3.4-3.9mm) is twice that (1.7mm) of the companion canine carotid artery @ ~0.001). A striking increase in the incremental modulus (E,,,) for the IJV vs the CCA (p
