International Journal for Numerical Methods in Biomedical Engineering

In the context of dynamic image-based computational fluid dynamics (DIB-CFD) modeling of cardiac system, the role of sub-valvular apparatus (chordae tendineae and papillary muscles) and the effects of different mitral valve (MV) opening/closure dynamics, have not been systemically determined. To provide a partial filling of this gap, in this study we performed DIB-CFD numerical experiments in the left ventricle, left atrium and aortic root, with the aim of highlighting the influence on the numerical results of two specific modeling scenarios: i) the presence of the sub-valvular apparatus, consisting of chordae tendineae and papillary muscles; ii) different MV dynamics models accounting for different use of leaflet reconstruction from imaging. This is performed for one healthy and one MV regurgitant subjects. Specifically, a systolic wall motion is reconstructed from time-resolved Cine-MRI images and imposed as boundary condition for the CFD numerical simulation. Analyzing the numerical results, we found that sub-valvular apparatus do not affect the global fluid dynamics quantities, although it creates local variations, such as the developing of vortexes or flow disturbances, which lead to different stress distributions on cardiac structures. Moreover, different MV dynamics are considered starting from Cine-MRI MV segmentation at different temporal configurations, and then they are compared and managed numerically through a resistive approach. The obtained results highlight the importance of including a sophisticated diastolic model of MV dynamics, which accounts for MV geometries during diastasis and A-wave, in terms of describing the disturbed flow and ventricular turbulence. Statements and DeclarationsThe authors have no relevant financial or non-financial interests to disclose.

A previously developed computational model for cardiovascular mechanics is here calibrated using typical values of 22 clinically observed hemodynamic properties in healthy human subjects. The model includes spatially resolved representations of the four heart chambers. The left ventricle is represented as a truncated thick-walled prolate spheroid, with three modes of deformation (short and long axis contraction and torsion). The other chambers are represented as full or partial thick-walled spherical shells. Wave propagation and reflection in the aorta are represented using a one-dimensional model. The closed-loop system is completed using lumped elements representing vascular resistances, compliances and inertances. The resulting system of coupled ordinary differential equations can be solved computationally in less than 0.1 s per cardiac cycle. In the present study, the values of 19 key input parameters to the model are estimated by minimizing the deviation of model predictions from the 22 observed hemodynamic properties. The resulting calibrated reference model provides a baseline for theoretical studies exploring the relationship between fundamental properties of the cardiovascular system, such as ventricular contractility and stiffness or vascular resistance and compliance, and clinically available measurements such as blood pressures, chamber volumes or valve flow waveforms.

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.

In this work we performed a computational image-based study of blood dynamics in the whole left heart, both in a healthy subject and in a patient with mitral valve regurgitation (MVR). We elaborated dynamic cine-MRI images with the aim of reconstructing the geometry and the corresponding motion of left ventricle, left atrium, mitral and aortic valves, and aortic root of the subjects. This allowed us to prescribe such motion to computational blood dynamics simulations where, for the first time, the whole left heart motion of the subject is considered, allowing us to obtain reliable subject-specific information. The final aim is to investigate and compare between the subjects the occurrence of turbulence and the risk of hemolysis and of thrombi formation. In particular, we modeled blood with the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian framework, with a Large Eddy Simulation model to describe the transition to turbulence and a resistive method to manage the valve dynamics, and we used a Finite Elements discretization implemented in an in-house code for the numerical solution. Our results highlighted that the regurgitant jet in the MVR case gave rise to a large amount of transition to turbulence in the left atrium resulting in a higher risk of formation of hemolysis. Moreover, MVR promoted a more complete washout of stagnant fiows in the left atrium during the systolic phase and in the left ventricle apex during diastole. NEW & NOTEWORTHYReconstruction from cine-MRI images of geometries and motion of the left heart (left atrium and ventricle, aortic root, aortic and mitral valve) of a healthy and mitral regurgitant patient. Prescription of such motion to a complete subject-specific computational fluid-dynamic simulation of the left heart. Investigation of turbulence in a regurgitant scenario. Study of the mechanisms of prevention from stagnant flows and hemolysis formation in the atrium.

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.

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.

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.

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.

The congenital heart disease univentricular heart (UVH) occurs with an incidence of 0.04-0.5% in newborns and is often treated with the Fontan procedure. In this intervention, the cardiac circulation is transformed into a singular circulation with only one ventricular chamber pumping. Hemodynamics the singular ventricle is a major research topic in cardiology and there exists a relationship between fluid dynamical features and cardiac behavior in health and disease. By visualizing the flow using Computational Fluid Dynamics (CFD) models, an option is created to investigate the flow in patient-specific geometries. CFD simulation of the pathological single right ventricle in contrast to the healthy left ventricle is the research object of the present work. The aim is the numerical comparison of the intraventricular flow within the ventricles. Based on this, flow formation in different anatomies of the ventricles is investigated. Patient-specific measurements of ventricles from three-dimensional real-time echocardiographic images served as the basis for the simulations with five single right ventricle (SRV) patients and two subjects with healthy left hearts (LV) investigated. Interpolation of these data reproduced the shape and continuous motion of the heart during a cardiac cycle. This motion was implemented into a CFD model with a moving mesh methodology. For comparison of the ventricles, the vortex formation as well as the occurring turbulent kinetic energy (TKE) and washout were evaluated. Vortex formation was assessed using the dimensionless vortex formation time (VFT). The results show significantly lower values for the VFT and the TKE in SRV patients than for the compared LV Patients. Furthermore, vortex formation does not progress to the apex in SRV patients. These findings were confirmed by a significantly lower washout in SRV patients. Flow simulation within the moving ventricle provides the possibility of more detailed analysis of the ventricular function. Simulation results show altered vortex formation and reduced washout of SRV in comparison to healthy LV. This information could provide important information for the planning and treatment of Fontan patients.

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.

Autoregulation and neurogliavascular coupling are key mechanisms that modulate myogenic tone (MT) in vessels to regulate cerebral blood flow (CBF) during resting state and periods of increased neural activity, respectively. To determine relative contributions of distinct vascular zones across different cortical depths in CBF regulation, we developed a simplified yet detailed and computationally efficient model of the mouse cerebrovasculature. The model integrates multiple simplifications and generalizations regarding vascular morphology, the hierarchical organization of mural cells, and potentiation/inhibition of MT in vessels. Our analysis showed that autoregulation is the result of the synergy between these factors, but achieving an optimal balance across all cortical depths and throughout the autoregulation range is a complex task. This complexity explains the non-uniformity observed experimentally in capillary blood flow at different cortical depths. In silico simulations of cerebral autoregulation support the idea that the cerebral vasculature does not maintain a plateau of blood flow throughout the autoregulatory range and consists of both flat and sloped phases. We learned that small-diameter vessels with large contractility, such as penetrating arterioles and precapillary arterioles, have major control over intravascular pressure at the entry points of capillaries and play a significant role in CBF regulation. However, temporal alterations in capillary diameter contribute moderately to cerebral autoregulation and minimally to functional hyperemia. In addition, hemodynamic analysis shows that while hemodynamics within capillaries remain relatively stable across all cortical depths throughout the entire autoregulation range, significant variability in hemodynamics can be observed within the first few branch orders of precapillary arterioles or transitional zone vessels. The computationally efficient cerebrovasculature model, proposed in this study, provides a novel framework for analyzing dynamics of the CBF regulation where hemodynamic and vasodynamic interactions are the foundation on which more sophisticated models can be developed. Author summaryBlood vessels dynamically adapt to the mechanical forces exerted by circulating blood. Appropriate adaptive responses to changes in mechanical force are central to the optimal functioning of the cerebral blood flow (CBF) regulatory system, and include processes such as cerebral autoregulation, vasomotion, and neurogliovascular coupling. This adaptation is driven by intercellular interactions, primarily modulated by factors such as vessel wall tension, shear stress, and strain. As our understanding of the biophysicochemical principles of CBF regulatory system has advanced, computational studies have become more detailed and sophisticated, providing practical in-silico environments to investigate its dynamics and gain insight into the underlying biology. In this study, I propose a method to create a computationally efficient platform where the interactions of hemodynamics with vessel segments can be modeled and studied in an in-silico setting. This method can lay the groundwork for more sophisticated computational studies of the CBF regulatory system, where hemodynamics are core elements of the system operation and the model can represent a more realistic version of this system.

AO_SCPLOWBSTRACTC_SCPLOWLumped (zero-dimensional) technique is a robust and widely used approach to mathematically model and explore bulk behaviour of different physical phenomena in a lower expense. In modelling of cardio/cerebrovascular fluid dynamics, this technique facilitates the assessment of relevant metrics such as flow, pressure, and temperature at different locations over a large network/domain. Furthermore, they can be employed as boundary conditions in multiscale modelling of physiological flows. In this methodology paper, a lumped model for the cardiovascular flow simulation along with a two-node thermoregulation model are employed. The lumped models are built upon previous studies and are amended appropriately to focus on cardiac function. The output of the coupled model can either be used for assessing the cardiac function in different physiological conditions or it can provide the input data for other investigations. Noteworthy to mention that, the present model has been specifically developed for investigation on the effects of atrial fibrillation on cardiac performance.

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.

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

Simulating the electrical activity of the human uterus has become a crucial tool for understanding the underlying biophysical phenomena, such as uterine contractions during pregnancy. Finite element models (FEM) offer valuable insights into these dynamics by providing a scalable framework to explore the propagation of electrical signals at the cellular and tissue levels. This study presents a finite element-based bidomain model to simulate the excitation propagation across the human uterus. Our model integrates cellular-level electrophysiological properties with tissue-level electrical propagation using the FEniCS Python library. A three-dimensional, realistic representation of uterine tissue is employed to simulate excitation patterns, contributing to a deeper understanding of uterine electrophysiology. The model can also be adapted to investigate pathological conditions such as preterm labor and test potential interventions. The developed simulation framework provides a scalable solution for the numerical challenges posed by solving complex, non-linear ordinary differential equations (ODEs) associated with uterine electrical activity. These simulations could offer a foundation for future research on uterine function and its related disorders.

Endovascular procedures provide surgeons and other interventionalists with minimally invasive methods to treat vascular diseases by passing guidewires, catheters, sheaths and treatment devices into the vasculature to and navigate toward a treatment site. The efficiency of this navigation affects patient outcomes, but is frequently compromised by catheter "herniation", in which the catheter-guidewire system bulges out from the intended endovascular pathway so that the interventionalist can no longer advance it. Here, we showed herniation to be a bifurcation phenomenon that can be predicted and controlled using mechanical characterizations of catheter-guidewire systems and patientspecific clinical imaging. We demonstrated our approach in laboratory models and, retrospectively, in patients who underwent procedures involving transradial neurovascular procedures with an endovascular pathway from the wrist, up in the arm, around the aortic arch, and into the neurovasculature. Our analyses identified a mathematical navigation stability criterion that predicted herniation in all of these settings. Results show that herniation can be predicted through bifurcation analysis, and provide a framework for selecting catheter-guidewire systems to avoid herniation in specific patient anatomy.

ObjectiveNowadays, the treatment of mitral valve prolapse involves two distinct repair techniques: chordal replacement (Neochordae technique) and leaflet resection (Resection technique). However, there is still a debate in the literature about which is the optimal one. In this context, we performed an image-based computational fluid dynamic study to evaluate blood dynamics in the two surgical techniques. MethodsWe considered a healthy subject (H) and two patients (N and R) who underwent surgery for the prolapse of the posterior leaflet and were operated with the Neochordae and Resection technique, respectively. Computational Fluid Dynamics (CFD) was employed with prescribed motion of the entire left heart coming from cine-MRI images, with a Large Eddy Simulation model to describe the transition to turbulence and a resistive method for managing valve dynamics. We created three different virtual scenarios where the operated mitral valves were inserted in the same left heart geometry of the healthy subject to study the differences attributed only to the two techniques. ResultsWe compared the three scenarios by quantitatively analyzing ventricular velocity patterns and pressures, transition to turbulence, and the ventricle ability to prevent thrombi formation. From these results we found that both the operated cases were able to restore almost physiological blood dynamic conditions, with some differences due to the reduced mobility of the Resection posterior leaflet. Conclusions: Our findings suggest that the Neochordae technique developed a slightly more physiological flow with respect to the Resection technique. The latter gave rise to a different direction of the mitral jet during diastole increasing the turbulence that is associated with ventricular effort and hemolysis, with also a larger ability to washout the ventricular apex preventing from thrombi formation.

Heart failure remains one of the leading causes of death especially among people over the age of 60 years worldwide. To develop effective therapy and suitable replacement materials for the heart muscle it is necessary to understand its biomechanical behaviour under load. This paper investigates the passive mechanical response of the sheep myocardia excised from three different regions of the heart. Due to the relatively higher cost and huge ethical demands in acquisition and testing of real animal heart models, this paper evaluates the fitting performances of five different constitutive models on the myocardial tissue responses. Ten sheep were sacrificed, and their hearts excised and transported within 3h to the testing biomechanical laboratory. The upper sections of the hearts above the short axes were carefully dissected out. Tissues were dissected from the mid-sections of the left ventricle, mid-wall and right ventricle for each heart. The epicardia and endocardia were then carefully sliced off each tissue to leave the myocardia. Stress-strain curves were calculated, filtered and resampled. The results show that Choi-Vito model was found to provide the best fit to the LV, the polynomial (Anisotropic) model to RV, the Four-Fiber Family model to RV, Holzapfel (2000) to RV, Holzapfel (2005) to RV and the Fung model to LV.

The Izhikevich artificial spiking neuron model is among the most employed models in neuromorphic engineering and computational neuroscience, due to the affordable computational effort to discretize it and its biological plausibility. It has been adopted also for applications with limited computational resources in embedded systems. It is important therefore to realize a compromise between error and computational expense to solve numerically the models equations. Here we investigate the effects of discretization and we study the solver that realizes the best compromise between accuracy and computational cost, given an available amount of Floating Point Operations per Second (FLOPS). We considered three fixed-step solvers for Ordinary Differential Equations (ODE), commonly used in computational neuroscience: Euler method, the Runge-Kutta 2 method and the Runge-Kutta 4 method. To quantify the error produced by the solvers, we used the Victor Purpura spike train Distance from an ideal solution of the ODE. Counterintuitively, we found that simple methods such as Euler and Runge Kutta 2 can outperform more complex ones (i.e. Runge Kutta 4) in the numerical solution of the Izhikevich model if the same FLOPS are allocated in the comparison. Moreover, we quantified the neuron rest time (with input under threshold resulting in no output spikes) necessary for the numerical solution to converge to the ideal solution and therefore to cancel the error accumulated during the spike train; in this analysis we found that the required rest time is independent from the firing rate and the spike train duration. Our results can generalize in a straightforward manner to other spiking neuron models and provide a systematic analysis of fixed step neural ODE solvers towards an accuracy-computational cost tradeoff.

The human aorta undergoes complex morphologic changes that indicate the evolution of disease. Finite element analysis enables the prediction of aortic pathologic states, but the absence of a biomechanical understanding hinders the applicability of this computational tool. We incorporate geometric information from computed tomography angiography (CTA) imaging scans into finite element analysis (FEA) to predict a trajectory of future geometries for four aortic disease patients. Through defining a geometric correspondence between two patient scans separated in time, a patient-specific FEA model can recreate the deformation of the aorta between the two time points, showing pathologic growth drives morphologic heterogeneity. A shape-size geometric feature space plotting the variance of the shape index versus the inverse square root of aortic surface area ({delta}[S] vs. [Formula]) quantitatively demonstrates the simulated breakdown in aortic shape. An increase in {delta}[S] closely parallels the true geometric progression of aortic disease patients.