Efficient sensitivity analysis for biomechanical models with correlated inputs.

In most variance-based sensitivity analysis (SA) approaches applied to biomechanical models, statistical independence of the model input is assumed. However, often the model inputs are correlated. This might alter the interpretation of the SA results, which may severely impact the guidance provided during model development and personalization. Potential reasons for the infrequent usage of SA techniques that account for input correlation are the associated high computational costs, especially for models with many parameters, and the fact that the input correlation structure is often unknown. The aim of this study was to propose an efficient correlated global sensitivity analysis method by applying a surrogate model-based approach. Furthermore, this article demonstrates how correlated SA should be interpreted and how the applied method can guide the modeler during model development and personalization, even when the correlation structure is not entirely known beforehand. The proposed methodology was applied to a typical example of a pulse wave propagation model and resulted in accurate SA results that could be obtained at a theoretically 27,000× lower computational cost compared to the correlated SA approach without employing a surrogate model. Furthermore, our results demonstrate that input correlations can significantly affect SA results, which emphasizes the need to thoroughly investigate the effect of input correlations during model development. We conclude that our proposed surrogate-based SA approach allows modelers to efficiently perform correlated SA to complex biomechanical models and allows modelers to focus on input prioritization, input fixing and model reduction, or assessing the dependency structure between parameters.

A realistic arteriovenous dialysis graft model for hemodynamic simulations.

OBJECTIVE: The hemodynamic benefit of novel arteriovenous graft (AVG) designs is typically assessed using computational models that assume highly idealized graft configurations and/or simplified boundary conditions representing the peripheral vasculature. The objective of this study is to evaluate whether idealized AVG models are suitable for hemodynamic evaluation of new graft designs, or whether more realistic models are required. METHODS: An idealized and a realistic, clinical imaging based, parametrized AVG geometry were created. Furthermore, two physiological boundary condition models were developed to represent the peripheral vasculature. We assessed how graft geometry (idealized or realistic) and applied boundary condition models of the peripheral vasculature (physiological or distal zero-flow) impacted hemodynamic metrics related to AVG dysfunction. RESULTS: Anastomotic regions exposed to high WSS (>7, ≤40 Pa), very high WSS (>40 Pa) and highly oscillatory WSS were larger in the simulations using the realistic AVG geometry. The magnitude of velocity perturbations in the venous segment was up to 1.7 times larger in the realistic AVG geometry compared to the idealized one. When applying a (non-physiological zero-flow) boundary condition that neglected blood flow to and from the peripheral vasculature, we observed large regions exposed to highly oscillatory WSS. These regions could not be observed when using either of the newly developed distal boundary condition models. CONCLUSION: Hemodynamic metrics related to AVG dysfunction are highly dependent on the geometry and the distal boundary condition model used. Consequently, the hemodynamic benefit of a novel graft design can be misrepresented when using idealized AVG modelling setups.

Computationally guided in-vitro vascular growth model reveals causal link between flow oscillations and disorganized neotissue.

Disturbed shear stress is thought to be the driving factor of neointimal hyperplasia in blood vessels and grafts, for example in hemodialysis conduits. Despite the common occurrence of neointimal hyperplasia, however, the mechanistic role of shear stress is unclear. This is especially problematic in the context of in situ scaffold-guided vascular regeneration, a process strongly driven by the scaffold mechanical environment. To address this issue, we herein introduce an integrated numerical-experimental approach to reconstruct the graft-host response and interrogate the mechanoregulation in dialysis grafts. Starting from patient data, we numerically analyze the biomechanics at the vein-graft anastomosis of a hemodialysis conduit. Using this biomechanical data, we show in an in vitro vascular growth model that oscillatory shear stress, in the presence of cyclic strain, favors neotissue development by reducing the secretion of remodeling markers by vascular cells and promoting the formation of a dense and disorganized collagen network. These findings identify scaffold-based shielding of cells from oscillatory shear stress as a potential handle to inhibit neointimal hyperplasia in grafts.

Haemodynamic optimisation of a dialysis graft design using a global optimisation approach.

Disturbed flow and the resulting non-physiological wall shear stress (WSS) at the graft-vein anastomosis play an important role in arteriovenous graft (AVG) patency loss. Modifying graft geometry with helical features is a popular approach to minimise the occurrence of detrimental haemodynamics and to potentially increase graft longevity. Haemodynamic optimisation of AVGs typically requires many computationally expensive computational fluid dynamics (CFD) simulations to evaluate haemodynamic performance of different graft designs. In this study, we aimed to develop a haemodynamically optimised AVG by using an efficient meta-modelling approach. A training dataset containing CFD evaluations of 103 graft designs with helical features was used to develop computationally low-cost meta-models for haemodynamic metrics related to graft dysfunction. During optimisation, the meta-models replaced CFD simulations that were otherwise needed to evaluate the haemodynamic performance of possible graft designs. After optimisation, haemodynamic performance of the optimised graft design was verified using a CFD simulation. The obtained optimised graft design contained both a helical graft centreline and helical ridge. Using the optimised design, the magnitude of flow disturbances and the size of the anastomotic areas exposed to non-physiological WSS was successfully reduced compared to a regular straight graft. Our meta-modelling approach allowed to reduce the total number of CFD model evaluations required for our design optimisation by approximately a factor 2000. The applied efficient meta-modelling technique was successful in identifying an optimal, helical graft design at relatively low computational costs. Future studies should evaluate the in vivo benefits of the developed graft design.

Computational Modelling Based Recommendation on Optimal Dialysis Needle Positioning and Dialysis Flow in Patients With Arteriovenous Grafts.

OBJECTIVE: Arteriovenous grafts (AVGs) typically lose patency within two years of creation due to venous neointimal hyperplasia, which is initiated by disturbed haemodynamics after AVG surgery. Haemodialysis needle flow can further disturb haemodynamics and thus impact AVG longevity. In this computational study it was assessed how dialysis flow and venous needle positioning impacts flow at the graft-vein anastomosis. Furthermore, it was studied how negative effects of dialysis needle flow could be mitigated. METHODS: Non-physiological wall shear stress and disturbed blood flow were assessed in an AVG model with and without dialysis needle flow. Needle distance to the venous anastomosis was set to 6.5, 10.0, or 13.5 cm, whereas dialysis needle flow was set to 200, 300 or 400 mL/min. Intraluminal needle tip depth was varied between superficial, central, or deep. The detrimental effects of dialysis needle flow were summarised by a haemodynamic score (HS), ranging from 0 (minimal) to 5 (severe). RESULTS: Dialysis needle flow resulted in increased disturbed flow and/or non-physiological wall shear stress in the venous peri-anastomotic region. Increasing cannulation distance from 6.5 to 13.5 cm reduced the HS by a factor 4.0, whereas a central rather than a deep or superficial needle tip depth reduced the HS by a maximum factor of 1.9. Lowering dialysis flow from 400 to 200 mL/min reduced the HS by a factor 7.4. CONCLUSION: Haemodialysis needle flow, cannulation location, and needle tip depth considerably increase the amount of disturbed flow and non-physiological wall shear stress in the venous anastomotic region of AVGs. Negative effects of haemodialysis needle flow could be minimised by more upstream cannulation, by lower dialysis flow and by ensuring a central needle tip depth. Since disturbed haemodynamics are associated with neointimal hyperplasia development, optimising dialysis flow and needle positioning during haemodialysis could play an important role in maintaining AVG patency.

Computational study on the haemodynamic and mechanical performance of electrospun polyurethane dialysis grafts.

Compliance mismatch between an arteriovenous dialysis graft (AVG) and the connected vein is believed to result in disturbed haemodynamics around the graft-vein anastomosis and increased mechanical loading of the vein. Both phenomena are associated with neointimal hyperplasia development, which is the main reason for AVG patency loss. In this study, we use a patient-specific fluid structure interaction AVG model to assess whether AVG haemodynamics and mechanical loading can be optimised by using novel electrospun polyurethane (ePU) grafts, since their compliance can be better tuned to match that of the native veins, compared to gold standard, expanded polytetrafluoroethylene (ePTFE) grafts. It was observed that the magnitude of flow disturbances in the vein and the size of anastomotic areas exposed to highly oscillatory shear ([Formula: see text]) and very high wall shear stress ([Formula: see text]) were largest for the ePTFE graft. Median strain and von Mises stress in the vein were similar for both graft types, whereas highest stress and strain were observed in the anastomosis of the ePU graft. Since haemodynamics were most favourable for the ePU graft simulation, AVG longevity might be improved by the use of ePU grafts.

The Role of One-Dimensional Model-Generated Inter-Subject Variations in Systemic Properties on Wall Shear Stress Indices of Intracranial Aneurysms.

Variations in systemic properties of the arterial tree, such as aging-induced vessel stiffness, can alter the shape of pressure and flow waveforms. As a consequence, the hemodynamics around a cerebral aneurysm change, and therefore, also the corresponding in- and outlet boundary conditions (BCs) used for three-dimensional (3D) calculations of hemodynamic indices. In this study, we investigate the effects of variations in systemic properties on wall shear stress (WSS) indices of a cerebral aneurysm. We created a virtual patient database by varying systemic properties within physiological ranges. BCs for 3D-CFD simulations were derived using a pulse wave propagation model for each realization of the virtual database. WSS indices were derived from the 3D simulations and their variabilities quantified. Variations in BCs, caused by changes in systemic properties, yielded variabilities in the WSS indices that were of the same order of magnitude as differences in these WSS indices between ruptured and unruptured aneurysms. Sensitivity analysis showed that the systemic properties impacted both in- and outlet BCs simultaneously and altered the WSS indices. We conclude that the influence of variations in patient-specific systemic properties on WSS indices should be evaluated when using WSS indices in multidisciplinary rupture prediction models.

Uncertainty quantification and sensitivity analysis of an arterial wall mechanics model for evaluation of vascular drug therapies.

Quantification of the uncertainty in constitutive model predictions describing arterial wall mechanics is vital towards non-invasive assessment of vascular drug therapies. Therefore, we perform uncertainty quantification to determine uncertainty in mechanical characteristics describing the vessel wall response upon loading. Furthermore, a global variance-based sensitivity analysis is performed to pinpoint measurements that are most rewarding to be measured more precisely. We used previously published carotid diameter-pressure and intima-media thickness (IMT) data (measured in triplicate), and Holzapfel-Gasser-Ogden models. A virtual data set containing 5000 diastolic and systolic diameter-pressure points, and IMT values was generated by adding measurement error to the average of the measured data. The model was fitted to single-exponential curves calculated from the data, obtaining distributions of constitutive parameters and constituent load bearing parameters. Additionally, we (1) simulated vascular drug treatment to assess the relevance of model uncertainty and (2) evaluated how increasing the number of measurement repetitions influences model uncertainty. We found substantial uncertainty in constitutive parameters. Simulating vascular drug treatment predicted a 6% point reduction in collagen load bearing ([Formula: see text]), approximately 50% of its uncertainty. Sensitivity analysis indicated that the uncertainty in [Formula: see text] was primarily caused by noise in distension and IMT measurements. Spread in [Formula: see text] could be decreased by 50% when increasing the number of measurement repetitions from 3 to 10. Model uncertainty, notably that in [Formula: see text], could conceal effects of vascular drug therapy. However, this uncertainty could be reduced by increasing the number of measurement repetitions of distension and wall thickness measurements used for model parameterisation.

Application of an Adaptive Polynomial Chaos Expansion on Computationally Expensive Three-Dimensional Cardiovascular Models for Uncertainty Quantification and Sensitivity Analysis.

When applying models to patient-specific situations, the impact of model input uncertainty on the model output uncertainty has to be assessed. Proper uncertainty quantification (UQ) and sensitivity analysis (SA) techniques are indispensable for this purpose. An efficient approach for UQ and SA is the generalized polynomial chaos expansion (gPCE) method, where model response is expanded into a finite series of polynomials that depend on the model input (i.e., a meta-model). However, because of the intrinsic high computational cost of three-dimensional (3D) cardiovascular models, performing the number of model evaluations required for the gPCE is often computationally prohibitively expensive. Recently, Blatman and Sudret (2010, "An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis," Probab. Eng. Mech., 25(2), pp. 183-197) introduced the adaptive sparse gPCE (agPCE) in the field of structural engineering. This approach reduces the computational cost with respect to the gPCE, by only including polynomials that significantly increase the meta-model's quality. In this study, we demonstrate the agPCE by applying it to a 3D abdominal aortic aneurysm (AAA) wall mechanics model and a 3D model of flow through an arteriovenous fistula (AVF). The agPCE method was indeed able to perform UQ and SA at a significantly lower computational cost than the gPCE, while still retaining accurate results. Cost reductions ranged between 70-80% and 50-90% for the AAA and AVF model, respectively.