An efficient framework for optimization and parameter sensitivity analysis in arterial growth and remodeling computations

Mechanical, structural, and morphological differences in the iliac arteries

Iliac arteries play a crucial role in peripheral blood circulation. They are susceptible to various diseases, including aneurysms and atherosclerosis. Structure, material properties, and biomechanical forces acting on different regions of the iliac vasculature may contribute to the localization and progression of these pathologies. We examined 33 arterial specimens from common iliac (CI), external iliac (EI), and internal iliac (II) arteries obtained from 11 human donors (62 ± 12 years). We conducted morphometric, mechanical, and structural analyses using planar biaxial tests, constitutive modeling, and bi-directional histology on transverse and axial sections. The iliac arteries exhibited increased tortuosity and varying disease distribution with age. CI and II arteries displayed non-uniform age-related disease progression around their circumference, while EI remained healthy even in older individuals. Trends in load-free and stress-free thickness varied along the iliac vasculature. Longitudinally, EI exhibited the highest compliance compared to other iliac vessels. In contrast, CI was stiffest longitudinally, and EI was the stiffest circumferentially. Material parameters for all iliac vessels are reported for four common constitutive relations. Elastin near the internal elastic lamina displayed greater waviness in EI and II compared to CI. Also, EI had the least glycosaminoglycans (GAGs) and the highest elastin content. Our findings highlight variations in the morphological, mechanical, and structural properties of iliac arteries along their length. This data can inform vascular disease development and computational studies, and guide the development of biomimetic repair materials and devices tailored to specific iliac locations, improving vascular repair strategies.

Mechanism Analysis of Vascular Calcification Based on Fluid Dynamics

Vascular calcification is the abnormal deposition of calcium phosphate complexes in blood vessels, which is regarded as the pathological basis of multiple cardiovascular diseases. The flowing blood exerts a frictional force called shear stress on the vascular wall. Blood vessels have different hydrodynamic properties due to discrepancies in geometric and mechanical properties. The disturbance of the blood flow in the bending area and the branch point of the arterial tree produces a shear stress lower than the physiological magnitude of the laminar shear stress, which can induce the occurrence of vascular calcification. Endothelial cells sense the fluid dynamics of blood and transmit electrical and chemical signals to the full-thickness of blood vessels. Through crosstalk with endothelial cells, smooth muscle cells trigger osteogenic transformation, involved in mediating vascular intima and media calcification. In addition, based on the detection of fluid dynamics parameters, emerging imaging technologies such as 4D Flow MRI and computational fluid dynamics have greatly improved the early diagnosis ability of cardiovascular diseases, showing extremely high clinical application prospects.

Hybrid Discrete-Continuum Multiscale Model of Tissue Growth and Remodeling

Tissue growth and remodeling (G&R) is often central to disease etiology and progression, so understanding G&R is essential for understanding disease and developing effective therapies. While the state-of-the-art in this regard is animal and cellular models, recent advances in computational tools offer another avenue to investigate G&R. A major challenge for computational models is bridging from the cellular scale (at which changes are actually occurring) to the macroscopic, geometric-scale (at which physiological consequences arise). Thus, many computational models simplify one scale or another in the name of computational tractability. In this work, we develop a discrete-continuum modeling scheme for analyzing G&R, in which we apply changes directly to the discrete cell and extracellular matrix (ECM) architecture and pass those changes up to a finite-element macroscale geometry. We demonstrate the use of the model in three case-study scenarios: the media of a thick-walled artery, and the media and adventitia of a thick-walled artery, and chronic dissection of an arterial wall. We analyze each case in terms of the new and insightful data that can be gathered from this technique, and we compare our results from this model to several others. STATEMENT OF SIGNIFICANCE: This work is significant in that it provides a framework for combining discrete, microstructural- and cellular-scale models to the growth and remodeling of large tissue structures (such as the aorta). It is a significant advance in that it couples the microscopic remodeling with an existing macroscopic finite element model, making it relatively easy to use for a wide range of conceptual models. It has the potential to improve understanding of many growth and remodeling processes, such as organ formation during development and aneurysm formation, growth, and rupture.

Constrained Mixture Models of Soft Tissue Growth and Remodeling - Twenty Years After

Soft biological tissues compromise diverse cell types and extracellular matrix constituents, each of which can possess individual natural configurations, material properties, and rates of turnover. For this reason, mixture-based models of growth (changes in mass) and remodeling (change in microstructure) are well-suited for studying tissue adaptations, disease progression, and responses to injury or clinical intervention. Such approaches also can be used to design improved tissue engineered constructs to repair, replace, or regenerate tissues. Focusing on blood vessels as archetypes of soft tissues, this paper reviews a constrained mixture theory introduced twenty years ago and explores its usage since by contrasting simulations of diverse vascular conditions. The discussion is framed within the concept of mechanical homeostasis, with consideration of solid-fluid interactions, inflammation, and cell signaling highlighting both past accomplishments and future opportunities as we seek to understand better the evolving composition, geometry, and material behaviors of soft tissues under complex conditions.

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-β1). 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.

Machine learning approaches to surrogate multifidelity Growth and Remodeling models for efficient abdominal aortic aneurysmal applications

Computational Growth and Remodeling (G&R) models have been widely used to capture the pathological development of arterial diseases and have shown promise for aiding clinical diagnosis, prognosis prediction, and staging classification. However, due to the high complexity of the arterial adaptation mechanism, high-fidelity arterial G&R simulation usually takes hours or even days, which hinders its application in clinical practice. To remedy this problem, we develop a computationally efficient arterial G&R simulation framework that comprehensively combines the physics-based G&R simulations and data-driven machine learning approaches. The proposed framework greatly enhances the computational efficiency of arterial G&R simulations, thereby enabling more time-consuming arterial applications, including personalized parameter estimation and arterial disease progression prediction. In particular, we achieve significant computational cost reduction mainly through two methods: (1) constructing a Multifidelity Surrogate (MFS) to approximate multifidelity G&R simulations by using a cokriging approach and (2) developing a novel iterative optimization algorithm for personalized parameter estimation. The proposed framework is demonstrated by estimating G&R model parameters and predicting individual aneurysm growth using follow-up CT images of Abdominal Aortic Aneurysms (AAAs) from 21 patients. Results show that the personalized parameters are satisfactorily estimated and the growth of AAAs is predicted within the clinically relevant time frame, i.e., less than 2 h, without a loss of accuracy.

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.

Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression

A key feature of living tissues is their capacity to remodel and grow in response to environmental cues. Within continuum mechanics, this process can be captured with the multiplicative split of the deformation gradient into growth and elastic contributions. The mechanical and biological response during tissue adaptation is characterized by inherent variability. Accounting for this uncertainty is critical to better understand tissue mechanobiology, and, moreover, it is of practical importance if we aim to develop predictive models for clinical use. However, the current gold standard in computational models of growth and remodeling remains the use of deterministic finite element (FE) simulations. Here we focus on tissue expansion, a popular technique in which skin is stretched by a balloon-like device inducing its growth. We construct FE models of tissue expansion with various levels of detail, and show that a sufficiently broad set of FE simulations from these models can be used to train an accurate and efficient multi-fidelity Gaussian process (GP) surrogate. The approach is not limited to simulation data, rather, it can fuse different kinds of data, including from experiments. The main appeal of the framework relies on the common experience that highly detailed models (or experiments) are more accurate but also more costly, while simpler models (or experiments) can be easily evaluated but are bound to have some error. In these situations, doing uncertainty analysis tasks with the high fidelity models alone is not feasible and, conversely, relying solely on low fidelity approximations is also undesirable. We show that a multi-fidelity GP outperforms the high fidelity GP and low fidelity GP when tested against the most detailed FE model. In turn, having trained the multi-fidelity GP model, we showcase the propagation of uncertainty from the mechanical and biological response parameters to the spatio-temporal growth outcomes. We expect that the methods and applications in this paper will enable future research in parameter calibration under uncertainty and uncertainty propagation in real clinical scenarios involving tissue growth and remodeling.

Optimization of Tissue-Engineered Vascular Graft Design Using Computational Modeling

Tissue-engineered vascular grafts hold great promise in many clinical applications, especially in pediatrics wherein growth potential is critical. A continuing challenge, however, is identification of optimal scaffold parameters for promoting favorable neovessel development. In particular, given the countless design parameters available, including those related to polymeric microstructure, material behavior, and degradation kinetics, the number of possible scaffold designs is almost limitless. Advances in computationally modeling the growth and remodeling of native blood vessels suggest that similar simulations could help reduce the search space for candidate scaffold designs in tissue engineering. In this study, we meld a computational model of in vivo neovessel formation with a surrogate management framework to identify optimal scaffold designs for use in the extracardiac Fontan circulation while comparing the utility of different objective functions. We show that evolving luminal radius and graft compliance can be matched to that of the native vein by the end of the simulation period with judicious combinations of scaffold parameters, although the inability to match these metrics at all times reveals constraints engendered by current materials. We emphasize further that there is yet a need to examine additional metrics, and combinations thereof, when seeking to optimize functionality and reduce the potential for adverse outcomes. Impact Statement Tissue-engineered vascular grafts have considerable promise for treating myriad conditions, and multiple designs are now in FDA-approved trials. Nevertheless, the search continues for the optimal design of the underlying polymeric scaffold. We present a novel melding of a computational model of vascular adaptation and a formal method of optimization that can aid in identifying optimal design parameters, with potential to save development time and costs while improving clinical outcomes.

Bayesian inference of constitutive model parameters from uncertain uniaxial experiments on murine tendons

Constitutive models for biological tissue are typically formulated as a mixture of constituents and the overall response is then assembled by superposition or compatibility. This ensures the stress response of the biological tissue to be in the range of a given constitutive relationship, guaranteeing that at least one parameter combination exists so that an experimental response can be sufficiently well captured. Another, perhaps more challenging, problem is to use constitutive models as a proxy to infer the structure/function of a biological tissue from experiments. In other words, we determine the optimal set of parameters by solving an inverse problem and use these parameters to infer the integrity of the tissue constituents. In previous studies, we focused on the mechanical stress-stretch response of the murine patellar tendon at various age and healing timepoints and solved the inverse problem using three constitutive models, i.e., the Freed-Rajagopal, Gasser-Ogden-Holzapfel and Shearer in order of increasing microstructural detail. Herein, we extend this work by adopting a Bayesian perspective on parameter estimation and implement the constitutive relations in the tulip library for uncertainty analysis, critically analyzing parameter marginals, correlations, identifiability and sensitivity. Our results show the importance of investigating the variability of parameter estimates and that results from optimization may be misleading, particularly for models with many parameters inferred from limited experimental evidence. In our study, we show that different age and healing conditions do not correspond to statistically significant separation among the Gasser-Ogden-Holzapfel and Shearer model parameters, while the phenomenological Freed-Rajagopal model is instead characterized by better indentifiability and parameter learning. Use of the complete experimental observations rather than averaged stress-stretch responses appears to positively constrain inference and results appear to be invariant with respect to the scaling of the experimental uncertainty.

Gradual loading ameliorates maladaptation in computational simulations of vein graft growth and remodelling

Vein graft failure is a prevalent problem in vascular surgeries, including bypass grafting and arteriovenous fistula procedures in which veins are subjected to severe changes in pressure and flow. Animal and clinical studies provide significant insight, but understanding the complex underlying coupled mechanisms can be advanced using computational models. Towards this end, we propose a new model of venous growth and remodelling (G&R) based on a constrained mixture theory. First, we identify constitutive relations and parameters that enable venous adaptations to moderate perturbations in haemodynamics. We then fix these relations and parameters, and subject the vein to a range of combined loads (pressure and flow), from moderate to severe, and identify plausible mechanisms of adaptation versus maladaptation. We also explore the beneficial effects of gradual increases in load on adaptation. A gradual change in flow over 3 days plus an initial step change in pressure results in fewer maladaptations compared with step changes in both flow and pressure, or even a gradual change in pressure and flow over 3 days. A gradual change in flow and pressure over 8 days also enabled a successful venous adaptation for loads as severe as the arterial loads. Optimization is used to accelerate parameter estimation and the proposed framework is general enough to provide a good starting point for parameter estimations in G&R simulations.

Potential biomechanical roles of risk factors in the evolution of thrombus-laden abdominal aortic aneurysms

Abdominal aortic aneurysms (AAAs) typically harbour an intraluminal thrombus (ILT), yet most prior computational models neglect biochemomechanical effects of thrombus on lesion evolution. We recently proposed a growth and remodelling model of thrombus-laden AAAs that introduced a number of new constitutive relations and associated model parameters. Because values of several of these parameters have yet to be elucidated by clinical data and could vary significantly from patient to patient, the aim of this study was to investigate the possible extent to which these parameters influence AAA evolution. Given that some of these parameters model potential effects of factors that influence the risk of rupture, this study also provides insight into possible roles of common risk factors on the natural history of AAAs. Despite geometrical limitations of a cylindrical domain, findings support current thought that smoking, hypertension, and female sex likely increase the risk of rupture. Although thrombus thickness is not a reliable risk factor for rupture, the model suggests that the presence of ILT may have a destabilizing effect on AAA evolution, consistent with histological findings from human samples. Finally, simulations support two hypotheses that should be tested on patient-specific geometries in the future. First, ILT is a potential source of the staccato enlargement observed in many AAAs. Second, ILT can influence rupture risk, positively or negatively, via competing biomechanical (eg, stress shielding) and biochemical (ie, proteolytic) effects. Although further computational and experimental studies are needed, the present findings highlight the importance of considering ILT when predicting aneurysmal enlargement and rupture risk.

Computational Fluid Dynamics and Additive Manufacturing to Diagnose and Treat Cardiovascular Disease

Noninvasive engineering models are now being used for diagnosing and planning the treatment of cardiovascular disease. Techniques in computational modeling and additive manufacturing have matured concurrently, and results from simulations can inform and enable the design and optimization of therapeutic devices and treatment strategies. The emerging synergy between large-scale simulations and 3D printing is having a two-fold benefit: first, 3D printing can be used to validate the complex simulations, and second, the flow models can be used to improve treatment planning for cardiovascular disease. In this review, we summarize and discuss recent methods and findings for leveraging advances in both additive manufacturing and patient-specific computational modeling, with an emphasis on new directions in these fields and remaining open questions.

Computational modeling and engineering in pediatric and congenital heart disease

PURPOSE OF REVIEW

Recent methodological advances in computational simulations are enabling increasingly realistic simulations of hemodynamics and physiology, driving increased clinical utility. We review recent developments in the use of computational simulations in pediatric and congenital heart disease, describe the clinical impact in modeling in single-ventricle patients, and provide an overview of emerging areas.

RECENT FINDINGS

Multiscale modeling combining patient-specific hemodynamics with reduced order (i.e., mathematically and computationally simplified) circulatory models has become the de-facto standard for modeling local hemodynamics and 'global' circulatory physiology. We review recent advances that have enabled faster solutions, discuss new methods (e.g., fluid structure interaction and uncertainty quantification), which lend realism both computationally and clinically to results, highlight novel computationally derived surgical methods for single-ventricle patients, and discuss areas in which modeling has begun to exert its influence including Kawasaki disease, fetal circulation, tetralogy of Fallot (and pulmonary tree), and circulatory support.

SUMMARY

Computational modeling is emerging as a crucial tool for clinical decision-making and evaluation of novel surgical methods and interventions in pediatric cardiology and beyond. Continued development of modeling methods, with an eye towards clinical needs, will enable clinical adoption in a wide range of pediatric and congenital heart diseases.

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.

A hypothesis-driven parametric study of effects of polymeric scaffold properties on tissue engineered neovessel formation

Continued advances in the tissue engineering of vascular grafts have enabled a paradigm shift from the desire to design for adequate suture retention, burst pressure and thrombo-resistance to the goal of achieving grafts having near native properties, including growth potential. Achieving this far more ambitious outcome will require the identification of optimal, not just adequate, scaffold structure and material properties. Given the myriad possible combinations of scaffold parameters, there is a need for a new strategy for reducing the experimental search space. Toward this end, we present a new modeling framework for in vivo neovessel development that allows one to begin to assess in silico the potential consequences of different combinations of scaffold structure and material properties. To restrict the number of parameters considered, we also utilize a non-dimensionalization to identify key properties of interest. Using illustrative constitutive relations for both the evolving fibrous scaffold and the neotissue that develops in response to inflammatory and mechanobiological cues, we show that this combined non-dimensionalization computational approach predicts salient aspects of neotissue development that depend directly on two key scaffold parameters, porosity and fiber diameter. We suggest, therefore, that hypothesis-driven computational models should continue to be pursued given their potential to identify preferred combinations of scaffold parameters that have the promise of improving neovessel outcome. In this way, we can begin to move beyond a purely empirical trial-and-error search for optimal combinations of parameters and instead focus our experimental resources on those combinations that are predicted to have the most promise.

Computational model of the in vivo development of a tissue engineered vein from an implanted polymeric construct

Advances in vascular tissue engineering have been tremendous over the past 15 years, yet there remains a need to optimize current constructs to achieve vessels having true growth potential. Toward this end, it has been suggested that computational models may help hasten this process by enabling time-efficient parametric studies that can reduce the experimental search space. In this paper, we present a first generation computational model for describing the in vivo development of a tissue engineered vein from an implanted polymeric scaffold. The model was motivated by our recent data on the evolution of mechanical properties and microstructural composition over 24 weeks in a mouse inferior vena cava interposition graft. It is shown that these data can be captured well by including both an early inflammatory-mediated and a subsequent mechano-mediated production of extracellular matrix. There remains a pressing need, however, for more data to inform the development of next generation models, particularly the precise transition from the inflammatory to the mechanobiological dominated production of matrix having functional capability.

Simulation based planning of surgical interventions in pediatric cardiology

Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.