A supervised learning-assisted multi-scale study for thermal and mechanical behavior of porous Silica

This paper presents a comprehensive investigation of mesoporous Silica utilizing a multi-scale modeling approach under periodic boundary conditions integrated with machine learning algorithms. The study begins with Molecular Dynamics (MD) simulations to extract Silica's elastic properties and thermal conductivity at the nano-scale, employing the Tersoff potential. Subsequently, the derived material characteristics are applied to a series of generated porous Representative Volume Elements (RVEs) at the microscale. This phase involves the exploration of porosity and void shape effects on Silica's thermal and mechanical properties, considering inhomogeneities' distributions along the X-axis and random dispersion of pore cells within a three-dimensional space. Furthermore, the influence of pore shape is examined by defining open and closed-cell models, encompassing spherical and ellipsoidal voids with aspect ratios of 2 and 4. To predict the properties of porous Silica, a shallow Artificial Neural Network (ANN) is deployed, utilizing geometric parameters of the RVEs and porosity. Subsequently, it is revealed that Silica's thermal and mechanical behavior is linked to pore geometry, distribution, and porosity model. Finally, to classify the behavior of porous Silica into three categories, quasi-isotropic, orthotropic, and transversely-isotropic, three methodologies of decision tree approach, K-Nearest Neighbors (KNN) algorithm, and Support Vector Machines (SVMs) are employed. Among these, SVMs employing a quadratic kernel function demonstrate robust performance in categorizing the thermal and mechanical behavior of porous Silica.

A Semi-Markov Approach to Study a Group of Kinesin Motors

We propose a general mathematical and computational approach to study cellular transport driven by a group of kinesin motors. It is a framework for multi-scale modeling that integrates kinetic models of single kinesin motors, including detachment and reattachment events, to study group behaviors of several motors. By formulating the problem as a semi-Markov process and applying a central limit theorem, asymptotic velocity and diffusivity can be readily calculated, which offers considerable computational advantage over Monte Carlo simulations in tasks such as parameter sensitivity analysis and model selection. We demonstrate the method with some examples. The importance of incorporating the intrinsic microscopic-level dynamics of individual motors is illustrated by showing how changes at the microscopic level propagate to the motor-cargo complex at a mesoscopic level. Particularly, we showcase an example in which changes in the second moment of single-motor characteristics gives rise to different first moment characteristics of the motor group.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

Planktos: An Agent-Based Modeling Framework for Small Organism Movement and Dispersal in a Fluid Environment with Immersed Structures

Multiscale modeling of marine and aerial plankton has traditionally been difficult to address holistically due to the challenge of resolving individual locomotion dynamics while being carried with larger-scale flows. However, such problems are of paramount importance, e.g., dispersal of marine larval plankton is critical for the health of coral reefs, and aerial plankton (tiny arthropods) can be used as effective agricultural biocontrol agents. Here we introduce the open-source, agent-based modeling software Planktos targeted at 2D and 3D fluid environments in Python. Agents in this modeling framework are relatively tiny organisms in sufficiently low densities that their effect on the surrounding fluid motion can be considered negligible. This library can be used for scientific exploration and quantification of collective and emergent behavior, including interaction with immersed structures. In this paper, we detail the implementation and functionality of the library along with some illustrative examples. Functionality includes arbitrary agent behavior obeying either ordinary differential equations, stochastic differential equations, or coded movement algorithms, all under the influence of time-dependent fluid velocity fields generated by computational fluid dynamics, experiments, or analytical models in domains with static immersed mesh structures with sliding or sticky collisions. In addition, data visualization tools provide images or animations with kernel density estimation and velocity field analysis with respect to deterministic agent behavior via the finite-time Lyapunov exponent.

Determination of pressure resistance of a partially stoppered vial by using a coupled CFD-0D model of lyophilization

Modeling lyophilization in a vial is frequently done on a single vial level. When setting up a numerical model, the main focus is on heat and mass transfer inside the lyophilizate, whereas the vapor dynamics in the headspace of the vial is taken into account simply through imposing the system pressure as a pressure boundary condition. The present paper offers a deeper insight into the interaction of the sublimated vapor flow and the corresponding vapor pressure conditions inside the headspace of a partially stoppered vial. This is achieved through a coupled numerical solution of the heat and mass transfer inside the product by means of a 0D model describing the frozen domain (ice) and the 3D fluid flow inside the vial geometry with the partially opened stopper, computed by means of Computational Fluid Dynamics. Due to low pressures, the slip flow regime within the continuum hypothesis has to be considered, leading to imposing velocity slip conditions at the solid walls. The 0D model is used for the computation of sublimation mass flow rate as well as heat transfer rate to the vial, with the results of the water vapor mass flow rate and the temperature communicated to the 3D CFD model as a new inlet boundary conditions for computation of compressible fluid flow dynamics inside the vial. The obtained CFD pressure field solution allows derivation of a pressure resistance model for a targeted vial stopper combination, which is then used in calculating the corresponding pressure drop in the headspace of the partially stoppered vial. The coupled CFD-0D model results are validated based on the results of dedicated experimental water runs on several vial and stopper geometries and show, that the vial geometry, but especially the installed stopper, alter the pressure field conditions inside the vial. The increased in-vial local vapor pressure values lead to a decrease of the mass flow rates and an increase of temperatures at the bottom of the product, which range from 0.6 K for the highest system pressure and up to 5.4 K for the lowest system pressure tested. The presented coupled model is suitable for the use in further studies of the impact of various vial forms as well as stoppers on the lyophilization dynamics in a vial.

Focusing on powder processing in dry powder inhalation product development, manufacturing and performance

Dry powder inhalers (DPI) are well established products for the delivery of actives via the pulmonary route. Various DPI products are marketed or developed for the treatment of local lung diseases such as chronic obstructive pulmonary disease (COPD), asthma or cystic fibrosis as well as systemic diseases targeted through inhaled delivery (i.e. Diabetes Mellitus). One of the key prerequisites of DPI formulations is that the aerodynamic size of the drug particles needs to be below 5 µm to enter deeply into the respiratory tract. These inherently cohesive inhalable size particles are either formulated as adhesive mixture with coarse carrier particles like lactose called carrier-based DPI or are formulated as free-flowing carrier-free particles (e.g. soft agglomerates, large hollow particles). In either case, it is common practice that drug and/or excipient particles of DPI formulations are obtained by processing API and API/excipients. The DPI manufacturing process heavily involves several particle and powder technologies such as micronization of the API, dry blending, powder filling and other particle engineering processes such as spray drying, crystallization etc. In this context, it is essential to thoroughly understand the impact of powder/particle properties and processing on the quality and performance of the DPI formulations. This will enable prediction of the processability of the DPI formulations and controlling the manufacturing process so that meticulously designed formulations are able to be finally developed as the finished DPI dosage form. This article is intended to provide a concise account of various aspects of DPI powder processing, including the process understanding and material properties that are important to achieve the desired DPI product quality. Various endeavors of model informed formulation/process design and development for DPI powder and PAT enabled process monitoring and control are also discussed.

Connectome 2.0: Developing the next-generation ultra-high gradient strength human MRI scanner for bridging studies of the micro-, meso- and macro-connectome

The first phase of the Human Connectome Project pioneered advances in MRI technology for mapping the macroscopic structural connections of the living human brain through the engineering of a whole-body human MRI scanner equipped with maximum gradient strength of 300 mT/m, the highest ever achieved for human imaging. While this instrument has made important contributions to the understanding of macroscale connectional topology, it has also demonstrated the potential of dedicated high-gradient performance scanners to provide unparalleled in vivo assessment of neural tissue microstructure. Building on the initial groundwork laid by the original Connectome scanner, we have now embarked on an international, multi-site effort to build the next-generation human 3T Connectome scanner (Connectome 2.0) optimized for the study of neural tissue microstructure and connectional anatomy across multiple length scales. In order to maximize the resolution of this in vivo microscope for studies of the living human brain, we will push the diffusion resolution limit to unprecedented levels by (1) nearly doubling the current maximum gradient strength from 300 mT/m to 500 mT/m and tripling the maximum slew rate from 200 T/m/s to 600 T/m/s through the design of a one-of-a-kind head gradient coil optimized to minimize peripheral nerve stimulation; (2) developing high-sensitivity multi-channel radiofrequency receive coils for in vivo and ex vivo human brain imaging; (3) incorporating dynamic field monitoring to minimize image distortions and artifacts; (4) developing new pulse sequences to integrate the strongest diffusion encoding and highest spatial resolution ever achieved in the living human brain; and (5) calibrating the measurements obtained from this next-generation instrument through systematic validation of diffusion microstructural metrics in high-fidelity phantoms and ex vivo brain tissue at progressively finer scales with accompanying diffusion simulations in histology-based micro-geometries. We envision creating the ultimate diffusion MRI instrument capable of capturing the complex multi-scale organization of the living human brain - from the microscopic scale needed to probe cellular geometry, heterogeneity and plasticity, to the mesoscopic scale for quantifying the distinctions in cortical structure and connectivity that define cyto- and myeloarchitectonic boundaries, to improvements in estimates of macroscopic connectivity.

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon

This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). A multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism is proposed first. Indeed, there are human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self-infection by susceptible individuals. The global stability of the disease-free equilibrium is shown when a given threshold T 0 is less or equal to 1 and the basic reproduction number R 0 is calculated. A convergence index T 1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of infectious extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. Using Partial Rank Correlation Coefficient with a three levels fractional experimental design, the sensitivity of  R 0 , T 0 and T 1 to control parameters is evaluated. Following this study, the most significant parameter is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into account economic impacts of SARS-CoV-2, optimal fighting strategies are determined and discussed. The study is applied to real and available data from Cameroon with a model fitting. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy against SARS-CoV-2.

The influence of boundary conditions and protein availability on the remodeling of cardiomyocytes

The heart muscle is capable of growing and remodeling in response to changes in its mechanical and hormonal environment. While this capability is essential to the healthy function of the heart, under extreme conditions it may also lead to heart failure. In this work, we derive a thermodynamically based and microscopically motivated model that highlights the influence of mechanical boundary conditions and hormonal changes on the remodeling process in cardiomyocytes. We begin with a description of the kinematics associated with the remodeling process. Specifically, we derive relations between the macroscopic deformation, the number of sarcomeres, the sarcomere stretch, and the number of myofibrils in the cell. We follow with the derivation of evolution equations that describe the production and the degradation of protein in the cytosol. Next, we postulate a dissipation-based formulation that characterizes the remodeling process. We show that this process stems from a competition between the internal energy, the entropy, the energy supplied to the system by ATP and other sources, and dissipation mechanisms. To illustrate the merit of this framework, we study four initial and boundary conditions: (1) a myocyte undergoing isometric contractions in the presence of either an infinite or a limited supply of proteins and (2) a myocyte that is free to dilate along the radial direction with an infinite and a limited supply of proteins. This work underscores the importance of boundary conditions on the overall remodeling response of cardiomyocytes, suggesting a plausible mechanism that might play a role in distinguishing eccentric vs. concentric hypertrophy.

ΛCDM and MOND: A debate about models or theory?

The debate between ΛCDM and MOND is often cast in terms of competing gravitational theories. However, recent philosophical discussion suggests that the ΛCDM-MOND debate demonstrates the challenges of multiscale modeling in the context of cosmological scales. I extend this discussion and explore what happens when the debate is thought to be about modeling rather than about theory, offering a model-focused interpretation of the ΛCDM-MOND debate. This analysis shows how a model-focused interpretation of the debate provides a better understanding of challenges associated with extension to a different scale or domain, which are tied to commitments about explanatory fit.

Advances in flux balance analysis by integrating machine learning and mechanism-based models

The availability of multi-omics data sets and genome-scale metabolic models for various organisms provide a platform for modeling and analyzing genotype-to-phenotype relationships. Flux balance analysis is the main tool for predicting flux distributions in genome-scale metabolic models and various data-integrative approaches enable modeling context-specific network behavior. Due to its linear nature, this optimization framework is readily scalable to multi-tissue or -organ and even multi-organism models. However, both data and model size can hamper a straightforward biological interpretation of the estimated fluxes. Moreover, flux balance analysis simulates metabolism at steady-state and thus, in its most basic form, does not consider kinetics or regulatory events. The integration of flux balance analysis with complementary data analysis and modeling techniques offers the potential to overcome these challenges. In particular machine learning approaches have emerged as the tool of choice for data reduction and selection of most important variables in big data sets. Kinetic models and formal languages can be used to simulate dynamic behavior. This review article provides an overview of integrative studies that combine flux balance analysis with machine learning approaches, kinetic models, such as physiology-based pharmacokinetic models, and formal graphical modeling languages, such as Petri nets. We discuss the mathematical aspects and biological applications of these integrated approaches and outline challenges and future perspectives.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

The effects of aging on the mechanical properties of the vitreous

The vitreous body is a viscoelastic gel-like network that fills the space between the lens and the retina in the eye. With aging, the vitreous undergoes a liquefaction process in which liquid pockets form in the gel network, thereby motivating the detachment of the vitreous from the retina in a process known as posterior vitreous detachment (PVD). The PVD process may lead to the formation of floaters and even result in partial or complete loss of vision. Experiments show that the liquefaction and the PVD processes alter the mechanical properties of the vitreous. In this work, we propose a microscopically motivated model that characterizes the changes in the mechanical properties of the vitreous due to aging. To this end, we distinguish between four vitreous states: a homogeneous vitreous, a liquefied vitreous, a vitreous that undergoes partial PVD, and a vitreous with full PVD. The model predicts the time-dependent and the steady-state response of the vitreous in each of the four states. The proposed framework is validated through a comparison with various experimental findings and captures the softening of the vitreous due to aging. We illustrate the importance of the age at which the PVD process begins and of the rate of the detachment process. In addition, we introduce a quantifiable parameter that describes the stage of PVD in the eye. Lastly, we employ our model to investigate the possibility of restoring the mechanical properties of a vitreous that has undergone PVD through the addition of reinforcing fibers to the gel. This work provides insight into the consequences of the age-related changes in the microstructure of the eye and serves as a motivation for new therapeutic measures.

An Integrated Computational Materials Engineering Framework to Analyze the Failure Behaviors of Carbon Fiber Reinforced Polymer Composites for Lightweight Vehicle Applications

A bottom-up multi-scale modeling approach is used to develop an Integrated Computational Materials Engineering (ICME) framework for carbon fiber reinforced polymer (CFRP) composites, which has the potential to reduce development to deployment lead time for structural applications in lightweight vehicles. In this work, we develop and integrate computational models comprising of four size scales to fully describe and characterize three types of CFRP composites. In detail, the properties of the interphase region are determined by an analytical gradient model and molecular dynamics analysis at the nano-scale, which is then incorporated into micro-scale unidirectional (UD) representative volume element (RVE) models to characterize the failure strengths and envelopes of UD CFRP composites. Then, the results are leveraged to propose an elasto-plastic-damage constitutive law for UD composites to study the fiber tows of woven composites as well as the chips of sheet molding compound (SMC) composites. Subsequently, the failure mechanisms and failure strengths of woven and SMC composites are predicted by the meso-scale RVE models. Finally, building upon the models and results from lower scales, we show that a homogenized macro-scale model can capture the mechanical performance of a hat-section-shaped part under four-point bending. Along with the model integration, we will also demonstrate that the computational results are in good agreement with experiments conducted at different scales. The present study illustrates the potential and significance of integrated multi-scale computational modeling tools that can virtually evaluate the performance of CFRP composites and provide design guidance for CFRP composites used in structural applications.

Modeling osteoinduction in titanium bone scaffold with a representative channel structure

Optimizing scaffold architecture for perfect osteointegration depends on good understanding of bone ingrowth in the porous space of implants. This study developed an immunoregulatory agent-based model to discover the osteoinduction mechanism in porous scaffolds. Immunoreaction, macrophage polarization, and the corresponding growth factors were combined in the model, and all played critical roles in recruiting osteogenic cells that migrated into the scaffolds. Angiogenesis was also considered in this model. The bone ingrowth predicted by the model coincides with results from published in vivo experiments. Simulation results suggested that the pore architecture affected the diffusion process of chemotactic factors in the scaffolds, subsequently influencing the complex reactions of diverse cells and the osteoinduction location. In flexural pore spaces, bone formation spread from the periphery into the center of scaffolds due to larger M2 phenotype macrophage populations colonizing boundary regions and the distribution of corresponding growth factors concentration. In straight channels, osteogenic cells migrated further inward and osteoinduction initiated in deeper position as a result of the deeper distribution of osteogenic cytokines concentration field.

Force distribution and multi-scale mechanics in smooth muscle tissues

The mechanical role of smooth muscle tissue in many physiological processes is vital to their healthy function. In this work, we provide a deeper understanding of the underlying mechanisms that govern the smooth muscle tissue response. Specifically, we model and investigate the distribution and the transmission of passive and active forces throughout the microstructure. Broadly, smooth muscle cells contain a structural network with two types of load carrying structures: (1) contractile units made of actin and myosin filaments, which are capable of generating force, and (2) intermediate filaments. The extracellular matrix comprises elastin and collagen fibers that can sustain stress. We argue that all of the load carrying constituents in the tissue participate in the generation and the transmission of passive and active forces. We begin by modeling the response of the elements in the smooth muscle cell and defining a network of contractile units and intermediate filaments through which forces are transferred. This allows to derive an expression for the stress that develops in the cell. Next, we assume a hyperelastic behavior for the extracellular matrix and determine the stress in the tissue. With appropriate kinematic constraints and equilibrium considerations, we relate the macroscopic deformation to the stretch of the individual load carrying structures. Consequently, the stress on each element in the tissue can be computed. To validate the framework, we consider a simple microstructure of a smooth muscle tissue and fit the model parameters to experimental findings. The framework is also used to delineate experimental evidence which suggests that the suppression of intermediate filaments reduces the active and passive forces in a tissue. We show that the degradation and the reduction of the number of intermediate filaments in the cell fully explains this observation.

Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). The extended theory offers an approximate mean-field dynamics for the synaptic input currents arising from populations of spiking neurons and synapses undergoing Tsodyks-Markram STP. The approximate mean-field dynamics accounts for both finite number of synapses and correlation between the two synaptic variables of the model (utilization and available resources) and its numerical implementation is simple. Comparisons with Monte Carlo simulations of the microscopic model show that in both feedforward and recurrent networks, the mesoscopic mean-field model accurately reproduces the first- and second-order statistics of the total synaptic input into a postsynaptic neuron and accounts for stochastic switches between Up and Down states and for population spikes. The extended mesoscopic population theory of spiking neural networks with STP may be useful for a systematic reduction of detailed biophysical models of cortical microcircuits to numerically efficient and mathematically tractable mean-field models.

Systems biology: current status and challenges

We put together a special issue on current approaches in systems biology with a focus on mathematical modeling of metabolic networks. Mathematical models have increasingly been used to unravel molecular mechanisms of complex dynamic biological processes. We here provide a short introduction into the topics covered in this special issue, highlighting current developments and challenges.

Subject-specific geometry affects acetabular contact pressure during gait more than subject-specific loading patterns

Finite element modeling (FEM) can predict hip cartilage contact mechanics. This study investigated how subject-specific boundary conditions and joint geometry affect acetabular cartilage contact mechanics using a multi-scale workflow. For two healthy subjects, musculoskeletal models calculated subject-specific hip kinematics and loading, which were used as boundary conditions for FEM. Cartilage contact mechanics were predicted using either generic or subject-specific FEM and boundary conditions. A subject-specific mesh resulted in a more lateral contact. Effects of subject-specific boundary conditions varied between both subjects. Results highlight the complex interplay between loading and kinematics and their effect on cartilage contact mechanics.

A microscopically motivated model for the remodeling of cardiomyocytes

We present a thermodynamically based model that captures the remodeling effects in cardiac muscle cells. This work begins with the formulation of the kinematics of a cardiomyocyte resulting from a prescribed macroscopic deformation and the reorganization of the internal structure. Specifically, relations between the macroscopic deformation and the number of sarcomeres, the sarcomere stretch, and the number of myofibrils in the cell are determined. The remodeling process is split into two separate phases-(1) elongation/shortening of the existing myofibrils by addition/detachment of sarcomeres and (2) formation of new myofibrils. The remodeling associated with each phase is modeled through a dissipation postulate. We show that remodeling is based on a competition between the internal energy, the entropy, the energy supplied to the system by ATP and other sources to drive the remodeling process, and dissipation mechanisms. While the variations in entropy associated with phase (1) are neglected, the substantial entropy loss associated with the formation of new myofibrils is determined. To illustrate the merit of the proposed framework, we compute the response of cardiomyocytes subjected to isometric axial stretch that are either free to deform or fixed in the transverse direction. We also examine the predictions of this model for cardiomyocytes subjected to various cyclic loadings. The proposed framework is capable of capturing a wide range of remodeling effects and agrees with experimental observations.

Multi-Scale Modeling of Head Kinematics and Brain Tissue Response to Blast Exposure

Injuries resulting from blast exposure have been increasingly prevalent in recent conflicts, with a particular focus on the risk of head injury. In the current study, a multibody model (GEBOD) was used to investigate the gross kinematics resulting from blast exposure, including longer duration events such as the fall and ground impact. Additionally, detailed planar head models, in the sagittal and transverse planes, were used to model the primary blast wave interaction with the head, and resulting tissue response. For severe blast load cases (scaled distance less than 2), the translational head accelerations during primary blast were found to increase as the height-of-burst (HOB) was lowered, while the HOB was found to have no effect for cases with scaled distance greater than 2. The HOB was found to affect both the magnitude and direction of rotational accelerations, with increasing magnitudes as the HOB deviated from the height of the head. The choice of ground contact stiffness was found to greatly affect the predicted head accelerations during ground impact. For a medium soil ground material, the kinematics during ground impact were greater for scaled distances exceeding 1.5, below which the primary blast produced greater kinematic head response.

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.

Fatigue of soft fibrous tissues: Multi-scale mechanics and constitutive modeling

In recent experimental studies a possible damage mechanism of collagenous tissues mainly caused by fatigue was disclosed. In this contribution, a multi-scale constitutive model ranging from the tropocollagen (TC) molecule level up to bundles of collagen fibers is proposed and utilized to predict the elastic and inelastic long-term tissue response. Material failure of collagen fibrils is elucidated by a permanent opening of the triple helical collagen molecule conformation, triggered either by overstretching or reaction kinetics of non-covalent bonds. This kinetics is described within a probabilistic framework of adhesive detachments of molecular linkages providing collagen fiber integrity. Both intramolecular and interfibrillar linkages are considered. The final constitutive equations are validated against recent experimental data available in literature for both uniaxial tension to failure and the evolution of fatigue in subsequent loading cycles. All material parameters of the proposed model have a clear physical interpretation.

STATEMENT OF SIGNIFICANCE

Irreversible changes take place at different length scales of soft fibrous tissues under supra-physiological loading and alter their macroscopic mechanical properties. Understanding the evolution of those histologic pathologies under loading and incorporating them into a continuum mechanical framework appears to be crucial in order to predict long-term evolution of various diseases and to support the development of tissue engineering.

A multi-scale method for modeling degradation of bioresorbable polyesters

A multi-scale model using the cellular automata (CA) and kinetic Monte Carlo (KMC) methods is presented to simulate the degradation process of bioresorbable polyesters such as polylactide (PLA), polyglycolide (PGA) and their copolymers. The model considers the underlying chemical and physical events such as polymer chain scission, oligomer production, crystallization induced by polymer chain scissions, oligomer diffusion and microstructure evolution due to erosion of the small chains. A macroscopic device is discretized into an array of mesoscopic cells. Each cellular lattice is assumed to be made of one polymer chain, which undergoes hydrolysis reaction. The polymer chain scission is modeled using a kinetic Monte Carlo method. Oligomer production, chain crystallization and formation of cavities due to polymer collapse are also modeled on the cellular lattice. Oligomer diffusion is modeled by using Fick's laws at the macroscopic scale. The diffusion coefficient is taken as dependent on the porosity caused by the formation of the cavities. The interactions among the microscopic hydrolysis reaction, mesoscopic formation of cavities and macroscopic diffusion are taken into account. The proposed method forms Multi Scale Cellular Monte Carlo Automata (MS-CMCA). The three-scale approach consists of continuous method and discrete method to deal with certainty problem with underlying stochastic phenomenon. Demonstration examples are provided which show that the model can fit with experimental data in the literature very well.

STATEMENT OF SIGNIFICANCE

The original work in this paper is a multi-scale method (including micro scale, mesoscopic scale, macro scale and their coupling) for modeling degradation of bioresorbable polyesters and provides understanding to the process of degradation of biodegradable polymers. The result denotes the solution is reliable. As we know, there have no papers recently to implement three scales modeling and its coupling. There is a two-scale model of amorphous polyester degradation described by Han and Pan (Acta Biomaterialia 2011), our model accounts for effects of re-crystallization to explain the degradation process from three scales and takes into account of copolymers. From our model, the molecular weight distribution with time, chain number with time, degree of crystallinity with time, the evolution of polymer inner shape, weight loss with time (which is found from calculation that both oligomer diffusion and small molecules solution work to the weight loss) can be obtained from the calculation of the three scale model.

Mechanistic mathematical models: An underused platform for HPV research

Health economic modeling has become an invaluable methodology for the design and evaluation of clinical and public health interventions against the human papillomavirus (HPV) and associated diseases. At the same time, relatively little attention has been paid to a different yet complementary class of models, namely that of mechanistic mathematical models. The primary focus of mechanistic mathematical models is to better understand the intricate biologic mechanisms and dynamics of disease. Inspired by a long and successful history of mechanistic modeling in other biomedical fields, we highlight several areas of HPV research where mechanistic models have the potential to advance the field. We argue that by building quantitative bridges between biologic mechanism and population level data, mechanistic mathematical models provide a unique platform to enable collaborations between experimentalists who collect data at different physical scales of the HPV infection process. Through such collaborations, mechanistic mathematical models can accelerate and enhance the investigation of HPV and related diseases.

Biology meets physics: Reductionism and multi-scale modeling of morphogenesis

A common reductionist assumption is that macro-scale behaviors can be described "bottom-up" if only sufficient details about lower-scale processes are available. The view that an "ideal" or "fundamental" physics would be sufficient to explain all macro-scale phenomena has been met with criticism from philosophers of biology. Specifically, scholars have pointed to the impossibility of deducing biological explanations from physical ones, and to the irreducible nature of distinctively biological processes such as gene regulation and evolution. This paper takes a step back in asking whether bottom-up modeling is feasible even when modeling simple physical systems across scales. By comparing examples of multi-scale modeling in physics and biology, we argue that the "tyranny of scales" problem presents a challenge to reductive explanations in both physics and biology. The problem refers to the scale-dependency of physical and biological behaviors that forces researchers to combine different models relying on different scale-specific mathematical strategies and boundary conditions. Analyzing the ways in which different models are combined in multi-scale modeling also has implications for the relation between physics and biology. Contrary to the assumption that physical science approaches provide reductive explanations in biology, we exemplify how inputs from physics often reveal the importance of macro-scale models and explanations. We illustrate this through an examination of the role of biomechanical modeling in developmental biology. In such contexts, the relation between models at different scales and from different disciplines is neither reductive nor completely autonomous, but interdependent.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

A triphasic constrained mixture model of engineered tissue formation under in vitro dynamic mechanical conditioning

While it has become axiomatic that mechanical signals promote in vitro engineered tissue formation, the underlying mechanisms remain largely unknown. Moreover, efforts to date to determine parameters for optimal extracellular matrix (ECM) development have been largely empirical. In the present work, we propose a two-pronged approach involving novel theoretical developments coupled with key experimental data to develop better mechanistic understanding of growth and development of dense connective tissue under mechanical stimuli. To describe cellular proliferation and ECM synthesis that occur at rates of days to weeks, we employ mixture theory to model the construct constituents as a nutrient-cell-ECM triphasic system, their transport, and their biochemical reactions. Dynamic conditioning protocols with frequencies around 1 Hz are described with multi-scale methods to couple the dissimilar time scales. Enhancement of nutrient transport due to pore fluid advection is upscaled into the growth model, and the spatially dependent ECM distribution describes the evolving poroelastic characteristics of the scaffold-engineered tissue construct. Simulation results compared favorably to the existing experimental data, and most importantly, distinguish between static and dynamic conditioning regimes. The theoretical framework for mechanically conditioned tissue engineering (TE) permits not only the formulation of novel and better-informed mechanistic hypothesis describing the phenomena underlying TE growth and development, but also the exploration/optimization of conditioning protocols in a rational manner.

Lessons learned from multi-scale modeling of the failing heart

Heart failure constitutes a major public health problem worldwide. Affected patients experience a number of changes in the electrical function of the heart that predispose to potentially lethal cardiac arrhythmias. Due to the multitude of electrophysiological changes that may occur during heart failure, the scientific literature is complex and sometimes ambiguous, perhaps because these findings are highly dependent on the etiology, the stage of heart failure, and the experimental model used to study these changes. Nevertheless, a number of common features of failing hearts have been documented. Prolongation of the action potential (AP) involving ion channel remodeling and alterations in calcium handling have been established as the hallmark characteristics of myocytes isolated from failing hearts. Intercellular uncoupling and fibrosis are identified as major arrhythmogenic factors. Multi-scale computational simulations are a powerful tool that complements experimental and clinical research. The development of biophysically detailed computer models of single myocytes and cardiac tissues has contributed greatly to our understanding of processes underlying excitation and repolarization in the heart. The electrical, structural, and metabolic remodeling that arises in cardiac tissues during heart failure has been addressed from different computational perspectives to further understand the arrhythmogenic substrate. This review summarizes the contributions from computational modeling and simulation to predict the underlying mechanisms of heart failure phenotypes and their implications for arrhythmogenesis, ranging from the cellular level to whole-heart simulations. The main aspects of heart failure are presented in several related sections. An overview of the main electrophysiological and structural changes that have been observed experimentally in failing hearts is followed by the description and discussion of the simulation work in this field at the cellular level, and then in 2D and 3D cardiac structures. The implications for arrhythmogenesis in heart failure are also discussed including therapeutic measures, such as drug effects and cardiac resynchronization therapy. Finally, the future challenges in heart failure modeling and simulation will be discussed.

Multi-scale exploration of the technical, economic, and environmental dimensions of bio-based chemical production

In recent years, bio-based chemicals have gained traction as a sustainable alternative to petrochemicals. However, despite rapid advances in metabolic engineering and synthetic biology, there remain significant economic and environmental challenges. In order to maximize the impact of research investment in a new bio-based chemical industry, there is a need for assessing the technological, economic, and environmental potentials of combinations of biomass feedstocks, biochemical products, bioprocess technologies, and metabolic engineering approaches in the early phase of development of cell factories. To address this issue, we have developed a comprehensive Multi-scale framework for modeling Sustainable Industrial Chemicals production (MuSIC), which integrates modeling approaches for cellular metabolism, bioreactor design, upstream/downstream processes and economic impact assessment. We demonstrate the use of the MuSIC framework in a case study where two major polymer precursors (1,3-propanediol and 3-hydroxypropionic acid) are produced from two biomass feedstocks (corn-based glucose and soy-based glycerol) through 66 proposed biosynthetic pathways in two host organisms (Escherichia coli and Saccharomyces cerevisiae). The MuSIC framework allows exploration of tradeoffs and interactions between economy-scale objectives (e.g. profit maximization, emission minimization), constraints (e.g. land-use constraints) and process- and cell-scale technology choices (e.g. strain design or oxygenation conditions). We demonstrate that economy-scale assessment can be used to guide specific strain design decisions in metabolic engineering, and that these design decisions can be affected by non-intuitive dependencies across multiple scales.

A multi-scale finite element model for investigation of chondrocyte mechanics in normal and medial meniscectomy human knee joint during walking

Mechanical signals experienced by chondrocytes (articular cartilage cells) modulate cell synthesis and cartilage health. Multi-scale modeling can be used to study how forces are transferred from joint surfaces through tissues to chondrocytes. Therefore, estimation of chondrocyte behavior during certain physical activities, such as walking, could provide information about how cells respond to normal and abnormal loading in joints. In this study, a 3D multi-scale model was developed for evaluating chondrocyte and surrounding peri- and extracellular matrix responses during gait loading within healthy and medial meniscectomy knee joints. The knee joint geometry was based on MRI, whereas the input used for gait loading was obtained from the literature. Femoral and tibial cartilages were modeled as fibril-reinforced poroviscoelastic materials, whereas menisci were considered as transversely isotropic. Fluid pressures in the chondrocyte and cartilage tissue increased up to 2MPa (an increase of 30%) in the meniscectomy joint compared to the normal, healthy joint. The elevated level of fluid pressure was observed during the entire stance phase of gait. A medial meniscectomy caused substantially larger (up to 60%) changes in maximum principal strains in the chondrocyte compared to those in the peri- or extracellular matrices. Chondrocyte volume or morphology did not change substantially due to a medial meniscectomy. Current findings suggest that during walking chondrocyte deformations are not substantially altered due to a medial meniscectomy, while abnormal joint loading exposes chondrocytes to elevated levels of fluid pressure and maximum principal strains (compared to strains in the peri- or extracellular matrices). These might contribute to cell viability and the onset of osteoarthritis.

Progression to multi-scale models and the application to food system intervention strategies

The aim of this article is to discuss how the systems science approach can be used to optimize intervention strategies in food animal systems. It advocates the idea that the challenges of maintaining a safe food supply are best addressed by integrating modeling and mathematics with biological studies critical to formulation of public policy to address these challenges. Much information on the biology and epidemiology of food animal systems has been characterized through single-discipline methods, but until now this information has not been thoroughly utilized in a fully integrated manner. The examples are drawn from our current research. The first, explained in depth, uses clinical mastitis to introduce the concept of dynamic programming to optimize management decisions in dairy cows (also introducing the curse of dimensionality problem). In the second example, a compartmental epidemic model for Johne's disease with different intervention strategies is optimized. The goal of the optimization strategy depends on whether there is a relationship between Johne's and Crohn's disease. If so, optimization is based on eradication of infection; if not, it is based on the cow's performance only (i.e., economic optimization, similar to the mastitis example). The third example focuses on food safety to introduce risk assessment using Listeria monocytogenes and Salmonella Typhimurium. The last example, practical interventions to effectively manage antibiotic resistance in beef and dairy cattle systems, introduces meta-population modeling that accounts for bacterial growth not only in the host (cow), but also in the cow's feed, drinking water and the housing environment. Each example stresses the need to progress toward multi-scale modeling. The article ends with examples of multi-scale systems, from food supply systems to Johne's disease. Reducing the consequences of foodborne illnesses (i.e., minimizing disease occurrence and associated costs) can only occur through an understanding of the system as a whole, including all its complexities. Thus the goal of future research should be to merge disciplines such as molecular biology, applied mathematics and social sciences to gain a better understanding of complex systems such as the food supply chain.

Multi-scale modeling for sustainable chemical production

With recent advances in metabolic engineering, it is now technically possible to produce a wide portfolio of existing petrochemical products from biomass feedstock. In recent years, a number of modeling approaches have been developed to support the engineering and decision-making processes associated with the development and implementation of a sustainable biochemical industry. The temporal and spatial scales of modeling approaches for sustainable chemical production vary greatly, ranging from metabolic models that aid the design of fermentative microbial strains to material and monetary flow models that explore the ecological impacts of all economic activities. Research efforts that attempt to connect the models at different scales have been limited. Here, we review a number of existing modeling approaches and their applications at the scales of metabolism, bioreactor, overall process, chemical industry, economy, and ecosystem. In addition, we propose a multi-scale approach for integrating the existing models into a cohesive framework. The major benefit of this proposed framework is that the design and decision-making at each scale can be informed, guided, and constrained by simulations and predictions at every other scale. In addition, the development of this multi-scale framework would promote cohesive collaborations across multiple traditionally disconnected modeling disciplines to achieve sustainable chemical production.