An experiment-based model of vein graft remodeling induced by shear stress

Distinct Temporal Pattern of the Prediction of Lumen Remodeling of Lower Extremity Vein Bypass Grafts by Initial Local Hemodynamics

We predicted human lower extremity vein bypass graft remodeling by hemodynamics. Computed tomography and duplex ultrasound scans of 55 patients were performed at 1 week and 1, 6, and 12 months post-implantation to obtain wall shear stress (WSS) and oscillatory shear index (OSI) at 1-mm intervals via computational fluid dynamics simulations. Graft remodeling was quantified by computed tomography-measured lumen diameter changes in the early (1 week-1 month), intermediate (1-6 months), and late (6-12 months) periods. Linear mixed-effect models were constructed to examine the overall relationship between remodeling and initial hemodynamics using the average data of all cross sections within the same graft. A significant association of graft remodeling with WSS (p < 0.001) and time (p = 0.001) was found; however, the effect size decreased with time (every 2.7 dyne/cm² increase of WSS was associated with a 0.39, 0.35, 0.002 mm diameter increase in the three periods, respectively). The association of remodeling with OSI was significant only in the intermediate period (every 0.1 increase of OSI was associated with a 0.25 mm lumen diameter decrease, p = 0.004). Therefore, the association of graft lumen remodeling with local hemodynamics has a distinct temporal pattern; WSS and OSI are predictive of remodeling only in certain postoperative periods.

Linking gene dynamics to vascular hyperplasia - Toward a predictive model of vein graft adaptation

Reductionist approaches, where individual pieces of a process are examined in isolation, have been the mainstay of biomedical research. While these methods are effective in highly compartmentalized systems, they fail to account for the inherent plasticity and non-linearity within the signaling structure. In the current manuscript, we present the computational architecture for tracking an acute perturbation in a biologic system through a multiscale model that links gene dynamics to cell kinetics, with the overall goal of predicting tissue adaptation. Given the complexity of the genome, the problem is made tractable by clustering temporal changes in gene expression into unique patterns. These cluster elements form the core of an integrated network that serves as the driving force for the response of the biologic system. This modeling approach is illustrated using the clinical scenario of vein bypass graft adaptation. Vein segments placed in the arterial circulation for treatment of advanced occlusive disease can develop an aggressive hyperplastic response that narrows the lumen, reduces blood flow, and induces in situ thrombosis. Reducing this hyperplastic response has been a long-standing but unrealized goal of biologic researchers in the field. With repeated failures of single target therapies, the redundant response pathways are thought to be a fundamental issue preventing progress towards a solution. Using the current framework, we demonstrate how theoretical genomic manipulations can be introduced into the system to shift the adaptation to a more beneficial phenotype, where the hyperplastic response is mitigated and the risk of thrombosis reduced. Utilizing our previously published rabbit vein graft genomic data, where grafts were harvested at time points ranging from 2 hours to 28 days and under differential flow conditions, and a customized clustering algorithm, five gene clusters that differentiated the low flow (i.e., pro-hyperplastic) from high flow (i.e., anti-hyperplastic) response were identified. The current analysis advances these general associations to create a model that identifies those genes sets most likely to be of therapeutic benefit. Using this approach, we examine the range of potential opportunities for intervention via gene cluster over-expression or inhibition, delivered in isolation or combination, at the time of vein graft implantation.

Patient-Specific, Multi-Scale Modeling of Neointimal Hyperplasia in Vein Grafts

Neointimal hyperplasia is amongst the major causes of failure of bypass grafts. The disease progression varies from patient to patient due to a range of different factors. In this paper, a mathematical model will be used to understand neointimal hyperplasia in individual patients, combining information from biological experiments and patient-specific data to analyze some aspects of the disease, particularly with regard to mechanical stimuli due to shear stresses on the vessel wall. By combining a biochemical model of cell growth and a patient-specific computational fluid dynamics analysis of blood flow in the lumen, remodeling of the blood vessel is studied by means of a novel computational framework. The framework was used to analyze two vein graft bypasses from one patient: a femoro-popliteal and a femoro-distal bypass. The remodeling of the vessel wall and analysis of the flow for each case was then compared to clinical data and discussed as a potential tool for a better understanding of the disease. Simulation results from this first computational approach showed an overall agreement on the locations of hyperplasia in these patients and demonstrated the potential of using new integrative modeling tools to understand disease progression.

Vein graft failure: from pathophysiology to clinical outcomes

Occlusive arterial disease is a leading cause of morbidity and mortality worldwide. Aside from balloon angioplasty, bypass graft surgery is the most commonly performed revascularization technique for occlusive arterial disease. Coronary artery bypass graft surgery is performed in patients with left main coronary artery disease and three-vessel coronary disease, whereas peripheral artery bypass graft surgery is used to treat patients with late-stage peripheral artery occlusive disease. The great saphenous veins are commonly used conduits for surgical revascularization; however, they are associated with a high failure rate. Therefore, preservation of vein graft patency is essential for long-term surgical success. With the exception of 'no-touch' techniques and lipid-lowering and antiplatelet (aspirin) therapy, no intervention has hitherto unequivocally proven to be clinically effective in preventing vein graft failure. In this Review, we describe both preclinical and clinical studies evaluating the pathophysiology underlying vein graft failure, and the latest therapeutic options to improve patency for both coronary and peripheral grafts.

Computational simulation of the adaptive capacity of vein grafts in response to increased pressure

Vein maladaptation, leading to poor long-term patency, is a serious clinical problem in patients receiving coronary artery bypass grafts (CABGs) or undergoing related clinical procedures that subject veins to elevated blood flow and pressure. We propose a computational model of venous adaptation to altered pressure based on a constrained mixture theory of growth and remodeling (G&R). We identify constitutive parameters that optimally match biaxial data from a mouse vena cava, then numerically subject the vein to altered pressure conditions and quantify the extent of adaptation for a biologically reasonable set of bounds for G&R parameters. We identify conditions under which a vein graft can adapt optimally and explore physiological constraints that lead to maladaptation. Finally, we test the hypothesis that a gradual, rather than a step, change in pressure will reduce maladaptation. Optimization is used to accelerate parameter identification and numerically evaluate hypotheses of vein remodeling.

Flow reversal promotes intimal thickening in vein grafts

OBJECTIVE

After vascular interventions, unidentified mechanisms disrupt the homeostasis of a focal narrowing to initiate an intimal thickening response. We hypothesize that perturbations in the hemodynamic microenvironment are the initiating event for this disruption of homeostasis and intimal thickening in vein bypass grafts. The objective of this study was to investigate the relation between local flow perturbations and its influence on the vein graft architecture.

METHODS

An external ligature was used to create an 80% focal midgraft stenosis in bilateral rabbit carotid vein grafts. A unilateral distal ligation created a ninefold difference in flow rate between high-flow and low-flow grafts. Ten vein grafts were harvested at 28 days and serially sectioned for morphologic evaluation and vein graft reconstruction. Computational fluid dynamics analyses were performed to examine the hemodynamic environment within these complex flow regions.

RESULTS

The largest intimal thickening occurred exclusively within the region immediately distal to the maximum stenosis in high-flow grafts, which was characterized by persistent flow separation and reversal for the entire cardiac cycle. In regions of low to moderate shear stress (<5 Pa), the typical inverse correlation between intimal thickness and wall shear was observed.

CONCLUSIONS

Regions of vein bypass grafts exposed to persistent flow reversal are most at risk for intimal thickening and loss of lumen.

Time and flow-dependent changes in the p27(kip1) gene network drive maladaptive vascular remodeling

OBJECTIVE

Although clinical studies have identified that a single nucleotide polymorphism in the p27(kip1) gene is associated with success or failure after vein bypass grafting, the underlying mechanisms for this difference are not well defined. Using a high-throughput approach in a flow-dependent vein graft model, we explored the differences in p27(kip1)-related genes that drive the enhanced hyperplastic response under low-flow conditions.

METHODS

Bilateral rabbit carotid artery interposition grafts with jugular vein were placed with a unilateral distal outflow branch ligation to create differential flow states. Grafts were harvested at 2 hours and at 1, 3, 7, 14, and 28 days after implantation, measured for neointimal area, and assayed for cell proliferation. Whole-vessel messenger RNA was isolated and analyzed using an Affymetrix (Santa Clara, Calif) gene array platform. Ingenuity Pathway Analysis (Ingenuity, Redwood City, Calif) was used to identify the gene networks surrounding p27(kip1). This gene set was then analyzed for temporal expression changes after graft placement and for differential expression in the alternate flow conditions.

RESULTS

Outflow branch ligation resulted in an eightfold difference in mean flow rates throughout the 28-day perfusion period (P < .001). Flow reduction led to a robust hyperplastic response, resulting in a significant increase in intimal area by 7 days (0.13 ± 0.04 mm(2) vs 0.014 ± 0.006 mm(2); P < .005) and progressive growth to 28 days (1.37 ± 0.05 mm(2) vs 0.39 ± 0.06 mm(2); P < .001). At 7 days, low-flow grafts demonstrated a burst of actively dividing intimal cells (36.4 ± 9.4 cells/mm(2) vs 11.5 ± 1.9 cells/mm(2); P = .04). Sixty-five unique genes within the microarray were identified as components of the p27(kip1) network. At a false discovery rate of 0.05, 26 genes demonstrated significant temporal changes, and two dominant patterns of expression were identified. Class comparison analysis identified differential expression of 11 genes at 2 hours and seven genes and 14 days between the high-flow and low-flow grafts (P < .05). At 2 hours, oncostatin M and cadherin 1 were the most differentially expressed. Cadherin 1 and protein kinase B exhibited the greatest differential expression at 14 days.

CONCLUSIONS

Alterations in flow and shear stress result in divergent patterns of vein graft remodeling. Associated with the dramatic increase in neointimal expansion observed in low-flow vs high-flow grafts is a subset of differentially expressed p27(kip1)-associated genes that correlate with critical stages in the adaptive response. These represent potential biologic targets whose activity may be altered to augment maladaptive vascular remodeling.

Correlates of saphenous vein graft hyperplasia and occlusion 1 year after coronary artery bypass grafting: analysis from the CASCADE randomized trial

BACKGROUND

Intimal hyperplasia of saphenous vein grafts (SVGs) can lead to subsequent graft atherosclerosis and occlusion after coronary artery bypass grafting (CABG). This study examined whether patient characteristics, anatomic factors, and medications are associated with SVG intimal hyperplasia and occlusion after CABG.

METHODS AND RESULTS

We performed a post hoc analysis of the Clopidogrel After Surgery for Coronary Artery Disease (CASCADE) trial, where 322 grafts were assessed by angiography and 90 grafts were examined by intravascular ultrasound at 1 year after CABG. We assessed the following correlates for intimal hyperplasia and occlusion: patient characteristics, discharge medications, target vessel characteristics, and SVG diameter. At 1 year, the SVG mean intimal area was 4.3 ± 2.1 mm(2), and the occlusion rate was 6.2% (13/209). Independent correlates of hyperplasia were larger SVG diameter (1.9 ± 0.2 mm(2)/mm; P<0.001), hypertension (0.7 ± 0.3 mm(2); P=0.03), and grafting to the right coronary territory (0.6 ± 0.3 mm(2); P=0.03), whereas statin (-0.8 ± 0.3 mm(2); P=0.01) and β-blocker use (-1.0 ± 0.4 mm(2); P=0.03) were associated with less hyperplasia. Low target vessel quality was an independent correlate of SVG occlusion (odds ratio, 5.2 ± 3.1; P<0.01).

CONCLUSIONS

Hypertension, SVG diameter, grafting to the right coronary artery, and low quality of the target vessel correlate with the development of SVG hyperplasia or occlusion by 1 year after CABG, whereas β-blockers and statins are associated with less SVG disease. These new findings further our understanding of SVG remodeling after bypass surgery and may guide future research to help prevent post-CABG SVG disease.

CLINICAL TRIAL REGISTRATION URL

http://www.clinicaltrials.gov. Unique identifier: NCT00228423.

Inhibition of vein graft stenosis with a c-jun targeting DNAzyme in a cationic liposomal formulation containing 1,2-dioleoyl-3-trimethylammonium propane (DOTAP)/1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE)

BACKGROUND/OBJECTIVES

Coronary artery bypass grafting (CABG) is among the most commonly performed heart surgical procedures. Saphenous vein graft failure due to stenosis impedes the longer-term success of CABG. A key cellular event in the process of vein graft stenosis is smooth muscle cell hyperplasia. In this study, we evaluated the effect of a DNAzyme (Dz13) targeting the transcription factor c-Jun in a rabbit model of vein graft stenosis in a cationic liposomal formulation containing 1,2-dioleoyl-3-trimethylammonium propane (DOTAP)/1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE). Dz13 in DOTAP/DOPE has undergone preclinical toxicological testing, and a Phase I clinical trial we recently conducted in basal cell carcinoma cancer patients demonstrates that it is safe and well tolerated after local administration.

METHODS

Effects of Dz13 in a formulation containing DOTAP/DOPE on smooth muscle cell (SMC) growth and c-Jun expression were assessed. Dz13 transfection was determined by cellular uptake of carboxyfluorescein-labeled Dz13. Autologous jugular vein to carotid artery transplantation was performed in New Zealand White rabbits to investigate the effect of the Dz13 in DOTAP/DOPE formulation on intimal hyperplasia.

RESULTS

Dz13/DOTAP/DOPE reduced SMC proliferation and c-Jun protein expression in vitro compared with an impotent form of Dz13 bearing a point mutation in its catalytic domain (Dz13.G>C). The Dz13(500 μg)/DOTAP/DOPE formed lipoplexes that were colloidally stable for up to 1h on ice (0°C) and 30 min at 37°C, allowing sufficient uptake by the veins. Dz13 (500 μg) inhibited neointima formation 28 d after end-to-side transplantation.

CONCLUSIONS

This formulation applied to veins prior to transplantation may potentially be useful in efforts to reduce graft failure.

Numerical analysis of non-Newtonian blood flow and wall shear stress in realistic single, double and triple aorto-coronary bypasses

Considering the fact that hemodynamics plays an important role in the patency and overall performance of implanted bypass grafts, this work presents a numerical investigation of pulsatile non-Newtonian blood flow in three different patient-specific aorto-coronary bypasses. The three bypass models are distinguished from each other by the number of distal side-to-side and end-to-side anastomoses and denoted as single, double and triple bypasses. The mathematical model in the form of time-dependent nonlinear system of incompressible Navier-Stokes equations is coupled with the Carreau-Yasuda model describing the shear-thinning property of human blood and numerically solved using the principle of the SIMPLE algorithm and cell-centred finite volume method formulated for hybrid unstructured tetrahedral grids. The numerical results computed for non-Newtonian and Newtonian blood flow in the three aorto-coronary bypasses are compared and analysed with emphasis placed on the distribution of cycle-averaged wall shear stress and oscillatory shear index. As shown in this study, the non-Newtonian blood flow in all of the considered bypass models does not significantly differ from the Newtonian one. Our observations further suggest that, especially in the case of sequential grafts, the resulting flow field and shear stimulation are strongly influenced by the diameter of the vessels involved in the bypassing.

A dynamical system that describes vein graft adaptation and failure

Adaptation of vein bypass grafts to the mechanical stresses imposed by the arterial circulation is thought to be the primary determinant for lesion development, yet an understanding of how the various forces dictate local wall remodeling is lacking. We develop a dynamical system that summarizes the complex interplay between the mechanical environment and cell/matrix kinetics, ultimately dictating changes in the vein graft architecture. Based on a systematic mapping of the parameter space, three general remodeling response patterns are observed: (1) shear stabilized intimal thickening, (2) tension induced wall thinning and lumen expansion, and (3) tension stabilized wall thickening. Notable is our observation that the integration of multiple feedback mechanisms leads to a variety of non-linear responses that would be unanticipated by an analysis of each system component independently. This dynamic analysis supports the clinical observation that the majority of vein grafts proceed along an adaptive trajectory, where grafts dilate and mildly thicken in response to the increased tension and shear, but a small portion of the grafts demonstrate a maladaptive phenotype, where progressive inward remodeling and accentuated wall thickening lead to graft failure.

Rule-based model of vein graft remodeling

When vein segments are implanted into the arterial system for use in arterial bypass grafting, adaptation to the higher pressure and flow of the arterial system is accomplished thorough wall thickening and expansion. These early remodeling events have been found to be closely coupled to the local hemodynamic forces, such as shear stress and wall tension, and are believed to be the foundation for later vein graft failure. To further our mechanistic understanding of the cellular and extracellular interactions that lead to global changes in tissue architecture, a rule-based modeling method is developed through the application of basic rules of behaviors for these molecular and cellular activities. In the current method, smooth muscle cell (SMC), extracellular matrix (ECM), and monocytes are selected as the three components that occupy the elements of a grid system that comprise the developing vein graft intima. The probabilities of the cellular behaviors are developed based on data extracted from in vivo experiments. At each time step, the various probabilities are computed and applied to the SMC and ECM elements to determine their next physical state and behavior. One- and two-dimensional models are developed to test and validate the computational approach. The importance of monocyte infiltration, and the associated effect in augmenting extracellular matrix deposition, was evaluated and found to be an important component in model development. Final model validation is performed using an independent set of experiments, where model predictions of intimal growth are evaluated against experimental data obtained from the complex geometry and shear stress patterns offered by a mid-graft focal stenosis, where simulation results show good agreements with the experimental data.

Longitudinal assessment of hemodynamic endpoints in predicting arteriovenous fistula maturation

Arteriovenous fistula (AVF) nonmaturation is currently a significant clinical problem; however, the mechanisms responsible for this have remained unanswered. Previous work by our group and others has suggested that anatomical configuration and the corresponding hemodynamic endpoints could have an important role in AVF remodeling. Thus, our goal was to assess the longitudinal (temporal) effect of wall shear stress (WSS) on remodeling process of AVFs with two different configurations. The hypothesis is that early assessment of hemodynamic endpoints such as temporal gradient of WSS will predict the maturation status of AVF at later time points. Two AVFs with curved (C-AVF) and straight (S-AVF) configurations were created between the femoral artery and vein of each pig. Three pigs were considered in this study and in total six AVFs (three C-AVF and three S-AVF) were created. The CT scan and ultrasound were utilized to numerically evaluate local WSS at 20 cross-sections along the venous segment of AVFs at 2D (D: days), 7D, and 28D postsurgery. These cross-sections were located at 1.5 mm increments from the anastomosis junction. Local WSS values at these cross-sections were correlated with their corresponding luminal area over time. The WSS in C-AVF decreased from 22.3 ± 4.8 dyn/cm(2) at 2D to 4.1 ± 5.1 dyn/cm(2) at 28D, while WSS increased in S-AVF from 13.0 ± 5.0 dyn/cm(2) at 2D to 36.7 ± 5.3 dyn/cm(2) at 28D. Corresponding to these changes in WSS levels, luminal area of C-AVF dilated (0.23 ± 0.14 cm(2) at 2D to 0.87 ± 0.14 cm(2) at 28D) with attendant increase in flow rate. However, S-AVF had minimal changes in area (0.26 ± 0.02 cm(2) at 2D to 0.27 ± 0.03 cm(2) at 28D) despite some increase in flow rate. Our results suggest that the temporal changes of WSS could have significant effects on AVF maturation. Reduction in WSS over time (regardless of initial values) may result in dilation (p < 0.05), while increase in WSS may be detrimental to maturation. Thus, creation of AVFs in a specific configuration which results in a decline in WSS over time may reduce AVF maturation failure.

Animal models for studying vein graft failure and therapeutic interventions

Vein grafts have been extensively used to bypass blockages in arteries, but are themselves subject to early closure by thrombosis or later obstruction by vein graft disease (neointimal hyperplasia and remodelling). Animal models are a crucial means of testing potential therapeutic and surgical interventions to prevent graft stenosis and occlusion. This review outlines many of the animal models of vein grafting. Recent studies include targeted gene therapy to prevent acute vein graft thrombosis and the use of folic acid to limit graft failure in diabetic pigs.

Mouse vein graft hemodynamic manipulations to enhance experimental utility

Mouse models serve as a tool to study vein graft failure. However, in wild-type mice, there is limited intimal hyperplasia, hampering efforts to identify anti-intimal hyperplasia therapies. Furthermore, vein graft wall remodeling has not been well quantified in mice. We hypothesized that simple hemodynamic manipulations can reproducibly augment intimal hyperplasia and remodeling end points in mouse vein grafts, thereby enhancing their experimental utility. Mouse inferior vena cava-to-carotid interposition isografts were completed using an anastomotic cuff technique. Three flow restriction manipulations were executed by ligating outflow carotid branches, creating an outflow common carotid stenosis, and constructing a midgraft stenosis. Flowmetry and ultrasonography were used perioperatively and at day 28. All ligation strategies decreased the graft flow rate and wall shear stress. Morphometry showed that intimal thickness increased by 26% via carotid branch ligation and by 80% via common carotid stenosis. Despite similar mean flow rates and shear stresses among the three manipulations, the flow waveform amplitudes were lowest with common carotid stenosis. The disordered flow of the midgraft stenosis yielded poststenotic dilatation. The creation of an outflow common carotid stenosis generates clinically relevant (poor runoff) vein graft low wall shear stress and offers a technically flexible method for enhancing the intimal hyperplasia response. Midgraft stenosis exhibits poststenotic positive wall remodeling. These reproducible approaches offer novel strategies for increasing the utility of mouse vein graft models.

Pulsatile ex vivo perfusion of human saphenous vein grafts under controlled pressure conditions increases MMP-2 expression

Background

The use of human saphenous vein grafts (HSVGs) as a bypass conduit is a standard procedure in the treatment of coronary artery disease while their early occlusion remains a major problem.

Methods

We have developed an ex vivo perfusion system, which uses standardized and strictly controlled hemodynamic parameters for the pulsatile and non-static perfusion of HSVGs to guarantee a reliable analysis of molecular parameters under different pressure conditions. Cell viability of HSVGs (n = 12) was determined by the metabolic conversion of 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl-tetrazolium bromide (MTT) into a purple formazan dye.

Results

Under physiological flow rates (10 mmHg) HSVGs remained viable for two weeks. Their exposure to arterial conditions (100 mmHg) was possible for one week without important reduction in viability. Baseline expression of matrix metalloproteinase-2 (MMP-2) after venous perfusion (2.2 ± 0.5, n = 5) was strongly up-regulated after exposure to arterial conditions for three days (19.8 ± 4.3) or five days (23.9 ± 6.1, p < 0.05). Zymographic analyses confirmed this increase on the protein level. Our results suggest that expression and activity of MMP-2 are strongly increased after exposure of HSVGs to arterial hemodynamic conditions compared to physiological conditions.

Conclusion

Therefore, our system might be helpful to more precisely understand the molecular mechanisms leading to an early failure of HSVGs.

The dynamics of vein graft remodeling induced by hemodynamic forces: a mathematical model

Although vein bypass grafting is one of the primary options for the treatment of arterial occlusive disease and provides satisfactory results at an early stage of the treatment, the patency is limited to a few months in many patients. When the vein is implanted in the arterial system, it adapts to the high flow rate and high pressure of the arterial environment by changing the sizes of its layers, and this remodeling is believed to be a precursor of future graft failure. Hemodynamic forces, such as wall shear stress (WSS) and wall tension, have been recognized as major factors impacting vein graft remodeling. Although a wide range of experimental evidence relating hemodynamic forces to vein graft remodeling has been reported, a comprehensive mathematical model describing the relationship among WSS, wall tension, and the structural adaptation of each individual layer of the vein graft wall is lacking. The current manuscript presents a comprehensive and robust framework for treating the complex interaction between the WSS, wall tension, and the structural adaptation of each individual layer of the vein graft wall. We modeled the intimal and medial area and the radius of external elastic lamina, which in combination dictate luminal narrowing and the propensity for graft occlusion. Central to our model is a logistic relationship between independent and dependent variables to describe the initial increase and later decrease in the growth rate. The detailed understanding of the temporal changes in vein graft morphology that can be extracted from the current model is critical in identifying the dominant contributions to vein graft failure and the further development of strategies to improve their longevity.

Adaptive changes in autogenous vein grafts for arterial reconstruction: clinical implications

For patients with the most severe manifestations of lower extremity arterial occlusive disease, bypass surgery using autogenous vein has been the most durable reconstruction. However, the incidence of bypass graft stenosis and graft failure remains substantial and wholesale improvements in patency are lacking. One potential explanation is that stenosis arises not only from over exuberant intimal hyperplasia, but also due to insufficient adaptation or remodeling of the vein to the arterial environment. Although in vivo human studies are difficult to conduct, recent advances in imaging technology have made possible a more comprehensive structural examination of vein bypass maturation. This review summarizes recent translational efforts to understand the structural and functional properties of human vein grafts and places it within the context of the rich existing literature of vein graft failure.

Hemodynamically driven vein graft remodeling: a systems biology approach

Despite intense investigation over several decades to understand the mechanisms of vein graft failure, few therapeutic modalities have emerged. Emphasis using standard reductionist approaches has been focused on cataloging the components involved in the early events following vein graft implantation, but limited insight has been gained in understanding the dynamic interaction of these components. We propose that the application of systems theory offers the opportunity for significant advances in this area. Focused on modeling the dynamic relationships that define living organisms, systems biology provides the necessary tools to further our understanding of the complex series of overlapping biologic events on surgical implantation of the vein graft. Through the use of ordinary differential equation and agent-based modeling techniques, we present our ongoing efforts to define the nonlinear interactions between hemodynamics and vascular adaptation.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.