The influence of contrast agent injection on physiological flow in the circle of Willis

Simulation-informed learning for time-resolved angiographic contrast agent concentration reconstruction

Three-dimensional Digital Subtraction Angiography (3D-DSA) is a well-established X-ray-based technique for visualizing vascular anatomy. Recently, four-dimensional DSA (4D-DSA) reconstruction algorithms have been developed to enable the visualization of volumetric contrast flow dynamics through time-series of volumes. This reconstruction problem is ill-posed mainly due to vessel overlap in the projection direction and geometric vessel foreshortening, which leads to information loss in the recorded projection images. However, knowledge about the underlying fluid dynamics can be leveraged to constrain the solution space. In our work, we implicitly include this information in a neural network-based model that is trained on a dataset of image-based blood flow simulations. The model predicts the spatially averaged contrast agent concentration for each centerline point of the vasculature over time, lowering the overall computational demand. The trained network enables the reconstruction of relative contrast agent concentrations with a mean absolute error of 0.02±0.02 and a mean absolute percentage error of 5.31±9.25 %. Moreover, the network is robust to varying degrees of vessel overlap and vessel foreshortening. Our approach demonstrates the potential of the integration of machine learning and blood flow simulations in time-resolved angiographic contrast agent concentration reconstruction.

First blood: An efficient, hybrid one- and zero-dimensional, modular hemodynamic solver

Low-dimensional (1D or 0D) models can describe the whole human blood circulation, for example, 1D distributed parameter model for the arterial network and 0D concentrated models for the heart or other organs. This paper presents a combined 1D-0D solver, called first_blood, that solves the governing equations of fluid dynamics to model low-dimensional hemodynamic effects. An extended method of characteristics is applied here to solve the momentum, and mass conservation equations and the viscoelastic wall model equation, mimicking the material properties of arterial walls. The heart and the peripheral lumped models are solved with a general zero-dimensional (0D) nonlinear solver. The model topology can be modular, that is, first_blood can solve any 1D-0D hemodynamic model. To demonstrate the applicability of first_blood, the human arterial system, the heart and the peripherals are modelled using the solver. The simulation time of a heartbeat takes around 2 s, that is, first_blood requires only twice the real-time for the simulation using an average PC, which highlights the computational efficiency. The source code is available on GitHub, that is, it is open source. The model parameters are based on the literature suggestions and on the validation of output data to obtain physiologically relevant results.

The Impact of a Limited Field-of-View on Computed Hemodynamics in Abdominal Aortic Aneurysms: Evaluating the Feasibility of Completing Ultrasound Segmentations with Parametric Geometries

To improve abdominal aortic aneurysm (AAA) rupture risk assessment, a large, longitudinal study on AAA hemodynamics and biomechanics is necessary, using personalized fluid-structure interaction (FSI) modeling. 3-dimensional, time-resolved ultrasound (3D+t US) is the preferred image modality to obtain the patient-specific AAA geometry for such a study, since it is safe, affordable and provides temporal information. However, the 3D+t US field-of-view (FOV) is limited and therefore often fails to capture the inlet and aorto-iliac bifurcation geometry. In this study, a framework was developed to add parametric inlet and bifurcation geometries to the abdominal aortic aneurysm geometry by employing dataset statistics and parameters of the AAA geometry. The impact of replacing the patient-specific inlet and bifurcation geometries, acquired using computed tomography (CT) scans, by parametric geometries was evaluated by examining the differences in hemodynamics (systolic and time-averaged wall shear stress and oscillatory shear index) in the aneurysm region. The results show that the inlet geometry has a larger effect on the AAA hemodynamics (median differences of 7.5 to 18.8%) than the bifurcation geometry (median differences all below 1%). Therefore, it is not feasible to replace the patient-specific inlet geometry by a generic one. Future studies should investigate the possibilities of extending the proximal FOV of 3D+t US. However, this study did show the feasibility of adding a parametric bifurcation geometry to the aneurysm geometry. After extending the proximal FOV, the obtained framework can be used to extract AAA geometries from 3D+t US for FSI simulations, despite the absence of the bifurcation geometry.

Mathematical Models for Blood Flow Quantification in Dialysis Access Using Angiography: A Comparative Study

Blood flow rate in dialysis (vascular) access is the key parameter to examine patency and to evaluate the outcomes of various endovascular interve7ntions. While angiography is extensively used for dialysis access–salvage procedures, to date, there is no image-based blood flow measurement application commercially available in the angiography suite. We aim to calculate the blood flow rate in the dialysis access based on cine-angiographic and fluoroscopic image sequences. In this study, we discuss image-based methods to quantify access blood flow in a flow phantom model. Digital subtraction angiography (DSA) and fluoroscopy were used to acquire images at various sampling rates (DSA—3 and 6 frames/s, fluoroscopy—4 and 10 pulses/s). Flow rates were computed based on two bolus tracking algorithms, peak-to-peak and cross-correlation, and modeled with three curve-fitting functions, gamma variate, lagged normal, and polynomial, to correct errors with transit time measurement. Dye propagation distance and the cross-sectional area were calculated by analyzing the contrast enhancement in the vessel. The calculated flow rates were correlated versus an in-line flow sensor measurement. The cross-correlation algorithm with gamma-variate curve fitting had the best accuracy and least variability in both imaging modes. The absolute percent error (mean ± SEM) of flow quantification in the DSA mode at 6 frames/s was 21.4 ± 1.9%, and in the fluoroscopic mode at 10 pulses/s was 37.4 ± 3.6%. The radiation dose varied linearly with the sampling rate in both imaging modes and was substantially low to invoke any tissue reactions or stochastic effects. The cross-correlation algorithm and gamma-variate curve fitting for DSA acquisition at 6 frames/s had the best correlation with the flow sensor measurements. These findings will be helpful to develop a software-based vascular access flow measurement tool for the angiography suite and to optimize the imaging protocol amenable for computational flow applications.

Complementing sparse vascular imaging data by physiological adaptation rules

Mathematical modeling of pressure and flow waveforms in blood vessels using pulse wave propagation (PWP) models has tremendous potential to support clinical decision making. For a personalized model outcome, measurements of all modeled vessel radii and wall thicknesses are required. In clinical practice, however, data sets are often incomplete. To overcome this problem, we hypothesized that the adaptive capacity of vessels in response to mechanical load could be utilized to fill in the gaps of incomplete patient-specific data sets. We implemented homeostatic feedback loops in a validated PWP model to allow adaptation of vessel geometry to maintain physiological values of wall stress and wall shear stress. To evaluate our approach, we gathered vascular MRI and ultrasound data sets of wall thicknesses and radii of central and arm arterial segments of 10 healthy subjects. Reference models (i.e., termed RefModel, n = 10) were simulated using complete data, whereas adapted models (AdaptModel, n = 10) used data of one carotid artery segment only, and the remaining geometries in this model were estimated using adaptation. We evaluated agreement between RefModel and AdaptModel geometries, as well as that between pressure and flow waveforms of both models. Limits of agreement (bias ± 2 SD of difference) between AdaptModel and RefModel radii and wall thicknesses were 0.2 ± 2.6 mm and -140 ± 557 µm, respectively. Pressure and flow waveform characteristics of the AdaptModel better resembled those of the RefModels as compared with the model in which the vessels were not adapted. Our adaptation-based PWP model enables personalization of vascular geometries even when not all required data are available.NEW & NOTEWORTHY To benefit personalized pulse wave propagation (PWP) modeling, we propose a novel method that, instead of relying on extensive data sets on vascular geometries, incorporates physiological adaptation rules. The developed vascular adaptation model adequately predicted arterial radius and wall thickness compared with ultrasound and MRI estimates, obtained in humans. Our approach could be used as a tool to facilitate personalized modeling, notably in case of missing data, as routinely found in clinical settings.

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.

Backward sensitivity analysis and reduced-order covariance estimation in noninvasive parameter identification for cerebral arteries

Using a previously developed inversion platform for functional cerebral medical imaging with ensemble Kalman filters, this work analyzes the sensitivity of the results with respect to different parameters entering the physical model and inversion procedure, such as the inlet flow rate from the heart, the choice of the boundary conditions, and the nonsymmetry in the network terminations. It also proposes an alternative low complexity construction for the covariance matrix of the hemodynamic parameters of a network of arteries including the circle of Willis. The platform takes as input patient-specific blood flow rates extracted from magnetic resonance angiography and magnetic resonance imaging (dicom files) and is applied to several available patients data. The paper presents full analysis of the results for one of these patients, including a sensitivity study with respect to the proximal and distal boundary conditions. The results notably show that the uncertainties on the inlet flow rate led to uncertainties of the same order of magnitude in the estimated parameters (blood pressure and elastic parameters) and that three-lumped parameters boundary conditions are necessary for a correct retrieval of the target signals.

Pressure and Flow Rate Changes During Contrast Injections in Cerebral Angiography: Correlation to Reflux Length

Cerebral angiography involves the antegrade injection of contrast media through a catheter into the vasculature to visualize the region of interest under X-ray imaging. Depending on the injection and blood flow parameters, the bolus of contrast can propagate in the upstream direction and proximal to the catheter tip, at which point contrast is said to have refluxed. In this in vitro study, we investigate the relationship of fundamental hemodynamic variables to this phenomenon. Contrast injections were carried out under steady and pulsatile flow using various vessel diameters, catheter sizes, working fluid flow rates, and injection rates. The distance from the catheter tip to the proximal edge of the contrast bolus, called reflux length, was measured on the angiograms; the relation of this reflux length to different hemodynamic parameters was evaluated. Results show that contrast reflux occurs when the pressure distal to the catheter tip increases to be greater than the pressure proximal to the catheter tip. The ratio of this pressure difference to the baseline flow rate, called reflux resistance here, was linearly correlated to the normalized reflux length (reflux length/vessel diameter). Further, the ratio of blood flow to contrast fluid momentums, called the Craya-Curtet number, was correlated to the normalized reflux length via a sigmoid function. A sigmoid function was also found to be representative of the relationship between the ratio of the Reynolds numbers of blood flow to contrast and the normalized reflux length. As described by previous reports, catheter based contrast injections cause substantial increases in local flow and pressure. Contrast reflux should generally be avoided during standard antegrade angiography. Our study shows two specific correlations between contrast reflux length and baseline and intra-injection parameters that have not been published previously. Further studies need to be conducted to fully characterize the phenomena and to extract reliable indicators of clinical utility. Parameters relevant to cerebral angiography are studied here, but the essential principles are applicable to all angiographic procedures involving antegrade catheter injections.

Computational Fluid Dynamics modeling of contrast transport in basilar aneurysms following flow-altering surgeries

In vivo measurement of blood velocity fields and flow descriptors remains challenging due to image artifacts and limited resolution of current imaging methods; however, in vivo imaging data can be used to inform and validate patient-specific computational fluid dynamics (CFD) models. Image-based CFD can be particularly useful for planning surgical interventions in complicated cases such as fusiform aneurysms of the basilar artery, where it is crucial to alter pathological hemodynamics while preserving flow to the distal vasculature. In this study, patient-specific CFD modeling was conducted for two basilar aneurysm patients considered for surgical treatment. In addition to velocity fields, transport of contrast agent was simulated for the preoperative and postoperative conditions using two approaches. The transport of a virtual contrast passively following the flow streamlines was simulated to predict post-surgical flow regions prone to thrombus deposition. In addition, the transport of a mixture of blood with an iodine-based contrast agent was modeled to compare and verify the CFD results with X-ray angiograms. The CFD-predicted patterns of contrast flow were qualitatively compared to in vivo X-ray angiograms acquired before and after the intervention. The results suggest that the mixture modeling approach, accounting for the flow rates and properties of the contrast injection, is in better agreement with the X-ray angiography data. The virtual contrast modeling assessed the residence time based on flow patterns unaffected by the injection procedure, which makes the virtual contrast modeling approach better suited for prediction of thrombus deposition, which is not limited to the peri-procedural state.

Finding the optimal deconvolution algorithm for MR perfusion in carotid stenosis: Correlations with angiographic cerebral circulation time

PURPOSE

The aim of our study is to explore the impacts of different deconvolution algorithms on correlations between CBF, MTT, CBV, TTP, Tmax from MR perfusion (MRP) and angiography cerebral circulation time (CCT).

METHODS

Retrospectively, 30 patients with unilateral carotid stenosis, and available pre-stenting MRP and angiography were included for analysis. All MRPs were conducted in a 1.5-T MR scanner. Standard singular value decomposition, block-circulant, and two delay-corrected algorithms were used as the deconvolution methods. All angiographies were obtained in the same bi-plane flat-detector angiographic machine. A contrast bolus of 12mL was administrated via angiocatheter at a rate of 8mL/s. The acquisition protocols were the same for all cases. CCT was defined as the difference between time to peak from the cavernous ICA and the parietal vein in lateral view. Pearson correlations were calculated for CCT and CBF, MTT, CBV, TTP, Tmax.

RESULTS

The correlation between CCT and MTT was highest with Tmax (r=0.65), followed by MTT (r=0.60), CBF (r=-0.57), and TTP (r=0.33) when standard singular value decomposition was used. No correlation with CBV was noted.

CONCLUSIONS

MRP using a singular value decomposition algorithm confirmed the feasibility of quantifying cerebral blood flow deficit in steno-occlusive disease within the angio-room. This approach might further improve patient safety by providing immediate cerebral hemodynamics without extraradiation and iodine contrast.

pyNS: an open-source framework for 0D haemodynamic modelling

A number of computational approaches have been proposed for the simulation of haemodynamics and vascular wall dynamics in complex vascular networks. Among them, 0D pulse wave propagation methods allow to efficiently model flow and pressure distributions and wall displacements throughout vascular networks at low computational costs. Although several techniques are documented in literature, the availability of open-source computational tools is still limited. We here present python Network Solver, a modular solver framework for 0D problems released under a BSD license as part of the archToolkit ( http://archtk.github.com ). As an application, we describe patient-specific models of the systemic circulation and detailed upper extremity for use in the prediction of maturation after surgical creation of vascular access for haemodialysis.

Flexible composition and execution of high performance, high fidelity multiscale biomedical simulations

Multiscale simulations are essential in the biomedical domain to accurately model human physiology. We present a modular approach for designing, constructing and executing multiscale simulations on a wide range of resources, from laptops to petascale supercomputers, including combinations of these. Our work features two multiscale applications, in-stent restenosis and cerebrovascular bloodflow, which combine multiple existing single-scale applications to create a multiscale simulation. These applications can be efficiently coupled, deployed and executed on computers up to the largest (peta) scale, incurring a coupling overhead of 1-10% of the total execution time.

Quantification of internal carotid artery flow with digital subtraction angiography: validation of an optical flow approach with Doppler ultrasound

BACKGROUND AND PURPOSE

Digital subtraction angiography is the reference standard technique to evaluate intracranial vascular anatomy and used on the endovascular treatment of vascular diseases. A dedicated optical flow-based algorithm was applied to DSA to measure arterial flow. The first quantification results of internal carotid artery flow validated with Doppler sonography are reported.

MATERIALS AND METHODS

We included 22 consecutive patients who underwent endovascular procedures. To assess the sensitivity of the algorithm to contrast agent-blood mixing dynamics, we acquired high-frame DSA series (60 images/s) with different injection rates: 1.5 mL/s (n = 19), 2.0 mL/s (n = 18), and 3.0 mL/s (n = 13). 3D rotational angiography was used to extract the centerline of the vessel and the arterial section necessary for volume flow calculation. Optical flow was used to measure flow velocities in straight parts of the ICAs; these data were further compared with Doppler sonography data. DSA mean flow rates were linearly regressed on Doppler sonography measurements, and regression slope coefficient bias from value 1 was analyzed within the 95% confidence interval.

RESULTS

DSA mean flow rates measured with the optical flow approach significantly matched Doppler sonography measurements (slope regression coefficient, b = 0.83 ± 0.19, P = .05) for injection rate = 2.0 mL/s and circulating volumetric blood flow <6 mL/s. For injection rate = 1.5 mL/s, volumetric blood flow <3 mL/s correlated well with Doppler sonography (b = 0.67 ± 0.33, P = .05). Injection rate = 3.0 mL/s failed to provide DSA-optical flow measurements correlating with Doppler sonography because of the lack of measurable pulsatility.

CONCLUSIONS

A new model-free optical flow technique was tested reliably on the ICA. DSA-based blood flow velocity measurements were essentially validated with Doppler sonography whenever the conditions of measurable pulsatility were achieved (injection rates = 1.5 and 2.0 mL/s).

An experimental investigation of the hemodynamic variations due to aplastic vessels within three-dimensional phantom models of the circle of Willis

A complete circle of Willis (CoW) is found in approximately 30-50% of the population. Anatomical variations, such as absent or surgically clamped vessels, can result in undesirable flow patterns. These can affect the brain's ability to maintain cerebral perfusion and the formation of cerebral aneurysms. An experimental test system was developed to simulate cerebral physiological conditions through three flexible 3D patient-specific models of complete and incomplete CoW geometries. Flow visualizations were performed with isobaric dyes and the mapped dye streamlines were tracked throughout the models. Three to seven flow impact locations were observed for all configurations, corresponding to known sites for aneurysmal formation. Uni and bi-directional cross-flows occurred along the communicating arteries. The greatest shunting of flow occurred for a missing pre-communicating anterior (A1) and posterior (P1) cerebral arteries. The anterior cerebral arteries had the greatest reduction (15-37%) in efferent flow rates for missing either a unilateral A1 or bilateral P1 segments. The bi-directional cross-flows, with multiple afferent flow mixing, observed along the communicating arteries may explain the propensity of aneurysm formation at these sites. Reductions in efferent flow rates due to aplastic vessel configurations may affect normal brain function.

Impact of blood rheology on wall shear stress in a model of the middle cerebral artery

Perturbations to the homeostatic distribution of mechanical forces exerted by blood on the endothelial layer have been correlated with vascular pathologies, including intracranial aneurysms and atherosclerosis. Recent computational work suggests that, in order to correctly characterize such forces, the shear-thinning properties of blood must be taken into account. To the best of our knowledge, these findings have never been compared against experimentally observed pathological thresholds. In this work, we apply the three-band diagram (TBD) analysis due to Gizzi et al. (Gizzi et al. 2011 Three-band decomposition analysis of wall shear stress in pulsatile flows. Phys. Rev. E 83, 031902. (doi:10.1103/PhysRevE.83.031902)) to assess the impact of the choice of blood rheology model on a computational model of the right middle cerebral artery. Our results show that, in the model under study, the differences between the wall shear stress predicted by a Newtonian model and the well-known Carreau-Yasuda generalized Newtonian model are only significant if the vascular pathology under study is associated with a pathological threshold in the range 0.94-1.56 Pa, where the results of the TBD analysis of the rheology models considered differs. Otherwise, we observe no significant differences.

The benefit of non contrast-enhanced magnetic resonance angiography for predicting vascular access surgery outcome: a computer model perspective

INTRODUCTION

Vascular access (VA) surgery, a prerequisite for hemodialysis treatment of end-stage renal-disease (ESRD) patients, is hampered by complication rates, which are frequently related to flow enhancement. To assist in VA surgery planning, a patient-specific computer model for postoperative flow enhancement was developed. The purpose of this study is to assess the benefit of non contrast-enhanced magnetic resonance angiography (NCE-MRA) data as patient-specific geometrical input for the model-based prediction of surgery outcome.

METHODS

25 ESRD patients were included in this study. All patients received a NCE-MRA examination of the upper extremity blood vessels in addition to routine ultrasound (US). Local arterial radii were assessed from NCE-MRA and converted to model input using a linear fit per artery. Venous radii were determined with US. The effect of radius measurement uncertainty on model predictions was accounted for by performing Monte-Carlo simulations. The resulting flow prediction interval of the computer model was compared with the postoperative flow obtained from US. Patients with no overlap between model-based prediction and postoperative measurement were further analyzed to determine whether an increase in geometrical detail improved computer model prediction.

RESULTS

Overlap between postoperative flows and model-based predictions was obtained for 71% of patients. Detailed inspection of non-overlapping cases revealed that the geometrical details that could be assessed from NCE-MRA explained most of the differences, and moreover, upon addition of these details in the computer model the flow predictions improved.

CONCLUSIONS

The results demonstrate clearly that NCE-MRA does provide valuable geometrical information for VA surgery planning. Therefore, it is recommended to use this modality, at least for patients at risk for local or global narrowing of the blood vessels as well as for patients for whom an US-based model prediction would not overlap with surgical choice, as the geometrical details are crucial for obtaining accurate flow predictions.

A lumped parameter model of cerebral blood flow control combining cerebral autoregulation and neurovascular coupling

Cerebral blood flow regulation is based on a variety of different mechanisms, of which the relative regulatory role remains largely unknown. The cerebral regulatory system expresses two regulatory properties: cerebral autoregulation and neurovascular coupling. Since partly the same mechanisms play a role in cerebral autoregulation and neurovascular coupling, this study aimed to develop a physiologically based mathematical model of cerebral blood flow regulation combining these properties. A lumped parameter model of the P2 segment of the posterior cerebral artery and its distal vessels was constructed. Blood flow regulation is exerted at the arteriolar level by vascular smooth muscle and implements myogenic, shear stress based, neurogenic, and metabolic mechanisms. In eight healthy subjects, cerebral autoregulation and neurovascular coupling were challenged by squat-stand maneuvers and visual stimulation using a checkerboard pattern, respectively. Cerebral blood flow velocity was measured using transcranial Doppler, whereas blood pressure was measured by finger volume clamping. In seven subjects, the model proposed fits autoregulation and neurovascular coupling measurement data well. Myogenic regulation is found to dominate the autoregulatory response. Neurogenic regulation, although only implemented as a first-order mechanism, describes neurovascular coupling responses to a great extent. It is concluded that our single, integrated model of cerebral blood flow control may be used to identify the main mechanisms affecting cerebral blood flow regulation in individual subjects.

A numerical method of reduced complexity for simulating vascular hemodynamics using coupled 0D lumped and 1D wave propagation models

A computational method of reduced complexity is developed for simulating vascular hemodynamics by combination of one-dimensional (1D) wave propagation models for the blood vessels with zero-dimensional (0D) lumped models for the microcirculation. Despite the reduced dimension, current algorithms used to solve the model equations and simulate pressure and flow are rather complex, thereby limiting acceptance in the medical field. This complexity mainly arises from the methods used to combine the 1D and the 0D model equations. In this paper a numerical method is presented that no longer requires additional coupling methods and enables random combinations of 1D and 0D models using pressure as only state variable. The method is applied to a vascular tree consisting of 60 major arteries in the body and the head. Simulated results are realistic. The numerical method is stable and shows good convergence.