Improved reduced-order modelling of cerebrovascular flow distribution by accounting for arterial bifurcation pressure drops

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

Deep learning-based semantic vessel graph extraction for intracranial aneurysm rupture risk management

PURPOSE

Intracranial aneurysms are vascular deformations in the brain which are complicated to treat. In clinical routines, the risk assessment of intracranial aneurysm rupture is simplified and might be unreliable, especially for patients with multiple aneurysms. Clinical research proposed more advanced analysis of intracranial aneurysm, but requires many complex preprocessing steps. Advanced tools for automatic aneurysm analysis are needed to transfer current research into clinical routine.

METHODS

We propose a pipeline for intracranial aneurysm analysis using deep learning-based mesh segmentation, automatic centerline and outlet detection and automatic generation of a semantic vessel graph. We use the semantic vessel graph for morphological analysis and an automatic rupture state classification.

RESULTS

The deep learning-based mesh segmentation can be successfully applied to aneurysm surface meshes. With the subsequent semantic graph extraction, additional morphological parameters can be extracted that take the whole vascular domain into account. The vessels near ruptured aneurysms had a slightly higher average torsion and curvature compared to vessels near unruptured aneurysms. The 3D surface models can be further employed for rupture state classification which achieves an accuracy of 83.3%.

CONCLUSION

The presented pipeline addresses several aspects of current research and can be used for aneurysm analysis with minimal user effort. The semantic graph representation with automatic separation of the aneurysm from the parent vessel is advantageous for morphological and hemodynamical parameter extraction and has great potential for deep learning-based rupture state classification.

Accelerated sequences of 4D flow MRI using GRAPPA and compressed sensing: A comparison against conventional MRI and computational fluid dynamics

PURPOSE

To evaluate hemodynamic markers obtained by accelerated GRAPPA (R = 2, 3, 4) and compressed sensing (R = 7.6) 4D flow MRI sequences under complex flow conditions.

METHODS

The accelerated 4D flow MRI scans were performed on a pulsatile flow phantom, along with a nonaccelerated fully sampled k-space acquisition. Computational fluid dynamics simulations based on the experimentally measured flow fields were conducted for additional comparison. Voxel-wise comparisons (Bland-Altman analysis, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>L</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {L}_2 $$</mml:annotation></mml:semantics> </mml:math> -norm metric), as well as nonderived quantities (velocity profiles, flow rates, and peak velocities), were used to compare the velocity fields obtained from the different modalities.

RESULTS

4D flow acquisitions and computational fluid dynamics depicted similar hemodynamic patterns. Voxel-wise comparisons between the MRI scans highlighted larger discrepancies at the voxels located near the phantom's boundary walls. A trend for all MR scans to overestimate velocity profiles and peak velocities as compared to computational fluid dynamics was noticed in regions associated with high velocity or acceleration. However, good agreement for the flow rates was observed, and eddy-current correction appeared essential for consistency of the flow rates measurements with respect to the principle of mass conservation.

CONCLUSION

GRAPPA (R = 2, 3) and highly accelerated compressed sensing showed good agreement with the fully sampled acquisition. Yet, all 4D flow MRI scans were hampered by artifacts inherent to the phase-contrast acquisition procedure. Computational fluid dynamics simulations are an interesting tool to assess these differences but are sensitive to modeling parameters.

Automated generation of 0D and 1D reduced-order models of patient-specific blood flow

Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computing cluster. One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood bulk flow and pressure waveforms with only a fraction of the cost. They can also accelerate uncertainty quantification, optimization, and design parameterization studies. Despite several prior studies generating 1D and 0D models and comparing them to 3D solutions, these were typically limited to either 1D or 0D and a singular category of vascular anatomies. This work proposes a fully automated and openly available framework to generate and simulate 1D and 0D models from 3D patient-specific geometries, automatically detecting vessel junctions and stenosis segments. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the open-source software platform SimVascular. We demonstrate the reduced-order approximation quality against rigid-wall 3D solutions in a comprehensive comparison with N = 72 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1% to 10% for both 1D and 0D models, measured at the outlets of terminal vessel branches. In general, 0D model errors were only slightly higher than 1D model errors despite requiring only a third of the 1D runtime. Automatically generated ROMs can significantly speed up model development and shift the computational load from high-performance machines to personal computers.

Flow control in the middle cerebral artery during thrombectomy: the effect of anatomy, catheter size and tip location

BACKGROUND

Catheter size, location and circle of Willis anatomy impact the flow conditions during interventional stroke therapy. The aim of the study was to systematically investigate the influence of these factors on flow control in the middle cerebral artery by means of a computational model based on 100 patients with stroke who received endovascular treatment.

METHODS

The dimensions of the cervical and intracranial cerebral arteries of 100 patients who received endovascular mechanical thrombectomy for acute ischemic stroke were measured and a three-dimensional model of the circle of Willis was created based on these data. Flow control in the middle cerebral artery with variations in catheter size, catheter location and configurations of collateral vessels was determined using a computational model. A total of 48 scenarios were analyzed.

RESULTS

Flow reversal with a distal aspiration catheter alone was not possible in the internal carotid artery and only sometimes possible in the middle cerebral artery (14 of 48 cases). The Catalyst 7 catheter was more often successful in achieving flow reversal than Catalyst 5 or 6 catheters (p<0.001). In a full circle of Willis anatomy, flow reversal was almost never possible. The absence of one or more communicating arteries significantly influenced flow direction compared with the full anatomy with all communicating arteries present (p=0.028).

CONCLUSION

Choosing the biggest possible aspiration catheter and locating it in the middle cerebral artery significantly increases the chances of successful flow control. Flow through the collaterals may impair the flow, and circle of Willis anatomy should be considered during aspiration thrombectomy.

A nonlinear multi-scale model for blood circulation in a realistic vascular system

In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille's Law, with pressure correction by elasticity and pressure drop estimation at vessels' junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy's Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.

A Distributed Lumped Parameter Model of Blood Flow

We propose a distributed lumped parameter (DLP) modeling framework to efficiently compute blood flow and pressure in vascular domains. This is achieved by developing analytical expressions describing expected energy losses along vascular segments, including from viscous dissipation, unsteadiness, flow separation, vessel curvature and vessel bifurcations. We apply this methodology to solve for unsteady blood flow and pressure in a variety of complex 3D image-based vascular geometries, which are typically approached using computational fluid dynamics (CFD) simulations. The proposed DLP framework demonstrated consistent agreement with CFD simulations in terms of flow rate and pressure distribution, with mean errors less than 7% over a broad range of hemodynamic conditions and vascular geometries. The computational cost of the DLP framework is orders of magnitude lower than the computational cost of CFD, which opens new possibilities for hemodynamics modeling in timely decision support scenarios, and a multitude of applications of imaged-based modeling that require ensembles of numerical simulations.

How patient specific are patient-specific computational models of cerebral aneurysms? An overview of sources of error and variability

Computational modeling of cerebral aneurysms, derived from clinical 3D angiography, has become widespread over the past 15 years. While such "image-based" or "patient-specific" models have shown promise for the assessment of rupture risk, much debate remains about their reliability in light of necessary modeling assumptions and incomplete or uncertain model input parameters derived from the clinic. The aims of this review were to walk through the various steps of this so-called patient-specific modeling pipeline and to highlight evidence supporting those steps that we can or cannot rely on. The relative importance of the different sources of error and variability on hemodynamic predictions is summarized, with recommendations to standardize for those that can be avoided and to pay closer attention those to that cannot.

A review on the reliability of hemodynamic modeling in intracranial aneurysms: why computational fluid dynamics alone cannot solve the equation

Computational blood flow modeling in intracranial aneurysms (IAs) has enormous potential for the assessment of highly resolved hemodynamics and derived wall stresses. This results in an improved knowledge in important research fields, such as rupture risk assessment and treatment optimization. However, due to the requirement of assumptions and simplifications, its applicability in a clinical context remains limited.This review article focuses on the main aspects along the interdisciplinary modeling chain and highlights the circumstance that computational fluid dynamics (CFD) simulations are embedded in a multiprocess workflow. These aspects include imaging-related steps, the setup of realistic hemodynamic simulations, and the analysis of multidimensional computational results. To condense the broad knowledge, specific recommendations are provided at the end of each subsection.Overall, various individual substudies exist in the literature that have evaluated relevant technical aspects. In this regard, the importance of precise vessel segmentations for the simulation outcome is emphasized. Furthermore, the accuracy of the computational model strongly depends on the specific research question. Additionally, standardization in the context of flow analysis is required to enable an objective comparison of research findings and to avoid confusion within the medical community. Finally, uncertainty quantification and validation studies should always accompany numerical investigations.In conclusion, this review aims for an improved awareness among physicians regarding potential sources of error in hemodynamic modeling for IAs. Although CFD is a powerful methodology, it cannot provide reliable information, if pre- and postsimulation steps are inaccurately carried out. From this, future studies can be critically evaluated and real benefits can be differentiated from results that have been acquired based on technically inaccurate procedures.

Flow-splitting-based computation of outlet boundary conditions for improved cerebrovascular simulation in multiple intracranial aneurysms

PURPOSE

Image-based hemodynamic simulations have great potential for precise blood flow predictions in intracranial aneurysms. Due to model assumptions and simplifications with respect to boundary conditions, clinical acceptance remains limited.

METHODS

Within this study, we analyzed the influence of outflow-splitting approaches on multiple aneurysm studies and present a new outflow-splitting approach that takes the precise morphological vessel cross sections into account. We provide a detailed comparison of five outflow strategies considering eight intracranial aneurysms: zero-pressure configuration (1), a flow splitting inspired by Murray's law with a square (2) and a cubic (3) vessel diameter, a flow splitting incorporating vessel bifurcations based on circular vessel cross sections (4) and our novel flow splitting including vessel bifurcations and anatomical vessel cross sections (5). Other boundary conditions remain constant. For each simulation and each aneurysm, we conducted an evaluation based on common hemodynamic parameters, e.g., normalized wall shear stress and inflow concentration index.

RESULTS

The comparison of five outflow strategies for image-based simulations shows a large variability regarding the parameters of interest. Qualitatively, our strategy based on anatomical cross sections yields a more uniform flow rate distribution with increased aneurysm inflow rates. The commonly used zero-pressure approach shows the largest variations, especially for more distal aneurysms. A rank ordering of multiple aneurysms in one patient might still be possible, since the ordering appeared to be independent of the outflow strategy.

CONCLUSIONS

The results reveal that outlet boundary conditions have a crucial impact on image-based blood flow simulations, especially for multiple aneurysm studies. We could confirm the advantages of the more complex outflow-splitting model (4) including an incremental improvement (5) compared to strategies (1), (2) and (3) for this application scenario. Furthermore, we discourage from using zero-pressure configurations that lack a physiological basis.

A multiscale computational modeling for cerebral blood flow with aneurysms and/or stenoses

A 1-dimensional (1D)-3-dimensional (3D) multiscale model for the human vascular network was proposed by combining a low-fidelity 1D modeling of blood circulation to account for the global hemodynamics with a detailed 3D simulation of a zonal vascular segment. The coupling approach involves a direct exchange of flow and pressure information at interfaces between the 1D and 3D models and thus enables patient-specific morphological models to be inserted into flow network with minimum computational efforts. The proposed method was validated with good agreements against 3 simplified test cases where experimental data and/or full 3D numerical solution were available. The application of the method in aneurysm and stenosis studies indicated that the deformation of the geometry caused by the diseases may change local pressure loss and as a consequence lead to an alteration of flow rate to the vessel segment.

Numerical investigation of the blood flow through the middle cerebral artery

Introduction: The middle cerebral artery (MCA) is one of the three major paired arteries that supply the blood to the cerebrum. In the present study, the three-dimensional (3D) blood flow in the left MCA was numerically simulated by using the medical imaging. Methods: The arterial geometry was obtained by applying the CT angiography of the MCA of a 75-year-old man. The blood flow was assumed to be laminar and unsteady. Numerical simulations were done by commercial software package COMSOL Multiphysics 5.2. In this software, the Galerkin's finite element method was applied to solve the governing equations. Results: It was found that the results obtained for the Newtonian and non-Newtonian models of blood do not differ from each other significantly. Thus, the Newtonian model for blood flow in the MCA is acceptable. Also, the most susceptible region of the MCA for Atherosclerosis was detected. Conclusion: It can be concluded that the application of the Newtonian model for the blood flowing in the MCA is acceptable. Also, atherosclerosis has the potential to occur at the middle of a branch of the MCA which has the highest geometrical curvature.

Better Than Nothing: A Rational Approach for Minimizing the Impact of Outflow Strategy on Cerebrovascular Simulations

BACKGROUND AND PURPOSE

Computational fluid dynamics simulations of neurovascular diseases are impacted by various modeling assumptions and uncertainties, including outlet boundary conditions. Many studies of intracranial aneurysms, for example, assume zero pressure at all outlets, often the default ("do-nothing") strategy, with no physiological basis. Others divide outflow according to the outlet diameters cubed, nominally based on the more physiological Murray's law but still susceptible to subjective choices about the segmented model extent. Here we demonstrate the limitations and impact of these outflow strategies, against a novel "splitting" method introduced here.

MATERIALS AND METHODS

With our method, the segmented lumen is split into its constituent bifurcations, where flow divisions are estimated locally using a power law. Together these provide the global outflow rate boundary conditions. The impact of outflow strategy on flow rates was tested for 70 cases of MCA aneurysm with 0D simulations. The impact on hemodynamic indices used for rupture status assessment was tested for 10 cases with 3D simulations.

RESULTS

Differences in flow rates among the various strategies were up to 70%, with a non-negligible impact on average and oscillatory wall shear stresses in some cases. Murray-law and splitting methods gave flow rates closest to physiological values reported in the literature; however, only the splitting method was insensitive to arbitrary truncation of the model extent.

CONCLUSIONS

Cerebrovascular simulations can depend strongly on the outflow strategy. The default zero-pressure method should be avoided in favor of Murray-law or splitting methods, the latter being released as an open-source tool to encourage the standardization of outflow strategies.