A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method

Numerical simulation and fast method for the 0D-1D multi-scale coupled model and its application in ischemic brain tissue blood flow problems

As living standards rise, more and more people are paying attention to their own health, especially issues such as cerebral thrombosis, cerebral infarction, and other cerebral blood flow problems. An accurate simulation of blood flow within cerebral vessels has emerged as a crucial area of research. In this study, we focus on microcirculatory blood flow in ischemic brain tissue and employ a 0D-1D geometric multi-scale coupled model to characterize this process. Given the intricate nature of human cerebral vessels, we apply a numerical method combining the finite element method and the third-order Runge-Kutta method to resolve the coupled model. To enhance computational efficiency, we introduce a fast method based on the reduced-order extrapolation algorithm. Our numerical example underscores the stability of the method and convergence accuracy to O h 3 + τ 3 , while significantly improving the accuracy and efficiency of blood flow simulation, making the mechanism analysis more accurate. Additionally, we present examples detailing variations and distribution of intracranial pressure and blood flow in ischemic brain tissue throughout a cardiac cycle. Both reduced vascular compliance and vascular stenosis can have adverse effects on intracranial cerebral pressure and blood flow, leading to insufficient local oxygen supply and negative effects on brain function. Meanwhile, there will also be corresponding changes in volume flow and pulsatile blood pressure.

Central arterial pressure estimation based on two peripheral pressure measurements using one-dimensional blood flow simulation

Aortic pressure can be estimated using one-dimensional arterial flow simulations. This study demonstrates that two peripheral pressure measurements can be used to acquire the central pressure curve through the patient-specific optimization of a set of system parameters. Radial and carotid pressure measurements and parameter optimization were performed in the case of 62 patients. The two calculated aortic curves were in good agreement, Systolic and Mean Blood Pressures differed on average by 0.5 and -0.5 mmHg, respectively. Good agreement was achieved with the transfer function method as well. The effect of carotid clamping is demonstrated using one resulting patient-specific arterial network.

Non-Invasive Tools in Perioperative Stroke Risk Assessment for Asymptomatic Carotid Artery Stenosis with a Focus on the Circle of Willis

This review aims to explore advancements in perioperative ischemic stroke risk estimation for asymptomatic patients with significant carotid artery stenosis, focusing on Circle of Willis (CoW) morphology based on the CTA or MR diagnostic imaging in the current preoperative diagnostic algorithm. Functional transcranial Doppler (fTCD), near-infrared spectroscopy (NIRS), and optical coherence tomography angiography (OCTA) are discussed in the context of evaluating cerebrovascular reserve capacity and collateral vascular systems, particularly the CoW. These non-invasive diagnostic tools provide additional valuable insights into the cerebral perfusion status. They support biomedical modeling as the gold standard for the prediction of the potential impact of carotid artery stenosis on the hemodynamic changes of cerebral perfusion. Intraoperative risk assessment strategies, including selective shunting, are explored with a focus on CoW variations and their implications for perioperative ischemic stroke and cognitive function decline. By synthesizing these insights, this review underscores the potential of non-invasive diagnostic methods to support clinical decision making and improve asymptomatic patient outcomes by reducing the risk of perioperative ischemic neurological events and preventing further cognitive decline.

Mechanistic insights on age-related changes in heart-aorta-brain hemodynamic coupling using a pulse wave model of the entire circulatory system

Age-related changes in aortic biomechanics can impact the brain by reducing blood flow and increasing pulsatile energy transmission. Clinical studies have shown that impaired cardiac function in patients with heart failure is associated with cognitive impairment. Although previous studies have attempted to elucidate the complex relationship between age-associated aortic stiffening and pulsatility transmission to the cerebral network, they have not adequately addressed the effect of interactions between aortic stiffness and left ventricle (LV) contractility (neither on energy transmission nor on brain perfusion). In this study, we use a well-established and validated one-dimensional blood flow and pulse wave computational model of the circulatory system to address how age-related changes in cardiac function and vasculature affect the underlying mechanisms involved in the LV-aorta-brain hemodynamic coupling. Our results reveal how LV contractility affects pulsatile energy transmission to the brain, even with preserved cardiac output. Our model demonstrates the existence of an optimal heart rate (near the normal human heart rate) that minimizes pulsatile energy transmission to the brain at different contractility levels. Our findings further suggest that the reduction in cerebral blood flow at low levels of LV contractility is more prominent in the setting of age-related aortic stiffening. Maintaining optimal blood flow to the brain requires either an increase in contractility or an increase in heart rate. The former consistently leads to higher pulsatile power transmission, and the latter can either increase or decrease subsequent pulsatile power transmission to the brain.NEW & NOTEWORTHY We investigated the impact of major aging mechanisms of the arterial system and cardiac function on brain hemodynamics. Our findings suggest that aging has a significant impact on heart-aorta-brain coupling through changes in both arterial stiffening and left ventricle (LV) contractility. Understanding the underlying physical mechanisms involved here can potentially be a key step for developing more effective therapeutic strategies that can mitigate the contributions of abnormal LV-arterial coupling toward neurodegenerative diseases and dementia.

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.

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

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

One-dimensional analysis method of pulsatile blood flow in arterial network for REBOA operations

Based on the generalized Darcy model, here we develop a linear one-dimensional (1D) composite model to predict the effects of the inserted balloon under REBOA operations on the dynamic characteristics of blood flow in flexible arterial networks. We first consider the effect of the decrease of cardiac output under different degrees of blood loss through employing the fourth-order lumped parameter model of cardiovascular system. Then, the effect of the inserted balloon is included by developing the relation between flow resistance and occlusion ratio with the neural network approach. Finally, the accuracy of the developed 1D composite model for REBOA operations, which can be solved analytically in the frequency domain, is verified by comparing to computational fluid dynamics (CFD) simulations. It is demonstrated that the 1D model is able to reproduce main features of the systemic circulation under balloon occlusion of the aorta during REBOA surgery. The 1D composite model could substantially reduce the computational time, which makes it possible to give the instant prediction of the working parameters during RABOA operations.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

The effect of cardiac properties on arterial pulse waves: An in-silico study

This study investigated the effects of cardiac properties variability on arterial pulse wave morphology using blood flow modelling and pulse wave analysis. A lumped-parameter model of the left part of the heart was coupled to a one-dimensional model of the arterial network and validated using reference pulse waveforms in turn verified by comparison with in vivo measurements. A sensitivity analysis was performed to assess the effects of variations in cardiac parameters on central and peripheral pulse waveforms. Results showed that left ventricle contractility, stroke volume, cardiac cycle duration, and heart valves impairment are determinants of central waveforms morphology, pulse pressure and its amplification. Contractility of the left atrium has negligible effects on arterial pulse waves. Results also suggested that it might be possible to infer left ventricular dysfunction by analysing the timing of the dicrotic notch and cardiac function by analysing PPG signals. This study has identified cardiac properties that may be extracted from in vivo central and peripheral pulse waves to assess cardiac function.

Optimised design of an arterial network model reproduces characteristic central and peripheral hemodynamic waveform features in young adults

Abstract

The arterial network in healthy young adults is thought to be structured to optimize wave reflection in the arterial system, producing an ascending aortic pressure waveform with three key features: early systolic peak, negative systolic augmentation and diastolic hump. One‐dimensional computer models have provided significant insights into arterial haemodynamics, but no previous models of the young adult have exhibited these three features. Given that this issue was likely to be related to unrepresentative or non‐optimized impedance properties of the model arterial networks, we developed a new ‘YoungAdult’ model that incorporated the following features: (i) a new and more accurate empirical equation for approximating wave speeds, based on area and relative distance to elastic–muscular arterial transition points; (ii) optimally matched arterial junctions; and (iii) an improved arterial network geometry that eliminated ‘within‐segment’ taper (which causes wave reflection in conduit arteries) whilst establishing ‘impedance‐preserving’ taper. These properties of the model led to wave reflection occurring predominantly at distal vascular beds, rather than in conduit arteries. The model predicted all three typical characteristics of an ascending aortic pressure waveform observed in young adults. When compared with non‐invasively acquired pressure and velocity measurements (obtained via tonometry and Doppler ultrasound in seven young adults), the model was also shown to reproduce the typical waveform morphology observed in the radial, brachial, carotid, temporal, femoral and tibial arteries. The YoungAdult model provides support for the concept that the arterial tree impedance in healthy young adults is exquisitely optimized, and it provides an important baseline model for investigating cardiovascular changes in ageing and disease states.

Key points

The origin of wave reflection in the arterial system is controversial, but reflection properties are likely to give rise to characteristic haemodynamic features in healthy young adults, including an early systolic peak, negative systolic augmentation and diastolic hump in the ascending aortic pressure waveform, and triphasic velocity profiles in peripheral arteries. Although computational modelling provides insights into arterial haemodynamics, no previous models have predicted all these features.

An established arterial network model was optimized by incorporating the following features: (i) a more accurate representation of arterial wave speeds; (ii) precisely matched junctions; and (iii) impedance‐preserving tapering, thereby minimizing wave reflection in conduit arteries in the forward direction. Comparison with in vivo data (n = 7 subjects) indicated that the characteristic waveform features in young adults were predicted accurately.

Our findings strongly imply that a healthy young arterial system is structured to optimize wave reflection in the main conduit arteries and that reflection of forward waves occurs primarily in the vicinity of vascular beds.

A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D-0D model to a limit cycle under baseline conditions, the model's ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible.

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.

Uncertainty quantification implementations in human hemodynamic flows

BACKGROUND AND OBJECTIVE

Human hemodynamic modeling is usually influenced by uncertainties occurring from a considerable unavailability of information linked to the boundary conditions and the physical properties used in the numerical models. Calculating the effect of these uncertainties on the numerical findings along the cardiovascular system is a demanding process due to the complexity of the morphology of the body and the area dynamics. To cope with all these difficulties, Uncertainty Quantification (UQ) methods seem to be an ideal tool.

RESULTS

This study focuses on analyzing and summarizing some of the recent research efforts and directions of implementing UQ in human hemodynamic flows by analyzing 139 research papers. Initially, the suitability of applying this approach is analyzed and demonstrated. Then, an overview of the most significant research work in various fields of biomedical hemodynamic engineering is presented. Finally, it is attempted to identify any possible forthcoming directions for research and methodological progress of UQ in biomedical sciences.

CONCLUSION

This review concludes that by finding the best statistical methods and parameters to represent the propagated uncertainties, while achieving a good interpretation of the interaction between input-output, is crucial for implementing UQ in biomedical sciences.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

Application of physics-based flow models in cardiovascular medicine: Current practices and challenges

Personalized physics-based flow models are becoming increasingly important in cardiovascular medicine. They are a powerful complement to traditional methods of clinical decision-making and offer a wealth of physiological information beyond conventional anatomic viewing using medical imaging data. These models have been used to identify key hemodynamic biomarkers, such as pressure gradient and wall shear stress, which are associated with determining the functional severity of cardiovascular diseases. Importantly, simulation-driven diagnostics can help researchers understand the complex interplay between geometric and fluid dynamic parameters, which can ultimately improve patient outcomes and treatment planning. The possibility to compute and predict diagnostic variables and hemodynamics biomarkers can therefore play a pivotal role in reducing adverse treatment outcomes and accelerate development of novel strategies for cardiovascular disease management.

On the poro-elastic models for microvascular blood flow resistance: An in vitro validation

Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young's modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the invitro and insilico simulation of different microvascular conditions.

Multiscale modeling of blood flow to assess neurological complications in patients supported by venoarterial extracorporeal membrane oxygenation

Computational blood flow models in large arteries elucidate valuable relationships between cardiovascular diseases and hemodynamics, leading to improvements in treatment planning and clinical decision making. One such application with potential to benefit from simulation is venoarterial extracorporeal membrane oxygenation (VA-ECMO), a support system for patients with cardiopulmonary failure. VA-ECMO patients develop high rates of neurological complications, partially due to abnormal blood flow throughout the vasculature from the VA-ECMO system. To better understand these hemodynamic changes, it is important to resolve complex local flow parameters derived from three-dimensional (3D) fluid dynamics while also capturing the impact of VA-ECMO support throughout the systemic arterial system. As high-resolution 3D simulations of the arterial network remain computationally expensive and intractable for large studies, a validated, multiscale model is needed to compute both global effects and high-fidelity local hemodynamics. In this work, we developed and demonstrated a framework to model hemodynamics in VA-ECMO patients using coupled 3D and one-dimensional (1D) models (1D→3D). We demonstrated the ability of these multiscale models to simulate complex flow patterns in specific regions of interest while capturing bulk flow throughout the systemic arterial system. We compared 1D, 3D, and 1D→3D coupled models and found that multiscale models were able to sufficiently capture both global and local hemodynamics in the cerebral arteries and aorta in VA-ECMO patients. This study is the first to develop and compare 1D, 3D, and 1D→ 3D coupled models on the larger arterial system scale in VA-ECMO patients, with potential use for other large scale applications.

Diagnostic performance of virtual fractional flow reserve derived from routine coronary angiography using segmentation free reduced order (1-dimensional) flow modelling

Introduction

Fractional flow reserve (FFR) improves assessment of the physiological significance of coronary lesions compared with conventional angiography. However, it is an invasive investigation. We tested the performance of a virtual FFR (1D-vFFR) using routine angiographic images and a rapidly performed reduced order computational model.

Methods

Quantitative coronary angiography (QCA) was performed in 102 with coronary lesions assessed by invasive FFR. A 1D-vFFR for each lesion was created using reduced order (one-dimensional) computational flow modelling derived from conventional angiographic images and patient specific estimates of coronary flow. The diagnostic accuracy of 1D-vFFR and QCA derived stenosis was compared against the gold standard of invasive FFR using area under the receiver operator characteristic curve (AUC).

Results

QCA revealed the mean coronary stenosis diameter was 44% ± 12% and lesion length 13 ± 7 mm. Following angiography calculation of the 1DvFFR took less than one minute. Coronary stenosis (QCA) had a significant but weak correlation with FFR (r = -0.2, p = 0.04) and poor diagnostic performance to identify lesions with FFR <0.80 (AUC 0.39, p = 0.09), (sensitivity - 58% and specificity - 26% at a QCA stenosis of 50%). In contrast, 1D-vFFR had a better correlation with FFR (r = 0.32, p = 0.01) and significantly better diagnostic performance (AUC 0.67, p = 0.007), (sensitivity - 92% and specificity - 29% at a 1D-vFFR of 0.7).

Conclusions

1D-vFFR improves the determination of functionally significant coronary lesions compared with conventional angiography without requiring a pressure-wire or hyperaemia induction. It is fast enough to influence immediate clinical decision-making but requires further clinical evaluation.

Towards enabling a cardiovascular digital twin for human systemic circulation using inverse analysis

An exponential rise in patient data provides an excellent opportunity to improve the existing health care infrastructure. In the present work, a method to enable cardiovascular digital twin is proposed using inverse analysis. Conventionally, accurate analytical solutions for inverse analysis in linear problems have been proposed and used. However, these methods fail or are not efficient for nonlinear systems, such as blood flow in the cardiovascular system (systemic circulation) that involves high degree of nonlinearity. To address this, a methodology for inverse analysis using recurrent neural network for the cardiovascular system is proposed in this work, using a virtual patient database. Blood pressure waveforms in various vessels of the body are inversely calculated with the help of long short-term memory (LSTM) cells by inputting pressure waveforms from three non-invasively accessible blood vessels (carotid, femoral and brachial arteries). The inverse analysis system built this way is applied to the detection of abdominal aortic aneurysm (AAA) and its severity using neural networks.

Conduit arterial wave reflection promotes pressure transmission but impedes hydraulic energy transmission to the microvasculature

With aging, a reduction in the stiffness gradient between elastic and muscular arteries is thought to reduce wave reflection in conduit arteries, leading to increased pulsatile pressure transmission into the microvasculature. This assumes that wave reflection limits pressure transmission in arteries. However, using a computational model, we showed that wave reflection promotes pulsatile pressure transmission, although it does limit hydraulic energy transmission. Increased microvascular pulse pressure with aging is instead related to decreasing arterial compliance.

Personalization of electro-mechanical models of the pressure-overloaded left ventricle: fitting of Windkessel-type afterload models

Computer models of left ventricular (LV) electro-mechanics (EM) show promise as a tool for assessing the impact of increased afterload upon LV performance. However, the identification of unique afterload model parameters and the personalization of EM LV models remains challenging due to significant clinical input uncertainties. Here, we personalized a virtual cohort of N = 17 EM LV models under pressure overload conditions. A global-local optimizer was developed to uniquely identify parameters of a three-element Windkessel (Wk3) afterload model. The sensitivity of Wk3 parameters to input uncertainty and of the EM LV model to Wk3 parameter uncertainty was analysed. The optimizer uniquely identified Wk3 parameters, and outputs of the personalized EM LV models showed close agreement with clinical data in all cases. Sensitivity analysis revealed a strong dependence of Wk3 parameters on input uncertainty. However, this had limited impact on outputs of EM LV models. A unique identification of Wk3 parameters from clinical data appears feasible, but it is sensitive to input uncertainty, thus depending on accurate invasive measurements. By contrast, the EM LV model outputs were less sensitive, with errors of less than 8.14% for input data errors of 10%, which is within the bounds of clinical data uncertainty. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Minor impact of constraint from perivascular flow probes on wave intensity analysis

Perivascular flow probes are considered the gold-standard for measuring volumetric blood flow in animal studies. Although flow probes are generally placed non-constrictively around the vessel of interest, pressure-elevating interventions performed during an experiment may lead to vessel expansion and some probe-vessel impingement, particularly in highly compliant vessels such as adult sheep aorta or major pulmonary arteries in fetus lambs. This study assessed to what extent such mild flow probe constraint may impact on wave intensity analysis. We also investigated whether errors arising from flow probe constraint could explain apparent pressure reflection indices (R_p > 1) that have been observed in fetus lamb pulmonary arteries under some experimental conditions. These questions were investigated with one-dimensional models of an adult sheep aorta and fetus lamb pulmonary artery, with a virtual flow probe incorporated as a non-linear external constraint term in the vessel constitutive equation. Model-derived flow and pressure were subjected to standard analysis procedures that would be applied experimentally (correcting for apparent velocity lags and calculating wave speed via the PU-loop method). For the adult sheep model, simulations covering a wide range of haemodynamic conditions revealed a mostly minor effect (<10%) of probe constraint on the intensity and pressure effects of the three major waves (forward compression wave, forward decompression wave, backward compression wave). Moreover, flow probe constraint had essentially no impact on R_p in the fetus lamb model, suggesting that such constraint is unlikely to be responsible for an observed R_p > 1. Mild flow probe constraint is likely to have little impact on wave intensity analysis.

Determining the impacts of venoarterial extracorporeal membrane oxygenation on cerebral oxygenation using a one-dimensional blood flow simulator

Venoarterial extracorporeal membrane oxygenation (VA-ECMO) is a mechanical system that provides rapid and short-term support for patients with cardiac failure. In many patients, pulmonary function is also impaired, resulting in poorly-oxygenated cardiac outflow competing against well-oxygenated VA-ECMO outflow, a condition known as North-South syndrome. North-South syndrome is a primary concern because of its potential to cause cerebral hypoxia, which has a critical influence on neurological complications often seen in this patient population. In order to reduce ischemic neurological complications, it is important to understand how clinical decisions regarding VA-ECMO parameters influence blood oxygenation. Here, we studied the impacts of flow rate and cannulation site on oxygenation using a one-dimensional (1D) model to simulate blood flow. Our model was initially tested by comparing blood flow results to those observed from experimental work in VA-ECMO patients. The 1D model was combined with a two-phase flow model to simulate oxygenation. Additionally, the influence of various other clinician-tunable parameters on oxygenation in the common carotid arteries (CCAs) were tested, including, blood viscosity, cannula position within the insertion artery, heart rate, and systemic vascular resistance (SVR), as well as geometrical changes such as arterial radius and length. Our results indicated that blood oxygenation to the brain strongly depended on the cannula insertion site and the VA-ECMO flow rate with a weaker but potentially significant dependence on arterial radius. During femoral cannulation, VA-ECMO flow rates greater than ~4.9L/min were needed to perfuse the CCAs. However, axillary and central cannulation began to perfuse the CCAs at significantly lower flow (~1L/min). These results may help explain the incidence of cerebral hypoxia in this patient population and the common need to change cannulation strategies during treatment to address this clinical problem. While this work describes patient-averaged results, determining these relationships between VA-ECMO parameters and cerebral hypoxia is an important step towards future work to develop patient-specific models that clinicians can use to improve outcomes.

Effects of myocardial function and systemic circulation on regional coronary perfusion

Cardiac-coronary interaction and the effects of its pathophysiological variations on spatial heterogeneity of coronary perfusion and myocardial work are still poorly understood. This hypothesis-generating study predicts spatial heterogeneities in both regional cardiac work and perfusion that offer a new paradigm on the vulnerability of the subendocardium to ischemia, particularly at the apex. We propose a mathematical and computational modeling framework to simulate the interaction of left ventricular mechanics, systemic circulation, and coronary microcirculation. The computational simulations revealed that the relaxation rate of the myocardium has a significant effect whereas the contractility has a marginal effect on both the magnitude and transmural distribution of coronary perfusion. The ratio of subendocardial to subepicardial perfusion density (Q_endo/Q_epi) changed by -12 to +6% from a baseline value of 1.16 when myocardial contractility was varied by +25 and -10%, respectively; Q_endo/Q_epi changed by 37% when sarcomere relaxation rate, b, was faster and increased by 10% from the baseline value. The model predicts axial differences in regional myocardial work and perfusion density across the wall thickness. Regional myofiber work done at the apex is 30-50% lower than at the center region, whereas perfusion density in the apex is lower by only 18% compared with the center. There are large axial differences in coronary flow and myocardial work at the subendocardial locations, with the highest differences located at the apex region. A mismatch exists between perfusion density and regional work done at the subendocardium. This mismatch is speculated to be compensated by coronary autoregulation.NEW & NOTEWORTHY We present a model of left ventricle perfusion based on an anatomically realistic coronary tree structure that includes its interaction with the systemic circulation. Left ventricular relaxation rate has a significant effect on the regional distribution of coronary flow and myocardial work.

Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data

Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise invasive measurements. To correctly simulate body hemodynamics, the viscoelastic properties of vessels walls are a key aspect to be taken into account as they play an essential role in cardiovascular behavior. The present work aims to apply the augmented fluid-structure interaction system of blood flow to real case studies to assess the validity of the model as a valuable resource to improve cardiovascular diagnostics and the treatment of pathologies. Main contributions of the paper include the evaluation of viscoelastic tube laws, estimation of viscoelastic parameters and comparison of models with literature results and in-vivo experiments. The ability of the model to correctly simulate pulse waveforms in single arterial segments is verified using literature benchmark test cases, designed taking into account a simple elastic behavior of the wall in the upper thoracic aorta and in the common carotid artery. Furthermore, in-vivo pressure waveforms, extracted from tonometric measurements performed on four human common carotid arteries and two common femoral arteries, are compared to numerical solutions. It is highlighted that the viscoelastic damping effect of arterial walls is required to avoid an overestimation of pressure peaks. Finally, an effective procedure to estimate the viscoelastic parameters of the model is herein proposed, which returns hysteresis curves of the common carotid arteries dissipating energy fractions in line with values calculated from literature hysteresis loops in the same vessel.

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.

A semi-active human digital twin model for detecting severity of carotid stenoses from head vibration-A coupled computational mechanics and computer vision method

In this work, we propose a methodology to detect the severity of carotid stenosis from a video of a human face with the help of a coupled blood flow and head vibration model. This semi-active digital twin model is an attempt to link noninvasive video of a patient face to the percentage of carotid occlusion. The pulsatile nature of blood flow through the carotid arteries induces a subtle head vibration. This vibration is a potential indicator of carotid stenosis severity, and it is exploited in the present study. A head vibration model has been proposed in the present work that is linked to the forces generated by blood flow with or without occlusion. The model is used to generate a large number of virtual head vibration data for different degrees of occlusion. In order to determine the in vivo head vibration, a computer vision algorithm is adopted to use human face videos. The in vivo vibrations are compared against the virtual vibration data generated from the coupled computational blood flow/vibration model. A comparison of the in vivo vibration is made against the virtual data to find the best fit between in vivo and virtual data. The preliminary results on healthy subjects and a patient clearly indicate that the model is accurate and it possesses the potential for detecting approximate severity of carotid artery stenoses.

A novel, FFT-based one-dimensional blood flow solution method for arterial network

In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for the vessel skin friction through the use of Womersley solution. To incorporate nonlinear effects, a novel approximation method is proposed to enable calculation of nonlinear corrections. Unlike similar methods available in the literature, the set of algebraic equations required for every harmonic is constructed automatically. The result is a generalized, robust and fast method to accurately capture the increasing pulse wave velocity downstream as well as steepening of the pulse front. The proposed method is shown to be appropriate for incorporating correct convection and diffusion coefficients. We show that the proposed method is fast and accurate and it can be an effective tool for 1D modelling of blood flow in human arterial networks.

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.

Studying The Sensitivity Of Coronary Blood Flow Using Nondimensional Analysis

Nondimensional analysis was used to develop a novel model of coronary blood flow. In addition to general hemodynamics, the model was used to study the sensitivity of the arterial flow to variations in characteristic lumped parameters. Experimental hemodynamic data obtained from four normal healthy pigs were used in the current study. The results suggest that the mean coronary arterial flow is primarily sensitive to the flow and elasticity parameters of the coronary vasculature. Other flow features were also studied, and it was shown that the sensitivities of the general flow waveforms are influenced to different extents by the perturbations of these parameters. More specifically, the flow coefficient affects the systolic inflow more than the diastolic portion; conversely, the elasticity coefficient has more impact on the diastolic period.

Influence of ageing on human body blood flow and heat transfer: A detailed computational modelling study

Ageing plays a fundamental role in arterial blood transport and heat transfer within a human body. The aim of this work is to provide a comprehensive methodology, based on biomechanical considerations, for modelling arterial flow and energy exchange mechanisms in the body accounting for age-induced changes. The study outlines a framework for age-related modifications within several interlinked subsystems, which include arterial stiffening, heart contractility variations, tissue volume and property changes, and thermoregulatory system deterioration. Some of the proposed age-dependent governing equations are directly extrapolated from experimental data sets. The computational framework is demonstrated through numerical experiments, which show the impact of such age-related changes on arterial blood pressure, local temperature distribution, and global body thermal response. The proposed numerical experiments show that the age-related changes in arterial convection do not significantly affect the tissue temperature distribution. Results also highlight age-related effects on the sweating mechanism, which lead to a significant reduction in heat dissipation and a subsequent rise in skin and core temperatures.

The dynamics of a healthy and infected red blood cell in flow through constricted channels: A DPD simulation

Understanding the dynamics of red blood cell (RBC) motion under in silico conditions is central to the development of cost-effective diagnostic tools. Specifically, unraveling the relationship between the rheological properties and the nature of shape change in the RBC (healthy or infected) can be extremely useful. In case of malarial infection, RBC progressively loses its deformability and tends to occlude the microvessel. In the present study, detailed mesoscopic simulations are performed to investigate the deformation dynamics of an RBC in flow through a constricted channel. Specifically, the manifestation of viscous forces (through flow rates) on the passage and blockage characteristics of a healthy red blood cell (hRBC) vis-á-vis an infected red blood cell (iRBC) are investigated. A finite-sized dissipative particle dynamics framework is used to model plasma in conjunction with a discrete model for the RBC. Instantaneous wall boundary method was used to model no-slip wall boundary conditions with a good control on the near-wall density fluctuations and compressibility effects. To investigate the microvascular occlusion, the RBC motion through 2 types of constricted channels, viz, (1) a tapered microchannel and (2) a stenosed-type microchannel, were simulated. It was observed that the deformation of an infected cell was much less compared with a healthy cell, with an attendant increase in the passage time. Apart from the qualitative features, deformation indices were obtained. The deformation of hRBC was sudden, while the iRBC deformed slowly as it traversed through the constriction. For higher flow rates, both hRBC and iRBC were found to undergo severe deformation. Even under low flow rates, hRBC could easily traverse past the constricted channel. However, for sufficiently slow flow rates (eg, capillary flows), the microchannel was found to be completely blocked by the iRBC.

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.

Major influence of a 'smoke and mirrors' effect caused by wave reflection on early diastolic coronary arterial wave intensity

KEY POINTS

Coronary wave intensity analysis (WIA) is an emerging technique for assessing upstream and downstream influences on myocardial perfusion. It is thought that a dominant backward decompression wave (BDW_dia ) is generated by a distal suction effect, while early-diastolic forward decompression (FDW_dia ) and compression (FCW_dia ) waves originate in the aorta. We show that wave reflection also makes a substantial contribution to FDW_dia , FCW_dia and BDW_dia , as quantified by a novel method. In 18 sheep, wave reflection accounted for ∼70% of BDW_dia , whereas distal suction dominated in a computer model representing a hypertensive human. Non-linear addition/subtraction of mechanistically distinct waves (e.g. wave reflection and distal suction) obfuscates the true contribution of upstream and downstream forces on measured waves (the 'smoke and mirrors' effect). The mechanisms underlying coronary WIA are more complex than previously thought and the impact of wave reflection should be considered when interpreting clinical and experimental data.

ABSTRACT

Coronary arterial wave intensity analysis (WIA) is thought to provide clear insight into upstream and downstream forces on coronary flow, with a large early-diastolic surge in coronary flow accompanied by a prominent backward decompression wave (BDW_dia ), as well as a forward decompression wave (FDW_dia ) and forward compression wave (FCW_dia ). The BDW_dia is believed to arise from distal suction due to release of extravascular compression by relaxing myocardium, while FDW_dia and FCW_dia are thought to be transmitted from the aorta into the coronary arteries. Based on an established multi-scale computational model and high-fidelity measurements from the proximal circumflex artery (Cx) of 18 anaesthetized sheep, we present evidence that wave reflection has a major impact on each of these three waves, with a non-linear addition/subtraction of reflected waves obscuring the true influence of upstream and downstream forces through concealment and exaggeration, i.e. a 'smoke and mirrors' effect. We also describe methods, requiring additional measurement of aortic WIA, for unravelling the separate influences of wave reflection versus active upstream/downstream forces on coronary waves. Distal wave reflection accounted for ∼70% of the BDW_dia in sheep, but had a lesser influence (∼25%) in the computer model representing a hypertensive human. Negative reflection of the BDW_dia at the coronary-aortic junction attenuated the Cx FDW_dia (by ∼40% in sheep) and augmented Cx FCW_dia (∼5-fold), relative to the corresponding aortic waves. We conclude that wave reflection has a major influence on early-diastolic WIA, and thus needs to be considered when interpreting coronary WIA profiles.

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.

On the impact of modelling assumptions in multi-scale, subject-specific models of aortic haemodynamics

Simulation of haemodynamics has become increasingly popular within the research community. Irrespective of the modelling approach (zero-dimensional (0D), one-dimensional (1D) or three-dimensional (3D)), in vivo measurements are required to personalize the arterial geometry, material properties and boundary conditions of the computational model. Limitations in in vivo data acquisition often result in insufficient information to determine all model parameters and, hence, arbitrary modelling assumptions. Our goal was to minimize and understand the impact of modelling assumptions on the simulated blood pressure, flow and luminal area waveforms by studying a small region of the systemic vasculature—the upper aorta—and acquiring a rich array of non-invasive magnetic resonance imaging and tonometry data from a young healthy volunteer. We first investigated the effect of different modelling assumptions for boundary conditions and material parameters in a 1D/0D simulation framework. Strategies were implemented to mitigate the impact of inconsistencies in the in vivo data. Average relative errors smaller than 7% were achieved between simulated and in vivo waveforms. Similar results were obtained in a 3D/0D simulation framework using the same inflow and outflow boundary conditions and consistent geometrical and mechanical properties. We demonstrated that accurate subject-specific 1D/0D and 3D/0D models of aortic haemodynamics can be obtained using non-invasive clinical data while minimizing the number of arbitrary modelling decisions.

A novel modelling approach to energy transport in a respiratory system

In this paper, energy transport in a respiratory tract is modelled using the finite element method for the first time. The upper and lower respiratory tracts are approximated as a 1-dimensional domain with varying cross-sectional and surface areas, and the radial heat conduction in the tissue is approximated using the 1-dimensional cylindrical coordinate system. The governing equations are solved using 1-dimensional linear finite elements with convective and evaporative boundary conditions on the wall. The results obtained for the exhalation temperature of the respiratory system have been compared with the available animal experiments. The study of a full breathing cycle indicates that evaporation is the main mode of heat transfer, and convection plays almost negligible role in the energy transport. This is in-line with the results obtained from animal experiments.

An implicit solver for 1D arterial network models

In this study, the 1D blood flow equations are solved using a newly proposed enhanced trapezoidal rule method (ETM), which is an extension to the simplified trapezoidal rule method. At vessel junctions, the conservation of mass and conservation of total pressure are held as system constraints using Lagrange multipliers that can be physically interpreted as external flow rates. The ETM scheme is compared with published arterial network benchmark problems and a dam break problem. Strengths of the ETM scheme include being simple to implement, intuitive connection to lumped parameter models, and no restrictive stability criteria such as the Courant-Friedrichs-Lewy (CFL) number. The ETM scheme does not require the use of characteristics at vessel junctions, or for inlet and outlet boundary conditions. The ETM forms an implicit system of equations, which requires only one global solve per time step for pressure, followed by flow rate update on the elemental system of equations; thus, no iterations are required per time step. Consistent results are found for all benchmark cases, and for a 56-vessel arterial network problem, it gives very satisfactory solutions at a spatial and time discretization that results in a maximum CFL of 3, taking 4.44 seconds per cardiac cycle. By increasing the time step and element size to produce a maximum CFL number of 15, the method takes only 0.39 second per cardiac cycle with only a small compromise on accuracy.

Modelling accidental hypothermia effects on a human body under different pathophysiological conditions

Accidental exposure to cold water environment is one of the most challenging situations in which hypothermia occurs. In the present work, we aim to characterise the energy balance of a human body subjected to such extreme environmental conditions. This study is carried out using a recently developed computational model and by setting boundary conditions needed to simulate the effect of cold surrounding environment. A major finding is the capacity of the body core regions to maintain their temperature high for a substantial amount of time, even under the most extreme environmental conditions. We also considered two disease states that highlight the spectrum of possible pathologies implicated in thermal regulation of the human body. These states are (i) cardiomyopathy, which affects the operating capacity of the heart, and (ii) malnutrition, which directly impairs the body’s ability to regulate heat exchange with the environment. We have found that cardiomyopathy has little influence on the thermal balance of the human body, whereas malnutrition has a profound negative effect on the thermal balance and leads to dramatic reduction in core temperature.

Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we comment on some theoretical differences among models and systematically compare them for physiologically relevant vessel parameters, network topology, and boundary data. In particular, the effect of the velocity profile is investigated in the cases of both smooth and discontinuous solutions, and a recommendation for a physiological model is provided. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.

Data assimilation for identification of cardiovascular network characteristics

A method to estimate the hemodynamics parameters of a network of vessels using an Ensemble Kalman filter is presented. The elastic moduli (Young's modulus) of blood vessels and the terminal boundary parameters are estimated as the solution of an inverse problem. Two synthetic test cases and a configuration where experimental data are available are presented. The sensitivity analysis confirms that the proposed method is quite robust even with a few numbers of observations. The simulations with the estimated parameters recovers target pressure or flow rate waveforms at given specific locations, improving the state-of-the-art predictions available in the literature. This shows the effectiveness and efficiency of both the parameter estimation algorithm and the blood flow model.

1-D blood flow modelling in a running human body

In this paper an attempt was made to simulate blood flow in a mobile human arterial network, specifically, in a running human subject. In order to simulate the effect of motion, a previously published immobile 1-D model was modified by including an inertial force term into the momentum equation. To calculate inertial force, gait analysis was performed at different levels of speed. Our results show that motion has a significant effect on the amplitudes of the blood pressure and flow rate but the average values are not effected significantly.

A novel method for non-invasively detecting the severity and location of aortic aneurysms

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstrates the methods’ ability to detect the location and severity of an aortic aneurysm through the analysis of flow waveforms in clinically accessible locations. Therefore, the proposed methodology shows a high potential for non-invasive aneurysm detectors/monitors.

An advanced computational bioheat transfer model for a human body with an embedded systemic circulation

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions.

FEA modeling and fluid flow simulation of human rectum with inserted bowel catheters

In this project, fluid flow and fluid-structure interaction are studied for the human lower gastrointestinal (GI) region. The study consists of two steps. First, we apply meshing methods to discretize both the human lower GI model and the catheter model at sufficient resolution suitable for importing into a Finite Element Analysis (FEA) tool. For model discretization, 3D models of the colon reconstructed from human MRI slices are used to obtain the valid inlet and outlet boundary surfaces. To resolve the viscous boundary layer in flow studies, a special structure of the near-wall volumetric mesh is built by triangular prisms that construct quasi-structured, multiple near-boundary sub-layers. Second, we study the computational fluid dynamics. Transient numerical calculation of flow profiles are conducted for velocity profiles, flow rate division, pressure gradient variation, and flow cosmetics. The analysis of biofluid interactions with medical catheters is conducted to help understand how the biofluid behaves in various conditions to address design related concerns such as leakage problems.

Methods of graph network reconstruction in personalized medicine

The paper addresses methods for generation of individualized computational domains on the basis of medical imaging dataset. The computational domains will be used in one-dimensional (1D) and three-dimensional (3D)-1D coupled hemodynamic models. A 1D hemodynamic model employs a 1D network of a patient-specific vascular network with large number of vessels. The 1D network is the graph with nodes in the 3D space which bears additional geometric data such as length and radius of vessels. A 3D hemodynamic model requires a detailed 3D reconstruction of local parts of the vascular network. We propose algorithms which extend the automated segmentation of vascular and tubular structures, generation of centerlines, 1D network reconstruction, correction, and local adaptation. We consider two modes of centerline representation: (i) skeletal segments or sets of connected voxels and (ii) curved paths with corresponding radii. Individualized reconstruction of 1D networks depends on the mode of centerline representation. Efficiency of the proposed algorithms is demonstrated on several examples of 1D network reconstruction. The networks can be used in modeling of blood flows as well as other physiological processes in tubular structures. Copyright © 2015 John Wiley & Sons, Ltd.