485 ISSN 0006-3509, Biophysics, 2019, Vol. 64, No. 3, pp. 485–492. © Pleiades Publishing, Inc., 2019. Russian Text © The Author(s), 2019, published in Biofizika, 2019, Vol. 64, No. 3, pp. 614–621. Analysis of the Flexural Rigidity of Vascular Grafts by Numerical Simulation Methods E. A. Ovcharenko a , K. U. Klyshnikov a, *, M. A. Rezvova a , L. V. Antonova a , T. V. Glushkova a , S. E. Vinokurov a , V. V. Sevostyanova a , E. O. Krivkina a , A. V. Batranin b , Yu. N. Zakharov c , V. G. Borisov c , Yu. A. Kudryavtseva a , and L. S. Barbarash a a Institute of Complex Issues of Cardiovascular Diseases, Kemerovo, 650002 Russia b Tomsk Polytechnic University, Tomsk, 634050 Russia c Kemerovo State University, Kemerovo, 650000 Russia *e-mail: klyshnikovk@gmail.com Received March 15, 2018; revised February 14, 2019; accepted February 18, 2019 Abstract—A numerical evaluation was performed to assess the efficiency of reinforcement of small-diameter vascular grafts made of polymeric materials. Based on the finite-element analysis, an algorithm was devel- oped to find the optimal parameters for the reinforcing layer and to evaluate its stress–strain state under con- ditions of longitudinal bending simulation. The findings may be useful for industrial and laboratory trials in studies of the strengthening properties of similar products. Keywords: vascular prosthesis, reinforcement, finite-element analysis, polymer DOI: 10.1134/S0006350919030163 INTRODUCTION Pathologies of small- and medium-sized arteries are among the main causes of deaths in the global pop- ulation. Reconstruction of such vessels is necessary for several million patients annually [1]. Tissue engineer- ing methods used to produce small-diameter vascular grafts have made it possible to obtain a new class of synthetic biodegradable prostheses for bypass surgery [2, 3]. A prerequisite to their efficient function is that vascular grafts match natural vessels in their main characteristics. In addition to their high biocompati- bility, controllable degradation kinetics, and the abil- ity to maintain their structural and functional integrity immediately after placing and at remodeling steps, the mechanical characteristics of vascular grafts should be satisfactory and ensure natural hemodynamics in the grafting region; i.e., a graft should have a certain flex- ural rigidity to maintain the lumen of the host vessel and a proper compliance to uniformly transmit the pulse waves. Electrospinning is the main method to construct small-diameter synthetic biodegradable vascular grafts. With the method, it is possible to imitate the microarchitecture of the native extracellular matrix and to model the cylindrical shape of a vessel with due regard to preserving the continuous rounded cross section [4]. The morphology of fibers ranging from tens to several microns in diameter can be controlled using electrospinning technology [4], thus obtaining surfaces with high permeability and an interconnected pore structure, which is preferential for products of this kind. However, in spite of the above advantages, certain mechanical properties of electrospun vascular grafts remain unsatisfactory; in particular, bending of the vessel may lead to its partial or full occlusion. This risk is important to consider when vessel grafts of sub- stantial lengths are implanted in regions where high dynamic bending loading is induced by surrounding tissues, as is the case with lower limb vessels in the regions of joints (e.g., femoropopliteal bypass). It is therefore necessary to develop a vascular scaffold that remains functional when exposed to shear and bend- ing stresses. One possible means to solve the problem is to take advantage of fused deposition modeling (FDM) principles in graft production. FDM is an additive manufacturing process and is broadly employed in producing three-dimensional models, in particular, in the new field of computer-aided tissue engineering [5]. In FDM, an object is built from a heated thermoplastic material, which is extruded through a nozzle placed over a collector to form a pre- set shape; the polymer extrusion rate and movements of the extrusion head are under computer numerical control [6]. Patterns built by FDM can be used as rein- forcing constructs and combined with other scaffold production technologies, such as vascular graft pro- duction via two-phase electrospinning, which allows Abbreviations: FDM, fused deposition modeling; PCL, poly- caprolactone. COMPLEX SYSTEMS BIOPHYSICS