Simulation of blood flow in deformable vessels using subject-specific geometry and spatially varying wall properties

Uncertainty quantification of the impact of peripheral arterial disease on abdominal aortic aneurysms in blood flow simulations

Peripheral arterial disease (PAD) and abdominal aortic aneurysms (AAAs) often coexist and pose significant risks of mortality, yet their mutual interactions remain largely unexplored. Here, we introduce a fluid mechanics model designed to simulate the haemodynamic impact of PAD on AAA-associated risk factors. Our focus lies on quantifying the uncertainty inherent in controlling the flow rates within PAD-affected vessels and predicting AAA risk factors derived from wall shear stress. We perform a sensitivity analysis on nine critical model parameters through simulations of three-dimensional blood flow within a comprehensive arterial geometry. Our results show effective control of the flow rates using two-element Windkessel models, although specific outlets need attention. Quantities of interest like endothelial cell activation potential (ECAP) and relative residence time are instructive for identifying high-risk regions, with ECAP showing greater reliability and adaptability. Our analysis reveals that the uncertainty in the quantities of interest is 187% of that of the input parameters. Notably, parameters governing the amplitude and frequency of the inlet velocity exert the strongest influence on the risk factors' variability and warrant precise determination. This study forms the foundation for patient-specific simulations involving PAD and AAAs which should ultimately improve patient outcomes and reduce associated mortality rates.

Adaptive Doppler bio-signal detector and time-frequency representation based on non-Liènard oscillator

The work presented here provides the guidelines and results for designing and implementing a highly sensitive modified Van der Pol - Duffing oscillator with a trigonometric damping function (VTD). This VTD can exhibit periodic and quasi-chaotic behavior necessary for application in weak signal detection. Here, we present two proposals: (1) A method based on a quasi-chaotic intermittent array (ANLIOA), whose all VTD parameters are calculated and fine-tuned toward a critical state between chaotic and periodic state through a Lyapunov exponent procedure, and (2) A method based on a single oscillator in an adaptive stopping oscillation system (ANLSOS), where VTD is established within an oscillatory regime. Both systems can detect non-stationary signals while reconstructing the time-frequency spectrogram in high resolution within severe noise conditions. The systems were adapted for the detection of a synthesized Doppler signal corresponding to the blood flow velocity profile from an artery. Comparative results using typical oscillators such as Duffing or Van der Pol demonstrate the superiority of the VTD oscillator in detection when used for both methods, whose mean absolute percentage error reached around 6% for a signal-to-noise ratio (SNR) of -10 dB. Furthermore, compared to other time-frequency methods, ANLIOA and ANLSOS promise high precision in detecting Doppler signals with low rates of frequency changes while minimizing energy emission and avoiding possible bio-thermal effects.

Toward a Mesoscopic Modeling Approach of Magnetohydrodynamic Blood Flow in Pathological Vessels: A Comprehensive Review

The investigation of magnetohydrodynamic (MHD) blood flow within configurations that are pertinent to the human anatomy holds significant importance in the realm of scientific inquiry because of its practical implications within the medical field. This article presents an exhaustive appraisal of the diverse applications of magnetohydrodynamics and their computational modeling in biological contexts. These applications are classified into two categories: simple flow and pulsatile flow. An alternative approach of traditional CFD methods called Lattice Boltzmann Method (LBM), a mesoscopic method based on kinetic theory, is introduced to solve complex problems, such as hemodynamics. The results show that the flow velocity reduces considerably by increasing the magnetic field intensity, and the flow separation area is minimized by the increase of magnetic field strength. The LBM with BGK collision model has shown good results in terms of precision. Finally, this literature review has revealed a number of potential avenues for further research. Suggestions for future works are proposed accordingly.

Bio-inspired microfluidics: A review

Biomicrofluidics, a subdomain of microfluidics, has been inspired by several ideas from nature. However, while the basic inspiration for the same may be drawn from the living world, the translation of all relevant essential functionalities to an artificially engineered framework does not remain trivial. Here, we review the recent progress in bio-inspired microfluidic systems via harnessing the integration of experimental and simulation tools delving into the interface of engineering and biology. Development of "on-chip" technologies as well as their multifarious applications is subsequently discussed, accompanying the relevant advancements in materials and fabrication technology. Pointers toward new directions in research, including an amalgamated fusion of data-driven modeling (such as artificial intelligence and machine learning) and physics-based paradigm, to come up with a human physiological replica on a synthetic bio-chip with due accounting of personalized features, are suggested. These are likely to facilitate physiologically replicating disease modeling on an artificially engineered biochip as well as advance drug development and screening in an expedited route with the minimization of animal and human trials.

The study on the impact of AAA wall motion on the hemodynamics based on 4D CT image data

Purpose: To analyze the effect of the physiological deformation of the vessel wall on the hemodynamics in the abdominal aortic aneurysm (AAA), this paper compared the hemodynamics in AAA based on the moving boundary (MB) simulation and the rigid wall (RW) simulation.

Method: Patient-specific models were reconstructed to generate mesh based on four-dimensional computed tomography angiography (4D CT) data. The dynamic mesh technique was used to achieve deformation of the vessel wall, surface mesh and volume mesh of the fluid domain were successively remeshed at each time step. Besides, another rigid wall simulation was performed. Hemodynamics obtained from these two simulations were compared.

Results: Flow field and wall shear stress (WSS) distribution are similar. When using the moving boundary method (MBM), mean time-averaged wall shear stress (TAWSS) is lower, mean oscillatory shear index (OSI) and mean relative residence time (RRT) are higher. When using the 10th and 20th percentile values for TAWSS and 80th and 90th percentile values for RRT, the ratios of areas with low TAWSS, high OSI and high RRT to the entire vessel wall are higher than those assuming the vessel as rigid. In addition, one overlapping region of low TAWSS, high OSI and high RRT by using the MBM is consistent with the location of thrombus obtained from the follow-up imaging data.

Conclusion: The hemodynamics results by using the MBM reflect a higher blood retention effect. This paper presents a potential tool to assess the risk of intraluminal thrombus (ILT) formation based on the MBM.

A Novel Computational Biomechanics Framework to Model Vascular Mechanopropagation in Deep Bone Marrow

The mechanical stimuli generated by body exercise can be transmitted from cortical bone into the deep bone marrow (mechanopropagation). Excitingly, a mechanosensitive perivascular stem cell niche is recently identified within the bone marrow for osteogenesis and lymphopoiesis. Although it is long known that they are maintained by exercise-induced mechanical stimulation, the mechanopropagation from compact bone to deep bone marrow vasculature remains elusive of this fundamental mechanobiology field. No experimental system is available yet to directly understand such exercise-induced mechanopropagation at the bone-vessel interface. To this end, taking advantage of the revolutionary in vivo 3D deep bone imaging, an integrated computational biomechanics framework to quantitatively evaluate the mechanopropagation capabilities for bone marrow arterioles, arteries, and sinusoids is devised. As a highlight, the 3D geometries of blood vessels are smoothly reconstructed in the presence of vessel wall thickness and intravascular pulse pressure. By implementing the 5-parameter Mooney-Rivlin model that simulates the hyperelastic vessel properties, finite element analysis to thoroughly investigate the mechanical effects of exercise-induced intravascular vibratory stretching on bone marrow vasculature is performed. In addition, the blood pressure and cortical bone bending effects on vascular mechanoproperties are examined. For the first time, movement-induced mechanopropagation from the hard cortical bone to the soft vasculature in the bone marrow is numerically simulated. It is concluded that arterioles and arteries are much more efficient in propagating mechanical force than sinusoids due to their stiffness. In the future, this in-silico approach can be combined with other clinical imaging modalities for subject/patient-specific vascular reconstruction and biomechanical analysis, providing large-scale phenotypic data for personalized mechanobiology discovery.

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.

An in silico validation framework for quantitative DCE-MRI techniques based on a dynamic digital phantom

Quantitative evaluation of an image processing method to perform as designed is central to both its utility and its ability to guide the data acquisition process. Unfortunately, these tasks can be quite challenging due to the difficulty of experimentally obtaining the "ground truth" data to which the output of a given processing method must be compared. One way to address this issue is via "digital phantoms", which are numerical models that provide known biophysical properties of a particular object of interest.  In this contribution, we propose an in silico validation framework for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) acquisition and analysis methods that employs a novel dynamic digital phantom. The phantom provides a spatiotemporally-resolved representation of blood-interstitial flow and contrast agent delivery, where the former is solved by a 1D-3D coupled computational fluid dynamic system, and the latter described by an advection-diffusion equation. Furthermore, we establish a virtual simulator which takes as input the digital phantom, and produces realistic DCE-MRI data with controllable acquisition parameters. We assess the performance of a simulated standard-of-care acquisition (Protocol A) by its ability to generate contrast-enhanced MR images that separate vasculature from surrounding tissue, as measured by the contrast-to-noise ratio (CNR). We find that the CNR significantly decreases as the spatial resolution (SRA, where the subscript indicates Protocol A) or signal-to-noise ratio (SNRA) decreases. Specifically, with an SNRA / SRA = 75 dB / 30 μm, the median CNR is 77.30, whereas an SNRA / SRA = 5 dB / 300 μm reduces the CNR to 6.40. Additionally, we assess the performance of simulated ultra-fast acquisition (Protocol B) by its ability to generate DCE-MR images that capture contrast agent pharmacokinetics, as measured by error in the signal-enhancement ratio (SER) compared to ground truth (PESER). We find that PESER significantly decreases the as temporal resolution (TRB) increases. Similar results are reported for the effects of spatial resolution and signal-to-noise ratio on PESER. For example, with an SNRB / SRB / TRB = 5 dB / 300 μm / 10 s, the median PESER is 21.00%, whereas an SNRB / SRB / TRB = 75 dB / 60 μm / 1 s, yields a median PESER of 0.90%. These results indicate that our in silico framework can generate virtual MR images that capture effects of acquisition parameters on the ability of generated images to capture morphological or pharmacokinetic features. This validation framework is not only useful for investigations of perfusion-based MRI techniques, but also for the systematic evaluation and optimization new MRI acquisition, reconstruction, and image processing techniques.

Generation of Augmented Capillary Network Optical Coherence Tomography Image Data of Human Skin for Deep Learning and Capillary Segmentation

The segmentation of capillaries in human skin in full-field optical coherence tomography (FF-OCT) images plays a vital role in clinical applications. Recent advances in deep learning techniques have demonstrated a state-of-the-art level of accuracy for the task of automatic medical image segmentation. However, a gigantic amount of annotated data is required for the successful training of deep learning models, which demands a great deal of effort and is costly. To overcome this fundamental problem, an automatic simulation algorithm to generate OCT-like skin image data with augmented capillary networks (ACNs) in a three-dimensional volume (which we called the ACN data) is presented. This algorithm simultaneously acquires augmented FF-OCT and corresponding ground truth images of capillary structures, in which potential functions are introduced to conduct the capillary pathways, and the two-dimensional Gaussian function is utilized to mimic the brightness reflected by capillary blood flow seen in real OCT data. To assess the quality of the ACN data, a U-Net deep learning model was trained by the ACN data and then tested on real in vivo FF-OCT human skin images for capillary segmentation. With properly designed data binarization for predicted image frames, the testing result of real FF-OCT data with respect to the ground truth achieved high scores in performance metrics. This demonstrates that the proposed algorithm is capable of generating ACN data that can imitate real FF-OCT skin images of capillary networks for use in research and deep learning, and that the model for capillary segmentation could be of wide benefit in clinical and biomedical applications.

Measuring wall shear stress distribution in the carotid artery in an African population: Computational fluid dynamics versus ultrasound doppler velocimetry

INTRODUCTION

Computational fluid dynamics (CFD) and ultrasound Doppler velocimetry are diagnostic tools useful for determining carotid artery segments susceptible to atheromatous plaque development. This study computes and compares the difference in Wall Shear Stress (WSS) measurements between these two methods.

METHODS

The carotid artery of 204 volunteers selected using simple random sampling were scanned using standard carotid doppler protocols. Four segments of the carotid artery - the common, internal, external carotid, and the carotid bulb were sonographically assessed. The intima-media thickness, diameter, peak systolic velocity, and end-diastolic velocity were measured at a point 2 cm away from the carotid bifurcation for the three segments, while the carotid bulb was measured at the bifurcation. A 2D incompressible Navier-Stokes Equation for modelling Newtonian, pulsatile, and laminar flow in a viscoelastic pipe was applied to model velocity flow across the carotid artery using COMSOL software. WSS values were computed for experimental and CFD measurements and the results were compared.

RESULTS

The WSS values generated by the model had respectively peak and average values of 19.81 N/cm² and 15.76 ± 1.81 N/cm² for the common carotid, 10.77 N/cm² and 7.57 ± 1.66 N/cm² for the internal carotid, 11.51 N/cm² and 8.05 ± 1.65 N/cm² for the external carotid, 37.55 N/cm² and 26.55 ± 6.62 N/cm² for the carotid bifurcation, 1.39 N/cm² and 3.13 ± 1.34 N/cm² for the carotid bulb. The model measurements matched doppler velocimetry measurements with <15% variation.

CONCLUSION

Model based WSS values were higher but comparable with doppler velocimetry measurements. The carotid bulb had low WSS and is therefore the segment highly disposed to atheromatous plaque formation.

IMPLICATIONS FOR PRACTICE

Subject-specific mathematical models could be incorporated during cardiovascular scan work up for accurate WSS distribution and early prediction of possible atherosclerotic sites.

Haemodynamic assessment of bicuspid aortic valve aortopathy: a systematic review of the current literature

Both genetic and haemodynamic theories explain the aetiology, progression and optimal management of bicuspid aortic valve aortopathy. In recent years, the haemodynamic theory has been explored with the help of magnetic resonance imaging and computational fluid dynamics. The objective of this review was to summarize the findings of these investigations with focus on the blood flow pattern and associated variables, including flow eccentricity, helicity, flow displacement, cusp opening angle, systolic flow angle, wall shear stress (WSS) and oscillatory shear index. A structured literature review was performed from January 1990 to January 2018 and revealed the following 3 main findings: (i) the bicuspid aortic valve is associated with flow eccentricity and helicity in the ascending aorta compared to healthy and diseased tricuspid aortic valve, (ii) flow displacement is easier to obtain than WSS and has been shown to correlate with valve morphology and type of aortopathy and (iii) the stenotic bicuspid aortic valve is associated with elevated WSS along the greater curvature of the ascending aorta, where aortic dilatation and aortic wall thinning are commonly found. We conclude that new haemodynamic variables should complement ascending aorta diameter as an indicator for disease progression and the type and timing of intervention. WSS describes the force that blood flow exerts on the vessel wall as a function of viscosity and geometry of the vessel, making it a potentially more reliable marker of disease progression.

Kouzani A, Mosadegh B, Gharaie S. Blood Pressure Sensors: Materials, Fabrication Methods, Performance Evaluations and Future Perspectives

Advancements in materials science and fabrication techniques have contributed to the significant growing attention to a wide variety of sensors for digital healthcare. While the progress in this area is tremendously impressive, few wearable sensors with the capability of real-time blood pressure monitoring are approved for clinical use. One of the key obstacles in the further development of wearable sensors for medical applications is the lack of comprehensive technical evaluation of sensor materials against the expected clinical performance. Here, we present an extensive review and critical analysis of various materials applied in the design and fabrication of wearable sensors. In our unique transdisciplinary approach, we studied the fundamentals of blood pressure and examined its measuring modalities while focusing on their clinical use and sensing principles to identify material functionalities. Then, we carefully reviewed various categories of functional materials utilized in sensor building blocks allowing for comparative analysis of the performance of a wide range of materials throughout the sensor operational-life cycle. Not only this provides essential data to enhance the materials' properties and optimize their performance, but also, it highlights new perspectives and provides suggestions to develop the next generation pressure sensors for clinical use.

Flow and deformation characteristics of a flexible microfluidic channel with axial gradients in wall elasticity

Axial gradients in wall elasticity may have significant implications in the deformation and flow characteristics of a narrow fluidic conduit, bearing far-reaching consequences in physiology and bio-engineering. Here, we present a theoretical and experimental framework for fluid-structure interactions in microfluidic channels with axial gradients in wall elasticity, in an effort to arrive at a potential conceptual foundation for in vitro study of mirovascular physiology. Towards this, we bring out the static deformation and steady flow characteristics of a circular microchannel made of polydimethylsiloxane (PDMS) bulk, considering imposed gradients in the substrate elasticity. In particular, we study two kinds of elasticity variations - a uniformly soft (or hard) channel with a central strip that is hard (or soft), and, increasing elasticity along the length of the channel. The former kind yields a centrally constricted (or expanded) deformed profile in response to the flow. The latter kind leads to increasingly bulged channel radius from inlet to outlet in response to flow. We also formulate an analytical model capturing the essential physics of the underlying elastohydrodynamic interactions. The theoretical predictions match favourably with the experimental observations and are also in line with reported results on stenosis in mice. The present framework, thus, holds the potential for acting as a fundamental design basis towards developing in vitro models for micro-circulation, capable of capturing exclusive artefacts of healthy and diseased conditions.

Computational fluid dynamic-derived wall shear stress of non-significant left main bifurcation disease may predict acute vessel thrombosis at 3-year follow-up

Wall shear stress (WSS) plays a pivotal role on plaque progression in coronary artery disease. We assess the prognostic role of baseline mean WSS in developing a bifurcation-located myocardial infarction (B-MI) over the following 3 years in angiographically non-significant LM bifurcation disease. For this purpose, we retrospectively reviewed the procedural and medical records of consecutive patients evaluated in our center from 1st January 2014 to 1st January 2019 who had a non-significant LM bifurcation disease as evaluated at coronary computed tomography angiography (CCTA) and confirmed by coronary angiography. Each bifurcation model was reconstructed on the patient-specific geometries derived from the CCTA. The population was divided into two groups: patients with (n = 12) and without B-MI (n = 20) over the following 3 years. Both the mean WSSprox of each branch and the WSSentire_lesion of each vessel, adjusted for the respective mean lesions lengths and 3-dimensional percentage of stenosis (DS%), resulted in independent predictors of 3-year B-MI. Multivariate Cox-regression analysis confirmed that a baseline mean WSSentire_model ≥ 5.05 Pa (HR 1.98, 95% CI 1.83-2.10, p = 0.001) was a predictor of 3-year B-MI independently from the entire mean lesions lengths (HR 1.56. 95% CI 1.43.1.68, p = 0.002) and DS% (HR 1.26, 95% CI 1.18-1.37, p = 0.03). In conclusion, in patients with angiographically non-significant LM bifurcation disease, both the mean WSSprox of each branch and WSSentire_lesion of each stenotic vessel predicted the occurrence of B-MI over the following 3 years. Moreover, the WSSentire_bifurcation ≥ 5.05 Pa seems to be a predictor of 3-year B-MI independently from the DS% and lesions lengths.

Personalized stent design for congenital heart defects using pulsatile blood flow simulations

Stent size selection and placement are among the most challenging tasks in the treatment of pulmonary artery stenosis in congenital heart defects (CHD). Patient-specific 3D model from CT or MR improves the understanding of the patient's anatomy and information about the hemodynamics aid in patient risk assessment and treatment planning. This work presents a new approach for personalized stent design in pulmonary artery interventions combining personalized patient geometry and hemodynamic simulations. First, the stent position is initialized using a geometric approach. Second, the stent and artery expansion, including the foreshortening behavior of the stent is simulated. Two stent designs are considered, a regular stent and a Y-stent for bifurcations. Computational fluid dynamics (CFD) simulations of the blood flow in the initial and expanded artery models are performed using patient-specific boundary conditions in form of a pulsatile inflow waveform, 3-element Windkessel outflow conditions, and deformable vessel walls. The simulations have been applied to 16 patient cases with a large variability of anatomies. Finally, the simulations have been clinically validated using retrospective imaging from angiography and pressure measurements. The simulated pressure, volume flow and flow velocity values were on the same order of magnitude as the reference values obtained from clinical measurements, and the simulated stent placement showed a positive impact on the hemodynamic values. Simulation of geometric changes combined with CFD simulations offers the possibility to optimize stent type, size, and position by evaluating different configurations before the intervention, and eventually allow to test customized stent geometries and new deployment techniques in CHD.

Impact of Patient-Specific Inflow Velocity Profile on Hemodynamics of the Thoracic Aorta

Computational fluid dynamics (CFD) provides a noninvasive method to functionally assess aortic hemodynamics. The thoracic aorta has an anatomically complex inlet comprising of the aortic valve and root, which is highly prone to different morphologies and pathologies. We investigated the effect of using patient-specific (PS) inflow velocity profiles compared to idealized profiles based on the patient's flow waveform. A healthy 31 yo with a normally functioning tricuspid aortic valve (subject A), and a 52 yo with a bicuspid aortic valve (BAV), aortic valvular stenosis, and dilated ascending aorta (subject B) were studied. Subjects underwent MR angiography to image and reconstruct three-dimensional (3D) geometric models of the thoracic aorta. Flow-magnetic resonance imaging (MRI) was acquired above the aortic valve and used to extract the patient-specific velocity profiles. Subject B's eccentric asymmetrical inflow profile led to highly complex velocity patterns, which were not replicated by the idealized velocity profiles. Despite having identical flow rates, the idealized inflow profiles displayed significantly different peak and radial velocities. Subject A's results showed some similarity between PS and parabolic inflow profiles; however, other parameters such as Flowasymmetry were significantly different. Idealized inflow velocity profiles significantly alter velocity patterns and produce inaccurate hemodynamic assessments in the thoracic aorta. The complex structure of the aortic valve and its predisposition to pathological change means the inflow into the thoracic aorta can be highly variable. CFD analysis of the thoracic aorta needs to utilize fully PS inflow boundary conditions in order to produce truly meaningful results.

Functional assessment of thoracic aortic aneurysms - the future of risk prediction?

INTRODUCTION

Treatment guidelines for the thoracic aorta concentrate on size, yet acute aortic dissection or rupture can occur when aortic size is below intervention criteria. Functional imaging and computational techniques are a means of assessing haemodynamic parameters involved in aortic pathology.

SOURCES OF DATA

Original articles, reviews, international guidelines.

AREAS OF AGREEMENT

Computational fluid dynamics and 4D flow MRI allow non-invasive assessment of blood flow parameters and aortic wall biomechanics.

AREAS OF CONTROVERSY

Aortic valve morphology (particularly bicuspid aortic valve) is associated with aneurysm of the ascending aorta, although the exact mechanism of aneurysm formation is not yet established.

GROWING POINTS

Haemodynamic assessment of the thoracic aorta has highlighted parameters which are linked with both clinical outcome and protein changes in the aortic wall. Wall shear stress, flow displacement and helicity are elevated in patients with bicuspid aortic valve, particularly at locations of aneurysm formation.

AREAS TIMELY FOR DEVELOPING RESEARCH

With further validation, functional assessment of the aorta may help identify patients at risk of aortic complications, and introduce new haemodynamic indices into management guidelines.

A PIV COMPARISON OF THE FLOW FIELD AND WALL SHEAR STRESS IN RIGID AND COMPLIANT MODELS OF HEALTHY CAROTID ARTERIES

Certain systems relevant to circulatory disease have walls which are neither rigid nor static, for example, the coronary arteries, the carotid artery and the heart chambers. In vitro modeling allows the fluid mechanics of the circulatory system to be studied without the ethical and safety issues associated with animal and human experiments. Computational methods in which the equations are coupled governing the flow and the elastic walls are maturing. Currently there is a lack of experimental data in compliant arterial systems to validate the numerical predictions. Previous experimental work has commonly used rigid wall boundaries, ignoring the effect of wall compliance. Particle Image Velocimetry is used to provide a direct comparison of both the flow field and wall shear stress (WSS) observed in experimental phantoms of rigid and compliant geometries representing an idealized common carotid artery. The input flow waveform and the mechanical response of the phantom are physiologically realistic. The results show that compliance affects the velocity profile within the artery. A rigid boundary causes severe overestimation of the peak WSS with a maximum relative difference of 61% occurring; showing compliance protects the artery from exposure to high magnitude WSS. This is important when trying to understand the development of diseases like atherosclerosis. The maximum, minimum and time averaged WSS in the rigid geometry was 2.3, 0.51 and 1.03[Formula: see text]Pa and in the compliant geometry 1.4, 0.58 and 0.84[Formula: see text]Pa, respectively.

Systems biology of the microvasculature

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell-cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.

Numerical simulation of the fluid structure interactions in a compliant patient-specific arteriovenous fistula

The objective of the study is to investigate numerically the fluid-structure interactions (FSI) in a patient-specific arteriovenous fistula (AVF) and analyze the degree of complexity that such a numerical simulation requires to provide clinically relevant information. The reference FSI simulation takes into account the non-Newtonian behavior of blood, as well as the variation in mechanical properties of the vascular walls along the AVF. We have explored whether less comprehensive versions of the simulation could still provide relevant results. The non-Newtonian blood model is necessary to predict the hemodynamics in the AVF because of the predominance of low shear rates in the vein. An uncoupled fluid simulation provides informative qualitative maps of the hemodynamic conditions in the AVF; quantitatively, the hemodynamic parameters are accurate within 20% maximum. Conversely, an uncoupled structural simulation with non-uniform wall properties along the vasculature provides the accurate distribution of internal wall stresses, but only at one instant of time within the cardiac cycle. The FSI simulation advantageously provides the time-evolution of both the hemodynamic and structural stresses. However, the higher computational cost renders a clinical use still difficult in routine.

A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models

We present a systematic comparison of computational hemodynamics in arteries between a one-dimensional (1-D) and a three-dimensional (3-D) formulation with deformable vessel walls. The simulations were performed using a series of idealized compliant arterial models representing the common carotid artery, thoracic aorta, aortic bifurcation, and full aorta from the arch to the iliac bifurcation. The formulations share identical inflow and outflow boundary conditions and have compatible material laws. We also present an iterative algorithm to select the parameters for the outflow boundary conditions by using the 1-D theory to achieve a desired systolic and diastolic pressure at a particular vessel. This 1-D/3-D framework can be used to efficiently determine material and boundary condition parameters for 3-D subject-specific arterial models with deformable vessel walls. Finally, we explore the impact of different anatomical features and hemodynamic conditions on the numerical predictions. The results show good agreement between the two formulations, especially during the diastolic phase of the cycle.

A computational framework for investigating the positional stability of aortic endografts

Endovascular aneurysm repair (Greenhalgh in N Engl J Med 362(20):1863-1871, 2010) techniques have revolutionized the treatment of thoracic and abdominal aortic aneurysm disease, greatly reducing the perioperative mortality and morbidity associated with open surgical repair techniques. However, EVAR is not free of important complications such as late device migration, endoleak formation and fracture of device components that may result in adverse events such as aneurysm enlargement, need for long-term imaging surveillance and secondary interventions or even death. These complications result from the device inability to withstand the hemodynamics of blood flow and to keep its originally intended post-operative position over time. Understanding the in vivo biomechanical working environment experienced by endografts is a critical factor in improving their long-term performance. To date, no study has investigated the mechanics of contact between device and aorta in a three-dimensional setting. In this work, we developed a comprehensive Computational Solid Mechanics and Computational Fluid Dynamics framework to investigate the mechanics of endograft positional stability. The main building blocks of this framework are: (1) Three-dimensional non-planar aortic and stent-graft geometrical models, (2) Realistic multi-material constitutive laws for aorta, stent, and graft, (3) Physiological values for blood flow and pressure, and (4) Frictional model to describe the contact between the endograft and the aorta. We introduce a new metric for numerical quantification of the positional stability of the endograft. Lastly, in the results section, we test the framework by investigating the impact of several factors that are clinically known to affect endograft stability.

Capillary networks in tumor angiogenesis: from discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis

Tumor angiogenesis, the growth of new capillaries from preexisting ones promoted by the starvation and hypoxia of cancerous cell, creates complex biological patterns. These patterns are captured by a hybrid model that involves high-order partial differential equations coupled with mobile, agent-based components. The continuous equations of the model rely on the phase-field method to describe the intricate interfaces between the vasculature and the host tissue. The discrete equations are posed on a cellular scale and treat tip endothelial cells as mobile agents. Here, we put the model into a coherent mathematical and algorithmic framework and introduce a numerical method based on isogeometric analysis that couples the discrete and continuous descriptions of the theory. Using our algorithms, we perform numerical simulations that show the development of the vasculature around a tumor. The new method permitted us to perform a parametric study of the model. Furthermore, we investigate different initial configurations to study the growth of the new capillaries. The simulations illustrate the accuracy and efficiency of our numerical method and provide insight into the dynamics of the governing equations as well as into the underlying physical phenomenon.

Flow-induced ATP release in patient-specific arterial geometries--a comparative study of computational models

The importance of the endothelium in the local regulation of blood flow is reflected by its influence on vascular tone by means of vasodilatory responses to many physiological stimuli. Regulatory pathways are affected by mass transport and wall shear stress (WSS), via mechanotransduction mechanisms. In the present work, we review the most relevant computational models that have been proposed to date, and introduce a general framework for modelling the responses of the endothelium to alteration in the flow, with a view to understanding the biomechanical processes involved in the pathways to endothelial dysfunction. Simulations are performed on two different patient-specific stenosed carotid artery geometries to investigate the influence of WSS and mass transport phenomena upon the agonist coupling response at the endothelium. In particular, results presented for two different models of WSS-dependent adenosine-5'-triphosphate (ATP) release reveal that existing paradigms may not account for the conditions encountered in vivo and may therefore not be adequate to model the kinetics of ATP at the endothelium.

Simulation based planning of surgical interventions in pediatric cardiology

Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.

Understanding the role of hemodynamics in the initiation, progression, rupture, and treatment outcome of cerebral aneurysm from medical image-based computational studies

About a decade ago, the first image-based computational hemodynamic studies of cerebral aneurysms were presented. Their potential for clinical applications was the result of a right combination of medical image processing, vascular reconstruction, and grid generation techniques used to reconstruct personalized domains for computational fluid and solid dynamics solvers and data analysis and visualization techniques. A considerable number of studies have captivated the attention of clinicians, neurosurgeons, and neuroradiologists, who realized the ability of those tools to help in understanding the role played by hemodynamics in the natural history and management of intracranial aneurysms. This paper intends to summarize the most relevant results in the field reported during the last years.

Lagrangian analysis of hemodynamics data from FSI simulation

We present the computation of lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid-structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in lagrangian measures of the flow between deformable and rigid-vessel models was observed.

An improved baseline model for a human arterial network to study the impact of aneurysms on pressure-flow waveforms

In this study, an improved and robust one-dimensional human arterial network model is presented. The one-dimensional blood flow equations are solved using the Taylor-locally conservative Galerkin finite element method. The model improvements are carried out by adopting parts of the physical models from different authors to establish an accurate baseline model. The predicted pressure-flow waveforms at various monitoring positions are compared against in vivo measurements from published works. The results obtained show that wave shapes predicted are similar to that of the experimental data and exhibit a good overall agreement with measured waveforms. Finally, computational studies on the influence of an abdominal aortic aneurysm are presented. The presence of aneurysms results in a significant change in the waveforms throughout the network.

Modeling and Simulation of 4D PET-CT and PET-MR Images

The driving force in the research and development of new hybrid PET-CT/MR imaging scanners is the production of images with optimum quality, accuracy, and resolution. However, the acquisition process is limited by several factors. Key issues are the respiratory and cardiac motion artifacts that occur during an imaging session. In this article the necessary tools for modeling and simulation of realistic high-resolution four-dimensional PET-CT and PET-MR imaging data are described. Beyond the need for four-dimensional simulations, accurate modeling of the acquisition process can be included within the reconstruction algorithms assisting in the improvement of image quality and accuracy of estimation of physiologic parameters from four-dimensional hybrid PET imaging.

Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data

Viscoelastic support has been previously established as a valuable modeling ingredient to represent the effect of surrounding tissues and organs in a fluid-structure vascular model. In this paper, we propose a complete methodological chain for the identification of the corresponding boundary support parameters, using patient image data. We consider distance maps of model to image contours as the discrepancy driving the data assimilation approach, which then relies on a combination of (1) state estimation based on the so-called SDF filtering method, designed within the realm of Luenberger observers and well adapted to handling measurements provided by image sequences, and (2) parameter estimation based on a reduced-order UKF filtering method which has no need for tangent operator computations and features natural parallelism to a high degree. Implementation issues are discussed, and we show that the resulting computational effectiveness of the complete estimation chain is comparable to that of a direct simulation. Furthermore, we demonstrate the use of this framework in a realistic application case involving hemodynamics in the thoracic aorta. The estimation of the boundary support parameters proves successful, in particular in that direct modeling simulations based on the estimated parameters are more accurate than with a previous manual expert calibration. This paves the way for complete patient-specific fluid-structure vascular modeling in which all types of available measurements could be used to estimate additional uncertain parameters of biophysical and clinical relevance.

Fluid-structure interaction simulations of the Fontan procedure using variable wall properties

Children born with single ventricle heart defects typically undergo a staged surgical procedure culminating in a total cavopulmonary connection (TCPC) or Fontan surgery. The goal of this work was to perform physiologic, patient-specific hemodynamic simulations of two post-operative TCPC patients by using fluid-structure interaction (FSI) simulations. Data from two patients are presented, and post-op anatomy is reconstructed from MRI data. Respiration rate, heart rate, and venous pressures are obtained from catheterization data, and inflow rates are obtained from phase contrast MRI data and are used together with a respiratory model. Lumped parameter (Windkessel) boundary conditions are used at the outlets. We perform FSI simulations by using an arbitrary Lagrangian-Eulerian finite element framework to account for motion of the blood vessel walls in the TCPC. This study is the first to introduce variable elastic properties for the different areas of the TCPC, including a Gore-Tex conduit. Quantities such as wall shear stresses and pressures at critical locations are extracted from the simulation and are compared with pressure tracings from clinical data as well as with rigid wall simulations. Hepatic flow distribution and energy efficiency are also calculated and compared for all cases. There is little effect of FSI on pressure tracings, hepatic flow distribution, and time-averaged energy efficiency. However, the effect of FSI on wall shear stress, instantaneous energy efficiency, and wall motion is significant and should be considered in future work, particularly for accurate prediction of thrombus formation.

Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation

Mounting evidence suggests that the pulsatile character of blood pressure and flow within large arteries plays a particularly important role as a mechano-biological stimulus for wall growth and remodeling. Nevertheless, understanding better the highly coupled interactions between evolving wall geometry, structure, and properties and the hemodynamics will require significantly more experimental data. Computational fluid-solid-growth models promise to aid in the design and interpretation of such experiments and to identify candidate mechanobiological mechanisms for the observed arterial adaptations. Motivated by recent aortic coarctation models in animals, we used a computational fluid-solid interaction model to study possible local and systemic effects on the hemodynamics within the thoracic aorta and coronary, carotid, and cerebral arteries due to a distal aortic coarctation and subsequent spatial variations in wall adaptation. In particular, we studied an initial stage of acute cardiac compensation (i.e., maintenance of cardiac output) followed by early arterial wall remodeling (i.e., spatially varying wall thickening and stiffening). Results suggested, for example, that while coarctation increased both the mean and pulse pressure in the proximal vessels, the locations nearest to the coarctation experienced the greatest changes in pulse pressure. In addition, after introducing a spatially varying wall adaptation, pressure, left ventricular work, and wave speed all increased. Finally, vessel wall strain similarly experienced spatial variations consistent with the degree of vascular wall adaptation.

Virtual Interventions for Image-based Blood Flow Computation

Image-based blood flow computation provides great promise for evaluation of vascular devices and assessment of surgical procedures. However, many previous studies employ idealized arterial and device models or only patient-specific models from the image data after device deployment, since the tools for model construction are unavailable or limited and tedious to use. Moreover, in contrast to retrospective studies from existing data, there is a pressing need for prospective analysis with the goal of surgical planning. Therefore, it is necessary to construct models with deployed devices in a fast, virtual and interactive fashion. The goal of this paper is to develop new geometric methods to deploy stents or stent grafts virtually to patient-specific geometric models constructed from a 3D segmentation of medical images. A triangular surface representing the vessel lumen boundary is extracted from the segmentation. The diseased portion is either clipped and replaced by the surface of a deployed device or rerouted in the case of a bypass graft. For diseased arteries close to bifurcations, bifurcated device models are generated. A method to map a 2D strut pattern on the surface of a device is also presented. We demonstrate three applications of our methods in personalized surgical planning for aortic aneurysms, aortic coarctation, and coronary artery stenosis using blood flow computation. Our approach enables prospective model construction and may help to expand the throughput required by routine clinical uses in the future.

Computational analysis of stresses acting on intermodular junctions in thoracic aortic endografts

PURPOSE

To evaluate the biomechanical and hemodynamic forces acting on the intermodular junctions of a multi-component thoracic endograft and elucidate their influence on the development of type III endoleak due to disconnection of stent-graft segments.

METHODS

Three-dimensional computer models of the thoracic aorta and a 4-component thoracic endograft were constructed using postoperative (baseline) and follow-up computed tomography (CT) data from a 69-year-old patient who developed type III endoleak 4 years after stent-graft placement. Computational fluid dynamics (CFD) techniques were used to quantitate the displacement forces acting on the device. The contact stresses between the different modules of the graft were then quantified using computational solid mechanics (CSM) techniques. Lastly, the intermodular junction frictional stability was evaluated using a Coulomb model.

RESULTS

The CFD analysis revealed that curvature and length are key determinants of the displacement forces experienced by each endograft and that the first 2 modules were exposed to displacement forces acting in opposite directions in both the lateral and longitudinal axes. The CSM analysis revealed that the highest concentration of stresses occurred at the junction between the first and second modules of the device. Furthermore, the frictional analysis demonstrated that most of the surface area (53%) of this junction had unstable contact. The predicted critical zone of intermodular stress concentration and frictional instability matched the location of the type III endoleak observed in the 4-year follow-up CT image.

CONCLUSION

The region of larger intermodular stresses and highest frictional instability correlated with the zone where a type III endoleak developed 4 years after thoracic stent-graft placement. Computational techniques can be helpful in evaluating the risk of endograft migration and potential for modular disconnection and may be useful in improving device placement strategies and endograft design.

Evaluating Design of Abdominal Aortic Aneurysm Endografts in a Patient-Specific Model Using Computational Fluid Dynamics

Computer modeling of blood flow in patient-specific anatomies can be a powerful tool for evaluating the design of implantable medical devices. We assessed three different endograft designs, which are implantable devices commonly used to treat patients with abdominal aortic aneurysms (AAAs). Once implanted, the endograft may shift within the patient’s aorta allowing blood to flow into the aneurismal sac. One potential cause for this movement is the pulsatile force experienced by the endograft over the cardiac cycle. We used contrast-enhanced computed tomography angiography (CTA) data from four patients with diagnosed AAAs to build patient-specific models using 3D segmentation. For each of the four patients, we constructed a baseline model from the patient’s preoperative CTA data. In addition, geometries characterizing three distinct endograft designs were created, differing by where each device bifurcated into two limbs (proximal bifurcation, mid bifurcation, and distal bifurcation). Computational fluid dynamics (CFD) was used to simulate blood flow, utilizing patient-specific boundary conditions. Pressures, flows, and displacement forces on the endograft surface were calculated. The curvature and surface area of each device was quantified for all patients. The magnitude of the total displacement force on each device ranged from 2.43 N to 8.68 N for the four patients examined. Within each of the four patient anatomies, the total displacement force was similar (varying at least by 0.12 N and at most by 1.43 N), although there were some differences in the direction of component forces. Proximal bifurcation and distal bifurcation geometries consistently generated the smallest and largest displacement forces, respectively, with forces observed in the mid bifurcation design falling in between the two devices. The smallest curvature corresponded to the smallest total displacement force, and higher curvature values generally corresponded to higher magnitudes of displacement force. The same trend was seen for the surface area of each device, with lower surface areas resulting in lower displacement forces and vise versa. The patient with the highest blood pressure displayed the highest magnitudes of displacement force. The data indicate that curvature, device surface area, and patient blood pressure impact the magnitude of displacement force acting on the device. Endograft design may influence the displacement force experienced by an implanted endograft, with the proximal bifurcation design showing a small advantage for minimizing the displacement force on endografts.