@article{chaudhuri2020,
   abstract = {Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials—they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell–matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine. This Review explores the role of viscoelasticity of tissues and extracellular matrices in cell–matrix interactions and mechanotransduction and the potential utility of viscoelastic biomaterials in regenerative medicine.},
   author = {Ovijit Chaudhuri and Justin Cooper-White and Paul A. Janmey and David J. Mooney and Vivek B. Shenoy},
   doi = {10.1038/s41586-020-2612-2},
   issn = {1476-4687},
   issue = {7822},
   journal = {Nature 2020 584:7822},
   keywords = {Humanities and Social Sciences,Science,multidisciplinary},
   month = {8},
   pages = {535-546},
   pmid = {32848221},
   publisher = {Nature Publishing Group},
   title = {Effects of extracellular matrix viscoelasticity on cellular behaviour},
   volume = {584},
   url = {https://www.nature.com/articles/s41586-020-2612-2},
   year = {2020},
}
@article{sheu2001,
   abstract = {The influence of glutaraldehyde as a crosslinking agent to increase the strength of collagen matrices for cell culture was examined in this study. Collagen solutions of 1% were treated with different concentrations (0-0.2%) of glutaraldehyde for 24h. The viscoelasticity of the resulting collagen gel solution was measured using dynamic mechanical analysis (DMA), which demonstrated that all collagen gel solutions examined followed the same model pattern. The creep compliance model of Voigt-Kelvin satisfactorily described the change of viscoelasticity expressed by these collagen gel solutions. These crosslinked collagen gel solutions were freeze-dried to form a matrix with a thickness of about 0.2-0.3mm. The break modulus of these collagen matrices measured by DMA revealed that the higher the degree of crosslinking, the higher the break modulus. The compatibility of fibroblasts isolated from nude mouse skin with these collagen matrices was found to be acceptable at a cell density of 3×105cells/cm2 with no contraction, even when using a concentration of glutaraldehyde of up to 0.2%. Copyright © 2001 Elsevier Science Ltd.},
   author = {Ming Thau Sheu and Ju Chun Huang and Geng Chang Yeh and Hsiu O. Ho},
   doi = {10.1016/S0142-9612(00)00315-X},
   issn = {0142-9612},
   issue = {13},
   journal = {Biomaterials},
   keywords = {Collagen,Dynamic mechanical analysis,Glutaraldehyde,Viscoelasticity},
   month = {7},
   pages = {1713-1719},
   pmid = {11396874},
   publisher = {Elsevier},
   title = {Characterization of collagen gel solutions and collagen matrices for cell culture},
   volume = {22},
   year = {2001},
}
@report{slater2017,
   author = {Katie Slater and Jeff Partridge and Himabindu Nandivada},
   title = {Tuning the Elastic Moduli of Corning ® Matrigel ® and Collagen I 3D Matrices by Varying the Protein Concentration Application Note},
   url = {https://www.corning.com/ catalog/cls/documents/application-notes/CLS-AC-AN-449.pdf},
   year = {2017},
}
@article{aisenbrey2020,
   abstract = {Matrigel, a basement-membrane matrix extracted from Engelbreth–Holm–Swarm mouse sarcomas, has been used for more than four decades for a myriad of cell-culture applications. However, Matrigel is limited in its applicability to cellular biology, therapeutic-cell manufacturing and drug discovery, owing to its complex, ill-defined and variable composition. Variations in the mechanical and biochemical properties within a single batch of Matrigel — and between batches — have led to uncertainty in cell-culture experiments and a lack of reproducibility. Moreover, Matrigel is not conducive to physical or biochemical manipulation, making it difficult to fine-tune the matrix to promote intended cell behaviours and achieve specific biological outcomes. Recent advances in synthetic scaffolds have led to the development of xenogenic-free, chemically defined, highly tunable and reproducible alternatives. In this Review, we assess the applications of Matrigel in cell culture, regenerative medicine and organoid assembly, detailing the limitations of Matrigel and highlighting synthetic-scaffold alternatives that have shown equivalent or superior results. Additionally, we discuss the hurdles that are limiting a full transition from Matrigel to synthetic scaffolds and provide a brief perspective on the future directions of synthetic scaffolds for cell-culture applications.},
   author = {Elizabeth A. Aisenbrey and William L. Murphy},
   doi = {10.1038/S41578-020-0199-8},
   issn = {20588437},
   issue = {7},
   journal = {Nature reviews. Materials},
   month = {7},
   pages = {539},
   pmid = {32953138},
   publisher = {NIH Public Access},
   title = {Synthetic alternatives to Matrigel},
   volume = {5},
   url = {/pmc/articles/PMC7500703/ /pmc/articles/PMC7500703/?report=abstract https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7500703/},
   year = {2020},
}
@article{puxkandl2002,
   abstract = {Collagen type I is the most abundant structural protein in tendon, skin and bone, and largely determines the mechanical behaviour of these connective tissues. To obtain a better understanding of th...},
   author = {R. Puxkandl and I. Zizak and O. Paris and J. Keckes and W. Tesch and S. Bernstorff and P. Purslow and P. Fratzl},
   doi = {10.1098/RSTB.2001.1033},
   issn = {09628436},
   issue = {1418},
   journal = {Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences},
   keywords = {Xray,collagen,mechanical properties,synchrotron,viscolelastic},
   month = {2},
   pages = {191-197},
   pmid = {11911776},
   publisher = {
				The Royal Society
			},
   title = {Viscoelastic properties of collagen: synchrotron radiation investigations and structural model},
   volume = {357},
   url = {https://royalsocietypublishing.org/doi/10.1098/rstb.2001.1033},
   year = {2002},
}
@article{giraud1998,
   abstract = {In this letter, we show that an eleven-velocity two-dimensional lattice Boltzmann model using several relaxation times obeys a Jeffreys viscoelastic constitutive law with full isotropic behavior. The connection between the free parameters of the model and the Jeffreys transport coefficients is made with the help of a modified Chapman-Enskog expansion taking into account large relaxation time effects. Numerical simulation of a pulsed Couette flow is performed leading to an excellent agreement with predictions.},
   author = {L. Giraud and D. D'Humières and P. Lallemand},
   doi = {10.1209/EPL/I1998-00296-0},
   issn = {0295-5075},
   issue = {6},
   journal = {Europhysics Letters},
   month = {6},
   pages = {625},
   publisher = {IOP Publishing},
   title = {A lattice Boltzmann model for Jeffreys viscoelastic fluid},
   volume = {42},
   url = {https://iopscience.iop.org/article/10.1209/epl/i1998-00296-0 https://iopscience.iop.org/article/10.1209/epl/i1998-00296-0/meta},
   year = {1998},
}
@article{roylance2001,
   author = {David Roylance},
   journal = {Department of Materials Science and Engineering--Massachusetts Institute of Technology, Cambridge MA},
   pages = {1-37},
   title = {Engineering viscoelasticity},
   volume = {2139},
   url = {https://mitocw.ups.edu.ec/courses/materials-science-and-engineering/3-11-mechanics-of-materials-fall-1999/modules/MIT3_11F99_visco.pdf},
   year = {2001},
}
@article{levental2009,
   abstract = {Tumors are characterized by extracellular matrix (ECM) remodeling and stiffening. The importance of ECM remodeling to cancer is appreciated; the relevance of stiffening is less clear. We found that breast tumorigenesis is accompanied by collagen crosslinking, ECM stiffening, and increased focal adhesions. Induction of collagen crosslinking stiffened the ECM, promoted focal adhesions, enhanced PI3 kinase (PI3K) activity, and induced the invasion of an oncogene-initiated epithelium. Inhibition of integrin signaling repressed the invasion of a premalignant epithelium into a stiffened, crosslinked ECM and forced integrin clustering promoted focal adhesions, enhanced PI3K signaling, and induced the invasion of a premalignant epithelium. Consistently, reduction of lysyl oxidase-mediated collagen crosslinking prevented MMTV-Neu-induced fibrosis, decreased focal adhesions and PI3K activity, impeded malignancy, and lowered tumor incidence. These data show how collagen crosslinking can modulate tissue fibrosis and stiffness to force focal adhesions, growth factor signaling and breast malignancy. © 2009 Elsevier Inc. All rights reserved.},
   author = {Kandice R. Levental and Hongmei Yu and Laura Kass and Johnathon N. Lakins and Mikala Egeblad and Janine T. Erler and Sheri F.T. Fong and Katalin Csiszar and Amato Giaccia and Wolfgang Weninger and Mitsuo Yamauchi and David L. Gasser and Valerie M. Weaver},
   doi = {10.1016/J.CELL.2009.10.027},
   issn = {0092-8674},
   issue = {5},
   journal = {Cell},
   keywords = {CELLBIO,HUMDISEASE},
   month = {11},
   pages = {891-906},
   pmid = {19931152},
   publisher = {Cell Press},
   title = {Matrix Crosslinking Forces Tumor Progression by Enhancing Integrin Signaling},
   volume = {139},
   year = {2009},
}
@article{malaspinas2010,
   abstract = {The simulation of viscoelastic fluids is a challenging task from the theoretical and numerical points of view. This class of fluids has been extensively studied with the help of classical numerical methods. In this paper we propose a new approach based on the lattice Boltzmann method in order to simulate linear and non-linear viscoelastic fluids and in particular those described by the Oldroyd-B and FENE-P constitutive equations. We study the accuracy and stability of our model on three different benchmarks: the 3D Taylor-Green vortex decay, the simplified 2D four-rolls mill, and the 2D Poiseuille flow. To our knowledge, the methodology described in this work is a first attempt for the simulation of non-trivial flows of viscoelastic fluids using the lattice Boltzmann method to discretize the constitutive and conservation equations. © 2010 Elsevier B.V.},
   author = {O. Malaspinas and N. Fiétier and M. Deville},
   doi = {10.1016/J.JNNFM.2010.09.001},
   issn = {0377-0257},
   issue = {23-24},
   journal = {Journal of Non-Newtonian Fluid Mechanics},
   keywords = {Lattice Boltzmann method,Viscoelastic fluid flows},
   month = {12},
   pages = {1637-1653},
   publisher = {Elsevier},
   title = {Lattice Boltzmann method for the simulation of viscoelastic fluid flows},
   volume = {165},
   year = {2010},
}
@article{ispolatov2002,
   abstract = {A lattice Boltzmann model for viscoelastic flow simulation is proposed. Elastic effects are taken into account within the framework of a Maxwell model. To test the approach, we estimate the transverse velocity autocorrelation function for a freely evolving system, and find clear manifestations of shear at large frequencies. We then characterize boundary-driven shear waves, and the resonant enhancement of shear oscillations in a periodically driven fluid confined within a capillary. The measured shear-wave dispersion relation is compared to that obtained from the Navier-Stokes equation with a Maxwell viscoelastic term, and good agreement is obtained. © 2002 The American Physical Society.},
   author = {Iaroslav Ispolatov and Martin Grant},
   doi = {10.1103/PhysRevE.65.056704},
   issn = {1063651X},
   issue = {5},
   journal = {Physical Review E},
   month = {5},
   pages = {056704},
   publisher = {American Physical Society},
   title = {Lattice Boltzmann method for viscoelastic fluids},
   volume = {65},
   url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.65.056704},
   year = {2002},
}
@article{sherman2015,
   abstract = {Collagen is the principal biopolymer in the extracellular matrix of both vertebrates and invertebrates. It is produced in specialized cells (fibroblasts) and extracted into the body by a series of intra and extracellular steps. It is prevalent in connective tissues, and the arrangement of collagen determines the mechanical response. In biomineralized materials, its fraction and spatial distribution provide the necessary toughness and anisotropy. We review the structure of collagen, with emphasis on its hierarchical arrangement, and present constitutive equations that describe its mechanical response, classified into three groups: hyperelastic macroscopic models based on strain energy in which strain energy functions are developed; macroscopic mathematical fits with a nonlinear constitutive response; structurally and physically based models where a constitutive equation of a linear elastic material is modified by geometric characteristics. Viscoelasticity is incorporated into the existing constitutive models and the effect of hydration is discussed. We illustrate the importance of collagen with descriptions of its organization and properties in skin, fish scales, and bone, focusing on the findings of our group.},
   author = {Vincent R. Sherman and Wen Yang and Marc A. Meyers},
   doi = {10.1016/J.JMBBM.2015.05.023},
   issn = {1751-6161},
   journal = {Journal of the Mechanical Behavior of Biomedical Materials},
   month = {12},
   pages = {22-50},
   pmid = {26144973},
   publisher = {Elsevier},
   title = {The materials science of collagen},
   volume = {52},
   year = {2015},
}
@article{gautieri2013,
   abstract = {Computer simulation has emerged as a powerful tool to investigate and design materials without ever making them. Predicting the properties and behavior of materials by computer simulation from the bottom-up perspective has long been a vision of computational materials scientists and, as computational power increases, modeling and simulation tools are becoming crucial to the investigation of material systems. The key to achieving this goal is using hierarchies of paradigms that seamlessly connect quantum mechanics to macroscopic systems. Particular progress has been made in relating molecular-scale chemistry to mesoscopic and macroscopic material properties essential to define the materiome. This chapter reviews large-scale atomistic and coarse-grain modeling methods commonly implemented to investigate the properties and behavior of natural and biological materials with nanostructured hierarchies. We present basic concepts of hierarchical multiscale modeling capable of providing a bottom-up description of chemically complex materials and some example applications related to the study of collagen material at different hierarchical levels.},
   author = {Alfonso Gautieri and Markus J. Buehler},
   doi = {10.1007/978-3-7091-1574-9_2/COVER},
   issn = {23093706},
   journal = {CISM International Centre for Mechanical Sciences, Courses and Lectures},
   keywords = {Bead Type,Collagen Molecule,Multiscale Modeling,Osteogenesis Imperfecta,Persistence Length},
   pages = {13-55},
   publisher = {Springer International Publishing},
   title = {Multi-scale modeling of biomaterials and tissues},
   volume = {546},
   url = {https://link.springer.com/chapter/10.1007/978-3-7091-1574-9_2},
   year = {2013},
}
@article{krueger2017,
   author = {Timm Krüger and Halim Kusumaatmaja and Alexandr Kuzmin and Orest Shardt and Goncalo Silva and Erlend Magnus Viggen},
   institution = {Springer International Publishing},
   journal = {Springer International Publishing},
   note = {https://github.com/lbm-principles-practice},
   title = {The lattice Boltzmann method},
   volume = {10},
   year = {2017},
}
@article{abhilash2014,
   abstract = {Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element-based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.},
   author = {A. S. Abhilash and Brendon M. Baker and Britta Trappmann and Christopher S. Chen and Vivek B. Shenoy},
   doi = {10.1016/j.bpj.2014.08.029},
   issn = {15420086},
   issue = {8},
   journal = {Biophysical Journal},
   month = {10},
   note = {Focuses on "pulling" effects},
   pages = {1829-1840},
   pmid = {25418164},
   publisher = {Biophysical Society},
   title = {Remodeling of fibrous extracellular matrices by contractile cells: Predictions from discrete fiber network simulations},
   volume = {107},
   year = {2014},
}
@article{guo2022,
   abstract = {Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.},
   author = {Yifan Guo and Mohammad R. K. Mofrad and Adrian Buganza Tepole},
   doi = {10.1063/5.0085025},
   issue = {3},
   journal = {Biophysics Reviews},
   month = {9},
   note = {Another review containing a bunch of nice references. Kind of hard to pull apart though since its very dense in information.},
   pages = {031303},
   publisher = {AIP Publishing},
   title = {On modeling the multiscale mechanobiology of soft tissues: Challenges and progress},
   volume = {3},
   year = {2022},
}
@article{liedekerke2015,
   abstract = {In this paper we present an overview of agent-based models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations, and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent-based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings, and capabilities of the major agent-based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center-based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.},
   author = {P Van Liedekerke and M M Palm and N Jagiella and D Drasdo},
   doi = {10.1007/s40571-015-0082-3},
   journal = {Comp. Part. Mech},
   keywords = {Agent-based modeling,Cell mechanics,Deformable cell models,Hybrid models,Lattice-based models,Lattice-free models},
   note = {Overview over ECM models},
   pages = {401-444},
   title = {Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results},
   volume = {2},
   year = {2015},
}
@article{rens2017,
   abstract = {During animal development and homeostasis, the structure of tissues, including muscles, blood vessels, and connective tissues, adapts to mechanical strains in the extracellular matrix (ECM). These strains originate from the differential growth of tissues or forces due to muscle contraction or gravity. Here we show using a computational model that by amplifying local strain cues, active cell contractility can facilitate and accelerate the reorientation of single cells to static strains. At the collective cell level, the model simulations show that active cell contractility can facilitate the formation of strings along the orientation of stretch. The computational model is based on a hybrid cellular Potts and finite-element simulation framework describing a mechanical cell-substrate feedback, where: 1) cells apply forces on the ECM, such that 2) local strains are generated in the ECM and 3) cells preferentially extend protrusions along the strain orientation. In accordance with experimental observations, simulated cells align and form stringlike structures parallel to static uniaxial stretch. Our model simulations predict that the magnitude of the uniaxial stretch and the strength of the contractile forces regulate a gradual transition between stringlike patterns and vascular networklike patterns. Our simulations also suggest that at high population densities, less cell cohesion promotes string formation.},
   author = {Elisabeth G. Rens and Roeland M.H. Merks},
   doi = {10.1016/J.BPJ.2016.12.012},
   issn = {0006-3495},
   issue = {4},
   journal = {Biophysical Journal},
   month = {2},
   pages = {755-766},
   pmid = {28256235},
   publisher = {Cell Press},
   title = {Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch},
   volume = {112},
   year = {2017},
}
@article{tsingos2022,
   abstract = {The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in multicellular tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is an outstanding challenge which cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has non-trivial structure and mechanics. Here, we extend the CPM with a bead-spring chain model of ECM fiber networks modelled using molecular dynamics. We model contractile cells pulling with discrete focal adhesion-like sites on the ECM fiber network, and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that contractile cell forces propagate over multiple cell radii scaling with power law exponent of ≈ −0.5 typical of viscoelastic ECM. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation to investigate how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

### Competing Interest Statement

The authors have declared no competing interest.},
   author = {Erika Tsingos and Bente Hilde Bakker and Koen A.E. Keijzer and Hermen Jan Hupkes and Roeland M.H. Merks},
   doi = {10.1101/2022.06.10.495667},
   journal = {bioRxiv},
   month = {7},
   pages = {2022.06.10.495667},
   publisher = {Cold Spring Harbor Laboratory},
   title = {Modelling the mechanical cross-talk between cells and fibrous extracellular matrix using hybrid cellular Potts and molecular dynamics methods},
   url = {https://www.biorxiv.org/content/10.1101/2022.06.10.495667v3 https://www.biorxiv.org/content/10.1101/2022.06.10.495667v3.abstract},
   year = {2022},
}
@article{rubenstein2008,
   abstract = {In this work, a cellular Potts model based on the differential adhesion hypothesis is employed to analyze the relative importance of select cell-cell and cell-extracellular matrix (ECM) contacts in glioma invasion. To perform these simulations, three types of cells and two ECM components are included. The inclusion of explicit ECM with an inhomogeneous fibrous component and a homogeneously dispersed afibrous component allows exploration of the importance of relative energies of cell-cell and cell-ECM contacts in a variety of environments relevant to in vitro and in vivo experimental investigations of glioma invasion. Simulations performed here focus chiefly on reproducing findings of in vitro experiments on glioma spheroids embedded in collagen I gels. For a given range and set ordering of energies associated with key cell-cell and cell-ECM interactions, our model qualitatively reproduces the dispersed glioma invasion patterns found for most glioma cell lines embedded as spheroids in collagen I gels of moderate concentration. In our model, we find that invasion is maximized at intermediate collagen concentrations, as occurs experimentally. This effect is seen more strongly in model gels composed of short collagen fibers than in those composed of long fibers, which retain significant connectivity even at low density. Additional simulations in aligned model matrices further elucidate how matrix structure dictates invasive patterns. Finally, simulations that allow invading cells to both dissolve and deposit ECM components demonstrate how Q-Potts models may be elaborated to allow active cell alteration of their surroundings. The model employed here provides a quantitative framework with which to bound the relative values of cell-cell and cell-ECM interactions and investigate how varying the magnitude and type of these interactions, as well as ECM structure, could potentially curtail glioma invasion. © 2008 by the Biophysical Society.},
   author = {Brenda M. Rubenstein and Laura J. Kaufman},
   doi = {10.1529/BIOPHYSJ.108.140624},
   issn = {0006-3495},
   issue = {12},
   journal = {Biophysical Journal},
   month = {12},
   note = {1 Type for Stroma, 1 Type for Collagen<br/><br/>Initial experiments: Static ECM<br/><br/>Then: ECM dissolution/deposition<br/>Not aligned with in vivo results<br/>Posits idea: Simulate more than two types of matrix},
   pages = {5661-5680},
   pmid = {18835895},
   publisher = {Cell Press},
   title = {The Role of Extracellular Matrix in Glioma Invasion: A Cellular Potts Model Approach},
   volume = {95},
   year = {2008},
}
@article{berghoff2018,
   abstract = {In the last decades, simulations have been established in several fields of science and industry to study various phenomena by solving, inter alia, partial differential equations. For an efficient use of current and future high performance computing systems, with many thousands of computation ranks, high node-level performance, scalable communication, and the omission of unnecessary calculations are of high priority in the development of new solvers. The challenge of contemporary simulation applications is to bridge the gap between the scales of the various physical processes. We introduce the NAStJA framework, a block-based MPI parallel solver for arbitrary algorithms, based on stencil code or other regular grid methods. NAStJA decomposes the domain of spatially complex structures into small cuboid blocks. A special feature of NAStJA is the dynamic block adaption which modifies the calculation domain around the region where the computation currently takes place, and hence avoids unnecessary calculations. This often occurs, inter alia, in phase-field simulations. Block creation and deletion is managed autonomously within local neighborhoods. A basic load balancing mechanism allows a re-distribution of newly created blocks to the involved computing ranks. The use of a multi-hop network, to distribute information to the entire domain, avoids collective all-gather communications. Thus, we can demonstrate excellent scaling. The present scaling tests substantiate the enormous advantage of this adaptive method. For certain simulation scenarios, we can show that the calculation effort and memory consumption can be reduced to only 3.5 percent, compared to the classical full-domain reference simulation. The overhead of 70-100 percent for the dynamic adapting block creation is significantly lower than the gain. The approach is not restricted to phase-field simulations, and can be employed in other domains of computational science to exploit sparsity of computing regions.},
   author = {Marco Berghoff and Ivan Kondov and Johannes Hotzer},
   doi = {10.1109/TPDS.2018.2819672},
   issn = {15582183},
   issue = {10},
   journal = {IEEE Transactions on Parallel and Distributed Systems},
   keywords = {Stencil code,distributed memory,load balancing,massively parallel performance,multi-hop network,partial differential equation,phase-field method,scalable parallel algorithms},
   month = {10},
   pages = {2282-2296},
   publisher = {IEEE Computer Society},
   title = {Massively Parallel Stencil Code Solver with Autonomous Adaptive Block Distribution},
   volume = {29},
   year = {2018},
}
@generic{frantz2010,
   author = {Christian Frantz and Kathleen M. Stewart and Valerie M. Weaver},
   doi = {10.1242/jcs.023820},
   issn = {00219533},
   issue = {24},
   journal = {Journal of Cell Science},
   month = {12},
   pages = {4195-4200},
   pmid = {21123617},
   title = {The extracellular matrix at a glance},
   volume = {123},
   year = {2010},
}
@article{herold2023,
   abstract = {Progress continues in the field of cancer biology, yet much remains to be unveiled regarding the mechanisms of cancer invasion. In particular, complex biophysical mechanisms enable a tumor to remodel the surrounding extracellular matrix (ECM), allowing cells to invade alone or collectively. Tumor spheroids cultured in collagen represent a simplified, reproducible 3D model system, which is sufficiently complex to recapitulate the evolving organization of cells and interaction with the ECM that occur during invasion. Recent experimental approaches enable high resolution imaging and quantification of the internal structure of invading tumor spheroids. Concurrently, computational modeling enables simulations of complex multicellular aggregates based on first principles. The comparison between real and simulated spheroids represents a way to fully exploit both data sources, but remains a challenge. We hypothesize that comparing any two spheroids requires first the extraction of basic features from the raw data, and second the definition of key metrics to match such features. Here, we present a novel method to compare spatial features of spheroids in 3D. To do so, we define and extract features from spheroid point cloud data, which we simulated using Cells in Silico (CiS), a high-performance framework for large-scale tissue modeling previously developed by us. We then define metrics to compare features between individual spheroids, and combine all metrics into an overall deviation score. Finally, we use our features to compare experimental data on invading spheroids in increasing collagen densities. We propose that our approach represents the basis for defining improved metrics to compare large 3D data sets. Moving forward, this approach will enable the detailed analysis of spheroids of any origin, one application of which is informing in silico spheroids based on their in vitro counterparts. This will enable both basic and applied researchers to close the loop between modeling and experiments in cancer research.},
   author = {Julian Herold and Eric Behle and Jakob Rosenbauer and Jacopo Ferruzzi and Alexander Schug},
   doi = {10.1371/journal.pcbi.1010471},
   issn = {15537358},
   issue = {3},
   journal = {PLoS Computational Biology},
   month = {3},
   pmid = {36996248},
   publisher = {Public Library of Science},
   title = {Development of a scoring function for comparing simulated and experimental tumor spheroids},
   volume = {19},
   year = {2023},
}
@article{berghoff2020,
   abstract = {Background: Discoveries in cellular dynamics and tissue development constantly reshape our understanding of fundamental biological processes such as embryogenesis, wound-healing, and tumorigenesis. High-quality microscopy data and ever-improving understanding of single-cell effects rapidly accelerate new discoveries. Still, many computational models either describe few cells highly detailed or larger cell ensembles and tissues more coarsely. Here, we connect these two scales in a joint theoretical model. Results: We developed a highly parallel version of the cellular Potts model that can be flexibly applied and provides an agent-based model driving cellular events. The model can be modular extended to a multi-model simulation on both scales. Based on the NAStJA framework, a scaling implementation running efficiently on high-performance computing systems was realized. We demonstrate independence of bias in our approach as well as excellent scaling behavior. Conclusions: Our model scales approximately linear beyond 10,000 cores and thus enables the simulation of large-scale three-dimensional tissues only confined by available computational resources. The strict modular design allows arbitrary models to be configured flexibly and enables applications in a wide range of research questions. Cells in Silico (CiS) can be easily molded to different model assumptions and help push computational scientists to expand their simulations to a new area in tissue simulations. As an example we highlight a 10003 voxel-sized cancerous tissue simulation at sub-cellular resolution.},
   author = {Marco Berghoff and Jakob Rosenbauer and Felix Hoffmann and Alexander Schug},
   doi = {10.1186/s12859-020-03728-7},
   issn = {14712105},
   issue = {1},
   journal = {BMC Bioinformatics},
   keywords = {Cellular Potts model,Massively parallel,Tissue growth},
   month = {10},
   pmid = {33023471},
   publisher = {BioMed Central Ltd},
   title = {Cells in Silico-introducing a high-performance framework for large-scale tissue modeling},
   volume = {21},
   year = {2020},
}
@inproceedings{scianna2013,
   abstract = {Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.},
   author = {Marco Scianna and Luigi Preziosi and Katarina Wolf},
   doi = {10.3934/mbe.2013.10.235},
   issn = {15471063},
   issue = {1},
   journal = {Mathematical Biosciences and Engineering},
   keywords = {Cell migration,Cellular Potts model,Extracellular matrix},
   month = {2},
   pages = {235-261},
   pmid = {23311371},
   title = {A cellular potts model simulating cell migration on and in matrix environments},
   volume = {10},
   year = {2013},
}
