Deep-learning-based real-time individualization for reduce-order haemodynamic model

The reduced-order lumped parameter model (LPM) has great computational efficiency in real-time numerical simulations of haemodynamics but is limited by the accuracy of patient-specific computation. This study proposed a method to achieve the individual LPM modeling with high accuracy to improve the practical clinical applicability of LPM. Clinical data was collected from two medical centres comprising haemodynamic indicators from 323 individuals, including brachial artery pressure waveforms, cardiac output data, and internal carotid artery flow waveforms. The data were expanded to 5000 synthesised cases that all fell within the physiological range of each indicator. LPM of the human blood circulation system was established. A double-path neural network (DPNN) was designed to input the waveforms of each haemodynamic indicator and their key features and then output the individual parameters of the LPM, which was labelled using a conventional optimization algorithm. Clinically collected data from the other 100 cases were used as the test set to verify the accuracy of the individual LPM parameters predicted by DPNN. The results show that DPNN provided good convergence in the training process. In the test set, compared with clinical measurements, the mean differences between each haemodynamic indicator and the estimate calculated by the individual LPM based on the DPNN were about 10 %. Furthermore, DPNN prediction only takes 4 s for 100 cases. The DPNN proposed in this study permits real-time and accurate individualization of LPM's. When facing medical issues involving haemodynamics, it lays the foundation for patient-specific numerical simulation, which may be beneficial for potential clinical application.

Multi-Dimensional Modeling of Cerebral Hemodynamics: A Systematic Review

The Circle of Willis (CoW) describes the arterial system in the human brain enabling the neurovascular blood supply. Neurovascular diseases like intracranial aneurysms (IAs) can occur within the CoW and carry the risk of rupture, which can lead to subarachnoid hemorrhage. The assessment of hemodynamic information in these pathologies is crucial for their understanding regarding detection, diagnosis and treatment. Multi-dimensional in silico approaches exist to evaluate these hemodynamics based on patient-specific input data. The approaches comprise low-scale (zero-dimensional, one-dimensional) and high-scale (three-dimensional) models as well as multi-scale coupled models. The input data can be derived from medical imaging, numerical models, literature-based assumptions or from measurements within healthy subjects. Thus, the most realistic description of neurovascular hemodynamics is still controversial. Within this systematic review, first, the models of the three scales (0D, 1D, 3D) and second, the multi-scale models, which are coupled versions of the three scales, were discussed. Current best practices in describing neurovascular hemodynamics most realistically and their clinical applicablility were elucidated. The performance of 3D simulation entails high computational expenses, which could be reduced by analyzing solely the region of interest in detail. Medical imaging to establish patient-specific boundary conditions is usually rare, and thus, lower dimensional models provide a realistic mimicking of the surrounding hemodynamics. Multi-scale coupling, however, is computationally expensive as well, especially when taking all dimensions into account. In conclusion, the 0D-1D-3D multi-scale approach provides the most realistic outcome; nevertheless, it is least applicable. A 1D-3D multi-scale model can be considered regarding a beneficial trade-off between realistic results and applicable performance.

Cerebral multi-autoregulation model based enhanced external counterpulsation treatment planning for cerebral ischemic stroke

Enhanced external counterpulsation (EECP) treatment for cerebral ischemic stroke patients with differing severity of stenosis, is subject to uncertainties due to the varying effects of the cerebral autoregulation mechanism on haemodynamics. The current study reports the development of a cerebral multi-autoregulation (MR) mathematical model, based on cerebral arteriole regulation of neurogenic, vascular smooth muscle reflex and shear stress mechanisms which takes into account the severity of stenosis. The model was evaluated by comparison to authentic clinical measurements of cerebral autoregulatory efficiency. Then it was applied to a 0D/3D geometric multi-scale haemodynamic model of a cerebral artery. Haemodynamic indicators were calculated under different pressurization durations of EECP to evaluate the efficacy for different stenosis lesions. Moderate stenosis of 50% to 60% produced excessive time-averaged wall shear stress in the distal area of the stenosis (>7 Pa) during prolonged pressurization and may result in damage to vascular endothelial cells. However, prolonged pressurization did not result in haemodynamic risk for severe stenosis of 70% to 80%, indicating that the duration of pressurization may be extended with increasing severity of stenosis. The current MR model accurately simulated cerebral blood flow and has relevance to the simulation of cerebral haemodynamics in a clinical setting.

Treatment strategy of different enhanced external counterpulsation frequencies for coronary heart disease and cerebral ischemic stroke: A hemodynamic numerical simulation study

BACKGROUND AND OBJECTIVES

Currently, enhanced external counterpulsation (EECP) devices mainly produce one counterpulsation per cardiac cycle. However, the effect of other frequencies of EECP on the hemodynamics of coronary and cerebral arteries is still unclear. It should be investigated whether one counterpulsation per cardiac cycle leads to the optimal therapeutic effect in patients with different clinical indications. Therefore, we measured the effects of different frequencies of EECP on the hemodynamics of coronary and cerebral arteries to determine the optimal counterpulsation frequency for the treatment of coronary heart disease and cerebral ischemic stroke.

METHODS

We established 0D/3D geometric multi-scale hemodynamics model of coronary and cerebral arteries in two healthy individuals, and performed clinical trials of EECP to verify the accuracy of the multi-scale hemodynamics model. The pressure amplitude (35 kPa) and pressurization duration (0.6 s) were fixed. The global and local hemodynamics of coronary and cerebral arteries were studied by changing counterpulsation frequency. Three frequency modes, including one counterpulsation in one, two and three cardiac cycles, were applied. Global hemodynamic indicators included diastolic / systolic blood pressure (D/S), mean arterial pressure (MAP), coronary artery flow (CAF), and cerebral blood flow (CBF), whereas local hemodynamic effects included area-time-averaged wall shear stress (ATAWSS) and oscillatory shear index (OSI). The optimal counterpulsation frequency was verified by analyzing the hemodynamic effects of different frequency modes of counterpulsation cycles and full cycles.

RESULTS

In the full cycle, CAF, CBF and ATAWSS of coronary and cerebral arteries were the highest when one counterpulsation per cardiac cycle was applied. However, in the counterpulsation cycle, the global and local hemodynamic indicators of coronary and cerebral artery reached the highest when one counterpulsation in one cardiac cycle or two cardiac cycles was applied.

CONCLUSIONS

For clinical application, the results of global hemodynamic indicators in the full cycle have more clinical practical significance. Combined with the comprehensive analysis of local hemodynamic indicators, it can be concluded that for coronary heart disease and cerebral ischemic stroke, applying one counterpulsation per cardiac cycle may provide the optimal benefit.

Deep learning-based hemodynamic prediction of carotid artery stenosis before and after surgical treatments

Hemodynamic prediction of carotid artery stenosis (CAS) is of great clinical significance in the diagnosis, prevention, and treatment prognosis of ischemic strokes. While computational fluid dynamics (CFD) is recognized as a useful tool, it shows a crucial issue that the high computational costs are usually required for real-time simulations of complex blood flows. Given the powerful feature-extraction capabilities, the deep learning (DL) methodology has a high potential to implement the mapping of anatomic geometries and CFD-driven flow fields, which enables accomplishing fast and accurate hemodynamic prediction for clinical applications. Based on a brain/neck CT angiography database of 280 subjects, image based three-dimensional CFD models of CAS were constructed through blood vessel extraction, computational domain meshing and setting of the pulsatile flow boundary conditions; a series of CFD simulations were undertaken. A DL strategy was proposed and accomplished in terms of point cloud datasets and a DL network with dual sampling-analysis channels. This enables multimode mapping to construct the image-based geometries of CAS while predicting CFD-based hemodynamics based on training and testing datasets. The CFD simulation was validated with the mass flow rates at two outlets reasonably agreed with the published results. Comprehensive analysis and error evaluation revealed that the DL strategy enables uncovering the association between transient blood flow characteristics and artery cavity geometric information before and after surgical treatments of CAS. Compared with other methods, our DL-based model trained with more clinical data can reduce the computational cost by 7,200 times, while still demonstrating good accuracy (error<12.5%) and flow visualization in predicting the two hemodynamic parameters. In addition, the DL-based predictions were in good agreement with CFD simulations in terms of mean velocity in the stenotic region for both the preoperative and postoperative datasets. This study points to the capability and significance of the DL-based fast and accurate hemodynamic prediction of preoperative and postoperative CAS. For accomplishing real-time monitoring of surgical treatments, further improvements in the prediction accuracy and flexibility may be conducted by utilizing larger datasets with specific real surgical events such as stent intervention, adopting personalized boundary conditions, and optimizing the DL network.

High-resolution cerebral blood flow simulation with a domain decomposition method and verified by the TCD measurement

BACKGROUND

An efficient and accurate blood flow simulation can be useful for understanding many vascular diseases. Accurately resolving the blood flow velocity based on patient-specific geometries and model parameters is still a major challenge because of complex geomerty and turbulence issues. In addition, obtaining results in a short amount of computing time is important so that the simulation can be used in the clinical environment. In this work, we present a parallel scalable method for the patient-specific blood flow simulation with focuses on its parallel performance study and clinical verification.

METHODS

We adopt a fully implicit unstructured finite element method for a patient-specific simulation of blood flow in a full precerebral artery. The 3D artery is constructed from MRI images, and a parallel Newton-Krylov method preconditioned with a two-level domain decomposition method is adopted to solve the large nonlinear system discretized from the time-dependent 3D Navier-Stokes equations in the artery with an integral outlet boundary condition. The simulated results are verified using the clinical data measured by transcranial Doppler ultrasound, and the parallel performance of the algorithm is studied on a supercomputer.

RESULTS

The simulated velocity matches the clinical measured data well. Other simulated blood flow parameters, such as pressure and wall shear stress, are within reasonable ranges. The results show that the parallel algorithm scales up to 2160 processors with a 49% parallel efficiency for solving a problem with over 20 million unstructured elements on a supercomputer. For a standard cerebral blood flow simulation case with approximately 4 million finite elements, the calculation of one cardiac cycle can be finished within one hour with 1000 processors.

CONCLUSION

The proposed method is able to perform high-resolution 3D blood flow simulations in a patient-specific full precerebral artery within an acceptable time, and the simulated results are comparable with the clinical measured data, which demonstrates its high potential for clinical applications.

Uncertainty quantification in cerebral circulation simulations focusing on the collateral flow: Surrogate model approach with machine learning

Collateral circulation in the circle of Willis (CoW), closely associated with disease mechanisms and treatment outcomes, can be effectively investigated using one-dimensional–zero-dimensional hemodynamic simulations. As the entire cardiovascular system is considered in the simulation, it captures the systemic effects of local arterial changes, thus reproducing collateral circulation that reflects biological phenomena. The simulation facilitates rapid assessment of clinically relevant hemodynamic quantities under patient-specific conditions by incorporating clinical data. During patient-specific simulations, the impact of clinical data uncertainty on the simulated quantities should be quantified to obtain reliable results. However, as uncertainty quantification (UQ) is time-consuming and computationally expensive, its implementation in time-sensitive clinical applications is considered impractical. Therefore, we constructed a surrogate model based on machine learning using simulation data. The model accurately predicts the flow rate and pressure in the CoW in a few milliseconds. This reduced computation time enables the UQ execution with 100 000 predictions in a few minutes on a single CPU core and in less than a minute on a GPU. We performed UQ to predict the risk of cerebral hyperperfusion (CH), a life-threatening condition that can occur after carotid artery stenosis surgery if collateral circulation fails to function appropriately. We predicted the statistics of the postoperative flow rate increase in the CoW, which is a measure of CH, considering the uncertainties of arterial diameters, stenosis parameters, and flow rates measured using the patients’ clinical data. A sensitivity analysis was performed to clarify the impact of each uncertain parameter on the flow rate increase. Results indicated that CH occurred when two conditions were satisfied simultaneously: severe stenosis and when arteries of small diameter serve as the collateral pathway to the cerebral artery on the stenosis side. These findings elucidate the biological aspects of cerebral circulation in terms of the relationship between collateral flow and CH.

Model-based evaluation of local hemodynamic effects of enhanced external counterpulsation

BACKGROUND AND OBJECTIVES

The treatment benefits of enhanced external counterpulsation (EECP) heavily depends on hemodynamics. Global hemodynamics of EECP can cause blood flow redistribution in the circulatory system whereas local hemodynamic effects act on vascular endothelial cells (VECs). Local hemodynamic effects of EECP on VECs are important in the treatment of atherosclerosis, but currently cannot be not evaluated. Herein we aim to establish evaluation models of local hemodynamic effects based on the global hemodynamic indicators.

METHODS

We established 0D/3D geometric multi-scale hemodynamic models of the coronary and cerebral artery of two healthy individuals to calculate the global hemodynamic indicators and the local hemodynamic effects. Clinical EECP trials were performed to verify the accuracy of the multi-scale hemodynamic model. The global hemodynamic indicators included diastolic blood pressure/systolic blood pressure (Q = D/S), mean arterial pressure (MAP), internal carotid artery flow (ICAF) and cerebral blood flow (CBF), whereas local hemodynamic effects focused on time-averaged wall shear stress (TAWSS). The correlation between these indicators was analyzed via Pearson correlation coefficient. Significantly related indicators were selected for curve-fitting to establish evaluation models of the coronary and cerebral artery. Moreover, clinical data of a coronary heart disease patient and a cerebral ischemic stroke patient were collected to verify the effectiveness of the application of the established evaluation models to real patients.

RESULTS

For coronary artery, TAWSS was correlated to Q = D/S and ICAF (P < 0.05), whereas for cerebral artery, TAWSS was correlated to MAP and CBF (P < 0.05). The mean square error (MSE) between the evaluated values using evaluation model and the calculated values using 0D/3D model of TAWSS of the coronary and cerebral artery were 5.4% and 1.0%, respectively. The MSE of evaluation model applied to real patients was greater than that applied to healthy individuals, but within an acceptable range.

CONCLUSIONS

The presented error demonstrated validity and accuracy of the evaluation models in clinical patients. Based on the evaluation models, global hemodynamic indicators could be used to evaluate the local hemodynamic effects under the current counterpulsation mode. With TAWSS range of 4-7 Pa as the target range, EECP strategies can further be optimized.

Impact of Respiratory Fluctuation on Hemodynamics in Human Cardiovascular System: A 0-1D Multiscale Model

To explore hemodynamic interaction between the human respiratory system (RS) and cardiovascular system (CVS), here we propose an integrated computational model to predict the CVS hemodynamics with consideration of the respiratory fluctuation (RF). A submodule of the intrathoracic pressure (ITP) adjustment is developed and incorporated in a 0-1D multiscale hemodynamic model of the CVS specified for infant, adolescent, and adult individuals. The model is verified to enable reasonable estimation of the blood pressure waveforms accounting for the RF-induced pressure fluctuations in comparison with clinical data. The results show that the negative ITP caused by respiration increases the blood flow rates in superior and inferior vena cavae; the deep breathing improves the venous return in adolescents but has less influence on infants. It is found that a marked reduction in ITP under pathological conditions can excessively increase the flow rates in cavae independent of the individual ages, which may cause the hemodynamic instability and hence increase the risk of heart failure. Our results indicate that the present 0-1D multiscale CVS model incorporated with the RF effect is capable of providing a useful and effective tool to explore the physiological and pathological mechanisms in association with cardiopulmonary interactions and their clinical applications.

Carotid Stump Pressure and Contralateral Internal Carotid Stenosis Ratio During Carotid Endarterectomies: 1D-0D Hemodynamic Simulation of Cerebral Perfusion

Objective: We selectively place carotid shunting when ipsilateral mean stump pressure is less than 40 mmHg during carotid endarterectomy (CEA). This study aimed to assess the validity of our selective shunting criterion by 1D-0D hemodynamic simulation technology.

Materials and Methods: We retrospectively reviewed 88 patients (95 cases) of CEA and divided them into two groups based on the degree of contralateral internal carotid artery (ICA) stenosis ratio, which was determined as severe when the peak systolic velocity ratio of the ICA to the common carotid artery was ≥4 by carotid duplex ultrasonography. Patients with severe stenosis or occlusion in contralateral ICA were classified as hypoperfusion group, and those without such contralateral ICA obstruction were classified as control group.

Results: Perioperatively, the mean carotid stump pressures were 33 mmHg in hypoperfusion group and 46 mmHg in the control group (P=0.006). We simulated changes in carotid stump pressure according to the changes in the contralateral ICA stenosis ratio. 1D-0D simulation indicated a sharp decline in carotid stump pressure when the contralateral stenosis ratio was >50%, while peripheral pressure of the middle cerebral arteries declined sharply at a ≥70% contralateral stenosis ratio. At this ratio, the direction of the ipsilateral cerebral arterial flow became inverted, the carotid stump pressure became dependent on the basilar artery circulation, and the ipsilateral middle cerebral artery became hypoperfused.

Conclusion: Our clinical and computer-simulated results confirmed the validation of our carotid shunting criterion and suggested that contralateral ICA stenosis ratio over 70% is a safe indication of selective shunting during CEA.

A parallel non-nested two-level domain decomposition method for simulating blood flows in cerebral artery of stroke patient

Numerical simulation of blood flows in patient-specific arteries can be useful for the understanding of vascular diseases, as well as for surgery planning. In this paper, we simulate blood flows in the full cerebral artery of stroke patients. To accurately resolve the flow in this rather complex geometry with stenosis is challenging and it is also important to obtain the results in a short amount of computing time so that the simulation can be used in pre- and/or post-surgery planning. For this purpose, we introduce a highly scalable, parallel non-nested two-level domain decomposition method for the three-dimensional unsteady incompressible Navier-Stokes equations with an impedance outlet boundary condition. The problem is discretized with a stabilized finite element method on unstructured meshes in space and a fully implicit method in time, and the large nonlinear systems are solved by a preconditioned parallel Newton-Krylov method with a two-level Schwarz method. The key component of the method is a non-nested coarse problem solved using a subset of processor cores and its solution is interpolated to the fine space using radial basis functions. To validate and verify the proposed algorithm and its highly parallel implementation, we consider a case with available clinical data and show that the computed result matches with the measured data. Further numerical experiments indicate that the proposed method works well for realistic geometry and parameters of a full size cerebral artery of an adult stroke patient on a supercomputers with thousands of processor cores.

A patient-specific modelling method of blood circulatory system for the numerical simulation of enhanced external counterpulsation

Lumped parameter model (LPM) is a common numerical model for hemodynamic simulation of human's blood circulatory system. The numerical simulation of enhanced external counterpulsation (EECP) is a typical biomechanical simulation process based on the LPM of blood circulatory system. In order to simulate patient-specific hemodynamic effects of EECP and develop best treatment strategy for each individual, this study developed an optimization algorithm to individualize LPM elements. Physiological data from 30 volunteers including approximate aortic pressure, cardiac output, ankle pressure and carotid artery flow were clinically collected as optimization objectives. A closed-loop LPM was established for the simulation of blood circulatory system. Aiming at clinical data, a sensitivity analysis for each element was conducted to identify the significant ones. We improved the traditional simulated annealing algorithm to iteratively optimize the sensitive elements. To verify the accuracy of the patient-specific model, 30 samples of simulated data were compared with clinical measurements. In addition, an EECP experiment was conducted on a volunteer to verify the applicability of the optimized model for the simulation of EECP. For these 30 samples, the optimization results show a slight difference between clinical data and simulated data. The average relative root mean square error is lower than 5%. For the subject of EECP experiment, the relative error of hemodynamic responses during EECP is lower than 10%. This slight error demonstrated a good state of optimization. The optimized modeling algorithm can effectively individualize the LPM for blood circulatory system, which is significant to the numerical simulation of patient-specific hemodynamics.

Long-term hemodynamic mechanism of enhanced external counterpulsation in the treatment of coronary heart disease: a geometric multiscale simulation

Enhanced external counterpulsation (EECP) is a noninvasive treatment method for coronary artery atherosclerosis that acts on the vascular endothelial cells. The intracoronary hemodynamic parameters that influence long-term treatment effect are the fundamental factors for the inhibition of intimal hyperplasia, which cannot be measured in real time. In order to optimize the long-term treatment effect of coronary heart disease, it is necessary to establish a method for quantified calculation of intracoronary hemodynamic parameters during counterpulsation to research the long-term hemodynamic mechanism of EECP. A geometric multiscale model coupled by the zero-dimensional (0D) lumped parameter model and the three-dimensional (3D) model of narrow coronary artery was established for the simulation of intracoronary hemodynamic environment. The 3D model was used to calculate the hemodynamic parameters such as wall shear stress (WSS) and oscillatory shear index (OSI), while the 0D model was used to simulate the blood circulatory system. Sequential pressure was applied to calves, thighs, and buttocks module in 0D model with the consideration of vessel collapse. Hemodynamic performance was compared with clinical reports to verify the effectiveness of the method. There were significant increases of the diastolic blood pressure (DBP), coronary flow, and the area-averaged WSS during application of EECP, while OSI behind stenosis has some decrease. The waveforms of coronary flow has good similarity with the clinical measured waveforms, and the differences between calculated mean arterial pressures (MAPs) and clinical measurements were within 1%. The fundamental factor in the cure of coronary heart disease by EECP is the improvement of WSS and the decrease of OSI. Comparing with the clinical reports, the immediate hemodynamic changes demonstrate the effectiveness of model. Intracoronary hemodynamic parameters during EECP could be acquired and the method could be used to simulate the long-term treatment effect of EECP. Graphical abstract.

Hemodynamic effects of enhanced external counterpulsation on cerebral arteries: a multiscale study

Background

Enhanced external counterpulsation (EECP) is an effective method for treating patients with cerebral ischemic stroke, while hemodynamics is the major contributing factor in the treatment of EECP. Different counterpulsation modes have the potential to lead to different acute and long-term hemodynamic changes, resulting in different treatment effects. However, various questions about appropriate counterpulsation modes for optimizing hemodynamic effects remain unanswered in clinical treatment.

Methods

A zero-dimensional/three-dimensional (0D/3D) geometric multiscale model of the cerebral artery was established to obtain acute hemodynamic indicators, including mean arterial pressure (MAP) and cerebral blood flow (CBF), as well as localized hemodynamic details for the cerebral artery, which includes wall shear stress (WSS) and oscillatory shear index (OSI). Counterpulsation was achieved by applying pressure on calf, thigh and buttock modules in the 0D model. Different counterpulsation modes including various pressure amplitudes and pressurization durations were applied to investigate hemodynamic responses, which impact acute and long-term treatment effects. Both vascular collapse and cerebral autoregulation were considered during counterpulsation.

Results

Variations of pressure amplitude and pressurization duration have different impacts on hemodynamic effects during EECP treatment. There were small differences in the hemodynamics when similar or different pressure amplitudes were applied to calves, thighs and buttocks. When increasing pressure amplitude was applied to the three body parts, MAP and CBF improved slightly. When pressure amplitude exceeded 200 mmHg, hemodynamic indicators almost never changed, demonstrating consistency with clinical data. However, hemodynamic indicators improved significantly with increasing pressurization duration. For pressurization durations of 0.5, 0.6 and 0.7 s, percentage increases for MAP during counterpulsation were 1.5%, 23.5% and 39.0%, for CBF were 1.2%, 23.4% and 41.6% and for time-averaged WSS were 0.2%, 43.5% and 85.0%, respectively.

Conclusions

When EECP was applied to patients with cerebral ischemic stroke, pressure amplitude applied to the three parts may remain the same. Patients may not gain much more benefit from EECP treatment by excessively increasing pressure amplitude above 200 mmHg. However, during clinical procedures, pressurization duration could be increased to 0.7 s during the cardiac circle to optimize the hemodynamics for possible superior treatment outcomes.

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.

A multiscale computational modeling for cerebral blood flow with aneurysms and/or stenoses

A 1-dimensional (1D)-3-dimensional (3D) multiscale model for the human vascular network was proposed by combining a low-fidelity 1D modeling of blood circulation to account for the global hemodynamics with a detailed 3D simulation of a zonal vascular segment. The coupling approach involves a direct exchange of flow and pressure information at interfaces between the 1D and 3D models and thus enables patient-specific morphological models to be inserted into flow network with minimum computational efforts. The proposed method was validated with good agreements against 3 simplified test cases where experimental data and/or full 3D numerical solution were available. The application of the method in aneurysm and stenosis studies indicated that the deformation of the geometry caused by the diseases may change local pressure loss and as a consequence lead to an alteration of flow rate to the vessel segment.

Quantification of near-wall hemodynamic risk factors in large-scale cerebral arterial trees

Detailed hemodynamic analysis of blood flow in pathological segments close to aneurysm and stenosis has provided physicians with invaluable information about the local flow patterns leading to vascular disease. However, these diseases have both local and global effects on the circulation of the blood within the cerebral tree. The aim of this paper is to demonstrate the importance of extending subject-specific hemodynamic simulations to the entire cerebral arterial tree with hundreds of bifurcations and vessels, as well as evaluate hemodynamic risk factors and waveform shape characteristics throughout the cerebral arterial trees. Angioarchitecture and in vivo blood flow measurement were acquired from healthy subjects and in cases with symptomatic intracranial aneurysm and stenosis. A global map of cerebral arterial blood flow distribution revealed regions of low to high hemodynamic risk that may significantly contribute to the development of intracranial aneurysms or atherosclerosis. Comparison of pre-intervention and post-intervention of pathological cases further shows large angular phase shift (~33.8°), and an augmentation of the peak-diastolic velocity. Hemodynamic indexes of waveform analysis revealed on average a 16.35% reduction in the pulsatility index after treatment from lesion site to downstream distal vessels. The lesion regions not only affect blood flow streamlines of the proximal sites but also generate pulse wave shift and disturbed flow in downstream vessels. This network effect necessitates the use of large-scale simulation to visualize both local and global effects of pathological lesions.

Flow instability detected in ruptured versus unruptured cerebral aneurysms at the internal carotid artery

Flow instability has emerged as a new hemodynamic metric hypothesized to have potential value in assessing the rupture risk of cerebral aneurysms. However, diverse findings have been reported in the literature. In the present study, high-resolution hemodynamic simulations were performed retrospectively on 35 aneurysms (10 ruptured & 25 unruptured) located at the internal carotid artery (ICA). Simulated hemodynamic parameters were statistically compared between the ruptured and unruptured aneurysms, with emphasis on examining the correlation of flow instability with the status of aneurysm rupture. Pronounced flow instability was detected in 20% (2 out of 10) of the ruptured aneurysms, whereas in 44% (11 out of 25) of the unruptured aneurysms. Statistically, the flow instability metric (quantified by the temporally and spatially averaged fluctuating kinetic energy over the aneurysm sac) did not differ significantly between the ruptured and unruptured aneurysms. In contrast, low wall shear stress area (LSA) and pressure loss coefficient (PLC) exhibited significant correlations with the status of aneurysm rupture. In conclusion, the present study suggests that the presence of flow instability may not correlate closely with the status of aneurysm rupture, at least for ICA aneurysms. On the other hand, the retrospective nature of the study and the small sample size may have to some extent compromised the reliability of the conclusion, and therefore large-scale prospective studies would be needed to further address the issue.

A computational model of the hepatic circulation applied to analyze the sensitivity of hepatic venous pressure gradient (HVPG) in liver cirrhosis

Measurement of hepatic venous pressure gradient (HVPG) is currently widely adopted to provide an estimate of portal pressure gradient (PPG) in the diagnosis and treatment of portal hypertension associated with liver cirrhosis. Despite the well-documented clinical utility of HVPG, it remains poorly understood how the relationship between HVPG and PPG is affected by factors involved in the pathogenesis and progression of cirrhosis. In the study, a computational model of the hepatic circulation calibrated to in vivo data was developed to simulate the procedure of HVPG measurement and quantitatively investigate the error of HVPG relative to PPG under various pathophysiological conditions. Obtained results confirmed the clinical consensus that HVPG is applicable to the assessment of portal hypertension caused by increased vascular resistance located primarily at the sinusoidal and postsinusoidal sites rather than at the presinusoidal site. On the other hand, our study demonstrated that the accuracy of HVPG measurement was influenced by many factors related to hepatic hemodynamics even in the case of sinusoidal portal hypertension. For instance, varying presinusoidal portal vascular resistance significantly altered the difference between HVPG and PPG, while an enhancement in portosystemic collateral flow tended to improve the accuracy of HVPG measurement. Moreover, it was found that presinusoidal and postsinusoidal vascular resistances interfered with each other with respect to their influence on HVPG measurement. These findings suggest that one should take into account patient-specific pathological conditions in order to achieve a better understanding and utilization of HVPG in the clinical practice.

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.

Multi-class and multi-scale models of complex biological phenomena

Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.