Figure 1.
Conceptual basis of the study.
Blunt headed arrows denote negative feedback loop, in which structural adaptation reduces heterogeneity in flow and oxygenation that is generated by heterogeneous vessel topology and lengths. The hypothesis is that this feedback loop is weaker (dashed curve) in tumors than in normal tissues. See text for further explanation.
Figure 2.
Summary of computational approach.
In-vivo experimental data on network structure (vessel diameter, length and connection pattern) were acquired during intravital microscopy (photomontage, left panel). Blood flow and oxygen distribution were calculated and diameter adaptation was simulated until a steady state was reached (computer visualization, right panel). Structural and functional parameters after simulated adaptation with different adaptation rules were compared with corresponding parameters for tumor and mesentery networks with measured diameters.
Figure 3.
Network characteristics and sensitivity parameters for simulated normal and tumor modes of vascular adaptation.
Top panel: Dependence of oxygen deficit and diameter mismatch on assumed adaptation mode. Filled triangles: results for experimentally measured vessel diameters for tumor network (red) and mesenteric networks (blue, mean with standard deviation). Open symbols: predicted results using vessel diameters obtained with normal, tumor or deterministic adaptation models for the tumor network (red squares) and for mesenteric networks (blue circles). When the tumor network is subjected to normal adaptation (red arrow), the resulting characteristics are close to those of mesentery networks with measured diameters. Conversely, when the mesentery networks are subject to tumor adaptation (blue arrow), they achieve tumor-like characteristics. If deterministic adaptation is assumed, low values for O2def and d3var are obtained which do not differ significantly for tumor and mesenteric networks. Lower panels: Sensitivity parameters for simulated diameter adaptation of mesenteric networks. Predicted parameter values for the optimization to characteristic network properties (O2def, d3var, Vtot, ΔP) as obtained with measured vessel diameters for the mesenteric networks (‘normal adaptation’, left) are compared to those obtained for tumor networks (‘tumor adaptation’, right). Mean data for three networks are shown with standard deviations. Significant differences are found for Ran-ks, kc, and ks but not for kh.
Figure 4.
Predicted effects of signals conducted along the vessel wall on network characteristics.
For a mesenteric network with 546 vessel segments, the conduction sensitivity was varied around the value used for ‘normal adaptation’ (vertical dashed line). Reduction of conduction strength below this level leads to a small increase in diameter mismatch and to development of a pronounced oxygen deficit despite a fixed level of bulk tissue perfusion.
Figure 5.
Computer visualizations of a mesenteric network and the tumor network color coded for .
Top row: results obtained with measured vessel diameters. Middle and bottom rows: simulated ‘normal adaptation’ and ‘tumor adaptation’. The tumor network with measured diameters and either network subjected to ‘tumor adaptation’ (right column) exhibit high structural heterogeneity and uneven flow distribution in comparison to the mesentery network and either network subjected to ‘normal adaptation’ (left column). For the adapted networks, results of individual randomized runs are shown. Values of oxygen deficit (O2def) and diameter mismatch (d3var) were similar to the mean values reported in Figure 3. For the sake of a better representation of individual vessel segments, only parts of the simulated networks are shown. The mesentery network comprised a total of 546 vessels supplying an area of about 4×7 mm, whereas the tumor vascular network comprised a total of 290 vessels in an area of about 1×0.8 mm.
Figure 6.
Schematic illustration showing hypothesized effect of information transfer on flow and oxygenation in networks.
Top: in normal tissue, information transfer ensures that long pathways (L) receive adequate flow and short pathways (S) are not overperfused. Bottom: in tumor tissue, loss of conducted responses causes functional shunting via short pathways (S). Long pathways (L) are underperfused and hypoxic. Red and blue colors denote high and low oxygen levels respectively.
Figure 7.
Functional and structural parameters for mesenteric networks obtained using measured vessel diameters and after simulated adaptation.
Upper panel: oxygen deficit, O2def. Lower panel: variability of cubed diameter at bifurcations, d3var. Three different adaptation modes are shown. The ‘deterministic adaptation’ (second bars from left) uses sensitivity parameters as previously established for mesenteric networks [56] without considering diameter measurement error or biological heterogeneity. Levels for oxygen deficit and structural heterogeneity are lower than those using measured diameters. Inclusion of diameter measurement error brings the parameters close to those obtained with experimentally observed vessel diameters (third bars from left). The further addition of a biological variability in vascular sensitivity to local stimuli and optimization of sensitivity parameters (kh, kc, ks and Ran-ks) allows for a close match of the simulation results to the experimental situation (normal adaptation, right bars). Mean values for three networks are shown with standard deviations.