Adaptive integration of history variables in constrained mixture models for organ-scale growth and remodeling.

In the last decades, many computational models have been developed to predict soft tissue growth and remodeling (G&R). The constrained mixture theory describes fundamental mechanobiological processes in soft tissue G&R and has been widely adopted in cardiovascular models of G&R. However, even after two decades of work, large organ-scale models are rare, mainly due to high computational costs (model evaluation and memory consumption), especially in long-range simulations. We propose two strategies to adaptively integrate history variables in constrained mixture models to enable large organ-scale simulations of G&R. Both strategies exploit that the influence of deposited tissue on the current mixture decreases over time through degradation. One strategy is independent of external loading, allowing the estimation of the computational resources ahead of the simulation. The other adapts the history snapshots based on the local mechanobiological environment so that the additional integration errors can be controlled and kept negligibly small, even in G&R scenarios with severe perturbations. We analyze the adaptively integrated constrained mixture model on a tissue patch for a parameter study and show the performance under different G&R scenarios. To confirm that adaptive strategies enable large organ-scale examples, we show simulations of different hypertension conditions with a real-world example of a biventricular heart discretized with a finite element mesh. In our example, adaptive integrations sped up simulations by a factor of three and reduced memory requirements to one-sixth. The reduction of the computational costs gets even more pronounced for simulations over longer periods. Adaptive integration of the history variables allows studying more finely resolved models and longer G&R periods while computational costs are drastically reduced and largely constant in time.

Hemodynamics and Wall Mechanics of Vascular Graft Failure.

Blood vessels are subjected to complex biomechanical loads, primarily from pressure-driven blood flow. Abnormal loading associated with vascular grafts, arising from altered hemodynamics or wall mechanics, can cause acute and progressive vascular failure and end-organ dysfunction. Perturbations to mechanobiological stimuli experienced by vascular cells contribute to remodeling of the vascular wall via activation of mechanosensitive signaling pathways and subsequent changes in gene expression and associated turnover of cells and extracellular matrix. In this review, we outline experimental and computational tools used to quantify metrics of biomechanical loading in vascular grafts and highlight those that show potential in predicting graft failure for diverse disease contexts. We include metrics derived from both fluid and solid mechanics that drive feedback loops between mechanobiological processes and changes in the biomechanical state that govern the natural history of vascular grafts. As illustrative examples, we consider application-specific coronary artery bypass grafts, peripheral vascular grafts, and tissue-engineered vascular grafts for congenital heart surgery as each of these involves unique circulatory environments, loading magnitudes, and graft materials.

A probabilistic neural twin for treatment planning in peripheral pulmonary artery stenosis.

The substantial computational cost of high-fidelity models in numerical hemodynamics has, so far, relegated their use mainly to offline treatment planning. New breakthroughs in data-driven architectures and optimization techniques for fast surrogate modeling provide an exciting opportunity to overcome these limitations, enabling the use of such technology for time-critical decisions. We discuss an application to the repair of multiple stenosis in peripheral pulmonary artery disease through either transcatheter pulmonary artery rehabilitation or surgery, where it is of interest to achieve desired pressures and flows at specific locations in the pulmonary artery tree, while minimizing the risk for the patient. Since different degrees of success can be achieved in practice during treatment, we formulate the problem in probability, and solve it through a sample-based approach. We propose a new offline-online pipeline for probabilistic real-time treatment planning which combines offline assimilation of boundary conditions, model reduction, and training dataset generation with online estimation of marginal probabilities, possibly conditioned on the degree of augmentation observed in already repaired lesions. Moreover, we propose a new approach for the parametrization of arbitrarily shaped vascular repairs through iterative corrections of a zero-dimensional approximant. We demonstrate this pipeline for a diseased model of the pulmonary artery tree available through the Vascular Model Repository.

High Shear Stress Reduces ERG Causing Endothelial-Mesenchymal Transition and Pulmonary Arterial Hypertension.

Pathological high shear stress (HSS, 100 dyn/cm 2 ) is generated in distal pulmonary arteries (PA) (100-500 µm) in congenital heart defects and in progressive PA hypertension (PAH) with inward remodeling and luminal narrowing. Human PA endothelial cells (PAEC) were subjected to HSS versus physiologic laminar shear stress (LSS, 15 dyn/cm 2 ). Endothelial-mesenchymal transition (EndMT), a feature of PAH not previously attributed to HSS, was observed. H3K27ac peaks containing motifs for an ETS-family transcription factor (ERG) were reduced, as was ERG-Krüppel-like factors (KLF)2/4 interaction and ERG expression. Reducing ERG by siRNA in PAEC during LSS caused EndMT; transfection of ERG in PAEC under HSS prevented EndMT. An aorto-caval shunt was preformed in mice to induce HSS and progressive PAH. Elevated PA pressure, EndMT and vascular remodeling were reduced by an adeno-associated vector that selectively replenished ERG in PAEC. Agents maintaining ERG in PAEC should overcome the adverse effect of HSS on progressive PAH.

A Fluid-Solid-Growth Solver for Cardiovascular Modeling.

We implement full, three-dimensional constrained mixture theory for vascular growth and remodeling into a finite element fluid-structure interaction (FSI) solver. The resulting "fluid-solid-growth" (FSG) solver allows long term, patient-specific predictions of changing hemodynamics, vessel wall morphology, tissue composition, and material properties. This extension from short term (FSI) to long term (FSG) simulations increases clinical relevance by enabling mechanobioloigcally-dependent studies of disease progression in complex domains.

A computational growth and remodeling framework for adaptive and maladaptive pulmonary arterial hemodynamics.

Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step toward predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.

Rapid model-guided design of organ-scale synthetic vasculature for biomanufacturing.

Our ability to produce human-scale bio-manufactured organs is critically limited by the need for vascularization and perfusion. For tissues of variable size and shape, including arbitrarily complex geometries, designing and printing vasculature capable of adequate perfusion has posed a major hurdle. Here, we introduce a model-driven design pipeline combining accelerated optimization methods for fast synthetic vascular tree generation and computational hemodynamics models. We demonstrate rapid generation, simulation, and 3D printing of synthetic vasculature in complex geometries, from small tissue constructs to organ scale networks. We introduce key algorithmic advances that all together accelerate synthetic vascular generation by more than 230 -fold compared to standard methods and enable their use in arbitrarily complex shapes through localized implicit functions. Furthermore, we provide techniques for joining vascular trees into watertight networks suitable for hemodynamic CFD and 3D fabrication. We demonstrate that organ-scale vascular network models can be generated in silico within minutes and can be used to perfuse engineered and anatomic models including a bioreactor, annulus, bi-ventricular heart, and gyrus. We further show that this flexible pipeline can be applied to two common modes of bioprinting with free-form reversible embedding of suspended hydrogels and writing into soft matter. Our synthetic vascular tree generation pipeline enables rapid, scalable vascular model generation and fluid analysis for bio-manufactured tissues necessary for future scale up and production.

A Computational Growth and Remodeling Framework for Adaptive and Maladaptive Pulmonary Arterial Hemodynamics.

Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step towards predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.

Tissue engineered vascular grafts transform into autologous neovessels capable of native function and growth.

Background: Tissue-engineered vascular grafts (TEVGs) have the potential to advance the surgical management of infants and children requiring congenital heart surgery by creating functional vascular conduits with growth capacity. Methods: Herein, we used an integrative computational-experimental approach to elucidate the natural history of neovessel formation in a large animal preclinical model; combining an in vitro accelerated degradation study with mechanical testing, large animal implantation studies with in vivo imaging and histology, and data-informed computational growth and remodeling models. Results: Our findings demonstrate that the structural integrity of the polymeric scaffold is lost over the first 26 weeks in vivo, while polymeric fragments persist for up to 52 weeks. Our models predict that early neotissue accumulation is driven primarily by inflammatory processes in response to the implanted polymeric scaffold, but that turnover becomes progressively mechano-mediated as the scaffold degrades. Using a lamb model, we confirm that early neotissue formation results primarily from the foreign body reaction induced by the scaffold, resulting in an early period of dynamic remodeling characterized by transient TEVG narrowing. As the scaffold degrades, mechano-mediated neotissue remodeling becomes dominant around 26 weeks. After the scaffold degrades completely, the resulting neovessel undergoes growth and remodeling that mimicks native vessel behavior, including biological growth capacity, further supported by fluid-structure interaction simulations providing detailed hemodynamic and wall stress information. Conclusions: These findings provide insights into TEVG remodeling, and have important implications for clinical use and future development of TEVGs for children with congenital heart disease.

In vivo development of tissue engineered vascular grafts: a fluid-solid-growth model.

Methods of tissue engineering continue to advance, and multiple clinical trials are underway evaluating tissue engineered vascular grafts (TEVGs). Whereas initial concerns focused on suture retention and burst pressure, there is now a pressing need to design grafts to have optimal performance, including an ability to grow and remodel in response to changing hemodynamic loads. Toward this end, there is similarly a need for computational methods that can describe and predict the evolution of TEVG geometry, composition, and material properties while accounting for changes in hemodynamics. Although the ultimate goal is a fluid-solid-growth (FSG) model incorporating fully 3D growth and remodeling and 3D hemodynamics, lower fidelity models having high computational efficiency promise to play important roles, especially in the design of candidate grafts. We introduce here an efficient FSG model of in vivo development of a TEVG based on two simplifying concepts: mechanobiologically equilibrated growth and remodeling of the graft and an embedded control volume analysis of the hemodynamics. Illustrative simulations for a model Fontan conduit reveal the utility of this approach, which promises to be particularly useful in initial design considerations involving formal methods of optimization which otherwise add considerably to the computational expense.

Hemodynamic performance of tissue-engineered vascular grafts in Fontan patients.

In the field of congenital heart surgery, tissue-engineered vascular grafts (TEVGs) are a promising alternative to traditionally used synthetic grafts. Our group has pioneered the use of TEVGs as a conduit between the inferior vena cava and the pulmonary arteries in the Fontan operation. The natural history of graft remodeling and its effect on hemodynamic performance has not been well characterized. In this study, we provide a detailed analysis of the first U.S. clinical trial evaluating TEVGs in the treatment of congenital heart disease. We show two distinct phases of graft remodeling: an early phase distinguished by rapid changes in graft geometry and a second phase of sustained growth and decreased graft stiffness. Using clinically informed and patient-specific computational fluid dynamics (CFD) simulations, we demonstrate how changes to TEVG geometry, thickness, and stiffness affect patient hemodynamics. We show that metrics of patient hemodynamics remain within normal ranges despite clinically observed levels of graft narrowing. These insights strengthen the continued clinical evaluation of this technology while supporting recent indications that reversible graft narrowing can be well tolerated, thus suggesting caution before intervening clinically.

From Uniaxial Testing of Isolated Layers to a Tri-Layered Arterial Wall: A Novel Constitutive Modelling Framework.

Mechanical testing and constitutive modelling of isolated arterial layers yields insight into the individual layers' mechanical properties, but per se fails to recapitulate the in vivo loading state, neglecting layer-specific residual stresses. The aim of this study was to develop a testing/modelling framework that integrates layer-specific uniaxial testing data into a three-layered model of the arterial wall, thereby enabling study of layer-specific mechanics under realistic (patho)physiological conditions. Circumferentially and axially oriented strips of pig thoracic aortas (n = 10) were tested uniaxially. Individual arterial layers were then isolated from the wall, tested, and their mechanical behaviour modelled using a hyperelastic strain energy function. Subsequently, the three layers were computationally assembled into a single flat-walled sample, deformed into a cylindrical vessel, and subjected to physiological tension-inflation. At the in vivo axial stretch of 1.10 ± 0.03, average circumferential wall stress was 75 ± 9 kPa at 100 mmHg, which almost doubled to 138 ± 15 kPa at 160 mmHg. A ~ 200% stiffening of the adventitia over the 60 mmHg pressure increase shifted layer-specific load-bearing from the media (65 ± 10% → 61 ± 14%) to the adventitia (28 ± 9% → 32 ± 14%). Our approach provides valuable insight into the (patho)physiological mechanical roles of individual arterial layers at different loading states, and can be implemented conveniently using simple, inexpensive and widely available uniaxial testing equipment.

Electrospun Tissue-Engineered Arterial Graft Thickness Affects Long-Term Composition and Mechanics.

Wall stress is often lower in tissue-engineered constructs than in comparable native tissues due to the use of stiff polymeric materials having thicker walls. In this work, we sought to design a murine arterial graft having a more favorable local mechanical environment for the infiltrating cells; we used electrospinning to enclose a compliant inner core of poly(glycerol sebacate) with a stiffer sheath of poly(caprolactone) to reduce the potential for rupture. Two scaffolds were designed that differed in the thickness of the core as previous computational simulations found that circumferential wall stresses could be increased in the core toward native values by increasing the ratio of the core:sheath. Our modified electrospinning protocols reduced swelling of the core upon implantation and eliminated residual stresses in the sheath, both of which had contributed to the occlusion of implanted grafts during pilot studies. For both designs, a subset of implanted grafts occluded due to thrombosis or ruptured due to suspected point defects in the sheath. However, there were design-based differences in collagen content and mechanical behavior during early remodeling of the patent samples, with the thinner-core scaffolds having more collagen and a stiffer behavior after 12 weeks of implantation than the thicker-core scaffolds. By 24 weeks, the thicker-core scaffolds also became stiff, with similar amounts of collagen but increased smooth muscle cell and elastin content. These data suggest that increasing wall stress toward native values may provide a more favorable environment for normal arterial constituents to form despite the overall stiffness of the construct remaining elevated due to the absolute increase in load-bearing constituents.

Effects of Braiding Parameters on Tissue Engineered Vascular Graft Development.

Tissue engineered vascular grafts (TEVGs) using scaffolds fabricated from braided poly(glycolic acid) (PGA) fibers coated with poly(glycerol sebacate) (PGS) are developed. The approach relies on in vivo tissue engineering by which neotissue forms solely within the body after a scaffold has been implanted. Herein, the impact of altering scaffold braid design and scaffold coating on neotissue formation is investigated. Several combinations of braiding parameters are manufactured and evaluated in a Beige mouse model in the infrarenal abdominal aorta. Animals are followed with 4D ultrasound analysis, and 12 week explanted vessels are evaluated for biaxial mechanical properties as well as histological composition. Results show that scaffold parameters (i.e., braiding angle, braiding density, and presence of a PGS coating) have interdependent effects on the resulting graft performance, namely, alteration of these parameters influences levels of inflammation, extracellular matrix production, graft dilation, neovessel distensibility, and overall survival. Coupling carefully designed in vivo experimentation with regression analysis, critical relationships between the scaffold design and the resulting neotissue that enable induction of favorable cellular and extracellular composition in a controlled manner are uncovered. Such an approach provides a potential for fabricating scaffolds with a broad range of features and the potential to manufacture optimized TEVGs.

Vascular dimorphism ensured by regulated proteoglycan dynamics favors rapid umbilical artery closure at birth.

The umbilical artery lumen closes rapidly at birth, preventing neonatal blood loss, whereas the umbilical vein remains patent longer. Here, analysis of umbilical cords from humans and other mammals identified differential arterial-venous proteoglycan dynamics as a determinant of these contrasting vascular responses. The umbilical artery, but not the vein, has an inner layer enriched in the hydrated proteoglycan aggrecan, external to which lie contraction-primed smooth muscle cells (SMC). At birth, SMC contraction drives inner layer buckling and centripetal displacement to occlude the arterial lumen, a mechanism revealed by biomechanical observations and confirmed by computational analyses. This vascular dimorphism arises from spatially regulated proteoglycan expression and breakdown. Mice lacking aggrecan or the metalloprotease ADAMTS1, which degrades proteoglycans, demonstrate their opposing roles in umbilical vascular dimorphism, including effects on SMC differentiation. Umbilical vessel dimorphism is conserved in mammals, suggesting that differential proteoglycan dynamics and inner layer buckling were positively selected during evolution.

Vascular adaptation in the presence of external support - A modeling study.

Vascular grafts have long been used to replace damaged or diseased vessels with considerable success, but a new approach is emerging where native vessels are merely supported, not replaced. Although external supports have been evaluated in diverse situations - ranging from aneurysmal disease to vein grafts or the Ross operation - optimal supports and procedures remain wanting. In this paper, we present a novel application of a growth and remodeling model well suited for parametrically exploring multiple designs of external supports while accounting for mechanobiological and immunobiological responses of the supported native vessel. These results suggest that a load bearing external support can reduce vessel thickening in response to pressure elevation. Results also suggest that the final adaptive state of the vessel depends on the structural stiffness of the support via a mechano-driven adaptation, although luminal encroachment may be a complication in the presence of chronic inflammation. Finally, the supported vessel can stiffen (structurally and materially) along circumferential and axial directions, which could have implications on overall hemodynamics and thus subsequent vascular remodeling. The proposed framework can provide valuable insights into vascular adaptation in the presence of external support, accelerate rational design, and aid translation of this emerging approach.

Spontaneous reversal of stenosis in tissue-engineered vascular grafts.

We developed a tissue-engineered vascular graft (TEVG) for use in children and present results of a U.S. Food and Drug Administration (FDA)-approved clinical trial evaluating this graft in patients with single-ventricle cardiac anomalies. The TEVG was used as a Fontan conduit to connect the inferior vena cava and pulmonary artery, but a high incidence of graft narrowing manifested within the first 6 months, which was treated successfully with angioplasty. To elucidate mechanisms underlying this early stenosis, we used a data-informed, computational model to perform in silico parametric studies of TEVG development. The simulations predicted early stenosis as observed in our clinical trial but suggested further that such narrowing could reverse spontaneously through an inflammation-driven, mechano-mediated mechanism. We tested this unexpected, model-generated hypothesis by implanting TEVGs in an ovine inferior vena cava interposition graft model, which confirmed the prediction that TEVG stenosis resolved spontaneously and was typically well tolerated. These findings have important implications for our translational research because they suggest that angioplasty may be safely avoided in patients with asymptomatic early stenosis, although there will remain a need for appropriate medical monitoring. The simulations further predicted that the degree of reversible narrowing can be mitigated by altering the scaffold design to attenuate early inflammation and increase mechano-sensing by the synthetic cells, thus suggesting a new paradigm for optimizing next-generation TEVGs. We submit that there is considerable translational advantage to combined computational-experimental studies when designing cutting-edge technologies and their clinical management.

A computational bio-chemo-mechanical model of in vivo tissue-engineered vascular graft development.

Stenosis is the primary complication of current tissue-engineered vascular grafts used in pediatric congenital cardiac surgery. Murine models provide considerable insight into the possible mechanisms underlying this situation, but they are not efficient for identifying optimal changes in scaffold design or therapeutic strategies to prevent narrowing. In contrast, computational modeling promises to enable time- and cost-efficient examinations of factors leading to narrowing. Whereas past models have been limited by their phenomenological basis, we present a new mechanistic model that integrates molecular- and cellular-driven immuno- and mechano-mediated contributions to in vivo neotissue development within implanted polymeric scaffolds. Model parameters are inferred directly from in vivo measurements for an inferior vena cava interposition graft model in the mouse that are augmented by data from the literature. By complementing Bayesian estimation with identifiability analysis and simplex optimization, we found optimal parameter values that match model outputs with experimental targets and quantify variability due to measurement uncertainty. Utility is illustrated by parametrically exploring possible graft narrowing as a function of scaffold pore size, macrophage activity, and the immunomodulatory cytokine transforming growth factor beta 1 (TGF-ß1). The model captures salient temporal profiles of infiltrating immune and synthetic cells and associated secretion of cytokines, proteases, and matrix constituents throughout neovessel evolution, and parametric studies suggest that modulating scaffold immunogenicity with early immunomodulatory therapies may reduce graft narrowing without compromising compliance.

Differential outcomes of venous and arterial tissue engineered vascular grafts highlight the importance of coupling long-term implantation studies with computational modeling.

Electrospinning is commonly used to generate polymeric scaffolds for tissue engineering. Using this approach, we developed a small-diameter tissue engineered vascular graft (TEVG) composed of poly-ε-caprolactone-co-l-lactic acid (PCLA) fibers and longitudinally assessed its performance within both the venous and arterial circulations of immunodeficient (SCID/bg) mice. Based on in vitro analysis demonstrating complete loss of graft strength by 12 weeks, we evaluated neovessel formation in vivo over 6-, 12- and 24-week periods. Mid-term observations indicated physiologic graft function, characterized by 100% patency and luminal matching with adjoining native vessel in both the venous and arterial circulations. An active and robust remodeling process was characterized by a confluent endothelial cell monolayer, macrophage infiltrate, and extracellular matrix deposition and remodeling. Long-term follow-up of venous TEVGs at 24 weeks revealed viable neovessel formation beyond graft degradation when implanted in this high flow, low-pressure environment. Arterial TEVGs experienced catastrophic graft failure due to aneurysmal dilatation and rupture after 14 weeks. Scaffold parameters such as porosity, fiber diameter, and degradation rate informed a previously described computational model of vascular growth and remodeling, and simulations predicted the gross differential performance of the venous and arterial TEVGs over the 24-week time course. Taken together, these results highlight the requirement for in vivo implantation studies to extend past the critical time period of polymer degradation, the importance of differential neotissue deposition relative to the mechanical (pressure) environment, and further support the utility of predictive modeling in the design, use, and evaluation of TEVGs in vivo. STATEMENT OF SIGNIFICANCE: Herein, we apply a biodegradable electrospun vascular graft to the arterial and venous circulations of the mouse and follow recipients beyond the point of polymer degradation. While venous implants formed viable neovessels, arterial grafts experienced catastrophic rupture due to aneurysmal dilation. We then inform a previously developed computational model of tissue engineered vascular graft growth and remodeling with parameters specific to the electrospun scaffolds utilized in this study. Remarkably, model simulations predict the differential performance of the venous and arterial constructs over 24 weeks. We conclude that computational simulations should inform the rational selection of scaffold parameters to fabricate tissue engineered vascular grafts that must be followed in vivo over time courses extending beyond polymer degradation.