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  • Journal article
    Pirola S, Cheng Z, Jarral OA, O'Regan DP, Pepper JR, Athanasiou T, Xu XYet al., 2017,

    On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics

    , Journal of Biomechanics, Vol: 60, Pages: 15-21, ISSN: 1873-2380

    Boundary conditions (BCs) are an essential part in computational fluid dynamics (CFD) simulations of blood flow in large arteries. Although several studies have investigated the influence of BCs on predicted flow patterns and hemodynamic wall parameters in various arterial models, there is a lack of comprehensive assessment of outlet BCs for patient-specific analysis of aortic flow. In this study, five different sets of outlet BCs were tested and compared using a subject-specific model of a normal aorta. Phase-contrast magnetic resonance imaging (PC-MRI) was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition. Computational results obtained with different outlet BCs were assessed in terms of their agreement with the PC-MRI velocity data and key hemodynamic parameters, such as pressure and flow waveforms and wall shear stress related indices. Our results showed that the best overall performance was achieved by using a well-tuned three-element Windkessel model at all model outlets, which not only gave a good agreement with in vivo flow data, but also produced physiological pressure waveforms and values. On the other hand, opening outlet BCs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features.

  • Conference paper
    Zhan W, Gedroyc W, Xu X,

    Numerical Simulation of Thermosensitive Liposome-mediated Delivery of Doxorubicin to Solid Tumour under High Intensity Focused Ultrasound Heating

    , International Conference on Computational and Mathematical Biomedical Engineering
  • Journal article
    Zhan W, Gedroyc W, Xu XY, 2017,

    The effect of tumour size on drug transport and uptake in 3-D tumour models reconstructed from magnetic resonance images

    , PLOS ONE, Vol: 12, ISSN: 1932-6203

    Drug transport and its uptake by tumour cells are strongly dependent on tumour properties, which vary in different types of solid tumours. By simulating the key physical and biochemical processes, a numerical study has been carried out to investigate the transport of anti-cancer drugs in 3-D tumour models of different sizes. The therapeutic efficacy for each tumour is evaluated by using a pharmacodynamics model based on the predicted intracellular drug concentration. Simulation results demonstrate that interstitial fluid pressure and interstitial fluid loss vary non-linearly with tumour size. Transvascular drug exchange, driven by the concentration gradient of unbound drug between blood and interstitial fluid, is more efficient in small tumours, owing to the low spatial-mean interstitial fluid pressure and dense microvasculature. However, this has a detrimental effect on therapeutic efficacy over longer periods as a result of enhanced reverse diffusion of drug to the blood circulation after the cessation of drug infusion, causing more rapid loss of drug in small tumours.

  • Journal article
    Gu B, Adjiman CS, Xu XY, 2016,

    The effect of feed spacer geometry on membrane performance and concentration polarisation based on 3D CFD simulations

    , Journal of Membrane Science, Vol: 527, Pages: 78-91, ISSN: 1873-3123

    Feed spacers are used in spiral wound reverse osmosis (RO) membrane modules to keep the membrane sheets apart as well as to enhance mixing. They are beneficial to membrane performance but at the expense of additional pressure loss. In this study, four types of feed spacer configurations are investigated, with a total of 20 geometric variations based on commercially available spacers and selected filament angles. The impact of feed spacer design on membrane performance is investigated by means of three-dimensional (3D) computational fluid dynamics (CFD) simulations, where the solution-diffusion model is employed for water and solute transport through RO membranes. Numerical simulation results show that, for the operating and geometric conditions examined, fully woven spacers outperform other spacer configurations in mitigating concentration polarisation (CP). When designed with a mesh angle of 60°, fully woven spacers also deliver the highest water flux, although the associated pressure drops are slightly higher than their nonwoven counterparts. Middle layer geometries with a mesh angle of 30° produce the lowest water flux. On the other hand, spacers with a mesh angle of 90° show the lowest pressure drop among all the filament arrangements examined. Furthermore, the computational model presented here can also be used to predict membrane performance for a given feed spacer type and geometry.

  • Journal article
    Menichini C, Cheng Z, Gibbs R, Xu XYet al., 2016,

    Predicting false lumen thrombosis in patient-specific models of aortic dissection

    , Journal of the Royal Society Interface, Vol: 13, ISSN: 1742-5689

    Aortic dissection causes splitting of the aortic wall layers, allowing blood to enter a ‘false lumen’ (FL). For type B dissection, a significant predictor of patient outcomes is patency or thrombosis of the FL. Yet, no methods are currently available to assess the chances of FL thrombosis. In this study, we present a new computational model that is capable of predicting thrombus formation, growth and its effects on blood flow under physiological conditions. Predictions of thrombus formation and growth are based on fluid shear rate, residence time and platelet distribution, which are evaluated through convection–diffusion–reaction transport equations. The model is applied to a patient-specific type B dissection for which multiple follow-up scans are available. The predicted thrombus formation and growth patterns are in good qualitative agreement with clinical data, demonstrating the potential applicability of the model in predicting FL thrombosis for individual patients. Our results show that the extent and location of thrombosis are strongly influenced by aortic dissection geometry that may change over time. The high computational efficiency of our model makes it feasible for clinical applications. By predicting which aortic dissection patient is more likely to develop FL thrombosis, the model has great potential to be used as part of a clinical decision-making tool to assess the need for early endovascular intervention for individual dissection patients.

  • Journal article
    Gu B, Xu XY, Adjiman CS, 2016,

    A predictive model for spiral wound reverse osmosis membrane modules: The effect of winding geometry and accurate geometric details

    , Computers and Chemical Engineering, Vol: 96, Pages: 248-265, ISSN: 1873-4375

    A new one-dimensional predictive model for spiral wound modules (SWMs) applied to reverse osmosis membrane systems is developed by incorporating a detailed description of the geometric features of SWMs and considering flow in two directions. The proposed model is found to capture existing experimental data well, with similar accuracy to the widely-used plate model in which the SWM is assumed to consist of multiple thin rectangular channels. However, physical parameters that should in principle be model-independent, such as membrane permeability, are found to differ significantly depending on which model is used, when the same data sets are used for parameter estimation. Conversely, when using the same physical parameter values in both models, the water recovery predicted by the plate-like model is 12–20% higher than that predicted by the spiral model. This discrepancy is due to differences in the description of geometric features, in particular the active membrane area and the variable channel heights through the module, which impact on predicted performance and energy consumption. A number of design variables – the number of membrane leaves, membrane dimensions, centre pipe radius and the height of feed and permeate channels – are varied and their effects on performance, energy consumption and calculated module size are analysed. The proposed spiral model provides valuable insights into the effects of complex geometry on the performance of the SWM as well as of the overall system, at a low computational cost.

  • Journal article
    Su J, Huang C, Gu Z, Chen C, Xu Xet al., 2016,

    An Efficient RIGID Algorithm and Its Application to the Simulation of Particle Transport in Porous Medium

    , Transport in Porous Media, Pages: 1-33, ISSN: 1573-1634

    RIGID algorithm was recently proposed to identify the contact state between spherical particles and arbitrary-shaped walls, demonstrating significantly improved robustness, accuracy and efficiency compared to existing methods. It is an important module when coupling computational fluid dynamics with discrete element model to simulate particle transport in porous media. The procedure to identify particle and surface contact state is usually time-consuming and takes a large part of the CPU time for discrete element simulations of dense particle flow in complex geometries, especially in cases with a large number of particle–wall collisions (e.g. particle transport in porous media). This paper presents a new version of RIGID algorithm, namely ERIGID, which further improves the efficiency of the original algorithm through a number of new strategies including the recursive algorithm for particle-face pair selection, angle-testing algorithm for determining particle-face relations and the smallest index filter for fast rejection and storage of time invariant. Several specially designed numerical experiments have been carried out to test the performance of ERIGID and verify the effectiveness of these strategies. Finally, the improved algorithm is used to simulate particle transport in a rock treated as a porous medium. Our numerical results reveal several important flow phenomena and the primary reason for particle trapping inside the rock.

  • Journal article
    Kandail HS, Hamady M, Xu XY, 2016,

    Hemodynamic Functions of Fenestrated Stent Graft under Resting, Hypertension, and Exercise Conditions.

    , Frontiers in Surgery, Vol: 3, ISSN: 2296-875X

    The aim of this study was to assess the hemodynamic performance of a patient-specific fenestrated stent graft (FSG) under different physiological conditions, including normal resting, hypertension, and hypertension with moderate lower limb exercise. A patient-specific FSG model was constructed from computed tomography images and was discretized into a fine unstructured mesh comprising tetrahedral and prism elements. Blood flow was simulated using Navier-Stokes equations, and physiologically realistic boundary conditions were utilized to yield clinically relevant results. For a given cycle-averaged inflow of 2.08 L/min at normal resting and hypertension conditions, approximately 25% of flow was channeled into each renal artery. When hypertension was combined with exercise, the cycle-averaged inflow increased to 6.39 L/min but only 6.29% of this was channeled into each renal artery, which led to a 438.46% increase in the iliac flow. For all the simulated scenarios and throughout the cardiac cycle, the instantaneous flow streamlines in the FSG were well organized without any notable flow recirculation. This well-organized flow led to low values of endothelial cell activation potential, which is a hemodynamic metric used to identify regions at risk of thrombosis. The displacement forces acting on the FSG varied with the physiological conditions, and the cycle-averaged displacement force at normal rest, hypertension, and hypertension with exercise was 6.46, 8.77, and 8.99 N, respectively. The numerical results from this study suggest that the analyzed FSG can maintain sufficient blood perfusion to the end organs at all the simulated conditions. Even though the FSG was found to have a low risk of thrombosis at rest and hypertension, this risk can be reduced even further with moderate lower limb exercise.

  • Journal article
    Carallo C, Tripolino C, De Franceschi MS, Irace C, Xu XY, Gnasso Aet al., 2016,

    Carotid endothelial shear stress reduction with aging is associated with plaque development in twelve years

    , Atherosclerosis, Vol: 251, Pages: 63-69, ISSN: 1879-1484

    BACKGROUND AND AIMS: Atherosclerosis is associated with clinical, biochemical and haemodynamic risk factors. In a group of subjects studied twelve years apart, we evaluated carotid plaque development in relation to baseline and to changes at follow-up in common carotid haemodynamic profile. METHODS: Forty-eight participants were recruited to a cardiovascular disease prevention programme. Atherosclerotic plaques were evaluated and scored by echography. Endothelial shear stress, circumferential wall tension, and Peterson's elastic modulus as an index of arterial stiffness, were computed by echo-Doppler, along with blood viscosity data. Binary logistic regression analyses were used to test the association among the development of atherosclerosis, cardiovascular risk factors and haemodynamic variations. Analyses were also performed on participants who presented at the follow-up with carotid haemodynamic variations in the left or right common carotid only. RESULTS: Participants (69% male) were aged 64.5 ± 9.7 years at follow-up. Peak and mean endothelial shear stress was significantly lower at follow-up as previously reported; circumferential wall tension and arterial stiffness were significantly higher. Carotid plaque scores increased after 12 years (0.39 ± 0.72 vs. 0.67 ± 0.86, p < 0.01). Of the 96 common carotids analysed, shear stress reduction with aging was an independent predictor of carotid atherosclerosis (B = -0.063; odds ratio = 0.94; p = 0.01). Out of 48 participants, 21 (44%) showed shear stress reduction with aging in only one side of the body and, on this side, the plaque score increased (0.52 ± 0.98 vs. 0.90 ± 0.94, p < 0.05), remaining unchanged in the contralateral carotid tree. CONCLUSIONS: Aging-related shear stress reduction is an independent predictor of atherosclerosis development.

  • Journal article
    Xu XY, Kandail H, Hamady M, 2016,

    Effect of a Flared Renal Stent on the Performance of Fenestrated Stent-Grafts at Rest and Exercise Conditions

    , Journal of Endovascular Therapy, Vol: 23, Pages: 809-820, ISSN: 1526-6028

    Purpose: To quantify the hemodynamic impact of a flared renal stent on the performance of fenestrated stent-grafts (FSGs) by analyzing flow patterns and wall shear stress–derived parameters in flared and nonflared FSGs in different physiologic scenarios. Methods: Hypothetical models of FSGs were created with and without flaring of the proximal portion of the renal stent. Flared FSGs with different dilation angles and protrusion lengths were examined, as well as a nonplanar flared FSG to account for lumbar curvature. Laminar and pulsatile blood flow was simulated by numerically solving Navier-Stokes equations. A physiologically realistic flow rate waveform was prescribed at the inlet, while downstream vasculature was modeled using a lumped parameter 3-element windkessel model. No slip boundary conditions were imposed at the FSG walls, which were assumed to be rigid. While resting simulations were performed on all the FSGs, exercise simulations were also performed on a flared FSG to quantify the effect of flaring in different physiologic scenarios. Results: For cycle-averaged inflow of 2.94 L/min (rest) and 4.63 L/min (exercise), 27% of blood flow was channeled into each renal branch at rest and 21% under exercise for all the flared FSGs examined. Although the renal flow waveform was not affected by flaring, flow within the flared FSGs was disturbed. This flow disturbance led to high endothelial cell activation potential (ECAP) values at the renal ostia for all the flared geometries. Reducing the dilation angle or protrusion length and exercise lowered the ECAP values for flared FSGs. Conclusion: Flaring of renal stents has a negligible effect on the time dependence of renal flow rate waveforms and can maintain sufficient renal perfusion at rest and exercise. Local flow patterns are, however, strongly dependent on renal flaring, which creates a local flow disturbance and may increase the thrombogenicity at the renal ostia. Smaller dilation angles, shorter protr

  • Journal article
    Singh SD, Xu XY, Pepper JR, Izgi C, Treasure T, Mohiaddin RHet al., 2016,

    Effects of aortic root motion on wall stress in the Marfan aorta before and after personalised aortic root support (PEARS) surgery

    , Journal of Biomechanics, Vol: 49, Pages: 2076-2084, ISSN: 1873-2380

    Aortic root motion was previously identified as a risk factor for aortic dissection due to increased longitudinal stresses in the ascending aorta. The aim of this study was to investigate the effects of aortic root motion on wall stress and strain in the ascending aorta and evaluate changes before and after implantation of personalised external aortic root support (PEARS). Finite element (FE) models of the aortic root and thoracic aorta were developed using patient-specific geometries reconstructed from pre- and post-PEARS cardiovascular magnetic resonance (CMR) images in three Marfan patients. The wall and PEARS materials were assumed to be isotropic, incompressible and linearly elastic. A static load on the inner wall corresponding to the patients' pulse pressure was applied. Cardiovascular MR cine images were used to quantify aortic root motion, which was imposed at the aortic root boundary of the FE model, with zero-displacement constraints at the distal ends of the aortic branches and descending aorta. Measurements of the systolic downward motion of the aortic root revealed a significant reduction in the axial displacement in all three patients post-PEARS compared with its pre-PEARS counterparts. Higher longitudinal stresses were observed in the ascending aorta when compared with models without the root motion. Implantation of PEARS reduced the longitudinal stresses in the ascending aorta by up to 52%. In contrast, the circumferential stresses at the interface between the supported and unsupported aorta were increase by up to 82%. However, all peak stresses were less than half the known yield stress for the dilated thoracic aorta.

  • Journal article
    Xu XY, Menichini C, 2016,

    Mathematical modeling of thrombus formation in idealized models of aortic dissection: Initial findings and potential applications

    , Journal of Mathematical Biology, Vol: 73, Pages: 1205-1226, ISSN: 1432-1416

    Aortic dissection is a major aortic catastrophe with a high morbidity and mortality risk caused by the formation of a tear in the aortic wall. The development of a second blood filled region defined as the “false lumen” causes highly disturbed flow patterns and creates local hemodynamic conditions likely to promote the formation of thrombus in the false lumen. Previous research has shown that patient prognosis is influenced by the level of thrombosis in the false lumen, with false lumen patency and partial thrombosis being associated with late complications and complete thrombosis of the false lumen having beneficial effects on patient outcomes. In this paper, a new hemodynamics-based model is proposed to predict the formation of thrombus in Type B dissection. Shear rates, fluid residence time, and platelet distribution are employed to evaluate the likelihood for thrombosis and to simulate the growth of thrombus and its effects on blood flow over time. The model is applied to different idealized aortic dissections to investigate the effect of geometric features on thrombus formation. Our results are in qualitative agreement with in-vivo observations, and show the potential applicability of such a modeling approach to predict the progression of aortic dissection in anatomically realistic geometries.

  • Journal article
    Xu XY, Piebalgs A, 2015,

    Towards a Multi-Physics Modelling Framework for Thrombolysis under the Influence of Blood Flow

    , Journal of the Royal Society Interface, ISSN: 1742-5689

    Thrombolytic therapy is an effective means of treating thromboembolic diseases but can also give rise to life-threatening side-effects. The infusion of a high drug concentration can provoke internal bleeding while an insufficient dose can lead to artery reocclusion. It is hoped that mathematical modelling of the process of clot lysis can lead to a better understanding and improvement of thrombolytic therapy. To this end, a multi-physics continuum model has been developed to simulate the dissolution of clot over time upon the addition of tissue plasminogen activator (tPA). The transport of tPA and other lytic proteins is modelled by a set of reaction-diffusion-convection equations, while blood flow is described by volume-averaged continuity and momentum equations. The clot is modelled as a fibrous porous medium with its properties being determined as a function of the fibrin fibre radius and voidage of the clot. A unique feature of the model is that it is capable of simulating the entire lytic process from the initial phase of lysis of an occlusive thrombus (diffusion-limited transport), the process of recanalization, to post-canalization thrombolysis under the influence of convective blood flow. The model has been used to examine the dissolution of a fully occluding clot in a simplified artery at different pressure drops. Our predicted lytic front velocities during the initial stage of lysis agree well with experimental and computational results reported by others. Following canalisation, clot lysis patterns are strongly influenced by local flow patterns which are symmetric at low pressure drops, but asymmetric at higher pressure drops which give rise to larger recirculation regions and extended areas of intense drug accumulation.

  • Journal article
    Singh SD, Xu XY, Wood NB, Pepper JR, Izgi C, Treasure T, Mohiaddin RHet al., 2015,

    Aortic flow patterns before and after personalised external aortic root support implantation in Marfan patients.

    , Journal of Biomechanics, Vol: 49, Pages: 100-111, ISSN: 1873-2380

    Implantation of a personalised external aortic root support (PEARS) in the Marfan aorta is a new procedure that has emerged recently, but its haemodynamic implication has not been investigated. The objective of this study was to compare the flow characteristics and hemodynamic indices in the aorta before and after insertion of PEARS, using combined cardiovascular magnetic resonance imaging (CMR) and computational fluid dynamics (CFD). Pre- and post-PEARS MR images were acquired from 3 patients and used to build patient-specific models and upstream flow conditions, which were incorporated into the CFD simulations. The results revealed that while the qualitative patterns of the haemodynamics were similar before and after PEARS implantation, the post-PEARS aortas had slightly less disturbed flow at the sinuses, as a result of reduced diameters in the post-PEARS aortic roots. Quantitative differences were observed between the pre- and post-PEARS aortas, in that the mean values of helicity flow index (HFI) varied by -10%, 35% and 20% in post-PEARS aortas of Patients 1, 2 and 3, respectively, but all values were within the range reported for normal aortas. Comparisons with MR measured velocities in the descending aorta of Patient 2 demonstrated that the computational models were able to reproduce the important flow features observed in vivo.

  • Journal article
    Malkawi A, Pirianov G, Torsney E, Chetter I, Sakalihasan N, Loftus IM, Nordon I, Huggins C, Charolidi N, Thompson M, Xu XY, Cockerill GWet al., 2015,

    Increased Expression of Lamin A/C Correlate with Regions of High Wall Stress in Abdominal Aortic Aneurysms.

    , Aorta (Stamford), Vol: 3, Pages: 152-166, ISSN: 2325-4637

    BACKGROUND: Since aortic diameter is the most -significant risk factor for rupture, we sought to identify stress-dependent changes in gene expression to illuminate novel molecular processes in aneurysm rupture. MATERIALS AND METHODS: We constructed finite element maps of abdominal computerized tomography scans (CTs) of seven abdominal aortic aneurysm (AAA) patients to map wall stress. Paired biopsies from high- and low-stress areas were collected at surgery using vascular landmarks as coordinates. Differential gene expression was evaluated by Illumina Array analysis, using the whole genome DNA-mediated, annealing, selection, extension, and ligation (DASL) gene chip (n = 3 paired samples). RESULTS: The sole significant candidate from this analysis, Lamin A/C, was validated at the protein level, using western blotting. Lamin A/C expression in the inferior mesenteric vein (IMV) of AAA patients was compared to a control group and in aortic smooth muscle cells in culture in response to physiological pulsatile stretch. -Areas of high wall stress (n = 7) correlate to those -regions which have the thinnest walls [778 µm (585-1120 µm)] in comparison to areas of lowest wall stress [1620 µm (962-2919 µm)]. Induced expression of Lamin A/C -correlated with areas of high wall stress from AAAs but was not significantly induced in the IMV from AAA patients compared to controls (n = 16). Stress-induced expression of Lamin A/C was mimicked by exposing aortic smooth muscle cells to prolonged pulsatile stretch. CONCLUSION: Lamin A/C protein is specifically increased in areas of high wall stress in AAA from patients, but is not increased on other vascular beds of aneurysm patients, suggesting that its elevation may be a compensatory response to the pathobiology leading to aneurysms.

  • Journal article
    Su J, Gu Z, Chen C, Xu XYet al., 2015,

    A two-layer mesh method for discrete element simulation of gas-particle systems with arbitrarily polyhedral mesh

    , INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Vol: 103, Pages: 759-780, ISSN: 0029-5981
  • Conference paper
    Zhan W, Gedroyc W, Xu X,

    Drug Delivery to Solid Tumour with High Intensity Focused Ultrasound Heating

    , The 21st CLSS-UK Annual Conference
  • Journal article
    Li Z-Y, Tan FPP, Soloperto G, Wood NB, Xu XY, Gillard JHet al., 2015,

    Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

    , COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING, Vol: 18, Pages: 1099-1107, ISSN: 1025-5842
  • Journal article
    Liu C, Krishnan J, Xu X-Y, 2015,

    Intrinsic and induced drug resistance mechanisms at the cellular and tissue scales

    , Integrative Biology, ISSN: 1757-9694
  • Journal article
    Singh SD, Xu XY, Pepper JR, Treasure T, Mohiaddin RHet al., 2015,

    Biomechanical properties of the Marfan's aortic root and ascending aorta before and after personalised external aortic root support surgery.

    , Medical Engineering & Physics, Vol: 37, Pages: 759-766, ISSN: 1873-4030

    Marfan syndrome is an inherited systemic connective tissue disease which may lead to aortic root disease causing dilatation, dissection and rupture of the aorta. The standard treatment is a major operation involving either an artificial valve and aorta or a complex valve repair. More recently, a personalised external aortic root support (PEARS) has been used to strengthen the aorta at an earlier stage of the disease avoiding risk of both rupture and major surgery. The aim of this study was to compare the stress and strain fields of the Marfan aortic root and ascending aorta before and after insertion of PEARS in order to understand its biomechanical implications. Finite element (FE) models were developed using patient-specific aortic geometries reconstructed from pre and post-PEARS magnetic resonance images in three Marfan patients. For the post-PEARS model, two scenarios were investigated-a bilayer model where PEARS and the aortic wall were treated as separate layers, and a single-layer model where PEARS was incorporated into the aortic wall. The wall and PEARS materials were assumed to be isotropic, incompressible and linearly elastic. A static load on the inner wall corresponding to the patients' pulse pressure was applied. Results from our FE models with patient-specific geometries show that peak aortic stresses and displacements before PEARS were located at the sinuses of Valsalva but following PEARS surgery, these peak values were shifted to the aortic arch, particularly at the interface between the supported and unsupported aorta. Further studies are required to assess the statistical significance of these findings and how PEARS compares with the standard treatment.

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