International Journal for Numerical Methods in Biomedical Engineering

Interactions of particles with unsteady non-linear viscous flows has widespread implications in physiological and biomedical systems. One key application where this plays a fundamental role is in the mechanism and etiology of embolic strokes. Specifically, there is a need to better understand how large occlusive emboli traverse complex vascular geometries, and block a vessel disrupting blood supply. Existing modeling approaches resort to key simplifications in terms of embolic particle shape, size, and their coupling to fluid flow. Here, we devise a novel computational model for resolving embolus-hemodynamics interactions for large non-spherical emboli approaching near occlusive regimes in anatomically real vascular segment. The formulation relies on extending an immersed finite element approach, coupled with a six degree-of-freedom particle dynamics model. The geometric complexities and their manifestation in embolus-flow and embolus-wall interactions are handles using a parametric shape representation, and projection of vessel signed distance fields on the particle boundaries. We illustrate our methodology and algorithmic details, as well as present examples of benchmark cases and convergence of our technique. Thereafter, we demonstrate a parametric study of large emboli for LVO strokes, showing that our methodology can capture the non-linear tumbling dynamics of emboli originating form their interactions with the flow and vessel walls; and resolve near-occlusive scenarios involving lubrication effects around the embolus and flow re-routing to non-occludes branches. This is a key methodological advancement in stroke modeling, as to the best of our knowledge this is the first modeling framework for LVO stroke and occlusion biofluid mechanics. Finally, even though we present our framework from the perspective of LVO strokes, the methodology as developed is broadly generalizable to two-way coupled fluid-particle interaction in unsteady viscous flows for a wide range of applications.

ObjectivesThrombotic deposition is a major consideration in the development of implantable cardiovascular devices. Recently, it has been experimentally demonstrated that localized changes in the blood shear rate -i.e. shear gradients-play a critical role in thrombogenesis. The goal of the present work is to develop a predictive computational model of platelet plug formation that can be used to assess the thrombotic burden of cardiovascular devices, introducing for the first time the role of shear gradients. We have developed a comprehensive model of platelet-mediated thrombogenesis which includes platelet transport in the blood flow, platelet activation and aggregation induced by both biochemical and mechanical factors, kinetics and mechanics of platelet adhesion, and changes in the local fluid dynamics due to the thrombus growth. MethodsA 2D computational model was developed using the multi-physics finite element solver COMSOL 5.6. The model can be described by a coupled set of convection-diffusion-reaction equations. Platelet adhesion at the surface was modeled via flux boundary conditions. Using a moving mesh for the surface, thrombus growth and consequent alterations in blood flow were modeled. In the case of a stenosis, the notions of shear stress induced platelet activation in the contraction zone and shear gradients induced platelet deposition in the expansion zone downstream of the stenosis were studied. ResultsThe model provides the spatial and temporal evolution of platelet plug in the flow field. The computed platelet plug size evolution was validated against literature data. The results confirm the importance of considering both mechanical and chemical aggregation of platelets. ConclusionsThe developed model represents a potentially useful tool for the optimization of the design of the cardiovascular device flow path.

Thrombosis refers to the formation of a thrombus, or a blood clot, within the body, which can occur either partially or completely. It serves as a crucial indicator of the severity of a patients medical condition, with the location and characteristics of thrombosis dictating its clinical implications. Hence, accurate diagnosis and effective management of thrombosis are paramount. In our current investigation, we incorporate the porous attributes of a thrombus using the Theory of Porous Media. This involves dividing the aggregate into solid, liquid, and nutrient phases and utilising volume fractions to capture microstructural details. Fluid flow through the porous media is modelled using a modified Darcy-Brinkman type equation, with interaction terms within balance equations facilitating the modelling of the mass exchange and other phase interactions. The shorter time scales are neglected. We present a comprehensive framework of equations and assumptions governing the behaviour of a strongly coupled multiphasic porous medium problem. Additionally, we introduce scenarios involving type B Aortic Dissection and false lumen geometries, providing a detailed outline of the problem setup. Thereafter, we present the potential of the model for thrombi growth. The simulation results are compared with velocity plots aligning with Magnetic Resonance Imaging data for three distinct cases with varying entry and exit tear sizes. Consequently, our proposed model offers a promising and reasonable approach for numerically simulating thrombosis and gaining insights into the underlying growth mechanics.

Atrial fibrillation (AF) disrupts the circulation of blood through the left atrium (LA), and may result in relative stasis in the left atrial appendage (LAA), increasing thromboembolic risk. Anticoagulant agents can lower this risk, but currently used agents target the common pathway central to the coagulation cascade, increasing bleeding risk. Anticoagulants such as factor XI/XII inhibitors target the initial phase of the intrinsic pathway, with a significantly lower associated bleeding risk. However, these agents efficacy in preventing thrombosis in patient-specific flow conditions is not fully understood. We hypothesized that patient-specific flow patterns in the LA and LAA not only influence the risk of thrombosis but also the effectiveness of anticoagulation agents. We simulated blood flow and the intrinsic coagulation pathway in patient-specific LA anatomies with and without factor XI/XII inhibition to test this hypothesis. We considered thirteen patients in sinus rhythm and AF, several of whom had an LAA clot or a history of transient ischemic attacks. We used computational fluid dynamics based on 4D CT imaging and a detailed 32-species coagulation system to run 247 simulations for 13 patients, systematically sweeping over a wide range of factor XI/XII inhibition levels. Implementing a novel multi-fidelity coagulation modeling approach accelerated computations by two orders of magnitude, enabling the large number of simulations performed. Our simulations provide spatiotemporally resolved maps of thrombin concentration throughout the LA, showing it peaks inside the LAA. Coagulation metrics based on peak LAA thrombin dynamics suggested patients could be classified as non-coagulating, moderately and severely coagulating cases. Severely coagulating cases had significantly slower flow and higher residence time than moderately coagulating patients inside the LAA, requiring stronger factor XI/XII inhibition to blunt thrombin growth. The methodology outlined in this study has the potential to enable personalized assessments of coagulation risk and tailor anticoagulation therapy based on medical imaging.

Recently, experimental and theoretical studies have revealed the potential of fractional calculus to represent viscoelastic blood vessel and arterial biomechanical properties. This paper presents five fractional-order models to describe the dynamic relationship between aortic blood pressure and volume, representing the apparent vascular compliance. The proposed model employs fractional-order capacitor element (FOC) to lump the complex and frequency dependence characteristics of arterial compliance. FOC combines both resistive and capacitive properties, which the fractional differentiation order, , can control. The proposed representations have been compared with generalized integer-order models of arterial compliance. All structures have been validated using different aortic pressure and flow rate waveforms collected from various human and animal species such as pigs and dogs. The results demonstrate that the fractional-order scheme can reconstruct the overall dynamic of the complex and frequency-dependent apparent compliance dynamic and reduce the complexity. The physiological relevance of the proposed models parameters was assessed by evaluating the variance-based global sensitivity analysis. Moreover, the simplest fractional-order representation has been embed in a global arterial lumped parameter representation to develop a novel fractional-order modified arterial Windkessel. The introduced arterial model has been validated by applying real human and animal hemodynamic data and shows an accurate reconstruction of the proximal blood pressure. The novel proposed paradigm confers a potential to be adopted in clinical practice and basic cardiovascular mechanics research.

Computational analysis of physiological and biomedical systems necessitate efficient geometry representations for high fidelity model predictions, including patient or device specificity. Particle-based Lagrangian computational approaches comprise a valuable approach to gain insights from quantitative velocity and pressure data from computational models. Examples include particle dynamics and transport in human vasculature for diseases such as stroke, thrombosis, and embolisms; and modern targeted drug delivery systems in the vascular network and respiratory airways. However, current particle simulation approaches can bear significant computational expense that scales with both number of particles and background fluid mesh resolution. A significant determinant of this computational expense is the contact resolution between particles and anatomically realistic vessel wall. Here, we develop an efficient particle dynamics model that leverages an implicit representation of real anatomical features using a signed distance field to efficiently resolve particle-wall contact. We outline the underlying algorithmic details, followed by a systematic illustration of performance and accuracy using simplified and analytically defined geometries and flow fields. Subsequently, we present a representative simulation of embolic particles along a human vascular segment where we compare our distance field-based approach against classical wall-contact checks based on assessing particle boundary intersection with triangulated surface mesh. Our approach transforms the underlying Lagrangian contact detection operation into an equivalent Eulerian operation, significantly speeding up bulk particle dynamics computations without significantly impacting accuracy or geometric fidelity.

This paper addresses a new global stability analysis for a specific class of nonlinear multi-compartment models with non-positive flows and whose balances are described by equilibrium sets. We apply the stability analysis to our physiological-based model of extracellular fluid used during dialysis therapy in end-stage kidney disease patients. To gain an in-depth understanding of the risk associated with fluid removal by the artificial kidney during the short time (3-5hrs) of the dialysis therapy, we use the stability results to analyze the solutions behavior of our model under standard ultrafiltration and patient-specific ultrafiltration profiles. Therefore, the standard ultrafiltration profiles do not guarantee optimal outcomes, and we highly recommend incorporating physiological insights into the ultrafiltration profiles to improve outcomes.

BackgroundAstrocyte endfoot processes are believed to cover all micro-vessels in the brain cortex and may play a significant role in fluid and substance transport into and out of the brain parenchyma. Detailed fluid mechanical models of diffusive and advective transport in the brain are promising tools to investigate theories of transport. MethodsWe derive theoretical estimates of astrocyte endfoot sheath permeability for advective and diffusive transport and its variation in microvascular networks from mouse brain cortex. The networks are based on recently published experimental data and generated endfoot patterns are based on Voronoi tessellations of the perivascular surface. We estimate corrections for projection errors in previously published data. ResultsWe provide structural-functional relationships between vessel radius and resistance that can be directly used in flow and transport simulations. We estimate endfoot sheath filtration coefficients in the range Lp = 0.2 x 10-10 m Pa-1 s-1 to 2.7 x 10-10 m Pa-1 s-1, diffusion membrane coefficients in the range CM = 0.5 x 103 m-1 to 6 x 103 m-1, and gap area fractions in the range 0.2 % to 0.6 %. ConclusionsThe astrocyte endfoot sheath surrounding microvessels forms a secondary barrier to extra-cellular transport, separating the extra-cellular space of the parenchyma and the perivascular space outside the endothelial layer. The filtration and membrane diffusion coefficients of the endfoot sheath are estimated to be an order of magnitude lower than the extra-cellular matrix while being two orders of magnitude higher than the vessel wall.

A novel hybrid model combining the lattice Boltzmann (LB) and finite difference (FD) methods is proposed to simulate transport in through a junction of actively contracting lymphatic vessels, while also handling flow of interstitial liquid in the surrounding porous tissue. Details of the dynamically flexing walls and valves in the lymphatic vessel and its near vicinity are modeled using a high-resolution LB method, whereas overall efficiency was significantly improved by using low-resolution FD in the larger tissue domain distant from the vessel. Pressure and velocity conditions at the interface between subdomains of the two numerical methods are matched by imposing a partial bounce-back ratio in LB corresponding to the permeability coefficient{kappa} in Darcys law for flow through porous media. Parameters governing the match between the algorithms at their interface can be estimated from the Kozeny-Carman relationship for porous media and further refined with a simpler, parallel flow geometry that also serves to validate the method. Test calculations show that the hybrid method is roughly four times faster than the LB method and permits computation over significantly larger domains. This method should be applicable to a large range of problems involving fluid flow in porous media with embedded conduits that have non-stationary boundaries. Author summaryIt is generally acknowledged that the finite difference method (FDM) is faster and requires less memory than the lattice Boltzmann method (LBM) for comparable domain sizes. However, LBM performs better for simulating fluid flow near complex, deformable, or moving boundaries. For this reason, it can be beneficial to create hybrid models that combine FDM and LBM. In this work, we use such a hybrid model to simulate a contracting lymphatic bifurcation in fluid. Our goal is to demonstrate the models robustness and high efficiency.

Peripheral artery disease currently affects over 202 million people worldwide. The ankle-brachial index is one of the most used measurements to assess a reduction in blood flow to the foot, but it is not able to characterise tissue perfusion. Information on tissue perfusion can be obtained, among others, through an MRI scan, which is time-consuming and can be painful if induction of ischemia is warranted for the scan. As an alternative, we model foot perfusion during a cuff-induced ischaemia test to characterise how occlusions in foot arteries affect perfusion in foot regions. Simulations are not patient-specific at this stage, and are conducted on a 1D arterial network model which includes 154 foot and calf arterial segments, providing a realistic description of the topology of the foot arterial vasculature. A baseline model characterizes perfusion in angiosomes under healthy conditions, which is then modified to reflect 42 pathological scenarios by introducing occlusions and different levels of collateral impairment. Results show a marked influence of collateral impairment on angiosome perfusion under the condition of a single-artery occlusion, highlighting the role of blood redistribution. If two feeding arteries are occluded, perfusion markedly decreases at all collateral impairment levels due to the severe reduction in incoming blood flow. These results provide a bridge between the angiosome-targeted and "best-vessel" strategies for revascularization, showing that both can be correct depending on collateral sufficiency. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=77 SRC="FIGDIR/small/692561v1_ufig1.gif" ALT="Figure 1"> View larger version (22K): org.highwire.dtl.DTLVardef@10d4da5org.highwire.dtl.DTLVardef@649775org.highwire.dtl.DTLVardef@13b8e4org.highwire.dtl.DTLVardef@cfbb3e_HPS_FORMAT_FIGEXP M_FIG C_FIG HighlightsO_LIWe propose a computational model of foot perfusion during a cuff-induced ischaemia test that allows the assessment of perfusion in each angiosome of the foot C_LIO_LIWe study how occlusions in the main feeding arteries of the foot impact tissue perfusion C_LIO_LIWe highlight the role of collateralization if adequate inflow is maintained C_LIO_LIResults show that both angiosome-targeted and "best-vessel" strategies for revascularization can be correct depending on arch patency and collateral sufficiency C_LI

In this paper we test various numerical methods for flow reconstruction based on both manufactured, idealized data and real patient data based on contrast enhanced magnetic resonance imaging after intrathecal contrast injection. As shown in previous studies, the imaging often display contrast gradients in localized regions although large areas have very small gradients. Velocities may as such be hard to assess in areas of low gradients. We compare optimal mass transfer with adjoint based data assimilation constrained by a convection diffusion equation. With well-chosen parameters the manufactured problems can be solved well in the idealized setting, but the performance is in general significantly worse in the patient specific setting. The methods predict maximal velocities well, but fail to reconstruct accurate velocity fields in areas without contrast gradients.

Thin structures such as heart valves and aortic dissection flaps interact dynamically with blood flow in human vessels. Their flexibility and capacity for large deformations generate complex, highly transient hemodynamic patterns over the cardiac cycle. Accurately resolving these interactions remains challenging for conventional boundary-fitted fluid-structure interaction approaches. We present an immersed boundary method for simulating thin structures in incompressible flow on unstructured grids. The method couples a stabilized finite element fluid solver with a nonlinear, rotation-free shell formulation through a direct forcing immersed boundary approach. The framework supports both weak (explicit) and strong (implicit) time-coupling strategies, enabling stable simulations over a wide range of solid-to-fluid density ratios. Hydrodynamic forces acting on thin structures are computed from fluid solutions sampled on both sides of the structure, allowing accurate force reconstruction for zero-thickness shells. To our knowledge, this is the first immersed boundary formulation that couples an unstructured finite element fluid solver with a two-dimensional, rotation-free shell model to simulate interactions between thin structures and incompressible flow. Fluid-structure coupling is achieved using predefined finite element shape functions, which provide consistent projection between Eulerian and Lagrangian fields without additional interpolation procedures. The framework is validated using three-dimensional benchmark problems involving thin structures. Then, valve-like model is used to compare strong and weak coupling strategies. Finally, the method is applied to an idealized type-B aortic dissection model. The proposed approach is implemented within the open-source software CRIMSON, a finite element platform for cardiovascular simulation.

The intracranial pressure is implicated in many homeostatic processes in the brain and is a fundamental parameter in several diseases such as e.g. idiopathic normal pressure hydrocephalus (iNPH). The presence of a small but persistent pulsatile intracranial pulsatile transmantle pressure gradient (on the order of a few mmHg/m at peak) has recently been demonstrated in iNPH subjects. A key question is whether pulsatile ICP and displacements can be induced by a small pressure gradient originating from the brain surface e.g. pial arteries alone. In this study, we model the brain parenchyma as either a linearly elastic or a poroelastic medium and impose a pulsatile pressure gradient acting between the ventricular and the pial surfaces. Using this high-resolution physics-based model, we compute the effect of the pulsatile pressure gradient on parenchyma displacement, volume change, fluid pressure, and fluid flux. The resulting displacement field is pulsatile and in qualitatively and quantitatively good agreement with the literature, both with elastic and poroelastic models. However, the pulsatile forces on the boundaries are not sufficient for pressure pulse propagation through the brain parenchyma. Our results suggest that pressure differences originating over the brain surface via e.g. pial artery pulsatility are not sufficient to drive interstitial fluid (ISF) flow within the brain parenchyma and that potential pressure gradients found within the parenchyma rather arise from local pressure pulsations of blood vessels within the brain parenchyma itself.

BackgroundBlood and fluid volume management in End-stage Kidney Disease (ESKD) patients plays an essential role in dialysis therapy to replace kidney function. Reliable knowledge of blood and fluid volumes before and during dialysis could be used to improve treatment outcomes significantly. ObjectiveThis study aims to develop an estimation approach providing predictable information on blood and fluid volumes before and during a regular dialysis routine. MethodsA new approach is developed to estimate blood volume, fluid overload, and vascular refilling parameters from dialysis data. The method utilizes a nonlinear fluid volume model, an optimization technique, and the Unscented Kalman Filter (UKF) incorporated with data. This method does not rely on restricted ultrafiltration (UF) and dilution protocols and uses the Fisher information matrix to quantify error estimation. ResultsAccurate estimations for blood volumes (5.9{+/-}0.07L and 4.8{+/-}0.03L) and interstitial fluid volumes (18.81{+/-}0.15L and 12.19{+/-}0.03) were calculated from dialysis data consisting of constant and stepwise UF profiles. We demonstrated that by implementing the estimated parameters into the model, a precise prediction of the measured hematocrit (HCT) can be achieved during the treatment. ConclusionWe showed that the result does not depend highly on initial conditions and can be accurately estimated from a short data segment. A new method, applicable to the current dialysis routine, is now available for ESKD patients to be implemented within the dialysis machines.

The growth of a tumor within a finite domain (skull) generates mechanical forces that alter the physical interactions among cells. The relationship between these forces and the tumor architecture remains an open problem subjected to extensive research. Recently, it has been determined that those regions of high mechanical compression can accelerate and intensify the invasive capacity of the malignant cells, forming an irregular tumor whose full extent and edges are difficult to identify. In the present paper, we propose a one-dimensional mathematical model that describes the process of proliferation and diffusion of glioma cells taking into account the mechanical compression generated during its expansion. Supported on the mixture theory, we model the brain-tumor system as a multiphase mixture of cancer cells, healthy cells, biological fluids and extracellular matrix whose densities determine the mechanical loads generated during the volumetric growth. Our model provides a detailed understanding of the pressure distribution on the interface boundary between healthy and cancer cells. It validates the hypothesis that the conferred ability of cancer cells to proliferate depends strongly on the mechanical pressure sensed. Through the analysis of the mechanical pressure, we determine that the anisotropic loads promote cancer cells to grow preferentially in the directions of low mechanical compression.

Diagnosis, risk analysis, and treatment of coronary artery disease (CAD) can be improved with a better understanding of cardiovascular flows. Numerical simulations can assist in achieving this understanding. The objective of this study is to compare the dynamics of blood flow in a diseased left circumflex artery (LCX) and its artificially restored counterpart representing its healthy state. This comparison is made to identify flow characteristics in the restored vessel that contribute to the development of CAD. The diseased LCX geometry was derived from computed tomography angiography data. The stenosed region of the diseased LCX was repaired by manually redefining cross-sections of the vessel, creating the restored geometry. To account for inaccuracies, variations of the restored LCX were made by dilating the repaired surface. Numerical simulations were conducted on all geometries and the results were compared. Alongside expected low wall shear stress, a region of high vorticity was present in all of the restored vessels near the location where CAD developed in the diseased vessel. Therefore, this research suggests that flow vorticity is relevant in assessing the risk for CAD, potentially improving the accuracy of non-invasive, computational diagnosis. Such improvements can also help avoid unnecessary invasive diagnosis methods and minimize risk.

Targeted drug delivery offers a promising approach for personalized medicine in treating vascular stenosis. However, biomechanical constraints, such as drug washout by high-velocity central blood flow and unintended absorption by healthy vascular walls, complicate the determination of optimal dosing locations. Conventional three-dimensional computational fluid dynamics (CFD) provides precise flow analysis but incurs prohibitive computational costs, making long-term tracking of plaque growth and reverse-engineering of optimal delivery highly inefficient. In this study, we propose a pseudo-3D stochastic growth model that dramatically reduces computational load while capturing the essential dynamics of plaque progression and regression. By modeling the advection-diffusion of lipid and drug particles as a discrete Markov process within a Stokes flow field, we simulate the morphological evolution of plaques under continuous and interrupted targeted therapies. Furthermore, by formulating the drug transport process as an absorbing Markov chain with boundaries at the healthy walls and vessel outlet, we calculate the exact reaching probability and mean first passage time (MFPT) to the plaque. Based on these probability distributions, we discover continuous "Optimal Dosing Curves", which indicate the most effective spatial coordinates for catheter-based drug release to maximize therapeutic efficacy. This mathematical framework not only elucidates the stochastic nature of vascular plaque dynamics but also provides a scalable, computationally efficient foundation for optimizing targeted drug delivery in personalized medicine.

This paper considers a simple theoretical model of blocking the passage of signals (action potentials) from sensory neurons and thereby effecting anesthesia without the use of anesthetics as a result of a sequence of unipolar current pulses generated by an external source. The proposed model allows the selection of parameters and the required frequency of the repetition of current pulses for the possible implementation of anesthesia depending on the electrical characteristics of the skin and the conductivity of the saline solution in which the myelinated nerve fibers are located.

Thoracic Endovascular Aortic Repair (TEVAR) is a minimally invasive procedure for the treatment of thoracic aortic pathologies, such as Thoracic Aortic Aneurysm (TAA). Computational simulations can provide valuable insights into TEVAR outcomes and complications prior to surgery, making them a useful tool in the procedural planning. In this work, Fluid-Structure Interaction (FSI) computational simulations are carried out in ten pre-TEVAR patient-specific TAA cases, for which post-TEVAR outcomes are known, to quantify the hemodynamic drag forces acting on the aortic wall. Based on these results, this study proposes a new risk factor R to predict the occurrence of type I and III endoleaks. The patient cohort is divided in a calibration set, used to associate specific R values with three different risk levels, and a validation set, to test the risk factor efficacy. Based on the risk factor values obtained for the calibration set, R[&le;] 0.33 is associated with low risk of endoleak formation, 0.33 < R[&le;] 0.67 with moderate risk, and R > 0.67 with high risk. Once it is applied to the validation set,the risk factor is able to predict the formation of a type Ia endoleak. The risk factor proposed in this work is capable of identifying all the endoleak cases analysed, as well as conditions known to increase the risk of TEVAR complications. This study represents a preliminary attempt to determine whether pre-TEVAR hemodynamics can effectively predict post-TEVAR complications and thereby aid clinicians in the pre-operative planning.

AbstractBroad clinical application of non-invasive intracranial pressure (ICP) monitoring using computational models requires a method of modeling ICP on the basis of easily measured patient data such as radial or brachial arterial blood pressure (ABP). These models may be highly complex, rendering them too slow for clinical and operational use, or may rely on data that is not consistently available. Coupling these models to an upstream vasculature component model decreases data requirements. For the purposes of clinical decision support at multi-hour timescales, two natural choices for model development are to increase intracranial model complexity or to include feedback mechanisms between ICP and vascular model components. We compare the performance of these two approaches by evaluating model estimates against observed ICP in the case of a slow hypertensive event from a publically available dataset. The simpler model with bi-directional feedback requires minimal identifiability and is sufficiently accurate over these timescales, while a more complex is difficult and expensive to identify well enough to be accurate. Furthermore, the bi-directional simple model operates orders of magnitude faster than the more anatomically accurate model when driven by high-resolution ABP. It may also be configured to use lower resolution ABP summary data that is consistently clinically available. The simpler models are fast enough to support future developments such as patient-specific parametrization and assimilation of other clinical data streams which are illustrated during the case of a complex ICP regime for a different patient. We present model comparisons to highlight the advantages of the incorporated simple model and its possible predictive power with further optimization.Competing Interest StatementThe authors have declared no competing interest.View Full Text