1 Introduction

AUTOGENOUS VEiN bypasses as well as synthetic grafts are commonly used as arterial bypass conduits. Even though prosthetic graft replacement of the aortofemoral arteries is satisfactory, problems with loss of patency is a significant limitation when they are used with infrainguinal bypasses. Experimentally it has been found that 12 weeks after implantation, 80 per cent of vein grafts remained patent in an animal model, whereas only 30 per cent of Dacron grafts and 15 per cent of PTFE grafts maintained patency (KIDSON, 1983). Even though autogenous vein grafts have proven to be very durable, segments of sufficient length are not always available and up to 30 per cent of the veins may be inadequate as bypass grafts (KIDSON, 1983). A number of studies have been reported suggesting that the compliance mismatch between the host artery and the graft is a causative factor for graft failure (ABBOTTand BOUCHIER-HAYES, 1978; K1NLEY and MARBLE, 1980; WALDEN et al., 1980; DEWEESE, 1985). KIDSON (1983) showed that vein grafts with in vivo compliance closer to that of arteries performed better in spite of the fact of significant arterialisation with marked wall thickening Correspondence should be addressed to Professor K. B. Chandran, Department of Biomedical Engineering, 1204 Engineering Building, University of Iowa, Iowa City, IA 52242, USA First received 26th March and in final form 23rd July 1991

9 IFMBE: 1992 Medical & Biological Engineering & Computing

after implantation. ABBOTT and BOUCHIER-HAYES (1978) suggested that the compliance mismatch between the host artery and the stiffer graft may contribute to abnormal haemodynamics in the anastomotic region resulting in later loss of patency. KINLEYand MARBLE(1980) have suggested that compliance mismatch at the anastomosis increases flow-induced shear stress, reduces distal perfusion and can predispose to anastomotic rupture. WALDEN et al. (1980) concluded that the clinical performance of synthetic grafts could improve by matching the viscoelastic properties of the grafts with the host arterial segment. GAVHS (1981) observed true para-anastomotic aneurysms of venous conduits adjacent to anastomoses with intact suture lines. However, with prosthetic conduits, pseudoaneurysms developed instead. HASSON et al. (1985) experimentally measured a consistent focal increase in compliance at 3.6mm on the arterial side of the anastomosis to approximately 1.5 times the control value. They termed the region of increased compliance as the paraanastomotic hypercompliant zone (PHZ) and suggested that cyclic stretching of this region results in anastomotic intimal hyperplasia. HASSON et al. (1986) used interrupted sutures to minimise the hyper-compliance. Hasson et al. also demonstrated that the compliance of the surgically exposed artery remained stable 24 hours after the procedure (HAssoN et al., 1984). However, the compliance

July 1992

413

decreased significantly after one week and reached a minimum two weeks after surgical exposure. They suggested that this postsurgical stiffening of the artery must be considered in matching the compliance of grafts with the host artery. TEODORI et al. (1986), using an in vitro model to measure the diameter and wall thickness changes and a theoretical elastic tube model of KUCHAR and OSTRACH (1966), suggested that the biomechanical forces generated at the anastomosis may not be a significant factor in the failure of small diameter prosthetic grafts. In this paper, a finite-element analysis of a model of two alternative end-to-end artery-graft anastomoses is presented. The results indicate the presence of a region of increased compliance in the arterial side of the anastomosis as well as a region of increased tensile stresses in the wall of the graft. The possible contribution of these results to graft failure is discussed. 2 F i n i t e - e l e m e n t analysis Finite-element (FE) models of two alternative end-toend artery-graft anastomoses were generated for this study. One was an artery-to-vein graft anastomosis and the other was an arterial anastomosis with either a Dacron or P T F E graft. The arterial internal diameter and wall thickness were assumed to be 4 mm and I mm, respectively (BURTON, 1971). The internal diameter of the vein and synthetic grafts were also assumed to have the same value (Table 1). Table 1 study

Artery Vein Dacron PTFE

Dimensions, elastic modulus and the compliance of the 9rafts used in this

Internal diameter, mm 4.0 4-0 4-0 4.0

Wall thickness, mm 1"0 0-5 1.0 1'0

The wall thickness for the prosthetic grafts was assumed to be I mm whereas the value for the vein graft was assumed to be 0.5ram (BURTON, 1971). The geometry of the artery and grafts were assumed to be cylindrical and the wall material to be made of an isotropic, homogeneous, incompressible, linear elastic medium in this simplified model. The magnitudes of the elastic modulus for the artery, as well as the bypass grafts was specified such that the compliance distal to the anastomosis would simulate values reported from in vivo studies (ABBOTT and BOUCHIERHAYES, 1978). The compliance of a vessel can be defined using the relationship C -

AD 1 D AP

vein is assumed to be thinner than the arterial wall, specification of a higher elastic modulus was necessary to simulate the compliance characteristics of the vein graft measured in vivo. It should also be pointed out that vein grafts undergo marked histological changes after implantation. This process of 'arterialisation' results in thickening of the walls even though the compliance of the vein graft does not appear to change (WALDEN et al., 1980). A general-purpose FE program ANSVS (Swanson Analysis, Inc., Pennsylvania) was employed in the static analysis reported in this work. The wall was divided into two layers and up to 108 eight-noded isoparametric threedimensional elements (STIF45) with up to 355 nodes were used in the analysis depending on the model under consideration. To simulate the incompressibility of the vessel wall, a Poisson's ratio of 0-499 was specified for the artery as well as for the grafts. Further increase in the number of elements by further subdivision of the arterial wall did not result in a significant increase in accuracy, and hence, modelling the arterial wall by two layers was deemed to be sufficient. Taking advantage of the axisymmety o f the model, only a segment of the artery/graft anastomosis was used in the analysis by the appropriate specification of the boundary conditions at the nodes. The distance between the anastomosis and the free end of the artery and graft was specified to be 4 cm. Fig. 1 shows the schematic of the model for an artery/prosthetic graft (Dacron or PTFE) as well as for an artery/vein graft model. To account for the

Compliance, per cent per kPa

Elastic modulus, E, Pa • 105

Computed

In vivo

4-55 17.55 19.00 22-00

0-585 0'234 0.140 0-121

0-586 0.233 0.140 0-122

difference in wall thickness for the artery and the vein, prismatic elements were also employed in the finiteelement mesh. At the free ends (distal to the anastomosis) the nodes were restricted from motion along the axial -4.0

artery

I

I

I

0 I

cm

prosthetic

I

graft

i

i

4-0 i

[

I

(1)

cm

"

anastomosis a

where C is the compliance, D is the internal diameter and AP is the pulse pressure. The elastic moduli for the artery and the various graft segments used in the analysis are included in Table 1. A comparison of the compared and the measured compliance distal to the anastomosis are also included in the table. In the static analysis performed in the present study, the pulse pressure was replaced by an assumed mean arterial pressure of 13.3kPa (100ram Hg). In the case of dynamic analysis, the pulse pressure can be superimposed onto the mean arterial pressure for a realistic simulation of in vivo loading. It can be observed from Table 1 that the elastic modulus value assumed for the wall of the vein graft is very high compared to that of the artery. Because the wall of the 414

-4.0 I

cm

I

artery I

!

0 I

vein I

]

graft I

I

4.0 I

cm

t/2

.

.

.

.

anastomosis

b

Fig. 1 Finite-element model of a simulated artery/yraft anastomosis. R: internal radius of the vessel; t: thickness of the vessel wall; Ap : applied arterial pressure load

Medical & Biological Engineering & Computing

July 1992

direction to simulate the tethering of the artery in vivo. SZILAGYI et al. (1960) suggested that implanting a graft with the internal diameter larger than that of the host artery will provide an optimum flow rate through the implant. To assess the effect of a graft with a larger diameter on both the compliance and stress distribution at the anastomosis, further analysis was performed by increasing the diameter of the synthetic graft to values 25 and 50 per cent larger than that of the host artery. At the junction of two conduits of dissimilar diameter, the graft with the larger diameter was assumed to taper to the diameter of the artery without distortion as a simplification.

3 Results

The distribution of compliance and the nondimensional principal stress (maximum tensile stress normalised with respect to the applied mean pressure) around the anastomosis with a vein graft subjected to a mean pressure of 13.3kPa (100mmHg) is shown in Fig. 2. An increase in

compliance is observed on the arterial side 4 mm from the anastomosis. A region of high tensile stress in the wall is also found 0.5 mm from the anastomosis on the graft side. A similar distribution of compliance and stress is observed with the artery/Dacron graft model (Fig. 3). With the Dacron graft, the increase in compliance on the arterial side is larger than the corresponding value for the artery/ vein model. Moreover, the maximum nondimensional principal stress with the Dacron graft is smaller than the corresponding value for the vein graft. The location and the magnitude of the maximum compliance as well as the maximum nondimensionalised principal stresses with the vein, Dacron and P T F E graft models are shown in Table 2. To study the effect of increased diameter of the bypass graft compared with the host artery, the finite-element model was analysed with the graft diameter being 25 and 50 per cent larger than that of the arterial diameter of 4mm. The distribution of compliance with larger diameter bypass grafts are shown in Fig. 4. Increasing the bypass graft diameter by 25 per cent of the host artery resulted in

0"60

0'6

7

0"55

s

0"50

i-

0'45

0"5 0 13_

t7

L_ (D Q_

0"40 U

E u

0'35

g

0"4

0'3

o_

0'30 u

g

E 0"25 o

0-2

L.

E o u

0"20 0"15 0.10

a r t e r y .m-

:3

-'2

-'i

0-1

--~ g r a f t

;

;

artery~-

i

0 -4

;

-b

-~graft

i -~2

-1

i

;

]

a

5.0 4.~

4"0 N

s

35

c o.

o. 3 0

c o

f

g

'~

E

2.5

c

E

c O c

2'0

c o c

artery

1

-'2

4-

1"5

--~graft

'

1"0 -4

'

d i s t a n c e , crn

artery~

-

=3

i

-2

4

~ graft

;

i

i

2

i

3

i

distance, cm

6

6

Fig. 2 Distribution of compliance and nondimensional principal

Fig. 3 Distribution of compliance and nondimensional principal

stress (maximum tensile stress normalised with respect to the applied mean arterial pressure) in the vicinity of an artery/vein 9raft anastomosis

stress (maximum stress normalised with respect to the applied mean arterial pressure) in the vicinity of an artery/ Dacron graft anastomosis

Medical & Biological Engineering & Computing

J u l y 1992

415

Table 2 Magnitudes of maximum compliance in the hypercompliant zone and the maximum nondimensional principal (maximum tensile stress normalised with respect to the applied mean arterial pressure) stress with their locations from the anastomosis Distance Distance Maximum

in m m from

Maximum

compliance,

anastomosis

Graft model

per cent per kPa

(on arterial side)

nondimensional principal stress

anastomosis (on the side of the graft)

Artery/vein Artery/Dacron Artery/PTFE

0"590 0.595 0.596

4.0 3.5 3.5

6-37 4-61 4.83

0'25 0"5 0'5

0'8

0.8

0.7

0-7

0'6

(3-

in m m from

Q-

/

0"6

o. 0'5

0"5

u

,- 0"4

0"4

X

O.

s u E 0'3

U

0"3

cI

(3.

5.

E o

E

o u

0"2

0'2

L 0'1

0 -4

artery.4J2 -

0.1

--~ g r a f t i 0

= 2

i 4

a r t e r y ~,~

0 -4

--~ g r a f t

_l2

0

I

I

I

0 b

2

4

0"8

0"7 o

.d

0"6i

(3-

~ o.~ I ~ o.3 (3

oE 0"2 u

v/ 0"1

0 -4

a r t e r y .4I -2

--=. graft L 0

i 2

I 4

distance, c m C

Fig. 4 Effect of increase of graft diameter on the distribution of compliance: (a) graft diameter

=

arterial diameter; (b) graft

diameter = 1"25 x arterial diameter; (c) graft diameter = 1.50 x arterial diameter

a slight increase in the hypercompliant zone at the arterial side of the anastomosis (Fig. 4b). However, increasing the graft diameter to 50 per cent resulted in a dramatic increase in the compliance at the hyper compliant zone (Fig. 4c). Furthermore, increasing the diameter of the graft also resulted in an increase of principal tensile stresses in the wall of the graft side of the anastomosis by three orders of magnitude. 416

4 Discussion In this study, a finite-element model of an artery/graft anastomosis was studied to delineate the effect of compliance mismatch on the distribution of compliance and stresses in the wall in the vicinity of the anastomosis. Our results showed the presence of increase in compliance of up to 2 per cent at a distance of 4mm from the anastomosis in the arterial side. It is interesting to note that at

Medical & Biological Engineering & Computing

July 1992

about the same location, HASSON et al. (1985) demonstrated the presence of a hypercompliant zone from in vivo experiments. In their study, an increase in compliance in the artery of up to 50 per cent was measured at about 3.5 mm from the anastomosis. Even though the increase in compliance shown in the present model is much smaller, the location of such an increase in compliance is similar to that present in the in vivo study. Our results were based on the analysis of static loading in a simplified model. With dynamic loading, and more realistic material property specifications for the arterial wall, our model may also show more significant increases in compliance in that location. Our study also demonstrated the existence of a region of relatively high tensile stresses in the wall on the graft side of the anastomosis. SZILAGYI et al. (1960) showed that implanting a graft with a larger diameter compared with the host artery resulted in an increase in the volume flow rate of blood in both end-to-end and end-to-side anastomoses. An increase of 60 per cent in the diameter of the graft over the host artery resulted in a 20 per cent increase in flow rate. The flow rate increased 67 per cent when the diameter of the bypass graft was increased 100 per cent. However, any further increase in diameter of the bypass graft resulted in a decrease in blood flow through the graft. Their work suggested that using a graft with a diameter 40-60 per cent larger than the host artery would be of advantage due to the increased flow rate through the graft. Our simulation suggests that the use of larger grafts could be detrimental due to the presence of significant increases in perianastomotic hypercompliance. The significance of compliance mismatch at the anastomosis remains controversial. ABBOTTand BOUCHIER-HAYES (1978) speculated that a 'closed' mismatch between a lowimpedance artery and a high-impedance graft may result in local stagnation of blood and an 'open' mismatch between a high-impedance graft and a low-impedance artery may result in local turbulent flow. Both of these abnormal haemodynamic patterns may result in complex phenomena at the fluid/wall interface with increased element residence time, and interaction of activated platelets and smooth muscle cells at the site of the mismatch. Studies by KINLEY and MARBLE (1980) suggested that flow separation and increased shear stresses due to eddies in the separation region at the 'open' anastomosis is the possible cause of endothelial cell injury and platelet activation. The region of hypercompliant zone, whose presence was demonstrated in the present study as well as in the in vivo studies by HASSON et al. (1985), are possible sites for flow separation and increased shear stress due to eddies. GAYLIS (1981) suggested that compliance mismatch between the graft and artery resulted in abnormal shear stresses at the anastomosis leading to the disruption of the arterial anastomosis and false aneurysm formation. TEODORI et al. (1986) used an in vitro experimental setup to measure the diameter and wall thickness changes in the vicinity of an anastomosis and used a theoretical algorithm to compute the shear stress developed at the wall of the artery and the graft. They concluded that the computed shear stress at the wall is 5-50 times smaller than that which had been predicted using an elastic tube model by KUCHAR and OSTRACH (1966) and hence suggested that the biomechanical forces generated at the anastomosis may not be a significant factor in the failure of the smalldiameter prosthetic grafts. However, the present study has shown that relatively high tensile stresses can be found in the wall of vein grafts. The high stresses may induce interaction of activated platelets and smooth muscle cells resulting in the formation of neointimal hyperplasia. Medical & Biological Engineering & Computing

There are certain limitations to this study which should be pointed out. This preliminary study was restricted to static loading, whereas the artery/graft anastomosis is normally subjected to a pulsatile load in vivo. Moreover, the effect of sutures at the junction between the artery and the graft on the mechanics of the anastomosis was not taken into account in this study. The material property of the artery was assumed to be linear and isotropic and hence any nonlinear effects were neglected. It has been suggested that the cyclic stretching due to pulsatile loading may lead to false aneurysm formation (GAYLIS, 1981). To analyse the effects of cyclic loading, a dynamic simulation would be necessary. The effect of dynamic loading on the mechanical stresses in the vicinity of the anastomosis will be more dramatic if both the viscoelastic and anisotropic behaviour of the vessel wall is also incorporated. In spite of these simplifications, this study confirms the presence of a hypercompliant zone which has been demonstrated with in vivo studies. Further studies incorporating the abovementioned factors may be useful in delineating the mechanical effects of compliance mismatch at anastomotic sites. Such model studies can provide valuable information on the mechanical effects of compliance mismatch and suggest design changes to minimise any adverse haemodynamic effects.

5 Summary Small-diameter prosthetic arterial grafts have poor longterm patency. Compliance mismatch between the host artery and graft has been suggested as a cause for failure. To analyse the effect of compliance mismatch on the distribution of compliance and stresses in the vicinity of an anastomosis, a static finite-element study was performed in this study. The following conclusions can be drawn from the study presented above. (a) A region of increased compliance was observed at 4 m m from the anastomosis on the arterial side. The compliance increase was larger with both synthetic grafts. (b) A region of increased stresses was also observed at 0.5mm from the anastomosis in the graft side. The magnitude of the maximum principal stresses was larger with the vein graft with a relatively thin wall. (e) Increasing the diameter of a graft with respect to that of the host artery results in a larger increase in the compliance of the artery in the vicinity of the anastomosis. This exaggerates the para-anastomotic hypercompliant zone. References ABBOTT, W. M. and BOUCHIER-HAYES, J. (1978) The role of mechanical properties in graft design. In Graft materials in vascular surgery. DARDIK H. (Ed.), Year Book Medical Publishers, Chicago, 59-78. BURTON,A. C., (1971) Physiology and biophysics of the circulation. Year Book Medical Publishers, Chicago. DEWEESE, J. A. (1985) Anastomotic neointimal fibrous hyperplasia. In Complications in vascular surgery, 2nd edn. BERNARD, V. M. and TOWNE, J. B. (Eds.), Grune & Stratton, Orlando, Florida, 157-170. GAVELS,H. (1981) Pathogenesis of anastomotic aneurysms. Surg., 90, 509-515. HASSON, J. E., MEGERMAN,J. and ABBOTT,W. A. (1984) Postsurgical changes in arterial compliance. Arch. Surg., 119, 788791. HASSON,J. E., MEGERMAN,J. and ABBOTT,W. A. (1985) Increased compliance near vascular anastomosis. J. Vasc. Surg., 2, 419423.

July 1992

417

HASSON, J. E., MEGERMAN, J. and ABBOTT, W. M. (1986) Suture technique and para-anastomotic compliance. Ibid., 3, 591-598. KIDSON, I. G. (1983) The effect of wall mechanical properties on patency of arterial grafts. Ann. R. Coll. Surg. of England, 65, 24-29. KINLEY, C. E. and MARBLE, A. E. (1980) Compliance: a continuing problem with vascular grafts. J. Cardiovasc. Surg., 21, 163-170. KUCHAR, N. R. and OSTRAC8, S. (1966) Flow in the entrance regions of circular elastic tubes. Biomed. Fluid Mech. Syrup. ASME, New York, 45-69. SZILAGYI, D. E., WHITCOMB, J. G., SCHENKER, W. and WAIBEL,P. (1960) The laws of fluid and arterial grafting. Surg., 47, 55-73. TEODORI,M. F., RODGERS,V. G. J., BRANT, A. M., BOROVETZ,H. S., WEBSTER, M. W., STEED, D. L. and PEITZMAN, A. B. (1986) Effect of compliance and diameter on stress at artificial anastomosis. Current Surg., Nov./Dec., 505-508. WALDEN,R., L'ITALIEN, G. J., MEGERMAN,J. and ABBOTT, W. M. (1980) Matched elastic properties and successful arterial grafting. Arch. Surg., 115, 1166-1169.

degree in Biomedical Engineering at the University of Iowa in May, 1990. She is currently working towards her Ph.D. degree in the Department of Civil Engineering at the University of Connecticut in Storrs, Connecticut.

G. J. Han was born in Pusan, Republic of Korea, in 1956 and studied Mechanics at the Seoul National University and the Korea Advanced Institute of Science & Technology in Seoul. After receiving his Master's degree, he served in the Dong-A University faculty from 1982 to 1986. He then joined the Graduate Program of Mechanical Engineering at the University of Iowa and obtained his Doctoral degree in December 1990. He is currently an Assistant Professor of Mechanical Engineering at Dong-A University. His research interests are in solid mechanics and the application of finite-element methods to problems in cardiovascular biomechanics.

Authors" biographies Krishnan B. Chandran was born in Madurai, India, in 1944. He received his BS in Physics from Madras University in 1963 and B. Tech degree in Mechanical Engineering from the Indian Institute of Technology, Madras in 1966. He received his Master's and Doctor of Science degrees in Mechanical Engineering from Washington University in St. Louis, Missouri, in 1969 and 1972, respectively. He joined the University of Iowa in 1978, where he is now Professor of Biomedical Engineering and Mechanical Engineering. His current research interests are in the area of cardiovascular biomechanics. He is a Fellow of ASME. Dongfen Gao was born in Jilin City, People's Republic of China, in 1960. She received her BS degree in Hydraulic Engineering at the College of Beijing Agricultural Engineering in August 1982. She served as an Assistant Instructor in the Department of Hydraulic & Architectural Engineering, the College of Beijing Agricultural Engineering, from August 1982 to May 1987. She received her MS

418

Henryk M. Baraniewski M D is Assistant Professor of Surgery at the University of Illinois at Chicago, USA. He received his MD from the University of Warsaw Medical School in 1967. He was resident and Assistant Professor in the Department of Surgery University of Warsaw, 1967-1982, and resident and Fellow in Surgery at Albany Medical Center and the University of Iowa 1984-1989. Dr John Corson is a Professor of Surgery and Director of Vascular Surgery at the University of Iowa Hospitals and Clinics. In 1968 he graduated MBCh.B from Edinburgh, UK. He emigrated to the USA in 1975. Following two years of surgical research he completed a general surgical residency at Boston University. In 1980-1981 he took a Vascular Fellowship at Harvard University at the Massachusetts General Hospital. Dr Corson has published extensive works on different aspects of peripheral vascular surgery and has a specific interest in vascular haemodynamics.

Medical & Biological Engineering & Computing

July 1992