Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model

Impact of arterial system alterations due to amputation on arterial stiffness and hemodynamics: a numerical study

Subjects with amputation of the lower limbs are at increased risk of cardiovascular mortality and morbidity. We hypothesize that amputation-induced alterations in the arterial tree negatively impact arterial biomechanics, blood pressure and flow behavior. These changes may interact with other biological factors, potentially increasing cardiovascular risk. To evaluate this hypothesis regarding the purely mechanical impact of amputation on the arterial tree, we used a simulation computer model including a detailed one-dimensional (1D) arterial network model (143 arterial segments) coupled with a zero-dimensional (0D) model of the left ventricle. Our simulations included five settings of the arterial network: (1) 4-limbs control, (2) unilateral amputee (right lower limb), (3) bilateral amputee (both lower limbs), (4) trilateral amputee (lower-limbs and right upper-limb), and (5) quadrilateral amputee (lower and upper limbs). Analysis of regional stiffness, as calculated by pulse wave velocity (PWV) for large-, medium- and small-sized arteries, showed that, while aortic stiffness did not change with increasing degree of amputation, stiffness of medium and smaller-sized arteries increased with greater amputation severity. Despite a staged decrease in cardiac output, the systolic and diastolic blood pressure values increased, resulting in an increase in both central and peripheral pulse pressures but with an attenuation of pulse pressure amplification. The most significant increase in peak systolic pressure and decrease in peak systolic blood flow was observed at the site of the abdominal aorta. Wave separation analysis indicated no changes in the shape of the forward and backward wave components. However, the results from wave intensity analysis showed that with extended amputation, there was an increase in peak forward wave intensity and a rise in the inverse peak of the backward wave intensity, suggesting potential alterations in cardiac hemodynamic load. In conclusion, this simulation study showed that biomechanical and hemodynamic changes in the arterial network geometry could interact with additional risk factors to increase the cardiovascular risk in patients with amputations.

The origin of intraluminal pressure waves in gastrointestinal tract

The gastrointestinal (GI) peristalsis is an involuntary wave-like contraction of the GI wall that helps to propagate food along the tract. Many GI diseases, e.g., gastroparesis, are known to cause motility disorders in which the physiological contractile patterns of the wall get disrupted. Therefore, to understand the pathophysiology of these diseases, it is necessary to understand the mechanism of GI motility. We present a coupled electromechanical model to describe the mechanism of GI motility and the transduction pathway of cellular electrical activities into mechanical deformation and the generation of intraluminal pressure (IP) waves in the GI tract. The proposed model consolidates a smooth muscle cell (SMC) model, an actin-myosin interaction model, a hyperelastic constitutive model, and a Windkessel model to construct a coupled model that can describe the origin of peristaltic contractions in the intestine. The key input to the model is external electrical stimuli, which are converted into mechanical contractile waves in the wall. The model recreated experimental observations efficiently and was able to establish a relationship between change in luminal volume and pressure with the compliance of the GI wall and the peripheral resistance to bolus flow. The proposed model will help us understand the GI tract's function in physiological and pathophysiological conditions.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Differential sensitivities to blood pressure variations in internal carotid and intracranial arteries: a numerical approach to stroke prediction

Stroke remains a global health concern, necessitating early prediction for effective management. Atherosclerosis-induced internal carotid and intra cranial stenosis contributes significantly to stroke risk. This study explores the relationship between blood pressure and stroke prediction, focusing on internal carotid artery (ICA) branches: middle cerebral artery (MCA), anterior cerebral artery (ACA), and their role in hemodynamics. Computational fluid dynamics (CFD) informed by the Windkessel model were employed to simulate patient-specific ICA models with introduced stenosis. Central to our investigation is the impact of stenosis on blood pressure, flow velocity, and flow rate across these branches, incorporating Fractional Flow Reserve (FFR) analysis. Results highlight differential sensitivities to blood pressure variations, with M1 branch showing high sensitivity, ACA moderate, and M2 minimal. Comparing blood pressure fluctuations between ICA and MCA revealed heightened sensitivity to potential reverse flow compared to ICA and ACA comparisons, emphasizing MCA's role. Blood flow adjustments due to stenosis demonstrated intricate compensatory mechanisms. FFR emerged as a robust predictor of stenosis severity, particularly in the M2 branch. In conclusion, this study provides comprehensive insights into hemodynamic complexities within major intracranial arteries, elucidating the significance of blood pressure variations, flow attributes, and FFR in stenosis contexts. Subject-specific data integration enhances model reliability, aiding stroke risk assessment and advancing cerebrovascular disease understanding.

Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue

The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.

An analytical method informed by clinical imaging data for estimating outlet boundary conditions in computational fluid dynamics analysis of carotid artery blood flow

Stroke occur mainly due to arterial thrombosis and rupture of cerebral blood vessels. Previous studies showed that blood flow-induced wall shear stress is an essential bio marker for estimating atherogenesis. It is a common practice to use computational fluid dynamics (CFD) simulations to calculate wall shear stress and to quantify blood flow. Reliability of predicted CFD results greatly depends on the accuracy of applied boundary conditions. Previously, the boundary conditions were estimated by varying values so that they matched the clinical data. It is applicable upon the availability of clinical data. Meanwhile, in most cases all that can be accessed are arterial geometry and inflow rate. Consequently, there is a need to devise a tool to estimate boundary values such as resistance and compliance of arteries. This study proposes an analytical framework to estimate the boundary conditions for a carotid artery based on the geometries of the downstream arteries available from clinical images.

A personalized 0D-1D model of cardiovascular system for the hemodynamic simulation of enhanced external counterpulsation

BACKGROUND AND OBJECTIVE

Enhanced external counterpulsation (EECP) is a non-invasive treatment modality capable of treating a variety of ischemic diseases. Currently, no effective methods of predicting the patient-specific hemodynamic effects of EECP are available. In this study, a personalized 0D-1D model of the cardiovascular system was developed for hemodynamic simulation to simulate the changes in blood flow in the EECP state and develop the best treatment protocol for each individual.

METHODS

A 0D-1D closed-loop model of the cardiovascular system was developed for hemodynamic simulation, consisting of a 1D wave propagation model for arteries, a 0D model for veins and capillaries, and a one-fiber model for the heart. Additionally, a simulation model coupling EECP with a 1D model was established. Physiological data, including the blood flow in different arteries, were clinically collected from 22 volunteers at rest and in the EECP state. Sensitivity analysis and a simulated annealing algorithm were used to build personalized 0D-1D models using the clinical data in the rest state as optimization objectives. Then, the clinical data on EECP were used to verify the applicability and accuracy of the personalized models.

RESULTS

The simulation results and clinical data were found to be in agreement for all 22 subjects, with waveform similarity coefficients (r) exceeding 90% for most arteries at rest and 80% for most arteries during EECP.

CONCLUSIONS

The 0D-1D closed-loop model and the optimized method can facilitate personalized modeling of the cardiovascular system using the data in the rest state and effectively predict the hemodynamic changes in the EECP state, which is significant for the numerical simulation of personalized hemodynamics. The model can also potentially be used to make decisions regarding patient-specific treatment.

Effects of dispersed fibres in myocardial mechanics, Part II: active response

This work accompanies the first part of our study "effects of dispersed fibres in myocardial mechanics: Part I passive response" with a focus on myocardial active contraction. Existing studies have suggested that myofibre architecture plays an important role in myocardial active contraction. Following the first part of our study, we firstly study how the general fibre architecture affects ventricular pump function by varying the mean myofibre rotation angles, and then the impact of fibre dispersion along the myofibre direction on myocardial contraction in a left ventricle model. Dispersed active stress is described by a generalised structure tensor method for its computational efficiency. Our results show that both the myofibre rotation angle and its dispersion can significantly affect cardiac pump function by redistributing active tension circumferentially and longitudinally. For example, larger myofibre rotation angle and higher active tension along the sheet-normal direction can lead to much reduced end-systolic volume and higher longitudinal shortening, and thus a larger ejection fraction. In summary, these two studies together have demonstrated that it is necessary and essential to include realistic fibre structures (both fibre rotation angle and fibre dispersion) in personalised cardiac modelling for accurate myocardial dynamics prediction.

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R² > .95) with experimental blood pressure data.

Mechano-chemo-biological Computational Models for Arteries in Health, Disease and Healing: From Tissue Remodelling to Drug-eluting Devices

This review aims to highlight urgent priorities for the computational biomechanics community in the framework of mechano-chemo-biological models. Recent approaches, promising directions and open challenges on the computational modelling of arterial tissues in health and disease are introduced and investigated, together with in silico approaches for the analysis of drug-eluting stents that promote pharmacological-induced healing. The paper addresses a number of chemo-biological phenomena that are generally neglected in biomechanical engineering models but are most likely instrumental for the onset and the progression of arterial diseases. An interdisciplinary effort is thus encouraged for providing the tools for an effective in silico insight into medical problems. An integrated mechano-chemo-biological perspective is believed to be a fundamental missing piece for crossing the bridge between computational engineering and life sciences, and for bringing computational biomechanics into medical research and clinical practice.

Effect of myofibre architecture on ventricular pump function by using a neonatal porcine heart model: from DT-MRI to rule-based methods

Myofibre architecture is one of the essential components when constructing personalized cardiac models. In this study, we develop a neonatal porcine bi-ventricle model with three different myofibre architectures for the left ventricle (LV). The most realistic one is derived from ex vivo diffusion tensor magnetic resonance imaging, and other two simplifications are based on rule-based methods (RBM): one is regionally dependent by dividing the LV into 17 segments, each with different myofibre angles, and the other is more simplified by assigning a set of myofibre angles across the whole ventricle. Results from different myofibre architectures are compared in terms of cardiac pump function. We show that the model with the most realistic myofibre architecture can produce larger cardiac output, higher ejection fraction and larger apical twist compared with those of the rule-based models under the same pre/after-loads. Our results also reveal that when the cross-fibre contraction is included, the active stress seems to play a dual role: its sheet-normal component enhances the ventricular contraction while its sheet component does the opposite. We further show that by including non-symmetric fibre dispersion using a general structural tensor, even the most simplified rule-based myofibre model can achieve similar pump function as the most realistic one, and cross-fibre contraction components can be determined from this non-symmetric dispersion approach. Thus, our study highlights the importance of including myofibre dispersion in cardiac modelling if RBM are used, especially in personalized models.

Fractional flow reserve-based 4D hemodynamic simulation of time-resolved blood flow in left anterior descending coronary artery

BACKGROUND

The purpose of this study was to investigate the feasibility of the non-invasive assessment of hemodynamic parameters with computational fluid dynamics in left anterior descending coronary artery based on invasive fractional flow reserve.

METHODS

A left coronary artery model based on computed tomography angiography was reconstructed using MIMICS 18.0 for computational fluid dynamics analysis. With actual fractional flow reserve measured from the patient, 4D hemodynamic profiles of time-resolved blood flow were simulated.

FINDINGS

The 4D blood flow simulation could provide extensive information of blood flow status. Hemodynamic parameters, such as velocity, wall shear stress and pressure were simulated throughout the cardiac cycle. There might be high flow velocities and high wall shear stress in the stenotic region throughout the whole cycle, both of which peaked in the case of the maximum inlet differential pressure. The reverse flow and vortex were detectable at the downstream areas beneath the stenotic site. The pressure remarkably increased near the proximal stenotic end and declined in the mid-stenosis. Moreover, the simulation results provided detailed and accurate mass flow measurements of hemodynamic parameters as well.

INTERPRETATION

The computational fluid dynamics analysis of 4D blood flow based on fractional flow reserve is feasible in left anterior descending coronary artery. It presents the merits of providing both qualitative and quantitative information for further investigation of the links between hemodynamic parameters and left anterior descending artery stenosis.

A novel porous media-based approach to outflow boundary resistances of 1D arterial blood flow models

In this paper we introduce a novel method for prescribing terminal boundary conditions in one-dimensional arterial flow networks. This is carried out by coupling the terminal arterial vessel with a poro-elastic tube, representing the flow resistance offered by microcirculation. The performance of the proposed porous media-based model has been investigated through several different numerical examples. First, we investigate model parameters that have a profound influence on the flow and pressure distributions of the system. The simulation results have been compared against the waveforms generated by three elements (RCR) Windkessel model. The proposed model is also integrated into a realistic arterial tree, and the results obtained have been compared against experimental data at different locations of the network. The accuracy and simplicity of the proposed model demonstrates that it can be an excellent alternative for the existing models.

An efficient full space-time discretization method for subject-specific hemodynamic simulations of cerebral arterial blood flow with distensible wall mechanics

A computationally inexpensive mathematical solution approach using orthogonal collocations for space discretization with temporal Fourier series is proposed to compute subject-specific blood flow in distensible vessels of large cerebral arterial networks. Several models of wall biomechanics were considered to assess their impact on hemodynamic predictions. Simulations were validated against in vivo blood flow measurements in six human subjects. The average root-mean-square relative differences were found to be less than 4.3% for all subjects with a linear elastic wall model. This discrepancy decreased further in a viscoelastic Kelvin-Voigt biomechanical wall. The results provide support for the use of collocation-Fourier series approach to predict clinically relevant blood flow distribution and collateral blood supply in large portions of the cerebral circulation at reasonable computational costs. It thus opens the possibility of performing computationally inexpensive subject-specific simulations that are robust and fast enough to predict clinical results in real time on the same day.

A multi-scale model of the coronary circulation applied to investigate transmural myocardial flow

Distribution of blood flow in myocardium is a key determinant of the localization and severity of myocardial ischemia under impaired coronary perfusion conditions. Previous studies have extensively demonstrated the transmural difference of ischemic vulnerability. However, it remains incompletely understood how transmural myocardial flow is regulated under in vivo conditions. In the present study, a computational model of the coronary circulation was developed to quantitatively evaluate the sensitivity of transmural flow distribution to various cardiovascular and hemodynamic factors. The model was further incorporated with the flow autoregulatory mechanism to simulate the regulation of myocardial flow in the presence of coronary artery stenosis. Numerical tests demonstrated that heart rate (HR), intramyocardial tissue pressure (P_im ), and coronary perfusion pressure (P_per ) were the major determinant factors for transmural flow distribution (evaluated by the subendocardial-to-subepicardial (endo/epi) flow ratio) and that the flow autoregulatory mechanism played an important compensatory role in preserving subendocardial perfusion against reduced P_per . Further analysis for HR variation-induced hemodynamic changes revealed that the rise in endo/epi flow ratio accompanying HR decrease was attributable not only to the prolongation of cardiac diastole relative to systole, but more predominantly to the fall in P_im . Moreover, it was found that P_im and P_per interfered with each other with respect to their influence on transmural flow distribution. These results demonstrate the interactive effects of various cardiovascular and hemodynamic factors on transmural myocardial flow, highlighting the importance of taking into account patient-specific conditions in the explanation of clinical observations.

Assessment of boundary conditions for CFD simulation in human carotid artery

Computational fluid dynamics (CFD) is an increasingly used method for investigation of hemodynamic parameters and their alterations under pathological conditions, which are important indicators for diagnosis of cardiovascular disease. In hemodynamic simulation models, the employment of appropriate boundary conditions (BCs) determines the computational accuracy of the CFD simulation in comparison with pressure and velocity measurements. In this study, we have first assessed the influence of inlet boundary conditions on hemodynamic CFD simulations. We selected two typical patients suspected of carotid artery disease, with mild stenosis and severe stenosis. Both patients underwent digital subtraction angiography (DSA), magnetic resonance angiography, and the invasive pressure guide wire measured pressure profile. We have performed computational experiments to (1) study the hemodynamic simulation outcomes of distributions of wall shear stress, pressure, pressure gradient and (2) determine the differences in hemodynamic performances caused by inlet BCs derived from DSA and Womersley analytical solution. Our study has found that the difference is related to the severity of the stenosis; the greater the stenosis, the more the difference ensues. Further, in our study, the two typical subjects with invasively measured pressure profile and thirty subjects with ultrasound Doppler velocimeter (UDV) measurement served as the criteria to evaluate the hemodynamic outcomes of wall shear stress, pressure, pressure gradient and velocity due to different outlet BCs based on the Windkessel model, structured-tree model, and fully developed flow model. According to the pressure profiles, the fully developed model appeared to have more fluctuations compared with the other two models. The Windkessel model had more singularities before convergence. The three outlet BCs models also showed good correlation with the UDV measurement, while the Windkessel model appeared to be slightly better ([Formula: see text]). The structured-tree model was seen to have the best performance in terms of available computational cost and accuracy. The results of our numerical simulation and the good correlation with the computed pressure and velocity with their measurements have highlighted the effectiveness of CFD simulation in patient-specific human carotid artery with suspected stenosis.

Determinant Factors for Arterial Hemodynamics in Hypertension: Theoretical Insights From a Computational Model-Based Study

Hypertension is a well-documented predictive factor for cardiovascular events. Clinical studies have extensively demonstrated the differential hemodynamic consequences of various antihypertensive drugs, but failed to clearly elucidate the underlying mechanisms due to the difficulty in performing a quantitative deterministic analysis based on clinical data that carry confounding information stemming from interpatient differences and the nonlinearity of cardiovascular hemodynamics. In the present study, a multiscale model of the cardiovascular system was developed to quantitatively investigate the relationships between hemodynamic variables and cardiovascular properties under hypertensive conditions, aiming to establish a theoretical basis for assisting in the interpretation of clinical observations or optimization of therapy. Results demonstrated that heart period, central arterial stiffness, and arteriolar radius were the major determinant factors for blood pressures and flow pulsatility indices both in large arteries and in the microcirculation. These factors differed in the degree and the way in which they affect hemodynamic variables due to their differential effects on wave reflections in the vascular system. In particular, it was found that the hemodynamic effects of varying arteriolar radius were considerably influenced by the state of central arterial stiffness, and vice versa, which implied the potential of optimizing antihypertensive treatment by selecting proper drugs based on patient-specific cardiovascular conditions. When analyzed in relation to clinical observations, the simulated results provided mechanistic explanations for the beneficial pressure-lowering effects of vasodilators as compared to β-blockers, and highlighted the significance of monitoring and normalizing arterial stiffness in the treatment of hypertension.

In vivo repeatability of the pulse wave inverse problem in human carotid arteries

Accurate arterial stiffness measurement would improve diagnosis and monitoring for many diseases. Atherosclerotic plaques and aneurysms are expected to involve focal changes in vessel wall properties; therefore, a method to image the stiffness variation would be a valuable clinical tool. The pulse wave inverse problem (PWIP) fits unknown parameters from a computational model of arterial pulse wave propagation to ultrasound-based measurements of vessel wall displacements by minimizing the difference between the model and measured displacements. The PWIP has been validated in phantoms, and this study presents the first in vivo demonstration. The common carotid arteries of five healthy volunteers were imaged five times in a single session with repositioning of the probe and subject between each scan. The 1D finite difference computational model used in the PWIP spanned from the start of the transducer to the carotid bifurcation, where a resistance outlet boundary condition was applied to approximately model the downstream reflection of the pulse wave. Unknown parameters that were estimated by the PWIP included a 10-segment linear piecewise compliance distribution and 16 discrete cosine transformation coefficients for each of the inlet boundary conditions. Input data was selected to include pulse waves resulting from the primary pulse and dicrotic notch. The recovered compliance maps indicate that the compliance increases close to the bifurcation, and the variability of the average pulse wave velocity estimated through the PWIP is on the order of 11%, which is similar to that of the conventional processing technique which tracks the wavefront arrival time (13%).

Effects of cardiac timing and peripheral resistance on measurement of pulse wave velocity for assessment of arterial stiffness

To investigate the effects of heart rate (HR), left ventricular ejection time (LVET) and wave reflection on arterial stiffness as assessed by pulse wave velocity (PWV), a pulse wave propagation simulation system (PWPSim) based on the transmission line model of the arterial tree was developed and was applied to investigate pulse wave propagation. HR, LVET, arterial elastic modulus and peripheral resistance were increased from 60 to 100 beats per minute (bpm), 0.1 to 0.45 seconds, 0.5 to 1.5 times and 0.5 to 1.5 times of the normal value, respectively. Carotid-femoral PWV (cfPWV) and brachial-ankle PWV (baPWV) were calculated by intersecting tangent method (cfPWV_tan and baPWV_tan), maximum slope (cfPWV_max and baPWV_max), and using the Moens-Korteweg equation ([Formula: see text] and [Formula: see text]). Results showed cfPWV and baPWV increased significantly with arterial elastic modulus but did not increase with HR when using a constant elastic modulus. However there were significant LVET dependencies of cfPWV_tan and baPWV_tan (0.17 ± 0.13 and 0.17 ± 0.08 m/s per 50 ms), and low peripheral resistance dependencies of cfPWV_tan, cfPWV_max, baPWV_tan and baPWV_max (0.04 ± 0.01, 0.06 ± 0.04, 0.06 ± 0.03 and 0.09 ± 0.07 m/s per 10% peripheral resistance), respectively. This study demonstrated that LVET dominates the effect on calculated PWV compared to HR and peripheral resistance when arterial elastic modulus is constant.

A FSI computational framework for vascular physiopathology: A novel flow-tissue multiscale strategy

A novel fluid-structure computational framework for vascular applications is herein presented. It is developed by combining the double multi-scale nature of vascular physiopathology in terms of both tissue properties and blood flow. Addressing arterial tissues, they are modelled via a nonlinear multiscale constitutive rationale, based only on parameters having a clear histological and biochemical meaning. Moreover, blood flow is described by coupling a three-dimensional fluid domain (undergoing physiological inflow conditions) with a zero-dimensional model, which allows to reproduce the influence of the downstream vasculature, furnishing a realistic description of the outflow proximal pressure. The fluid-structure interaction is managed through an explicit time-marching approach, able to accurately describe tissue nonlinearities within each computational step for the fluid problem. A case study associated to a patient-specific aortic abdominal aneurysmatic geometry is numerically investigated, highlighting advantages gained from the proposed multiscale strategy, as well as showing soundness and effectiveness of the established framework for assessing useful clinical quantities and risk indexes.

Patient-specific structural effects on hemodynamics in the ischemic lower limb artery

Lower limb peripheral artery disease is a prevalent chronic non-communicable disease without obvious symptoms. However, the effect of ischemic lower limb peripheral arteries on hemodynamics remains unclear. In this study, we investigated the variation of the hemodynamics caused by patient-specific structural artery characteristics. Computational fluid dynamic simulations were performed on seven lower limb (including superficial femoral, deep femoral and popliteal) artery models that were reconstructed from magnetic resonance imaging. We found that increased wall shear stress (WSS) was mainly caused by the increasing severity of stenosis, bending, and branching. Our results showed that the increase in the WSS value at a stenosis at the bifurcation was 2.7 Pa. In contrast, the isolated stenosis and branch caused a WSS increase of 0.7 Pa and 0.5 Pa, respectively. The WSS in the narrow popliteal artery was more sensitive to a reduction in radius. Our results also demonstrate that the distribution of the velocity and pressure gradient are highly structurally related. At last, Ultrasound Doppler velocimeter measured result was presented as a validation. In conclusion, the distribution of hemodynamics may serve as a supplement for clinical decision-making to prevent the occurrence of a morbid or mortal ischemic event.

Sensitivity of flow patterns in aneurysms on the anterior communicating artery to anatomic variations of the cerebral arterial network

Recent studies raised increasing concern about the reliability of computer models in reproducing in vivo hemodynamics in cerebral aneurysms. Boundary condition problem is among the most frequently addressed issues since three-dimensional (3-D) modeling is usually restricted to local arterial segments. The present study focused on aneurysms on the anterior communicating artery (ACoA) which represent a large subgroup of detected cerebral aneurysms and, in particular, have a relatively high risk of rupture compared to aneurysms located in other regions. The sensitivity of blood flows in three ACoA aneurysms to boundary conditions was investigated using 3-D hemodynamic models. The boundary conditions of the 3-D models were predicted by a one-dimensional (1-D) model of the cerebral arterial network. The parameters of the 1-D model were assigned based respectively on population-averaged data and patient-specific data derived from medical images, yielding a population-generic model and a patient-specific model. In addition, particle image velocimetry (PIV) experiments were performed to validate the code used to simulate intra-aneurysmal blood flows. Obtained results showed that switching the boundary conditions of the aneurysm models from population-generic ones to patient-specific ones led to pronounced changes in simulated intra-aneurysmal flow patterns in terms of vortex structure, impingement region and the magnitude and spatial distribution of wall shear stress and oscillatory shear index. In particular, the way and the degree in which hemodynamic quantities are influenced by boundary conditions exhibited pronounced inter-patient variability. In summary, our study underlines the importance of patient-specific treatment of boundary conditions in model studies focusing on ACoA aneurysms.

Functional assessment of the stenotic carotid artery by CFD-based pressure gradient evaluation

The functional assessment of a hemodynamic significant stenosis base on blood pressure variation has been applied for evaluation of the myocardial ischemic event. This functional assessment shows great potential for improving the accuracy of the classification of the severity of carotid stenosis. To explore the value of grading the stenosis using a pressure gradient (PG)-we had reconstructed patient-specific carotid geometries based on MRI images-computational fluid dynamics were performed to analyze the PG in their stenotic arteries. Doppler ultrasound image data and the corresponding MRI image data of 19 patients with carotid stenosis were collected. Based on these, 31 stenotic carotid arterial geometries were reconstructed. A combinatorial boundary condition method was implemented for steady-state computer fluid dynamics simulations. Anatomic parameters, including tortuosity (T), the angle of bifurcation, and the cross-sectional area of the remaining lumen, were collected to investigate the effect on the pressure distribution. The PG is highly correlated with the severe stenosis (r = 0.902), whereas generally, the T and the angle of the bifurcation negatively correlate to the pressure drop of the internal carotid artery stenosis. The calculation required <10 min/case, which made it prepared for the fast diagnosis of the severe stenosis. According to the results, we had proposed a potential threshold value for distinguishing severe stenosis from mild-moderate stenosis (PG = 0.88). In conclusion, the PG could serve as the additional factor for improving the accuracy of grading the severity of the stenosis.