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By Jen-Huang Huang, Jeongyun Kim, Nitin Agrawal, Arjun P. Sudarsan,
Joseph E. Maxim, Arul Jayaraman,* and Victor M. Ugaz*
Living systems face a fundamental challenge of orchestrating
exchange of nutrients and oxygen throughout 3D space in order
to satisfy their metabolic needs.[1] In nature, vascular networks
have evolved to elegantly address this problem by incorporating
highly branched fractal-like architectures that are efficiently
space-filling while minimizing the energy required to sustain
transport.[2,3] The ability to mimic these features in vitro would be
immensely beneficial in the field of tissue engineering, where
diffusion limitations generally restrict the maximum thickness of
constructs to a few hundred microns.[4–6] Here, we address this
need by introducing a nearly instantaneous method to embed
branched 3D microvascular networks inside plastic materials. In
this microfabrication process, a high level of electric charge is first
implanted inside a polymer dielectric using electron beam
irradiation. The accumulated energy is then discharged in a
controlled manner to locally vaporize and fracture the material,
leaving behind a network of branched microchannels arranged in
a tree-like architecture with diameters ranging from 10 mm to
1 mm. Modulating the irradiation profile and discharge locations
allows the networks’ morphology and interconnectivity to be
precisely tailored. Interconnected networks with multiple fluidic
access points can be straightforwardly constructed, and quantification of their branching characteristics reveals remarkable
similarity to naturally occurring vasculature. This method can be
applied in a variety of polymers, and may help enable production
of organ-sized tissue scaffolds containing embedded vasculature.
The hierarchy of length scales that comprise vascular networks
(ranging from mm–mm in diameter) and the need for these
structures to be widely accessible throughout a sizeable 3D
volume present significant manufacturing challenges. Photolithography-based microfabrication technology has been extensively examined as a potential avenue to address some of these
issues.[7–14] Here, planar micromachining is harnessed to
produce 2D microchannel arrays that can be stacked in a
layer-by-layer fashion to achieve a limited degree of three-
[*] Prof. A. Jayaraman, Prof. V. M. Ugaz, J.-H. Huang, J. Kim, N. Agrawal,
A. P. Sudarsan
Artie McFerrin Department of Chemical Engineering, Texas A&M
College Station, TX 77843 (USA)
E-mail: [email protected]; [email protected]
Prof. A. Jayaraman
Department of Biomedical Engineering, Texas A&M University
College Station TX 77843 (USA)
J. E. Maxim
National Center for Electron Beam Research, Texas A&M University
College Station, TX 77845 (USA)
DOI: 10.1002/adma.200900584
Adv. Mater. 2009, 21, 3567–3571
dimensionality.[15] But assembly of large-scale multi-tiered
structures is tedious, and the inherently planar nature of the
individual layers restricts the network’s topological complexity.
More recent developments have enabled fully 3D flow architectures to be produced using methods including solid freeform
fabrication, stereolithography, and direct printing.[5,16–18] But
these approaches generally involve time consuming serial
processes, and the optimal range of feature sizes associated
with each technology is often relatively narrow. Many of these
processes are also challenging to scale up toward levels feasible
for mass production.[19]
We have developed a fabrication method that uniquely
overcomes these limitations, enabling branched 3D microvascular networks incorporating a wide range of microchannel
diameters to be rapidly constructed in a variety of plastic materials
(Fig. 1). This process harnesses electron beam irradiation to
implant a high level of electric charge inside a substrate so that the
energy released upon discharge will be sufficiently intense to
locally vaporize and fracture the surrounding material. In this
way, networks of highly branched tree-like microchannels are
produced that become permanently embedded within the
substrate. The formation and growth of these electrostatic
discharge structures (i.e., Lichtenberg figures or Lichtenberg
trees) are analogous to lightning phenomena that occur during
thunderstorms when charge accumulation within clouds exceeds
the breakdown potential of the surrounding atmosphere.[20–22]
We first explored applying this process to construct 3D vascular
microchannel networks in acrylic plastic substrates by irradiating
blocks of polished poly(methyl methacrylate) (PMMA) using a
10 MeV electron beam to implant a prescribed charge distribution
(typical space charge densities are on the order of 1 mC cm2),[22]
after which the energized blocks were discharged by one of two
methods. In the first approach (Fig. 1a), release of the
accumulated charge was achieved by striking the irradiated
block with the sharp tip of a grounded electrode. The point source
of electrical grounding and the mechanical stress associated with
the physical impact of striking the block combine to produce an
immediate and rapid energy release.[21] Alternatively, a defect
(e.g., a small hole 1 mm in diameter) was intentionally
introduced on the surface of the block prior to irradiation that
served as a nucleation site for spontaneous discharge upon
exposure to the electron beam without the need for further
physical contact (Fig. 1b). In either case, the rapid and intense
release of electrostatic energy instantaneously generated a
hierarchically branched microchannel array penetrating throughout the entire volume of the block and originating from either
the point of contact with the grounded electrode or the nucleation
site created on the surface (Fig. 1c and Supporting Information
Movie 1). Networks formed using the grounded contact method
ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Rapid Fabrication of Bio-inspired 3D Microfluidic
Vascular Networks
beam (dose). Penetration depth profiles in
absorbing media reflect the distribution of
complex and tortuous paths traveled by
incident electrons, and can be inferred using
a combination of experimental dose distribution data[23] and penetration range calculations
based on the continuous slowing down
approximation (CSDA).[24] The CSDA analysis
predicts a maximum penetration depth of
4.3 cm for PMMA, implying that most
electrons would pass through the 2.54 cm thick
acrylic blocks and yield little or no charge
accumulation. Since the beam energy is fixed,
we controlled the penetration depth by inserting polyethylene attenuators into the beam path
to ensure that a majority of the incident
electrons became implanted inside the PMMA
blocks. Exposure dose from the continuous
irradiation source was controlled by adjusting
the speed of a conveyor that transported
the blocks through the beam. We found that
a speed of 10 ft min1 (1 ft ¼ 0.3048 m)
permitted sufficient charge accumulation
[ faster speeds resulted in weak discharges that
generated tiny thread-like microchannels,
slower speeds yielded regions where locally
violent discharges produced large globule-like
features that obscured the underlying branched
network morphology (Supporting Information
Fig. 1)]. Proper selection of penetration depth
and irradiation dose enabled us to reproducibly
achieve a high level of control over the
microchannel network architectures constructed using electrostatic discharge.
Flow-through perfusion capabilities necesFigure 1. Harnessing electrostatic discharge phenomena to rapidly construct branched 3D
microvascular networks. a) In the grounded contact method, electron beam irradiation is used sarily require interconnected networks possesto implant a high level of internal electric charge inside a dielectric substrate. A grounded sing multiple access points for inlet and outlet
electrode is then brought into contact with the substrate surface, initiating sudden energy release streams. These architectures can be straightthat locally vaporizes the surrounding material leaving behind a tree-like branched microchannel forwardly constructed using a multi-step
network. b) In the spontaneous discharge method, a defect (e.g., small hole) is first created on the
process whereby an initial discharge network
substrate surface prior to irradiation. When the internal electric charge exceeds a critical level
upon exposure to the electron beam, the defect acts as a nucleation site for spontaneous energy is first implanted using either of the methods
release. The grounded contact method yields a more ‘‘tree-like’’ morphology while microchannels illustrated in Figure 1, after which the substrate
produced by spontaneous discharge permeate the substrate more uniformly. c) Image sequence is re-irradiated by the electron beam one or
from a video recording of discharge by grounded contact shows that energy release is nearly more additional times in order to nucleate
instantaneous with subsequent weaker discharges persisting over longer timescales. All photo- further discharges. These secondary spontagraphs depict microchannel networks in 1 inch 3 inch 3 inch polished acrylic blocks. Note neously generated microchannels originate
that all networks extend in 3D throughout the volume of the blocks. Scale bars, 1 cm.
from nucleation sites defined by positioning
one or more small holes at desired locations
along perimeter of the block, and naturally become intercongenerally incorporate more tree-like architectures consisting of a
nected with the network already embedded inside the substrate
well-defined central trunk several mm in diameter with progres(Fig. 2a). The location of each nucleation site and the number of
sively finer branches extending outward, while spontaneous
irradiation/discharge cycles can be adjusted to manipulate the
discharge yields microchannels that are more randomly dispersed
size, morphology, and density of the resulting microchannel
throughout the substrate (e.g., see photos in Fig. 1a and b).
network (Fig. 2b–e). Each discharge nucleation site provides an
The morphology and branching characteristics of the microindependent access point for fluid injection or collection. Flow
channel networks are largely dictated by the magnitude and
and interconnectivity can be directly observed by introducing
distribution of accumulated charge inside the substrate prior to
tracer dye solutions using a syringe pump to permit visualization,
discharge. This level of accumulation is in turn determined by an
both in 2D by recording images of a subset of the network
interplay between i) the penetration depth (range) of the
occupying a specific focal plane (Fig. 3a), and in 3D by using
impinging electrons and ii) the time of exposure to the incident
ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2009, 21, 3567–3571
Adv. Mater. 2009, 21, 3567–3571
ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
than those formed in the acrylic blocks (300 mm at the
trunk to 20 mm near the tips), likely reflecting
differences in dielectric properties between materials.
Microchannels produced by electrostatic discharge
mimic many attributes of naturally occurring vasculature where a well-defined global architecture persists
despite the fact that no two networks are completely
identical at all structural levels. The extent of this
self-similarity becomes evident when we compare the
branching characteristics of microchannel networks
produced in three identical acrylic blocks exposed to
different irradiation and discharge conditions (Fig. 4).
Discharge networks were first embedded in each block
using the grounded contact method (Fig. 1a). The blocks
were then exposed to additional cycles of re-irradiation
and spontaneous discharge, during which the embedded
branched network continued to grow and expand.[21]
Quantitative descriptors of the corresponding network
morphologies based on consideration of a bifurcation
model where a parent channel of diameter d0 splits into
two daughter channels of diameters d1 and d2 (Fig. 4a)
were then extracted from analysis of images acquired
along the midplane of each block [multiple branches
originating from exactly the same point (trifurcations,
etc.) were rarely observed]. Remarkably, these data
indicate that although the network density increases
with each subsequent irradiation/discharge cycle, the
average bifurcation angle and fractal dimension remain
Figure 2. Interconnected branched microvascular networks with multiple fluidic relatively unchanged and within physiological ranges
access points. a) A single branched microchannel network is first constructed using observed in living systems (Table 1).[25–27] These results
either of the methods described in Figure 1. One or more additional nucleation sites demonstrate that all three networks share a fundamenare then created on the surface and the block is re-irradiated to initiate further tally similar underlying architecture despite clear
spontaneous discharges originating at each site. Microchannel networks created in
differences in network density. A more detailed picture
1 inch 3 inch 3 inch polished acrylic blocks b–d), and a 1.5 inch diameter (dia.), 4.5
inch long polished acrylic rod e) become interconnected during the subsequent was obtained by examining the variation in the ratio
irradiation/discharge steps providing multiple locations for fluidic injection and between the parent and daughter cross-sectional areas
collection. The extent of branching in the embedded networks is progressively (area ratio) and the bifurcation index (Fig. 4b–d). These
increased by the additional irradiation/discharge cycles. Scale bars, 1 cm.
data show that the network comprises a distribution of
bifurcations ranging from symmetric (d2/d1 ¼ 1) to
asymmetric (d2/d1 < 1) that are not only self-similar among all
confocal laser scanning microscopy (Supporting Information
Movie 2). Analysis of these images reveals a fractal-like
three blocks, but also mirror the features of physiologically
microchannel architecture incorporating a hierarchy of diameters
relevant vasculature.[28]
ranging from 500 mm at the ‘‘trunk’’ of the tree structure to
The architecture of naturally occurring vascular networks is
10 mm near the tips of the outermost branches. Some of the
often described in terms of Murray’s law,[29] a model based on
microchannels incorporate dead ends, mostly at the highest levels
energy minimization arguments that predicts a system-wide state
of branching (i.e., the tips of the branches), yielding an
of uniform shear stress corresponds to a global scaling of flow rate
architecture analogous to a capillary bed where the smallest
with the cube of vessel diameter.[2,3,30] Considering the case of
ducts at the ends of the network may not be physically
bifurcations from a parent channel to two daughter channels,
interconnected but are densely arrayed to facilitate diffusive
Murray’s law implies that d0k ¼ d1k þ d2k where a value of k ¼ 3 is
transport between neighboring branches.
predicted under ideal conditions (e.g., laminar, non-pulsatile
We also wanted to determine whether electrostatic discharge
flow). Analysis of the branched networks in Figure 4 yield
could be harnessed to embed branched vascular networks in
exponents in the vicinity of 2.1 < k < 2.3 (Table 1), within the
biodegradable substrate materials relevant for tissue engineering
range of available physiological data (deviations from k ¼ 3 are
by testing the process using thermally molded blocks of
common and attributable to departures from the idealized flow
poly(lactic acid) (PLA). Here, we used the spontaneous discharge
conditions assumed in the formulation of Murray’s law).[27,31–34]
approach (Fig. 1b) to define the network’s point of origin by
Furthermore, it is notable that the physics of electrostatic
creating nucleation sites at specific surface locations (Fig. 3b). We
discharge phenomena yield networks whose scaling exponents
find that electrostatic discharge is robustly applicable to PLA
naturally approach k ¼ 2 owing to the requirement for the
substrates, with interconnected networks possessing channel
minimization of electrical resistance.[35] Optimal networks for
diameters comparable to but within a slightly narrower range
diffusive mass transport inherently share this k ¼ 2 scaling
Table 1. Quantitative characteristics [a]of branched microchannel networks.
Irradiation/ Network
Average Average Median
density [%] bifurcation
angle u [8]
exponent, k
Parameters were determined from analysis of images reconstructed from microvascular networks embedded in acrylic blocks upon exposure to multiple irradiation/
discharge cycles (Fig. 4b–d). Network density represents the fraction of the total
image area occupied by the microchannel network (i.e., number of pixels associated
with the network divided by total pixels in the image).
Figure 3. Branched microvascular networks embedded in acrylic and PLA
substrates incorporate a hierarchy of microchannel diameters. a) Injecting
an aqueous solution of blue food dye into an interconnected microchannel
array in a 1 inch 3 inch 3 inch polished acrylic block with three fluidic
access points enables direct visualization of the flow network (scale bar,
1 cm). A close-up view reveals the tree-like microvascular hierarchy (point
1, 350 mm; point 2, 90 mm; point 3, 45 mm; point 4, 10 mm dia.).
b) Branched microvascular network embedded in a 1.5 cm 5 cm 8 cm
8 cm molded PLA block (scale bar, 2 cm; point 1, 180 mm; point 2, 70 mm;
point 3, 40 mm; point 4, 20 mm dia.).
(consistent with physiological observations indicating a transition
from k ¼ 3 in larger vessels near the base of arterial trees to k ¼ 2
in the capillary beds[36]), an observation further supported by
fractal dimension values in the vicinity of 1.8.[37] These data imply
that branched microchannels constructed using electrostatic
discharge inherently possess morphologies ideally suited to
satisfy the transport requirements of tissue engineering applications.
The qualitative and quantitative resemblance of these
branched 3D microchannel networks to anatomical vascular
trees is remarkable in terms of both global architecture and local
morphology. In addition to providing a convenient
platform to study transport and flow in branched
3D microfluidic networks, these similarities introduce the exciting possibility of harnessing electrostatic discharge phenomena as a new tool to embed
vascular networks in tissue scaffold materials so
they can support cell culture throughout much
larger volumes than are currently possible. Unlike
conventional microfabrication processes, this
method enables large-scale bio-inspired 3D flow
networks containing a wide range of channel
dimensions to be instantaneously constructed in a
straightforward non-serial manner amenable to
Figure 4. Microvascular networks produced under different irradiation/discharge conditions
incorporate morphologically similar branching characteristics. a) Quantitative branching
parameters corresponding to bifurcation from a parent channel of diameter d0 into two
daughter channels of diameters d1 and d2. b–d) Characterization of microchannel networks
originating in the center of three identical 1 inch 3 inch 3 inch polished acrylic blocks
subjected to b) 1, c) 2, and d) 3 successive irradiation/discharge cycles (ensembles of 935,
1665, and 2401 data points are plotted, respectively). All three networks exhibit a similar
relationship between the area ratio and bifurcation index despite differences in the overall
network density (inset). The area ratio data are mostly clustered about the limiting theoretical
range between 1 and 21/3 corresponding to Murray’s law exponents of k ¼ 3 and 2,
respectively [28] (average and median values are reported in Table 1).
Sample Preparation: Polished acrylic rectangular blocks
(1 inch 3 inch 3 inch, 1 inch ¼ 2.54 cm) and cylindrical
rods (1.5 inch dia., 4.5 inch long) were purchased from
Trio Display (San Diego, CA, USA). Polished blocks are
desirable when constructing discharge networks using the
grounded contact method because they reduce nucleation
of unwanted spontaneous discharges that may occur due
to surface imperfections. Rectangular blocks of PLA were
thermally molded from pelletized resin (NatureWorks
grade 3051; Jamplast Inc., Ellisville, MO, USA). Pellets
were loaded into molds constructed from poly(dimethyl
siloxane) and heated to 180 8C in vacuum for 2 h, after
which the vacuum was released and heating continued for
an additional hour. The mold was then removed from the
oven and cooled at room temperature so that the PLA
blocks (1.5 cm 5 cm 8 cm) could be easily released.
Electrostatic Discharge: Experiments were performed at
the National Center for Electron Beam Research at Texas
ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2009, 21, 3567–3571
This work was supported by the National Institutes of Health under
grant NIH R21-EB005965, monitored by Dr. Rosemarie Hunziker. We are
grateful to Prof. Suresh Pillai and the staff at the National Center
for Electron Beam Research (Texas A&M) for assistance with the
electron beam irradiation experiments. J. K. acknowledges partial support
through a post-doctoral fellowship grant from Dankook University, Korea.
We also thank Jamplast, Inc. for generously donating the PLA resin. J. H.
and J. K. contributed equally and should be considered joint first authors.
N. A. and A. P. S. contributed equally and are listed alphabetically.
Supporting Information is available online from Wiley InterScience or from
the author.
Received: February 18, 2009
Published online: July 10, 2009
Adv. Mater. 2009, 21, 3567–3571
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ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
A&M University. This system employs a 15 kW linear accelerator to produce
a single 10 MeV electron beam directed upward from below the sample.
The energy of the incident beam was attenuated using three sheets of 5 mm
thick high-density polyethylene (HDPE) to achieve the target dose at the
desired depth inside the substrate. An estimate of the maximum
penetration depth was obtained using CSDA range data at 10 MeV
provided in the NIST ESTAR Database of Stopping Powers and Ranges for
Electrons (physics.nist.gov/PhysRefData/Star/Text/ESTAR.html, last
accessed October 2008). Applying these parameters (RCSDA,PMMA ¼
5.158 g cm2, rPMMA ¼ 1.19 g cm3; RCSDA,HDPE ¼ 4.833 g cm2,
rHDPE ¼ 0.957 g cm3) yields average penetration depths of 4.33 and
4.06 cm in PMMA and HDPE, respectively. For light particles like electrons,
the CSDA range represents a maximum upper-limit value of the actual
penetration depth (experimental data place the peak dose at
RPMMA ¼ 2.8–3 g cm2) [23] that is useful to determine the attenuation
needed to maximize the implanted charge. The substrate and attenuating
sheets were mounted on a cardboard carrier tray and transported though
the electron beam by a conveyor at a speed of 10 ft min1. Microchannel
networks formed by spontaneous discharge became embedded inside the
substrate immediately upon exposure to the beam (holes of 1 mm
diameter were drilled to a depth of about 1 cm, tapering to a point near the
bottom of the hole; we did not observe a strong effect of hole size on the
features of the resulting network, but this was not systematically
investigated). In the grounded contact method, irradiated substrates were
discharged using a hammer to strike the surface with a sharp-tipped metal
tool (e.g., a nail or needle) connected to a grounded cable.
Flow Analysis: Interconnectivity and flow within the vascular networks
were quantified by injecting an aqueous solution of blue food dye using a
syringe pump at a flow rate of 0.1 mL min1. Volumetric imaging of the
microvascular networks was performed using a Leica TCS SP5 Confocal
microscope (scan speed 400 Hz) to scan blocks injected with Rhodamine B
dye (Sigma–Aldrich). Image stack data were then assembled into 3D
reconstructions. Instrument limitations (e.g., acquisition times of several
hours) restricted the allowable imaging volume to a small subregion of the
overall network.
Image Analysis: Branching characteristics were quantified by using
photographic images of the networks acquired along the midplane of each
block (Supporting Information Fig. 2) as a basis to render digital
reconstructions using Neuromantic software (www.rdg.ac.uk/neuromantic/, downloaded April 2008), after which the software package L-Measure
(cng.gmu.edu:8080/Lm/pdfs/lmhomepg.jsp, downloaded May 2008) was
used to extract quantitative parameters. Fractal dimension calculations
were performed using Fractalyse analysis software (www.fractalyse.org,
downloaded December 2008). All software packages are freely available.