A standard way to treat this condition is to use a Drug Eluting cardiovascular Stent (DES). A lot of research has been dedicated on the functionality of DES and its effect on restoring blood flow. This is because its design affects the spatial distribution of wall shear stress, which can influence restenosis of the blood vessel walls [3]. Computational Fluid Dynamics (CFD) is considered the dominant methodology to investigate such processes, as it enables individualised risk prediction and virtual treatment planning. CFD models are now considered to be the main clinical tools that can provide insight on matters such as the blood flow based on different stent shapes, the characterisation of pressure and flow fields or the computation of arterial wall shear stress [4-7].
This work aims to introduce the Discrete Element Methodology (DEM) as an innovative way to simulate the real stent expansion and investigate restoration of blood flow by using CFD. The presented model also demonstrates the capabilities and effectiveness of implementing the Graphics Processing Unit (GPU) [8, 9] combined with the Central Processing Unit (CPU) [10-12] technologies to run this simulation. DEM is a method that describes the overall (macroscopic) behaviour of assemblies of particle systems as the result of the interaction of their constitutive individual elements. Opposite to the traditional continuum-based methods, it is based on discrete particles each governed by fundamental laws of physics and mechanics. The method uses an explicit numerical scheme in which the interaction of the particles is monitored contact by contact and their motion is modelled particle by particle [13]. Nowadays, DEM is considered a standard tool for investigating the flow of granular media with applications in geotechnical and environmental engineering, mining, mineral processing and manufacturing [14-19].
This work presents a novel approach of simulating the functionality of a DES and the stent-vessel wall interactions, followed by blood flow in the post-stenting stage. The presented model was divided in three different phases; i) the pre-stenting phase, that simulates the problematic blood flow prior to the introduction of the DES, by using CFD ii) the stenting phase, that replicates the process of stent expansion and fat compression, by using DEM and iii) the post-stenting phase, that simulates the restoration of blood flow, with the use of CFD. Each part of the model was described by different assemblies of particles, replicating the elastic nature of the arterial walls and the compressibility of the fat. The arterial walls were modelled as a bonded cylinder of particles, while the fat as a bonded block of particles attached to the vessel walls. Furthermore, an innovative methodology is proposed for the creation of the stent in which a particle prototype was used to mimic its radial expansion.
The simulation was comprised of 20000 particles in total using the multi-sphere approach and run for 50 seconds of real time. The time was based on the work of Pinton and Lemos (2016) and Hovasse et.al. (2013) who concluded that the recommended stent deployment duration should be above 25 seconds. This was based on a clinical study performed in numerous patients in which the average time of a stent system to accommodate pressure and achieve stability ranked between 30-380 seconds. For this project, a commercial software (EDEM) from DEM Solutions LTD was implemented. A customized code was written with the use of the Application Programming Interface (API) that describes the bonded particle model. EDEM’s GPU solver was used to reduce the overall simulation time.
The aforementioned numerical model used EDEM’s bonded particle capability, that allows particles to be bonded together to form solid shapes. Each bond is modelled as a cylinder that behaves as an elastic beam following the Potyondy and Cundall (2004) model. In addition, the Edinburgh Elasto-Plastic Adhesion model was employed to describe the compressive behaviour of the fat following the work done by Thakur et.al. (2014). This contact model allows plastic deformation to be included in the contact mechanics equations, resulting in elasto-plastic behaviour of particles. Finally, the radial expansion of the stent was modelled with the use of a customised API code that allowed for the creation of a time-dependant expansion of the particle prototype at a specific rate.
Finally, this work presents a way of accelerating such demanding simulations by performing DEM calculations using GPU technology. GPU solvers provide very fast computational speeds compared to simulations on multi-core CPUs. This process has been performed with the use of the EDEM GPU solver engine, which has been created by DEM Solutions LTD. Double precision Open Computing Language (OpenCL) [24] framework has been implemented in the EDEM simulation engine for the NVIDIA Quadro GP100 graphics card and includes a physics model equivalent to the CPU version to satisfy the required accuracy. The GPU configuration employed a combination of GPU and 8 CPU cores for the DEM solver.
References
1. Fogarotto, F., Finite Element Analysis of Coronary Stenting, in Facolta di Injegneria. 2011, Universita degli Studi di Pavia: Pavia, Italy.
2. Boudoulas, K.D., et al., Coronary Atherosclerosis: Pathophysiologic Basis for Diagnosis and Management. Progress in Cardiovascular Diseases, 2016. 58(6): p. 676-692, http://www.sciencedirect.com/science/article/pii/S0033062016300299.
3. Gijsen, F.J.H., et al., Simulation of stent deployment in a realistic human coronary artery. BioMedical Engineering OnLine, 2008. 7: p. 23-23, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2525649/.
4. Morris, P.D., et al., Computational fluid dynamics modelling in cardiovascular medicine. Heart, 2016. 102(1): p. 18-28.
5. LaDisa, J.F., et al., Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries. American Journal of Physiology - Heart and Circulatory Physiology, 2005. 288(5): p. H2465-H2475.
6. Chien, S., Mechanotransduction and endothelial cell homeostasis: the wisdom of the cell. American Journal of Physiology - Heart and Circulatory Physiology, 2007. 292(3): p. H1209-H1224.
7. Yu, Y., et al., The conical stent in coronary artery improves hemodynamics compared with the traditional cylindrical stent. International Journal of Cardiology, 2017. 227: p. 166-171, http://www.sciencedirect.com/science/article/pii/S0167527316335112.
8. Gan, J.Q., Z.Y. Zhou, and A.B. Yu, A GPU-based DEM approach for modelling of particulate systems. Powder Technology, 2016. 301: p. 1172-1182, http://www.sciencedirect.com/science/article/pii/S0032591016304648.
9. Washizawa, T. and Y. Nakahara, Parallel Computing of Discrete Element Method on GPU. Applied Mathematics, 2013. Vol.04No.01: p. 6, //www.scirp.org/journal/PaperInformation.aspx?PaperID=27503.
10. Kuck, D.L., Structure of Computers and Computations. 1978: John Wiley \\& Sons, Inc. 611.
11. Willhalm, T., R. Dementiev, and P. Fay. Intel Performance Counter Monitor - A better way to measure CPU utilization. 2017; Available from: https://software.intel.com/en-us/articles/intel-performance-counter-monitor.
12. Liebowitz, M., C. Kusek, and R. Spies, VMware vSphere Performance: Designing CPU, Memory, Storage, and Networking for Performance-Intensive Workloads. 2014: SYBEX Inc. 264.
13. Cundall, P.A. and O.D.L. Strack, A discrete numerical model for granular assemblies. Géotechnique, 1979. 29(1): p. 47-65, http://www.icevirtuallibrary.com/doi/abs/10.1680/geot.1979.29.1.47.
14. Sousani, M., Kenneth, I-I. E., Ingham, D., Pourkashanian, M., Sheng, Y., Modelling of hydraulic fracturing process by coupled discrete element and fluid dynamic methods. Environmental Earth Sciences, 2014. 72(9): p. 3383-3399, http://dx.doi.org/10.1007/s12665-014-3244-3.
15. Sousani, M., Ingham, D., Pourkashanian, M., Sheng, Y., Kenneth, I-I. E., Simulation of the hydraulic fracturing process of fractured rocks by the discrete element method. Environmental Earth Sciences, 2015. 73(12): p. 8451-8469, http://dx.doi.org/10.1007/s12665-014-4005-z.
16. Qiu, L.-c. and C.-y. Wu, A hybrid DEM/CFD approach for solid-liquid flows. Journal of Hydrodynamics, 2014. 26(1): p. 19-25, http://www.sciencedirect.com/science/article/pii/S1001605814600032.
17. Hobbs, A., Simulation of an aggregate dryer using coupled CFD and DEM methods. International Journal of Computational Fluid Dynamics, 2009. 23(2): p. 199-207, http://dx.doi.org/10.1080/10618560802680971.
18. Afsharpoor, A., et al., CFD modeling of the effect of polymer elasticity on residual oil saturation at the pore-scale. Journal of Petroleum Science and Engineering, 2012. 94–95: p. 79-88, http://www.sciencedirect.com/science/article/pii/S0920410512001696.
19. Chaudhuri, B., F.J. Muzzio, and M.S. Tomassone, Modeling of heat transfer in granular flow in rotating vessels. Chemical Engineering Science, 2006. 61(19): p. 6348-6360, http://www.sciencedirect.com/science/article/pii/S0009250906003393.
20. Pinton, F.A. and P.A. Lemos, Inflation time in stent deployment: How long is enough? Catheterization and Cardiovascular Interventions, 2016. 87(1): p. 73-74, http://dx.doi.org/10.1002/ccd.26387.
21. Hovasse, T., et al., Duration of balloon inflation for optimal stent deployment: Five Seconds Is Not Enough. Catheterization and Cardiovascular Interventions, 2013. 81(3): p. 446-453, http://dx.doi.org/10.1002/ccd.23343.
22. Potyondy, D.O. and P.A. Cundall, A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 2004. 41(8): p. 1329-1364, http://www.sciencedirect.com/science/article/pii/S1365160904002874.
23. Thakur, S.C., et al., Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model. Granular Matter, 2014. 16(3): p. 383-400, https://doi.org/10.1007/s10035-014-0506-4.
24. Khronos OpenCL Working Group, The OpenCL Specification, L. Howes, Editor. 2015.
See more of this Group/Topical: Poster Sessions