Constitutive laws with damage effect for the human great saphenous vein
Introduction
The great saphenous vein (GSV) is a large, subcutaneous, superficial vein of the human leg. The vein runs along the length of the lower limb, see Fig. 1(a). A healthy human GSV wall consists of three layers, namely intima, media and adventitia from inner to outer surface of the wall (Spary and Roberts, 1977, Thine et al., 1980, Milroy et al., 1989, Naim and Elsharawy, 2005). Generally, the intima is thin as 60.07 µm ± 1.12, composed of endothelium and an internal elastic lamina next to the media. The media mean thickness is 360.54 µm± 4.56, in which there are longitudinally orientated smooth muscle cells next to the intima and circular smooth muscle cells next to the adventitia. The two smooth muscle layers are separated by collagen fibres. The adventitia is full of collagen fibres with some fibroblasts and capillaries as well as longitudinally orientated smooth muscle cells (Naim and Elsharawy, 2005). Presently, there is little information about collagen fibre orientation and dispersion in the human GSVs. A mean fibre orientation of 37 ± 6° against the circumferential direction in the media (Vesely et al., 2014a) was observed in comparison with 40° in the media of porcine vascular tissues (including vena cava, abdominal aorta and iliac artery) (Snowhill and Silver, 2005). In the adventitia of the porcine vascular tissues, the fibre mean orientation was 60° from the circumferential direction (Snowhill and Silver, 2005).
A segment of GSV can be harvested and utilised to connect the blocked coronary artery and the aorta to build a bypass duct, see Fig. 1(b), consequently the blood can stream into the coronary artery again to make the arrested heart recovery. The idea that the human GSV is used clinically as a coronary artery bypass graft (CABG) can be traced back to 1930's (Diodato and Chedrawy, 2014). However, the direct coronary artery surgery by using CABG technique began in 1968 in the USA actually (Miller and Dodge, 1977). Presently, coronary artery disease (CAD) is a main cause of mortality worldwide. In England, for example, NHS carries out nearly 20,000 CABGs every year (http://www.nhs.uk/conditions/Coronary-artery-bypass/Pages/Introduction.aspx).
After CABG surgery, the GSV CABGs have to undergo an arterialization process. In the process, unfortunately, some GSV CABGs can remodel and develop various diseases, such as aneurysms, thrombosis, atherosclerosis and fibro-intimal hyperplasia, which are associated with smooth muscle cells and extracellular matrix (Hassantash et al., 2008, Vlodaver and Edwards, 1971, Walts et al., 1982, Ramirez et al., 2012). In the first post-surgery month, 13–14% of CABGs occlude because of thrombosis. By the end of the first year of the surgery, intimal hyperplasia develops to reduce graft diameter by 25–30%. In the following years, grafts occlude at a rate of 2% per year as intimal hyperplasia develops. Beyond 5 years, vein grafts are in atherosclerosis due to necrosis, haemorrhage, calcification, and thrombosis (de Vries et al., 2016). The remodelling, disease and failure are related closely to physiological haemodynamic conditions in the coronary artery (de Vries et al., 2016) and passive biomechanical properties of GSV such as compliance (Zachrisson et al., 2011).
Some attention has been paid to passive biomechanical properties of GSV by using experiment in vitro since 1960's. These experimental contributions can be divided into four categories: (1) global property constant measurements, such as compliance (Khalil et al., 1968, Bocking and Roach, 1974, Walden et al., 1980), pressure-diameter relationships (Angelini et al., 1987, Stooker et al., 2003, Paranjothi et al., 2011), rupture pressure (Archie and Green, 1990) and circumferential and longitudinal incremental Young's moduli (Wesly et al., 1975) by making use of vessel segment inflation method and an incremental Young's modulus by bugle method (Forouzandeh et al., 2013); (2) ultimate stress and strain as well as stiffness etc. by using uniaxial tensile test on circumferential and longitudinal specimens (Psaila and Mehuish, 1989, Donovan et al., 1990); (3) stress-strain curves with uniaxial tensile test on circumferential and longitudinal specimens (Ozturk et al., 2013, Hamedani et al., 2012); (4) biaxial stress-strain curves measured by using vessel segment inflation approach (Zhao et al., 2007, Vesely et al., 20142014b, Vesely et al., 2015). These experimental results have provided a valuable basis for further investigations. Importantly, a micro-fibrillary damage could be observed in GSV tissue under a low intraluminal pressure, namely in a range of 50–60 mmHg (Ozturk et al., 2013).
Compliance mismatch between a GSV CABG and the coronary artery can degrade the graft performance and result in a loss of patency, which is the degree of openness of a vessel, in terms of time after surgery (Abbott et al., 1987). Compliance of GSV can be correlated to CABG patency (Salacinski et al., 2001). Incremental Young's modulus, ultimate stress and strain, stiffness, and stress-strain curves, however, haven’t found any clinical applications in CABGs presently.
Under coronary artery haemodynamic conditions, a GSV CABG will be subject to an intraluminal pressure as high as 100–150 mmHg (Siogkas et al., 2015), how the deformation of GSV CABG to develop in this condition and the corresponding levels of stress and strain/stretch are of vital important to understanding of its actual working situation and mechanisms for its remodelling and disease occurrence from a biomechanics point of view. Unfortunately, this issue has not been addressed; further, the micro-fibrillary damage observed in GSV tissue under an intraluminal pressure as low as 50–60 mmHg (Ozturk et al., 2013) has not been included in constitutive laws of GSV in literature so far.
In the paper, it is attempted to develop constitutive laws of GSV by involving collagen fibre orientation dispersion and micro-fibrillary damage effect based on stress-strain/stretch data obtained by uniaxial tensile test and vessel segment inflation test, i.e. tubular biaxial inflation test found in literature. Then these constitutive laws are applied into coronary artery haemodynamic conditions to predict the stress and stretch levels of CABG by employing a thin-walled vessel model. Thirdly, the suitability of these constitutive laws for coronary artery physiological environment is evaluated against clinical observations on post-surgery CABG diameter. Finally, micro-fibrillary damage threshold and hypothesis on the reason why GSV remodels are proposed and discussed. These constitutive models and the established method for determining model constants could be meaningful in biomedical engineering and clinical application.
Section snippets
Experiment data adopted
The specimens harvested from human GSV segments in the longitudinal/axial direction and the cut ring from the segments along the circumferential/transverse direction were stretched by using uniaxial tensile test method on an ordinary material testing machine in Hamedani et al. (2012). The specimens and patients information are tabulated in Table 1. Even though the experiment was made on five pairs of specimens (circumferential and longitudinal), just four specimen pairs were tested
Constitutive laws from uniaxial tensile tests
The model constants of constitutive law for four GSV samples such as SV2–5 are illustrated in Table 2 and a comparison of the Cauchy stress-stretch curves predicted with these constants is made in Fig. 4 against the experimental data of SV2–5. Generally, the stress-stretch curves predicted with the constitutive law with damage effect and extracted model constants are good agreement with the experimental measurements in the maximum error of 6.04% and the minimum error of 1.31%.
Since the
Discussions
In the paper, an analytical approach is proposed to handle experimental data in uniaxial tensile test or tubular biaxial inflation test on GSV segments and then the corresponding constitutive laws with sub-failure/damage effect are established, eventually they are applied into the physiological environment of coronary artery. In consequence, the biomechanical performance of a GSV CABG is evaluated under coronary artery physiological conditions before the surgery. This method is significant in
Conclusions
In the paper, constitutive laws with damage effect based on a strain energy function were developed by using existing either uniaxial tensile test data on specimens harvested from the human GSV segments longitudinally and circumferentially or tubular biaxial inflation test results on GSV segments. The GSV segments were considered as a composite of homogenous matrix and anisotropic two families of collagen fibre; and the nine model constants in the laws are determined inversely with MATLAB
Funding
This study was not funded by anybody.
Conflict of interest
The author has no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by the author.
References (52)
- et al.
Effect of compliance mismatch on vascular graft patency
J. Vasc. Surg.
(1987) - et al.
Mechanical and histologic changes in canine vein grafts
J. Surg. Res.
(1988) - et al.
Material and structural characterization of human saphenous vein
J. Vasc. Surg.
(1990) - et al.
Constitutive modeling of jugular vein-derived venous valve leaflet tissues
J. Mech. Behav. Biomed. Mater.
(2017) - et al.
Biaxial mechanical behavior of bovine saphenous venous valve leaflets
J. Mech. Behav. Biomed. Mater.
(2018) - et al.
Vein graft failure
J. Vasc. Surg.
(2015) - et al.
Pressure-diameter relationship in the human greater saphenous vein
Ann. Thorac. Surg.
(2003) - et al.
Elasticity with energy limiters for modelling dynamics failure propagation
Int. J. Solid Struct.
(2010) - et al.
Constitutive modelling of human saphenous veins at overloading pressures
J. Mech. Behav. Biomed. Mater.
(2015) Prediction of arterial failure based on a microstructural bi-layer fiber-matrix model with softening
J. Biomech.
(2008)
Modeling failure of soft anisotropic materials with application to arteries
J. Mech. Behav. Biomed. Mater.
A model of growth and rupture of abdominal aortic aneurysm
J. Biomech.
Manual pressure distension of the human saphenous vein changes its biomechanical properties-implication for coronary artery bypass grafting
J. Biomech.
A structural constitutive model for viscoelastic rheological behavior of human saphenous vein using experimental assays
Int. J. Med. Health Biomed. Bioeng. Pharm. Eng.
Nature and pressure dependence of damage induced by distension of human saphenous vein coronary artery bypass grafts
Cardiovasc. Res.
aphenous vein rupture pressure, ans carotid endarterectomy vein patch reconstruction
Surgery
The elastic properties of the human great saphenous vein in relation to primary varicose veins
Can. J. Physiol. Pharmacol.
Thirty-day vein remodeling is predictive of midterm graft patency after lower extremity bypass
J. Vasc. Surg.
Hyperplastic modelling of arterial layers with distributed collagen fibre orientations
J. R. Soc. Interface
Shear stress and saphenous vein remodeling ex vivo
J. Biomech.
Comparison between mechanical properties of human saphenous vein and umbilical vein
Biomed. Eng. Online
Pathophysiology of aortocoronary saphenous vein bypass graft disease
Asian Cardiovasc. Thorac. Ann.
Biaxial mechanical properties of bovine jugular venous valve leaflet tissues
Biomech. Model. Mechanobiol.
Cited by (3)
Revascularisation of type 2 diabetics with coronary artery disease: Insights and therapeutic targeting of O-GlcNAcylation
2021, Nutrition, Metabolism and Cardiovascular DiseasesInflation-extension behaviour of the human vena saphena magna
2020, Experimental Stress Analysis - 58th International Scientific Conference, EAN 2020