Multiscale modeling and simulation of brain blood flow

Particle-based MR modeling with diffusion, microstructure, and enzymatic reactions

PURPOSE

To develop a novel particle-based in silico MR model and demonstrate applications of this model to signal mechanisms which are affected by the spatial organization of particles, including metabolic reaction kinetics, microstructural effects on diffusion, and radiofrequency (RF) refocusing effects in gradient-echo sequences.

METHODS

The model was developed by integrating a forward solution of the Bloch equations with a Brownian dynamics simulator. Simulation configurations were then designed to model MR signal dynamics of interest, with a primary focus on hyperpolarized 13C MRI methods. Phantom scans and spectrophotometric assays were conducted to validate model results in vitro.

RESULTS

The model accurately reproduced the reaction kinetics of enzyme-mediated conversion of pyruvate to lactate. When varying proportions of restrictive structure were added to the reaction volume, nonlinear changes in the reaction rate measured in vitro were replicated in silico. Modeling of RF refocusing effects characterized the degree of diffusion-weighted contribution from preserved residual magnetization in nonspoiled gradient-echo sequences.

CONCLUSIONS

These results show accurate reproduction of a range of MR signal mechanisms, establishing the model's capability to investigate the multifactorial signal dynamics such as those underlying hyperpolarized 13C MRI data.

Flow reduction due to arterial catheterization during stroke treatment - A computational study using a distributed compartment model

The effectiveness of various stroke treatments depends on the anatomical variability of the cerebral vasculature, particularly the collateral blood vessel network. Collaterals at the level of the Circle of Willis and distal collaterals, such as the leptomeningeal arteries, serve as alternative avenues of flow when the primary pathway is obstructed during an ischemic stroke. Stroke treatment typically involves catheterization of the primary pathway, and the potential risk of further flow reduction to the affected brain area during this treatment has not been previously investigated. To address this clinical question, we derived the lumped parameters for catheterized blood vessels and implemented a corresponding distributed compartment (0D) model. This 0D model was validated against an experimental model and benchmark test cases solved using a 1D model. Additionally, we compared various off-center catheter trajectories modeled using a 3D solver to this 0D model. The differences between them were minimal, validating the simplifying assumption of the central catheter placement in the 0D model. The 0D model was then used to simulate blood flows in realistic cerebral arterial networks with different collateralization characteristics. Ischemic strokes were modeled by occlusion of the M1 segment of the middle cerebral artery in these networks. Catheters of different diameters were inserted up to the obstructed segment and flow alterations in the network were calculated. Results showed up to 45% maximum blood flow reduction in the affected brain region. These findings suggest that catheterization during stroke treatment may have a further detrimental effect for some patients with poor collateralization.

Impact of continuous-flow mechanical circulatory support on cerebrospinal fluid motility

BACKGROUND

Mechanical circulatory support (MCS), including ventricular assist devices (VADs), have emerged as promising therapeutic alternatives for end-stage congestive heart failure (CHF). The latest generation of these devices are continuous flow (CF) blood pumps. While there have been demonstrated benefits to patient outcomes due to CF-MCS, there continue to be significant clinical challenges. Research to-date has concentrated on mitigating thromboembolic risk (stroke), while the downstream impact of CF-MCS on the cerebrospinal fluid (CSF) flow has not been well investigated. Disturbances in the CSF pressure and flow patterns are known to be associated with neurologic impairment and diseased states. Thus, here we seek to develop an understanding of the pathophysiologic consequences of CF-MCS on CSF dynamics.

METHODS

We built and validated a computational framework using lumped parameter modeling of cardiovascular, cerebrovascular physics, CSF dynamics, and autoregulation. A sensitivity analysis was performed to confirm robustness of the modeling framework. Then, we characterized the impact of CF-MCS on the CSF and investigated cardiovascular conditions of healthy and end-stage heart failure.

RESULTS

Modeling results demonstrated appropriate hemodynamics and indicated that CSF pressure depends on blood flow pulsatility more than CSF flow. An acute equilibrium between CSF production and absorption was observed in the CF-MCS case, characterized by CSF pressure remaining elevated, and CSF flow rates remaining below healthy, but higher than CHF states.

CONCLUSION

This research has advanced our understanding of the impact of CF-MCS on CSF dynamics and cerebral hemodynamics.

An anatomically detailed arterial-venous network model. Cerebral and coronary circulation

In recent years, several works have addressed the problem of modeling blood flow phenomena in veins, as a response to increasing interest in modeling pathological conditions occurring in the venous network and their connection with the rest of the circulatory system. In this context, one-dimensional models have proven to be extremely efficient in delivering predictions in agreement with in-vivo observations. Pursuing the increase of anatomical accuracy and its connection to physiological principles in haemodynamics simulations, the main aim of this work is to describe a novel closed-loop Anatomically-Detailed Arterial-Venous Network (ADAVN) model. An extremely refined description of the arterial network consisting of 2,185 arterial vessels is coupled to a novel venous network featuring high level of anatomical detail in cerebral and coronary vascular territories. The entire venous network comprises 189 venous vessels, 79 of which drain the brain and 14 are coronary veins. Fundamental physiological mechanisms accounting for the interaction of brain blood flow with the cerebro-spinal fluid and of the coronary circulation with the cardiac mechanics are considered. Several issues related to the coupling of arterial and venous vessels at the microcirculation level are discussed in detail. Numerical simulations are compared to patient records published in the literature to show the descriptive capabilities of the model. Furthermore, a local sensitivity analysis is performed, evidencing the high impact of the venous circulation on main cardiovascular variables.

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.

Cerebral hemodynamics during atrial fibrillation: Computational fluid dynamics analysis of lenticulostriate arteries using 7 T high-resolution magnetic resonance imaging

Atrial fibrillation (AF) is the most common cardiac arrhythmia, inducing irregular and faster heart beating. Aside from disabling symptoms-such as palpitations, chest discomfort, and reduced exercise capacity-there is growing evidence that AF increases the risk of dementia and cognitive decline, even in the absence of clinical strokes. Among the possible mechanisms, the alteration of deep cerebral hemodynamics during AF is one of the most fascinating and least investigated hypotheses. Lenticulostriate arteries (LSAs)-small perforating arteries perpendicularly departing from the anterior and middle cerebral arteries and supplying blood flow to basal ganglia-are especially involved in silent strokes and cerebral small vessel diseases, which are considered among the main vascular drivers of dementia. We propose for the first time a computational fluid dynamics analysis to investigate the AF effects on the LSAs hemodynamics by using 7 T high-resolution magnetic resonance imaging (MRI). We explored different heart rates (HRs)-from 50 to 130 bpm-in sinus rhythm and AF, exploiting MRI data from a healthy young male and internal carotid artery data from validated 0D cardiovascular-cerebral modeling as inflow condition. Our results reveal that AF induces a marked reduction of wall shear stress and flow velocity fields. This study suggests that AF at higher HR leads to a more hazardous hemodynamic scenario by increasing the atheromatosis and thrombogenesis risks in the LSAs region.

Feasibility of Vascular Parameter Estimation for Assessing Hypertensive Pregnancy Disorders

Hypertensive pregnancy disorders (HPDs), such as pre-eclampsia, are leading sources of both maternal and fetal morbidity in pregnancy. Noninvasive imaging, such as ultrasound (US) and magnetic resonance imaging (MRI), is an important tool for predicting and monitoring these high risk pregnancies. While imaging can measure hemodynamic parameters, such as uterine artery pulsatility and resistivity indices (PI and RI), the interpretation of such metrics for disease assessment relies on ad hoc standards, which provide limited insight to the physical mechanisms underlying the emergence of hypertensive pregnancy disorders. To provide meaningful interpretation of measured hemodynamic data in patients, advances in computational fluid dynamics can be brought to bear. In this work, we develop a patient-specific computational framework that combines Bayesian inference with a reduced-order fluid dynamics model to infer parameters, such as vascular resistance, compliance, and vessel cross-sectional area, known to be related to the development of hypertension. The proposed framework enables the prediction of hemodynamic quantities of interest, such as pressure and velocity, directly from sparse and noisy MRI measurements. We illustrate the effectiveness of this approach in two systemic arterial network geometries: an aorta with branching carotid artery and a maternal pelvic arterial network. For both cases, the model can reconstruct the provided measurements and infer parameters of interest. In the case of the maternal pelvic arteries, the model can make a distinction between the pregnancies destined to develop hypertension and those that remain normotensive, expressed through the value range of the predicted absolute pressure.

A nonlinear multi-scale model for blood circulation in a realistic vascular system

In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille's Law, with pressure correction by elasticity and pressure drop estimation at vessels' junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy's Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.

Tissue clearing and imaging methods for cardiovascular development

Tissue imaging in 3D using visible light is limited and various clearing techniques were developed to increase imaging depth, but none provides universal solution for all tissues at all developmental stages. In this review, we focus on different tissue clearing methods for 3D imaging of heart and vasculature, based on chemical composition (solvent-based, simple immersion, hyperhydration, and hydrogel embedding techniques). We discuss in detail compatibility of various tissue clearing techniques with visualization methods: fluorescence preservation, immunohistochemistry, nuclear staining, and fluorescent dyes vascular perfusion. We also discuss myocardium visualization using autofluorescence, tissue shrinking, and expansion. Then we overview imaging methods used to study cardiovascular system and live imaging. We discuss heart and vessels segmentation methods and image analysis. The review covers the whole process of cardiovascular system 3D imaging, starting from tissue clearing and its compatibility with various visualization methods to the types of imaging methods and resulting image analysis.

Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease

Understanding the mechanics of blood flow is necessary for developing insights into mechanisms of physiology and vascular diseases in microcirculation. Given the limitations of technologies available for assessing in vivo flow fields, in vitro methods based on traditional microfluidic platforms have been developed to mimic physiological conditions. However, existing methods lack the capability to provide accurate assessment of these flow fields, particularly in vessels with complex geometries. Conventional approaches to quantify flow fields rely either on analyzing only visual images or on enforcing underlying physics without considering visualization data, which could compromise accuracy of predictions. Here, we present artificial-intelligence velocimetry (AIV) to quantify velocity and stress fields of blood flow by integrating the imaging data with underlying physics using physics-informed neural networks. We demonstrate the capability of AIV by quantifying hemodynamics in microchannels designed to mimic saccular-shaped microaneurysms (microaneurysm-on-a-chip, or MAOAC), which signify common manifestations of diabetic retinopathy, a leading cause of vision loss from blood-vessel damage in the retina in diabetic patients. We show that AIV can, without any a priori knowledge of the inlet and outlet boundary conditions, infer the two-dimensional (2D) flow fields from a sequence of 2D images of blood flow in MAOAC, but also can infer three-dimensional (3D) flow fields using only 2D images, thanks to the encoded physics laws. AIV provides a unique paradigm that seamlessly integrates images, experimental data, and underlying physics using neural networks to automatically analyze experimental data and infer key hemodynamic indicators that assess vascular injury.

4D blood flow model for dose calculation to circulating blood and lymphocytes

To better understand how radiotherapy delivery parameters affect the depletion of circulating lymphocytes in patients treated for intra-cranial tumors, we developed a computational human body blood flow model (BFM), that enables to estimate the dose to the circulating blood during the course of fractionated radiation therapy. A hemodynamic cardiovascular system based on human body reference values was developed to distribute the cardiac output to 24 different organs, described by a discrete Markov Chain. For explicit intracranial blood flow modeling, we extracted major cerebral vasculature from MRI data of a patient and complemented them with an extension network of generic vessels in the frontal and occipital lobes to guarantee even overall blood supply to the entire brain volume. An explicit Monte Carlo simulation was implemented to track the propagation of each individual blood particle (BP) through the brain and time-dependent radiation fields, accumulating dose along their trajectories. The cerebral model includes 1050 path lines and explicitly simulates more than 266 000 BP at any given time that are tracked with a time resolution of 10 ms. The entire BFM for the whole body contains 22 178 000 BP, corresponding to 4200 BP per ml of blood. We have used the model to investigate the difference between proton and photon therapy, and the effect of different dose rates and patient characteristics on the dose to the circulating blood pool. The mean dose to the blood pool is estimated to be 0.06 and 0.13 Gy after 30 fractions of proton and photon therapy, respectively, and the highest dose to 1% of blood was found to be 0.19 Gy and 0.34 Gy. The fraction of blood volume receiving any dose after the first fraction is significantly lower for proton therapy, 10.1% compared to 18.4% for the photon treatment plan. 90% of the blood pool will have received dose after the 11th fraction using photon therapy compared to the 21st fraction with proton therapy. Higher dose rates can effectively reduce the fraction of blood irradiated to low doses but increase the amount of blood receiving high doses. Patient characteristics such as blood pressure, gender and age lead to smaller effects than variations in the dose rate. We developed a 4D human BFM including recirculating to estimate the radiation dose to the circulating blood during intracranial treatment and demonstrate its application to proton- versus photon-based delivery, various dose rates and patient characteristics. The radiation dose estimation to the circulating blood provides us better insight into the origins of radiation-induced lymphopenia.

Methods to measure, model and manipulate fluid flow in brain

The brain consists of a complex network of cells and matrix that is cushioned and nourished by multiple types of fluids: cerebrospinal fluid, blood, and interstitial fluid. The movement of these fluids through the tissues has recently gained more attention due to implications in Alzheimer's Disease and glioblastoma. Therefore, methods to study these fluid flows are necessary and timely for the current study of neuroscience. Imaging modalities such as magnetic resonance imaging have been used clinically and pre-clinically to image flows in healthy and diseased brains. These measurements have been used to both parameterize and validate models of fluid flow both computational and in vitro. Both of these models can elucidate the changes to fluid flow that occur during disease and can assist in linking the compartments of fluid flow with one another, a difficult challenge experimentally. In vitro models, though in limited use with fluid flow, allow the examination of cellular responses to physiological flow. To determine causation, in vivo methods have been developed to manipulate flow, including both physical and pharmacological manipulations, at each point of fluid movement of origination resulting in exciting findings in the preclinical setting. With new targets, such as the brain-draining lymphatics and glymphatic system, fluid flow and tissue drainage within the brain is an exciting and growing research area. In this review, we discuss the methods that currently exist to examine and test hypotheses related to fluid flow in the brain as we attempt to determine its impact on neural function.

A new framework for assessing subject-specific whole brain circulation and perfusion using MRI-based measurements and a multi-scale continuous flow model

A large variety of severe medical conditions involve alterations in microvascular circulation. Hence, measurements or simulation of circulation and perfusion has considerable clinical value and can be used for diagnostics, evaluation of treatment efficacy, and for surgical planning. However, the accuracy of traditional tracer kinetic one-compartment models is limited due to scale dependency. As a remedy, we propose a scale invariant mathematical framework for simulating whole brain perfusion. The suggested framework is based on a segmentation of anatomical geometry down to imaging voxel resolution. Large vessels in the arterial and venous network are identified from time-of-flight (ToF) and quantitative susceptibility mapping (QSM). Macro-scale flow in the large-vessel-network is accurately modelled using the Hagen-Poiseuille equation, whereas capillary flow is treated as two-compartment porous media flow. Macro-scale flow is coupled with micro-scale flow by a spatially distributing support function in the terminal endings. Perfusion is defined as the transition of fluid from the arterial to the venous compartment. We demonstrate a whole brain simulation of tracer propagation on a realistic geometric model of the human brain, where the model comprises distinct areas of grey and white matter, as well as large vessels in the arterial and venous vascular network. Our proposed framework is an accurate and viable alternative to traditional compartment models, with high relevance for simulation of brain perfusion and also for restoration of field parameters in clinical brain perfusion applications.

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

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

Influence of microvascular sutures on shear strain rate in realistic pulsatile flow

Arterial thrombus formation is directly related to the mechanical shear experienced by platelets within flow. High shear strain rates (SSRs) and large shear gradients cause platelet activation, aggregation and production of thrombus. This study, for the first time, investigates the influence of pulsatile flow on local haemodynamics within sutured microarterial anastomoses. We measured physiological arterial waveform velocities experimentally using Doppler ultrasound velocimetry, and a representative example was applied to a realistic sutured microarterial geometry. Computational geometries were created using measurements taken from sutured chicken femoral arteries. Arterial SSRs were predicted using computational fluid dynamics (CFD) software, to indicate the potential for platelet activation, deposition and thrombus formation. Predictions of steady and sinusoidal inputs were compared to analyse whether the addition of physiological pulse characteristics affects local intravascular flow characteristics. Simulations were designed to evaluate flow in pristine and hand-sutured microarterial anastomoses, each with a steady-state and sinusoidal pulse component. The presence of sutures increased SSR_max in the anastomotic region by factors of 2.1 and 2.3 in steady-state and pulsatile flows respectively, when compared to a pristine vessel. SSR values seen in these simulations are analogous to the presence of moderate arterial stenosis. Steady-state simulations, driven by a constant inflow velocity equal to the peak systolic velocity (PSV) of the measured pulsatile flow, underestimated SSRs by ∼ 9% in pristine, and ∼ 19% in sutured vessels compared with a realistic pulse. Sinusoidal flows, with equivalent frequency and amplitude to a measured arterial waveform, represent a slight improvement on steady-state simulations, but still SSRs are underestimated by 1-2%. We recommend using a measured arterial waveform, of the form presented here, for simulating pulsatile flows in vessels of this nature. Under realistic pulsatile flow, shear gradients across microvascular sutures are high, of the order ∼ 7.9 × 10⁶ m^-1 s^-1, which may also be associated with activation of platelets and formation of aggregates.

A parallel fluid-solid coupling model using LAMMPS and Palabos based on the immersed boundary method

The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the Jeffery orbits of an ellipsoid particle in shear flow, red blood cell stretching test, and effective blood viscosity flowing in tubes. It demonstrated essentially linear scaling from 512 to 8192 cores for both strong and weak scaling cases. The computing time for the coupling increased with the solid fraction. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code.

Multiscale modelling of blood flow in cerebral microcirculation: Details at capillary scale control accuracy at the level of the cortex

Aging or cerebral diseases may induce architectural modifications in human brain microvascular networks, such as capillary rarefaction. Such modifications limit blood and oxygen supply to the cortex, possibly resulting in energy failure and neuronal death. Modelling is key in understanding how these architectural modifications affect blood flow and mass transfers in such complex networks. However, the huge number of vessels in the human brain—tens of billions—prevents any modelling approach with an explicit architectural representation down to the scale of the capillaries. Here, we introduce a hybrid approach to model blood flow at larger scale in the brain microcirculation, based on its multiscale architecture. The capillary bed, which is a space-filling network, is treated as a porous medium and modelled using a homogenized continuum approach. The larger arteriolar and venular trees, which cannot be homogenized because of their fractal-like nature, are treated as a network of interconnected tubes with a detailed representation of their spatial organization. The main contribution of this work is to devise a proper coupling model at the interface between these two components. This model is based on analytical approximations of the pressure field that capture the strong pressure gradients building up in the capillaries connected to arterioles or venules. We evaluate the accuracy of this model for both very simple architectures with one arteriole and/or one venule and for more complex ones, with anatomically realistic tree-like vessels displaying a large number of coupling sites. We show that the hybrid model is very accurate in describing blood flow at large scales and further yields a significant computational gain by comparison with a classical network approach. It is therefore an important step towards large scale simulations of cerebral blood flow and lays the groundwork for introducing additional levels of complexity in the future.

Molecular dynamics simulations indicate that deoxyhemoglobin, oxyhemoglobin, carboxyhemoglobin, and glycated hemoglobin under compression and shear exhibit an anisotropic mechanical behavior

We developed a new mechanical model for determining the compression and shear mechanical behavior of four different hemoglobin structures. Previous studies on hemoglobin structures have focused primarily on overall mechanical behavior; however, this study investigates the mechanical behavior of hemoglobin, a major constituent of red blood cells, using steered molecular dynamics (SMD) simulations to obtain anisotropic mechanical behavior under compression and shear loading conditions. Four different configurations of hemoglobin molecules were considered: deoxyhemoglobin (deoxyHb), oxyhemoglobin (HbO₂), carboxyhemoglobin (HbCO), and glycated hemoglobin (HbA_1C). The SMD simulations were performed on the hemoglobin variants to estimate their unidirectional stiffness and shear stiffness. Although hemoglobin is structurally denoted as a globular protein due to its spherical shape and secondary structure, our simulation results show a significant variation in the mechanical strength in different directions (anisotropy) and also a strength variation among the four different hemoglobin configurations studied. The glycated hemoglobin molecule possesses an overall higher compressive mechanical stiffness and shear stiffness when compared to deoxyhemoglobin, oxyhemoglobin, and carboxyhemoglobin molecules. Further results from the models indicate that the hemoglobin structures studied possess a soft outer shell and a stiff core based on stiffness.

Physiome approach for the analysis of vascular flow reserve in the heart and brain

This work reviews the key aspects of coronary and neurovascular flow reserves with an emphasis on physiomic modeling characteristics by the use of a variety of numerical approaches. First, we explain the definition of fractional flow reserve (FFR) in coronary artery and introduce its clinical significance. Then, computational researches for obtaining FFR are reviewed, and their clinical outcomes are compared. In the case of cerebrovascular reserve (CVR), in spite of substantial progress in the simulation of cerebral hemodynamics, only a few computational studies exist. Thus, we discuss the limitations of CVR simulation study and suggest the challenging issue to overcome these. Also, the future direction of physiomic researches for the flow reserves in coronary arteries and cerebral arteries is described. Also, we introduce a machine learning algorithm trained by the existing physiomic simulation data of flow reserve and suggest a prospective research direction related to this.

A computational study of cancer hyperthermia based on vascular magnetic nanoconstructs

The application of hyperthermia to cancer treatment is studied using a novel model arising from the fundamental principles of flow, mass and heat transport in biological tissues. The model is defined at the scale of the tumour microenvironment and an advanced computational scheme called the embedded multiscale method is adopted to solve the governing equations. More precisely, this approach involves modelling capillaries as one-dimensional channels carrying flow, and special mathematical operators are used to model their interaction with the surrounding tissue. The proposed computational scheme is used to analyse hyperthermic treatment of cancer based on systemically injected vascular magnetic nanoconstructs carrying super-paramagnetic iron oxide nanoparticles. An alternating magnetic field is used to excite the nanoconstructs and generate localized heat within the tissue. The proposed model is particularly adequate for this application, since it has a unique capability of incorporating microvasculature configurations based on physiological data combined with coupled capillary flow, interstitial filtration and heat transfer. A virtual tumour model is initialized and the spatio-temporal distribution of nanoconstructs in the vascular network is analysed. In particular, for a reference iron oxide concentration, temperature maps of several different hypothesized treatments are generated in the virtual tumour model. The observations of the current study might in future guide the design of more efficient treatments for cancer hyperthermia.