A physics-informed deep learning framework for modeling of coronary in-stent restenosis.

Machine learning (ML) techniques have shown great potential in cardiovascular surgery, including real-time stenosis recognition, detection of stented coronary anomalies, and prediction of in-stent restenosis (ISR). However, estimating neointima evolution poses challenges for ML models due to limitations in manual measurements, variations in image quality, low data availability, and the difficulty of acquiring biological quantities. An effective in silico model is necessary to accurately capture the mechanisms leading to neointimal hyperplasia. Physics-informed neural networks (PINNs), a novel deep learning (DL) method, have emerged as a promising approach that integrates physical laws and measurements into modeling. PINNs have demonstrated success in solving partial differential equations (PDEs) and have been applied in various biological systems. This paper aims to develop a robust multiphysics surrogate model for ISR estimation using the physics-informed DL approach, incorporating biological constraints and drug elution effects. The model seeks to enhance prediction accuracy, provide insights into disease progression factors, and promote ISR diagnosis and treatment planning. A set of coupled advection-reaction-diffusion type PDEs is constructed to track the evolution of the influential factors associated with ISR, such as platelet-derived growth factor (PDGF), the transforming growth factor- ß (TGF- ß ), the extracellular matrix (ECM), the density of smooth muscle cells (SMC), and the drug concentration. The nature of PINNs allows for the integration of patient-specific data (procedure-related, clinical and genetic, etc.) into the model, improving prediction accuracy and assisting in the optimization of stent implantation parameters to mitigate risks. This research addresses the existing gap in predictive models for ISR using DL and holds the potential to enhance patient outcomes through predictive risk assessment.

Computational modeling of in-stent restenosis: Pharmacokinetic and pharmacodynamic evaluation.

Persistence of the pathology of in-stent restenosis even with the advent of drug-eluting stents warrants the development of highly resolved in silico models. These computational models assist in gaining insights into the transient biochemical and cellular mechanisms involved and thereby optimize the stent implantation parameters. Within this work, an already established fully-coupled Lagrangian finite element framework for modeling the restenotic growth is enhanced with the incorporation of endothelium-mediated effects and pharmacological influences of rapamycin-based drugs embedded in the polymeric layers of the current generation drug-eluting stents. The continuum mechanical description of growth is further justified in the context of thermodynamic consistency. Qualitative inferences are drawn from the model developed herein regarding the efficacy of the level of drug embedment within the struts as well as the release profiles adopted. The framework is then intended to serve as a tool for clinicians to tune the interventional procedures patient-specifically.

In-vivo assessment of vascular injury for the prediction of in-stent restenosis.

BACKGROUND: Despite optimizations of coronary stenting technology, a residual risk of in-stent restenosis (ISR) remains. Vessel wall injury has important impact on the development of ISR. While injury can be assessed in histology, there is no injury score available to be used in clinical practice. METHODS: Seven rats underwent abdominal aorta stent implantation. At 4 weeks after implantation, animals were euthanized, and strut indentation, defined as the impression of the strut into the vessel wall, as well as neointimal growth were assessed. Established histological injury scores were assessed to confirm associations between indentation and vessel wall injury. In addition, stent strut indentation was assessed by optical coherence tomography (OCT) in an exemplary clinical case. RESULTS: Stent strut indentation was associated with vessel wall injury in histology. Furthermore, indentation was positively correlated with neointimal thickness, both in the per-strut analysis (r = 0.5579) and in the per-section analysis (r = 0.8620; both p ≤ 0.001). In a clinical case, indentation quantification in OCT was feasible, enabling assessment of injury in vivo. CONCLUSION: Assessing stent strut indentation enables periprocedural assessment of stent-induced damage in vivo and therefore allows for optimization of stent implantation. The assessment of stent strut indentation might become a valuable tool in clinical practice.

A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation.

Development of in silico models that capture progression of diseases in soft biological tissues are intrinsic in the validation of the hypothesized cellular and molecular mechanisms involved in the respective pathologies. In addition, they also aid in patient-specific adaptation of interventional procedures. In this regard, a fully-coupled high-fidelity Lagrangian finite element framework is proposed within this work which replicates the pathology of in-stent restenosis observed post stent implantation in a coronary artery. Advection-reaction-diffusion equations are set up to track the concentrations of the platelet-derived growth factor, the transforming growth factor-ß, the extracellular matrix, and the density of the smooth muscle cells. A continuum mechanical description of volumetric growth involved in the restenotic process, coupled to the evolution of the previously defined vessel wall constituents, is presented. Further, the finite element implementation of the model is discussed, and the behavior of the computational model is investigated via suitable numerical examples. Qualitative validation of the computational model is presented by emulating a stented artery. Patient-specific data are intended to be integrated into the model to predict the risk of in-stent restenosis, and thereby assist in the tuning of stent implantation parameters to mitigate the risk.

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity.

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio [Formula: see text] (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate [Formula: see text] applied to the RBC. However, the membrane viscosity [Formula: see text] plays a major role in a realistic description of RBC dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity [Formula: see text] on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios [Formula: see text], larger values of [Formula: see text] lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing [Formula: see text] or increasing [Formula: see text] results in a qualitatively but not quantitatively similar behaviour. All results are obtained by means of mesoscale numerical simulations based on the lattice Boltzmann models. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Loading and relaxation dynamics of a red blood cell.

We use mesoscale numerical simulations to investigate the unsteady dynamics of a single red blood cell (RBC) subjected to an external mechanical load. We carry out a detailed comparison between the loading (L) dynamics, following the imposition of the mechanical load on the RBC at rest, and the relaxation (R) dynamics, allowing the RBC to relax to its original shape after the sudden arrest of the mechanical load. Such a comparison is carried out by analyzing the characteristic times of the two corresponding dynamics, i.e., tL and tR. When the intensity of the mechanical load is small enough, the two kinds of dynamics are symmetrical (tL≈tR) and independent of the typology of mechanical load (intrinsic dynamics); otherwise, in marked contrast, an asymmetry is found, wherein the loading dynamics is typically faster than the relaxation one. This asymmetry manifests itself with non-universal characteristics, e.g., dependency on the applied load and/or on the viscoelastic properties of the RBC membrane. To deepen such a non-universal behaviour, we consider the viscosity of the erythrocyte membrane as a variable parameter and focus on three different typologies of mechanical load (mechanical stretching, shear flow, elongational flow): this allows to clarify how non-universality builds up in terms of the deformation and rotational contributions induced by the mechanical load on the membrane. Finally, we also investigate the effect of the elastic shear modulus on the characteristic times tL and tR. Our results provide crucial and quantitative information on the unsteady dynamics of RBC and its membrane response to the imposition/cessation of external mechanical loads.

On the effects of membrane viscosity on transient red blood cell dynamics.

Computational Fluid Dynamics (CFD) is currently used to design and improve the hydraulic properties of biomedical devices, wherein the large scale blood circulation needs to be simulated by accounting for the mechanical response of red blood cells (RBCs) at the mesoscale. In many practical instances, biomedical devices work on time-scales comparable to the intrinsic relaxation time of RBCs: thus, a systematic understanding of the time-dependent response of erythrocyte membranes is crucial for the effective design of such devices. So far, this information has been deduced from experimental data, which do not necessarily adapt to the broad variety of fluid dynamic conditions that can be encountered in practice. This work explores the novel possibility of studying the time-dependent response of an erythrocyte membrane to external mechanical loads via mesoscale numerical simulations, with a primary focus on the detailed characterisation of the RBC relaxation time tc following the arrest of the external mechanical load. The adopted mesoscale model exploits a hybrid Immersed Boundary-Lattice Boltzmann Method (IB-LBM), coupled with the Standard Linear Solid (SLS) model to account for the RBC membrane viscosity. We underscore the key importance of the 2D membrane viscosity µm to correctly reproduce the relaxation time of the RBC membrane. A detailed assessment of the dependencies on the typology and strength of the applied mechanical loads is also provided. Overall, our findings open interesting future perspectives for the study of the non-linear response of RBCs immersed in time-dependent strain fields.

The variational multiscale formulation for the fully-implicit log-morphology equation as a tensor-based blood damage model.

We derive a variational multiscale (VMS) finite element formulation for a viscoelastic, tensor-based blood damage model. The tensor equation is numerically stabilized by a logarithmic shape tensor description that prevents unphysical, negative eigenvalues. The resulting VMS stabilization terms for this so-called log-morph equation are presented together with their special numerical treatment. Results for a 2D rotating stirrer test case obtained from log-morph simulations with both SUPG and VMS stabilization show significantly improved numerical behavior if compared with Galerkin/least squares (GLS) stabilized untransformed morphology simulation results. The newly proposed method is also successfully applied to a state-of-the-art centrifugal ventricular assist device (VAD), and clear advantages of the VMS stabilization compared with the SUPG-stabilized formulation are presented.

Strain-based blood damage estimation for computational design of ventricular assist devices.

AIMS: Computational fluid dynamics (CFD) is used to predict damage of red blood cells (RBCs) in ventricular assist devices (VADs). The damage is measured by the hemoglobin ratio in the blood plasma. METHODS: A power law is used to relate the hemoglobin ratio to shear stress and exposure time. For the shear stress measure, the common stress-based model is compared to a strain-based model, which predicts the deformation of RBCs in the VAD. For both models an Eulerian approach is used.In this study, new parameters are determined for the power law of the strain-based model. Hereby, the power law is fitted to data of experiments performed at the University of Maryland, Baltimore. RESULTS: As an example, blood damage in a benchmark blood pump of the U.S. Food and Drug Administration (FDA) is computed with a stress-based and a strain-based model using the new parameter set as well as parameter sets that were obtained in previous studies. CONCLUSIONS: Critical locations in the pump, as identified with the stress-based and the strain-based model, differ significantly between the two models.

Recent advances in computational methodology for simulation of mechanical circulatory assist devices.

Ventricular assist devices (VADs) provide mechanical circulatory support to offload the work of one or both ventricles during heart failure. They are used in the clinical setting as destination therapy, as bridge to transplant, or more recently as bridge to recovery to allow for myocardial remodeling. Recent developments in computational simulation allow for detailed assessment of VAD hemodynamics for device design and optimization for both children and adults. Here, we provide a focused review of the recent literature on finite element methods and optimization for VAD simulations. As VAD designs typically fall into two categories, pulsatile and continuous flow devices, we separately address computational challenges of both types of designs, and the interaction with the circulatory system with three representative case studies. In particular, we focus on recent advancements in finite element methodology that have increased the fidelity of VAD simulations. We outline key challenges, which extend to the incorporation of biological response such as thrombosis and hemolysis, as well as shape optimization methods and challenges in computational methodology.

Transient stress-based and strain-based hemolysis estimation in a simplified blood pump.

We compare two approaches to numerical estimation of mechanical hemolysis in a simplified blood pump model. The stress-based model relies on the instantaneous shear stress in the blood flow, whereas the strain-based model uses an additional tensor equation to relate distortion of red blood cells to a shear stress measure. We use the newly proposed least-squares finite element method (LSFEM) to prevent negative concentration fields and show a stable and volume preserving LSFEM for the tensor equation. Application of both models to a simplified centrifugal blood pump at three different operating conditions shows that the stress-based model overestimates the rate of hemolysis. The strain-based model is found to deliver lower hemolysis rates because it incorporates a more detailed description of biophysical phenomena into the simulation process.

Space-time least-squares finite element method for convection-reaction system with transformed variables.

We present a method to solve a convection-reaction system based on a least-squares finite element method (LSFEM). For steady-state computations, issues related to recirculation flow are stated and demonstrated with a simple example. The method can compute concentration profiles in open flow even when the generation term is small. This is the case for estimating hemolysis in blood. Time-dependent flows are computed with the space-time LSFEM discretization. We observe that the computed hemoglobin concentration can become negative in certain regions of the flow; it is a physically unacceptable result. To prevent this, we propose a quadratic transformation of variables. The transformed governing equation can be solved in a straightforward way by LSFEM with no sign of unphysical behavior. The effect of localized high shear on blood damage is shown in a circular Couette-flow-with-blade configuration, and a physiological condition is tested in an arterial graft flow.

A validated CFD model to predict O2 and CO2 transfer within hollow fiber membrane oxygenators.

Hollow fiber oxygenators provide gas exchange to and from the blood during heart surgery or lung recovery. Minimal fiber surface area and optimal gas exchange rate may be achieved by optimization of hollow fiber shape and orientation (1). In this study, a modified CFD model is developed and validated with a specially developed micro membrane oxygenator (MicroMox). The MicroMox was designed in such a way that fiber arrangement and bundle geometry are highly reproducible and potential flow channeling is avoided, which is important for the validation. Its small size (V(Fluid)=0.04 mL) allows the simulation of the entire bundle of 120 fibers. A non-Newtonian blood model was used as simulation fluid. Physical solubility and chemical bond of O2 and CO2 in blood was represented by the numerical model. Constant oxygen partial pressure at the pores of the fibers and a steady state flow field was used to calculate the mass transport. In order to resolve the entire MicroMox fiber bundle, the mass transport was simulated for symmetric geometry sections in flow direction. In vitro validation was achieved by measurements of the gas transfer rates of the MicroMox. All measurements were performed according to DIN EN 12022 (2) using porcine blood. The numerical simulation of the mass transfer showed good agreement with the experimental data for different mass flows and constant inlet partial pressures. Good agreement could be achieved for two different fiber configurations. Thus, it was possible to establish a validated model for the prediction of gas exchange in hollow fiber oxygenators.

Methods of design, simulation, and control for the development of new VAD/TAH concepts.

Cardiovascular diseases are a major cause of death worldwide. If medical treatments fail to restore adequate blood flow in a patient, mechanical support is needed. To date, many different types of blood pumps have been developed, but only few are clinically available. This review article describes the challenges involved in this field of research and gives an overview of the development process. Past developments as well as current and new technologies and approaches applied are summarized. Finally, a perspective for improved devices is discussed.

[Assisted circulation: an overview from a clinical perspective]. / Assistierte Zirkulation: ein Uberblick aus klinischer Sicht.

A higher grade cardiac failure is associated with poor prognosis. In addition to medical conservative treatment and traditional cardiac surgery, in the past years different forms of an assisted circulation evolved. Short-term devices serve to bridge an acute life-threatening situation. The chosen system is dependent on the anticipated clinical course. It is possible to fall back on slightly assisting techniques up to a complete takeover of the cardiac pump function. In the case of severe cardiac failure, the question for transplantation has to be addressed because transplantation is the treatment of choice to date. For an assisted circulation in cases of chronic congestive failure, devices of different generations are available. First generation pulsatile systems are used for assistance of the left ventricle and results have been shown to be superior to medical therapy (REMATCH). With second generation continuous-flow systems, results regarding infections, thromboembolism and also quality of life appear to be further improved. Contact-free centrifugal pumps as third generation systems are in clinical evaluation. So-called "total artificial hearts" are successfully used for bridge-to-transplantation. Taken together, a graded safe treatment of cardiac failure is available today. In the near future, it could be possible to reach results similar to those of cardiac transplantation.

Restructuring of colloidal aggregates in shear flows and limitations of the free-draining approximation.

We investigated the restructuring behavior of colloidal aggregates by means of the discrete element method. We used a recently proposed model [V. Becker, H. Briesen, Physical Review E 78 (6) (2008) 061404] for tangential inter-particle forces, capable of supporting bending moments. We extended this model by the capability of supporting torsional moments. The time evolution of the aggregates' radius of gyration was tracked and a power law relation between the number of primary particles and the final radius of gyration was found. For the hydrodynamic drag forces the free-draining approximation is employed. We investigated the quality of the free-draining approximation by fully resolved finite element simulations for small aggregates. We found that the free-draining approximation overestimates the drag forces and we identified the usage of effective shear rates as a possible ansatz for reduced modeling of hydrodynamic forces.

Interactive blood damage analysis for ventricular assist devices.

Ventricular Assist Devices (VADs) support the heart in its vital task of maintaining circulation in the human body when the heart alone is not able to maintain a sufficient flow rate due to illness or degenerative diseases. However, the engineering of these devices is a highly demanding task. Advanced modeling methods and computer simulations allow the investigation of the fluid flow inside such a device and in particular of potential blood damage. In this paper we present a set of visualization methods which have been designed to specifically support the analysis of a tensor-based blood damage prediction model. This model is based on the tracing of particles through the VAD, for each of which the cumulative blood damage can be computed. The model's tensor output approximates a single blood cell's deformation in the flow field. The tensor and derived scalar data are subsequently visualized using techniques based on icons, particle visualization, and function plotting. All these techniques are accessible through a Virtual Reality-based user interface, which features not only stereoscopic rendering but also natural interaction with the complex three-dimensional data. To illustrate the effectiveness of these visualization methods, we present the results of an analysis session that was performed by domain experts for a specific data set for the MicroMed DeBakey VAD.

Hemolysis estimation in a centrifugal blood pump using a tensor-based measure.

Hemolysis in the GYRO centrifugal blood pump, under development at the Baylor College of Medicine, Houston, TX, is numerically predicted using the newly proposed tensor-based blood-damage model, as well as a traditional model. Three typical operating conditions for the pump are simulated with a special-purpose finite element-based flow solver, and a novel approach for tracing the pathlines in discretely represented time-varying flow in a complex domain is presented, and 271 pathlines are traced through the pump. Hemolysis is computed along the pathlines, and the accumulated hemolysis at the outflow is converted into standard clinical units. The cumulative hemolysis at the outlet of the pump is weighted with the flow rate associated with the pathlines, and a temporal average is obtained by releasing the tracer particles at different time intervals. Numerical predictions are compared to experimental hemolysis studies performed according to the American Society for Testing and Materials standards at the Baylor College of Medicine. The tensor-based blood-damage model is found to match very well with the experimental results, whereas the traditional model overpredicts the hemolysis. The success of the tensor-based blood-damage model is attributed to its construction, which accounts for blood-specific physical properties and phenomena. Hemolysis values at the typical operating conditions of the pump are found to be within the clinically accepted range.

Shape optimization in unsteady blood flow: a numerical study of non-Newtonian effects.

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.

Shape optimization in steady blood flow: a numerical study of non-Newtonian effects.

We investigate the influence of the fluid constitutive model on the outcome of shape optimization tasks, motivated by optimal design problems in biomedical engineering. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. The generalized Newtonian treatment exhibits striking differences in the velocity field for smaller shear rates. We apply sensitivity-based optimization procedure to a flow through an idealized arterial graft. For this problem we study the influence of the inflow velocity, and thus the shear rate. Furthermore, we introduce an additional factor in the form of a geometric parameter, and study its effect on the optimal shape obtained.