Toward a multi-scale computational model of arterial adaptation in hypertension: verification of a multi-cell agent based model

A perfectly imperfect engine: Utilizing the digital twin paradigm in pulmonary hypertension

Pulmonary hypertension (PH) is a severe medical condition with a number of treatment options, the majority of which are introduced without consideration of the underlying mechanisms driving it within an individual and thus a lack of tailored approach to treatment. The one exception is a patient presenting with apparent pulmonary arterial hypertension and shown to have vaso-responsive disease, whose clinical course and prognosis is significantly improved by high dose calcium channel blockers. PH is however characterized by a relative abundance of available data from patient cohorts, ranging from molecular data characterizing gene and protein expression in different tissues to physiological data at the organ level and clinical information. Integrating available data with mechanistic information at the different scales into computational models suggests an approach to a more personalized treatment of the disease using model-based optimization of interventions for individual patients. That is, constructing digital twins of the disease, customized to a patient, promises to be a key technology for personalized medicine, with the aim of optimizing use of existing treatments and developing novel interventions, such as new drugs. This article presents a perspective on this approach in the context of a review of existing computational models for different aspects of the disease, and it lays out a roadmap for a path to realizing it.

Arterial tissues and their inflammatory response to collagen damage: A continuum in silico model coupling nonlinear mechanics, molecular pathways, and cell behavior

Damage in soft biological tissues causes an inflammatory reaction that initiates a chain of events to repair the tissue. This work presents a continuum model and its in silico implementation that describe the cascade of mechanisms leading to tissue healing, coupling mechanical as well as chemo-biological processes. The mechanics is described by means of a Lagrangian nonlinear continuum mechanics framework and follows the homogenized constrained mixtures theory. Plastic-like damage, growth and remodeling as well as homeostasis are taken into account. The chemo-biological pathways account for two molecular and four cellular species, and are activated by damage of collagen molecules in fibers. To consider proliferation, differentiation, diffusion and chemotaxis of species, diffusion-advection-reaction equations are employed. To the best of authors' knowledge, the proposed model combines for the first time such high number of chemo-mechano-biological mechanisms in a consistent continuum biomechanical framework. The resulting set of coupled differential equations describe balance of linear momentum, evolution of kinematic variables as well as mass balance equations. They are discretized in time according to a backward Euler finite difference scheme, and in space through a finite element Galerkin discretization. The features of the model are firstly demonstrated presenting the species dynamics and highlighting the influence of damage intensities on the growth outcome. In terms of a biaxial test, the chemo-mechano-biological coupling and the model's applicability to reproduce normal as well as pathological healing are shown. A last numerical example underlines the model's applicability to complex loading scenarios and inhomogeneous damage distributions. Concluding, the present work contributes towards comprehensive in silico models in biomechanics and mechanobiology.

A Multiscale Approach for Predicting Certain Effects of Hand-Transmitted Vibration on Finger Arteries

Prolonged exposure to strong hand-arm vibrations can lead to vascular disorders such as Vibration White Finger (VWF). We modeled the onset of this peripheral vascular disease in two steps. The first consists in assessing the reduction in shearing forces exerted by the blood on the walls of the arteries (Wall Shear Stress—WSS) during exposure to vibrations. An acute but repeated reduction in WSS can lead to arterial stenosis characteristic of VWF. The second step is devoted to using a numerical mechano-biological model to predict this stenosis as a function of WSS. WSS is reduced by a factor of 3 during exposure to vibration of 40 m·s−2. This reduction is independent of the frequency of excitation between 31 Hz and 400 Hz. WSS decreases logarithmically when the amplitude of the vibration increases. The mechano-biological model simulated arterial stenosis of 30% for an employee exposed for 4 h a day for 10 years. This model also highlighted the chronic accumulation of matrix metalloproteinase 2. By considering daily exposure and the vibratory level, we can calculate the degree of stenosis, thus that of the disease for chronic exposure to vibrations.

Multiscale Modeling of Vascular Remodeling Induced by Wall Shear Stress

Objective

Hemodynamics-induced low wall shear stress (WSS) is one of the critical reasons leading to vascular remodeling. However, the coupling effects of WSS and cellular kinetics have not been clearly modeled. The aim of this study was to establish a multiscale modeling approach to reveal the vascular remodeling behavior under the interaction between the macroscale of WSS loading and the microscale of cell evolution.

Methods

Computational fluid dynamics (CFD) method and agent-based model (ABM), which have significantly different characteristics in temporal and spatial scales, were adopted to establish the multiscale model. The CFD method is for the second/organ scale, and the ABM is for the month/cell scale. The CFD method was used to simulate blood flow in a vessel and obtain the WSS in a vessel cross-section. The simulations of the smooth muscle cell (SMC) proliferation/apoptosis and extracellular matrix (ECM) generation/degradation in a vessel cross-section were performed by using ABM. During the simulation of the vascular remodeling procedure, the damage index of the SMC and ECM was defined as deviation from the obtained WSS. The damage index decreased gradually to mimic the recovery of WSS-induced vessel damage.

Results

(1) The significant wall thickening region was consistent with the low WSS region. (2) There was no evident change of wall thickness in the normal WSS region. (3) When the damage index approached to 0, the amount and distribution of SMCs and ECM achieved a stable state, and the vessel reached vascular homeostasis.

Conclusion

The established multiscale model can be used to simulate the vascular remodeling behavior over time under various WSS conditions.

Mechano-chemo-biological Computational Models for Arteries in Health, Disease and Healing: From Tissue Remodelling to Drug-eluting Devices

This review aims to highlight urgent priorities for the computational biomechanics community in the framework of mechano-chemo-biological models. Recent approaches, promising directions and open challenges on the computational modelling of arterial tissues in health and disease are introduced and investigated, together with in silico approaches for the analysis of drug-eluting stents that promote pharmacological-induced healing. The paper addresses a number of chemo-biological phenomena that are generally neglected in biomechanical engineering models but are most likely instrumental for the onset and the progression of arterial diseases. An interdisciplinary effort is thus encouraged for providing the tools for an effective in silico insight into medical problems. An integrated mechano-chemo-biological perspective is believed to be a fundamental missing piece for crossing the bridge between computational engineering and life sciences, and for bringing computational biomechanics into medical research and clinical practice.

Agent-based model provides insight into the mechanisms behind failed regeneration following volumetric muscle loss injury

Skeletal muscle possesses a remarkable capacity for repair and regeneration following a variety of injuries. When successful, this highly orchestrated regenerative process requires the contribution of several muscle resident cell populations including satellite stem cells (SSCs), fibroblasts, macrophages and vascular cells. However, volumetric muscle loss injuries (VML) involve simultaneous destruction of multiple tissue components (e.g., as a result of battlefield injuries or vehicular accidents) and are so extensive that they exceed the intrinsic capability for scarless wound healing and result in permanent cosmetic and functional deficits. In this scenario, the regenerative process fails and is dominated by an unproductive inflammatory response and accompanying fibrosis. The failure of current regenerative therapeutics to completely restore functional muscle tissue is not surprising considering the incomplete understanding of the cellular mechanisms that drive the regeneration response in the setting of VML injury. To begin to address this profound knowledge gap, we developed an agent-based model to predict the tissue remodeling response following surgical creation of a VML injury. Once the model was able to recapitulate key aspects of the tissue remodeling response in the absence of repair, we validated the model by simulating the tissue remodeling response to VML injury following implantation of either a decellularized extracellular matrix scaffold or a minced muscle graft. The model suggested that the SSC microenvironment and absence of pro-differentiation SSC signals were the most important aspects of failed muscle regeneration in VML injuries. The major implication of this work is that agent-based models may provide a much-needed predictive tool to optimize the design of new therapies, and thereby, accelerate the clinical translation of regenerative therapeutics for VML injuries.

[Review of studies on the biomechanical modelling of the coupling effect between stent degradation and blood vessel remodeling]

The dynamic coupling of stent degradation and vessel remodeling can influence not only the structural morphology and material property of stent and vessel, but also the development of in-stent restenosis. The research achievements of biomechanical modelling and analysis of stent degradation and vessel remodeling were reviewed; several noteworthy research perspectives were addressed, a stent-vessel coupling model was developed based on stent damage function and vessel growth function, and then concepts of matching ratio and risk factor were established so as to evaluate the treatment effect of stent intervention, which may lay the scientific foundation for the structure design, mechanical analysis and clinical application of biodegradable stent.

Notch in mechanotransduction - from molecular mechanosensitivity to tissue mechanostasis

Tissue development and homeostasis are controlled by mechanical cues. Perturbation of the mechanical equilibrium triggers restoration of mechanostasis through changes in cell behavior, while defects in these restorative mechanisms lead to mechanopathologies, for example, osteoporosis, myopathies, fibrosis or cardiovascular disease. Therefore, sensing mechanical cues and integrating them with the biomolecular cell fate machinery is essential for the maintenance of health. The Notch signaling pathway regulates cell and tissue fate in nearly all tissues. Notch activation is directly and indirectly mechanosensitive, and regulation of Notch signaling, and consequently cell fate, is integral to the cellular response to mechanical cues. Fully understanding the dynamic relationship between molecular signaling, tissue mechanics and tissue remodeling is challenging. To address this challenge, engineered microtissues and computational models play an increasingly large role. In this Review, we propose that Notch takes on the role of a 'mechanostat', maintaining the mechanical equilibrium of tissues. We discuss the reciprocal role of Notch in the regulation of tissue mechanics, with an emphasis on cardiovascular tissues, and the potential of computational and engineering approaches to unravel the complex dynamic relationship between mechanics and signaling in the maintenance of cell and tissue mechanostasis.

Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells

Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of [Formula: see text] and [Formula: see text] fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris-Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.

Lateral induction limits the impact of cell connectivity on Notch signaling in arterial walls

It is well known that arteries grow and remodel in response to mechanical stimuli. Vascular smooth muscle cells are the main mediators of this process, as they can switch phenotype from contractile to synthetic, and vice-versa, based on the surrounding bio-chemo-mechanical stimuli. A correct regulation of this phenotypic switch is fundamental to obtain and maintain arterial homeostasis. Notch, a mechanosensitive signaling pathway, is one of the main regulators of the vascular smooth muscle cell phenotype. Therefore, understanding Notch dynamics is key to elucidate arterial growth, remodeling, and mechanobiology. We have recently developed a one-dimensional agent-based model to investigate Notch signaling in arteries. However, due to its one-dimensional formulation, the model cannot be adopted to study complex nonsymmetrical geometries and, importantly, it cannot capture the realistic "cell connectivity" in arteries, here defined as the number of cell neighbors. Notch functions via direct cell-cell contact; thus, the number of cell neighbors could be an essential feature of Notch dynamics. Here, we extended the agent-based model to a two-dimensional formulation, to investigate the effects of cell connectivity on Notch dynamics and cell phenotypes in arteries. The computational results, supported by a sensitivity analysis, indicate that cell connectivity has marginal effects when Notch dynamics is dominated by the process of lateral induction, which induces all cells to have a uniform phenotype. When lateral induction is weaker, cells exhibit a nonuniform phenotype distribution and the percentage of synthetic cells within an artery depends on the number of neighbors.

A fully coupled framework for in silico investigation of in-stent restenosis

Finite element analysis (FEA) can be implemented along with Agent-based model (ABM) to investigate the biomechanical and mechanobiological mechanisms of pathophysiological processes. However, traditional ABM-FEA approaches are often partially coupled and lack the feedback responses from biological analysis. To overcome this problem, a fully coupled ABM-FEA framework is developed in this paper by linking the macro-scale and cell-scale modules bi-directionally. Numerical studies of the in-stent restenosis process are conducted using the proposed approach and comparisons are made between the two types of frameworks. A reduction in lumen loss rate, which is possibly caused by the time-varying stresses, is observed in the fully coupled simulations. The re-endothelialisation process is also simulated under different frameworks and the simulation results show strong inhibition of endothelial cells to vascular restenosis. The proposed method is proved to be effective to explain the biomechanical-mechanobiological coupling characteristics of the restenosis problem and can be utilized for stent design and optimization.

Agent-based model illustrates the role of the microenvironment in regeneration in healthy and mdx skeletal muscle

Duchenne muscular dystrophy (DMD) is a progressive muscle-wasting disease with no effective treatment. Multiple mechanisms are thought to contribute to muscle wasting, including increased susceptibility to contraction-induced damage, chronic inflammation, fibrosis, altered satellite stem cell (SSC) dynamics, and impaired regenerative capacity. The goals of this project were to 1) develop an agent-based model of skeletal muscle that predicts the dynamic regenerative response of muscle cells, fibroblasts, SSCs, and inflammatory cells as a result of contraction-induced injury, 2) calibrate and validate the model parameters based on comparisons with published experimental measurements, and 3) use the model to investigate how changing isolated and combined factors known to be associated with DMD (e.g., altered fibroblast or SSC behaviors) influence muscle regeneration. Our predictions revealed that the percent of injured muscle that recovered 28 days after injury was dependent on the peak SSC counts following injury. In simulations with near-full cross-sectional area recovery (healthy, 4-wk mdx, 3-mo mdx), the SSC counts correlated with the extent of initial injury; however, in simulations with impaired regeneration (9-mo mdx), the peak SSC counts were suppressed relative to initial injury. The differences in SSC counts between these groups were emergent predictions dependent on altered microenvironment factors known to be associated with DMD. Multiple cell types influenced the peak number of SSCs, but no individual parameter predicted the differences in SSC counts. This finding suggests that interventions to target the microenvironment rather than SSCs directly could be an effective method for improving regeneration in impaired muscle. NEW & NOTEWORTHY A computational model predicted that satellite stem cell (SSC) counts are correlated with muscle cross-sectional area (CSA) recovery following injury. In simulations with impaired CSA recovery, SSC counts are suppressed relative to healthy muscle. The suppressed SSC counts were an emergent model prediction, because all simulations had equal initial SSC counts. Fibroblast and anti-inflammatory macrophage counts influenced SSC counts, but no single factor was able to predict the pathological differences in SSC counts that lead to impaired regeneration.

Agent-based computational model of retinal angiogenesis simulates microvascular network morphology as a function of pericyte coverage

OBJECTIVE

Define a role for perivascular cells during developmental retinal angiogenesis in the context of EC Notch1-DLL4 signaling at the multicellular network level.

METHODS

The retinal vasculature is highly sensitive to growth factor-mediated intercellular signaling. Although EC signaling has been explored in detail, it remains unclear how PC function to modulate these signals that lead to a diverse set of vascular network patterns in health and disease. We have developed an ABM of retinal angiogenesis that incorporates both ECs and PCs to investigate the formation of vascular network patterns as a function of pericyte coverage. We use our model to test the hypothesis that PC modulate Notch1-DLL4 signaling in endothelial cell-endothelial cell interactions.

RESULTS

Agent-based model (ABM) simulations that include PCs more accurately predict experimentally observed vascular network morphologies than simulations that lack PCs, suggesting that PCs may influence sprouting behaviors through physical blockade of endothelial intercellular connections.

CONCLUSIONS

This study supports a role for PCs as a physical buffer to signal propagation during vascular network formation-a barrier that may be important for generating healthy microvascular network patterns.

Mechanosensitivity of Jagged-Notch signaling can induce a switch-type behavior in vascular homeostasis

Hemodynamic forces and Notch signaling are both known as key regulators of arterial remodeling and homeostasis. However, how these two factors integrate in vascular morphogenesis and homeostasis is unclear. Here, we combined experiments and modeling to evaluate the impact of the integration of mechanics and Notch signaling on vascular homeostasis. Vascular smooth muscle cells (VSMCs) were cyclically stretched on flexible membranes, as quantified via video tracking, demonstrating that the expression of Jagged1, Notch3, and target genes was down-regulated with strain. The data were incorporated in a computational framework of Notch signaling in the vascular wall, where the mechanical load was defined by the vascular geometry and blood pressure. Upon increasing wall thickness, the model predicted a switch-type behavior of the Notch signaling state with a steep transition of synthetic toward contractile VSMCs at a certain transition thickness. These thicknesses varied per investigated arterial location and were in good agreement with human anatomical data, thereby suggesting that the Notch response to hemodynamics plays an important role in the establishment of vascular homeostasis.

Mechanobiological model of arterial growth and remodeling

A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).

An agent-based model of leukocyte transendothelial migration during atherogenesis

A vast amount of work has been dedicated to the effects of hemodynamics and cytokines on leukocyte adhesion and trans-endothelial migration (TEM) and subsequent accumulation of leukocyte-derived foam cells in the artery wall. However, a comprehensive mechanobiological model to capture these spatiotemporal events and predict the growth and remodeling of an atherosclerotic artery is still lacking. Here, we present a multiscale model of leukocyte TEM and plaque evolution in the left anterior descending (LAD) coronary artery. The approach integrates cellular behaviors via agent-based modeling (ABM) and hemodynamic effects via computational fluid dynamics (CFD). In this computational framework, the ABM implements the diffusion kinetics of key biological proteins, namely Low Density Lipoprotein (LDL), Tissue Necrosis Factor alpha (TNF-α), Interlukin-10 (IL-10) and Interlukin-1 beta (IL-1β), to predict chemotactic driven leukocyte migration into and within the artery wall. The ABM also considers wall shear stress (WSS) dependent leukocyte TEM and compensatory arterial remodeling obeying Glagov's phenomenon. Interestingly, using fully developed steady blood flow does not result in a representative number of leukocyte TEM as compared to pulsatile flow, whereas passing WSS at peak systole of the pulsatile flow waveform does. Moreover, using the model, we have found leukocyte TEM increases monotonically with decreases in luminal volume. At critical plaque shapes the WSS changes rapidly resulting in sudden increases in leukocyte TEM suggesting lumen volumes that will give rise to rapid plaque growth rates if left untreated. Overall this multi-scale and multi-physics approach appropriately captures and integrates the spatiotemporal events occurring at the cellular level in order to predict leukocyte transmigration and plaque evolution.

Computational Modeling of Muscle Regeneration and Adaptation to Advance Muscle Tissue Regeneration Strategies

Skeletal muscle has an exceptional ability to regenerate and adapt following injury. Tissue engineering approaches (e.g. cell therapy, scaffolds, and pharmaceutics) aimed at enhancing or promoting muscle regeneration from severe injuries are a promising and active field of research. Computational models are beginning to advance the field by providing insight into regeneration mechanisms and therapies. In this paper, we summarize the contributions computational models have made to understanding muscle remodeling and the functional implications thereof. Next, we describe a new agent-based computational model of skeletal muscle inflammation and regeneration following acute muscle injury. Our computational model simulates the recruitment and cellular behaviors of key inflammatory cells (e.g. neutrophils and M1 and M2 macrophages) and their interactions with native muscle cells (muscle fibers, satellite stem cells, and fibroblasts) that result in the clearance of necrotic tissue and muscle fiber regeneration. We demonstrate the ability of the model to track key regeneration metrics during both unencumbered regeneration and in the case of impaired macrophage function. We also use the model to simulate regeneration enhancement when muscle is primed with inflammatory cells prior to injury, which is a putative therapeutic intervention that has not yet been investigated experimentally. Computational modeling of muscle regeneration, pursued in combination with experimental analyses, provides a quantitative framework for evaluating and predicting muscle regeneration and enables the rational design of therapeutic strategies for muscle recovery.

Prior Distributions of Material Parameters for Bayesian Calibration of Growth and Remodeling Computational Model of Abdominal Aortic Wall

For the accurate prediction of the vascular disease progression, there is a crucial need for developing a systematic tool aimed toward patient-specific modeling. Considering the interpatient variations, a prior distribution of model parameters has a strong influence on computational results for arterial mechanics. One crucial step toward patient-specific computational modeling is to identify parameters of prior distributions that reflect existing knowledge. In this paper, we present a new systematic method to estimate the prior distribution for the parameters of a constrained mixture model using previous biaxial tests of healthy abdominal aortas (AAs). We investigate the correlation between the estimated parameters for each constituent and the patient's age and gender; however, the results indicate that the parameters are correlated with age only. The parameters are classified into two groups: Group-I in which the parameters ce, ck1, ck2, cm2,Ghc, and ϕe are correlated with age, and Group-II in which the parameters cm1, Ghm, G1e, G2e, and α are not correlated with age. For the parameters in Group-I, we used regression associated with age via linear or inverse relations, in which their prior distributions provide conditional distributions with confidence intervals. For Group-II, the parameter estimated values were subjected to multiple transformations and chosen if the transformed data had a better fit to the normal distribution than the original. This information improves the prior distribution of a subject-specific model by specifying parameters that are correlated with age and their transformed distributions. Therefore, this study is a necessary first step in our group's approach toward a Bayesian calibration of an aortic model. The results from this study will be used as the prior information necessary for the initialization of Bayesian calibration of a computational model for future applications.

Do endothelial cells dream of eclectic shape?

Endothelial cells (ECs) exhibit dramatic plasticity of form at the single- and collective-cell level during new vessel growth, adult vascular homeostasis, and pathology. Understanding how, when, and why individual ECs coordinate decisions to change shape, in relation to the myriad of dynamic environmental signals, is key to understanding normal and pathological blood vessel behavior. However, this is a complex spatial and temporal problem. In this review we show that the multidisciplinary field of Adaptive Systems offers a refreshing perspective, common biological language, and straightforward toolkit that cell biologists can use to untangle the complexity of dynamic, morphogenetic systems.

Investigating biocomplexity through the agent-based paradigm

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex.

A prospective overview of the essential requirements in molecular modeling for nanomedicine design

Nanotechnology has presented many new challenges and opportunities in the area of nanomedicine design. The issues related to nanoconjugation, nanosystem-mediated targeted drug delivery, transitional stability of nanovehicles, the integrity of drug transport, drug-delivery mechanisms and chemical structural design require a pre-estimated and determined course of assumptive actions with property and characteristic estimations for optimal nanomedicine design. Molecular modeling in nanomedicine encompasses these pre-estimations and predictions of pertinent design data via interactive computographic software. Recently, an increasing amount of research has been reported where specialized software is being developed and employed in an attempt to bridge the gap between drug discovery, materials science and biology. This review provides an assimilative and concise incursion into the current and future strategies of molecular-modeling applications in nanomedicine design and aims to describe the utilization of molecular models and theoretical-chemistry computographic techniques for expansive nanomedicine design and development.

Novel multiscale modeling tool applied to Pseudomonas aeruginosa biofilm formation

Multiscale modeling is used to represent biological systems with increasing frequency and success. Multiscale models are often hybrids of different modeling frameworks and programming languages. We present the MATLAB-NetLogo extension (MatNet) as a novel tool for multiscale modeling. We demonstrate the utility of the tool with a multiscale model of Pseudomonas aeruginosa biofilm formation that incorporates both an agent-based model (ABM) and constraint-based metabolic modeling. The hybrid model correctly recapitulates oxygen-limited biofilm metabolic activity and predicts increased growth rate via anaerobic respiration with the addition of nitrate to the growth media. In addition, a genome-wide survey of metabolic mutants and biofilm formation exemplifies the powerful analyses that are enabled by this computational modeling tool.

Multiscale computational models of complex biological systems

Integration of data across spatial, temporal, and functional scales is a primary focus of biomedical engineering efforts. The advent of powerful computing platforms, coupled with quantitative data from high-throughput experimental methodologies, has allowed multiscale modeling to expand as a means to more comprehensively investigate biological phenomena in experimentally relevant ways. This review aims to highlight recently published multiscale models of biological systems, using their successes to propose the best practices for future model development. We demonstrate that coupling continuous and discrete systems best captures biological information across spatial scales by selecting modeling techniques that are suited to the task. Further, we suggest how to leverage these multiscale models to gain insight into biological systems using quantitative biomedical engineering methods to analyze data in nonintuitive ways. These topics are discussed with a focus on the future of the field, current challenges encountered, and opportunities yet to be realized.

Extracellular matrix and the mechanics of large artery development

The large, elastic arteries, as their name suggests, provide elastic distention and recoil during the cardiac cycle in vertebrate animals. The arteries are distended from the pressure of ejecting blood during the active contraction of the left ventricle (LV) during systole and recoil to their original dimensions during relaxation of the LV during diastole. The cyclic distension occurs with minimal energy loss, due to the elastic properties of one of the major structural extracellular matrix (ECM) components, elastin. The maximum distension is limited to prevent damage to the artery by another major ECM component, collagen. The mix of ECM components in the wall largely determines the passive mechanical behavior of the arteries and the subsequent load on the heart during systole. While much research has focused on initial artery formation, there has been less attention on the continuing development of the artery to produce the mature composite wall complete with endothelial cells (ECs), smooth muscle cells (SMCs), and the necessary mix of ECM components for proper cardiovascular function. This review focuses on the physiology of large artery development, including SMC differentiation and ECM production. The effects of hemodynamic forces and ECM deposition on the evolving arterial structure and function are discussed. Human diseases and mouse models with genetic mutations in ECM proteins that affect large artery development are summarized. A review of constitutive models and growth and remodeling theories is presented, along with future directions to improve understanding of ECM and the mechanics of large artery development.

Integration of experimental and computational approaches to sprouting angiogenesis

PURPOSE OF REVIEW

We summarize recent experimental and computational studies that investigate molecular and cellular mechanisms of sprouting angiogenesis. We discuss how experimental tools have unveiled new opportunities for computational modeling by providing detailed phenomenological descriptions and conceptual models of cell-level behaviors underpinned by high-quality molecular data. Using recent examples, we show how new understanding results from bridging computational and experimental approaches.

RECENT FINDINGS

Experimental data extends beyond the tip cell vs. stalk cell paradigm, and involves numerous molecular inputs such as vascular endothelial growth factor and Notch. This data is being used to generate and validate computational models, which can then be used to predict the results of hypothetical experiments that are difficult to perform in the laboratory, and to generate new hypotheses that account for system-wide interactions. As a result of this integration, descriptions of critical gradients of growth factor-receptor complexes have been generated, and new modulators of cell behavior have been described.

SUMMARY

We suggest that the recent emphasis on the different stages of sprouting angiogenesis, and integration of experimental and computational approaches, should provide a way to manage the complexity of this process and help identify new regulatory paradigms and therapeutic targets.

Modelling the lymphatic system: challenges and opportunities

The lymphatic system is a vital part of the circulatory and immune systems, and plays an important role in homeostasis by controlling extracellular fluid volume and in combating infection. Nevertheless, there is a notable disparity in terms of research effort expended in relation to the treatment of lymphatic diseases in contrast to the cardiovascular system. While similarities to the cardiovascular system exist, there are considerable differences in their anatomy and physiology. This review outlines some of the challenges and opportunities for those engaged in modelling biological systems. The study of the lymphatic system is still in its infancy, the vast majority of the models presented in the literature to date having been developed since 2003. The number of distinct models and their variants are few in number, and only one effort has been made thus far to study the entire lymphatic network; elements of the lymphatic system such as the nodes, which act as pumps and reservoirs, have not been addressed by mathematical models. Clearly, more work will be necessary in combination with experimental verification in order to progress and update the knowledge on the function of the lymphatic system. As our knowledge and understanding of its function increase, new and more effective treatments of lymphatic diseases are bound to emerge.

Ensuring congruency in multiscale modeling: towards linking agent based and continuum biomechanical models of arterial adaptation

There is a need to develop multiscale models of vascular adaptations to understand tissue-level manifestations of cellular level mechanisms. Continuum-based biomechanical models are well suited for relating blood pressures and flows to stress-mediated changes in geometry and properties, but less so for describing underlying mechanobiological processes. Discrete stochastic agent-based models are well suited for representing biological processes at a cellular level, but not for describing tissue-level mechanical changes. We present here a conceptually new approach to facilitate the coupling of continuum and agent-based models. Because of ubiquitous limitations in both the tissue- and cell-level data from which one derives constitutive relations for continuum models and rule-sets for agent-based models, we suggest that model verification should enforce congruency across scales. That is, multiscale model parameters initially determined from data sets representing different scales should be refined, when possible, to ensure that common outputs are consistent. Potential advantages of this approach are illustrated by comparing simulated aortic responses to a sustained increase in blood pressure predicted by continuum and agent-based models both before and after instituting a genetic algorithm to refine 16 objectively bounded model parameters. We show that congruency-based parameter refinement not only yielded increased consistency across scales, it also yielded predictions that are closer to in vivo observations.