Multiscale Dynamic Model Research Articles

Multiscale modelling of mass transfer in gas jets and bubble plumes

AbstractThe injection of high‐speed gas streams into liquids is common in many industrial applications, such as sparging in multiphase reactors and contacting in mass transfer devices. Modelling the fluid dynamics and associated heat and mass transfer processes in such a system is complex because it involves many governing scales and drastic changes in physical properties. In this study, one formulation of a multiscale computational fluid dynamics model is proposed to simulate the fluid dynamics and mass transfer in such systems. The model uses volume‐of‐fluid interface capturing in regions where high mesh resolution can be attained and the drift‐flux or mixture model approximation in regions where mesh resolution is too low to directly resolve interface dynamics. The model was developed to provide a tunable, automatic transition between the two modelling approaches for both fluid dynamics and mass transfer predictions. The approach was validated through a comparison with results from two published studies. In the first case, the implementation of the drift‐flux model was validated through the simulation of a dispersed gas bubble plume injected into a cylindrical tank. In the second case, the fluid dynamics and mass transfer predictions were compared to results from an experimental study involving the horizontal injection of air into a rectangular tank filled with water for the application of aeration. The results show that the modelling approach can provide a good prediction of the experimental data using only limited fitting of empirical parameters, making it applicable to a broad range of other applications.

Machine learning-based modeling and operation for ALD of SiO2 thin-films using data from a multiscale CFD simulation

Atomic layer deposition (ALD) is a widely utilized deposition technology in the semiconductor industry due to its superior ability to generate highly conformal films and to deposit materials into high aspect-ratio geometric structures. However, ALD experiments remain expensive and time-consuming, and the existing first-principles based models have not yet been able to provide solutions to key process outputs that are computationally efficient, which is necessary for on-line optimization and real-time control. In this work, a multiscale data-driven model is proposed and developed to capture the macroscopic process domain dynamics with a linear parameter varying model, and to characterize the microscopic domain film growth dynamics with a feed-forward artificial neural network (ANN) model. The multiscale data-driven model predicts the transient deposition rate from the following four key process operating parameters that can be manipulated, measured or estimated by process engineers: precursor feed flow rate, operating pressure, surface heating, and transient film coverage. Our results demonstrate that the multiscale data-driven model can efficiently characterize the transient input-output relationship for the SiO2 thermal ALD process using bis(tertiary-butylamino)silane (BTBAS) as the Si precursor. The multiscale data-driven model successfully reduces the computational time from 0.6 to 1.2h for each time step, which is required for the first-principles based multiscale computational fluid dynamics (CFD) model, to less than 0.1s, making its real-time usage feasible. The developed data-driven modeling methodology can be further generalized and used for other thermal ALD or similar deposition systems, which will greatly enhance the feasibility of industrial manufacturing processes.

Agent-based models of inflammation in translational systems biology: A decade later.

Agent-based modeling is a rule-based, discrete-event, and spatially explicit computational modeling method that employs computational objects that instantiate the rules and interactions among the individual components ("agents") of system. Agent-based modeling is well suited to translating into a computational model the knowledge generated from basic science research, particularly with respect to translating across scales the mechanisms of cellular behavior into aggregated cell population dynamics manifesting at the tissue and organ level. This capacity has made agent-based modeling an integral method in translational systems biology (TSB), an approach that uses multiscale dynamic computational modeling to explicitly represent disease processes in a clinically relevant fashion. The initial work in the early 2000s using agent-based models (ABMs) in TSB focused on examining acute inflammation and its intersection with wound healing; the decade since has seen vast growth in both the application of agent-based modeling to a wide array of disease processes as well as methodological advancements in the use and analysis of ABM. This report presents an update on an earlier review of ABMs in TSB and presents examples of exciting progress in the modeling of various organs and diseases that involve inflammation. This review also describes developments that integrate the use of ABMs with cutting-edge technologies such as high-performance computing, machine learning, and artificial intelligence, with a view toward the future integration of these methodologies. This article is categorized under: Translational, Genomic, and Systems Medicine > Translational Medicine Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Models of Systems Properties and Processes > Organismal Models.

Multiscale modeling of dislocation patterns and simulation of nanoscale plasticity in body-centered cubic (BCC) single crystals

Understanding dislocation multiplication, interactions, and hence crystal plasticity has been a long-standing challenge of major scientific significance. Combining atomistic enriched constitutive law with continuum finite element formulation, we developed a multiscale framework to capture geometrically-compatible dislocation patterns in Body Centered Cubic (BCC) single crystals. This dislocation pattern dynamics framework was successfully applied to study crystal plasticity in Face Centered Cubic (FCC) crystals before, coined as the Multiscale Crystal Defect Dynamics (MCDD) method. Inheriting from MCDD method, we now established a multiscale dislocation pattern dynamics model for BCC crytals with the following novelties: (1) Comparing with molecular dynamics approach, MCDD can predict crystal plasticity in BCC crystals in a more efficient way and in larger scale; (2) MCDD can capture the geometrically-compatible dislocation pattern distribution and evolution in BCC crystals, and (3) MCDD can capture the size effect of crystal plasticity in single BCC crystals at nanoscale, or to simulate size-dependent plasticity in BCC single crystals. In particular, we have successfully simulated crystal plasticity in a BCC crystal at the sub-micron scale by using a serial computing code in a desktop environment.

Numerical simulation of welding fume lung dosimetry

Exposures to airborne particles and toxic gases generated by welding fabrication activities will potentially lead to various diseases. Accurate information on the transport and deposition of such aerosols in the respiratory system is critically needed for precise health risk assessments. To address the data demand mentioned above, a multiscale computational fluid-particle dynamics (CFPD) model was developed in this study. Specifically, a virtual fabrication shop was integrated with a virtual human in the numerical model to evaluate the effects of ventilation condition, particle size, and gas species on the lung uptakes of those welding fume particles and gases. Welding fume particle and gases transmission, transport, and deposition have been simulated and analyzed starting from the emission source to the subject-specific human respiratory system via oral inhalation. Spherical iron particles with diameters of 100, 190, and 830 nm were simulated. The transport and absorption of NOx and CO were predicted too. Steady-state inhalation with 11.87 L/min was applied with two different air filter ventilation conditions. The numerical results indicate that the ventilation condition can significantly influence welding gas transport and deposition. The pulmonary gas absorption rate is much higher at poor ventilation conditions. The air-tissue absorption coefficient is another crucial factor that can impact pulmonary gas absorption. The total particle deposition fractions (TDFs) from mouth/nose to generation 6 (G6) are less than 18.0%, and particles mostly deposit in the oral cavity. Regional and local particle deposition data demonstrate that particles tend to enter the two upper lobes more than the other three lobes. In summary, this study paves the way to build a personalized in silico tool based on CFPD models for noninvasive precise health risk assessments associated with different welding activities.

Multiscale computational fluid dynamics modeling of thermal atomic layer deposition with application to chamber design

This work develops a first-principles-based three-dimensional, multiscale computational fluid dynamics (CFD) model, together with reactor geometry optimizations, of SiO2 thin-film thermal atomic layer deposition (ALD) using bis(tertiary-butylamino)silane (BTBAS) and ozone as precursors. Specifically, an accurate macroscopic CFD model of the ALD reactor chamber gas-phase development is integrated with a detailed microscopic kinetic Monte Carlo (kMC) model that was developed in Ding et al. (2019), accounting for the microscopic lattice structure, atomic interactions and detailed surface chemical reactions. The multiscale information exchange and the transient simulation of the microscopic distributed kMC algorithms and the macroscopic CFD model are achieved through a parallel processing message passing interface (MPI) structure. Additionally, density functional theory (DFT)-based calculations are adopted to compute the key thermodynamic and kinetic parameters for the microscopic thin-film growth process. Recognizing the transient non-uniformity and the possibility to reduce the current ALD cycle time, the optimal configuration of reactor geometry is designed and evaluated including a showerhead panel adjustment and geometry modifications on reactor inlet and upstream. It is demonstrated that with suitable reactor chamber design the required BTBAS ALD half-cycle time can be reduced by 39.6%.

A Multiscale Dynamical Modeling and Identification Framework for Spike-Field Activity.

Dynamical encoding models characterize neural activity with low-dimensional hidden states that dynamically evolve in time and gienerate behavior. Current methods have identified these models from single-scale activity, either spikes or fields. However, behavior is simultaneously encoded across multiple spatiotemporal scales of activity, from spikes of individual neurons to neural population activity measured through fields. Identifying a multiscale dynamical model to extract hidden states that simultaneously describe spike-field activities is challenging because of their fundamental differences. Spikes are binary-valued with fast millisecond time-scales while fields are continuous-valued with slower time-scales. Here, we develop a novel multiscale dynamical modeling and identification algorithm to simultaneously characterize multiscale spike-field dynamics and extract multiscale hidden states. We also devise a modal approach to dissociate task-relevant and task-irrelevant dynamics. Using extensive simulations, we show that the algorithm accurately identifies a multiscale dynamical model to simultaneously describe spike-field dynamics. Furthermore, the algorithm extracts hidden states that are multiscale, i.e., contain information from both spikes and fields and accurately predict behavior. Finally, the algorithm detects which of the identified dynamics are task-relevant and to what extent. This multiscale dynamical modeling and identification framework can help study neural dynamics across spatiotemporal scales and may facilitate future neurotechnologies.

Multi-scale graph modeling and analysis of locomotion dynamics towards sensor-based dementia assessment

Dementia is a general neurodegenerative disorder beyond normal aging, which is not only overwhelming for the patients, but also negatively affects their caregivers and families. In the state of the art, paper-based survey methods such as the Mini-Mental State Examination (MMSE) and Montreal Cognitive Assessment (MoCA) are widely used for the assessment of dementia conditions. However, these methods require lab visits or administration from nurses, physicians and examiners, and are limited in the ability to track temporal degradation (or daily variations) of dementia conditions. With rapid advances in sensing technology, there is growing interest in the development of new, sensor-based methods that provide more flexibility in dementia monitoring and require minimal interventions from practitioners. In this article, we propose a new, sensor-based method that estimates dementia conditions with daily locomotion data. The proposed methodology is evaluated and validated with both simulation and real-world case studies. Experimental results show the compelling predictive accuracy, with both true positive and true negative rates above 85%. This article shows that sensor-based methods have great potential for real-time monitoring of temporal variations of dementia conditions from daily gait locomotion dynamics.

The Influence of Rotary Blood Pump Speed Modulation on the Risk of Intraventricular Thrombosis.

Rotary left ventricular assist devices (LVADs) are commonly operated at a constant speed, attenuating blood flow pulsatility. Speed modulation of rotary LVADs has been demonstrated to improve vascular pulsatility and pump washout. The effect of LVAD speed modulation on intraventricular flow dynamics is not well understood, which may have an influence on thromboembolic events. This study aimed to numerically evaluate intraventricular flow characteristics with a speed modulated LVAD. A severely dilated anatomical left ventricle was supported by a HeartWare HVAD in a three-dimensional multiscale computational fluid dynamics model. Three LVAD operating scenarios were evaluated: constant speed and sinusoidal co- and counter-pulsation. In all operating scenarios, the mean pump speed was set to restore the cardiac output to 5.0L/min. Co- and counter-pulsation was speed modulated with an amplitude of 750rpm. The risk of thrombosis was evaluated based on blood residence time, ventricular washout, kinetic energy densities, and a pulsatility index map. Blood residence time for co-pulsation was on average 1.8 and 3.7% lower than constant speed and counter-pulsation mode, respectively. After introducing fresh blood to displace preexisting blood for 10 cardiac cycles, co-pulsation had 1.5% less old blood in comparison to counter-pulsation. Apical energy densities were 84 and 27% higher for co-pulsation in comparison to counter-pulsation and constant speed mode, respectively. Co-pulsation had an increased pulsatility index around the left ventricular outflow tract and mid-ventricle. Improved flow dynamics with co-pulsation was caused by increased E-wave velocities which minimized blood stasis. In the studied scenario and from the perspective of intraventricular flow dynamics, co-pulsation of rotary LVADs could minimize the risk of intraventricular thrombosis.

The Crisis of Reproducibility, the Denominator Problem and the Scientific Role of Multi-scale Modeling

The “Crisis of Reproducibility” has received considerable attention both within the scientific community and without. While factors associated with scientific culture and practical practice are most often invoked, I propose that the Crisis of Reproducibility is ultimately a failure of generalization with a fundamental scientific basis in the methods used for biomedical research. The Denominator Problem describes how limitations intrinsic to the two primary approaches of biomedical research, clinical studies and preclinical experimental biology, lead to an inability to effectively characterize the full extent of biological heterogeneity, which compromises the task of generalizing acquired knowledge. Drawing on the example of the unifying role of theory in the physical sciences, I propose that multi-scale mathematical and dynamic computational models, when mapped to the modular structure of biological systems, can serve a unifying role as formal representations of what is conserved and similar from one biological context to another. This ability to explicitly describe the generation of heterogeneity from similarity addresses the Denominator Problem and provides a scientific response to the Crisis of Reproducibility.

A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics.

In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Identifying multiscale hidden states to decode behavior.

A key element needed in a brain-machine interface (BMI) decoder is the encoding model, which relates the neural activity to intended movement. The vast majority of work have used a representational encoding model, which assumes movement parameters are directly encoded in neural activity. Recent work have in turn suggested the existence of neural dynamics that represent behavior. This recent evidence motivates developing dynamical encoding models with hidden states that encode movement. Regardless of their type, encoding models have vastly characterized a single scale of activity, e.g., either spikes or local field potentials (LFP). In our recent work we developed a multiscale representational encoding model to simultaneously characterize and decode discrete spikes and continuous field activity. However, learning a multiscale dynamical model from simultaneous spike-field recordings in the presence of hidden states is challenging. Here we present an unsupervised learning algorithm for estimating a multiscale state-space model with hidden states and validate it using spike-LFP activity during a reaching movement. We use the learned multiscale statespace model and a corresponding decoder to identify hidden states from spike-LFP activity. We then decode the movement trajectories using these hidden states. We find that the identified states can accurately decode the trajectories. Moreover, we demonstrate that adding LFP to spikes improves the decoding accuracy, suggesting that our unsupervised learning algorithm incorporates information across scales. This learning algorithm could serve as a new tool to study encoding across scales and to enhance future BMI systems.

Inhibition of high shear arterial thrombosis by charged nanoparticles.

Platelet accumulation under high shear rates at the site of atherosclerotic plaque rupture leads to myocardial infarction and stroke. Current antiplatelet therapies remain ineffective within a large percentage of the population, while presenting significant risks for bleeding. We explore a novel way to inhibit arterial thrombus formation by biophysical means without the use of platelet inactivating drugs. Our computational multi-scale dynamics model has predicted that charged particles of a specific size may entangle von Willebrand Factor (vWF) polymers and reduce the amount of elongation at high shear rates. We tested this hypothesis experimentally for negatively charged nanoparticles (CNP) to inhibit arterial thrombus formation. CNP of a particular size and charge inhibited thrombus formation, with a 10-fold peak inhibition over control conditions of thrombotic occlusion. Particles of differing material composition, size, and charge had little effect as predicted by computational studies. Surprisingly, the dose response curve was not sigmoidal, but exhibited a peak at 1.5 CNP:vWF proteins, which was not predicted by the model. This study describes a new antithrombotic agent that may have a different mechanism of action than current pharmaceutical therapies.

IMS-DTM: Incremental Multi-Scale Dynamic Topic Models

Dynamic topic models (DTM) are commonly used for mining latent topics in evolving web corpora. In this paper, we note that a major limitation of the conventional DTM based models is that they assume a predetermined and fixed scale of topics. In reality, however, topics may have varying spans and topics of multiple scales can co-exist in a single web or social media data stream. Therefore, DTMs that assume a fixed epoch length may not be able to effectively capture latent topics and thus negatively affect accuracy. In this paper, we propose a Multi-Scale Dynamic Topic Model (MS-DTM) and a complementary Incremental Multi-Scale Dynamic Topic Model (IMS-DTM) inference method that can be used to capture latent topics and their dynamics simultaneously, at different scales. In this model, topic specific feature distributions are generated based on a multi-scale feature distribution of the previous epochs; moreover, multiple scales of the current epoch are analyzed together through a novel multi-scale incremental Gibbs sampling technique. We show that the proposed model significantly improves efficiency and effectiveness compared to the single scale dynamic DTMs and prior models that consider only multiple scales of the past.

Simple multi-scale modeling of the transmission dynamics of the 1905 plague epidemic in Bombay

The first few disease generations of an infectious disease outbreak is the most critical phase to implement control interventions. The lack of accurate data and information during the early transmission phase hinders the application of complex compartmental models to make predictions and forecasts about important epidemic quantities. Thus, simpler models are often times better tools to understand the early dynamics of an outbreak particularly in the context of limited data. In this paper we mechanistically derive and fit a family of logistic models to spatial-temporal data of the 1905 plague epidemic in Bombay, India. We systematically compare parameter estimates, reproduction numbers, model fit, and short-term forecasts across models at different spatial resolutions. At the same time, we also assess the presence of sub-exponential growth dynamics at different spatial scales and investigate the role of spatial structure and data resolution (district level data and city level data) using simple structured models. Our results for the 1905 plague epidemic in Bombay indicates that it is possible for the growth of an epidemic in the early phase to be sub-exponential at sub-city level, while maintaining near exponential growth at an aggregated city level. We also show that the rate of movement between districts can have a significant effect on the final epidemic size.

Comparative study on the hydrodynamics and mixing characteristics of a new-type particle mixer

The characteristics of particle flow and mixing have a considerable influence on mass and heat transfer, as well as product quality. In order to further enhance the particle mixing in an internally circulating fluidized bed (ICFB), especially along the radial direction, four slots were opened on the draft tube of an ICFB mixer. Hydrodynamic characteristics were investigated by using a multi-scale computational fluid dynamics (CFD) model incorporating the EMMS drag. The prediction in terms of cross-sectionally averaged solid holdup and particle velocity were compared to experimental data for validation. Compared with a traditional ICFB mixer, the new mixer with four slots opening on the draft tube presents strong radial particle flow through the slots, and thereby provides better mixing performance. It is found that nearly 25.4% to 29.7% of gas in the draft tube bypasses and flows through the slots into the annulus. With increase in the superficial gas velocity in the draft tube from 0.3 m/s to 0.45 m/s, the total particle circulation mass flux in the new ICFB mixer increases from 4.87 kg/s to 10.86 kg/s. The mixing index reaches about 0.98 in the new ICFB mixer.

Multiscale three-dimensional CFD modeling for PECVD of amorphous silicon thin films

The development of a three-dimensional, multiscale computational fluid dynamics (CFD) model is presented here which aims to capture the deposition of amorphous silicon thin films via plasma-enhanced chemical vapor deposition (PECVD). The macroscopic reactor scale and the microscopic thin film growth domains which define the multiscale model are linked using a dynamic boundary which is updated at the completion of each time step. A novel parallel processing scheme built around a message passing interface (MPI) structure, in conjunction with a distributed collection of kinetic Monte Carlo algorithms, is applied in order to allow for transient simulations to be conducted using a mesh with greater than 1.5 million cells. Due to the frequent issue of thickness non-uniformity in thin film production, an improved PECVD reactor design is proposed. The resulting geometry is shown to reduce the product offset from ∼ 25 nm to less than 13 nm using identical deposition parameters.

Ventricular flow dynamics with varying LVAD inflow cannula lengths: In-silico evaluation in a multiscale model

Left ventricular assist devices are associated with thromboembolic events, which are potentially caused by altered intraventricular flow. Due to patient variability, differences in apical wall thickness affects cannula insertion lengths, potentially promoting unfavourable intraventricular flow patterns which are thought to be correlated to the risk of thrombosis. This study aimed to present a 3D multiscale computational fluid dynamic model of the left ventricle (LV) developed using a commercial software, Ansys, and evaluate the risk of thrombosis with varying inflow cannula insertion lengths in a severely dilated LV. Based on a HeartWare HVAD inflow cannula, insertion lengths of 5, 19, 24 and 50 mm represented cases of apical hypertrophy, typical ranges of apical thicknesses and an experimental length, respectively. The risk of thrombosis was evaluated based on blood washout, residence time, instantaneous blood stagnation and a pulsatility index. By introducing fresh blood to displace pre-existing blood in the LV, after 5 cardiac cycles, 46.7%, 45.7%, 45.1% and 41.8% of pre-existing blood remained for insertion lengths of 5, 19, 24 and 50 mm, respectively. Compared to the 50 mm insertion, blood residence time was at least 9%, 7% and 6% higher with the 5, 19 and 24 mm insertion lengths, respectively. No instantaneous stagnation at the apex was observed directly after the E-wave. Pulsatility indices adjacent to the cannula increased with shorter insertion lengths. For the specific scenario studied, a longer insertion length, relative to LV size, may be advantageous to minimise thrombosis by increasing LV washout and reducing blood residence time.

Computational Investigation of a Self-Powered Fontan Circulation.

Children born with anatomic or functional "single ventricle" must progress through two or more major operations to sustain life. This management sequence culminates in the total cavopulmonary connection, or "Fontan" operation. A consequence of the "Fontan circulation", however, is elevated central venous pressure and inadequate ventricular preload, which contribute to continued morbidity. We propose a solution to these problems by increasing pulmonary blood flow using an "injection jet" (IJS) in which the source of blood flow and energy is the ventricle itself. The IJS has the unique property of lowering venous pressure while enhancing pulmonary blood flow and ventricular preload. We report preliminary results of an analysis of this circulation using a tightly-coupled, multi-scale computational fluid dynamics model. Our calculations show that, constraining the excess volume load to the ventricle at 50% (pulmonary to systemic flow ratio of 1.5), an optimally configured IJS can lower venous pressure by 3mmHg while increasing systemic oxygen delivery. Even this small decrease in venous pressure may have substantial clinical impact on the Fontan patient. These findings support the potential for a straightforward surgical modification to decrease venous pressure, and perhaps improve clinical outcome in selected patients.

Multi-scale immunoepidemiological modeling of within-host and between-host HIV dynamics: systematic review of mathematical models.

ObjectiveThe objective of this study is to conduct a systematic review of multi-scale HIV immunoepidemiological models to improve our understanding of the synergistic impact between the HIV viral-immune dynamics at the individual level and HIV transmission dynamics at the population level.BackgroundWhile within-host and between-host models of HIV dynamics have been well studied at a single scale, connecting the immunological and epidemiological scales through multi-scale models is an emerging method to infer the synergistic dynamics of HIV at the individual and population levels.MethodsWe reviewed nine articles using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework that focused on the synergistic dynamics of HIV immunoepidemiological models at the individual and population levels.ResultsHIV immunoepidemiological models simulate viral immune dynamics at the within-host scale and the epidemiological transmission dynamics at the between-host scale. They account for longitudinal changes in the immune viral dynamics of HIV+ individuals, and their corresponding impact on the transmission dynamics in the population. They are useful to analyze the dynamics of HIV super-infection, co-infection, drug resistance, evolution, and treatment in HIV+ individuals, and their impact on the epidemic pathways in the population. We illustrate the coupling mechanisms of the within-host and between-host scales, their mathematical implementation, and the clinical and public health problems that are appropriate for analysis using HIV immunoepidemiological models.ConclusionHIV immunoepidemiological models connect the within-host immune dynamics at the individual level and the epidemiological transmission dynamics at the population level. While multi-scale models add complexity over a single-scale model, they account for the time varying immune viral response of HIV+ individuals, and the corresponding impact on the time-varying risk of transmission of HIV+ individuals to other susceptibles in the population.