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EXPRESS SUMMARY ARTICLE The Full-length version of this article is also available, published online February 6, 2004 as doi:10.1096/fj.03-0933fje. |
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Department of Biomedical Engineering, University of Virginia Health System, Charlottesville, Virginia, USA
3Correspondence: Box 800759, Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22908, USA. E-mail: tskalak{at}virginia.edu
SPECIFIC AIMS
The aim of this study was to develop a cellular automata (CA) computational model that integrates epigenetic stimuli, molecular signals, and cellular behaviors to predict microvascular network patterning events during vessel growth and vascular network remodeling. We determined predictive capabilities of the CA model by stimulating microvascular remodeling (both in the CA model and in vivo) and by comparing independent network patterning data generated by the CA model to experimental results. The CA model identified a functional remodeling signaling module which integrates a number of signals that could not be studied together in a purely experimental approach.
PRINCIPAL FINDINGS
1. Development of a CA model of microvascular remodeling
We developed a two-dimensional cellular automata (CA) computational model of mammalian microvascular remodeling that incorporated independent behaviors of thousands of simulated cells with different origins and types, in addition to dynamic spatial and temporal growth factor profiles within their tissue environment. In the CA model, individual cell behaviors and growth factor profiles were governed by a set of rules obtained from previously published, independent experimental data. Each rule governed specific cells rather than the entire system in the simulation space, which is a primary feature of the decentralized modeling approach presented here. Rules included, for example, cell proliferation rates, cell migration rates, growth factor diffusion coefficients, and cell–cell contact requirements. Simulated cell populations included those cells known to participate in microvascular remodeling (endothelial cells, smooth muscle cells, and perivascular cells) and interstitial fibroblasts. Interstitial fibroblasts were placed randomly into tissue space at a spatial density consistent with in vivo, two-dimensional rat mesentery tissue. Individual vascular cells were arranged into blood vessels in such a way that the simulated network architectures corresponded morphologically and topographically to in vivo microvascular network architectures obtained from images of in vivo two-dimensional microvascular networks (Fig. 2)
. As simulated cells responded independently and dynamically to the set of rules in real time, they created emergent microvascular remodeling (Fig. 1
A and Fig. 2
), including angiogenesis (quantified in terms of vessel length extension) and arterialization (quantified in terms of increases in lengths of vessels coated by myosin heavy chain-positive cells and/or smooth muscle 
-actin positive cells).
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2. Predicting microvascular network remodeling in response to elevated hemodynamic stress
Alterations in hemodynamic stresses in microvasculature produce a variety of cellular responses including differentiation, proliferation, growth factor production, etc. Such cellular responses can manifest themselves as a microvascular remodeling event. In the simulation, microvascular remodeling was stimulated in the CA model by implementing a hemodynamic remodeling stimulus by applying specific mechanical stresses derived from previous in vivo observations to individual cells and groups of cells along vascular segments in simulated networks.
For the CA simulation of arterial remodeling, the hemodynamic remodeling stimulus corresponded to in vivo interventions which targeted specific mesenteric microvessel networks with a set of microligations to induce elevated circumferential wall strain (varying between 6.1±3.9% and 23±1.4% depending on vessel type) and pressure (17.1±2.3% and 42.55±18% in arterioles and venules, respectively). As observed in the experimental model, wall shear rate was not changed throughout networks after imposing the stimulation.
As in the in vivo work, chronic effects of elevated hemodynamic stresses included a twofold increase in total coverage of cells expressing smooth muscle myosin heavy chain (SM-MHC) (ie., contractile smooth muscle cells) on microvessels in affected networks after a period of 5 d. Extension of contractile smooth muscle cells along newly formed arterioles and venules was contiguous with coating of existing arteriolar and venous segments, which is consistent with patterns observed in vivo. Arteriolar development observed in the CA model was not statistically different from experimentally observed changes in in-vivo SM-MHC-positive cell coverage in microvessels subjected to the same hemodynamic conditions. At the final experimental and simulated time point, day 10, total coverage of cells expressing SM-MHC in vivo and in the CA model were maintained at statistically similar levels, further verifying the predictive capacity of the CA model, with respect to this metric.
3. Predicting microvascular patterning changes in response to spatially focal growth factor delivery
Patterning of microvascular networks during the remodeling process depends on a combination of growth factor stimuli. By itself however, VEGF164, an angiogenic agent that is upregulated in ischemic tissues, has been shown to be a potent stimulus for capillary growth and network remodeling. To better understand how an exogenous state-altering stimulus orchestrates microvascular network remodeling in concert with endogenous growth factors and to further test predictive capabilities of the CA model, we attempted to spatially direct microvascular patterning changes using focal exogenous applications of VEGF164. A point source of VEGF164 was incorporated into simulated tissue space of the CA model. An analogous intervention was delivered in vivo via alginate microdelivery beads implanted into microvascular beds of rat dorsal subcutaneous tissues. System state-altering stimuli of VEGF164 generated localized network remodeling in the CA model and in vivo, and we compared experimental microvascular network patterning changes with those predicted by the CA model.
The CA model predicted increases in vascular length density (370+29 mm/mm3) 14 d after simulated treatment with VEGF164 point source, specifically in regions of tissue receiving growth factor stimulus. This observation was consistent with that measured in vivo in response to analogous focal growth factor stimulation. Focal VEGF164 treatment in vivo generated a directed growth response that was not seen in adjacent tissue quadrants containing vehicle control microbeads, and vascular length density increased to 480 + 41 mm/mm3 14 d after treatment. The CA model generated a directed angiogenic growth in response to focal VEGF164 stimulus and quantitatively and graphically recapitulated in vivo network remodeling in terms of vascular length density increases.
The CA model also predicted vessel maturation over time, characterized by increases in total lengths of vessels containing smooth muscle -actin-expressing perivascular cells in response to growth factor stimulus. After 14 d, average length of simulated vessels containing smooth muscle -actin-expressing perivascular cells (striped bars) was significantly increased from that measured on day 4. A statistically similar maturation response was measured in remodeled experimental networks at these time points. This suggests that the CA model is capable of predicting one aspect of arteriogenesis (vascular smooth muscle cell coverage extension) in growth factor-stimulated microvascular networks.
4. Discovery of a functional signaling module for microvascular remodeling
In confirming that the CA model was capable of independently predicting experimentally accurate patterning metrics for microvascular remodeling in response to two epigenetic stimuli, the CA model has identified a functional patterning module. This module consists of growth factor signals (including vascular endothelial growth factor, transforming growth factor-ß, and platelet derived growth factor-BB) and cell-to-cell contact signals, which govern cellular behavior within the simulated tissue environment. This module is defined by a specific set of molecular and cellular signals and links two epigenetic signals (hemodynamic stress changes and focal growth factor release) to endogenous signals in the dynamic tissue environment. The complex systems biology approach taken in development of the CA model rationally integrates independent data to identify a functional module that is capable of governing microvascular remodeling.
CONCLUSIONS AND SIGNIFICANCE
We show that mammalian tissue assembly can be predicted in silico using a coherent multicellular CA simulation comprised of autonomous individual cell behaviors controlled by epigenetic factors over a range of spatial and time scales. Microvascular patterning simulation was able to identify functional patterning modules comprised of epigenetic factors linked to a specific set of endogenous molecular and mechanical signals. This has not been possible using any combination of experimental approaches previously. Furthermore, simulated modules predicted network assembly, patterning, and remodeling that was independently verified via direct experimental observations.
We also show the ability to spatially direct growth and remodeling of the vascular system. Practical application of the general methodology to the microvascular system is not only of significance for rational design of therapeutic revascularization strategies, but also potentially useful in tissue engineering that requires substantial vascularization, in morphogenesis and developmental biology, and in reparative medicine in the adult organism. In addition to predicting directed growth of new microvessel networks, the CA model is useful for examining the role of mechanical factors in inducing maturation of existing microvessel networks.
An unresolved issue is that in this CA model we have chosen to neglect other molecules and stimuli that may be upstream or downstream of those incorporated here. We argue that the set modeled in this simulation represents one functional module of signaling pathways whose effects have been quantified at the cellular level and that guide aggregate multicellular system behavior. To consider microvessel maintenance, for example, one would incorporate angiopoietin and placental growth factor molecules.
Epigenetic stimuli (rational nurture guiding intrinsic nature) are powerful forces that sculpt tissue systems throughout life. Epigenetic engineering is a new therapeutic frontier that considers nonmolecular upstream stimuli that drive adult tissue remodeling and assembly, occurring as environmental components of the organism’s normal course of life, including mechanical cues in tissues as diverse as bone and blood vessels. This is of broad interest because of the possibility to direct beneficial adaptations without inducing direct genetic modifications. The in silico approach presented here leaves implicit all intracellular signaling or energetic pathways not critical to intercellular interactions, allowing the simulation to capture emergent systems behavior. CA simulation offers a method to rationally harness such epigenetic stimuli to achieve desired tissue assembly. This in silico approach offers insight into two aspects that were previously inaccessible in living multicellular systems: 1) a basic understanding of emergent systems growth and adaptation behaviors, and 2) a method to perform epigenetic engineering of tissue systems, particularly vascular tissues, based on rational harnessing of naturally-occurring remodeling mechanisms.
FOOTNOTES
1 To read the full text of this article, go to http://www.fasebj.org/cgi/doi/10.1096/fj.03-0933fje; doi: 10.1096/fj.03-0933fje 
2 These authors contributed equally to this work.
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, significantly different from in vivo steady state; P<0.05.; scale bar, 120 µm.)