Modeling of angioadaptation: insights for vascular development

Abstract

Vascular beds are generated by vasculogenesis and sprouting angiogenesis, and these processes have strong stochastic components. As a result, vascular patterns exhibit significant heterogeneity with respect to the topological arrangement of the individual vessel segments and the characteristics (length, number of segments) of different arterio-venous pathways. This structural heterogeneity tends to cause heterogeneous distributions of flow and oxygen availability in tissue. However, these quantities must be maintained within tolerable ranges to allow normal tissue function. This is achieved largely through adjustment of vascular flow resistance by control of vessel diameters. While short-term diameter control by changes in vascular tone in arterioles and small arteries plays an important role, in the long term an even more important role is played by structural adaptation (angioadaptation), occurring in response to metabolic and hemodynamic signals. The effectiveness, stability and robustness of this angioadaptation depend sensitively on the nature and strength of the vascular responses involved and their interactions with the network structure. Mathematical models are helpful in understanding these complex interactions, and can be used to simulate the consequences of failures in sensing or signal transmission mechanisms. For the tumor microcirculation, this strategy of combining experimental observations with theoretical models, has led to the hypothesis that dysfunctional information transport via vascular connexins is a major cause of the observed vascular pathology and increased heterogeneity in oxygen distribution.

Fig. 1. Sprouting and splitting angiogenesis. During sprouting angiogenesis, local fields of pro-angiogenic factors in the tissue, for instance generated in response to hypoxia, induce stochastic growth of new vessels

The generation of a functional and efficient network requires pruning of redundant segments, governed by local hemodynamic and metabolic signals. Splitting angiogenesis (intussusception), in contrast, allows continuous feedback control by hemodynamic and metabolic conditions. Red: arterioles; brown: capillaries; blue: venules.

Fig. 2. Roles of wall shear stress, metabolic, conducted and convected signals in structural adaptation

(A,B) Local action of adaptive signals; (C,D) Modes of metabolic information transfer. Left column: mechanisms of signal generation. Center column: stimuli and responses. Dashed lines show feedback pathways (blunt heads indicate negative feedback). Right column: Significance for network properties. Flow directions are indicated by small black arrows. (A) Shear stress (τ) generated by flowing blood is sensed by endothelial cells and stimulates structural increase in diameter. For a given blood flow, shear stress decreases, giving a negative feedback. However, for a given driving pressure increased diameter will lead to increased flow, causing positive feedback. Shear stress response generates a progression from larger to smaller vessels correlated with flow rates in the arterial and venous trees. Transmural pressure difference leads to a circumferential wall stress (σ) which in turn stimulates diameter decrease. Wall stress response generates the arterio-venous asymmetry with small arterial and larger venous vessels. (B) Tissue hypoxia leads to release of metabolic signal substances that diffuse into blood and stimulate increased diameter and increased flow, which improves oxygen availability and may also lead to faster washout of metabolic signal substance. The metabolic response enables the vasculature to respond to tissue metabolic demands and stabilizes parallel flow pathways. (C) Conducted signals generated in distal vessels are propagated upstream to feeding arterioles (orange arrow). Short arterio-venous connections (green circle) remain small and do not form functional shunts. For conduction, it is relevant that signals travel only in the direction against the blood flow (upstream) and do not reenter smaller side-branches (blunted arrow). (D) In the downstream direction, convection of metabolic substances allows for information propagation to draining vessels.

Fig. 3. Methods for simulation of structural diameter adaptation

Experimental data on network structure and microvascular rheology serve as the basis to calculate blood flow and oxygen transport in networks with a given angioarchitecture. Stimuli derived from hemodynamic and metabolic conditions are used to predict diameter adaptation for each vessel according to a set of general adaptation rules to be tested. The properties of the vascular network after simulated adaptation are then compared with experimental network data (segment flow velocity, hematocrit and diameter) to assess the adequacy of the adaptation rules used and to optimize adaptation parameters.

Fig. 4. Responses to oxygen supply-demand mismatch

(A) Left: Network containing a vessel with low perfusion resulting in hypoxia (blue color). Right: Enlarged view of hypoxic region. Signals generated in the vessel wall or the parenchymal tissue (green arrows) increase in proportion to local oxygen deficiency and stimulate diameter increase. This increase increases perfusion and oxygen availability constituting a negative feedback between tissue hypoxia and metabolic signaling. (B) If vessel density is too low, diameter increases lead to increased blood flow but oxygen supply of remote tissue cells remains inadequate. Supply of remote tissue cells requires stimulation of angiogenesis by tissue derived metabolic signals. (C) New vessel generated by sprouting angiogenesis (dashed line) results in reduction of diffusion distances and adequate tissue oxygenation.

Fig. 5. Faulty vascular adaptation as a cause for aberrant tumor microcirculatory properties

Vascular patterns generated by using normal and modified (‘tumor’) adaptation rules in a mesenteric network (upper row) and a tumor network (lower row) are compared to results obtained with experimentally measured vessel diameters. Experimental data are shown in the left column. Simulated ‘normal adaptation’ (middle column), using standard model parameters optimized for normal network characteristics leads to adequate blood flow distribution in both the normal and the tumor network. In contrast, simulated ‘tumor adaptation’ (right column), with abolished information transfer via conduction results in increased structural heterogeneity, functional shunting and large underperfused areas, in comparison to the mesenteric network.

Fig. 6. Integrated view of physiological processes controlling vascular structure and function

Vascular regulation includes short term changes of vessel diameter effected by vascular smooth muscle and tone (right), long term changes of vessel diameter and wall mass by structural adaptation (middle), and changes in vessel number by elimination of unnecessary vessels by pruning or generation of new vessels by the sprouting and splitting modes of angiogenesis (left). These responses of a vascular bed are controlled by metabolic and hemodynamic signals derived, e.g., from the tissue, the vessel wall or red cells, and by hemodynamic signals (wall shear stress, τ; wall stress, σ). The different modes of vascular regulation are closely interrelated and may be induced by different combinations of the involved stimuli and by specific temporal and dynamic patterns of these stimuli (see text for further explanations).