Preclinical validation of the advection diffusion flow estimation method using computational patient specific coronary tree phantoms.

Coronary computed tomography angiography (CCTA) does not allow the quantification of reduced blood flow due to coronary artery disease (CAD). In response, numerical methods based on the CCTA image have been developed to compute coronary blood flow and assess the impact of disease. However to compute blood flow in the coronary arteries, numerical methods require specification of boundary conditions that are difficult to estimate accurately in a patient-specific manner. We describe herein a new noninvasive flow estimation method, called Advection Diffusion Flow Estimation (ADFE), to compute coronary artery flow from CCTA to use as boundary conditions for numerical models of coronary blood flow. ADFE uses image contrast variation along the tree-like structure to estimate flow in each vessel. For validating this method we used patient specific software phantoms on which the transport of contrast was simulated. This controlled validation setting enables a direct comparison between estimated flow and actual flow and a detailed investigation of factors affecting accuracy. A total of 10 CCTA image data sets were processed to extract all necessary information for simulating contrast transport. A spectral element method solver was used for computing the ground truth simulations with high accuracy. On this data set, the ADFE method showed a high correlation coefficient of 0.998 between estimated flow and the ground truth flow together with an average relative error of only 1 % . Comparing the ADFE method with the best method currently available (TAFE) for image-based blood flow estimation, which showed a correlation coefficient of 0.752 and average error of 20 % , it can be concluded that the ADFE method has the potential to significantly improve the quantification of coronary artery blood flow derived from contrast gradients in CCTA images.

Scale-Resolving Simulations of Steady and Pulsatile Flow Through Healthy and Stenotic Heart Valves.

Blood-flow downstream of stenotic and healthy aortic valves exhibits intermittent random fluctuations in the velocity field which are associated with turbulence. Such flows warrant the use of computationally demanding scale-resolving models. The aim of this work was to compute and quantify this turbulent flow in healthy and stenotic heart valves for steady and pulsatile flow conditions. Large eddy simulations (LESs) and Reynolds-averaged Navier-Stokes (RANS) simulations were used to compute the flow field at inlet Reynolds numbers of 2700 and 5400 for valves with an opening area of 70 mm2 and 175 mm2 and their projected orifice-plate type counterparts. Power spectra and turbulent kinetic energy were quantified on the centerline. Projected geometries exhibited an increased pressure-drop (>90%) and elevated turbulent kinetic energy levels (>147%). Turbulence production was an order of magnitude higher in stenotic heart valves compared to healthy valves. Pulsatile flow stabilizes flow in the acceleration phase, whereas onset of deceleration triggered (healthy valve) or amplified (stenotic valve) turbulence. Simplification of the aortic valve by projecting the orifice area should be avoided in computational fluid dynamics (CFD). RANS simulations may be used to predict the transvalvular pressure-drop, but scale-resolving models are recommended when detailed information of the flow field is required.

The impact of shape uncertainty on aortic-valve pressure-drop computations.

Patient-specific image-based computational fluid dynamics (CFD) is widely adopted in the cardiovascular research community to study hemodynamics, and will become increasingly important for personalized medicine. However, segmentation of the flow domain is not exact and geometric uncertainty can be expected which propagates through the computational model, leading to uncertainty in model output. Seventy-four aortic-valves were segmented from computed tomography images at peak systole. Statistical shape modeling was used to obtain an approximate parameterization of the original segmentations. This parameterization was used to train a meta-model that related the first five shape mode coefficients and flowrate to the CFD-computed transvalvular pressure-drop. Consequently, shape uncertainty in the order of 0.5 and 1.0 mm was emulated by introducing uncertainty in the shape mode coefficients. A global variance-based sensitivity analysis was performed to quantify output uncertainty and to determine relative importance of the shape modes. The first shape mode captured the opening/closing behavior of the valve and uncertainty in this mode coefficient accounted for more than 90% of the output variance. However, sensitivity to shape uncertainty is patient-specific, and the relative importance of the fourth shape mode coefficient tended to increase with increases in valvular area. These results show that geometric uncertainty in the order of image voxel size may lead to substantial uncertainty in CFD-computed transvalvular pressure-drops. Moreover, this illustrates that it is essential to assess the impact of geometric uncertainty on model output, and that this should be thoroughly quantified for applications that wish to use image-based CFD models.

Spectroscopic photoacoustic imaging of cartilage damage.

OBJECTIVE: Osteoarthritis (OA) is a chronic joint disease characterized by progressive degradation of cartilage. It affects more than 10% of the people aged over 60 years-old worldwide with a rising prevalence due to the increasingly aging population. OA is a major source of pain, disability, and socioeconomic cost. Currently, the lack of effective diagnosis and affordable imaging options for early detection and monitoring of OA presents the clinic with many challenges. Spectroscopic Photoacoustic (sPA) imaging has the potential to reveal changes in cartilage composition with different degrees of damage, based on optical absorption contrast. DESIGN: In this study, the capabilities of sPA imaging and its potential to characterize cartilage damage were explored. To this end, 15 pieces of cartilage samples from patients undergoing a total joint replacement were collected and were imaged ex vivo with sPA imaging at a wide optical spectral range (between 500 nm and 1,300 nm) to investigate the photoacoustic properties of cartilage tissue. All the PA spectra of the cartilage samples were analyzed and compared to the corresponding histological results. RESULTS: The collagen related PA spectral changes were clearly visible in our imaging data and were related to different degrees of cartilage damage. The results are in good agreement with histology and the current gold standard, i.e., the Mankin score. CONCLUSIONS: This study demonstrates the potential and possible clinical application of sPA imaging in OA.

Combining statistical shape modeling, CFD, and meta-modeling to approximate the patient-specific pressure-drop across the aortic valve in real-time.

BACKGROUND: Advances in medical imaging, segmentation techniques, and high performance computing have stimulated the use of complex, patient-specific, three-dimensional Computational Fluid Dynamics (CFD) simulations. Patient-specific, CFD-compatible geometries of the aortic valve are readily obtained. CFD can then be used to obtain the patient-specific pressure-flow relationship of the aortic valve. However, such CFD simulations are computationally expensive, and real-time alternatives are desired. AIM: The aim of this work is to evaluate the performance of a meta-model with respect to high-fidelity, three-dimensional CFD simulations of the aortic valve. METHODS: Principal component analysis was used to build a statistical shape model (SSM) from a population of 74 iso-topological meshes of the aortic valve. Synthetic meshes were created with the SSM, and steady-state CFD simulations at flow-rates between 50 and 650 mL/s were performed to build a meta-model. The meta-model related the statistical shape variance, and flow-rate to the pressure-drop. RESULTS: Even though the first three shape modes account for only 46% of shape variance, the features relevant for the pressure-drop seem to be captured. The three-mode shape-model approximates the pressure-drop with an average error of 8.8% to 10.6% for aortic valves with a geometric orifice area below 150 mm2 . The proposed methodology was least accurate for aortic valve areas above 150 mm2 . Further reduction to a meta-model introduces an additional 3% error. CONCLUSIONS: Statistical shape modeling can be used to capture shape variation of the aortic valve. Meta-models trained by SSM-based CFD simulations can provide an estimate of the pressure-flow relationship in real-time.

A Metamodeling Approach for Instant Severity Assessment and Uncertainty Quantification of Iliac Artery Stenoses.

Two-dimensional (2D) or three-dimensional (3D) models of blood flow in stenosed arteries can be used to patient-specifically predict outcome metrics, thereby supporting the physicians in decision making processes. However, these models are time consuming which limits the feasibility of output uncertainty quantification (UQ). Accurate surrogates (metamodels) might be the solution. In this study, we aim to demonstrate the feasibility of a generalized polynomial chaos expansion-based metamodel to predict a clinically relevant output metric and to quantify the output uncertainty. As an example, a metamodel was constructed from a recently developed 2D model that was shown to be able to estimate translesional pressure drops in iliac artery stenoses (-0.9 ± 12.7 mmHg, R2 = 0.81). The metamodel was constructed from a virtual database using the adaptive generalized polynomial chaos expansion (agPCE) method. The constructed metamodel was then applied to 25 stenosed iliac arteries to predict the patient-specific pressure drop and to perform UQ. Comparing predicted pressure drops of the metamodel and in vivo measured pressure drops, the mean bias (-0.2 ± 13.7 mmHg) and the coefficient of determination (R2 = 0.80) were as good as of the original 2D computational fluid dynamics (CFD) model. UQ results of the 2D and metamodel were comparable. Estimation of the uncertainty interval using the original 2D model took 14 days, whereas the result of the metamodel was instantly available. In conclusion, it is feasible to quantify the uncertainty of the output metric and perform sensitivity analysis (SA) instantly using a metamodel. Future studies should investigate the possibility to construct a metamodel of more complex problems.

Unmixing multi-spectral photoacoustic sources in human carotid plaques using non-negative independent component analysis.

Multi-spectral photoacoustic imaging (MSPAI) is promising for morphology assessment of carotid plaques; however, obtaining unique spectral characteristics of chromophores is cumbersome. We used MSPAI and non-negative independent component analysis (ICA) to unmix distinct signal sources in human carotid plaques blindly. The feasibility of the method was demonstrated on a plaque phantom with hemorrhage and cholesterol inclusions, and plaque endarterectomy samples ex vivo. Furthermore, the results were verified with histology using Masson's trichrome staining. Results showed that ICA could separate recent hemorrhages from old hemorrhages. Additionally, the signatures of cholesterol inclusion were also captured for the phantom experiment. Artifacts were successfully removed from signal sources. Histologic examinations showed high resemblance with the unmixed components and confirmed the morphologic distinction between recent and mature hemorrhages. In future pre-clinical studies, unmixing could be used for morphology assessment of intact human plaque samples.

A geometry-based model for non-invasive estimation of pressure gradients over iliac artery stenoses.

The aim of this study was to develop and verify a model that provides an accurate estimation of the trans-lesion hyperemic pressure gradient in iliac artery stenoses in seconds by only using patient-specific geometric properties obtained from 3-dimensional rotational angiography (3DRA). Twenty-one patients with symptomatic peripheral arterial disease (PAD), iliac artery stenoses and an ultrasound based peak systolic velocity ratio between 2.5 and 5.0 underwent 3DRA and intra-arterial pressure measurements under hyperemic conditions. For each lesion, geometric properties were extracted from the 3DRA images using quantitative vascular analysis software. Hyperemic blood flow was estimated based on stenosis geometry using an empirical relation. The geometrical properties and hyperemic flow were used to estimate the pressure gradient by means of the geometry-based model. The predicted pressure gradients were compared with in vivo measured intra-arterial pressure measurements performed under hyperemic conditions. The developed geometry-based model showed good agreement with the measured hyperemic pressure gradients resulting in a concordance correlation coefficient of 0.86. The mean bias ±â€¯2SD between the geometry-based model and in vivo measurements was comparable to results found by evaluating the actual computational fluid dynamics model (-1.0 ±â€¯14.7 mmHg vs -0.9 ±â€¯12.7 mmHg). The developed model estimates the trans-lesional pressure gradient in seconds without the need for an additional computational fluid dynamics software package. The results justify further study to assess the potential use of a geometry-based model approach to estimate pressure gradient on non-invasive CTA or MRA, thereby reducing the need for diagnostic angiography in patients suffering from PAD.

The influence of model order reduction on the computed fractional flow reserve using parameterized coronary geometries.

Computational fluid dynamics (CFD) models combined with patient-specific imaging data are used to non-invasively predict functional significance of coronary lesions. This approach to predict the fractional flow reserve (FFR) is shown to have a high diagnostic accuracy when comparing against invasively measured FFR. However, one of the main drawbacks is the high computational effort needed for preprocessing and computations. Hence, uncertainty quantification may become unfeasible. Reduction of complexity is desirable, computationally inexpensive models with high diagnostic accuracy are preferred. We present a parametric comparison study for three types of CFD models (2D axisymmetric, Semi-3D and 3D) in which we study the impact of model reduction on three models on the predicted FFR. In total 200 coronary geometries were generated for seven geometrical characteristics e.g. stenosis severity, stenosis length and vessel curvature. The effect of time-averaged flow was investigated using unsteady, mean steady and a root mean square (RMS) steady flow. The 3D unsteady model was regarded as reference model. Results show that when using an unsteady or RMS flow, predicted FFR hardly varies between models contrary to using average flows. The 2D model with RMS flow has a high diagnostic accuracy (0.99), reduces computational time by a factor 162,000 and the introduced model error is well below the clinical relevant differences. Stenosis severity, length, curvature and tapering cause most discrepancies when using a lower order model. An uncertainty analysis showed that this can be explained by the low variability that is caused by variations in stenosis asymmetry.

Perfusion dynamics assessment with Power Doppler ultrasound in skeletal muscle during maximal and submaximal cycling exercise.

PURPOSE: Assessment of limitations in the perfusion dynamics of skeletal muscle may provide insight in the pathophysiology of exercise intolerance in, e.g., heart failure patients. Power doppler ultrasound (PDUS) has been recognized as a sensitive tool for the detection of muscle blood flow. In this volunteer study (N = 30), a method is demonstrated for perfusion measurements in the vastus lateralis muscle, with PDUS, during standardized cycling exercise protocols, and the test-retest reliability has been investigated. METHODS: Fixation of the ultrasound probe on the upper leg allowed for continuous PDUS measurements. Cycling exercise protocols included a submaximal and an incremental exercise to maximal power. The relative perfused area (RPA) was determined as a measure of perfusion. Absolute and relative reliability of RPA amplitude and kinetic parameters during exercise (onset, slope, maximum value) and recovery (overshoot, decay time constants) were investigated. RESULTS: A RPA increase during exercise followed by a signal recovery was measured in all volunteers. Amplitudes and kinetic parameters during exercise and recovery showed poor to good relative reliability (ICC ranging from 0.2-0.8), and poor to moderate absolute reliability (coefficient of variation (CV) range 18-60%). CONCLUSIONS: A method has been demonstrated which allows for continuous (Power Doppler) ultrasonography and assessment of perfusion dynamics in skeletal muscle during exercise. The reliability of the RPA amplitudes and kinetics ranges from poor to good, while the reliability of the RPA increase in submaximal cycling (ICC = 0.8, CV = 18%) is promising for non-invasive clinical assessment of the muscle perfusion response to daily exercise.

How to define the hemodynamic significance of an equivocal iliofemoral artery stenosis: Review of literature and outcomes of an international questionnaire.

Purpose The goal of the study was to review current literature regarding the diagnosis of equivocal (50-70%) iliofemoral artery stenosis and compare these findings with the daily practice of an international panel of endovascular experts. Methods The Medline Database was searched for relevant publications, and an electronic survey was sent to experts in the field covering the following topics: definition of an equivocal iliofemoral artery stenosis, angiographic visualization and investigation protocols of an equivocal stenosis, intra-arterial pressure measurements, and definition of hemodynamic significance of an equivocal iliofemoral artery stenosis using a physiologic measure. Results Of the 37 invited endovascular experts, 21 (53.8%) agreed to participate in the survey. Analysis of existing literature shows that the level of evidence for diagnosing equivocal iliofemoral artery stenosis is mediocre and is not being implemented by experts in the field. Conclusion Studies have shown that a stenosis of between 50% and 70% iliofemoral lumen diameter reduction shows a wide range of trans-stenotic pressure gradients. Equivocal iliofemoral artery stenosis can best be identified using three-dimensional quantitative vascular analysis software. Although evidence for a clear hemodynamic cutoff point is weak, performing trans-lesion intra-arterial pressure measurements at rest and during maximal hyperemia is preferred. Diagnosing iliofemoral artery stenosis solely on lumen diameter reduction is inadequate.

Patient Specific Wall Stress Analysis and Mechanical Characterization of Abdominal Aortic Aneurysms Using 4D Ultrasound.

OBJECTIVES: The aim of this study was to perform wall stress analysis (WSA) using 4D ultrasound (US) in 40 patients with an abdominal aortic aneurysm (AAA). The geometries and wall stress results were compared with computed tomography (CT) in seven patients. Additionally, the WSA models were calibrated using 4D motion estimation, resulting in patient specific material parameters that were compared among patients. METHODS: 4D-US images were acquired for 40 patients (AAA diameter 27-52 mm). Patient specific AAA geometries and wall motion were extracted from the 4D-US. WSA was performed and corresponding patient specific material properties were derived. For seven patients, CT data were available and analyzed for geometry and wall stress comparison. RESULTS: The 4D-US based 99th percentile wall stress ranged from 198 to 390 kPa. Regression analysis showed no significant relation between wall stress and diameter of the AAA. The similarity indices between US and CT were very good and ranged between 0.90 and 0.96, and the 25th, 50th, 75th, and 95th percentile wall stresses of the US and CT data were in agreement. The characterized patient specific shear modulus had a median of 1.1 MPa (interquartile range, 0.7-1.4 MPa). Based on the maximum AAA diameter, the AAAs were divided in a small, medium, and large diameter groups. The largest AAAs revealed an increased wall stiffness compared with the smallest AAAs. CONCLUSIONS: 4D ultrasound is applicable for wall stress analysis of AAAs, and offers the opportunity to perform wall stress analysis over time, also for AAAs who do not qualify for a CT or magnetic resonance imaging. Moreover, the patient specific material properties can be determined, which could possibly improve risk assessment.

Personalization of models with many model parameters: an efficient sensitivity analysis approach.

Uncertainty quantification and global sensitivity analysis are indispensable for patient-specific applications of models that enhance diagnosis or aid decision-making. Variance-based sensitivity analysis methods, which apportion each fraction of the output uncertainty (variance) to the effects of individual input parameters or their interactions, are considered the gold standard. The variance portions are called the Sobol sensitivity indices and can be estimated by a Monte Carlo (MC) approach (e.g., Saltelli's method [1]) or by employing a metamodel (e.g., the (generalized) polynomial chaos expansion (gPCE) [2, 3]). All these methods require a large number of model evaluations when estimating the Sobol sensitivity indices for models with many parameters [4]. To reduce the computational cost, we introduce a two-step approach. In the first step, a subset of important parameters is identified for each output of interest using the screening method of Morris [5]. In the second step, a quantitative variance-based sensitivity analysis is performed using gPCE. Efficient sampling strategies are introduced to minimize the number of model runs required to obtain the sensitivity indices for models considering multiple outputs. The approach is tested using a model that was developed for predicting post-operative flows after creation of a vascular access for renal failure patients. We compare the sensitivity indices obtained with the novel two-step approach with those obtained from a reference analysis that applies Saltelli's MC method. The two-step approach was found to yield accurate estimates of the sensitivity indices at two orders of magnitude lower computational cost.

A 1D pulse wave propagation model of the hemodynamics of calf muscle pump function.

The calf muscle pump is a mechanism which increases venous return and thereby compensates for the fluid shift towards the lower body during standing. During a muscle contraction, the embedded deep veins collapse and venous return increases. In the subsequent relaxation phase, muscle perfusion increases due to increased perfusion pressure, as the proximal venous valves temporarily reduce the distal venous pressure (shielding). The superficial and deep veins are connected via perforators, which contain valves allowing flow in the superficial-to-deep direction. The aim of this study is to investigate and quantify the physiological mechanisms of the calf muscle pump, including the effect of venous valves, hydrostatic pressure, and the superficial venous system. Using a one-dimensional pulse wave propagation model, a muscle contraction is simulated by increasing the extravascular pressure in the deep venous segments. The hemodynamics are studied in three different configurations: a single artery-vein configuration with and without valves and a more detailed configuration including a superficial vein. Proximal venous valves increase effective venous return by 53% by preventing reflux. Furthermore, the proximal valves shielding function increases perfusion following contraction. Finally, the superficial system aids in maintaining the perfusion during the contraction phase and reduces the refilling time by 37%.

A novel passive left heart platform for device testing and research.

Integration of biological samples into in vitro mock loops is fundamental to simulate real device's operating conditions. We developed an in vitro platform capable of simulating the pumping function of the heart through the external pressurization of the ventricle. The system consists of a fluid-filled chamber, in which the ventricles are housed and sealed to exclude the atria from external loads. The chamber is connected to a pump that drives the motion of the ventricular walls. The aorta is connected to a systemic impedance simulator, and the left atrium to an adjustable preload. The platform reproduced physiologic hemodynamics, i.e. aortic pressures of 120/80 mmHg with 5 L/min of cardiac output, and allowed for intracardiac endoscopy. A pilot study with a left ventricular assist device (LVAD) was also performed. The LVAD was connected to the heart to investigate aortic valve functioning at different levels of support. Results were consistent with the literature, and high speed video recordings of the aortic valve allowed for the visualization of the transition between a fully opening valve and a permanently closed configuration. In conclusion, the system showed to be an effective tool for the hemodynamic assessment of devices, the simulation of surgical or transcatheter procedures and for visualization studies.

Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model.

Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space.

A continuum model for platelet plug formation, growth and deformation.

A numerical framework for modelling platelet plug dynamics is presented in this work. It consists of an extension of a biochemical and plug growth model with a solid mechanics model for the plug coupled with a fluid-structure interaction model for the blood flow-plug system. The platelet plug is treated as a neo-Hookean elastic solid, of which the implementation is based on an updated Lagrangian approach. The framework is applied to different haemodynamic configurations coupled with different shear moduli of the plug. Results about plug growth, shape and size, as well as the stress distribution, are shown. Based on the simulations performed, we conclude that the deformability of the platelet plug is essential for its growth.

A mock circulation model for cardiovascular device evaluation.

The aim of this study was to develop an integrated mock circulation system that functions in a physiological manner for testing cardiovascular devices under well-controlled circumstances. In contrast to previously reported mock loops, the model includes a systemic, pulmonary, and coronary circulation, an elaborate heart contraction model, and a realistic heart rate control model. The behavior of the presented system was tested in response to changes in left ventricular contractile states, loading conditions, and heart rate. For validation purposes, generated hemodynamic parameters and responses were compared to literature. The model was implemented in a servo-motor driven mock loop, together with a relatively simple lead-lag controller. The pressure and flow signals measured closely mimicked human pressure under both physiological and pathological conditions. In addition, the system's response to changes in preload, afterload, and heart rate indicate a proper implementation of the incorporated feedback mechanisms (frequency and cardiac function control). Therefore, the presented mock circulation allows for generic in vitro testing of cardiovascular devices under well-controlled circumstances.

A continuum model for platelet plug formation and growth.

When the wall of a blood vessel is damaged, the immediate response of the body to prevent blood loss is the creation of a platelet plug. The process is both chemical (platelets are chemically activated to adhere to the injured wall) and mechanical (platelets are convected by blood flow, which interacts with the forming plug). A continuum model for platelet plug formation and growth is presented in this work, which allows to study the interaction between platelet plug morphology and local haemodynamics. The numerical framework consists of two parts: a biochemical model combined with a new plug growth model. The biochemical model is a system of convection-diffusion-reaction equations, each of which represents the dynamics of platelets and chemicals involved in the plug formation process. The plug growth model defines the plug interface displacement based on the outcome of the biochemical model, that is, on the number of deposited bounded platelets on the injured part of the vessel wall. Results for different cases are shown, together with a comparison between the sole biochemical model and the complete model that includes plug growth. The framework opens the way to the development of continuum models for full blood clot formation and growth in physiologically relevant configurations.