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Multiscale Understanding of Vascular Adaptation: The Vein Graft Model

By Marc Garbey, Stefano Casarin, and Scott Berceli

Cardiovascular diseases continue to dominate humanity’s morbidity and mortality [1]. Contemporary therapies for occlusive arterial diseases include angioplasties, stent deployment, endarterectomies, and bypasses. However, these procedures suffer from unacceptably high failure rates due to re-occlusive events, resulting mainly from unfavorable vascular adaptation.

Vascular adaptation following local injury occurs due to a combination of intimal hyperplasia (thickening of the innermost layer of a blood vessel) and inward remodeling (shrinking of the blood vessel wall). Over the past three decades, researchers have used a wide variety of approaches to investigate intimal hyperplasia and wall remodeling in an effort to identify novel therapeutic strategies. Despite incremental progress, no durable treatments have evolved to become clinical realities.

Due to its potential impact on improving post-surgical outcomes, vascular adaptation has been the target of several mathematical modeling-based studies. Employing standard approaches used by biologists to condense a problem to its core components, prior strategies have focused largely on reductionist approaches and used deterministic, continuous models to describe the physical and biological components of vascular disease progression. However, advancing the understanding of such a complex phenomenon requires the integration of divergent types of data into quantitative models that can be used to predict vascular dynamics and remodeling outcomes [3].

Although early attempts to manipulate the remodeling response proposed a variety of single-bullet approaches, failure of these efforts suggests that intersection of targeted strategies would help overcome the redundant biology in this complex system. Using the integration of multiscale modeling and experimental techniques, one can identify and manipulate critical gene targets in vivo to improve vein graft durability. Specifically, we hypothesize that a gene regulatory network—modulated by defined blood shearing forces—determines the global adaptive response of the vein graft wall following acute injury.

Unlike many other disease processes within the vascular system, which occur in the time scale of decades, vein bypass graft failure occurs in the timeframe of weeks to months. With a well-defined initial condition (i.e., normal vein at the time of implantation [3]) and well-characterized environmental exposure (i.e., pressure and flows of the arterial circulation), the pathophysiology of vein graft disease is suitable for mathematical modeling.

To abate the incidence of this failed adaptation, we suggest an efficient post-surgical therapy at the genetic level. We thus propose a multiscale model that can replicate the graft’s healing and detail the level of impact of targeted genes on the healing process. A key feature of our model is its capability to link the genetic, cellular, and tissue levels with feedback bridges in such a way that every single variation from an equilibrium point is reflected on all other elements; this creates a highly-organized, multiscale loop (see Figure 1).

Figure 1. A loop of interdependent events, where the dynamic interplay between physical forces and gene networks regulates the early graft remodeling and describes the graft arterialization process. Image courtesy of [2].

A mechano-biological description is able to develop a variety of frameworks reflecting our initial understanding of the graft’s healing process. For example, one may use the set of incompressible Navier-Stokes (NS) equations to describe flow in the lumen and provide shear stress values along the wall. A hyperelastic model of tissue deformation coupled with NS supplies the transmural pressure and strain energy distribution inside the wall. A reaction-diffusion equation estimates the delivery and distribution of a growth factor inside the wall, offering a simplified link between the lumen wall thickening—triggered by shear stress value—and cellular functions.

A gene regulatory network modulates the response to these mechanical conditions within this integrated system. The level of gene expression dictates specific cellular functions, such as cell proliferation, death, mobility, and matrix deposition.  An agent-based model (ABM), which replicates the basic cellular functions triggered by gene expression, describes the resulting tissue adaptation at the cellular level. Finally, the resulting variations in tissue morphology influence the local mechanical environment, with these closed-loop events continuing across time scales ranging from seconds to months. This complex model is implemented in a modular way and can take advantage of heterogeneous high-performance computing architecture. Most importantly, the model’s agility expresses the ongoing discussion between experimentalists, computational scientists, and practicing clinicians who provide critical insight into the ultimate utility of this approach. There is indeed no point in reproducing the exact biology or flow conditions — even if this was possible, analyzing the model would eventually become as complicated as studying the animal model itself! Instead, the art is the development of a portfolio of models available on demand to address the specific needs of patients [7].

Figure 2. Dynamical system (DS) flow chart illustrating the primary interacting elements in vein graft adaptation. Image courtesy of [4].
Figure 1 provides a good sense of how various feedback loops regulate the adaptation phenomenon. In view of the first model implementation, a dynamical system (DS) calibrated on experimental observations was developed to classify the dominant mechanisms that modulate both intima hyperplasia formation and wall remodeling. A top-down approach—nicely described in Figure 2—regulates the DS. Surprisingly enough, the DS allows us to give a sense of positive or negative adaptation, interpreted as convergence to critical points in the phase space. Even though simple in nature, this conceptual system has shown that adaptation may come at the price of numerous oscillations in lumen geometry, a phenomenon commonly observed by clinicians but previously unexplained [4].

An important goal of this model is to provide insights into the significance of spatial dependency among cellular and matrix elements, individuating a match against histologic data with the ability to contribute much more information on the fundamental cellular events that lead to unique pattern formations (see Figure 3) [6]. Such level of detail is aimed at delivering a deeper understanding of the fundamental mechanisms without getting lost in the specifics. An important advancement has been cross-validating the upscale DS and multiscale ABM, offering different tools and contrasting approaches to investigate various aspects of the biology that lead to the same biologic conclusion [5]. Our focus has been to develop an ABM that is nimble yet fundamentally sound, and able to present the necessary level of complexity without slavishly reproducing an exact replica of the multitude of biologic networks within the system. While it is unlikely that such an ambitious goal could even be achieved, this would far outstrip the experimental capabilities that are critical to fueling the accuracy and reproducibility of such a model. 

However, our main goal remains not only to reproduce known experiences but also to identify opportunities for therapeutic intervention. With this in mind, the model must evolve towards an approach that integrates gene activity in a manner facilitating virtual gene therapy trials that predict the clinical impact of the proposed intervention. In a sense, the multiscale model is a systematic way to integrate disparate experimental data—corresponding to measurement of the biomechanical environment, gene expression, cell replication, and tissue remodeling—into a coherent representation of a complex, dynamic system.

Figure 3. Clinical observation of a vein graft success and failure six months after surgery (left), replicated with an agent-based model (right). The black portion represents the lumen, the pink portion represents the tunica intima, and the beige portion represents the tunica media. Image courtesy of [5].

As the experimental data keeps adding up, one must calibrate and partially validate the model at various scale levels. The modular approach of the construction grants important flexibility in achieving this crucial task. Once validated at various levels, the integrated model allows one to test the outcome of intersecting gene therapies, and can offer the potential to prolong lumen patency, improve long-term effects, and provide targets for clinical investigation [2].

Given the inherent uncertainty of experimental biologic data, it is unrealistic to expect such a high degree of model precision so as to arrive at a single optimum solution. Instead, the anticipation is that the development and systematic application of this model can narrow the range of potential gene therapies from millions of possibilities to a handful that are able to be tested and eventually made patient specific. It may also help to prevent trapping the research with the “magic bullet” approach, which relies on some new protein discovery that works in a Petri dish but eventually fails due to the system’s feedback mechanisms.

Although multiscale modeling has taken a foothold in many disciplines across the biomedical research landscape, its application to clinical disease has been sparse. While our focus has been on the vascular system and its response to surgical manipulation, on a more fundamental level this work sets the template for integrating experimental data with a computational framework to explore the potential of genomic modification to improve patient outcomes or eradicate a disease process. On a broader scale, such an approach is readily adaptable to a range of human pathologies that present a discrete initiating event and interact with the environment during disease progression.  Cancer biology—where a genetic trigger leads to cell activation and uncontrolled growth—and life-threatening sepsis—where an acute infection leads to hemodynamic instability and collapse—present promising areas for further expansion of this novel architecture.

[1] American Heart Association. (2016). Heart Disease, Stroke and Research Statistics At-a-Glance. Retrieved from
[2] Casarin, S., Berceli, S.A., & Garbey, M. (2017). Linking Gene Dynamics to Intimal Hyperplasia – A Predictive Model of Vein Graft Adaptation. Proc. Comp. Sci., 108, 1842-51.
[3] De Vries, M.R., Simons, K.H., Jukema, J.W., Braun, J., & Quax, P.H.A. (2016). Vein graft failure: from pathophysiology to clinical outcomes. Nat. Rev.: Cardiol., 13, 451-470. 
[4] Garbey, M., & Berceli, S.A. (2013). A dynamical system that describes vein graft adaptation and failure. J. Theor. Biol., 336, 209-220. 
[5] Garbey, M., Casarin, S., & Berceli, S.A. (2017). Vascular Adaptation: Pattern Formation and Cross Validation between an Agent Based Model and a Dynamical System. J. Theor. Biol., 429, 149-163.  
[6] Garbey, M., Rahman, M., & Berceli, S.A. (2015). A multiscale computational framework to understand vascular adaptation. J. Comput. Sci., 8, 32-47.
 [7] Zhang, Y., Barocas, V.H., Berceli, S.A., Clancy, C.E., Eckman, D.M., Garbey, M….Trayanova, N.A. (2016). Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention. Ann. Biomed. Eng., 44(9), 2642-60.

Marc Garbey co-founded (with Barbara Bass) the concept of computational surgery. He is the scientific director of the Center of Computational Surgery at the Houston Methodist Hospital, professor of applied mathematics at the University of La Rochelle, and adjunct professor in the Department of Bioengineering at Texas A&M University. Stefano Casarin is a postdoctoral research fellow at the Center for Computational Surgery at Houston Methodist Research Institute and Vice President of International Affairs at the Methodist Association of Professional and Trainee Affairs. Scott Berceli, M.D., Ph.D., is a professor of surgery and bioengineering at the University of Florida and Chief of Vascular Surgery at the North Florida/South Georgia Veterans Health System.

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