A mechanobiologically equilibrated constrained mixture model for growth and remodeling of soft tissues

[EN] Growth and remodeling of soft tissues is a dynamic process and several theoretical frameworks have been developed to analyze the time-dependent, mechanobiological and/or biomechanical responses of these tissues to changes in external loads. Importantly, general processes can often be conveniently separated into truly non-steady contributions and steady-state ones. Depending on characteristic times over which the external loads are applied, time-dependent models can sometimes be specialized to respective time-independent formulations that simplify the mathematical treatment without compromising the goodness of the particularized solutions. Very few studies have analyzed the long-term, steady-state responses of soft tissue growth and remodeling following a direct approach. Here, we derive a mechanobiologically equilibrated formulation that arises from a general constrained mixture model. We see that integral-type evolution equations that characterize these general models can be written in terms of an equivalent set of time-independent, nonlinear algebraic equations that can be solved efficiently to yield long-term outcomes of growth and remodeling processes in response to sustained external stimuli. We discuss the mathematical conditions, in terms of orders of magnitude, that yield the particularized equations and illustrate results numerically for general arterial mechano-adaptations.Universidad Politecnica de Madrid; Ministerio de Educacion, Cultura y Deporte of Spain, Grant/Award Number: CAS17/00068; Ministerio de Economia y Competitividad of Spain, Grant/Award Number: DPI2015-69801-R; National Institutes of Health, Grant/Award Numbers: R01HL086418, R01HL105297, R01HL128602, U01HL116323Latorre, M.; Humphrey, JD. (2018). A mechanobiologically equilibrated constrained mixture model for growth and remodeling of soft tissues. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 98(12):2048-2071. https://doi.org/10.1002/zamm.20170030220482071981

Modeling mechano-driven and immuno-mediated aortic maladaptation in hypertension

[EN] Uncontrolled hypertension is a primary risk factor for diverse cardiovascular diseases and thus remains responsible for significant morbidity and mortality. Hypertension leads to marked changes in the composition, structure, properties, and function of central arteries; hence, there has long been interest in quantifying the associated wall mechanics. Indeed, over the past 20 years there has been increasing interest in formulating mathematical models of the evolving geometry and biomechanical behavior of central arteries that occur during hypertension. In this paper, we introduce a new mathematical model of growth (changes in mass) and remodeling (changes in microstructure) of the aortic wall for an animal model of induced hypertension that exhibits both mechano-driven and immuno-mediated matrix turnover. In particular, we present a bilayered model of the aortic wall to account for differences in medial versus adventitial growth and remodeling and we include mechanical stress and inflammatory cell density as determinants of matrix turnover. Using this approach, we can capture results from a recent report of adventitial fibrosis that resulted in marked aortic maladaptation in hypertension. We submit that this model can also be used to identify novel hypotheses to guide future experimentation.This work was supported, in part, by grants from the US NIH: R01 HL105297 (to C.A. Figueroa and J.D. Humphrey), U01 HL116323 (to J.D. Humphrey and G.E. Karniadakis), R01 HL128602 (to J.D. Humphrey, C.K. Breuer, and Y. Wang), P01 HL134605 (to G. Tellides and J.D. Humphrey via a PPG Award to D. Rifkin, NYU), and R03 EB021430 (to J.D. Humphrey); from the Ministerio de Educacion, Cultura y Deporte of Spain: CAS17/00068 (to M. Latorre); and from Universidad Politecnica de Madrid: 'Ayudas al personal docente e investigador para estancias breves en el extranjero 2017' (to M. Latorre). Additional support was given to M. Latorre by grant DPI2015-69801-R from the Direccion General de Proyectos de Investigacion, Ministerio de Economia y Competitividad of Spain (to F.J. Montans and J.M. Benitez). ML gratefully acknowledges the support given by the Department of Biomedical Engineering, Yale University, during his postdoctoral stayLatorre, M.; Humphrey, JD. (2018). Modeling mechano-driven and immuno-mediated aortic maladaptation in hypertension. Biomechanics and Modeling in Mechanobiology. 17(5):1497-1511. https://doi.org/10.1007/s10237-018-1041-81497151117

Fast, rate-independent, finite element implementation of a 3D constrained mixture model of soft tissue growth and remodeling

[EN] Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.This work was supported, in part, by grants from the NIH, USA (R01 HL128602, P01 HL134605, U01 HL142518) and DoD, USA (W81 XWH1810518)Latorre, M.; Humphrey, JD. (2020). Fast, rate-independent, finite element implementation of a 3D constrained mixture model of soft tissue growth and remodeling. Computer Methods in Applied Mechanics and Engineering. 368:1-33. https://doi.org/10.1016/j.cma.2020.11315613336

Mechanobiological stability of biological soft tissues

[EN] Like all other materials, biological soft tissues are subject to general laws of physics, including those governing mechanical equilibrium and stability. In addition, however, these tissues are able to respond actively to changes in their mechanical and chemical environment. There is, therefore, a pressing need to understand such processes theoretically. In this paper, we present a new rate-based constrained mixture formulation suitable for studying mechanobiological equilibrium and stability of soft tissues exposed to transient or sustained changes in material composition or applied loading. These concepts are illustrated for canonical problems in arterial mechanics, which distinguish possible stable versus unstable mechanobiological responses. Such analyses promise to yield insight into biological processes that govern both health and disease progression.This work was supported, in part, by grants from the US NIH, namely, R01 HL105297 (to C.A. Figueroa and J.D. Humphrey), R01 HL128602 (to J.D. Humphrey, C.K. Breuer, and Y. Wang), P01 HL134605 (to G. Tellides and J.D. Humphrey via a PPG to D. Rifkin), and U01 HL142518 (to J.D. Humphrey and G.E. Karniadakis)Latorre, M.; Humphrey, JD. (2019). Mechanobiological stability of biological soft tissues. Journal of the Mechanics and Physics of Solids. 125:298-325. https://doi.org/10.1016/j.jmps.2018.12.01329832512

Data Workflow in Large Scale Simulations of Blood Flow in Aneurysms

Aneurysms are responsibile for significant morbidity and mortality, and there is a need for an increased understanding of all the aspects of the natural history of these lesions. We are currently working to extend our analyses with the goal of creating models of aneurysmal progression that are able to predict rupture risk through the description of the evolving geometry, structure, properties, and loads. Realization of patient specific models of the blood circulation necessitates a complex computationally and data intensive procedure that starts from the collection of medical images in a clinical setting and encompasses several stages of data processing on (and transfer to and from) specialized hardware, which include high-performance and visualization clusters as well as consumer workstations and local drives for final storage

From Transcript to Tissue: Multiscale Modeling from Cell Signaling to Matrix Remodeling

[EN] Tissue-level biomechanical properties and function derive from underlying cell signaling, which regulates mass deposition, organization, and removal. Here, we couple two existing modeling frameworks to capture associated multiscale interactions¿one for vessel-level growth and remodeling and one for cell-level signaling¿and illustrate utility by simulating aortic remodeling. At the vessel level, we employ a constrained mixture model describing turnover of individual wall constituents (elastin, intramural cells, and collagen), which has proven useful in predicting diverse adaptations as well as disease progression using phenomenological constitutive relations. Nevertheless, we now seek an improved mechanistic understanding of these processes; we replace phenomenological relations in the mixture model with a logic-based signaling model, which yields a system of ordinary differential equations predicting changes in collagen synthesis, matrix metalloproteinases, and cell proliferation in response to altered intramural stress, wall shear stress, and exogenous angiotensin II. This coupled approach promises improved understanding of the role of cell signaling in achieving tissue homeostasis and allows us to model feedback between vessel mechanics and cell signaling. We verify our model predictions against data from the hypertensive murine infrarenal abdominal aorta as well as results from validated phenomenological models, and consider effects of noisy signaling and heterogeneous cell populations.This work was supported by Grants from the US NIH (R01 HL105297, P01 HL134605, R01 HL139796, U01 HL142518, R01 HL146723)Irons, L.; Latorre, M.; Humphrey, JD. (2021). From Transcript to Tissue: Multiscale Modeling from Cell Signaling to Matrix Remodeling. Annals of Biomedical Engineering. 48(7):1701-1715. https://doi.org/10.1007/s10439-020-02713-81701171548

Complementary roles of mechanotransduction and inflammation in vascular homeostasis

Arteries are exposed to relentless pulsatile haemodynamic loads, but via mechanical homeostasis they tend to maintain near optimal structure, properties and function over long periods in maturity in health. Numerous insults can compromise such homeostatic tendencies, however, resulting in maladaptations or disease. Chronic inflammation can be counted among the detrimental insults experienced by arteries, yet inflammation can also play important homeostatic roles. In this paper, we present a new theoretical model of complementary mechanobiological and immunobiological control of vascular geometry and composition, and thus properties and function. We motivate and illustrate the model using data for aortic remodelling in a common mouse model of induced hypertension. Predictions match the available data well, noting a need for increased data for further parameter refinement. The overall approach and conclusions are general, however, and help to unify two previously disparate literatures, thus leading to deeper insight into the separate and overlapping roles of mechanobiology and immunobiology in vascular health and disease

Computational modeling predicts immuno-mechanical mechanisms of maladaptive aortic remodeling in hypertension

[EN] Uncontrolled hypertension is a major risk factor for myriad cardiovascular diseases. Among its many effects, hypertension increases central artery stiffness which in turn is both an initiator and indicator of disease. Despite extensive clinical, animal, and basic science studies, the biochemomechanical mechanisms by which hypertension drives aortic stiffening remain unclear. In this paper, we show that a new computational model of aortic growth and remodeling can capture differential effects of induced hypertension on the thoracic and abdominal aorta in a common mouse model of disease. Because the simulations treat the aortic wall as a constrained mixture of different constituents having different material properties and rates of turnover, one can gain increased insight into underlying constituent-level mechanisms of aortic remodeling. Model results suggest that the aorta can mechano-adapt locally to blood pressure elevation in the absence of marked inflammation, but large increases in inflammation drive a persistent maladaptive phenotype characterized primarily by adventitial fibrosis. Moreover, this fibrosis appears to occur via a marked increase in the rate of deposition of collagen having different material properties in the absence of a compensatory increase in the rate of matrix degradation. Controlling inflammation thus appears to be key to reducing fibrosis, but therapeutic strategies should not compromise the proteolytic activity of the wall that is essential to mechanical homeostasis.This work was supported, in part, by grants from the US NIH: R01 HL105297, U01 HL116323, U01 HL142518, and P01 HL134605Latorre, M.; Bersi, MR.; Humphrey, JD. (2019). Computational modeling predicts immuno-mechanical mechanisms of maladaptive aortic remodeling in hypertension. International Journal of Engineering Science. 141:35-46. https://doi.org/10.1016/j.ijengsci.2019.05.014354614

Međudjelovanje intraluminalnog tromba i aneurizmatične stijenke aorte

Aneurizma abdominalne aorte (AAA) je nepovratno, lokalizirano proširenje infrarenalne aorte koje u veüini (oko 80%) sluþajeva sadrži intraluminalni tromb (ILT). Ovdje predstavljen je prvi model rasta i restrukturiranja aneurizme abdominalne aorte koji uzima u obzir sveobuhvatni utjecaj intraluminalnog tromba na stijenku aorte: kako s mehaniþkog gledišta (utjecaj tromba na raspodjelu naprezanja unutar stijenke aorte, a time i na proizvodnju i uklanjanje strukturalno bitnih dijelova stijenke aorte), tako i sa biokemijskog (utjecaj proteolitiþki aktivnog intraluminalnog tromba na poveüanje razgradnje komponenti stijenke krvne žile), u nadi da üe to pomoüi boljem razumijevanju patofiziologije aneurizmi. Model üe biti ograniþen na osnosimetriþnu cilindriþnu geometriju