A Multiple Time Stepping Algorithm for Efficient Multiscale Modeling of Platelets Flowing in Blood Plasma

[Research progress of coarse-grained molecular dynamics in drug carrier materials]

As one of the traditional computer simulation techniques, molecular simulation can intuitively display and quantify molecular structure and explain experimental phenomena from the microscopic molecular level. When the simulation system increases, the amount of calculation will also increase, which will cause a great burden on the simulation system. Coarse-grained molecular dynamics is a method of mesoscopic molecular simulation, which can simplify the molecular structure and improve computational efficiency, as a result, coarse-grained molecular dynamics is often used when simulating macromolecular systems such as drug carrier materials. In this article, we reviewed the recent research results of using coarse-grained molecular dynamics to simulate drug carriers, in order to provide a reference for future pharmaceutical preparation research and accelerate the entry of drug research into the era of precision drug design.

Machine Learning for Cardiovascular Biomechanics Modeling: Challenges and Beyond

Recent progress in machine learning (ML), together with advanced computational power, have provided new research opportunities in cardiovascular modeling. While classifying patient outcomes and medical image segmentation with ML have already shown significant promising results, ML for the prediction of biomechanics such as blood flow or tissue dynamics is in its infancy. This perspective article discusses some of the challenges in using ML for replacing well-established physics-based models in cardiovascular biomechanics. Specifically, we discuss the large landscape of input features in 3D patient-specific modeling as well as the high-dimensional output space of field variables that vary in space and time. We argue that the end purpose of such ML models needs to be clearly defined and the tradeoff between the loss in accuracy and the gained speedup carefully interpreted in the context of translational modeling. We also discuss several exciting venues where ML could be strategically used to augment traditional physics-based modeling in cardiovascular biomechanics. In these applications, ML is not replacing physics-based modeling, but providing opportunities to solve ill-defined problems, improve measurement data quality, enable a solution to computationally expensive problems, and interpret complex spatiotemporal data by extracting hidden patterns. In summary, we suggest a strategic integration of ML in cardiovascular biomechanics modeling where the ML model is not the end goal but rather a tool to facilitate enhanced modeling.

Models of Shear-Induced Platelet Activation and Numerical Implementation With Computational Fluid Dynamics Approaches

Shear-induced platelet activation is one of the critical outcomes when blood is exposed to elevated shear stress. Excessively activated platelets in the circulation can lead to thrombus formation and platelet consumption, resulting in serious adverse events such as thromboembolism and bleeding. While experimental observations reveal that it is related to the shear stress level and exposure time, the underlying mechanism of shear-induced platelet activation is not fully understood. Various models have been proposed to relate shear stress levels to platelet activation, yet most are modified from the empirically calibrated power-law model. Newly developed multiscale platelet models are tested as a promising approach to capture a single platelet's dynamic shape during activation, but it would be computationally expensive to employ it for a large-scale analysis. This paper summarizes the current numerical models used to study the shear-induced platelet activation and their computational applications in the risk assessment of a particular flow pattern and clot formation prediction.

Multiphysics and multiscale modeling of microthrombosis in COVID-19

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. Because of the infectious nature of SARS-CoV-2, patients’ fresh blood samples are limited to access for in vitro experimental investigations. Herein, we employ a novel multiscale and multiphysics computational framework to perform predictive modeling of the pathological thrombus formation in the microvasculature using data from patients with COVID-19. This framework seamlessly integrates the key components in the process of blood clotting, including hemodynamics, transport of coagulation factors and coagulation kinetics, blood cell mechanics and adhesive dynamics, and thus allows us to quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19. Our simulation results show that among the coagulation factors considered, antithrombin and factor V play more prominent roles in promoting thrombosis. Our simulations also suggest that recruitment of WBCs to the endothelial cells exacerbates thrombogenesis and contributes to the blockage of the blood flow. Additionally, we show that the recent identification of flowing blood cell clusters could be a result of detachment of WBCs from thrombogenic sites, which may serve as a nidus for new clot formation. These findings point to potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19. Altogether, our computational framework provides a powerful tool for quantitative understanding of the mechanism of pathological thrombus formation and offers insights into new therapeutic approaches for treating COVID-19 associated thrombosis.

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. We employ a novel multiphysics and multiscale computational framework to investigate the underlying mechanism of the pathological formation of microthrombi and circulating cell clusters in COVID-19. We quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19, through which we identify the potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19.

Online Machine Learning for Accelerating Molecular Dynamics Modeling of Cells

We developed a biomechanics-informed online learning framework to learn the dynamics with ground truth generated with multiscale modeling simulation. It was built on Summit-like supercomputers, which were also used to benchmark and validate our framework on one physiologically significant modeling of deformable biological cells. We generalized the century-old equation of Jeffery orbits to a new equation of motion with additional parameters to account for the flow conditions and the cell deformability. Using simulation data at particle-based resolutions for flowing cells and the learned parameters from our framework, we validated the new equation by the motions, mostly rotations, of a human platelet in shear blood flow at various shear stresses and platelet deformability. Our online framework, which surrogates redundant computations in the conventional multiscale modeling by solutions of our learned equation, accelerates the conventional modeling by three orders of magnitude without visible loss of accuracy.

Recent Advances in Computational Modeling of Biomechanics and Biorheology of Red Blood Cells in Diabetes

Diabetes mellitus, a metabolic disease characterized by chronically elevated blood glucose levels, affects about 29 million Americans and more than 422 million adults all over the world. Particularly, type 2 diabetes mellitus (T2DM) accounts for 90-95% of the cases of vascular disease and its prevalence is increasing due to the rising obesity rates in modern societies. Although multiple factors associated with diabetes, such as reduced red blood cell (RBC) deformability, enhanced RBC aggregation and adhesion to the endothelium, as well as elevated blood viscosity are thought to contribute to the hemodynamic impairment and vascular occlusion, clinical or experimental studies cannot directly quantify the contributions of these factors to the abnormal hematology in T2DM. Recently, computational modeling has been employed to dissect the impacts of the aberrant biomechanics of diabetic RBCs and their adverse effects on microcirculation. In this review, we summarize the recent advances in the developments and applications of computational models in investigating the abnormal properties of diabetic blood from the cellular level to the vascular level. We expect that this review will motivate and steer the development of new models in this area and shift the attention of the community from conventional laboratory studies to combined experimental and computational investigations, aiming to provide new inspirations for the development of advanced tools to improve our understanding of the pathogenesis and pathology of T2DM.

A multiscale model for multiple platelet aggregation in shear flow

We developed a multiscale model for simulating aggregation of multiple, free-flowing platelets in low-intermediate shear viscous flow, in which aggregation is mediated by the interaction of αIIbβ3 receptors on the platelet membrane and fibrinogen (Fg). This multiscale model uses coarse grained molecular dynamics (CGMD) for platelets at the microscales and dissipative particle dynamics (DPD) for the shear flow at the macroscales, employing our hybrid aggregation force field for modeling molecular level receptor ligand bonds. We define an aggregation tensor and use it to quantify the molecular level contact characteristics between platelets in an aggregate. We perform numerical studies under different flow conditions for platelet doublets and triplets and evaluate the contact area, detaching force and minimum distance between different pairs of platelets in an aggregate. We also present the dynamics of applied stress and velocity magnitude distributions on the platelet membrane during aggregation and quantify the increase in stress in the contact region under different flow conditions. Integrating the knowledge from our previously validated models, together with new aggregation scenarios, our model can dynamically quantify aggregation characteristics and map stress and velocity distribution on the platelet membrane which are difficult to measure in vitro, thus providing an insight into mechanotransduction bond formation response of platelets to flow-induced shear stresses. This modeling framework, together with the tensor method for quantifying inter-platelet contact, can be extended to simulate and analyze larger aggregates and their adhesive properties.

Artificial Intelligence for Accelerating Time Integrations in Multiscale Modeling

We developed a novel data-driven Artificial Intelligence-enhanced Adaptive Time Stepping algorithm (AI-ATS) that can adapt timestep sizes to underlying biophysical dynamics. We demonstrated its values in solving a complex biophysical problem, at multiple spatiotemporal scales, that describes platelet dynamics in shear blood flow. In order to achieve a significant speedup of this computationally demanding problem, we integrated a framework of novel AI algorithms into the solution of the platelet dynamics equations. Our framework involves recurrent neural network-based autoencoders by the Long Short-Term Memory and the Gated Recurrent Units as the first step for memorizing the dynamic states in long-term dependencies for the input time series, followed by two fully-connected neural networks to optimize timestep sizes and step jumps. The computational efficiency of our AI-ATS is underscored by assessing the accuracy and speed of a multiscale simulation of the platelet with the standard time stepping algorithm (STS). By adapting the timestep size, our AI-ATS guides the omission of multiple redundant time steps without sacrificing significant accuracy of the dynamics. Compared to the STS, our AI-ATS achieved a reduction of 40% unnecessary calculations while bounding the errors of mechanical and thermodynamic properties to 3%.

Integrating blood cell mechanics, platelet adhesive dynamics and coagulation cascade for modelling thrombus formation in normal and diabetic blood

Normal haemostasis is an important physiological mechanism that prevents excessive bleeding during trauma, whereas the pathological thrombosis especially in diabetics leads to increased incidence of heart attacks and strokes as well as peripheral vascular events. In this work, we propose a new multiscale framework that integrates seamlessly four key components of blood clotting, namely transport of coagulation factors, coagulation kinetics, blood cell mechanics and platelet adhesive dynamics, to model the development of thrombi under physiological and pathological conditions. We implement this framework to simulate platelet adhesion due to the exposure of tissue factor in a three-dimensional microchannel. Our results show that our model can simulate thrombin-mediated platelet activation in the flowing blood, resulting in platelet adhesion to the injury site of the channel wall. Furthermore, we simulate platelet adhesion in diabetic blood, and our results show that both the pathological alterations in the biomechanics of blood cells and changes in the amount of coagulation factors contribute to the excessive platelet adhesion and aggregation in diabetic blood. Taken together, this new framework can be used to probe synergistic mechanisms of thrombus formation under physiological and pathological conditions, and open new directions in modelling complex biological problems that involve several multiscale processes.

A predictive multiscale model for simulating flow-induced platelet activation: Correlating in silico results with in vitro results

Flow-induced platelet activation prompts complex filopodial formation. Continuum methods fail to capture such molecular-scale mechanisms. A multiscale numerical model was developed to simulate this activation process, where a Dissipative Particle Dynamics (DPD) model of viscous blood flow is interfaced with a Coarse Grained Molecular Dynamics (CGMD) platelet model. Embedded in DPD blood flow, the macroscopic dynamic stresses are interactively transferred to the CGMD model, inducing intra-platelet associated events. The platelets activate by a biomechanical transductive linkage chain and dynamically change their shape in response. The models are fully coupled via a hybrid-potential interface and multiple time-stepping (MTS) schemes for handling the disparity between the spatiotemporal scales. Cumulative hemodynamic stresses that may lead to platelet activation are mapped on the surface membrane and simultaneously transmitted to the cytoplasm and cytoskeleton. Upon activation, the flowing platelets lose their quiescent discoid shape and evolve by forming filopodia. The model predictions were validated by a set of in vitro experiments, Platelets were exposed to various combinations of shear stresses and durations in our programmable hemodynamic shearing device (HSD). Their shape change was measured at multiple time points using scanning electron microscopy (SEM). The CGMD model parameters were fine-tuned by interrogating a parameter space established in these experiments. Segmentation of the SEM imaging streams was conducted by a deep machine learning system. This model can be further employed to simulate shear mediated platelet activation thrombosis initiation and to study the effects of modulating platelet properties to enhance their shear resistance via mechanotransduction pathways.

Occlusive thrombosis in arteries

Thrombus formation in major arteries is life threatening. In this review article, we discuss how an arterial thrombus can form under pathologically high shear stresses, with bonding rates estimated to be the fastest Kon values in biochemistry. During occlusive thrombosis in arteries, the growth rate of the thrombus explodes to capture a billion platelets in about 10 min. Close to 100% of all platelets passing the thrombus are captured by long von Willebrand factor (vWF) strands that quickly form tethered nets. The nets grow in patches where shear stress is high, and the local concentration of vWF is elevated due to α-granule release by previously captured platelets. This rapidly formed thrombus has few red blood cells and so has a white appearance and is much stronger and more porous than clots formed through coagulation. Understanding and modeling the biophysics of this event can predict totally new approaches to prevent and treat heart attacks and strokes.

Probing eukaryotic cell mechanics via mesoscopic simulations

Cell mechanics has proven to be important in many biological processes. Although there is a number of experimental techniques which allow us to study mechanical properties of cell, there is still a lack of understanding of the role each sub-cellular component plays during cell deformations. We present a new mesoscopic particle-based eukaryotic cell model which explicitly describes cell membrane, nucleus and cytoskeleton. We employ Dissipative Particle Dynamics (DPD) method that provides us with the unified framework for modeling of a cell and its interactions in the flow. Data from micropipette aspiration experiments were used to define model parameters. The model was validated using data from microfluidic experiments. The validated model was then applied to study the impact of the sub-cellular components on the cell viscoelastic response in micropipette aspiration and microfluidic experiments.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

A multiscale biomechanical model of platelets: Correlating with in-vitro results

Using dissipative particle dynamics (DPD) combined with coarse grained molecular dynamics (CGMD) approaches, we developed a multiscale deformable platelet model to accurately describe the molecular-scale intra-platelet constituents and biomechanical properties of platelets in blood flow. Our model includes the platelet bilayer membrane, cytoplasm and an elaborate elastic cytoskeleton. Correlating numerical simulations with published in-vitro experiments, we validated the biorheology of the cytoplasm, the elastic response of membrane to external stresses, and the stiffness of the cytoskeleton actin filaments, resulting in an accurate representation of the molecular-level biomechanical microstructures of platelets. This enabled us to study the mechanotransduction process of the hemodynamic stresses acting onto the platelet membrane and transmitted to these intracellular constituents. The platelets constituents continuously deform in response to the flow induced stresses. To the best of our knowledge, this is the first molecular-scale platelet model that can be used to accurately predict platelets activation mechanism leading to thrombus formation in prosthetic cardiovascular devices and in vascular disease processes. This model can be further employed to study the effects of novel therapeutic approaches of modulating platelet properties to enhance their shear resistance via mechanotransduction pathways.

Scalability Test of Multiscale Fluid-Platelet Model for Three Top Supercomputers

We have tested the scalability of three supercomputers: the Tianhe-2, Stampede and CS-Storm with multiscale fluid-platelet simulations, in which a highly-resolved and efficient numerical model for nanoscale biophysics of platelets in microscale viscous biofluids is considered. Three experiments involving varying problem sizes were performed: Exp-S: 680,718-particle single-platelet; Exp-M: 2,722,872-particle 4-platelet; and Exp-L: 10,891,488-particle 16-platelet. Our implementations of multiple time-stepping (MTS) algorithm improved the performance of single time-stepping (STS) in all experiments. Using MTS, our model achieved the following simulation rates: 12.5, 25.0, 35.5 μs/day for Exp-S and 9.09, 6.25, 14.29 μs/day for Exp-M on Tianhe-2, CS-Storm 16-K80 and Stampede K20. The best rate for Exp-L was 6.25 μs/day for Stampede. Utilizing current advanced HPC resources, the simulation rates achieved by our algorithms bring within reach performing complex multiscale simulations for solving vexing problems at the interface of biology and engineering, such as thrombosis in blood flow which combines millisecond-scale hematology with microscale blood flow at resolutions of micro-to-nanoscale cellular components of platelets. This study of testing the performance characteristics of supercomputers with advanced computational algorithms that offer optimal trade-off to achieve enhanced computational performance serves to demonstrate that such simulations are feasible with currently available HPC resources.

A comprehensive study on different modelling approaches to predict platelet deposition rates in a perfusion chamber

Thrombus formation is a multiscale phenomenon triggered by platelet deposition over a protrombotic surface (eg. a ruptured atherosclerotic plaque). Despite the medical urgency for computational tools that aid in the early diagnosis of thrombotic events, the integration of computational models of thrombus formation at different scales requires a comprehensive understanding of the role and limitation of each modelling approach. We propose three different modelling approaches to predict platelet deposition. Specifically, we consider measurements of platelet deposition under blood flow conditions in a perfusion chamber for different time periods (3, 5, 10, 20 and 30 minutes) at shear rates of 212 s⁻¹, 1390 s⁻¹ and 1690 s⁻¹. Our modelling approaches are: i) a model based on the mass-transfer boundary layer theory; ii) a machine-learning approach; and iii) a phenomenological model. The results indicate that the three approaches on average have median errors of 21%, 20.7% and 14.2%, respectively. Our study demonstrates the feasibility of using an empirical data set as a proxy for a real-patient scenario in which practitioners have accumulated data on a given number of patients and want to obtain a diagnosis for a new patient about whom they only have the current observation of a certain number of variables.