Uncertainty quantification of wall shear stress in intracranial aneurysms using a data-driven statistical model of systemic blood flow variability

Reduced order modelling of intracranial aneurysm flow using proper orthogonal decomposition and neural networks

Reduced order modelling (ROMs) methods, such as proper orthogonal decomposition (POD), systematically reduce the dimensionality of high-fidelity computational models and potentially achieve large gains in execution speed. Machine learning (ML) using neural networks has been used to overcome limitations of traditional ROM techniques when applied to nonlinear problems, which has led to the recent development of reduced order models augmented by machine learning (ML-ROMs). However, the performance of ML-ROMs is yet to be widely evaluated in realistic applications and questions remain regarding the optimal design of ML-ROMs. In this study, we investigate the application of a non-intrusive parametric ML-ROM to a nonlinear, time-dependent fluid dynamics problem in a complex 3D geometry. We construct the ML-ROM using POD for dimensionality reduction and neural networks for interpolation of the ROM coefficients. We compare three different network designs in terms of approximation accuracy and performance. We test our ML-ROM on a flow problem in intracranial aneurysms, where flow variability effects are important when evaluating rupture risk and simulating treatment outcomes. The best-performing network design in our comparison used a two-stage POD reduction, a technique rarely used in previous studies. The best-performing ROM achieved mean test accuracies of 98.6% and 97.6% in the parent vessel and the aneurysm, respectively, while providing speed-up factors of the order10 5 $$ {10}^5 $$ .

Hemodynamics of thrombus formation in intracranial aneurysms: An in silico observational study

How prevalent is spontaneous thrombosis in a population containing all sizes of intracranial aneurysms? How can we calibrate computational models of thrombosis based on published data? How does spontaneous thrombosis differ in normo- and hypertensive subjects? We address the first question through a thorough analysis of published datasets that provide spontaneous thrombosis rates across different aneurysm characteristics. This analysis provides data for a subgroup of the general population of aneurysms, namely, those of large and giant size (>10 mm). Based on these observed spontaneous thrombosis rates, our computational modeling platform enables the first in silico observational study of spontaneous thrombosis prevalence across a broader set of aneurysm phenotypes. We generate 109 virtual patients and use a novel approach to calibrate two trigger thresholds: residence time and shear rate, thus addressing the second question. We then address the third question by utilizing this calibrated model to provide new insight into the effects of hypertension on spontaneous thrombosis. We demonstrate how a mechanistic thrombosis model calibrated on an intracranial aneurysm cohort can help estimate spontaneous thrombosis prevalence in a broader aneurysm population. This study is enabled through a fully automatic multi-scale modeling pipeline. We use the clinical spontaneous thrombosis data as an indirect population-level validation of a complex computational modeling framework. Furthermore, our framework allows exploration of the influence of hypertension in spontaneous thrombosis. This lays the foundation for in silico clinical trials of cerebrovascular devices in high-risk populations, e.g., assessing the performance of flow diverters in aneurysms for hypertensive patients.

Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases

Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.

In-silico trial of intracranial flow diverters replicates and expands insights from conventional clinical trials

The cost of clinical trials is ever-increasing. In-silico trials rely on virtual populations and interventions simulated using patient-specific models and may offer a solution to lower these costs. We present the flow diverter performance assessment (FD-PASS) in-silico trial, which models the treatment of intracranial aneurysms in 164 virtual patients with 82 distinct anatomies with a flow-diverting stent, using computational fluid dynamics to quantify post-treatment flow reduction. The predicted FD-PASS flow-diversion success rates replicate the values previously reported in three clinical trials. The in-silico approach allows broader investigation of factors associated with insufficient flow reduction than feasible in a conventional trial. Our findings demonstrate that in-silico trials of endovascular medical devices can: (i) replicate findings of conventional clinical trials, and (ii) perform virtual experiments and sub-group analyses that are difficult or impossible in conventional trials to discover new insights on treatment failure, e.g. in the presence of side-branches or hypertension.

In-silico trials rely on virtual populations and interventions simulated using patient-specific models and may offer a solution to lower costs. Here, the authors present the flow diverter performance assessment in-silico trial, which models the treatment of intracranial aneurysms with a flow-diverting stent.

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.

How patient-specific do internal carotid artery inflow rates need to be for computational fluid dynamics of cerebral aneurysms?

BACKGROUND

Computational fluid dynamics (CFD) has become a popular tool for studying 'patient-specific' blood flow dynamics in cerebral aneurysms; however, rarely are the inflow boundary conditions patient-specific. We aimed to test the impact of widespread reliance on generalized inflow rates.

METHODS

Internal carotid artery (ICA) flow rates were measured via 2D cine phase-contrast MRI for 24 patients scheduled for endovascular therapy of an ICA aneurysm. CFD models were constructed from 3D rotational angiography, and pulsatile inflow rates imposed as measured by MRI or estimated using an average older-adult ICA flow waveform shape scaled by a cycle-average flow rate (Q_avg) derived from the patient's ICA cross-sectional area via an assumed inlet velocity.

RESULTS

There was good overall qualitative agreement in the magnitudes and spatial distributions of time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and spectral power index (SPI) using generalized versus patient-specific inflows. Sac-averaged quantities showed moderate to good correlations: R²=0.54 (TAWSS), 0.80 (OSI), and 0.68 (SPI). Using patient-specific Q_avg to scale the generalized waveform shape resulted in near-perfect agreement for TAWSS, and reduced bias, but not scatter, for SPI. Patient-specific waveform had an impact only on OSI correlations, which improved to R²=0.93.

CONCLUSIONS

Aneurysm CFD demonstrates the ability to stratify cases by nominal hemodynamic 'risk' factors when employing an age- and vascular-territory-specific recipe for generalized inflow rates. Q_avg has a greater influence than waveform shape, suggesting some improvement could be achieved by including measurement of patient-specific Q_avg into aneurysm imaging protocols.

Inter-patient variations in flow boundary conditions at middle cerebral artery from 7T PC-MRI and influence on Computational Fluid Dynamics of intracranial aneurysms

BACKGROUND

Computational fluid dynamics(CFD) of intracranial aneurysms requires flow boundary conditions(BCs) as inputs. Patient-specific BCs are usually unavailable and substituted by literature-derived generic BCs. Therefore, we investigated inter-patient BC variations and their influence on middle cerebral artery aneurysmal hemodynamics.

METHOD

We retrospectively collected CT angiography and 7-T Phase-Contrast(PC)-MRI data from eight middle-cerebral-artery bifurcation aneurysms to reconstruct the geometry and measure the arterial flowrates, respectively. The coefficient of variation(CoV) was calculated for the inlet flowrate and the pulsatility index(PI). The outflow split estimated by Murray's law was compared with PC-MRI measurements. For each aneurysm, we performed seven simulations: "baseline" using PC-MRI-derived BCs and the other six with changing BCs to explore the influence of BC variations on hemodynamics.

RESULTS

From PC-MRI, the inlet flowrate was 1.94 ± 0.71 cm³/s(CoV = 36%) and PI was 0.37 ± 0.13(CoV = 34%). The outflow split estimated by Murray's law deviated by 15.3% compared to PC-MRI. Comparing to "baseline" models, ±36% variations in inlet flowrate caused -61% to +89% changes in time-averaged wall shear stress(WSS), -37% to +32% in normalized WSS(NWSS; by parent-artery), and -42% to +126% in oscillatory shear index(OSI). The ±34% variations in PI caused, -46% to +67% in OSI. Applying ±15% variations in outflow split led to inflow jet deflection and -41% to +52% changes in WSS, -41% to +47% in NWSS, and -44% to +144% in OSI.

CONCLUSION

Inflow rate and outflow split have a drastic impact on hemodynamics of intracranial aneurysms. Inlet waveform has a negligible impact on WSS and NWSS but major impact on OSI. CFD-based models need to consider such sensitivity.

Hemodynamics of Cerebral Aneurysms: Connecting Medical Imaging and Biomechanical Analysis

In the last two decades, numerous studies have conducted patient-specific computations of blood flow dynamics in cerebral aneurysms and reported correlations between various hemodynamic metrics and aneurysmal disease progression or treatment outcomes. Nevertheless, intra-aneurysmal flow analysis has not been adopted in current clinical practice, and hemodynamic factors usually are not considered in clinical decision making. This review presents the state of the art in cerebral aneurysm imaging and image-based modeling, discussing the advantages and limitations of each approach and focusing on the translational value of hemodynamic analysis. Combining imaging and modeling data obtained from different flow modalities can improve the accuracy and fidelity of resulting velocity fields and flow-derived factors that are thought to affect aneurysmal disease progression. It is expected that predictive models utilizing hemodynamic factors in combination with patient medical history and morphological data will outperform current risk scores and treatment guidelines. Possible future directions include novel approaches enabling data assimilation and multimodality analysis of cerebral aneurysm hemodynamics.

Incorporating variability of patient inflow conditions into statistical models for aneurysm rupture assessment

BACKGROUND

Hemodynamic patterns have been associated with cerebral aneurysm instability. For patient-specific computational fluid dynamics (CFD) simulations, the inflow rates of a patient are typically not known. The aim of this study was to analyze the influence of inter- and intra-patient variations of cerebral blood flow on the computed hemodynamics through CFD simulations and to incorporate these variations into statistical models for aneurysm rupture prediction.

METHODS

Image data of 1820 aneurysms were used for patient-specific steady CFD simulations with nine different inflow rates per case, capturing inter- and intra-patient flow variations. Based on the computed flow fields, 17 hemodynamic parameters were calculated and compared for the different flow conditions. Next, statistical models for aneurysm rupture were trained in 1571 of the aneurysms including hemodynamic parameters capturing the flow variations either by defining hemodynamic "response variables" (model A) or repeatedly randomly selecting flow conditions by patients (model B) as well as morphological and patient-specific variables. Both models were evaluated in the remaining 249 cases.

RESULTS

All hemodynamic parameters were significantly different for the varying flow conditions (p < 0.001). Both the flow-independent "response" model A and the flow-dependent model B performed well with areas under the receiver operating characteristic curve of 0.8182 and 0.8174 ± 0.0045, respectively.

CONCLUSIONS

The influence of inter- and intra-patient flow variations on computed hemodynamics can be taken into account in multivariate aneurysm rupture prediction models achieving a good predictive performance. Such models can be applied to CFD data independent of the specific inflow boundary conditions.

Population-specific modelling of between/within-subject flow variability in the carotid arteries of the elderly

Computational fluid dynamics models are increasingly proposed for assisting the diagnosis and management of vascular diseases. Ideally, patient-specific flow measurements are used to impose flow boundary conditions. When patient-specific flow measurements are unavailable, mean values of flow measurements across small cohorts are used as normative values. In reality, both the between-subjects and within-subject flow variabilities are large. Consequently, neither one-shot flow measurements nor mean values across a cohort are truly indicative of the flow regime in a given person. We develop models for both the between-subjects and within-subject variability of internal carotid flow. A log-linear mixed effects model is combined with a Gaussian process to model the between-subjects flow variability, while a lumped parameter model of cerebral autoregulation is used to model the within-subject flow variability in response to heart rate and blood pressure changes. The model parameters are identified from carotid ultrasound measurements in a cohort of 103 elderly volunteers. We use the models to study intracranial aneurysm flow in 54 subjects under rest and exercise and conclude that OSI, a common wall shear-stress derived quantity in vascular CFD studies, may be too sensitive to flow fluctuations to be a reliable biomarker.

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.

Influence of aging-induced flow waveform variation on hemodynamics in aneurysms present at the internal carotid artery: A computational model-based study

The variation of blood flow waveform in the internal carotid artery (ICA) with age is a well-documented hemodynamic phenomenon, but little is known about how such variation affects the characteristics of blood flow in aneurysms present in the region. In the study, hemodynamic simulations were conducted for 26 ICA aneurysms, with flow waveforms measured in the ICAs of young and older adults being used respectively to set the inflow boundary conditions. Obtained results showed that replacing the young-adult flow waveform with the older-adult one led to little changes (<10%) in simulated time-averaged wall shear stress (WSS), transient maximum WSS, relative residence time and trans-aneurysm pressure loss coefficient, but resulted in a marked increase (32.36 ± 17.24%) in oscillatory shear index (OSI). Frequency-domain wave analysis revealed that the progressive enhancement of low-frequency harmonics dominated the observed flow waveform variation with age and was a major factor contributing to the increase in OSI. Cross-sectional comparisons among the aneurysms further revealed that the degree of increase in OSI correlated positively with some specific morphological features of aneurysm, such as aspect ratio and size ratio. In summary, the study demonstrates that the variation in flow waveform with age augments the oscillation of WSS in ICA aneurysms, which underlies the importance of setting patient-specific boundary conditions in hemodynamic studies on cerebral aneurysms, especially those involving long-term patient follow-up or cross-sectional comparison among patients of different ages.

Thrombosis in Cerebral Aneurysms and the Computational Modeling Thereof: A Review

Thrombosis is a condition closely related to cerebral aneurysms and controlled thrombosis is the main purpose of endovascular embolization treatment. The mechanisms governing thrombus initiation and evolution in cerebral aneurysms have not been fully elucidated and this presents challenges for interventional planning. Significant effort has been directed towards developing computational methods aimed at streamlining the interventional planning process for unruptured cerebral aneurysm treatment. Included in these methods are computational models of thrombus development following endovascular device placement. The main challenge with developing computational models for thrombosis in disease cases is that there exists a wide body of literature that addresses various aspects of the clotting process, but it may not be obvious what information is of direct consequence for what modeling purpose (e.g., for understanding the effect of endovascular therapies). The aim of this review is to present the information so it will be of benefit to the community attempting to model cerebral aneurysm thrombosis for interventional planning purposes, in a simplified yet appropriate manner. The paper begins by explaining current understanding of physiological coagulation and highlights the documented distinctions between the physiological process and cerebral aneurysm thrombosis. Clinical observations of thrombosis following endovascular device placement are then presented. This is followed by a section detailing the demands placed on computational models developed for interventional planning. Finally, existing computational models of thrombosis are presented. This last section begins with description and discussion of physiological computational clotting models, as they are of immense value in understanding how to construct a general computational model of clotting. This is then followed by a review of computational models of clotting in cerebral aneurysms, specifically. Even though some progress has been made towards computational predictions of thrombosis following device placement in cerebral aneurysms, many gaps still remain. Answering the key questions will require the combined efforts of the clinical, experimental and computational communities.

Mathematical Modeling and Virtual Reality Simulation of Surgical Tool Interactions With Soft Tissue: A Review and Prospective

This is an informed assessment of the state of the art and an extensive inventory of modeling approaches and methods for soft tissue/medical cutting tool interaction and of the associated medical processes and phenomena. Modeling and simulation through numerical, theoretical, computational, experimental, and other methods was discussed in comprehensive review sections each of which is concluded with a plausible prospective discussion biased toward the development of so-called virtual reality (VR) simulator environments. The finalized prospective section reflects on the future demands in the area of soft tissue cutting modeling and simulation mostly from a conceptual angle with emphasis on VR development requirements including real-time VR simulator response, cost-effective “close-to-reality” VR implementations, and other demands. The review sections that serve as the basis for the suggested prospective needs are categorized based on: (1) Major VR simulator applications including virtual surgery education, training, operation planning, intraoperative simulation, image-guided surgery, etc. and VR simulator types, e.g., generic, patient-specific and surgery-specific and (2) Available numerical, theoretical, and computational methods in terms of robustness, time effectiveness, computational cost, error control, and accuracy of modeling of certain types of virtual surgical interventions and their experimental validation, geared toward ethically driven artificial “phantom” tissue-based approaches. Digital data processing methods used in modeling of various feedback modalities in VR environments are also discussed.

Use of the FDA nozzle model to illustrate validation techniques in computational fluid dynamics (CFD) simulations

A "credible" computational fluid dynamics (CFD) model has the potential to provide a meaningful evaluation of safety in medical devices. One major challenge in establishing "model credibility" is to determine the required degree of similarity between the model and experimental results for the model to be considered sufficiently validated. This study proposes a "threshold-based" validation approach that provides a well-defined acceptance criteria, which is a function of how close the simulation and experimental results are to the safety threshold, for establishing the model validity. The validation criteria developed following the threshold approach is not only a function of Comparison Error, E (which is the difference between experiments and simulations) but also takes in to account the risk to patient safety because of E. The method is applicable for scenarios in which a safety threshold can be clearly defined (e.g., the viscous shear-stress threshold for hemolysis in blood contacting devices). The applicability of the new validation approach was tested on the FDA nozzle geometry. The context of use (COU) was to evaluate if the instantaneous viscous shear stress in the nozzle geometry at Reynolds numbers (Re) of 3500 and 6500 was below the commonly accepted threshold for hemolysis. The CFD results ("S") of velocity and viscous shear stress were compared with inter-laboratory experimental measurements ("D"). The uncertainties in the CFD and experimental results due to input parameter uncertainties were quantified following the ASME V&V 20 standard. The CFD models for both Re = 3500 and 6500 could not be sufficiently validated by performing a direct comparison between CFD and experimental results using the Student's t-test. However, following the threshold-based approach, a Student's t-test comparing |S-D| and |Threshold-S| showed that relative to the threshold, the CFD and experimental datasets for Re = 3500 were statistically similar and the model could be considered sufficiently validated for the COU. However, for Re = 6500, at certain locations where the shear stress is close the hemolysis threshold, the CFD model could not be considered sufficiently validated for the COU. Our analysis showed that the model could be sufficiently validated either by reducing the uncertainties in experiments, simulations, and the threshold or by increasing the sample size for the experiments and simulations. The threshold approach can be applied to all types of computational models and provides an objective way of determining model credibility and for evaluating medical devices.

Virtual endovascular treatment of intracranial aneurysms: models and uncertainty

Virtual endovascular treatment models (VETMs) have been developed with the view to aid interventional neuroradiologists and neurosurgeons to pre-operatively analyze the comparative efficacy and safety of endovascular treatments for intracranial aneurysms. Based on the current state of VETMs in aneurysm rupture risk stratification and in patient-specific prediction of treatment outcomes, we argue there is a need to go beyond personalized biomechanical flow modeling assuming deterministic parameters and error-free measurements. The mechanobiological effects associated with blood clot formation are important factors in therapeutic decision making and models of post-treatment intra-aneurysmal biology and biochemistry should be linked to the purely hemodynamic models to improve the predictive power of current VETMs. The influence of model and parameter uncertainties associated to each component of a VETM is, where feasible, quantified via a random-effects meta-analysis of the literature. This allows estimating the pooled effect size of these uncertainties on aneurysmal wall shear stress. From such meta-analyses, two main sources of uncertainty emerge where research efforts have so far been limited: (1) vascular wall distensibility, and (2) intra/intersubject systemic flow variations. In the future, we suggest that current deterministic computational simulations need to be extended with strategies for uncertainty mitigation, uncertainty exploration, and sensitivity reduction techniques. WIREs Syst Biol Med 2017, 9:e1385. doi: 10.1002/wsbm.1385 For further resources related to this article, please visit the WIREs website.