Computational Growth Model Research Articles

AMBER: A Modular Model for Tumor Growth, Vasculature and Radiation Response.

Computational models of tumor growth are valuable for simulating the dynamics of cancer progression and treatment responses. In particular, agent-based models (ABMs) tracking individual agents and their interactions are useful for their flexibility and ability to model complex behaviors. However, ABMs have often been confined to small domains or, when scaled up, have neglected crucial aspects like vasculature. Additionally, the integration into tumor ABMs of precise radiation dose calculations using gold-standard Monte Carlo (MC) methods, crucial in contemporary radiotherapy, has been lacking. Here, we introduce AMBER, an Agent-based fraMework for radioBiological Effects in Radiotherapy that computationally models tumor growth and radiation responses. AMBER is based on a voxelized geometry, enabling realistic simulations at relevant pre-clinical scales by tracking temporally discrete states stepwise. Its hybrid approach, combining traditional ABM techniques with continuous spatiotemporal fields of key microenvironmental factors such as oxygen and vascular endothelial growth factor, facilitates the generation of realistic tortuous vascular trees. Moreover, AMBER is integrated with TOPAS, an MC-based particle transport algorithm that simulates heterogeneous radiation doses. The impact of radiation on tumor dynamics considers the microenvironmental factors that alter radiosensitivity, such as oxygen availability, providing a full coupling between the biological and physical aspects. Our results show that simulations with AMBER yield accurate tumor evolution and radiation treatment outcomes, consistent with established volumetric growth laws and radiobiological understanding. Thus, AMBER emerges as a promising tool for replicating essential features of tumor growth and radiation response, offering a modular design for future expansions to incorporate specific biological traits.

Modulation of mechanosensitive genes during embryonic aortic arch development.

Early embryonic aortic arches (AA) are a dynamic vascular structures that are in the process of shaping into the great arteries of cardiovascular system. Previously, a time-lapsed mechanosensitive gene expression map was established for AA subject to altered mechanical loads in the avian embryo. To validate this map, we investigated effects on vascular microstructure and material properties following the perturbation of key genes using an in-house microvascular gene knockdown system. All siRNA vectors show a decrease in the expression intensity of desired genes with no significant differences between vectors. In TGFβ3 knockdowns, we found a reduction in expression intensities of TGFβ3 (≤76%) and its downstream targets such as ELN (≤99.6%), Fbn1 (≤60%), COL1 (≤52%) and COL3 (≤86%) and an increase of diameter in the left AA (23%). MMP2 knockdown also reduced expression levels in MMP2 (≤30%) and a 6-fold increase in its downstream target COL3 with a decrease in stiffness of the AA wall and an increase in the diameter of the AA (55%). These in vivo measurements were confirmed using immunohistochemistry, western blotting and a computational growth model of the vascular extracellular matrix (ECM). Localized spatial genetic modification of the aortic arch region governs the vascular phenotype and ECM composition of the embryo and can be integrated with mechanically-induced congenital heart disease models.

Mathematical and computational modeling of tomato growth for 3D printing

Mathematical and computational modeling of tomato growth for 3D printing

Computational modeling of microalgal biofilm growth in heterogeneous rotating algal biofilm reactors (RABRs) for wastewater treatment

Rotating algal biofilm reactors (RABRs) are innovative systems designed to cultivate microalgae biofilms efficiently. In this paper, we have developed a novel mathematical model to accurately capture the growth dynamics of algae biofilms within RABR. By considering the spatial heterogeneity of the RABR, we introduce a PDE-based model that addresses the spatial variations across the substratum, enabling a more accurate simulation of biofilm growth in RABRs. The photosynthesis process is modeled through reactive kinetics, driving the growth of the algae biofilm. To analyze the system's behavior, we employ finite difference numerical methods to solve the complex PDE model. We then conduct extensive numerical simulations to understand algae biofilm growth in the RABR environment under various operational factors and environmental conditions. One primary focus in these simulations is to investigate the impact of various harvesting strategies, harvesting frequencies, light intensity, and light exposure on the overall biomass productivity of the algae biofilm. The numerical results provide valuable insights into optimizing algae biofilm growth and designing harvesting techniques in RABR systems. Our proposed novel mathematical model provides an effective platform for the theoretical investigation and design of RABRs for wastewater treatment.

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta

Thoracic aortic aneurysms are characterized by a progressive loss of biomechanical functionality resulting from degenerative changes in wall composition, microstructure, and mechanical properties. Among the many causes of these lesions, Marfan syndrome is the most common heritable condition, resulting from mutations to the gene that codes the elastin-associated glycoprotein fibrillin-1. Key histopathological features of the aneurysmal Marfan aorta include extensive degradation of elastic fibres, significant remodelling of fibrillar collagens and compromised smooth muscle cell function. Computational growth and remodelling models have confirmed the importance of compromised elastic fibre integrity in aneurysmal dilatation, but we show here that this contributor alone is not sufficient to describe biomechanical data collected from the two most common mouse models of Marfan syndrome. Rather, our simulations suggest that compromised mechanosensing and mechanoregulation of extracellular matrix by mural cells also play central roles in the natural history. Determination of optimal disease-contributing parameters further suggests a rapid reduction in cellular mechanosensing and mechanoregulation relative to diminished elastic fibre integrity, highlighting the importance of inter- and intra-lamellar elastin in the Marfan aorta. Aneurysmal dilatation in Marfan syndrome thus results from multiple contributors to progressive degeneration of the aortic wall, and computational mechanobiological models can help disentangle these contributions.

A multiphysical computational model of myocardial growth adopted to human pathological ventricular remodelling

We present a novel three-dimensional constitutive model that describes an electro-visco-elastic-growth response on the myocardium with a fully implicit staggered solution procedure for the strong electromechanical coupling. The novel formulations of the myocardium allows us to simulate and analyze the remodelling of actively contracting human ventricular heart models which consist of growing viscoelastic myocardium where the growth direction is determined based on its mechanical state at each time step. The total deformation gradient is multiplicatively decomposed into a mechanical-active part and a growth part, where the mechanical-active part is further split into elastic, viscous, and active components. Unconditional stability of time integration is ensured by a backward Euler integration scheme. With the developed model, the myocardium can experience stretch-driven longitudinal (fibre) growth and stress-driven transverse (cross-fibre) growth. To validate the developed approach, two simulations regarding pathological ventricular remodelling are implemented: two divergent types of remodelling of a left ventricular model driven by hemodynamic overloads and ventricular remodelling triggered by acute myocardial ischemia in a biventricular heart model.

Persistent non-homeostatic remodeling of aortic collagen following a brief episode of hypertension: A computational study

The healthy adult aorta exhibits a remarkable homeostatic ability to respond to sustained changes in hemodynamic loads under many circumstances, but this mechanical homeostasis can be compromised or lost in natural aging and diverse pathological processes. Herein, we investigate persistent non-homeostatic changes in the composition and mechanical properties of the thoracic aorta in adult wild-type mice following 14 days of angiotensin II-induced hypertension. We employ a multiscale computational model of arterial growth and remodeling driven by mechanosensitive and angiotensin II-related cell signaling pathways. We find that experimentally observed findings can only be recapitulated computationally if the collagen deposited during the transient period of hypertension has altered properties (deposition stretch, fiber angle, crosslinking) compared with the collagen produced in the original homeostatic state. Some of these changes are predicted to persist for at least six months after blood pressure is restored to normal levels, consistent with the experimental findings.

A multiscale computational model of arterial growth and remodeling including Notch signaling.

Blood vessels grow and remodel in response to mechanical stimuli. Many computational models capture this process phenomenologically, by assuming stress homeostasis, but this approach cannot unravel the underlying cellular mechanisms. Mechano-sensitive Notch signaling is well-known to be key in vascular development and homeostasis. Here, we present a multiscale framework coupling a constrained mixture model, capturing the mechanics and turnover of arterial constituents, to a cell-cell signaling model, describing Notch signaling dynamics among vascular smooth muscle cells (SMCs) as influenced by mechanical stimuli. Tissue turnover was regulated by both Notch activity, informed by in vitro data, and a phenomenological contribution, accounting for mechanisms other than Notch. This novel framework predicted changes in wall thickness and arterial composition in response to hypertension similar to previous in vivo data. The simulations suggested that Notch contributes to arterial growth in hypertension mainly by promoting SMC proliferation, while other mechanisms are needed to fully capture remodeling. The results also indicated that interventions to Notch, such as external Jagged ligands, can alter both the geometry and composition of hypertensive vessels, especially in the short term. Overall, our model enables a deeper analysis of the role of Notch and Notch interventions in arterial growth and remodeling and could be adopted to investigate therapeutic strategies and optimize vascular regeneration protocols.

Modeling of Growth using an Immersed Finite Element Method

AbstractTo prevent remeshing, we explore the use of a non‐boundary‐fitted finite element method for the computational modeling of growth including contact mechanics. Accordingly, we utilize a mesh‐related mapping procedure for the use of implicit geometry description by a level set function within the framework of immersed methods. Hence, our framework provides a setting to include patient‐specific geometries based on imaging data as we use a level set function for the implicit geometry description. In this contribution, we show that the proposed approach is a viable alternative for problems with mesh‐related obstacles, in particular when large growth simulations on complex patient‐specific geometries are of primary interest.

Verification, validation, and parameter study of a computational model for corrosion pit growth adopting the level-set method. Part I: Corrosion

Corrosion is a phenomenon observed in structural components in corrosive environments such as pipelines, bridges, aircrafts, turbines, etc. The computational model of corrosion should enjoy two features: a) accurately considering the electrochemistry of corrosion and b) properly dealing with the moving interface between solid and electrolyte. There are several approaches to model corrosion such as using FEM with mesh refinement algorithms, combining FEM and level-set method, employing finite volume methods, adopting peridynamic formulation, and utilizing phase field models. Because of its accuracy, lower computational cost, and robust dealing with multiple pit merging, the model which combines FEM with level-set method is selected to be more extensively assessed in this paper. Part I focuses on demonstrating the model’s capabilities of simulating pitting corrosion through a set of numerical examples which include numerical solution verification, experimental validation, and uncertainty quantification of model parameters and properties.

WITHDRAWN: Computational modeling of multiple myeloma growth and tumor aggregate formation

The mechanical signals received from the multiple myeloma microenvironment play a key role in bone marrow cancer development. However, the complexity of the cues received hinders the development of a novel and effective treatment. As such, agent-based computational models that consider coupled fluid and mechanical dynamics for every single cell may provide distinct perspectives and key information to adequately identify the specific tumor microenvironment. We have developed a novel 3D agent-based computational model that considers coupled fluid and particle dynamics to study multiple myeloma cell growth in response to the stimuli received from the cell microenvironment. Cell processes such as cell–cell interactions, cell maturation, and cell proliferation were considered by implementing user-defined functions in the commercial software Fluent. To calibrate and validate the developed model, we performed two experiments comparing the results of cell sedimentation velocity and cell proliferation with in vitro results. The results of the model were also compared with a finite element method model previously developed in-house. As the cells proliferated, the number of cell–cell and cell–extracellular matrix contacts increased ( ∼ 6.1% per hour), which reduced the cell maturation time ( ∼ 69.7%). Once the cells started to form aggregates, the proliferation process speeded up ( ∼ 9.9% per hour). Saturation of cell proliferation was observed after long-term simulation. Our results are qualitatively consistent with the in vitro results. In addition, they show that the cell proliferation rate increased as the number of cells considered increased. Furthermore, in a very dense aggregation, the lack of space prevented proliferation of internal cells. The model developed herein has significant advantages compared to the previous model in terms of computation, as it results in a significant reduction (84%–91%) in computational costs, thus allowing a more realistic simulation. • Agent-based model coupled with a continuous fluid model for Multiple Myeloma cell simulation. • Based on specific cell conditions, the model has been applied to study Multiple Myeloma cells’ growth and tumor aggregation formation. • Results have been validated with the literature, in-vitro experiments developed by the authors, and a previous in-house Finite Element model. • Cell maturation is stimulated by the increase in cell–cell and cell-ECM interactions, but it is inhibited by a lack of space in the inner parts of cell aggregations. • Computational costs have been reduced when compared to the previous Finite Element model.

Semi-Automated Quantitative Evaluation of Neuron Developmental Morphology In Vitro Using the Change-Point Test.

Neuron morphology gives rise to distinct axons and dendrites and plays an essential role in neuronal functionality and circuit dynamics. In rat hippocampal neurons, morphological development occurs over roughly one week in vitro. This development has been qualitatively described as occurring in 5 stages. Still, there is a need to quantify cell growth to monitor cell culture health, understand cell responses to sensory cues, and compare experimental results and computational growth model predictions. To address this need, embryonic rat hippocampal neurons were observed in vitro over six days, and their processes were quantified using both standard morphometrics (degree, number of neurites, total length, and tortuosity) and new metrics (distance between change points, relative turning angle, and the number of change points) based on the Change-Point Test to track changes in path trajectories. Of the standard morphometrics, the total length of neurites per cell and the number of endpoints were significantly different between 0.5, 1.5, and 4 days in vitro, which are typically associated with Stages 2-4. Using the Change-Point Test, the number of change points and the average distance between change points per cell were also significantly different between those key time points. This work highlights key quantitative characteristics, both among common and novel morphometrics, that can describe neuron development in vitro and provides a foundation for analyzing directional changes in neurite growth for future studies.

Biodegradable external wrapping promotes favorable adaptation in an ovine vein graft model

Vein grafts, the most commonly used conduits in multi-vessel coronary artery bypass grafting surgery, have high intermediate- and long-term failure rates. The abrupt and marked increase in hemodynamic loads on the vein graft is a known contributor to failure. Recent computational modeling suggests that veins can more successfully adapt to an increase in mechanical load if the rate of loading is gradual. Applying an external wrap or support at the time of surgery is one way to reduce the transmural load, and this approach has improved performance relative to an unsupported vein graft in several animal studies. Yet, a clinical trial in humans has shown benefits and drawbacks, and mechanisms by which an external wrap affects vein graft adaptation remain unknown. This study aims to elucidate such mechanisms using a multimodal experimental and computational data collection pipeline. We quantify morphometry using magnetic resonance imaging, mechanics using biaxial testing, hemodynamics using computational fluid dynamics, structure using histology, and transcriptional changes using bulk RNA-sequencing in an ovine carotid-jugular interposition vein graft model, without and with an external biodegradable wrap that allows loads to increase gradually. We show that a biodegradable external wrap promotes luminal uniformity, physiological wall shear stress, and a consistent vein graft phenotype, namely, it prevents over-distension, over-thickening, intimal hyperplasia, and inflammation, and it preserves mechanotransduction. These mechanobiological insights into vein graft adaptation in the presence of an external support can inform computational growth and remodeling models of external support and facilitate design and manufacturing of next-generation external wrapping devices. Statement of significanceExternal mechanical support is emerging as a promising technology to prevent vein graft failure following coronary bypass graft surgery. While variants of this technology are currently under investigation in clinical trials, the fundamental mechanisms of adaptation remain poorly understood. We employ an ovine carotid-jugular interposition vein graft model, with and without an external biodegradable wrap to provide mechanical support, and probe vein graft adaptation using a multimodal experimental and computational data collection pipeline. We quantify morphometry using magnetic resonance imaging, mechanics using biaxial testing, fluid flow using computational fluid dynamics, vascular composition and structure using histology, and transcriptional changes using bulk RNA sequencing. We show that the wrap mitigates vein graft failure by promoting multiple adaptive mechanisms (across biological scales).

Bone tissue growth in ultrasonically stimulated bioinspired scaffolds

We develop computational models of bone growth in ultrasonically stimulated porous tissue scaffolds with uniform square pores and a bioinspired structure. While bone growth in the bioinspired scaffolds is slower, it produces amounts of bone comparable to the square pore scaffold, making the bioinspired structure ideal for enhancing bone growth with better structural integrity. Controlling the initial mesenchymal stem cell distribution in the scaffolds also affects the growth rate and total bone formation, which could be further useful for controlling bone growth in the scaffold based on an individual’s physiology.

Semantic maturation during the comprehension-expression gap in late and typical talkers.

This study investigates the influence of semantic maturation on early lexical development by examining the impact of contextual diversity-known to influence semantic development-on word promotion from receptive to productive vocabularies (i.e., comprehension-expression gap). Study 1 compares the vocabularies of 3685 American-English-speaking typical talkers (TTs) and late talkers (LTs; 16-30 months old; 1257 females, 1021 gender unknown; ethnicity unknown; data downloaded in 2018) and finds that LTs, with a longer preverbal phase, produced nouns with lower contextual diversity (R2 =.80), but verbs with higher contextual diversity (R2 =.13). Study 2 compares computational network growth models of semantic maturation and finds that verbs require more semantic maturation than nouns, and TTs produce words that are more semantically mature than LTs.

The correlation between cell and nucleus size is explained by an eukaryotic cell growth model.

In eukaryotes, the cell volume is observed to be strongly correlated with the nuclear volume. The slope of this correlation depends on the cell type, growth condition, and the physical environment of the cell. We develop a computational model of cell growth and proteome increase, incorporating the kinetics of amino acid import, protein/ribosome synthesis and degradation, and active transport of proteins between the cytoplasm and the nucleoplasm. We also include a simple model of ribosome biogenesis and assembly. Results show that the cell volume is tightly correlated with the nuclear volume, and the cytoplasm-nucleoplasm transport rates strongly influence the cell growth rate as well as the cell/nucleus volume ratio (C/N ratio). Ribosome assembly and the ratio of ribosomal proteins to mature ribosomes also influence the cell volume and the cell growth rate. We find that in order to regulate the cell growth rate and the cell/nucleus volume ratio, the cell must optimally control groups of kinetic and transport parameters together, which could explain the quantitative roles of canonical growth pathways. Finally, although not explicitly demonstrated in this work, we point out that it is possible to construct a detailed proteome distribution using our model and RNAseq data, provided that a quantitative cell division mechanism is known.

Reduced Smooth Muscle Contractile Capacity Facilitates Maladaptive Arterial Remodeling.

Albeit seldom considered explicitly, the vasoactive state of a central artery can contribute to luminal control and thereby affect the in vivo values of flow-induced wall shear stress and pressure-induced intramural stress, which in turn are strong determinants of wall growth and remodeling. Here, we test the hypothesis that diminished vasoactive capacity compromises effective mechano-adaptations of central arteries. Toward this end, we use consistent methods to re-interpret published data on common carotid artery remodeling in a nonpharmacologic mouse model of induced hypertension and a model of connective tissue disorder that results in Marfan syndrome. The mice have identical genetic backgrounds and, in both cases, the data are consistent with the hypothesis considered. In particular, carotid arteries with strong (normal) vasoactive capacity tend to maintain wall thickness and in vivo axial stretch closer to homeostatic, thus resulting in passive circumferential wall stress and energy storage close to normal. We conclude that effective vasoactivity helps to control the biomechanical state in which the cells and matrix turnover, thus helping to delineate mechano-adaptive from maladaptive remodeling. Future analyses of experimental data and computational models of growth and remodeling should account for this strong coupling between smooth muscle contractile capacity and central arterial remodeling.

Protocol for mapping the variability in cell wall mechanical bending behavior in living leaf pavement cells.

Mechanical properties, size and geometry of cells, and internal turgor pressure greatly influence cell morphogenesis. Computational models of cell growth require values for wall elastic modulus and turgor pressure, but very few experiments have been designed to validate the results using measurements that deform the entire thickness of the cell wall. New wall material is synthesized at the inner surface of the cell such that full-thickness deformations are needed to quantify relevant changes associated with cell development. Here, we present an integrated, experimental-computational approach to analyze quantitatively the variation of elastic bending behavior in the primary cell wall of living Arabidopsis (Arabidopsis thaliana) pavement cells and to measure turgor pressure within cells under different osmotic conditions. This approach used laser scanning confocal microscopy to measure the 3D geometry of single pavement cells and indentation experiments to probe the local mechanical responses across the periclinal wall. The experimental results were matched iteratively using a finite element model of the experiment to determine the local mechanical properties and turgor pressure. The resulting modulus distribution along the periclinal wall was nonuniform across the leaf cells studied. These results were consistent with the characteristics of plant cell walls which have a heterogeneous organization. The results and model allowed the magnitude and orientation of cell wall stress to be predicted quantitatively. The methods also serve as a reference for future work to analyze the morphogenetic behaviors of plant cells in terms of the heterogeneity and anisotropy of cell walls.

Emergence of urban growth patterns from human mobility behavior.

Cities grow in a bottom-up manner, leading to fractal-like urban morphologies characterized by scaling laws. The correlated percolation model has succeeded in modeling urban geometries by imposing strong spatial correlations; however, the origin of the underlying mechanisms behind spatially correlated urban growth remains largely unknown. Our understanding of human movements has recently been revolutionized thanks to the increasing availability of large-scale human mobility data. This paper introduces a computational urban growth model that captures spatially correlated urban growth with a micro-foundation in human mobility behavior. We compare the proposed model with three empirical datasets, discovering that strong social interactions and long-term memory effects in human movements are two fundamental principles responsible for fractal-like urban morphology, along with the three important laws of urban growth. Our model connects the empirical findings in urban growth patterns and human mobility behavior.

Passive biaxial mechanical behavior of newborn mouse aorta with and without elastin

Aortic wall material properties are needed for computational models and for comparisons across developmental and disease states. There has been abundant work in comparing aortic material properties across disease states, but limited work across developmental states. We performed passive biaxial mechanical testing on newborn mouse aorta with (Eln+/+) and without (Eln−/−) elastin. Elastin provides elasticity to the aortic wall and is necessary for survival beyond birth in the mouse. Mechanically functional elastin is challenging to create in vitro and so Eln−/− aorta can be a comparison for tissue engineered arteries with limited elastin amounts. We found that a traditional arterial strain energy function provided reasonable fits to newborn mouse aorta and generally predicted lower material constants in Eln−/− compared to Eln+/+ aorta. At physiologic pressures, the circumferential stresses and moduli trended lower in Eln−/− compared to Eln+/+ aorta. Increased blood pressure in Eln−/− mice helps to alleviate the differences in stresses and moduli. Increased blood pressure also serves to partially offload stresses in the isotropic compared to the anisotropic component of the wall. The baseline material parameters can be used in computational models of growth and remodeling to improve understanding of developmental mechanobiology and tissue engineering strategies.