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PLoS Computational BiologySystems BiologyPeer-reviewed journal article

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

Ahmadreza GhaffarizadehiD, Randy W. HeilandiD, Samuel H. FriedmaniD, Shannon M. MumenthaleriD, Paul MackliniD

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Abstract

Many multicellular systems problems can only be understood by studying how cells move, grow, divide, interact, and die. Tissue-scale dynamics emerge from systems of many interacting cells as they respond to and influence their microenvironment. The ideal \"virtual laboratory\" for such multicellular systems simulates both the biochemical microenvironment (the \"stage\") and many mechanically and biochemically interacting cells (the \"players\" upon the stage).\n\nPhysiCell--physics-based multicellular simulator--is an open source agent-based simulator that provides both the stage and the players for studying many interacting cells in dynamic tissue microenvironments. It builds upon a multi-substrate biotransport solver to link cell phenotype to multiple diffusing substrates and signaling factors. It includes biologically-driven sub-models for cell cycling, apoptosis, necrosis, solid and fluid volume changes, mechanics, and motility \"out of the box.\" The C++ code has minimal dependencies, making it simple to maintain and deploy across platforms. PhysiCell has been parallelized with OpenMP, and its performance scales linearly with the number of cells. Simulations up to 105-106 cells are feasible on quad-core desktop workstations; larger simulations are attainable on single HPC compute nodes.\n\nWe demonstrate PhysiCell by simulating the impact of necrotic core biomechanics, 3-D geometry, and stochasticity on the dynamics of hanging drop tumor spheroids and ductal carcinoma in situ (DCIS) of the breast. We demonstrate stochastic motility, chemical and contact-based interaction of multiple cell types, and the extensibility of PhysiCell with examples in synthetic multicellular systems (a \"cellular cargo delivery\" system, with application to anti-cancer treatments), cancer heterogeneity, and cancer immunology. PhysiCell is a powerful multicellular systems simulator that will be continually improved with new capabilities and performance improvements. It also represents a significant independent code base for replicating results from other simulation platforms. The PhysiCell source code, examples, documentation, and support are available under the BSD license at http://PhysiCell.MathCancer.org and http://PhysiCell.sf.net.\n\nAuthor SummaryThis paper introduces PhysiCell: an open source, agent-based modeling framework for 3-D multicellular simulations. It includes a standard library of sub-models for cell fluid and solid volume changes, cycle progression, apoptosis, necrosis, mechanics, and motility. PhysiCell is directly coupled to a biotransport solver to simulate many diffusing substrates and cell-secreted signals. Each cell can dynamically update its phenotype based on its microenvironmental conditions. Users can customize or replace the included sub-models.\n\nPhysiCell runs on a variety of platforms (Linux, OSX, and Windows) with few software dependencies. Its computational cost scales linearly in the number of cells. It is feasible to simulate 500,000 cells on quad-core desktop workstations, and millions of cells on single HPC compute nodes. We demonstrate PhysiCell by simulating the impact of necrotic core biomechanics, 3-D geometry, and stochasticity on hanging drop tumor spheroids (HDS) and ductal carcinoma in situ (DCIS) of the breast. We demonstrate contact- and chemokine-based interactions among multiple cell types with examples in synthetic multicellular bioengineering, cancer heterogeneity, and cancer immunology.\n\nWe developed PhysiCell to help the scientific community tackle multicellular systems biology problems involving many interacting cells in multi-substrate microenvironments. PhysiCell is also an independent, cross-platform codebase for replicating results from other simulators.

In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 4 (21 Dec 2017) · CC BY 4.0

Open source off-lattice agent-based C++ simulator PhysiCell, coupled to the BioFVM diffusion solver, simulates 3-D multicellular tissues with cost linear in cell number, reaching roughly 10^6 cells.

Existing 3-D multicellular frameworks each have drawbacks: some cannot scale beyond about 10^5 cells, some are closed source or need many dependencies, none ships cycle, death and necrosis models, and their PDE solvers generally handle diffusing factors one at a time. PhysiCell links standard phenotype sub-models and fluid/solid volume regulation to BioFVM multi-substrate biotransport, in cross-platform C++ that needs only two external dependencies.

Key results

  1. ShownWall-clock cost per simulated hour grew roughly linearly with agent count on both a desktop and a single HPC node. A 3-D spheroid reached about 10^6 cells in a few days of wall time.

    HPC node (dual 6-core Xeon X5690, 24 threads): ~10^6 cells after 67 h (deterministic, 17 simulated days) to 76 h (stochastic, 18.2 days), with output saved hourly. Desktop (i7-4790, 8 threads): past 573,000 cells (~14.6 days) in ~80 h. The 24-thread node outperformed the 8-thread desktop by a factor of 2 to 2.5. · Performance testing (summary); Test platforms; Performance scaling

  2. ShownIn simulated hanging drop spheroids, oxygen gradients restricted division to an outer rim, so diameter grew linearly. The necrotic core formed a network of fluid voids because shrinking necrotic cells kept adhering, a structure resembling an in vitro spheroid image.

    Started from ~2300 cells in an 8 mm^3 domain with 38 mmHg boundary pO2; both necrosis models reached ~10^6 cells by 18 days. Deterministic necrosis grew faster (~5% difference in diameter and ~26% in cell count at day 18). The resemblance to an HCC827 spheroid image is qualitative; void features are ~1 to 10 μm. · Hanging drop tumor spheroids; Deterministic versus stochastic necrosis; Figure legends

  3. ShownStochastic oxygen-dependent necrosis gave a mixed viable/necrotic transition zone, while threshold necrosis gave a sharp boundary, yet in DCIS (ductal carcinoma in situ) both grew at the same coarse rate. Confinement in the duct collapsed the necrotic voids seen in spheroids.

    DCIS in a 1 mm duct segment (317.5 μm diameter) over 30 days: both models grew at ~1 cm/year while their cell counts differed by 21%. Mixing was strongest at the tumor's leading edge. The 3-D runs did not reproduce the rim/necrotic-core tears predicted by earlier 2-D models. · Ductal carcinoma in situ (DCIS); Comparison of necrosis models; comparison with…; Comparison with prior 2-D modeling results; Figure legends

  4. ShownConvergence tests support the default time steps: the mechanics and volume sub-models are first-order accurate in time, stochastic phase transitions reproduce coarse-grained ODE behavior, and solving many diffusing substrates together costs far less than solving each PDE separately.

    Relaxation tests on two overlapping cells and on a compressed 50,000-cell cluster converged first-order in Δt; Δtmech 0.1 min and Δtcells 6 min kept relative errors at 5% or less. 100 runs per Δt of the Ki67-advanced and apoptosis models matched ODE theory at Δtcell 6 and 60 min. BioFVM: 10 PDEs on 1,000,000 voxels took ~2.6 times the time of one PDE. · Biochemical microenvironment; Time steps; Convergence and validation testing

  5. SuggestedUser-written rules for contact adhesion, chemotaxis and drug damage produced emergent multicellular behaviors: cargo-delivering biorobots, clonal selection in heterogeneous tumors, and an immune attack in which strongly biased homing let peripheral tumor cells escape and regrow.

    Anti-cancer biorobots (10% worker and 90% cargo cells injected after 1 week; cargo released below 10 mmHg pO2) killed tumor cells but stopped delivering once hypoxia eased; raising the threshold to 15 mmHg only reduced this. Immune model: 7500 immune cells added at two weeks (bias b = 0.5) shrank the tumor within days, sparing less immunogenic cells, before regrowth. · “Biorobots”; Anti-cancer biorobots; Cancer heterogeneity and immune response; Adding an immune response

Methods, data and reproducibility

Off-lattice, cell-centered agent-based model in C++/OpenMP that extends BioFVM agents. Each cell carries a Phenotype with stochastic cycle/death transitions, ODE volume sub-models, potential-based adhesion/repulsion with inertialess velocities and biased motility, updated on three separated time steps while BioFVM solves multi-substrate reaction-diffusion.

  • In silico hanging drop tumor spheroid in an 8 mm^3 fluid domain with 38 mmHg boundary oxygen, comparing deterministic and stochastic necrosis over 18 days · n = ~2300 initial cells; ~10^6 cells at 18 days · 10.6084/m9.figshare.5716600; 10.6084/m9.figshare.5716597
  • In silico ductal carcinoma in situ (DCIS) in a 1 mm breast duct segment of 317.5 μm diameter, both necrosis models, 30 days · 10.6084/m9.figshare.5716480; 10.6084/m9.figshare.5721088.v1
  • Hanging drop spheroid image of HCC827 non-small cell lung carcinoma (Mumenthaler lab) used for qualitative comparison with the necrotic core structure
  • 2-D biorobots cargo-delivery simulation (director, cargo and worker cells) and an anti-cancer variant with no director cells that homes along oxygen gradients · n = Anti-cancer variant: 10% worker / 90% cargo cell injection · 10.6084/m9.figshare.5721136; 10.6084/m9.figshare.5721145
  • 2-D heterogeneous tumor with per-cell oncoprotein p drawn from a normal distribution (mean 1, SD 0.3) scaling cycle entry · 10.6084/m9.figshare.5721151
  • 3-D tumor immune response simulation extending the heterogeneity model with chemotactic, adhesive, killing immune cells · n = 7500 immune cells introduced at two weeks · 10.6084/m9.figshare.5717887
  • Numerical convergence tests: two overlapping cells, a compressed cell cluster, single-cell volume models, and stochastic cycle/apoptosis runs · n = 50,000-cell cluster; 100 simulations per Δt
Methods & tools
PhysiCell (C++ agent-based multicellular simulator), BioFVM (multi-substrate reaction-diffusion solver), pugixml (XML parsing), OpenMP parallelization, Locally one-dimensional operator splitting with Thomas tridiagonal solver, Second-order Adams-Bashforth position update, Backward/forward Euler ODE integration, Cell-cell interaction data structure (IDS) for neighbor search, Ki67 Advanced and live-cells cycle models, Deterministic and stochastic necrosis models, g++ / MinGW-w64, PhysiCell virtual appliance (VirtualBox)
Software & environment
C++11 compiler with OpenMP; pugixml and BioFVM bundled. The HDS/DCIS tests ran on PhysiCell 1.0.0 with g++ 4.9.1 (MinGW-w64, Windows 7) and g++ 4.8.4 (Ubuntu 14.04). Later examples ran on PhysiCell 1.2.1 with g++ 7.1.0 (Windows 10). A virtual appliance (.ova) is also offered.
Assay conditions & compute
Desktop: quad-core i7-4790, 3.60 GHz, 8 threads, 16 GB. HPC node: dual 6-core Xeon X5690, 3.47 GHz, 24 threads, 48 GB. Later examples: i7-4770K, 4.06 GHz, 8 threads, 32 GB. ~10^6 cells took 67 to 76 h on the HPC node.
Reproducibility gaps
Full equations, parameter values and convergence results are only in supplementary S1 Text. Xcode's g++ lacks OpenMP, so OSX users need Homebrew/MacPorts g++. MultiCellDS import/export is not fully implemented.
Limitations (6)
  • BioFVM (as of Version 1.1.7) has no advective transport, so advection-dominated problems need user-supplied solvers. There is no built-in extracellular matrix model, only suggested workarounds such as anchor points or a non-diffusing ECM substrate. · stated by the authors
  • Cells are modeled from their centers with no explicit morphology, so elongation, fusion, polarized adhesion and orientation are not modeled. SBML-based ODE integration, direct pressure/strain calculation and graphical design or analysis tools are also still missing. · stated by the authors
  • Neighbor-interaction testing is the main bottleneck. Cell volume can vary by a factor of 100, so neighbor lists grow where cells are small, and the cost-vs-cell-count slope can be up to 100 times steeper in necrosis-dominated simulations. · stated by the authors
  • The late divergence between deterministic and stochastic spheroid growth may come from differences in hypoxic gradients, but more simulations are needed to exclude stochastic effects. Coarse DCIS growth outputs alone cannot discriminate between the two necrosis models. · stated by the authors
  • Comparison with biology in the main text is qualitative (one spheroid image and DCIS pathology features). HDS and DCIS outcomes are reported per model with no stated replicate counts or variability estimates. · noted in this summary
  • The main text has no head-to-head runtime or accuracy benchmark against Chaste, CompuCell3D, TiSim or other frameworks on a shared test problem; the comparison is a feature review deferred to S1 Text. · noted in this summary

Read this if you build agent-based models of tumors, engineered tissues or immune-cancer interactions and need an open source 3-D simulator linking cell mechanics and phenotype to many diffusing substrates.

Citations
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FWCI
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