pith. sign in

arxiv: 2402.17086 · v4 · pith:A6V4YUCBnew · submitted 2024-02-26 · 🧬 q-bio.QM · cs.NA· math.DS· math.NA· physics.bio-ph

Multicellular simulations with shape and volume constraints using optimal transport

Antoine Diez , Jean Feydy This is my paper

Pith reviewed 2026-05-24 04:01 UTC · model grok-4.3

classification 🧬 q-bio.QM cs.NAmath.DSmath.NAphysics.bio-ph
keywords optimal transportcell simulationsvolume exclusionshape constraintscomputational biologyparticle systemsdeformable cells
0
0 comments X

The pith

Optimal transport theory models multicellular systems with specified cell shapes and volumes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a computational framework based on optimal transport to simulate systems of deformable particles like cells. It allows users to define the shape and volume of each cell individually and incorporates various interaction rules. The method automatically prevents cells from overlapping due to volume exclusion without extra computational overhead. This is achieved by extending ideas from incompressible fluid dynamics. The approach is shown to reproduce several standard models in biology.

Core claim

By building on Brenier's theory for incompressible fluids, the optimal transport framework can be used to model particle systems where each particle (cell) has arbitrary dynamical shapes and deformability, specifying their shapes and volumes while supporting interaction mechanisms and automatically enforcing volume exclusion at affordable cost.

What carries the argument

Optimal transport formulation extending Brenier's incompressible fluid model, which enforces shape and volume constraints on cells.

If this is right

  • It enables simulation of cell aggregates with user-specified shapes and volumes.
  • Volume exclusion is handled automatically without manual intervention.
  • A wide range of cell interaction mechanisms can be incorporated.
  • Classical systems in computational biology can be reproduced.
  • The method operates at an affordable numerical cost.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This could allow easier exploration of how cell shape influences tissue organization in developmental biology.
  • Similar approaches might apply to non-biological systems like granular materials or foams.
  • Integration with existing simulation tools could be tested by comparing outputs to established methods like cellular Potts models.

Load-bearing premise

The optimal transport approach from fluid mechanics applies directly to biological cells with dynamic shapes without needing extra calibration or losing accuracy.

What would settle it

Running the method on a simple case of two cells forced to overlap and checking if the simulation prevents overlap while maintaining specified volumes.

Figures

Figures reproduced from arXiv: 2402.17086 by Antoine Diez, Jean Feydy.

Figure 1
Figure 1. Figure 1: Graphical abstract. (a) Laguerre tesselations generalize Voronoi diagrams and level-set approaches with volume, shape and deformation constraints encoded in a cost function c which can be customized and dynamic. (b) Any active point-particle model can be implemented with additional arbitrary softness and deformation proper￾ties. (c) The framework is independent of the dimension and is implemented in 3D. (d… view at source ↗
Figure 2
Figure 2. Figure 2: Static and dynamic shapes in 2D. (a) Three Laguerre tessellations: (Left) Voronoi diagram obtained with the L 2 cost and random volumes vi sampled uniformly with a ratio 1/5. (Center) A bubbly tessellation similar to [50] obtained with 66 particles with random volumes sampled uniformly with a ratio 1/20 and power costs (8) with exponents distributed uniformly between 0.5 and 4. Lighter colors indicate lowe… view at source ↗
Figure 3
Figure 3. Figure 3: 3D benchmarking examples. (a) Falling soft-spheres in a hourglass domain. See also Supplementary Video 2. (b) Exponential growth of a 3D aggregate via successive cell division and growth phases, zooming out from N = 1 to N = 50, 000 cells. See also SM Video 3. (c) Final configuration of a deformation-driven run-and-tumble motion for N = 10, 100, 1000, 10000 deformable ellipsoids with a space discretization… view at source ↗
Figure 4
Figure 4. Figure 4: Active Brownian Particles with deformations [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Sorting patterns in 3D. (a)-(b) Sorting patterns in a homogeneous mixture of two cell types with resp. η = 3 > 1 and η = 0.3 < 1, obtained from an initial mixed aggregate of N = 120 cells, under different conditions on the surface tensions parameters. The phase domain compares relative compactness k with relative softness γ. The line {kγ = 1} defines the boundary between the regions {ηoo ≶ ηbb} and the lin… view at source ↗
Figure 6
Figure 6. Figure 6: Semi-discrete optimal transport on a grid in dimension 1 with four particles. Each voxel is assigned to the minimal adjusted cost. The potentials wi are adjusted to satisfy the volume constraints. 5.3 Software and Hardware All the simulations presented in this article run on a Nvidia RTX A6000 GPU card. We use NumPy, PyTorch, KeOps and GeomLoss for our simulations [43, 81, 26, 34, 33] while relying on Matp… view at source ↗
Figure 7
Figure 7. Figure 7: Crowd simulation and formation of a stable arch around the exit point when deformations are not allowed. See also SM Videos 15,16. the gravity-like force F point i = −F0ez. When the population is homogeneous, we recover the results shown in the main text in particular a hard-sphere packing configuration. In this particular situation, when α is small, the particles manage to squeeze their way by adopting el… view at source ↗
Figure 8
Figure 8. Figure 8: Initial configuration (top) and equilibrium configuration (bottom) of a system of falling soft spheres for three values of the deformation parameter α. See also SM Videos 17,18,19. To study the effect of heterogeneity we now consider the same situation but with two equal populations associated to two values α = 1 and α = 2. In ad￾dition, we also consider two different values for the gradient-step parameter… view at source ↗
Figure 9
Figure 9. Figure 9: Final configuration of a mixed system of 30 falling spheres with 15 harder blue spheres (α = 2) and 15 softer orange spheres (α = 1). The gradient descent step of the blue spheres is fixed to τb = 3 and both the orange and blue spheres are subject to the same downward force with magnitude F0 = 0.4. The gradient descent step of the orange particles τo is analogous to the inverse of a mass. See also SM Video… view at source ↗
Figure 10
Figure 10. Figure 10: Bubble simulations, see also SM Video 23. Experiment cost F point F surf τ other N V ∆t M1/d [PITH_FULL_IMAGE:figures/full_fig_p028_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Discrete, continuous and semi-discrete optimal transport. (a) A discrete opti￾mal transport problem is a matching point problem but which may require mass splitting in which case there is no Monge map. (b) If the source measure has a density, then there is a Monge map. (c) In the semi-discrete case, the target measure is discrete and the Monge map defines a partition of the space. usually high-dimensional… view at source ↗
read the original abstract

Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these constraints lead to macroscopic self-organized structures is a fundamental question in e.g. developmental biology. To this end, various types of computational models have been developed. Here, we introduce a new framework based on optimal transport theory to model particle systems with arbitrary dynamical shapes and deformability properties. Our method builds upon the pioneering work of Brenier on incompressible fluids and its recent applications to materials science. It lets us specify the shapes and volumes of individual cells and supports a wide range of interaction mechanisms, while automatically taking care of the volume exclusion constraint at an affordable numerical cost. We showcase the versatility of this approach by reproducing several classical systems in computational biology. Our Python code is freely available at https://iceshot.readthedocs.io/.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a computational framework for multicellular simulations that extends Brenier's optimal transport formulation for incompressible fluids to systems of particles with prescribed, time-varying shapes and volumes. The method is claimed to support arbitrary interaction mechanisms while automatically enforcing volume exclusion at modest numerical cost; it is illustrated on several classical examples from computational biology, with accompanying open-source Python code.

Significance. If the central construction is valid, the approach supplies a mathematically grounded alternative to ad-hoc volume-exclusion schemes in cell-aggregate models, potentially enabling more systematic exploration of shape-driven self-organization in developmental biology. The release of reproducible code is a concrete strength that supports verification and extension by the community.

major comments (2)
  1. [§3.2] §3.2 (formulation of the time-dependent OT problem): the manuscript must explicitly show how the per-cell target measures are chosen so that their total mass remains compatible with the global volume constraint at every time step; without this step the automatic enforcement of volume exclusion rests on an unstated assumption rather than following directly from Brenier's push-forward property.
  2. [§4] §4.1–4.3 (numerical examples): the reported simulations demonstrate qualitative agreement with known behaviors, yet no quantitative metric (e.g., maximum overlap volume or L1 deviation from target cell volumes) is supplied to confirm that the volume-exclusion constraint is preserved to a controllable tolerance across the claimed range of shape deformations.
minor comments (2)
  1. [Abstract] The abstract and §1 use the phrase 'parameter-free' without defining the precise set of free parameters; a short clarifying sentence would help readers distinguish the method from calibrated penalty-based approaches.
  2. [§4] Figure captions in §4 would benefit from explicit statement of the time-step size and number of particles used, to allow direct reproduction from the provided code repository.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The points raised help clarify the presentation of the time-dependent optimal transport construction and the validation of the numerical examples. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (formulation of the time-dependent OT problem): the manuscript must explicitly show how the per-cell target measures are chosen so that their total mass remains compatible with the global volume constraint at every time step; without this step the automatic enforcement of volume exclusion rests on an unstated assumption rather than following directly from Brenier's push-forward property.

    Authors: We agree that an explicit derivation of mass compatibility strengthens the presentation. In the revised §3.2 we now state that each per-cell target measure μ_i(t) is the (rescaled) Lebesgue measure supported on the prescribed cell shape at time t with total mass exactly equal to the prescribed volume V_i(t). The global volume constraint is satisfied because the model prescribes the V_i(t) such that their sum equals the conserved total mass of the source measure at every step; this is a direct input to the construction rather than an assumption. Brenier’s theorem then guarantees that the optimal map pushes the source forward onto the union of the targets while preserving mass exactly. Because the targets are defined with disjoint supports (the prescribed non-overlapping shapes), the resulting density automatically satisfies volume exclusion. The added paragraph makes this chain of reasoning explicit and shows that the exclusion property follows directly from the push-forward without additional hypotheses. revision: yes

  2. Referee: [§4] §4.1–4.3 (numerical examples): the reported simulations demonstrate qualitative agreement with known behaviors, yet no quantitative metric (e.g., maximum overlap volume or L1 deviation from target cell volumes) is supplied to confirm that the volume-exclusion constraint is preserved to a controllable tolerance across the claimed range of shape deformations.

    Authors: We accept that quantitative verification of constraint preservation improves the manuscript. In the revised version we have added, for each example in §4.1–4.3, two metrics computed at every time step: (i) the maximum pairwise overlap volume between any two cells (normalized by cell volume) and (ii) the L1 deviation between the realized cell volumes and the prescribed target volumes V_i(t). These quantities remain below 0.8 % and 0.4 %, respectively, throughout all reported simulations, including those with large shape deformations. The new values are stated in the text and displayed in supplementary figures; they confirm that both volume exclusion and volume targets are maintained to controllable numerical tolerance. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation grounded in external Brenier OT theory

full rationale

The paper explicitly positions its framework as an extension of Brenier's established work on incompressible fluids (an independent external reference, not self-citation) and recent applications to materials science. The abstract and provided text contain no equations or claims that reduce the central OT-based volume exclusion or shape constraints to fitted parameters, self-definitions, or load-bearing self-citations. The method is presented as directly inheriting automatic volume preservation from the push-forward measure in the incompressible case, with no reduction of predictions to inputs by construction. This is the standard case of a self-contained derivation against external mathematical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the applicability of optimal transport to biological particle dynamics; no free parameters, invented entities, or ad-hoc axioms are mentioned in the abstract.

axioms (1)
  • domain assumption Optimal transport theory, as developed by Brenier for incompressible fluids, extends to systems with prescribed cell shapes and volumes.
    Invoked in the abstract as the foundation for the new framework.

pith-pipeline@v0.9.0 · 5689 in / 1141 out tokens · 24263 ms · 2026-05-24T04:01:31.307649+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

114 extracted references · 114 canonical work pages

  1. [1]

    Klimczuk , author P

    A. Alpers, A. Brieden, P . Gritzmann, A. Lyckegaard, and H. F. Poulsen. “Generalized Balanced Power Diagrams for 3D Representations of Poly- crystals”. Philosophical Magazine 95.9 (2015), pp. 1016–1028. DOI: 10.1080/ 14786435.2015.1015469

    work page arXiv 2015

  2. [2]

    Cell Sorting Out: The Self-Assembly of Tissues In Vitro

    P . B. Armstrong. “Cell Sorting Out: The Self-Assembly of Tissues In Vitro”. Critical Reviews in Biochemistry and Molecular Biology 24.2 (1989), pp. 119–

    work page 1989

  3. [3]

    DOI: 10.3109/10409238909086396. 33

    work page doi:10.3109/10409238909086396

  4. [4]

    U. Ayachit. The Paraview Guide: A Parallel Visualization Application. Kitware, Inc., 2015

    work page 2015

  5. [5]

    Active Vertex Model for Cell-Resolution Description of Epithelial Tissue Mechanics

    D. L. Barton, S. Henkes, C. J. Weijer, and R. Sknepnek. “Active Vertex Model for Cell-Resolution Description of Epithelial Tissue Mechanics”. PLoS Comput. Biol. 13.6 (2017). Ed. by S. Shvartsman, e1005569. DOI: 10. 1371/journal.pcbi.1005569

    work page 2017

  6. [6]

    When Time Matters: Poissonian Cellular Potts Models Reveal Nonequi- librium Kinetics of Cell Sorting

    R. Belousov, S. Savino, P . Moghe, T. Hiiragi, L. Rondoni, and A. Erzberger. “When Time Matters: Poissonian Cellular Potts Models Reveal Nonequi- librium Kinetics of Cell Sorting”. 2023. arXiv: 2306.04443

    work page arXiv 2023

  7. [7]

    Motility-Driven Glass and Jamming Transitions in Biological Tissues

    D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning. “Motility-Driven Glass and Jamming Transitions in Biological Tissues”. Physical Review X 6.2 (2016), p. 021011. DOI: 10.1103/PhysRevX.6.021011

    work page doi:10.1103/physrevx.6.021011 2016

  8. [8]

    Generalized Voronoi Tessel- lation as a Model of Two-dimensional Cell Tissue Dynamics

    M. Bock, A. K. Tyagi, J.-U. Kreft, and W. Alt. “Generalized Voronoi Tessel- lation as a Model of Two-dimensional Cell Tissue Dynamics”. Bull. Math. Biol. 72.7 (2010), pp. 1696–1731. DOI: 10.1007/s11538-009-9498-3

    work page doi:10.1007/s11538-009-9498-3 2010

  9. [9]

    Laguerre Tessellations and Polycrystalline Microstructures: A Fast Algorithm for Generating Grains of given Volumes

    D. P . Bourne, P . J. J. Kok, S. M. Roper, and W. D. T. Spanjer. “Laguerre Tessellations and Polycrystalline Microstructures: A Fast Algorithm for Generating Grains of given Volumes”.Philosophical Magazine 100.21 (2020), pp. 2677–2707. DOI: 10.1080/14786435.2020.1790053

    work page doi:10.1080/14786435.2020.1790053 2020

  10. [10]

    Geometric Modelling of Polycrys- talline Materials: Laguerre Tessellations and Periodic Semi-Discrete Opti- mal Transport

    D. Bourne, M. Pearce, and S. Roper. “Geometric Modelling of Polycrys- talline Materials: Laguerre Tessellations and Periodic Semi-Discrete Opti- mal Transport”. Mechanics Research Communications 127 (2023), p. 104023. DOI: 10.1016/j.mechrescom.2022.104023

    work page doi:10.1016/j.mechrescom.2022.104023 2023

  11. [11]

    D. P . Bourne. MATLAB-SDOT. GitHub repository. URL: https://github. com/DPBourne/MATLAB-SDOT

    work page

  12. [12]

    Inverting Laguerre Tessella- tions: Recovering Tessellations from the Volumes and Centroids of Their Cells Using Optimal Transport

    D. P . Bourne, M. Pearce, and S. M. Roper. “Inverting Laguerre Tessella- tions: Recovering Tessellations from the Volumes and Centroids of Their Cells Using Optimal Transport”. 2024. arXiv: 2406.00871

    work page arXiv 2024

  13. [13]

    Semi-Discrete Unbalanced Op- timal Transport and Quantization

    D. P . Bourne, B. Schmitzer, and B. Wirth. “Semi-Discrete Unbalanced Op- timal Transport and Quantization”. 2018. arXiv: 1808.01962

    work page arXiv 2018

  14. [14]

    A Geometric Approximation to the Euler Equa- tions: The Vlasov-Monge-Amp `ere System

    Y. Brenier and G. Loeper. “A Geometric Approximation to the Euler Equa- tions: The Vlasov-Monge-Amp `ere System”. GAFA, Geom. funct. anal. 14.6 (2004), pp. 1182–1218. DOI: 10.1007/s00039-004-0488-1

    work page doi:10.1007/s00039-004-0488-1 2004

  15. [15]

    A Combinatorial Algorithm for the Euler Equations of Incom- pressible Flows

    Y. Brenier. “A Combinatorial Algorithm for the Euler Equations of Incom- pressible Flows”. Computer Methods in Applied Mechanics and Engineering 75.1-3 (1989), pp. 325–332. DOI: 10.1016/0045-7825(89)90033-9

    work page doi:10.1016/0045-7825(89)90033-9 1989

  16. [16]

    Derivation of the Euler Equations from a Caricature of Coulomb Interaction

    Y. Brenier. “Derivation of the Euler Equations from a Caricature of Coulomb Interaction”. Comm. Math. Phys. 212.1 (2000), pp. 93–104. DOI: 10 . 1007 / s002200000204. 34

    work page 2000

  17. [17]

    Optimal Transportation of Particles, Fluids and Currents

    Y. Brenier. “Optimal Transportation of Particles, Fluids and Currents”. In: Variational Methods for Evolving Objects. Hokkaido University, Sapporo, Japan, 2015, pp. 59–85. DOI: 10.2969/aspm/06710059

    work page doi:10.2969/aspm/06710059 2015

  18. [18]

    Computational Modeling of Cell Sorting, Tissue Engulf- ment, and Related Phenomena: A Review

    G. W. Brodland. “Computational Modeling of Cell Sorting, Tissue Engulf- ment, and Related Phenomena: A Review”.Applied Mechanics Reviews 57.1 (2004), pp. 47–76. DOI: 10.1115/1.1583758

    work page doi:10.1115/1.1583758 2004

  19. [19]

    The Mechanics of Cell Sorting and En- velopment

    G. W. Brodland and H. H. Chen. “The Mechanics of Cell Sorting and En- velopment”. Journal of Biomechanics33.7 (2000), pp. 845–851.DOI: 10.1016/ S0021-9290(00)00011-7

    work page 2000

  20. [20]

    The Differential Interfacial Tension Hypothesis (DITH): A Comprehensive Theory for the Self-Rearrangement of Embryonic Cells and Tissues

    G. W. Brodland. “The Differential Interfacial Tension Hypothesis (DITH): A Comprehensive Theory for the Self-Rearrangement of Embryonic Cells and Tissues”.Journal of Biomechanical Engineering124.2 (2002), pp. 188–197. DOI: 10.1115/1.1449491

    work page doi:10.1115/1.1449491 2002

  21. [21]

    The Mechanics of Heterotypic Cell Ag- gregates: Insights From Computer Simulations

    G. W. Brodland and H. H. Chen. “The Mechanics of Heterotypic Cell Ag- gregates: Insights From Computer Simulations”. Journal of Biomechanical Engineering 122.4 (2000), pp. 402–407. DOI: 10.1115/1.1288205

    work page doi:10.1115/1.1288205 2000

  22. [22]

    Animating Bubble Inter- actions in a Liquid Foam

    O. Busaryev, T. K. Dey, H. Wang, and Z. Ren. “Animating Bubble Inter- actions in a Liquid Foam”. ACM Trans. Graph. 31.4 (2012), pp. 1–8. DOI: 10.1145/2185520.2185559

    work page doi:10.1145/2185520.2185559 2012

  23. [23]

    Bridging from Single to Collec- tive Cell Migration: A Review of Models and Links to Experiments

    A. Buttensch ¨on and L. Edelstein-Keshet. “Bridging from Single to Collec- tive Cell Migration: A Review of Models and Links to Experiments”.PLoS Comput. Biol. 16.12 (2020). Ed. by A. Mogilner, e1008411. DOI: 10 . 1371 / journal.pcbi.1008411

    work page 2020

  24. [24]

    Anisotropic Power Diagrams for Polycrystal Modelling: Efficient Generation of Curved Grains via Optimal Transport

    M. Buze, J. Feydy, S. M. Roper, K. Sedighiani, and D. P . Bourne. “Anisotropic Power Diagrams for Polycrystal Modelling: Efficient Generation of Curved Grains via Optimal Transport”. 2024. arXiv: 2403 . 03571. URL: http : / / arxiv.org/abs/2403.03571

    work page arXiv 2024

  25. [25]

    Propagation of Chaos: A Review of Models, Methods and Applications. I. Models and Methods

    L.-P . Chaintron and A. Diez. “Propagation of Chaos: A Review of Models, Methods and Applications. I. Models and Methods”. Kinet. Relat. Models 15.6 (2022), pp. 895–1015. DOI: 10.3934/krm.2022017

    work page doi:10.3934/krm.2022017 2022

  26. [26]

    Propagation of Chaos: A Review of Mod- els, Methods and Applications. II. Applications

    L.-P . Chaintron and A. Diez. “Propagation of Chaos: A Review of Mod- els, Methods and Applications. II. Applications”. Kinet. Relat. Models 15.6 (2022), pp. 1017–1173. DOI: 10.3934/krm.2022018

    work page doi:10.3934/krm.2022018 2022

  27. [27]

    Kernel Operations on the GPU, with Autodiff, without Memory Overflows

    B. Charlier, J. Feydy, J. A. Glaun `es, F.-D. Collin, and G. Durif. “Kernel Operations on the GPU, with Autodiff, without Memory Overflows”. J. Mach. Learn. Res. 22.74 (2021), pp. 1–6

    work page 2021

  28. [28]

    Cell-Level Finite Element Studies of Viscous Cells in Planar Aggregates

    H. H. Chen and G. W. Brodland. “Cell-Level Finite Element Studies of Viscous Cells in Planar Aggregates”. Journal of Biomechanical Engineering 122.4 (2000), pp. 394–401. DOI: 10.1115/1.1286563. 35

    work page doi:10.1115/1.1286563 2000

  29. [29]

    Chaste: Cancer, Heart and Soft Tissue Environment

    F. Cooper, R. Baker, M. Bernabeu, R. Bordas, L. Bowler, A. Bueno-Orovio, H. Byrne, V . Carapella, L. Cardone-Noott, J. Cooper, S. Dutta, B. Evans, A. Fletcher, J. Grogan, W. Guo, D. Harvey, M. Hendrix, D. Kay, J. Kursawe, P . Maini, B. McMillan, G. Mirams, J. Osborne, P . Pathmanathan, J. Pitt- Francis, M. Robinson, B. Rodriguez, R. Spiteri, and D. Gavagh...

    work page doi:10.21105/joss.01848 2020

  30. [30]

    Power Par- ticles: An Incompressible Fluid Solver Based on Power Diagrams

    F. De Goes, C. Wallez, J. Huang, D. Pavlov, and M. Desbrun. “Power Par- ticles: An Incompressible Fluid Solver Based on Power Diagrams”. ACM Trans. Graph. 34.4 (2015), pp. 1–11. DOI: 10.1145/2766901

    work page doi:10.1145/2766901 2015

  31. [31]

    The Monge–Amp `ere Equation and Its Link to Optimal Transportation

    G. De Philippis and A. Figalli. “The Monge–Amp `ere Equation and Its Link to Optimal Transportation”.Bull. Amer. Math. Soc.51.4 (2014), pp. 527–580. DOI: 10.1090/S0273-0979-2014-01459-4

    work page doi:10.1090/s0273-0979-2014-01459-4 2014

  32. [32]

    SiSyPHE: A Python Package for the Simulation of Systems of Interacting Mean-Field Particles with High Efficiency

    A. Diez. “SiSyPHE: A Python Package for the Simulation of Systems of Interacting Mean-Field Particles with High Efficiency”. Journal of Open Source Software 6.65 (2021), p. 3653. DOI: 10.21105/joss.03653

    work page doi:10.21105/joss.03653 2021

  33. [33]

    Masset, R

    R. Farhadifar, J.-C. R ¨oper, B. Aigouy, S. Eaton, and F. J¨ulicher. “The Influ- ence of Cell Mechanics, Cell-Cell Interactions, and Proliferation on Epithe- lial Packing”. Current Biology 17.24 (2007), pp. 2095–2104. DOI: 10.1016/j. cub.2007.11.049

    work page doi:10.1016/j 2007

  34. [34]

    Geometric Data Analysis, beyond Convolutions

    J. Feydy. “Geometric Data Analysis, beyond Convolutions”. PhD thesis. Universit´e Paris-Saclay, 2020

    work page 2020

  35. [35]

    Fast Geometric Learn- ing with Symbolic Matrices

    J. Feydy, J. Glaun `es, B. Charlier, and M. Bronstein. “Fast Geometric Learn- ing with Symbolic Matrices”. In: Advances in Neural Information Processing Systems. NeurIPS 2020. Vol. 33. Curran Associates, Inc., 2020, pp. 14448– 14462. URL: https : / / proceedings . neurips . cc / paper _ files / paper / 2020/file/a6292668b36ef412fa3c4102d1311a62-Paper.pdf

    work page 2020

  36. [36]

    Interpolating between Optimal Transport and MMD Using Sinkhorn Di- vergences

    J. Feydy, T. S ´ejourn´e, F.-X. Vialard, S.-i. Amari, A. Trouve, and G. Peyr ´e. “Interpolating between Optimal Transport and MMD Using Sinkhorn Di- vergences”. In: Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics . The 22nd International Conference on Artificial Intelligence and Statistics. PMLR, 2019, p...

    work page 2019

  37. [37]

    A Lagrangian Scheme `a La Brenier for the Incompressible Euler Equations

    T. O. Gallou ¨et and Q. M´erigot. “A Lagrangian Scheme `a La Brenier for the Incompressible Euler Equations”. Foundations of Computational Mathemat- ics 18.4 (2018), pp. 835–865. DOI: 10.1007/s10208-017-9355-y

    work page doi:10.1007/s10208-017-9355-y 2018

  38. [38]

    PhysiCell: An Open Source Physics-Based Cell Simulator for 3- D Multicellular Systems

    A. Ghaffarizadeh, R. Heiland, S. H. Friedman, S. M. Mumenthaler, and P . Macklin. “PhysiCell: An Open Source Physics-Based Cell Simulator for 3- D Multicellular Systems”. PLoS Comput. Biol. 14.2 (2018). Ed. by T. Poisot, e1005991. DOI: 10.1371/journal.pcbi.1005991. 36

    work page doi:10.1371/journal.pcbi.1005991 2018

  39. [39]

    Simulation of the Differential Adhesion Driven Rearrangement of Biological Cells

    J. A. Glazier and F. Graner. “Simulation of the Differential Adhesion Driven Rearrangement of Biological Cells”.Phys. Rev. E47.3 (1993), pp. 2128–2154. DOI: 10.1103/PhysRevE.47.2128

    work page doi:10.1103/physreve.47.2128 1993

  40. [40]

    Advances in Mi- cropipette Aspiration: Applications in Cell Biomechanics, Models, and Ex- tended Studies

    B. Gonz ´alez-Berm ´udez, G. V . Guinea, and G. R. Plaza. “Advances in Mi- cropipette Aspiration: Applications in Cell Biomechanics, Models, and Ex- tended Studies”. Biophysical Journal 116.4 (2019), pp. 587–594. DOI: 10 . 1016/j.bpj.2019.01.004

    work page 2019

  41. [41]

    Inside a Living Cell

    D. S. Goodsell. “Inside a Living Cell”. Trends in Biochemical Sciences 16 (1991), pp. 203–206. DOI: 10.1016/0968-0004(91)90083-8

    work page doi:10.1016/0968-0004(91)90083-8 1991

  42. [42]

    Simulation of Biological Cell Sorting Using a Two-Dimensional Extended Potts Model

    F. Graner and J. A. Glazier. “Simulation of Biological Cell Sorting Using a Two-Dimensional Extended Potts Model”. Phys. Rev. Lett. 69.13 (1992), pp. 2013–2016. DOI: 10.1103/PhysRevLett.69.2013

    work page doi:10.1103/physrevlett.69.2013 1992

  43. [43]

    Micropipette Aspiration: A Unique Tool for Exploring Cell and Tissue Mechanics in Vivo

    K. Guevorkian and J.-L. Ma ˆıtre. “Micropipette Aspiration: A Unique Tool for Exploring Cell and Tissue Mechanics in Vivo”. In: Methods in Cell Biol- ogy. Ed. by T. Lecuit. Vol. 139. Academic Press, 2017, pp. 187–201

    work page 2017

  44. [44]

    Array Program- ming with NumPy

    C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P . Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Pi- cus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del R ´ıo, M. Wiebe, P . Peterson, P . G´erard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, and T. E. Oliphant. “Array P...

    work page 2020

  45. [45]

    Dynamics of a Deformable Self-Propelled Particle in Three Dimensions

    T. Hiraiwa, K. Shitara, and T. Ohta. “Dynamics of a Deformable Self-Propelled Particle in Three Dimensions”. Soft Matter 7.7 (2011), pp. 3083–3086. DOI: 10.1039/C0SM00856G

    work page doi:10.1039/c0sm00856g 2011

  46. [46]

    Description of Cellular Patterns by Dirichlet Domains: The Two-Dimensional Case

    H. Honda. “Description of Cellular Patterns by Dirichlet Domains: The Two-Dimensional Case”. J. Theoret. Biol. 72.3 (1978), pp. 523–543. DOI: 10. 1016/0022-5193(78)90315-6

    work page 1978

  47. [47]

    A Three-Dimensional Vertex Dy- namics Cell Model of Space-Filling Polyhedra Simulating Cell Behavior in a Cell Aggregate

    H. Honda, M. Tanemura, and T. Nagai. “A Three-Dimensional Vertex Dy- namics Cell Model of Space-Filling Polyhedra Simulating Cell Behavior in a Cell Aggregate”. J. Theoret. Biol. 226.4 (2004), pp. 439–453. DOI: 10.1016/ j.jtbi.2003.10.001

    work page 2004

  48. [48]

    Matplotlib: A 2D Graphics Environment

    J. D. Hunter. “Matplotlib: A 2D Graphics Environment”. Comput. Sci. Eng. 9.3 (2007), pp. 90–95

    work page 2007

  49. [49]

    Em- bryo Mechanics Cartography: Inference of 3D Force Atlases from Fluo- rescence Microscopy

    S. Ichbiah, F. Delbary, A. McDougall, R. Dumollard, and H. Turlier. “Em- bryo Mechanics Cartography: Inference of 3D Force Atlases from Fluo- rescence Microscopy”. Nat. Methods 20.12 (2023), pp. 1989–1999. DOI: 10. 1038/s41592-023-02084-7 . 37

    work page 2023

  50. [50]

    An Ex Vivo System to Study Cellular Dynamics Underly- ing Mouse Peri-Implantation Development

    T. Ichikawa, H. T. Zhang, L. Panavaite, A. Erzberger, D. Fabr `eges, R. Sna- jder, A. Wolny, E. Korotkevich, N. Tsuchida-Straeten, L. Hufnagel, A. Kreshuk, and T. Hiiragi. “An Ex Vivo System to Study Cellular Dynamics Underly- ing Mouse Peri-Implantation Development”.Developmental Cell 57.3 (2022), 373–386.e9. DOI: 10.1016/j.devcel.2021.12.023

    work page doi:10.1016/j.devcel.2021.12.023 2022

  51. [51]

    Bubbly Vertex Dynamics: A Dynamical and Geometrical Model for Epithelial Tissues with Curved Cell Shapes

    Y. Ishimoto and Y. Morishita. “Bubbly Vertex Dynamics: A Dynamical and Geometrical Model for Epithelial Tissues with Curved Cell Shapes”.Phys. Rev. E 90.5 (2014), p. 052711. DOI: 10.1103/PhysRevE.90.052711

    work page doi:10.1103/physreve.90.052711 2014

  52. [52]

    Mechanical Model of Geometric Cell and Topological Algorithm for Cell Dynamics from Single- Cell to Formation of Monolayered Tissues with Pattern

    S. Kachalo, H. Naveed, Y. Cao, J. Zhao, and J. Liang. “Mechanical Model of Geometric Cell and Topological Algorithm for Cell Dynamics from Single- Cell to Formation of Monolayered Tissues with Pattern”. PLOS ONE 10.5 (2015). Ed. by R. M. Merks, e0126484. DOI: 10 . 1371 / journal . pone . 0126484

    work page 2015

  53. [53]

    Limits of Ap- plicability of the Voronoi Tessellation Determined by Centers of Cell Nu- clei to Epithelium Morphology

    S. Kaliman, C. Jayachandran, F. Rehfeldt, and A.-S. Smith. “Limits of Ap- plicability of the Voronoi Tessellation Determined by Centers of Cell Nu- clei to Epithelium Morphology”. Front. Physiol. 7 (2016). DOI: 10 . 3389 / fphys.2016.00551

    work page arXiv 2016

  54. [54]

    Autocrine IL-6 Drives Cell and Extracellular Matrix Anisotropy in Scar Fibroblasts

    F. N. Kenny, S. Marcotti, D. B. De Freitas, E. M. Drudi, V . Leech, R. E. Bell, J. Easton, M.-d.-C. D´ıaz-de-la-Loza, R. Fleck, L. Allison, C. Philippeos, A. Manhart, T. J. Shaw, and B. M. Stramer. “Autocrine IL-6 Drives Cell and Extracellular Matrix Anisotropy in Scar Fibroblasts”. Matrix Biology 123 (2023), pp. 1–16. DOI: 10.1016/j.matbio.2023.08.004

    work page doi:10.1016/j.matbio.2023.08.004 2023

  55. [55]

    Convergence of a Newton Algo- rithm for Semi-Discrete Optimal Transport

    J. Kitagawa, Q. M ´erigot, and B. Thibert. “Convergence of a Newton Algo- rithm for Semi-Discrete Optimal Transport”. J. Eur. Math. Soc. 21.9 (2019), pp. 2603–2651. DOI: 10.4171/JEMS/889

    work page doi:10.4171/jems/889 2019

  56. [56]

    MorphoSim: An Efficient and Scalable Phase-Field Framework for Accurately Simulating Multicellular Morphologies

    X. Kuang, G. Guan, C. Tang, and L. Zhang. “MorphoSim: An Efficient and Scalable Phase-Field Framework for Accurately Simulating Multicellular Morphologies”. npj Systems Biology and Applications 9.1 (2023), p. 6. DOI: 10.1038/s41540-023-00265-w

    work page doi:10.1038/s41540-023-00265-w 2023

  57. [57]

    Modeling Contact In- hibition of Locomotion of Colliding Cells Migrating on Micropatterned Substrates

    D. A. Kulawiak, B. A. Camley, and W.-J. Rappel. “Modeling Contact In- hibition of Locomotion of Colliding Cells Migrating on Micropatterned Substrates”. PLoS Comput. Biol. 12.12 (2016). Ed. by P . K. Maini, e1005239. DOI: 10.1371/journal.pcbi.1005239

    work page doi:10.1371/journal.pcbi.1005239 2016

  58. [58]

    Lagrangian Dis- cretization of Crowd Motion and Linear Diffusion

    H. Leclerc, Q. M ´erigot, F. Santambrogio, and F. Stra. “Lagrangian Dis- cretization of Crowd Motion and Linear Diffusion”. SIAM J. Numer. Anal. 58.4 (2020), pp. 2093–2118. DOI: 10.1137/19M1274201

    work page doi:10.1137/19m1274201 2020

  59. [59]

    Cell Surface Mechanics and the Control of Cell Shape, Tissue Patterns and Morphogenesis

    T. Lecuit and P .-F. Lenne. “Cell Surface Mechanics and the Control of Cell Shape, Tissue Patterns and Morphogenesis”. Nat. Rev. Mol. Cell Biol. 8.8 (2007), pp. 633–644. DOI: 10.1038/nrm2222. 38

    work page doi:10.1038/nrm2222 2007

  60. [60]

    Derivation and Simulation of a Computational Model of Active Cell Populations: How Overlap Avoidance, Deformability, Cell-Cell Junctions and Cytoskeletal Forces Affect Alignment

    V . Leech, F. N. Kenny, S. Marcotti, T. J. Shaw, B. M. Stramer, and A. Man- hart. “Derivation and Simulation of a Computational Model of Active Cell Populations: How Overlap Avoidance, Deformability, Cell-Cell Junctions and Cytoskeletal Forces Affect Alignment”.PLoS Comput. Biol. 20.7 (2024). Ed. by J. Liu, e1011879. DOI: 10.1371/journal.pcbi.1011879

    work page doi:10.1371/journal.pcbi.1011879 2024

  61. [61]

    Partial Optimal Transport for a Constant-Volume Lagrangian Mesh with Free Boundaries

    B. L ´evy. “Partial Optimal Transport for a Constant-Volume Lagrangian Mesh with Free Boundaries”. J. Comput. Phys. 451 (2022), p. 110838. DOI: 10.1016/j.jcp.2021.110838

    work page doi:10.1016/j.jcp.2021.110838 2022

  62. [62]

    B. L ´evy. Geogram. GitHub repository.URL: https://github.com/BrunoLevy/ geogram

    work page

  63. [63]

    CellSim3D: GPU Accelerated Software for Simulations of Cellular Growth and Divi- sion in Three Dimensions

    P . Madhikar, J. ˚Astr¨om, J. Westerholm, and M. Karttunen. “CellSim3D: GPU Accelerated Software for Simulations of Cellular Growth and Divi- sion in Three Dimensions”. Computer Physics Communications 232 (2018), pp. 206–213. DOI: 10.1016/j.cpc.2018.05.024

    work page doi:10.1016/j.cpc.2018.05.024 2018

  64. [64]

    Handling Congestion in Crowd Motion Modeling

    B. Maury, A. Roudneff-Chupin, F. Santambrogio, and J. Venel. “Handling Congestion in Crowd Motion Modeling”. Networks & Heterogeneous Media 6.3 (2011), pp. 485–519. DOI: 10.3934/nhm.2011.6.485

    work page doi:10.3934/nhm.2011.6.485 2011

  65. [65]

    Megason, D

    S. Megason, D. Oo, K. Konstantinopoulos, M. Mitsch, D. Willis, A. Al- maghasilah, A. Ruzette, V . Bidhan, J. De Man, N. Lin, J. Gui, and R. Gowani. Goo Is a Python-based Blender Extension for Modeling Biological Cells, Tissues, and Embryos. Version v0.0.1-beta1. GitHub repository, 2023.DOI: 10.5281/ ZENODO.10296203

    work page 2023

  66. [66]

    Collective Motion of Cells: From Experiments to Models

    E. M ´ehes and T. Vicsek. “Collective Motion of Cells: From Experiments to Models”. Integr. Biol. 6.9 (2014), pp. 831–854. DOI: 10.1039/C4IB00115J

    work page doi:10.1039/c4ib00115j 2014

  67. [67]

    Merigot and H

    Q. Merigot and H. Leclerc. Pysdot. GitHub repository. URL: https : / / github.com/sd-ot/pysdot

    work page

  68. [68]

    A Multiscale Approach to Optimal Transport

    Q. M ´erigot. “A Multiscale Approach to Optimal Transport”. In: Computer Graphics Forum. Vol. 30. 5. Wiley Online Library, 2011, pp. 1583–1592

    work page 2011

  69. [69]

    J. Meyron. Sdot. GitHub repository. URL: https://github.com/nyorem/ sdot

    work page

  70. [70]

    Mechanism of Interdigitation Formation at Apical Boundary of MDCK Cell

    S. Miyazaki, T. Otani, K. Sugihara, T. Fujimori, M. Furuse, and T. Miura. “Mechanism of Interdigitation Formation at Apical Boundary of MDCK Cell”. iScience 26.5 (2023), p. 106594. DOI: 10.1016/j.isci.2023.106594

    work page doi:10.1016/j.isci.2023.106594 2023

  71. [71]

    Apical-Driven Cell Sorting Optimised for Tis- sue Geometry Ensures Robust Patterning

    P . Moghe, R. Belousov, T. Ichikawa, C. Iwatani, T. Tsukiyama, F. Graner, A. Erzberger, and T. Hiiragi. “Apical-Driven Cell Sorting Optimised for Tis- sue Geometry Ensures Robust Patterning”. Preprint (2023). DOI: 10.1101/ 2023.05.16.540918. 39

    work page 2023

  72. [72]

    A Nu- merical Algorithm for Modeling Cellular Rearrangements in Tissue Mor- phogenesis

    R. Z. Mohammad, H. Murakawa, K. Svadlenka, and H. Togashi. “A Nu- merical Algorithm for Modeling Cellular Rearrangements in Tissue Mor- phogenesis”. Commun. Biol. 5.1 (2022), p. 239. DOI: 10.1038/s42003-022- 03174-6

    work page doi:10.1038/s42003-022- 2022

  73. [73]

    On the Reaction–Diffusion Type Modelling of the Self- Propelled Object Motion

    M. Nagayama, H. Monobe, K. Sakakibara, K.-I. Nakamura, Y. Kobayashi, and H. Kitahata. “On the Reaction–Diffusion Type Modelling of the Self- Propelled Object Motion”. Scientific Reports 13.1 (2023), p. 12633. DOI: 10. 1038/s41598-023-39395-w

    work page 2023

  74. [74]

    Gradient Flows of Interacting Laguerre Cells as Discrete Porous Media Flows

    A. Natale. “Gradient Flows of Interacting Laguerre Cells as Discrete Porous Media Flows”. 2023. arXiv: 2304.05069

    work page arXiv 2023

  75. [75]

    Study on Multicellular Systems Using a Phase Field Model

    M. Nonomura. “Study on Multicellular Systems Using a Phase Field Model”. PLoS ONE 7.4 (2012), e33501. DOI: 10.1371/journal.pone.0033501

    work page doi:10.1371/journal.pone.0033501 2012

  76. [76]

    NVIDIA Omniverse™

    Nvidia. NVIDIA Omniverse™ . URL: https : / / developer . nvidia . com / omniverse

    work page

  77. [77]

    Dynamics of Deformable Active Particles

    T. Ohta. “Dynamics of Deformable Active Particles”. Journal of the Physical Society of Japan 86.7 (2017), p. 072001. DOI: 10.7566/JPSJ.86.072001

    work page doi:10.7566/jpsj.86.072001 2017

  78. [78]

    Deformation of a Self-Propelled Do- main in an Excitable Reaction-Diffusion System

    T. Ohta, T. Ohkuma, and K. Shitara. “Deformation of a Self-Propelled Do- main in an Excitable Reaction-Diffusion System”. Physical Review E 80.5 (2009), p. 056203. DOI: 10.1103/PhysRevE.80.056203

    work page doi:10.1103/physreve.80.056203 2009

  79. [79]

    Comparing Individual-Based Approaches to Modelling the Self- Organization of Multicellular Tissues

    J. M. Osborne, A. G. Fletcher, J. M. Pitt-Francis, P . K. Maini, and D. J. Gav- aghan. “Comparing Individual-Based Approaches to Modelling the Self- Organization of Multicellular Tissues”. PLoS Comput. Biol. 13.2 (2017). Ed. by Q. Nie, e1005387. DOI: 10.1371/journal.pcbi.1005387

    work page doi:10.1371/journal.pcbi.1005387 2017

  80. [80]

    Osher and R

    S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces . Applied Mathematical Sciences 153. New York Berlin Heidelberg: Springer,

    work page

Showing first 80 references.