Cell-generated traction forces and the resulting matrix deformation modulate microvascular alignment and growth during angiogenesis

Abstract

The details of the mechanical factors that modulate angiogenesis remain poorly understood. Previous in vitro studies of angiogenesis using microvessel fragments cultured within collagen constructs demonstrated that neovessel alignment can be induced via mechanical constraint of the boundaries (i.e., boundary conditions). The objective of this study was to investigate the role of mechanical boundary conditions in the regulation of angiogenic alignment and growth in an in vitro model of angiogenesis. Angiogenic microvessels within three-dimensional constructs were subjected to different boundary conditions, thus producing different stress and strain fields during growth. Neovessel outgrowth and orientation were quantified from confocal image data after 6 days. Vascularity and branching decreased as the amount of constraint imposed on the culture increased. In long-axis constrained hexahedral constructs, microvessels aligned parallel to the constrained axis. In contrast, constructs that were constrained along the short axis had random microvessel orientation. Finite element models were used to simulate the contraction of gels under the various boundary conditions and to predict the local strain field experienced by microvessels. Results from the experiments and simulations demonstrated that microvessels aligned perpendicular to directions of compressive strain. Alignment was due to anisotropic deformation of the matrix from cell-generated traction forces interacting with the mechanical boundary conditions. These findings demonstrate that boundary conditions and thus the effective stiffness of the matrix regulate angiogenesis. This study offers a potential explanation for the oriented vascular beds that occur in native tissues and provides the basis for improved control of tissue vascularization in both native tissues and tissue-engineered constructs.

Keywords: angiogenesis; deformation; image analysis; morphometry; orientation; strain.

Fig. 1.

Culture geometry and boundary conditions used in experiments. A: Lab-Tek II culture chamber containing Teflon molds and long-axis constrained (LAC) stainless steel mesh. B: assembled culture chambers for all boundary conditions (left), stainless steel meshes (middle), and 3-dimensional (3D) collagen cultures after removal of Teflon molds (right). The region that was imaged and quantified by laser scanning confocal microscopy is shown as a white box. The Lab-Tek chambers used for the hexahedral constructs measured 49 × 19 × 11 mm, whereas the chambers used in the circular constructs measured 23 × 19 × 11 mm.

Fig. 2.

Schematic showing boundary conditions for each of the 6 groups (left), expected state of strain [E] at center of construct due to cell generated traction forces (middle), and expected state of stress [T] at center of construct due to cell generated traction forces (right) in Cartesian coordinates. The approximate location of 3D image acquisition by laser scanning confocal microscopy is shown as a small white box. The signs (+ or −) are indicated for the expected strains and stresses, with negative signs on the strain indicating compression and positive signs on the stresses indicating tensile force. The notation “∼0” indicates that the strain component is expected to be very small relative to the others, but not necessarily exactly 0.

Fig. 3.

Engineering strain in each direction (E_xx, E_yy, E_zz) and volume ratios calculated by measuring edge displacement of contracting cultures at day 6. No edge displacement and therefore strain occurred along the constrained directions for certain boundary conditions [E_xx = 0.0 for LAC; E_yy = 0.0 for short-axis constrained (SAC)]. The SAC group contracted only 6.9% along the x-axis, which was significantly less than the 40.3% for the unconstrained (U) group (*P < 0.001). Overall, the volume of unconstrained constructs was reduced by ∼70%, whereas the volume contraction at the geometric center of the LAC constructs was 57.3% (*P = 0.086). The estimated volume contraction of the SAC constructs of 42.8% was significantly less than that of the unconstrained constructs (*P = 0.001). Bars indicate standard error.

Fig. 4.

Z-projections from confocal images of microvessels after day 6. A: hexahedral boundary conditions U, LAC, and SAC. During imaging, the long axis of hexahedral constructs was aligned with the horizontal (x-) axis of the imaging plane. B: circular boundary conditions, circular unconstrained (CU) and circular constrained (CC).

Fig. 5.

Quantitative measurements of microvessel growth for different boundary conditions. A: microvessel vascularity tended to decrease as gels became more constrained. Vascularity for the long-short axis constrained (LSAC) group was significantly lower than that in the U (*P = 0.004) and LAC groups (*P = 0.044). Vascularity in the CC boundary condition was significantly less than that in the CU condition (*P = 0.017). B: average segment length tended to increase as the gel became more constrained. Segment length in the CC cultures was significantly greater than that in the CU cultures (*P = 0.043). C: microvessel branching tended to decrease as the gel became more constrained. Branching within the CC boundary condition culture was significantly reduced relative to the unconstrained control, CU (*P = 0.020). Bars indicate standard error.

Fig. 6.

Microvessel alignment and anisotropy within the XY-plane. A: length-normalized distributions of orientation for hexahedral constructs. The 10° bin represents angles from 0° to 10°, which are parallel to the long axis (x-axis). The 90° bin represents angles from 80° to 90° and is parallel to the short axis (y-axis). The LAC group was significantly different from at least 1 other boundary condition in all but the 30° and 40° angle bins (*P < 0.05). A completely random distribution should have ∼11% in each angle bin, represented by the dashed line. B: microvessel anisotropy as determined by fast Fourier transform (FFT) analysis. A value of 0.0 represents random organization, whereas a value of 1.0 represents complete alignment. The LAC boundary condition had a significantly higher anisotropy value than all the other boundary conditions, as expected based on the angle distributions in A. The cylindrical constructs had similar anisotropy values to the other randomly organized hexahedral boundary conditions. The LAC group had a high anisotropy value of 0.7, which was significantly greater than all other conditions when analyzed by FFT (*P < 0.001). Bars indicate standard error.

Fig. 7.

Microvessel alignment relative to the z-axis. Length-normalized distributions of orientation for the hexahedral constructs (A) and cylindrical constructs (B) are shown. The 10° bin represents angles from 0° to 10°, which are parallel to the z-axis of the hexahedral constructs. The 90° bin represents angles from 80° to 90° and is parallel to the XY-plane of the hexahedral constructs. Most of the vessel segments for all of the boundary conditions were parallel to the XY-plane. Significant differences were detected between U and the other groups in the 70°, 80°, and 90° angle bins (*P < 0.01). The unconstrained cultures U and CU were significantly different than the other constrained cultures in all but the 10° and 20° angle bins (*P < 0.05). Bars indicate standard error.

Fig. 8.

Contraction of LAC vascularized gels after cutting their attachment to the boundary. To determine whether LAC vascularized gels were under elastic stress due to cell-induced compaction, gel cutting experiments were performed. After 4 days in vitro, LAC gels in the control group were given fresh media, whereas LAC gels in the Cytochalasin D (CytoD) group received fresh media plus 10 μM CytoD. CytoD inhibits actin polymerization. Twenty minutes later, 1 end of the LAC gels was cut free from the boundary constraint using a scalpel. Gels were returned to the incubator, and digital images were captured 5 min later. Imaging continued every 20 min (72 images over 24 h). A glass mirror under the gels was used to obtain multiple culture dimensions. Culture length, height, and width were measured with ImageJ calibrated to optical markers in the same focal plane. Top: control LAC gel at 5 min and 24 h after separation from the boundary constraint. Middle: LAC gel treated with CytoD at 5 min and 24 h after separation. Bottom: remaining length (% of initial length) versus time after cutting. Neither the control nor the CytoD-treated gels exhibited any significant contraction at 5 min after separation. Over the subsequent 24 h, control LAC gels contracted 40% along the long axis. In contrast, the CytoD-treated LAC gels did not exhibit any measureable contraction. These results verify that little if any elastic stress accumulates within the extracellular matrix (ECM) of LAC gels during the culture period, and contraction after separation from the boundary constraint is due to cell contractility.

Fig. 9.

Finite element (FE) simulations of microvessel-induced contraction of the constrained vascularized constructs. A: LAC model is shown at left, and the SAC model is shown at right. The initial configuration is shown above, and the deformed configuration (i.e., day 6 of growth) is shown below. B–E: global engineering strain was calculated from both the experimental constructs (black) and FE models (gray) using edge displacement and the definition (L–L_o)/L_o. Local strain, or the principal components of the infinitesimal strain tensor, was measured for the geometric center of the FE models and reported in white. Engineering strain was calculated along the X-, Y-, and Z-dimension (B and C), and these results were used to calculate the volume change ratio that occurred over the deformation (E). Bars indicate standard error. No bars are present on the FE data (i.e., N = 1 simulation).

Fig. 10.

Anisotropic deformation of the matrix due to cellular contractility is sufficient to cause microvascular alignment, independent of any other cellular behavior. Mapping the displacement field from the LAC FE model onto a distribution of randomly oriented microvessels results in a new alignment pattern that closely resembles alignment within the experimental LAC constructs. A: day 0, initial mesh geometry with the microvessel dataset positioned at geometric center. B: day 6, with the use of FE displacement field to map the microvessels, a new alignment pattern emerged due to contraction in the Y- and Z-directions. C: length-normalized distributions microvessel angle with the long axis (x-axis). The 10° angle bin represents angles from 0° to 10°, which were parallel to the long axis (x-axis). The 90° angle bin represents angles from 80° to 90° and was parallel to the short axis (y-axis). The angle orientation distribution before mapping (●) indicates random microvessel orientation. After mapping (○), microvessels were preferentially aligned along the long axis. Orientation data from LAC construct experiments are shown as well (▲). Error bars indicate standard error. Sim, simulation.