Blood flow simulations in the aortic arch in relation to haemodynamic wall shear stress and obesity-induced vascular changes

Introduction The aorta is the largest artery in the human body, with a complex geometry and flow dynamics. Locations of arterial curvature and bifurcation are known to be prone to endothelial dysfunction, one of the early biological markers for atherosclerotic lesions that underlie most cardiovascular diseases [1]-[2]. However, the influence of local anatomical and haemodynamic factors, such as wall shear stress (WSS), on lesion development is not well established [3]. This is particularly relevant to conditions of obesity, which is believed to accelerate the initiation and progression of vascular changes, and may be associated with vascular remodelling, inducing increased vessel diameters and wall thickness [4]. In this study, we hypothesize normal and obesity-altered arterial conditions to investigate the effect of a range of anatomical and flow parameters on the haemodynamic environment. To that end, we utilised 3D computational fluid dynamic (CFD) modelling methods; such methods have become an essential tool in the study of cardiovascular diseases and can be indirectly incorporated into clinical practice by improving our understanding of the underlying mechanisms of such diseases. Methods Simplified three-dimensional aortic arch geometries were created using the ANSA pre-processor (BETA CAE Systems), while numerical simulations were performed with the open source platform OpenFOAM®, using physiological parameters adopted from the literature [5]. Preliminary results consider both steady and timedependent (pulsatile) flow for the solution of the incompressible Newtonian Navier-Stokes equations. The boundary conditions studied include different inlet profiles with both steady and pulsatile flow. Computational fluid dynamic analysis focussed on the variance of flow parameters, specifically velocity, pressure, and wall shear stress, for the different boundary conditions. Results & Discussion The results demonstrate the importance of normal and obesity-altered arterial conditions for aortic arch models. The branch flow splits in both steady-state and unsteady calculations influence the shear stresses developed on the aortic wall. Time-dependent metrics such as the time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI), indicate locations of disturbed flow. Conclusion In this work, simulations were conducted on simplified aortic arch configurations for various boundary conditions that could quantify the impact of such parameters and find associations with early signs of vascular changes in obese patients. The future direction of this work is to improve the accuracy of the simulations by implementing more complex boundary conditions, namely the windkessel model to account for the resistance and capacitance of peripheral arteries. The investigation will then be extended to patient-specific aortic models to confirm the results of this work. Acknowledgments This work is supported in part from the University of Strathclyde Research Studentship Scheme (SRSS) Student Excellence Awards (SEA) Project No 1619, and the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 749185. References 1. Caro C., Fitz-Gerald J., Schroter R. Proceedings of the Royal Society of London Series B 1971; 177(46):109-159. 2. M. E. DeBakey, G. M. Lawrie, and D. H. Glaeser. Annals of Surgery 1985; 201(2): 115–131. 3. Kazakidi A, Sherwin SJ, Weinberg PD. J R Soc Interface 2009; 6(35):539-548 4. Wildman RP. et al. Diabetes Care 2004; 27(12):2997-2999. 5. Vasava P. et al., Comput Math Methods Med. 2012; 861837

Investigating the role of haematocrit in foetal circulation : a multi-compartment lumped parameter model

Foetal circulation is a complex system that differs from the corresponding neonatal and adult system. Current understanding of the foetal haemodynamics is limited1, while the role of haematocrit at different gestational ages has not yet been investigated extensively. Computational models can aid elucidate circulation haemodynamics2. To this end, this contribution proposes a multi-compartment lumped parameter model of the foetal circulatory system to investigate the effect of haematocrit variations on the systemic arterial flow

Fluid-structure interaction simulation of flow-mediated dilation of a straight arterial conduit

Introduction Flow-mediated dilation (FMD) is a key non-invasive clinical assessment of endothelial dysfunction, an indicator of early atherosclerosis and cardiovascular diseases. FMD involves the measurement of an artery dilation, e.g. of the brachial, radial, femoral, or popliteal artery, induced by transient hyperaemia, following a temporary ischemic occlusion of a distal arterial segment. Such transient conditions, however, may also involve changes in the wall shear stress (WSS), blood pressure, and wall stiffness which have not been clearly established in relation to early vascular changes. This work aims to clarify the role of these flow-related mechanisms by investigating the haemodynamic environment of a straight arterial conduit with compliant walls during FMD. Methods By implementing a strongly-coupled fluid-structure interaction (FSI) solver within the open-source OpenFOAMextend library [1], the arterial vessel was modelled as a quarter cylinder with an in-vivo measured hyperaemic inflow condition (by [2]). The FSI solver follows a partitioned approach with separated solvers for fluid and structure, and an implicit coupling method between fluid and solid, with interface values being passed from one solver to the other. The solution of the fluid flow is based on the finite volume method (FVM), while the solid is solved by a Lagrangian FVM solver. The mesh motion for both the fluid and the solid, due to the interface displacement, is updated at every timestep using a dynamic mesh solver in OpenFOAM based on the Laplace equation discretisation. Prior examples of FSI simulations in OpenFOAM and the foam-extend project have demonstrated its use for cardiovascular flows [3]. Results & Discussion The results demonstrate the diameter change during FMD, while haemodynamic shear stresses and pressure values are also analysed. Current results are being used for correlating the displacement of the arterial walls and the prescribed in-vivo inlet velocity. Conclusion The methodology has been established for subsequent simulations. Future work will investigate the FMD in idealised and anatomically-correct bifurcated arterial models with prescribed ischemic occlusion of the distal branching arteries. It will also include the investigation of further haemodynamic metrics, such as the timeaveraged wall shear stress, the oscillatory shear index, and the transverse WSS, in comparison with in-vivo data. Acknowledgments This work is supported in part from the University of Strathclyde International Strategic Partner (ISP) Research Studentships, and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 749185. References 1. Extend-Project (2018) The foam-extend. https://sourceforge.net/projects/foam-extend/ 2. van Bussel, FCG et al. A control systems approach to quantify wall shear stress normalization by flowmediated dilation in the brachial artery. PloS one (2015) 10:e0115977 3. Tukovic, Zeljko, Karaˇc, Aleksandar, Cardiff, Philip, Jasak, Hrvoje and Ivankovic, Alojz. (2018). OpenFOAM Finite Volume Solver for Fluid-Solid Interaction. Transactions of FA- MENA. 42. 1-31. 10.21278/TOF.42301

Octopus-inspired multi-arm robotic swimming

The outstanding locomotor and manipulation characteristics of the octopus have recently inspired the development, by our group, of multi-functional robotic swimmers, featuring both manipulation and locomotion capabilities, which could be of significant engineering interest in underwater applications. During its little-studied arm-swimming behavior, as opposed to the better known jetting via the siphon, the animal appears to generate considerable propulsive thrust and rapid acceleration, predominantly employing movements of its arms. In this work, we capture the fundamental characteristics of the corresponding complex pattern of arm motion by a sculling profile, involving a fast power stroke and a slow recovery stroke. We investigate the propulsive capabilities of a multi-arm robotic system under various swimming gaits, namely patterns of arm coordination, which achieve the generation of forward, as well as backward, propulsion and turning. A lumped-element model of the robotic swimmer, which considers arm compliance and the interaction with the aquatic environment, was used to study the characteristics of these gaits, the effect of various kinematic parameters on propulsion, and the generation of complex trajectories. This investigation focuses on relatively high-stiffness arms. Experiments employing a compliant-body robotic prototype swimmer with eight compliant arms, all made of polyurethane, inside a water tank, successfully demonstrated this novel mode of underwater propulsion. Speeds of up to 0.26 body lengths per second (approximately 100 mm s(-1)), and propulsive forces of up to 3.5 N were achieved, with a non-dimensional cost of transport of 1.42 with all eight arms and of 0.9 with only two active arms. The experiments confirmed the computational results and verified the multi-arm maneuverability and simultaneous object grasping capability of such systems

A multi-compartment lumped-parameter model for assessing the role of haematocrit in foetal circulation

Foetal circulation, being different from neonatal and adult circulation, is an intricate system. Current knowledge of its haemodynamics is limited 1, while the role of haematocrit at different gestational ages has not yet been examined extensively. This work aims to investigate the effect of haematocrit variations using a multi-compartment lumped parameter model (LPM) of the foetal circulation. The LPM model is developed in Simulink® and includes19 elastic arterial segments and 12 peripheral vascular beds, represented, respectively, by electrical circuits and a 3-element Windkessel model 2,3. Previous data1,2and allometric laws 4 were used to calculate the inflow and boundary conditions for a 33-week gestational age and foetus weight. Two validation studies were completed, one comparing results with adult flow waveforms and another examining the foetal Isthmic Flow Index. Different values of haematocrit (Hct), ranging from 10% to 80% Hct, were investigated, representing a range of anaemic, healthy, and polycythaemic conditions. Results from the validation studies were in good agreement with literature. The foetal LPM enabled calculations of blood flow waveforms at various arterial positions. Computations with 10%, 45%, and 80% Hct were further performed to demonstrate the effect of haematocrit on the foetal arterial flow. A clear difference between the 45% and 80%Hctmodels at the position of the ascending aorta was evident, whereas no apparent difference was detected between the models for 10% and 45% Hct. Similarly, this effect was manifested at the positions of the aortic isthmus, the thoracic aorta, and the umbilical artery. However, at the position of the ductus arteriosus there was no difference between the three models. Finally, the calculations revealed an almost exponential relationship between mean resistance and Hematocrit. Investigating haematocrit variations revealed an important effect on the foetal circulation, resulting insignificant changes in vascular resistances and the pulsatility indices of the flow rate waveforms. Further investigation is required aiming at the improvement of the accuracy of the inflow and boundary conditions

Computational analysis of intrastriatal delivery of collagen

INTRODUCTION: Parkinson’s disease (PD) is a degenerative disorder that affects dopaminergic neurons in substantia nigra. Recently, cell therapy has emerged as a promising therapeutic strategy, with biomaterials being used to facilitate the cell deposition through intrastriatal injection. However, the existing delivery approaches have shown limited success in clinical translation. This study aims to develop a device for the delivery of a cell-embedded in situ forming collagen hydrogel. Here, computational approaches on the delivery of collagen to the striatum are presented, to gain insight into different parameters affecting the delivery. METHODS: The delivery of collagen was modelled computationally in the two-dimensional space. The striatum was modelled as a circular space, with an area of 3.98 cm2 corresponding to the mean volume of putamen in PD patients. Within the finite volume method framework, the Volume of Fluid (VOF) method was used, assuming two isothermal and immiscible fluids. The collagen flow was considered incompressible, with non-Newtonian fluid behavior characterized experimentally, and constant inlet velocity corresponding to a maximum delivery volume. RESULTS & DISCUSSION: The interaction between the collagen and the brain tissue phases was analyzed, using two types of needle tips, a blunt needle tip and bevel needle tip (Fig. 1A, 1B). Alpha indicates the phase distribution, with a=1 indicating collagen, a=0, brain tissue and 0<a<1 indicating the interface. The effects of collagen injection on the pressure fields within the striatum were also examined (Fig. 1C, 1D). A difference in the pressure between the two needle tips was observed, with the bevel tip showing higher pressure on the site of the delivery. CONCLUSIONS: The intrastriatal injection of a hydrogel is a complex process and computational analysis of the delivery can help identify the obstacles facing clinical translation. Further analysis is required including 3D reconstruction from MRI images and modelling in the three-dimensional space

Numerical analysis of collagen injection to the striatum

Parkinson’s disease (PD) is a degenerative disorder that affects dopaminergic neurons in the substantia nigra. In PD, the dopaminergic neurons degenerate, resulting in less dopamine being available for neurotransmission. Cell therapy, along with the use of biomaterials, has emerged as a promising therapeutic strategy. However, the existing delivery approaches have shown limited success in clinical translation1. This study aims to develop a device for the delivery of a cell-embedded in situ forming collagen hydrogel. Here, computational approaches on the delivery of collagen to the striatum are presented, to gain insight into different parameters affecting the delivery

Numerical simulation of a synthetic jet with OpenFoam

Numerical simulations of flow surrounding a synthetic jet actuating device are presented. By modifying a dynamic mesh technique available in OpenFoam-a well-documented open-source solver for fluid dynamics, detailed computations of the sinusoidal motion of the synthetic jet diaphragm were possible. Numerical solutions were obtained by solving the two dimensional incompressible viscous N-S equations, with the use of a second order implicit time marching scheme and a central finite volume method for spatial discretization in both streamwise and crossflow directions. A systematic parametric study is reported here, in which the external Reynolds number, the diaphragm amplitude and frequency, and the slot dimensions are varied

Hemodynamics in the pulmonary bifurcation : effect of geometry and boundary conditions

Introduction Pulmonary regurgitation [1] and obstruction in the left pulmonary artery [2], the most common complications affecting adult patients with repaired tetralogy of Fallot, are known to lead to right ventricular dilatation and dysfunction. Long-term pulmonary stenosis is also hypothesized to lead to abnormal lung development and elevated pulmonary vascular resistance [3]. Pulmonary valve replacement is deemed necessary in these patients, but the optimal timing to perform the surgery is still ambiguous [1]. The aim of this study is to numerically investigate the blood flow development in the pulmonary bifurcation of adult patients with congenital heart defects. In this work, we present results from a parametric analysis, where the effect of geometry (branch angle, origin, branch obstruction) and boundary conditions (unsteady flow, Reynolds number, pressure difference at the outlets, and non-Newtonian models) were examined. Methods Blood flow simulations were performed in simplified models of the pulmonary bifurcation, using a validated finite volume scheme in OpenFOAM®. Physiological and pathological conditions were assumed and local velocities, wall shear stress values, velocity and pressure distributions were evaluated. The fluid was considered incompressible and governed by the Newtonian Navier-Stokes equations. The Power Law, CrossPower Law, the Casson, and the Bird-Carreau non-Newtonian models were also investigated. Results & Discussion Blood flow in the pulmonary bifurcation is highly dependent on the local geometrical characteristics and the boundary conditions assumed. Flow separation increases with the branching angle, the branch origin, and stenosis. Branch obstruction and boundary conditions have, further, a significant effect on velocities and shear stresses developed on the vessel wall. The presence of peripheral stenosis and pressure difference at the branch outlets affects significantly the flow splits in the daughter branches. Finally, pressure ratios are considered to provide a good indication of flow discrepancies between the different cases tested. Evaluation of the results on more complex 3D anatomically-correct geometries is necessary. Future work will involve reconstruction of patient-specific models using CT and MRI data from adult patients with congenital heart diseases. More realistic boundary conditions will also be considered, including the pulsatile nature of blood flow and Windkessel models at the branch outlets to account for peripheral resistance. Conclusion Computational fluid dynamics tools have been utilised in this study to investigate the effect of a range of different geometrical characteristics and boundary conditions. The main findings of this study concern a new effect of the branch origin, and a notable branch flow split analysis under conditions of peripheral stenosis and pressure difference in the branch outlets. Acknowledgments This work is supported in part by the University of Strathclyde Research Studentship Scheme (SRSS) Research Excellence Awards (REA), Project No 1208 and the European Union’s Horizon 2020 research and innovation programme, under the Marie Skłodowska-Curie grant agreement No 749185. References 1. Kogon B.E. et al. Seminars in Thoracic and Cardiovascular Surgery 2015; 27:57-64. 2. McElhinney D.B. et al. The Annals of Thoracic Surgery 1998; 65:1120-1126. 3. Harris M.A. et al. Cardiovascular Imaging 2011; 4:506-513

Characterization of Flow Dynamics in the Pulmonary Bifurcation of Patients With Repaired Tetralogy of Fallot: A Computational Approach

The hemodynamic environment of the pulmonary bifurcation is of great importance for adult patients with repaired tetralogy of Fallot (rTOF) due to possible complications in the pulmonary valve and narrowing of the left pulmonary artery (LPA). The aim of this study was to computationally investigate the effect of geometrical variability and flow split on blood flow characteristics in the pulmonary trunk of patient-specific models. Data from a cohort of seven patients was used retrospectively and the pulmonary hemodynamics was investigated using averaged and MRI-derived patient-specific boundary conditions on the individualized models, as well as a statistical mean geometry. Geometrical analysis showed that curvature and tortuosity are higher in the LPA branch, compared to the right pulmonary artery (RPA), resulting in complex flow patterns in the LPA. The computational analysis also demonstrated high time-averaged wall shear stress (TAWSS) at the outer wall of the LPA and the wall of the RPA proximal to the junction. Similar TAWSS patterns were observed for averaged boundary conditions, except for a significantly modified flow split assigned at the outlets. Overall, this study enhances our understanding about the flow development in the pulmonary bifurcation of rTOF patients and associates some morphological characteristics with hemodynamic parameters, highlighting the importance of patient-specificity in the models. To confirm these findings, further studies are required with a bigger cohort of patients