The multi-scale modelling of coronary blood flow

Modelling coronary flow and myocardial perfusion by integrating a structured-tree coronary flow model and a hyperelastic left ventricle model

BACKGROUND AND OBJECTIVE

There is an increasing demand to establish integrated computational models that facilitate the exploration of coronary circulation in physiological and pathological contexts, particularly concerning interactions between coronary flow dynamics and myocardial motion. The field of cardiology has also demonstrated a trend toward personalised medicine, where these integrated models can be instrumental in integrating patient-specific data to improve therapeutic outcomes. Notably, incorporating a structured-tree model into such integrated models is currently absent in the literature, which presents a promising prospect. Thus, the goal here is to develop a novel computational framework that combines a 1D structured-tree model of coronary flow in human coronary vasculature with a 3D left ventricle model utilising a hyperelastic constitutive law, enabling the physiologically accurate simulation of coronary flow dynamics.

METHODS

We adopted detailed geometric information from previous studies of both coronary vasculature and left ventricle to construct the coronary flow model and the left ventricle model. The structured-tree model for coronary flow was expanded to encompass the effect of time-varying intramyocardial pressure on intramyocardial blood vessels. Simultaneously, the left ventricle model served as a robust foundation for the calculation of intramyocardial pressure and subsequent quantitative evaluation of myocardial perfusion. A one-way coupling framework between the two models was established to enable the evaluation and examination of coronary flow dynamics and myocardial perfusion.

RESULTS

Our predicted coronary flow waveforms aligned well with published experimental data. Our model precisely captured the phasic pattern of coronary flow, including impeded or even reversed flow during systole. Moreover, our assessment of coronary flow, considering both globally and regionally averaged intramyocardial pressure, demonstrated that elevated intramyocardial pressure corresponds to increased impeding effects on coronary flow. Furthermore, myocardial blood flow simulated from our model was comparable with MRI perfusion data at rest, showcasing the capability of our model to predict myocardial perfusion.

CONCLUSIONS

The integrated model introduced in this study presents a novel approach to achieving physiologically accurate simulations of coronary flow and myocardial perfusion. It holds promise for its clinical applicability in diagnosing insufficient myocardial perfusion.

A comprehensive mathematical model for cardiac perfusion

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes-Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.

Rapid virtual fractional flow reserve using 3D computational fluid dynamics

Aims

Over the last ten years, virtual Fractional Flow Reserve (vFFR) has improved the utility of Fractional Flow Reserve (FFR), a globally recommended assessment to guide coronary interventions. Although the speed of vFFR computation has accelerated, techniques utilising full 3D computational fluid dynamics (CFD) solutions rather than simplified analytical solutions still require significant time to compute.

Methods and results

This study investigated the speed, accuracy and cost of a novel 3D-CFD software method based upon a graphic processing unit (GPU) computation, compared with the existing fastest central processing unit (CPU)-based 3D-CFD technique, on 40 angiographic cases. The novel GPU simulation was significantly faster than the CPU method (median 31.7 s (Interquartile Range (IQR) 24.0-44.4s) vs. 607.5 s (490-964 s), P < 0.0001). The novel GPU technique was 99.6% (IQR 99.3-99.9) accurate relative to the CPU method. The initial cost of the GPU hardware was greater than the CPU (£4080 vs. £2876), but the median energy consumption per case was significantly less using the GPU method (8.44 (6.80-13.39) Wh vs. 2.60 (2.16-3.12) Wh, P < 0.0001).

Conclusion

This study demonstrates that vFFR can be computed using 3D-CFD with up to 28-fold acceleration than previous techniques with no clinically significant sacrifice in accuracy.

Oxygen-sensing pathways below autoregulatory threshold act to sustain myocardial oxygen delivery during reductions in perfusion pressure

The coronary circulation has an innate ability to maintain constant blood flow over a wide range of perfusion pressures. However, the mechanisms responsible for coronary autoregulation remain a fundamental and highly contested question. This study interrogated the local metabolic hypothesis of autoregulation by testing the hypothesis that hypoxemia-induced exaggeration of the metabolic error signal improves the autoregulatory response. Experiments were performed on open-chest anesthetized swine during stepwise changes in coronary perfusion pressure (CPP) from 140 to 40 mmHg under normoxic (n = 15) and hypoxemic (n = 8) conditions, in the absence and presence of dobutamine-induced increases in myocardial oxygen consumption (MVO2) (n = 5-7). Hypoxemia (PaO2 < 40 mmHg) decreased coronary venous PO2 (CvPO2) ~ 30% (P < 0.001) and increased coronary blood flow ~ 100% (P < 0.001), sufficient to maintain myocardial oxygen delivery (P = 0.14) over a wide range of CPPs. Autoregulatory responsiveness during hypoxemia-induced reductions in CvPO2 were associated with increases of autoregulatory gain (Gc; P = 0.033) but not slope (P = 0.585) over a CPP range of 120 to 60 mmHg. Preservation of autoregulatory Gc (P = 0.069) and slope (P = 0.264) was observed during dobutamine administration ± hypoxemia. Reductions in coronary resistance in response to decreases in CPP predominantly occurred below CvPO2 values of ~ 25 mmHg, irrespective of underlying vasomotor reserve. These findings support the presence of an autoregulatory threshold under which oxygen-sensing pathway(s) act to preserve sufficient myocardial oxygen delivery as CPP is reduced during increases in MVO2 and/or reductions in arterial oxygen content.

Numerical investigation of arterial stenosis location affecting hemodynamics considering microcirculation function

BACKGROUND

In recent years, arterial stenosis has become one of the serious diseases threatening people's life and health.

OBJECTIVE

The main purpose of the present study is to examine the changes of hemodynamic parameters in different stenosis locations of arteries.

METHODS

An arterial stenosis model with fluid-structure interaction and microcirculation as the outlet boundary of seepage is adopted in this paper. Considering the interaction between blood and arterial wall, a numerical simulation is carried out using the finite element method.

RESULTS

The results show that hemodynamic parameters are sensitive to the change of stenosis location. The closer to the microcirculation zone the stenosis location, the lower the blood flow velocity, pressure and the wall shear stress. In addition, the velocity trend is transformed from the gradual increase to decrease with the increasing distance away from the inlet when the stenosis location moves to the microcirculation zone.

CONCLUSION

This work proves that the stenosis location has a great influence on hemodynamics based on microcirculation function. Microcirculation is an important factor that cannot be ignored in the numerical simulation of arterial hemodynamics. The numerical results could provide the potential of clinical preconditions for disease diagnosis and treatment.

Mechanism of exercise intolerance in heart diseases predicted by a computer model of myocardial demand-supply feedback system

BACKGROUND AND OBJECTIVE

The myocardial demand-supply feedback system plays an important role in augmenting blood supply in response to exercise-induced increased myocardial demand. During this feedback process, the myocardium and coronary blood flow interact bidirectionally at many different levels.

METHODS

To investigate these interactions, a novel computational framework that considers the closed myocardial demand-supply feedback system was developed. In the framework coupling the systemic circulation of the left ventricle and coronary perfusion with regulation, myocardial work affects coronary perfusion via flow regulation mechanisms (e.g., metabolic regulation) and myocardial-vessel interactions, whereas coronary perfusion affects myocardial contractility in a closed feedback system. The framework was calibrated based on the measurements from healthy subjects under graded exercise conditions, and then was applied to simulate the effects of graded exercise on myocardial demand-supply under different physiological and pathological conditions.

RESULTS

We found that the framework can recapitulate key features found during exercise in clinical and animal studies. We showed that myocardial blood flow is increased but maximum hyperemia is reduced during exercise, which led to a reduction in coronary flow reserve. For coronary stenosis and myocardial inefficiency, the model predicts that an increase in heart rate is necessary to maintain the baseline cardiac output. Correspondingly, the resting coronary flow reserve is exhausted and the range of heart rate before exhaustion of coronary flow reserve is reduced. In the presence of metabolic regulation dysfunction, the model predicts that the metabolic vasodilator signal is higher at rest, saturates faster during exercise, and as a result, causes quicker exhaustion of coronary flow reserve.

CONCLUSIONS

Model predictions showed that the coronary flow reserve deteriorates faster during graded exercise, which in turn, suggests a decrease in exercise tolerance for patients with stenosis, myocardial inefficiency and metabolic flow regulation dysfunction. The findings in this study may have clinical implications in diagnosing cardiovascular diseases.

Index of microcirculatory resistance: state-of-the-art and potential applications in computational simulation of coronary artery disease

The dysfunction of coronary microcirculation is an important cause of coronary artery disease (CAD). The index of microcirculatory resistance (IMR) is a quantitative evaluation of coronary microcirculatory function, which provides a significant reference for the prediction, diagnosis, treatment, and prognosis of CAD. IMR also plays a key role in investigating the interaction between epicardial and microcirculatory dysfunctions, and is closely associated with coronary hemodynamic parameters such as flow rate, distal coronary pressure, and aortic pressure, which have been widely applied in computational studies of CAD. However, there is currently a lack of consensus across studies on the normal and pathological ranges of IMR. The relationships between IMR and coronary hemodynamic parameters have not been accurately quantified, which limits the application of IMR in computational CAD studies. In this paper, we discuss the research gaps between IMR and its potential applications in the computational simulation of CAD. Computational simulation based on the combination of IMR and other hemodynamic parameters is a promising technology to improve the diagnosis and guide clinical trials of CAD.

It's clearly the heart! Optical transparency, cardiac tissue imaging, and computer modelling

Recent developments in clearing and microscopy enable 3D imaging with cellular resolution up to the whole organ level. These methods have been used extensively in neurobiology, but their uptake in other fields has been much more limited. Application of this approach to the human heart and effective use of the data acquired present challenges of scale and complexity. Four interlinked issues need to be addressed: 1) efficient clearing and labelling of heart tissue, 2) fast microscopic imaging of human-scale samples, 3) handling and processing of multi-terabyte 3D images, and 4) extraction of structural information in computationally tractable structure-based models of cardiac function. Preliminary studies show that each of these requirements can be achieved with the appropriate application and development of existing technologies.

On the relevance of boundary conditions and viscosity models in blood flow simulations in patient-specific aorto-coronary bypass models

Physiologically realistic results are the aim of every blood flow simulation. This is not different in aorto-coronary bypasses where the properties of the coronary circulation may significantly affect the relevance of the performed simulations. By considering three patient-specific bypass geometries, the present article focuses on two aspects of the coronary blood flow - its phasic flow pattern and its behaviour affected by blood rheology. For the phasic flow property, a multiscale modelling approach is chosen as a means to assess the ability of five different types of coronary boundary conditions (mean arterial pressure, Windkessel model and three lumped parameter models) to attain realistic coronary haemodynamics. From the analysed variants of boundary conditions, the best option in terms of physiological characteristics and its potential for use in patient-based simulations, is utilised to account for the effect of shear-dependent viscosity on the resulting haemodynamics and wall shear stress stimulation. Aside from the Newtonian model, the blood rheology is approximated by two non-Newtonian models in order to determine whether the choice of a viscosity model is important in simulations involving coronary circulation. A comprehensive analysis of obtained results demonstrated notable superiority of all lumped parameter models, especially in comparison to the constant outlet pressure, which regardless of bypass type gave overestimated and physiologically misleading results. In terms of rheology, it was noted that blood in undamaged coronary arteries behaves as a Newtonian fluid, whereas in vessels with atypical lumen geometry, such as that of anastomosis or stenosis, its shear-thinning behaviour should not be ignored.

Effect of Material and Population on the Delivery of Nanoparticles to an Atherosclerotic Plaque: A Patient-specific In Silico Study

Coronary artery disease (CAD) is the prevalent reason of mortality all around the world. Targeting CAD, specifically atherosclerosis, with controlled delivery of micro and nanoparticles, as drug carriers, is a very proficient approach. In this work, a patient-specific and realistic model of an atherosclerotic plaque in the left anterior descending (LAD) artery was created by image-processing of CT-scan images and implementing a finite-element mesh. Next, a fluid-solid interaction simulation considering the physiological boundary conditions was conducted. By considering the simulated force fields and particle-particle interactions, the correlation between injected particles at each cardiac cycle and the surface density of adhered particles over the atherosclerotic plaque (SDP) were examined. For large particles (800 and 1000 nm) the amount of SDP on the plaque increased significantly when the number of the injected particles became higher. However, by increasing the number of the injected particles, for the larger particles (800 and 1000 nm) the increase in SDP was about 50% greater than that of the smaller ones (400 and 600 nm). Furthermore, for constant number of particles, depending on their size, different trends in SDP were observed. Subsequently, the distribution and adhesion of metal-based nanoparticles including SiO₂, Fe₃O₄, NiO₂, silver and gold with different properties were simulated. The injection of metal particles with medium density among the considered particles resulted in the highest SDP. Remarkably, the affinity, the geometrical features, and the biophysical factors involved in the adhesion outweighed the effect of difference in the density of particles on the SDP. Finally, the consideration of the lift force in the simulations significantly reduced the SDP and consistently decreased the particle residence time in the studied domain.

Blood Flow Modeling in Coronary Arteries: A Review

Atherosclerosis is one of the main causes of cardiovascular events, namely, myocardium infarction and cerebral stroke, responsible for a great number of deaths every year worldwide. This pathology is caused by the progressive accumulation of low-density lipoproteins, cholesterol, and other substances on the arterial wall, narrowing its lumen. To date, many hemodynamic studies have been conducted experimentally and/or numerically; however, this disease is not yet fully understood. For this reason, the research of this pathology is still ongoing, mainly, resorting to computational methods. These have been increasingly used in biomedical research of atherosclerosis because of their high-performance hardware and software. Taking into account the attempts that have been made in computational techniques to simulate realistic conditions of blood flow in both diseased and healthy arteries, the present review aims to give an overview of the most recent numerical studies focused on coronary arteries, by addressing the blood viscosity models, and applied physiological flow conditions. In general, regardless of the boundary conditions, numerical studies have been contributed to a better understanding of the development of this disease, its diagnosis, and its treatment.

Numerical modeling in arterial hemodynamics incorporating fluid-structure interaction and microcirculation

Background

The effects of arterial wall compliance on blood flow have been revealed using fluid-structure interaction in last decades. However, microcirculation is not considered in previous researches. In fact, microcirculation plays a key role in regulating blood flow. Therefore, it is very necessary to involve microcirculation in arterial hemodynamics.

Objective

The main purpose of the present study is to investigate how wall compliance affects the flow characteristics and to establish the comparisons of these flow variables with rigid wall when microcirculation is considered.

Methods

We present numerical modeling in arterial hemodynamics incorporating fluid-structure interaction and microcirculation. A novel outlet boundary condition is employed to prescribe microcirculation in an idealised model.

Results

The novel finding in this work is that wall compliance under the consideration of microcirculation leads to the increase of wall shear stress in contrast to rigid wall, contrary to the traditional result that wall compliance makes wall shear stress decrease when a constant or time dependent pressure is specified at an outlet.

Conclusions

This work provides the valuable study of hemodynamics under physiological and realistic boundary conditions and proves that wall compliance may have a positive impact on wall shear stress based on this model. This methodology in this paper could be used in real model simulations.

Spatial Configuration of Abdominal Aortic Aneurysm Analysis as a Useful Tool for the Estimation of Stent-Graft Migration

The aim of this study was to prepare a self-made mathematical algorithm for the estimation of risk of stent-graft migration with the use of data on abdominal aortic aneurysm (AAA) size and geometry of blood flow through aneurysm sac before or after stent-graft implantation. AngioCT data from 20 patients aged 50–60 years, before and after stent-graft placement in the AAA was analyzed. In order to estimate the risk of stent-graft migration for each patient we prepared an opposite spatial configuration of virtually reconstructed stent-graft with long body or short body. Thus, three groups of 3D geometries were analyzed: 20 geometries representing 3D models of aneurysm, 20 geometries representing 3D models of long body stent-grafts, and 20 geometries representing 3D models of short body stent-graft. The proposed self-made algorithm demonstrated its efficiency and usefulness in estimating wall shear stress (WSS) values. Comparison of the long or short type of stent-graft with AAA geometries allowed to analyze the implants’ spatial configuration. Our study indicated that short stent-graft, after placement in the AAA sac, generated lower drug forces compare to the long stent-graft. Each time shape factor was higher for short stent-graft compare to long stent-graft.

Allometric scaling patterns among the human coronary artery tree, myocardial mass, and coronary artery flow

Human coronary artery tree is a physiological transport system for oxygen and vital materials through a hierarchical vascular network to match the energy demands of myocardium, which has the highest oxygen extraction ratio among body organs and heavily depends on the blood flow for its energy supply. Therefore, it would be reasonable to expect that the key design principle of this arterial network is to minimize energy expenditure, which can be described by allometric scaling law. We enrolled patients who underwent coronary computed tomography angiography without obstructive lesion. The cumulative arterial length (L), volume (V), and diameter (D) in relation to the artery-specific myocardial mass (M) were assessed. Flow rate (Q) was computed using quantitative flow ratio (QFR) measurement in patients who underwent invasive angiography. A total of 638 arteries from 43 patients (mean age 61 years, male gender 65%) were analyzed. A significant power-law relationship was found among L-M, V-M, D-M, V-L, D-L, and V-D, and also among Q-M, Q-L, Q-V, and Q-D in 106 arteries interrogated with QFR (p < .001, all). Our results suggest that the fundamental design principle of the human coronary arterial network may follow allometric scaling law.

Personalized Interventions: A Reality in the Next 20 Years or Pie in the Sky

There is no better representation of the need for personalization of care than the breadth and complexity of congenital heart disease. Advanced imaging modalities are now standard of care in the field, and the advancements being made to three-dimensional visualization technologies are growing as a means of pre-procedural preparation. Incorporating emerging modeling approaches, such as computational fluid dynamics, will push the limits of our ability to predict outcomes, and this information may be both obtained and utilized during a single procedure in the future. Artificial intelligence and customized devices may soon surface as realistic tools for the care of patients with congenital heart disease, as they are showing growing evidence of feasibility within other fields. This review illustrates the great strides that have been made and the persistent challenges that exist within the field of congenital interventional cardiology, a field which must continue to innovate and push the limits to achieve personalization of the interventions it provides.

On the Validation of a Multiple-Network Poroelastic Model Using Arterial Spin Labeling MRI Data

The Multiple-Network Poroelastic Theory (MPET) is a numerical model to characterize the transport of multiple fluid networks in the brain, which overcomes the problem of conducting separate analyses on individual fluid compartments and losing the interactions between tissue and fluids, in addition to the interaction between the different fluids themselves. In this paper, the blood perfusion results from MPET modeling are partially validated using cerebral blood flow (CBF) data obtained from arterial spin labeling (ASL) magnetic resonance imaging (MRI), which uses arterial blood water as an endogenous tracer to measure CBF. Two subjects—one healthy control and one patient with unilateral middle cerebral artery (MCA) stenosis are included in the validation test. The comparison shows several similarities between CBF data from ASL and blood perfusion results from MPET modeling, such as higher blood perfusion in the gray matter than in the white matter, higher perfusion in the periventricular region for both the healthy control and the patient, and asymmetric distribution of blood perfusion for the patient. Although the partial validation is mainly conducted in a qualitative way, it is one important step toward the full validation of the MPET model, which has the potential to be used as a testing bed for hypotheses and new theories in neuroscience research.

A hemodynamic model with a seepage condition and fluid-structure interactions for blood flow in arteries with symmetric stenosis

To strengthen the detailed understanding of arterial stenosis, we construct a novel hemodynamic model. Frequently used symmetric stenosis is employed in this work. Being different from a traditional model, this numerical model adopts microcirculation resistance as an outlet boundary condition, which is called a seepage condition. Meanwhile, fluid-structure interactions are used in the numerical simulation considering the interrelationship of blood and arterial wall. Our results indicate that (i) the region upstream of stenosis experiences very high pressures during cardiac cycles, (ii) pressure drops much faster as the flow moves into the stenotic region, and (iii) high flow velocities and high shear stresses occur in the post-stenosis region. This work provides evidence that there is a strong effect of the function of microcirculation on stenosis. This contributes to evaluating potential stenotic behavior in arteries and is pivotal in guiding disease treatment.

Model and Application to Support the Coronary Artery Diseases (CAD): Development and Testing

Cardiovascular diseases are among the main causes of morbidity, disability, and mortality. Most of them occur because of an atherosclerotic plaque developing within a coronary artery, which can cause a narrowing of the vessel lumen (coronary stenosis) or even break it. It is, therefore, useful to evaluate the role of the stress state of the endothelial layer of the arterial tissue, both for the maintenance of the blood circulation and for the implications in presence of a pathology that can lead to thromboembolic complications. The aim of the following study was to develop and test an application that is able to evaluate specific hemodynamic shear stress indicators in coronary arteries at different percentages of stenosis and in different patients' specific conditions. The application, based on Java, allows users to view the results of simulations performed on a coronary anatomy that can be customized with a stenosis of different degrees and positions. Being in possession of a predictive tool for disturbed flow factors may be important for the location and development of atherosclerotic plaque. Moreover, the application can be a valid tool to help in the evaluation of the condition and in the follow-up of the coronary affected by pathology.

A seepage outlet boundary condition in hemodynamics modeling

BACKGROUND

In computational fluid dynamics (CFD) models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions.

OBJECTIVE

As an important part of the arterial circulation, microcirculation plays important roles in many aspects, such as substance exchange, interstitial fluid generation and inverse flow. It is necessary to consider microcirculation in hemodynamics modeling. This is a methodological paper to test and validate a new type of boundary condition never applied to microcirculation before.

METHODS

In order to address this issue, we introduce microcirculation as a seepage outlet boundary condition in computational hemodynamics. Microcirculation is treated as a porous medium in this paper. Numerical comparisons of the seepage and traditional boundary conditions are made.

RESULTS

The results show that the seepage boundary condition has significant impacts on numerical simulation. Under the seepage boundary condition, the fluctuation range of the pressures progressively rises in the artery zone. The results obtained from the traditional boundary condition show that the pressure fluctuation range gradually falls. In addition, the wall shear stresses under the traditional outlet boundary condition are much higher than those under the seepage outlet boundary condition.

CONCLUSIONS

The proposed boundary condition is more suitable in hemodynamics modeling.

3D Blood Vessels Reconstruction Based on Segmented CT Data for Further Simulations of Hemodynamic in Human Artery Branches

We aimed at the reconstruction of the branches of human aortic arch for blood perfusion analysis used later in the Computational Fluid Dynamic (CFD). The reconstruction was performed based on segmentation results obtained from CT data. Two segmentation algorithms, region growing and level set were implemented. Obtained binary segmentation results were next evaluated by the expert and corrected if needed. The final reconstruction was used for preparation of a numerical grid and for further calculation of blood hemodynamic. The collected data composed of blood velocity and blood flow rate in function of time were compared with USG-Doppler data. Results demonstrate that proposed algorithm may be useful for initial reconstruction of human cardiac system, however its accuracy needs to be improved as further manual corrections are still needed.

EFFECTS OF POROSITY IN A SEEPAGE MODEL ON HEMODYNAMICS

In this paper, we numerically investigate the effects of porosity on hemodynamics using a seepage outlet boundary condition. The results with the porosities [Formula: see text] and [Formula: see text] are compared. The comparison of the results shows that there are identical pressure, velocity and wall shear stress distributions in the artery zone; however, the velocities and wall shear stresses in the microcirculation zone with [Formula: see text] are almost as twice as those with [Formula: see text]. This work suggests that the porosity changes do not provoke variations in the artery zone, but they lead to the differences of the velocities and wall shear stresses in the microcirculation zone. The results may be the explanation of syndrome X.

Effects of freezing, fixation and dehydration on surface roughness properties of porcine left anterior descending coronary arteries

BACKGROUND

To allow measurements of surface roughness to be made of coronary arteries using various imaging techniques, chemical processing, such as fixation and dehydration, is commonly used. Standard protocols suggest storing fresh biological tissue at -40°C. The aim of this study was to quantify the changes caused by freezing and chemical processing to the surface roughness measurements of coronary arteries, and to determine whether correction factors are needed for surface roughness measurements of coronary arteries following chemical processes typically used before imaging these arteries.

METHODS

Porcine left anterior descending coronary arteries were dissected ex vivo. Surface roughness was then calculated following three-dimensional reconstruction of surface images obtained using an optical microscope. Surface roughness was measured before and after a freeze cycle to assess changes during freezing, after chemical fixation, and again after dehydration, to determine changes during these steps of chemical processing.

RESULTS

No significant difference was caused due to the freeze cycle (p>0.05). There was no significant difference in the longitudinally measured surface roughness (Ra_L=0.99±0.39μm; p>0.05) of coronary arteries following fixation and dehydration either. However, the circumferentially measured surface roughness increased significantly following a combined method of processing (Ra_C=1.36±0.40, compared 1.98±0.27μm, respectively; p<0.05). A correction factor can compensate for the change Ra_Cβ=Ra_C1+0.46in Ra_C due to processing of tissue, Where Ra_Cβ, the corrected Ra_C, had a mean of 1.31±0.21μm.

CONCLUSIONS

Independently, freezing, fixation and dehydration do not alter the surface roughness of coronary arteries. Combined, however, fixation and dehydration significantly increase the circumferential, but not longitudinal, surface roughness of coronary arteries.

Distributed and Lumped Parameter Models for the Characterization of High Throughput Bioreactors

Next generation bioreactors are being developed to generate multiple human cell-based tissue analogs within the same fluidic system, to better recapitulate the complexity and interconnection of human physiology [1, 2]. The effective development of these devices requires a solid understanding of their interconnected fluidics, to predict the transport of nutrients and waste through the constructs and improve the design accordingly. In this work, we focus on a specific model of bioreactor, with multiple input/outputs, aimed at generating osteochondral constructs, i.e., a biphasic construct in which one side is cartilaginous in nature, while the other is osseous. We next develop a general computational approach to model the microfluidics of a multi-chamber, interconnected system that may be applied to human-on-chip devices. This objective requires overcoming several challenges at the level of computational modeling. The main one consists of addressing the multi-physics nature of the problem that combines free flow in channels with hindered flow in porous media. Fluid dynamics is also coupled with advection-diffusion-reaction equations that model the transport of biomolecules throughout the system and their interaction with living tissues and C constructs. Ultimately, we aim at providing a predictive approach useful for the general organ-on-chip community. To this end, we have developed a lumped parameter approach that allows us to analyze the behavior of multi-unit bioreactor systems with modest computational effort, provided that the behavior of a single unit can be fully characterized.

Accurate and Standardized Coronary Wave Intensity Analysis

OBJECTIVE

Coronary wave intensity analysis (cWIA) has increasingly been applied in the clinical research setting to distinguish between the proximal and distal mechanical influences on coronary blood flow. Recently, a cWIA-derived clinical index demonstrated prognostic value in predicting functional recovery postmyocardial infarction. Nevertheless, the known operator dependence of the cWIA metrics currently hampers its routine application in clinical practice. Specifically, it was recently demonstrated that the cWIA metrics are highly dependent on the chosen Savitzky-Golay filter parameters used to smooth the acquired traces. Therefore, a novel method to make cWIA standardized and automatic was proposed and evaluated in vivo.

METHODS

The novel approach combines an adaptive Savitzky-Golay filter with high-order central finite differencing after ensemble-averaging the acquired waveforms. Its accuracy was assessed using in vivo human data. The proposed approach was then modified to automatically perform beat wise cWIA. Finally, the feasibility (accuracy and robustness) of the method was evaluated.

RESULTS

The automatic cWIA algorithm provided satisfactory accuracy under a wide range of noise scenarios (≤10% and ≤20% error in the estimation of wave areas and peaks, respectively). These results were confirmed when beat-by-beat cWIA was performed.

CONCLUSION

An accurate, standardized, and automated cWIA was developed. Moreover, the feasibility of beat wise cWIA was demonstrated for the first time.

SIGNIFICANCE

The proposed algorithm provides practitioners with a standardized technique that could broaden the application of cWIA in the clinical practice as enabling multicenter trials. Furthermore, the demonstrated potential of beatwise cWIA opens the possibility investigating the coronary physiology in real time.

Impact of coronary bifurcation morphology on wave propagation

The branching pattern of the coronary vasculature is a key determinant of its function and plays a crucial role in shaping the pressure and velocity wave forms measured for clinical diagnosis. However, although multiple scaling laws have been proposed to characterize the branching pattern, the implications they have on wave propagation remain unassessed to date. To bridge this gap, we have developed a new theoretical framework by combining the mathematical formulation of scaling laws with the wave propagation theory in the pulsatile flow regime. This framework was then validated in multiple species using high-resolution cryomicrotome images of porcine, canine, and human coronary networks. Results demonstrate that the forward well-matchedness (no reflection for pressure/flow waves traveling from the coronary stem toward the microcirculation) is a salient feature in the coronary vasculature, and this result remains robust under many scenarios of the underlying pulse wave speed distribution assumed in the network. This result also implies a significant damping of the backward traveling waves, especially for smaller vessels (radius, <0.3 mm). Furthermore, the theoretical prediction of increasing area ratios (ratio between the area of the mother and daughter vessels) in more symmetric bifurcations found in the distal circulation was confirmed by experimental measurements. No differences were observed by clustering the vessel segments in terms of transmurality (from epicardium to endocardium) or perfusion territories (left anterior descending, left circumflex, and right coronary artery).

Modelling levels of nitrous oxide exposure for healthcare professionals during EMONO usage

BACKGROUND

Computational fluid dynamics (CFD) has been used to compute nitrous oxide (N2O) levels within a room during the administration of an equimolar mix of N2O/oxygen (EMONO) in the clinical setting. This study modelled realistic scenarios of EMONO usage in hospital or primary care, in order to estimate the potential N2O exposure of healthcare professionals (HCP) with routine EMONO use and to provide guidance for EMONO users.

METHODS

Sixteen scenarios were defined by carrying out a survey of practitioners. CFD simulations were performed for each scenario and N2O concentrations over time were calculated. N2O exposures (time-weighted average of concentration over 8 h [TWA-8 h]) were calculated at the HCPs' mouth to be compared with a predefined occupational exposure limit (OEL).

RESULTS

Administration duration and ventilation type were the main factors influencing N2O levels; ventilation type also influenced wash-out time between EMONO administrations. N2O concentration showed a plume distribution towards the ceiling and was highly heterogeneous, highlighting the importance of measurement location. Although estimated TWA-8 h varied widely, 13 of the 16 scenarios had an N2O TWA-8 h of <100 parts per million.

CONCLUSIONS

Data demonstrate that EMONO usage in well ventilated rooms - as recommended - helps to ensure that N2O exposure does not exceed the OEL and does not signal any major risks for HCPs when recommendations are followed. Although these data are numerical simulations and should be considered as such, they can provide guidance for EMONO users.

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit.

A Novel Attempt to Standardize Results of CFD Simulations Basing on Spatial Configuration of Aortic Stent-Grafts

Currently, studies connected with Computational Fluid Dynamic (CFD) techniques focus on assessing hemodynamic of blood flow in vessels in different conditions e.g. after stent-graft’s placement. The paper propose a novel method of standardization of results obtained from calculations of stent-grafts' “pushing forces” (cumulative WSS—Wall Shear Stress), and describes its usefulness in diagnostic process. AngioCT data from 27 patients were used to reconstruct 3D geometries of stent-grafts which next were used to create respective reference cylinders. We made an assumption that both the side surface and the height of a stent-graft and a reference cylinder were equal. The proposed algorithm in conjunction with a stent-graft “pushing forces” on an implant wall, allowed us to determine which spatial configuration of a stent-graft predispose to the higher risk of its migration. For stent-grafts close to cylindrical shape (shape factor φ close to 1) WSS value was about 267Pa, while for stent-grafts different from cylindrical shape (φ close to 2) WSS value was about 635Pa. It was also noticed that deformation in the stent-graft’s bifurcation part impaired blood flow hemodynamic. Concluding the proposed algorithm of standardization proved its usefulness in estimating the WSS values that may be useful in diagnostic process. Angular bends or tortuosity in bifurcations of an aortic implant should be considered in further studies of estimation of the risk of implantation failure.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.

Development of an In Vitro Model to Characterize the Effects of Transcatheter Aortic Valve on Coronary Artery Flow

Impairment of coronary artery flow, in either acute or chronic conditions, is a severe complication of transcatheter aortic valve (TAV) implantation, which can arise due to improper TAV positioning. However, little work has been done to quantify the effects of the TAV positioning on the coronary flow. In this study, a realistic in vitro model of coronary artery flow was developed and used to investigate the impact of TAV deployed orientations on coronary flow. The coronary hemodynamics was first replicated mathematically using a lumped parameter model with time-varying myocardial resistance. Based on the analytical model, two stepper motor controlled stopcock valves were integrated in a left heart simulator to represent the variable myocardial resistance in the experimental setup. The coronary flow and pressure waveforms obtained from the in vitro system were consistent with published data. With a TAV deployed in different orientations, the measured results demonstrated that TAV orientation does not have a significant impact on the coronary flow. The developed in vitro model can be further utilized to simulate coronary flow under various pathological conditions.

Computational fluid dynamics modelling in cardiovascular medicine

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards ‘digital patient’ or ‘virtual physiological human’ representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

An effective model of blood flow in capillary beds

In this article we derive applicable expressions for the macroscopic compliance and resistance of microvascular networks. This work yields a lumped-parameter model to describe the hemodynamics of capillary beds. Our derivation takes into account the multiscale nature of capillary networks, the influence of blood volume and pressure on the effective resistance and compliance, as well as, the nonlinear interdependence between these two properties. As a result, we obtain a simple and useful model to study hypotensive and hypertensive phenomena. We include two implementations of our theory: (i) pulmonary hypertension where the flow resistance is predicted as a function of pulmonary vascular tone. We derive from first-principles the inverse proportional relation between resistance and compliance of the pulmonary tree, which explains why the RC factor remains nearly constant across a population with increasing severity of pulmonary hypertension. (ii) The critical closing pressure in pulmonary hypotension where the flow rate dramatically decreases due to the partial collapse of the capillary bed. In both cases, the results from our proposed model compare accurately with experimental data.

Biomechanical rationale of coronary artery bypass grafting of multivessel disease

The biomechanical model of human coronary arteries was modified for improving the quality of diagnosis and surgical treatment for coronary heart disease. The problem of hemodynamics in the left coronary artery with multivessel bed disease - 45% stenosis of the anterior descending branch and 75% stenosis of the circumflex branch - was particularly considered. Numerical simulation of the coronary arterial bypass of the main trunk was carried out to estimate the functional condition of the coronary arteries after restoring myocardial blood supply by surgery.

A clinically oriented introduction and review on finite element models of the human cochlea

Due to the inaccessibility of the inner ear, direct in vivo information on cochlear mechanics is difficult to obtain. Mathematical modelling is a promising way to provide insight into the physiology and pathology of the cochlea. Finite element method (FEM) is one of the most popular discrete mathematical modelling techniques, mainly used in engineering that has been increasingly used to model the cochlea and its elements. The aim of this overview is to provide a brief introduction to the use of FEM in modelling and predicting the behavior of the cochlea in normal and pathological conditions. It will focus on methodological issues, modelling assumptions, simulation of clinical scenarios, and pathologies.

Impedance boundary conditions for general transient hemodynamics

We discuss the implementation and calibration of a new generalized structured tree boundary condition for hemodynamics. The main idea is to approximate the impedance corresponding to the vessels downstream from a specific outlet. Unlike previous impedance conditions, the one considered here is applicable to general transient flows as opposed to periodic ones only. The physiological character of the approach significantly simplifies calibration. We also describe a novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost. The strength of the approach is illustrated and validated on several examples through comparison with clinical data.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

Multiscale modeling is a promising tool for the study of coronary hemodynamics. A key strength of this approach is that it accounts for microvascular properties and extravascular forces that differ regionally and transmurally, as well as wave propagation effects in the conduit arteries. However, little validation of such models has been reported and no models of the newborn coronary circulation have been described. We therefore validated a multiscale model of the left coronary circulation using high-fidelity data from nine adult sheep and nine newborn lambs and investigated whether wave propagation effects are more prominent in adults, whose body size (and hence wave transit distance) is greater. The model consisted of a one-dimensional (1D) network of the major conduit arteries and a lumped parameter model of microvascular beds. Intramyocardial pressure was considered to arise via contraction-related myocyte thickening and transmission of ventricular cavity pressure into the heart wall. 1D network geometry from published human anatomical data was scaled using myocardial weights, while subject-specific aortic pressure/flow and ventricular pressure formed model inputs. Total vascular resistance was determined iteratively from measured mean circumflex coronary flow (CxQ), but no fitting of phasic aspects of the waveform was performed. Excellent agreement was obtained between simulated and measured CxQ waveforms in most cases. Detailed flow waveform analysis did not clearly reveal a greater prominence of wave propagation effects in adults compared with newborns. This multiscale model is likely to be useful for investigating wave phenomena and phasic aspects of coronary flow in adults and during development.

Perfusion territories subtended by penetrating coronary arteries increase in size and decrease in number toward the subendocardium

Blood flow distribution within the myocardium and the location and extent of areas at risk in case of coronary artery disease are dependent on the distribution and morphology of intramural vascular crowns. Knowledge of the intramural vasculature is essential in novel multiscale and multiphysics modeling of the heart. For this study, eight canine hearts were analyzed with an imaging cryomicrotome, developed to acquire high-resolution spatial data on three-dimensional vascular structures. The obtained vasculature was skeletonized, and for each penetrating artery starting from the epicardium, the dependent vascular crown was defined. Three-dimensional Voronoi tessellation was applied with the end points of the terminal segments as center points. The centroid of end points in each branch allowed classification of the corresponding perfusion territories in subendocardial, midmyocardial, and subepicardial. Subendocardial regions have relatively few territories of about 0.5 ml in volume having their own penetrating artery at the epicardium, whereas the subepicardium is perfused by a multitude of small perfusion territories, in the order of 0.01 ml. Vascular volume density of small arteries up till 400 μm was 3.2% at the subendocardium territories but only 0.8% in the subepicardium territories. Their higher volume density corresponds to compensation for flow impeding forces by cardiac contraction. These density differences result in different scaling law properties of vascular volume and tissue mass per territory type. This novel three-dimensional quantitative analysis may form the basis for patient-specific computational models on coronary perfusion and aid the interpretation of image-based clinical methods for assessing the transmural perfusion distribution.

Impact of coronary tortuosity on coronary blood supply: a patient-specific study

BACKGROUND

Tortuous coronary arteries are commonly observed in clinical screenings and it may cause a reduction of the coronary pressure. However, whether this reduction leads to significant decreasing in the coronary blood supply is still unknown. The purpose of this study was to investigate the effect of the coronary tortuosity (CT) on the coronary blood supply.

METHOD

A computational fluid dynamics (CFD) study was conducted to evaluate the impact of tortuosity on the coronary blood supply. Two patient-specific left anterior descending coronary artery (LAD) models and the corresponding non-tortuous models were reconstructed to perform three-dimensional CFD analysis. The lumped parameter model was coupled to the outlet of the simulated branches to represent the absent downstream vasculatures. The rest and exercise conditions were modeled by specifying proper boundary conditions.

RESULT

Under resting condition, the mean flow rate could be maintained by decreasing less than 8% of the downstream vascular bed's resistance for tortuous models. While during exercise (maximal dilatation condition), the maximal coronary blood supply would reduce up to 14.9% due to tortuosity. Assuming that the flow rate can be maintained by the auto-regulation effect under the maximal dilatation condition, the distal resistances for CT models still have to reduce more than 23% to maintain blood perfusion.

CONCLUSIONS

Coronary tortuosity has minor influence on coronary blood supply at rest; while during exercise, patients with CT may lack the ability to adjust distal resistance sufficiently to compensate for the extra resistances generated by tortuosity and this may further lead to an ineffective regulation of the blood supply.

Combining wet and dry research: experience with model development for cardiac mechano-electric structure-function studies

Since the development of the first mathematical cardiac cell model 50 years ago, computational modelling has become an increasingly powerful tool for the analysis of data and for the integration of information related to complex cardiac behaviour. Current models build on decades of iteration between experiment and theory, representing a collective understanding of cardiac function. All models, whether computational, experimental, or conceptual, are simplified representations of reality and, like tools in a toolbox, suitable for specific applications. Their range of applicability can be explored (and expanded) by iterative combination of 'wet' and 'dry' investigation, where experimental or clinical data are used to first build and then validate computational models (allowing integration of previous findings, quantitative assessment of conceptual models, and projection across relevant spatial and temporal scales), while computational simulations are utilized for plausibility assessment, hypotheses-generation, and prediction (thereby defining further experimental research targets). When implemented effectively, this combined wet/dry research approach can support the development of a more complete and cohesive understanding of integrated biological function. This review illustrates the utility of such an approach, based on recent examples of multi-scale studies of cardiac structure and mechano-electric function.