Discrete multi-physics: A mesh-free model of blood flow in flexible biological valve including solid aggregate formation

The Effect of Polymer-Solvent Interaction on the Swelling of Polymer Matrix Tablets: A Magnetic Resonance Microscopy Study Complemented by Bond Fluctuation Model Simulations

Polymer matrix tablets are an important drug-delivery system widely used for oral drug administration. Understanding the tablet hydration process, both experimentally and theoretically, is, thus, very important for the development of drug delivery systems that exhibit high drug loading capacity and controlled release potential. In this study, we used magnetic resonance microscopy (MRM) to nondestructively and dynamically analyze the water hydration process of xanthan-based tablets. The swelling process was characterized by well-resolved fronts of erosion, swelling, and penetration. The experimental results were complemented by numerical simulations of the polymer matrix hydration process. In the simulations, the polymer tablet matrix was modeled as an assembly of interacting chains with embedded drug particles, while its hydration process was mediated by interaction with solvent particles. The swelling dynamics were modeled within a Monte Carlo-based bond fluctuation model (BFM) that elegantly accounted for steric and nearest-neighbor interactions. This study provides an efficient experimental-theoretical approach for the study of polymer matrix swelling processes.

Development of a digital twin of a tablet that mimics a real solid dosage form: Differences in the dissolution profile in conventional mini-USP II and a biorelevant colon model

The performance of colon-targeted solid dosage forms is commonly assessed using standardised pharmacopeial dissolution apparatuses like the USP II or the miniaturised replica, the mini-USP II. However, these fail to replicate the hydrodynamics and shear stresses in the colonic environment, which is crucial for the tablet's drug release process. In this work, computer simulations are used to create a digital twin of a dissolution apparatus and to develop a method to create a digital twin of a tablet that behaves realistically. These models are used to investigate the drug release profiles and shear rates acting on a tablet at different paddle speeds in the mini-USP II and biorelevant colon models to understand how the mini-USP II can be operated to achieve more realistic (i.e., in vivo) hydrodynamic conditions. The behaviour of the tablet and the motility patterns used in the simulations are derived from experimental and in vivo data, respectively, to obtain profound insights into the tablet's disintegration/drug release processes. We recommend an "on-off" operating mode in the mini-USP II to generate shear rate peaks, which would better reflect the in vivo conditions of the human colon instead of constant paddle speed.

Simulating the Hydrodynamic Conditions of the Human Ascending Colon: A Digital Twin of the Dynamic Colon Model

The performance of solid oral dosage forms targeting the colon is typically evaluated using standardised pharmacopeial dissolution apparatuses. However, these fail to replicate colonic hydrodynamics. This study develops a digital twin of the Dynamic Colon Model; a physiologically representative in vitro model of the human proximal colon. Magnetic resonance imaging of the Dynamic Colon Model verified that the digital twin robustly replicated flow patterns under different physiological conditions (media viscosity, volume, and peristaltic wave speed). During local contractile activity, antegrade flows of 0.06-0.78 cm s^-1 and backflows of -2.16--0.21 cm s^-1 were measured. Mean wall shear rates were strongly time and viscosity dependent although peaks were measured between 3.05-10.12 s^-1 and 5.11-20.34 s^-1 in the Dynamic Colon Model and its digital twin respectively, comparable to previous estimates of the USPII with paddle speeds of 25 and 50 rpm. It is recommended that viscosity and shear rates are considered when designing future dissolution test methodologies for colon-targeted formulations. In the USPII, paddle speeds >50 rpm may not recreate physiologically relevant shear rates. These findings demonstrate how the combination of biorelevant in vitro and in silico models can provide new insights for dissolution testing beyond established pharmacopeial methods.

Modelling Particle Agglomeration on through Elastic Valves under Flow

This work proposes a model of particle agglomeration in elastic valves replicating the geometry and the fluid dynamics of a venous valve. The fluid dynamics is simulated with Smooth Particle Hydrodynamics, the elastic leaflets of the valve with the Lattice Spring Model, while agglomeration is modelled with a 4-2 Lennard-Jones potential. All the models are combined together within a single Discrete Multiphysics framework. The results show that particle agglomeration occurs near the leaflets, supporting the hypothesis, proposed in previous experimental work, that clot formation in deep venous thrombosis is driven by the fluid dynamics in the valve.

How to Modify LAMMPS: From the Prospective of a Particle Method Researcher

LAMMPS is a powerful simulator originally developed for molecular dynamics that, today, also accounts for other particle-based algorithms such as DEM, SPH, or Peridynamics. The versatility of this software is further enhanced by the fact that it is open-source and modifiable by users. This property suits particularly well Discrete Multiphysics and hybrid models that combine multiple particle methods in the same simulation. Modifying LAMMPS can be challenging for researchers with little coding experience. The available material explaining how to modify LAMMPS is either too basic or too advanced for the average researcher. In this work, we provide several examples, with increasing level of complexity, suitable for researchers and practitioners in physics and engineering, who are familiar with coding without been experts. For each feature, step by step instructions for implementing them in LAMMPS are shown to allow researchers to easily follow the procedure and compile a new version of the code. The aim is to fill a gap in the literature with particular reference to the scientific community that uses particle methods for (discrete) multiphysics.

Modelling and Simulation of the Drug Release from a Solid Dosage Form in the Human Ascending Colon: The Influence of Different Motility Patterns and Fluid Viscosities

For colonic drug delivery, the ascending part of the colon is the most favourable site as it offers the most suitable environmental conditions for drug dissolution. Commonly, the performance of a drug formulation is assessed using standardised dissolution apparatus, which does not replicate the hydrodynamics and shear stress evoked by wall motion in the colon. In this work, computer simulations are used to analyse and understand the influence of different biorelevant motility patterns on the disintegration/drug release of a solid dosage form (tablet) under different fluid conditions (viscosities) to mimic the ascending colonic environment. Furthermore, the ability of the motility pattern to distribute the drug in the ascending colon luminal environment is analysed to provide data for a spatiotemporal concentration profile. The motility patterns used are derived from in vivo data representing different motility patterns in the human ascending colon. The applied motility patterns show considerable differences in the drug release rate from the tablet, as well as in the ability to distribute the drug along the colon. The drug dissolution/disintegration process from a solid dosage form is primarily influenced by the hydrodynamic and shear stress it experiences, i.e., a combination of motility pattern and fluid viscosity. Reduced fluid motion leads to a more pronounced influence of diffusion in the tablet dissolution process. The motility pattern that provoked frequent single shear stress peaks seemed to be more effective in achieving a higher drug release rate. The ability to simulate drug release profiles under biorelevant colonic environmental conditions provides valuable feedback to better understand the drug formulation and how this can be optimised to ensure that the drug is present in the desired concentration within the ascending colon.

The virtual physiological human gets nerves! How to account for the action of the nervous system in multiphysics simulations of human organs

This article shows how to couple multiphysics and artificial neural networks to design computer models of human organs that autonomously adapt their behaviour to environmental stimuli. The model simulates motility in the intestine and adjusts its contraction patterns to the physical properties of the luminal content. Multiphysics reproduces the solid mechanics of the intestinal membrane and the fluid mechanics of the luminal content; the artificial neural network replicates the activity of the enteric nervous system. Previous studies recommended training the network with reinforcement learning. Here, we show that reinforcement learning alone is not enough; the input–output structure of the network should also mimic the basic circuit of the enteric nervous system. Simulations are validated against in vivo measurements of high-amplitude propagating contractions in the human intestine. When the network has the same input–output structure of the nervous system, the model performs well even when faced with conditions outside its training range. The model is trained to optimize transport, but it also keeps stress in the membrane low, which is exactly what occurs in the real intestine. Moreover, the model responds to atypical variations of its functioning with ‘symptoms’ that reflect those arising in diseases. If the healthy intestine model is made artificially ill by adding digital inflammation, motility patterns are disrupted in a way consistent with inflammatory pathologies such as inflammatory bowel disease.

Combined Peridynamics and Discrete Multiphysics to Study the Effects of Air Voids and Freeze-Thaw on the Mechanical Properties of Asphalt

This paper demonstrates the use of peridynamics and discrete multiphysics to assess micro crack formation and propagation in asphalt at low temperatures and under freezing conditions. Three scenarios are investigated: (a) asphalt without air voids under compressive load, (b) asphalt with air voids and (c) voids filled with freezing water. The first two are computed with Peridynamics, the third with peridynamics combined with discrete multiphysics. The results show that the presence of voids changes the way cracks propagate in the material. In asphalt without voids, cracks tend to propagate at the interface between the mastic and the aggregate. In the presence of voids, they ‘jump’ from one void to the closest void. Water expansion is modelled by coupling Peridynamics with repulsive forces in the context of Discrete Multiphysics. Freezing water expands against the voids’ internal surface, building tension in the material. A network of cracks forms in the asphalt, weakening its mechanical properties. The proposed methodology provides a computational tool for generating samples of ‘digital asphalt’ that can be tested to assess the asphalt properties under different operating conditions.

The duality between particle methods and artificial neural networks

The algorithm behind particle methods is extremely versatile and used in a variety of applications that range from molecular dynamics to astrophysics. For continuum mechanics applications, the concept of ‘particle’ can be generalized to include discrete portions of solid and liquid matter. This study shows that it is possible to further extend the concept of ‘particle’ to include artificial neurons used in Artificial Intelligence. This produces a new class of computational methods based on ‘particle-neuron duals’ that combines the ability of computational particles to model physical systems and the ability of artificial neurons to learn from data. The method is validated with a multiphysics model of the intestine that autonomously learns how to coordinate its contractions to propel the luminal content forward (peristalsis). Training is achieved with Deep Reinforcement Learning. The particle-neuron duality has the advantage of extending particle methods to systems where the underlying physics is only partially known, but we have observations that allow us to empirically describe the missing features in terms of reward function. During the simulation, the model evolves autonomously adapting its response to the available observations, while remaining consistent with the known physics of the system.

A smoothed particle hydrodynamics study of the collapse for a cylindrical cavity

In this study, we propose a mesh-free (particle-based) Smoothed Particle Hydrodynamics model for simulating a Rayleigh collapse. Both empty and gas cavities are investigates and the role of heat diffusion is also accounted for. The system behaves very differently according to the ratio between the characteristic time of collapse and the characteristic time of thermal diffusion. This study identifies five different possible behaviours that range from isothermal to adiabatic.

The role of valve stiffness in the insurgence of deep vein thrombosis

Deep vein thrombosis is a life-threatening development of blood clots in deep veins. Immobility and blood flow stagnancy are typical risk factors indicating that fluid dynamics play an important role in the initiation of venous clots. However, the roles of physical parameters of the valves and flow conditions in deep vein thrombosis initiation have not been fully understood. Here, we describe a microfluidics in vitro method that enabled us to explore the role of valve elasticity using in situ fabrication and characterisation. In our experimental model the stiffness of each valve leaflet can be controlled independently, and various flow conditions were tested. The resulting complex flow patterns were detected using ghost particle velocimetry and linked to localised thrombus formation using whole blood and an aqueous suspension of polystyrene particles. In particular, valves with leaflets of similar stiffness had clot formation on the valve tips whereas valves with leaflets of different stiffness had clot formation in the valve pocket.

Fluid-structure interaction of blood flow around a vein valve

Introduction: Venous valves are a type of one-way valves which conduct blood flow toward the heart and prevent its backflow. Any malfunction of these organs may cause serious problems in the circulatory system. Numerical simulation can give us detailed information and point to point data such as velocity, wall shear stress, and von Mises stress from veins with small diameters, as obtaining such data is almost impossible using current medical devices. Having detailed information about fluid flow and valves' function can help the treatment of the related diseases. Methods: In the present work, the blood flow through a venous valve considering the flexibility of the vein wall and valve leaflets is investigated numerically. The governing equations of fluid flow and solid domain are discretized and solved by the Galerkin finite element method. Results: The obtained results showed that the blood velocity increases from inlet to the leaflets and then decreases passing behind the valve. A pair of vortices and the trapped region was observed just behind the valves. These regions have low shear stresses and are capable of sediment formation. Conclusion: The von Mises stress which is a criterion for the breakdown of solid materials was obtained. It was also observed that a maximum value occurred at the bottom of the leaflets.

Using Discrete Multiphysics Modelling to Assess the Effect of Calcification on Hemodynamic and Mechanical Deformation of Aortic Valve

This study proposes a 3D particle-based (discrete) multiphysics approach for modelling calcification in the aortic valve. Different stages of calcification (from mild to severe) were simulated, and their effects on the cardiac output were assessed. The cardiac flow rate decreases with the level of calcification. In particular, there is a critical level of calcification below which the flow rate decreases dramatically. Mechanical stress on the membrane is also calculated. The results show that, as calcification progresses, spots of high mechanical stress appear. Firstly, they concentrate in the regions connecting two leaflets; when severe calcification is reached, then they extend to the area at the basis of the valve.

Modelling and simulation of the hydrodynamics and mixing profiles in the human proximal colon using Discrete Multiphysics

The proximal part of the colon offers opportunities to prolong the absorption window following oral administration of a drug. In this work, we used computer simulations to understand how the hydrodynamics in the proximal colon might affect the release from dosage forms designed to target the colon. For this purpose, we developed and compared three different models: a completely-filled colon, a partially-filled colon and a partially-filled colon with a gaseous phase present (gas-liquid model). The highest velocities of the liquid were found in the completely-filled model, which also shows the best mixing profile, defined by the distribution of tracking particles over time. No significant differences with regard to the mixing and velocity profiles were found between the partially-filled model and the gas-liquid model. The fastest transit time of an undissolved tablet was found in the completely-filled model. The velocities of the liquid in the gas-liquid model are slightly higher along the colon than in the partially-filled model. The filling level has an impact on the exsisting shear forces and shear rates, which are decisive factors in the development of new drugs and formulations.

A Coarse Grained Model for Viscoelastic Solids in Discrete Multiphysics Simulations

Viscoelastic bonds intended for Discrete Multiphysics (DMP) models are developed to allow the study of viscoelastic particles with arbitrary shape and mechanical inhomogeneity that are relevant to the pharmaceutical sector and that have not been addressed by the Discrete Element Method (DEM). The model is applied to encapsulate particles with a soft outer shell due, for example, to the partial ingress of moisture. This was validated by the simulation of spherical homogeneous linear elastic and viscoelastic particles. The method is based on forming a particle from an assembly of beads connected by springs or springs and dashpots that allow the sub-surface stress fields to be computed, and hence an accurate description of the gross deformation. It is computationally more expensive than DEM, but could be used to define more effective interaction laws.

Effects of size and elasticity on the relation between flow velocity and wall shear stress in side-wall aneurysms: A lattice Boltzmann-based computer simulation study

Blood flow in an artery is a fluid-structure interaction problem. It is widely accepted that aneurysm formation, enlargement and failure are associated with wall shear stress (WSS) which is exerted by flowing blood on the aneurysmal wall. To date, the combined effect of aneurysm size and wall elasticity on intra-aneurysm (IA) flow characteristics, particularly in the case of side-wall aneurysms, is poorly understood. Here we propose a model of three-dimensional viscous flow in a compliant artery containing an aneurysm by employing the immersed boundary-lattice Boltzmann-finite element method. This model allows to adequately account for the elastic deformation of both the blood vessel and aneurysm walls. Using this model, we perform a detailed investigation of the flow through aneurysm under different conditions with a focus on the parameters which may influence the wall shear stress. Most importantly, it is shown in this work that the use of flow velocity as a proxy for wall shear stress is well justified only in those sections of the vessel which are close to the ideal cylindrical geometry. Within the aneurysm domain, however, the correlation between wall shear stress and flow velocity is largely lost due to the complexity of the geometry and the resulting flow pattern. Moreover, the correlations weaken further with the phase shift between flow velocity and transmural pressure. These findings have important implications for medical applications since wall shear stress is believed to play a crucial role in aneurysm rupture.

Interaction of Shock Waves with Discrete Gas Inhomogeneities: A Smoothed Particle Hydrodynamics Approach

In this study, we propose a smoothed particle hydrodynamics model for simulating a shock wave interacting with cylindrical gas inhomogeneities inside a shock tube. When the gas inhomogeneity interacts with the shock wave, it assumes different shapes depending on the difference in densities between the gas inhomogeneity and the external gas. The model uses a piecewise smoothing length approach and is validated by comparing the results obtained with experimental and CFD data available in the literature. In all the cases considered, the evolution of the inhomogeneity is similar to the experimental shadowgraphs and is at least as accurate as the CFD results in terms of timescale and shape of the gas inhomogeneity.

Deep Multiphysics and Particle–Neuron Duality: A Computational Framework Coupling (Discrete) Multiphysics and Deep Learning

There are two common ways of coupling first-principles modelling and machine learning. In one case, data are transferred from the machine-learning algorithm to the first-principles model; in the other, from the first-principles model to the machine-learning algorithm. In both cases, the coupling is in series: the two components remain distinct, and data generated by one model are subsequently fed into the other. Several modelling problems, however, require in-parallel coupling, where the first-principle model and the machine-learning algorithm work together at the same time rather than one after the other. This study introduces deep multiphysics; a computational framework that couples first-principles modelling and machine learning in parallel rather than in series. Deep multiphysics works with particle-based first-principles modelling techniques. It is shown that the mathematical algorithms behind several particle methods and artificial neural networks are similar to the point that can be unified under the notion of particle–neuron duality. This study explains in detail the particle–neuron duality and how deep multiphysics works both theoretically and in practice. A case study, the design of a microfluidic device for separating cell populations with different levels of stiffness, is discussed to achieve this aim.

Deep multiphysics: Coupling discrete multiphysics with machine learning to attain self-learning in-silico models replicating human physiology

OBJECTIVES

The objective of this study is to devise a modelling strategy for attaining in-silico models replicating human physiology and, in particular, the activity of the autonomic nervous system.

METHOD

Discrete Multiphysics (a multiphysics modelling technique) and Reinforcement Learning (a Machine Learning algorithm) are combined to achieve an in-silico model with the ability of self-learning and replicating feedback loops occurring in human physiology. Computational particles, used in Discrete Multiphysics to model biological systems, are associated to (computational) neurons: Reinforcement Learning trains these neurons to behave like they would in real biological systems.

RESULTS

As benchmark/validation, we use the case of peristalsis in the oesophagus. Results show that the in-silico model effectively learns by itself how to propel the bolus in the oesophagus.

CONCLUSIONS

The combination of first principles modelling (e.g. multiphysics) and machine learning (e.g. Reinforcement Learning) represents a new powerful tool for in-silico modelling of human physiology. Biological feedback loops occurring, for instance, in peristaltic or metachronal motion, which until now could not be accounted for in in-silico models, can be tackled by the proposed technique.

Effect of valve lesion on venous valve cycle: A modified immersed finite element modeling

The present study aimed to understand the effect of venous valve lesion on the valve cycle. A modified immersed finite element method was used to model the blood–tissue interactions in the pathological vein. The contact process between leaflets or between leaflet and sinus was evaluated using an adhesive contact method. The venous valve modeling was validated by comparing the results of the healthy valve with those of experiments and other simulations. Four valve lesions induced by the abnormal elasticity variation were considered for the unhealthy valve: fibrosis, atrophy, incomplete fibrosis, and incomplete atrophy. The opening orifice area was inversely proportional to the structural stiffness of the valve, while the transvalvular flow velocity was proportional to the structural stiffness of the valve. The stiffening of the fibrotic leaflet led to a decrease in the orifice area and a stronger jet. The leaflet and blood wall shear stress (WSS) in fibrosis was the highest. The softening of the atrophic leaflet resulted in overly soft behavior. The venous incompetence and reflux were observed in atrophy. Also, the atrophic leaflet in incomplete atrophy exhibited weak resistance to the hemodynamic action, and the valve was reluctant to be closed owing to the large rotation of the healthy leaflet. Low blood WSS and maximum leaflet WSS existed in all the cases. A less biologically favorable condition was found especially in the fibrotic leaflet, involving a higher mechanical cost. This study provided an insight into the venous valve lesion, which might help understand the valve mechanism of the diseased vein. These findings will be more useful when the biology is also understood. Thus, more biological studies are needed.

Discrete multi-physics simulations of diffusive and convective mass transfer in boundary layers containing motile cilia in lungs

In this paper, the mass transfer coefficient (permeability) of boundary layers containing motile cilia is investigated by means of discrete multi-physics. The idea is to understand the main mechanisms of mass transport occurring in a ciliated-layer; one specific application being inhaled drugs in the respiratory epithelium. The effect of drug diffusivity, cilia beat frequency and cilia flexibility is studied. Our results show the existence of three mass transfer regimes. A low frequency regime, which we called shielding regime, where the presence of the cilia hinders mass transport; an intermediate frequency regime, which we have called diffusive regime, where diffusion is the controlling mechanism; and a high frequency regime, which we have called convective regime, where the degree of bending of the cilia seems to be the most important factor controlling mass transfer in the ciliated-layer. Since the flexibility of the cilia and the frequency of the beat changes with age and health conditions, the knowledge of these three regimes allows prediction of how mass transfer varies with these factors.

Modelling and simulation of flow and agglomeration in deep veins valves using discrete multi physics

The hemodynamics in flexible deep veins valves is modelled by means of discrete multi-physics and an agglomeration algorithm is implemented to account for blood accrual in the flow. Computer simulations of a number of valves typologies are carried out. The results show that the rigidity and the length of the valve leaflets play a crucial role on both mechanical stress and stagnation in the flow. Rigid and short membranes may be inefficient in preventing blood reflux, but reduce the volume of stagnant blood potentially lowering the chances of thrombosis. Additionally, we also show that in venous valves, cell agglomeration is driven by stagnation rather than mechanical stress.