Synthetic Capillaries to Control Microscopic Blood Flow

Capillaries pervade human physiology. The mean intercapillary distance is only about 100 μm in human tissue, which indicates the extent of nutrient diffusion. In engineered tissue the lack of capillaries, along with the associated perfusion, is problematic because it leads to hypoxic stress and necrosis. However, a capillary is not easy to engineer due to its complex cytoarchitecture. Here, it is shown that it is possible to create in vitro, in about 30 min, a tubular microenvironment with an elastic modulus and porosity consistent with human tissue that functionally mimicks a bona fide capillary using “live cell lithography”(LCL) to control the type and position of cells on a composite hydrogel scaffold. Furthermore, it is established that these constructs support the forces associated with blood flow, and produce nutrient gradients similar to those measured in vivo. With LCL, capillaries can be constructed with single cell precision—no other method for tissue engineering offers such precision. Since the time required for assembly scales with the number of cells, this method is likely to be adapted first to create minimal functional units of human tissue that constitute organs, consisting of a heterogeneous population of 100–1000 cells, organized hierarchically to express a predictable function.

where E denotes the elastic modulus, v the Poisson ratio, and ) (  is a function of the indenter geometry (Methods). 28 However, rigorous application of infinitesimal theory demands an infinitely large specimen relative to both the indentation depth and the radius of the indenter, otherwise nonlinearities arise.
To gauge the stiffness, the elastic modulus (E) was measured by nano-indentation experiments performed with an atomic force microscope (AFM) the indentation depth () was calculated from the difference in the z-sensor and the deflection of the cantilever (Fig. S1). Two different probes were used: a blunted conical silicon tip of 7-10 nm radius (designated as the "sharp tip," Fig. S2a left, upper inset); and a tip modified by rigidly attaching a gold microsphere with a 1.5-3 m diameter (designated at the "gold tip," Fig. S2a left, lower inset). To measure the elastic modulus, voxels with and without cells in them were positioned under the cantilever, and then a small volume was deformed by extending the cantilever while the deflection was measured. The resulting indentation force (F) was calculated from Hooke's law.
Regardless of the tip and the voxel size and shape, the data consistently showed a linear relationship between the indentation force and the function  (Figs. S2a-c, left). However, the sharp tip consistently showed a much higher modulus compared to the gold tip (Table   Interestingly, the mechanical properties of voxels incorporating cells can reflect either the cell or the gel modulus, depending on the scale of the measurement (Table 1). The apparent elastic modulus for a voxel including an hMVEC was determined to be EPEG+cell 110 ± 20 kPa ( Fig.   S2c, left) using a sharp tip, which seems to reflect the PEGDA modulus described above, not that of an EC. In contrast, indentation with a gold tip revealed a modulus of EPEG+cell 4.0 ± 0.9 kPa, similar to other ECs measured alone 24 or just PEGDA measured with a gold tip. In contrast, the modulus of a Gel-MA voxel incorporating an hNF measured with a sharp tip was EGel+cell 35 ± 1 kPa, which was similar to that of a fibroblast, 25 whereas the stiffness measured with a gold tip was only 2.0 ± 0.6 kPa, which was more indicative of Gel-MA.
A lower modulus implies a sparser cross-link density in the gel and higher diffusivity through it. To corroborate the modulus measurements, the mesh size was inferred from the swelling ratio Q = Weq/Wdry obtained by weighing a voxel to determine equilibrium weight (Weq) and dry weights (Wdry). 31 To achieve sub-picogram resolution, the weight was inferred from the shift in the resonant frequency of an AFM cantilever that occurs when the cantilever was loaded with a voxel. When cantilevers were loaded with PEGDA or Gel-MA, a shift in the resonant frequencies of fdryPEG = -0.29±0.02 kHz, fwetPEG = -2.60±0.05 kHz and fdryPEG = -0.29±0.02 kHz, andfdryGEL = -6.2±0.1 Hz and fwetGEL = -67±9 Hz were observed (Figs. 2a,b,right). For an accurate mass estimate, the shifts were corrected to account for non-uniform distribution of the load (Table S1). Subsequently, the shifts were translated to estimates for Q: i.e. QPEG = 10.12 and QGEL = 10.75, respectively. The molecular weight between cross-links (MC) was determined from the swelling ratio using the Peppas-Merrill model (see Methods), which was then used to estimate the mesh size (Tables 1, S2). It was observed that  was statistically larger for Gel-MA, , implying a sparser cross-link density, which corroborates the lower modulus observed in the nano-indentation experiments.
The corresponding porosity, which was estimated to be 90.1% and 90.7% for PEGDA and Gel-MA respectively, factors into the effective diffusion coefficient through the porous medium. To test this last assertion, the diffusion of a surrogate protein, fluorescent streptavidin, was tracked through the hydrogels using confocal microscopy (see supplement and i.e. streptavidin diffusivity in PEGDA was less than 2% of the bulk value, which indicates a mesh size comparable to the size of the solute. Thus, a larger mesh size implies a higher diffusivity for nutrients and waste. However, due to the inhomogeneous distribution of water in a voxel containing a cell, it may be necessary to invoke more general kinetics beyond Fick's law to precisely account for material transport.  The same data plotted over a larger indentation range.

Table S2. The parameters used to calculate the molecular weight between cross-links (Mn) and mesh size () for PEGDA and Gel-MA. The parameter l represents the average value of the bond length between C-C and C-O bonds in the polymer repeat unit;
Mr is the molecular mass of the repeat unit; Cn is the characteristic ratio for polymer, v, is the specific volume of bulk polymer in the amorphous state, V1 is the molar volume of the solvent, V2,r and V2,s are the volume fraction of the polymer at the relaxed state and swelling equilibrium, and  is the Flory-Huggins parameter, respectively.

Hydrogel l (nm) Mr (g/mol) Cn v (cm 3 /g) V1 (g/mol) V2s (=Q)
V2r ( at 1 L/min using a syringe pump. To measure the uptake of streptavidin into the gel, a 100 mlong line scan along the x-axis was continuously acquired using a 63 water immersion objective excited with an argon ion laser. The mean intensity of the line segment within the hydrogel is plotted versus time (blue line) (Figs. S3a,b). Once the data was acquired, it was fit (red line) using custom MATLAB code using a model for the mass transport in a porous sphere with a diameter a and diffusivity D, the ratio of the mass uptake, M(t), relative to the mass at infinite  The Golgi apparatus is localized near the lumen due to transmural pressure, while the nucleus is forced away from the lumen. Sections 1 m thick were taken along the z-axis by confocal microscopy. Notice that because only 3 consecutive z-slices were used to generate this image, not all of the hMVECs have the localization of Golgi apparatus detected.   VIDEOS V1, V2. Washed 10% human erythrocytes (red blood cells) perfusing through synthetic capillaries 180 m 2 and 560 m 2 in cross-sectional area, respectively. The erythrocytes flow through the capillary under pressure of 1 kPa. The images were acquired every 20 ms. The mean axial velocity of the erythrocytes under these conditions was about Vax = 0.90 mm/s (V1) and Vax = 0.082 mm/s (V2). VIDEO V3. Time-lapse imaging of a metastatic breast cancer cell (MDA-MB-231) in a synthetic capillary. Images were acquired every 10 ms using a confocal microscope, although specific z-height was chosen. The video shows initial 4 hr after imaging was started. VIDEO V4. Human whole blood perfusing through a synthetic capillary. Whole human blood perfusing through a synthetic capillary about 310 m 2 in cross-sectional area. The blood flowed through the capillary under a differential pressure of 2.5 kPa. The video was compiled from a series of confocal frames through the lumen of the capillary acquired every 16 ms; the total duration was 150 s.