HPA lectin and P53 immunohistochemistry of CRC tissue specimens.

<p>Left: light microscopy images of colorectal tissue sections (5 μm) incubated with HPA (10 μg/ml) and streptavidin-HRP (5 μg/ml) or incubated with the anti-P53 antibody (1:200) and biotinylated horse rabbit anti-mouse IgG (1:1000) as indicated. The brown colouration indicates the peroxidase reaction with DAB/H₂O₂, the nuclei were counterstained with haematoxylin (blue). Magnification X400. Right: Table showing results for HPA, P53 and <i>KRAS</i> analysis.</p

A Validated Multiscale In-Silico Model for Mechano-sensitive Tumour Angiogenesis and Growth

<div><p>Vascularisation is a key feature of cancer growth, invasion and metastasis. To better understand the governing biophysical processes and their relative importance, it is instructive to develop physiologically representative mathematical models with which to compare to experimental data. Previous studies have successfully applied this approach to test the effect of various biochemical factors on tumour growth and angiogenesis. However, these models do not account for the experimentally observed dependency of angiogenic network evolution on growth-induced solid stresses. This work introduces two novel features: the effects of hapto- and mechanotaxis on vessel sprouting, and mechano-sensitive dynamic vascular remodelling. The proposed three-dimensional, multiscale, in-silico model of dynamically coupled angiogenic tumour growth is specified to in-vivo and in-vitro data, chosen, where possible, to provide a physiologically consistent description. The model is then validated against in-vivo data from murine mammary carcinomas, with particular focus placed on identifying the influence of mechanical factors. Crucially, we find that it is necessary to include hapto- and mechanotaxis to recapitulate observed time-varying spatial distributions of angiogenic vasculature.</p></div

Normalised vascular density when mechano- and haptotaxis is included or discarded in the angiogenesis model.

<p>Comparison of the numerically predicted normalised vascular density when blood vessel sprouting is modulated by chemo-, mechano- and haptotaxis against the simplified chemotaxis case. Vascular density is defined as the ratio of the surface area of the blood vessels to the tissue volume, and is normalised against the corresponding initial value (day-0).</p

Capillary-tip extension velocity and vessel wall mechanical model.

<p>A: Extension rate of vascular-tip endothelial cells versus the capillary radius expressed by an exponential decay function, fitted to reported in-vitro angiogenesis experiments [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005259#pcbi.1005259.ref044" target="_blank">44</a>]. B: Stress–strain plot of the constitutive equation used to describe the biomechanics of the blood vessels, including the pressure which induces vessel collapse, <i>p</i>_c.</p

History plots of the parameters characterising the morphology of the microvascular tree.

<p>Numerically predicted parameters λ_v and <i>δ</i>_v-max with respect to time, compared to in-vivo measurements in murine mammary carcinoma (MCaIV-type) [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005259#pcbi.1005259.ref022" target="_blank">22</a>]. A: The geometrical exponent, λ_v, is obtained after linear regression on the pair of data: frequency of voxels versus the distance to nearest vessel (<i>δ</i>_v) [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005259#pcbi.1005259.ref065" target="_blank">65</a>] while the vertical bars denote standard deviation of the mean.</p

Flow diagram of the coupled multiscale solver.

<p>Schematic representation of the work flow diagram of the three-dimensional tumour growth and angiogenesis model that shows the interaction between the biochemical module, the vascular network module and the solid and fluid mechanics solver modules.</p

Average tissue hydrostatic pressure (THP) spatial distribution at various time instants.

<p>Various snapshots of THP—i.e. the mean solid stress—distribution evaluated at fourteen azimuthal directions, plotted with respect to the radial distance from the tumour centre. Positive pressure is compressive and negative extensive, while the vertical bars denote standard deviation. The vertical red line in the plots defines the tumour–host interface boundary, while the vertical bars denote the THP standard deviation. Notably, during the tumour development mechanical forces are propagating, in the form of a pressure wave, with an approximately linearly increasing amplitude in time.</p

Predictions of the normalised vascular density as a function of time.

<p>Increase of tumour vascular network density with respect to time when varying: A: the TAF angiogenesis threshold <i>τ</i>*, and B: the capillary wall stiffness, <i>E</i>_w-max. See also description in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005259#pcbi.1005259.g007" target="_blank">Fig 7</a> for the definition of the normalised vascular density.</p

Interstitial fluid pressure (IFP) spatial distribution at various time instants.

<p>Within 24 hours of relatively slow avascular tumour growth, tumour-secreted angiogenic chemical factors have sufficiently diffused in the extracellular space. In the tumour-induced angiogenesis simulation, day-1 marks the formation and elongation of new blood vessel sprouts. The vertical red line in the plots defines the tumour–host interface boundary which corresponds to the averaged tumour radius, where the centre of the cancer mass is at zero radial distance. The solid line corresponds to the mean IFP distribution, evaluated at fourteen azimuthal directions, while the vertical bars denote the IFP standard deviation. These plots also illustrate the gradual increase of the cancer mass, while depicting the significant variability of IFP in the vicinity of the tumour interstitium.</p

Perfusion state of the vascular network in time.

<p>Following [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005259#pcbi.1005259.ref048" target="_blank">48</a>], hypo-perfused vessels are characterised as those with mean intravascular velocity below 0.1 mm/s, perfused vessels are those falling in the range of [0.1, 0.5] mm/s, and the rest (>0.5 mm/s) are considered well-perfused blood vessels. The percentage of collapsed vessels fell between approximately 4–6% with respect to the total amount of vessels in the vascular tree.</p