A procedure to simulate coronary artery bypass graft surgery

New Computational Approach to Shunt Design in Congenital Heart Palliation

Shunts are commonly used to redirect blood to pulmonary arteries in procedures that palliate congenital cardiovascular defects. Previous clinical studies and hemodynamic simulations reveal a critical role of shunt diameter in balancing flow to pulmonary versus systemic vessels, but the biomechanical process of creating the requisite anastomosis between the shunt and host vessel has received little attention. Here, we report a new Lagrange multiplier-based finite element approach that represents the shunt and host vessels as individual structures and predicts the anastomosis geometry and attachment force that result when the shunt is sutured at an incision in the host, followed by pressurization. Simulations suggest that anastomosis orifice opening increases markedly with increasing length of the host incision and moderately with increasing blood pressure. The host artery is further predicted to conform to common stiff synthetic shunts, whereas more compliant umbilical vessel shunts should conform to the host, with orifice area transitioning between these two extremes via a Hill-type function of shunt stiffness. Moreover, a direct relationship is expected between attachment forces and shunt stiffness. This new computational approach promises to aid in surgical planning for diverse vascular shunts by predicting in vivo pressurized geometries.

Role of Vessel Microstructure in the Longevity of End-to-Side Grafts

Compliance mismatch between the graft and the host artery of an end-to-side (ETS) arterial bypass graft anastomosis increases the intramural stress in the ETS graft-artery junction, and thus may compromise its long-term patency. The present study takes into account the effects of collagen fibers to demonstrate how their orientations alter the stresses. The stresses in an ETS bypass graft anastomosis, as a man-made bifurcation, are compared to those of its natural counterpart with different fiber orientations. Both of the ETS bypass graft anastomosis and its natural counterpart have identical geometric and material models and only their collagen fiber orientations are different. The results indicate that the fiber orientation mismatch between the graft and the host artery may increase the stresses at both the heel and toe regions of the ETS anastomosis (the maximum principal stress at the heel and toe regions increased by 72% and 12%, respectively). Our observations, thus, propose that the mismatch between the collagen fiber orientations of the graft and the host artery, independent of the effect of the suture line, may induce aberrant stresses to the anastomosis of the bypass graft.

Suture Line Response of End-to-Side Anastomosis: A Stress Concentration Methodology

End-to-side vascular anastomosis has a considerable complexity regarding the suturing of the juncture line between the artery and the graft. The present study proposes a stress-concentration methodology for the prediction of the stress distribution at the juncture line, aiming to provide generic expressions describing the response of an end-to-side anastomosis. The proposed methodology is based on general results obtained from the analysis of pipe connections, a topic that has been investigated in recent years in the field of offshore structural engineering. A key aspect for implementing the stress-concentration-factor approach is the recognition that the axial load due to pressure and flow dynamics exerted along the graft axis controls the "hot spots" on the juncture line, which in turn affects the mechanical response of the sutures. Several parameters, identified to influence the suture line response, are introduced in closed-form expressions for the suture line response calculations. The obtained results compare favorably with finite element results published in the literature. The proposed model predicts analytically the suture line response of end-to-side anastomosis, while capturing the influence of and interdependence among the problem parameters. Lower values of the graft radius, the distance between sequential stitches, and the intersecting angle between the artery and the graft are some of the key parameters that reduce the suture line response. The findings of this study are broad in scope and potentially applicable to improving the end-to-side anastomosis technique through improved functionality of the sutures and optimal selection of materials and anastomosis angle.

Dynamic behavior of suture-anastomosed arteries and implications to vascular surgery operations

BACKGROUND

Routine vascular surgery operations involve stitching of disconnected human arteries with themselves or with artificial grafts (arterial anastomosis). This study aims to extend current knowledge and provide better-substantiated understanding of the mechanics of end-to-end anastomosis through the development of an analytical model governing the dynamic behavior of the anastomotic region of two initially separated arteries.

METHODS

The formulation accounts for the arterial axial-circumferential deformation coupling and suture-artery interaction. The proposed model captures the effects of the most important parameters, including the geometric and mechanical properties of artery and sutures, number of sutures, loading characteristics, longitudinal residual stresses, and suture pre-tensioning.

RESULTS

Closed-form expressions are derived for the system response in terms of arterial radial displacement, anastomotic gap, suture tensile force, and embedding stress due to suture-artery contact interaction. Explicit objective functionalities are established to prevent failure at the anastomotic interface.

CONCLUSIONS

The mathematical formulation reveals useful interrelations among the problem parameters, thus making the proposed model a valuable tool for the optimal selection of materials and improved functionality of the sutures. By virtue of their generality and directness of application, the findings of this study can ultimately form the basis for the development of vascular anastomosis guidelines pertaining to the prevention of post-surgery implications.

Comparison between mechanical properties of human saphenous vein and umbilical vein

Background

As a main cause of mortality in developed countries, Coronary Artery Disease (CAD) is known as silent killer with a considerable cost to be dedicated for its treatment. Coronary Artery Bypass Graft (CABG) is a common remedy for CAD for which different blood vessels are used as a detour. There is a lack of knowledge about mechanical properties of human blood vessels used for CABG, and while these properties have a great impact on long-term patency of a CABG. Thus, studying these properties, especially those of human umbilical veins which have not been considered yet, looks utterly necessary.

Methods

Umbilical vein, as well as human Saphenous vein, are respectively obtained after cesarean and CABG. First, histological tests were performed to investigate different fiber contents of the samples. Having prepared samples carefully, force-displacement results of samples were rendered to real stress–strain measurements and then a fourth-order polynomial was used to prove the non-linear behavior of these two vessels.

Results

Results were analyzed in two directions, i.e. circumferentially and longitudinally, which then were compared with each other. The comparison between stiffness and elasticity of these veins showed that Saphenous vein’s stiffness is much higher than that of umbilical vein and also, it is less stretchable. Furthermore, for both vessels, longitudinal stiffness was higher than that of circumferential and in stark contrast, stretch ratio in circumferential direction came much higher than longitudinal orientation.

Conclusion

Blood pressure is very high in the region of aorta, so there should be a stiff blood vessel in this area and previous investigations showed that stiffer vessels would have a better influence on the flow of bypass. To this end, the current study has made an attempt to compare these two blood vessels’ stiffness, finding that Saphenous vein is stiffer than umbilical vein which is somehow as stiff as rat aortic vessels. As blood vessel’s stiffness is directly related to elastin and mainly collagen content, results showed the lower amount of these two contents in umbilical vein regarding Saphenous vein.

Virtual Interventions for Image-based Blood Flow Computation

Image-based blood flow computation provides great promise for evaluation of vascular devices and assessment of surgical procedures. However, many previous studies employ idealized arterial and device models or only patient-specific models from the image data after device deployment, since the tools for model construction are unavailable or limited and tedious to use. Moreover, in contrast to retrospective studies from existing data, there is a pressing need for prospective analysis with the goal of surgical planning. Therefore, it is necessary to construct models with deployed devices in a fast, virtual and interactive fashion. The goal of this paper is to develop new geometric methods to deploy stents or stent grafts virtually to patient-specific geometric models constructed from a 3D segmentation of medical images. A triangular surface representing the vessel lumen boundary is extracted from the segmentation. The diseased portion is either clipped and replaced by the surface of a deployed device or rerouted in the case of a bypass graft. For diseased arteries close to bifurcations, bifurcated device models are generated. A method to map a 2D strut pattern on the surface of a device is also presented. We demonstrate three applications of our methods in personalized surgical planning for aortic aneurysms, aortic coarctation, and coronary artery stenosis using blood flow computation. Our approach enables prospective model construction and may help to expand the throughput required by routine clinical uses in the future.

Constitutive modelling of arteries

This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

Characterization of the highly nonlinear and anisotropic vascular tissues from experimental inflation data: a validation study toward the use of clinical data for in-vivo modeling and analysis

We study whether an inverse modeling approach is applicable for characterizing vascular tissue subjected to various levels of internal pressure and axial stretch that approximate in-vivo conditions. To compensate for the limitation of axial-displacement/pressure/diameter data typical of clinical data, which does not provide information about axial force, we propose to constrain the ratio of axial to circumferential elastic moduli to a typical range. Vessel wall constitutive behavior is modeled with a transversely isotropic hyperelastic equation that accounts for dispersed collagen fibers. A single-layer and a bi-layer approximation to vessel ultrastructure are examined, as is the possibility of obtaining the fiber orientation as part of the optimization. Characterization is validated against independent pipette-aspiration biaxial data on the same samples. It was found that the single-layer model based on homogeneous wall assumption could not reproduce the validation data. In contrast, the constrained bi-layer model was in excellent agreement with both types of experimental data. Due to covariance, estimations of fiber angle were slightly outside of the normal range, which can be resolved by predefining the angles to normal values. Our approach is relatively invariant to a constant or a variable axial response. We believe that it is suitable for in-vivo characterization.

A new constitutive model for multi-layered collagenous tissues

Collagenous tissues such as the aneurysmal wall or the aorta are multi-layered structures with the mean fibre alignments distinguishing one layer from another. A constitutive representation of the multiple collagen layers is not yet developed, and hence the aim of the present study. The proposed model is based on the constitutive theory of finite elasticity and is characterized by an anisotropic strain-energy function which takes the material structure into account. The passive tissue behaviour is modelled and the related mechanical response is assumed to be dominated by elastin and collagen. While elastin is modelled by the neo-Hookean material the constitutive response of collagen is assumed to be transversely isotropic for each individual layer and based on an exponential function. The proposed constitutive function is polyconvex which ensures material stability. The model has five independent material parameters, each of which has a clear physical interpretation: the initial stiffnesses of the collagen fabric in the two principal directions, the shear modulus pertaining to the non-collagenous matrix material, a parameter describing the level of nonlinearity of the collagen fabric, and the angle between the principal directions of the collagen fabric and the reference coordinate system. An extension-inflation test of the adventitia of a human femoral artery is simulated by means of the finite element method and an error function is minimized by adjusting the material parameters yielding a good agreement between the model and the experimental data.

Analog electrical model of the coronary circulation in case of multiple revascularizations

In this work, we propose an analog electrical model of the coronary circulation for patients with obstructive disease undergoing revascularization. In this clinical situation, the collateral circulation to the occluded artery is difficult to ascertain via preoperative measurements and well-developed collaterals might induce long-term restenosis of the revascularized artery due to flow competition mechanisms. The proposed model allows an original biomechanical analysis of per-operative hemodynamic data in order to assess quantitative evaluation of pressures and flows inside the native stenosed arteries, the collateral network and the bypass grafts. Average cardiac cycle values are analysed. In the case of 3-vessel disease and chronic occlusion of the right coronary artery, the quantitative results confirm the protective effects of the collateral flows in the pathological situation, but also show that the revascularization of the occluded right artery is fully justified since the collateral flows remain low, even when the left territory is revascularized. The model thus provides a computational tool to evaluate therapeutic strategies for each patient.