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Role of mechanical cues and hypoxia on the growth of tumor cells in strong and weak confinement: A dual in vitro–in silico approach

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Science Advances  25 Mar 2020:
Vol. 6, no. 13, eaaz7130
DOI: 10.1126/sciadv.aaz7130
  • Fig. 1 Experimental configuration.

    (A) Coaxial coextrusion in air then alginate capsule stabilization within the calcium bath. (B) Coextrusion within the calcium bath allowing for formation of alginate tubes. (C) Experimental observation of the strain permits, knowing the mechanical properties of the alginate shell, to recover numerically the exerted pressure on tumor cell.

  • Fig. 2 Mathematical model characteristics.

    (A) Description of the physical system. The considered mixture consists of tumor cells (t), the medium (m), and oxygen nutrient species (n) with the mass fraction of n being negligible with respect to t and m. Local properties of the phase depend on its composition. In the domain, high concentration gradients are allowed. (B) Evolution of the system bulk free energy as function of tumor cell mass fraction, ωt. (C) Evolution of the bulk counterpart of the chemical potential. Values of ωt near the equilibrium mass fraction, ωteq, identify areas occupied by the MCTS. In particular, when ωt<ωteq, cells tend to aggregate, while when ωt>ωteq, they repel each other. This mutual repulsion results in an increase in the pressure in the cell aggregate.

  • Fig. 3 Geometry and BCs.

    At the cylindrical symmetry axis (BC1) and symmetry plan (BC2), no normal fluxes are permitted. At the structure inner walls (BC3): Mass fraction of tumor cells is set equal to zero; normal component of chemical potential gradient is set equal to zero; convective-type BC for oxygen; and mechanical stress is fixed equal to the hydrostatic pressure in the external medium. (A) Capsule experimental and computational models. (B) Tube experimental and computational models.

  • Fig. 4 MCTS growth within the alginate capsule.

    (A) Kinetics of cell aggregate growth in the confined and free cases: Symbols are experimental data, and solid lines are numerical results. The grey dashed line shows the a posteriori estimate of the capsule inner radius. Confluence is indicated with vertical dashed lines. Bottom right insert shows the temporal evolution of the cell concentration in the core of the tumor aggregate. Upper left insert magnifies the differences observed in the few hours preceding confluence between confined and free spheroids. The regime difference is highlighted by the red surface. (B) At 54 hours: Experimental spatial distribution of cells (upper left corner), mass fraction of tumor cells within the domain (upper right corner), oxygen mass fraction (lower right corner), and pressure distribution (lower left corner). (C to E) Respective distributions of tumors mass fraction, oxygen mass fraction, and pressure along the radius at different times [dark lines refer to the results depicted in (B)].

  • Fig. 5 Cell aggregate growing within the alginate tube.

    (A) Length of the cylindroid and pressure in the center versus time: Symbols are experimental data, while solid lines are numerical results. (B) Experimental spatial distribution of cells (upper left corner), mass fraction of tumor cells within the domain (upper right corner), oxygen mass fraction (lower right corner), and pressure distribution (lower left corner). (C to E) Respective distribution of tumor mass fraction, oxygen mass fraction, and pressure along the longitudinal axis of the tube at different times. Dots in the pressure plot show pressure estimated from measured displacement at the center of the tumor cylindroid at the corresponding times.

  • Table 1 Numerical parameters.

    ParameterSymbolReference rangesIdentified valueUnit
    Surface tensionσ(19): 1–201.2mN m−1
    Tumor cells mobilityM2 × 10−16m5 s−1 J−1
    Growth rateγt(4): 0.01–0.030.026s−1
    Inhibition pressurep¯10.8kPa
    Critical inhibition pressurep¯2(10,11): 2–152.0kPa
    Inhibition mass fraction of oxygenω2¯(4): 3 × 10−6 to 4 ×∙10−68 × 10−6
    Critical inhibition mass fraction of oxygenω1¯(4): 1 × 10−6 to 3 × 10−61 × 10−6
    Pseudoconvective exchange coefficienthalgCalculated4.5 × 10−5s−1
    Oxygen diffusion in the mediumDnm(30): 1.2 × 10−9 to 1.4 × 10−92.7 × 10−9m2 s−1
    External mass fraction of oxygenωnextPrescribed9 × 10−6
    Oxygen consumption due to metabolismγnm(4)2 × 10−3s−1
    Oxygen consumption due to growthγng(4)2.6 × 10−3s−1
    Spherical capsule inner radiusrsPrescribed90 × 10−6m
    Cylindrical capsule inner radiusrcPrescribed52 × 10−6m
    Tube heighthcPrescribed800 × 10−6m
    Capsule and tubes wall thicknesstPrescribed30 × 10−6m

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/13/eaaz7130/DC1

    Movie S1. Phase-contrast time-lapse video of a growing multicellular spheroid in a spherical capsule.

    Movie S2. Phase-contrast time-lapse video of growing multicellular cylindroids in a cylindrical capsule.

    Movie S3. Numerical simulations of aggregate growth in spherical capsule.

    Movie S4. Numerical simulations of aggregate growth in tubular capsule.

    Fig. S1. Images of tumor aggregate growth in alginate capsule.

    Fig. S2. Pressure and oxygen mass fraction tumor cell growth dependence.

    Fig. S3. Numerical diffusive flow in alginate capsule.

    Fig. S4. Influence of hypoxia on volume evolution for spherical and tubular capsule.

    Fig. S5. Numerical radial plots of tubular capsule primary variables.

    Fig. S6. Tube radius as a function of distance from the cylindroid center along the main axis.

  • Supplementary Materials

    The PDF file includes:

    • Legends for movies S1 to S4
    • Fig. S1. Images of tumor aggregate growth in alginate capsule.
    • Fig. S2. Pressure and oxygen mass fraction tumor cell growth dependence.
    • Fig. S3. Numerical diffusive flow in alginate capsule.
    • Fig. S4. Influence of hypoxia on volume evolution for spherical and tubular capsule.
    • Fig. S5. Numerical radial plots of tubular capsule primary variables.
    • Fig. S6. Tube radius as a function of distance from the cylindroid center along the main axis.

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Phase-contrast time-lapse video of a growing multicellular spheroid in a spherical capsule.
    • Movie S2 (.mp4 format). Phase-contrast time-lapse video of growing multicellular cylindroids in a cylindrical capsule.
    • Movie S3 (.avi format). Numerical simulations of aggregate growth in spherical capsule.
    • Movie S4 (.avi format). Numerical simulations of aggregate growth in tubular capsule.

    Files in this Data Supplement:

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