Multiscale biphasic modelling of peritumoural collagen microstructure: The effect of tumour growth on permeability and fluid flow

<div><p>We present an in-silico model of avascular poroelastic tumour growth coupled with a multiscale biphasic description of the tumour–host environment. The model is specified to in-vitro data, facilitating biophysically realistic simulations of tumour spheroid growth into a dense collagen hydrogel. We use the model to first confirm that passive mechanical remodelling of collagen fibres at the tumour boundary is driven by solid stress, and not fluid pressure. The model is then used to demonstrate the influence of collagen microstructure on peritumoural permeability and interstitial fluid flow. Our model suggests that at the tumour periphery, remodelling causes the peritumoural stroma to become more permeable in the circumferential than radial direction, and the interstitial fluid velocity is found to be dependent on initial collagen alignment. Finally we show that solid stresses are negatively correlated with peritumoural permeability, and positively correlated with interstitial fluid velocity. These results point to a heterogeneous, microstructure-dependent force environment at the tumour–peritumoural stroma interface.</p></div

Initial state meshes at both scales.

<p>The tumour spheroid octant is shown as a red wire frame and has radius 0.1 mm; the peritumoural stroma is shown as an opaque blue volume has thickness 0.5 mm; and each RVE has a side length of approximately 20 microns (axes are not to scale).</p

Initial collagen microarchitecture influences final collagen alignment and fluid flow.

<p>Row-wise from top: Final state network principal orientation eigenvectors in the first layer of the PTS, for an initially (A) random and (B) aligned PTS. The colour bar indicates alignment with respect to the tumour boundary: 0 for circumferential, 1 for perpendicular. Final state network alignments for an initially (C) random and (D) aligned PTS. Final spherical IFV components near the tumour boundary, for an initially (E) random and (F) aligned PTS.</p

Final state variables in space and time.

<p>A: Final spherical solid stress components and IFP over radial distance. B: Final spherical solid stress components and IFP over time, integrated over the PTS volume. C: Final spherical permeability components over radial distance; inset shows a zoom into the tumour-PTS boundary. D: Final spherical permeability components over time, integrated over the PTS volume; inset shows the same for the region 0.1mm <<i>r</i> < 0.2mm. E: Final spherical IFV components over radial distance. F: Final spherical IFV components over time, integrated over the PTS volume. All time-dependent plots are normalised with respect to the initial volume of the PTS.</p

Tumour growth causes collagen remodelling.

<p>From top to bottom: final state peritumoural stroma mesh (both scales); final state RVEs from the (A) 5th, (B) 3rd and (C) 1st layers of the PTS; (D) histograms of the scalar product between the principal network permeability, <i>K</i>_<i>pvec</i>, and principal network orientation vectors, Ω_<i>pvec</i>; and (E) the scalar product between the principal network permeability and interstitial fluid velocity, <i>V</i>_<i>pvec</i>, for each RVE in the 1st layer of elements in the PTS. The arrows centred on each RVE show the principal eigenvectors of the network orientation (grey) and permeability (red), and the interstitial fluid velocity (blue).</p

Comparison of simulated breast shape (with texture) before and 3 months after surgery.

<p>Baseline biomechanical model (wireframe) with fitted upright surface scan that visualises the skin and oreola texture before surgery (left column). In view of the recorded surgical plan (cf. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159766#pone.0159766.g004" target="_blank">Fig 4</a>), the surgical simulation tool predicted the breast shape following BCT (right column). The breast deformations resulted from the in-silico analysis are then projected onto the original surface scan to visualise the textured post-surgical breast shape.</p

Validation results of the in-silico model and the surface optical scans.

<p>Validation results of the in-silico model and the surface optical scans.</p

Snapshots of the cell and capillary density predictions during wound healing simulation.

<p>Numerical results of the wound healing simulation for patient-specific model <i>P-3</i> (in supine) depicting the evolution of cell and capillary density at various time instants. The operated breast is clipped to facilitate visualisation of the dynamic changes of the species in the wounded area. The left and right column depict the (normalised dimensionless) cell and capillary density, respectively.</p

Vector representation of breast surface deformation after BCT.

<p>Arrow vector representation of the computed displacement field on the breast surface of the patient-specific post-operative model (after wound healing) with respect to the pre-operative setting in the upright position (transparent grey surface). The tan-coloured background surface corresponds to the chest wall boundary of the in-silico model. Note that all breast geometries are shown in the same scale.</p

Flowchart of the multiscale FE solver.

<p>The red-dash line frames the mechano-biological wound healing, angiogenesis and wound contraction numerical methodology (where WH/C is wound healing/contraction).</p