Estimation of stresses in arterial tissue: from residual stresses to material parameters

In the past decades a considerable amount of literature has been published addressing the study of the mechanical behavior of arterial walls. In these works, researchers have developed constitutive models and characterized the typical ranges for the values of material parameters of vascular tissues. Moreover, the existence of residual stresses in configurations free of loads was revealed, and its impact in the general stress state of the tissue was quantified. Currently, ex-vivo experiments such as inflation-extension tests and biaxial stress tests are extensively used for the estimation of the constitutive parameters in arterial wall probes. Also, destructive experiments involving radial cutting of specimens and the separation of arterial layers are used to identify layer-specific residual deformations (and stresses). For the latter scenario, material parameters are assumed to be known. In this context, a technique for the simultaneous characterization of residual deformations and material parameters in the arterial wall is proposed. This approach is based on data tipically obtained from inflation-extension tests, assuming that the material configuration and the radial displacement of the vessel is known for different load conditions given by fixed axial stretch and internal pressure values. The characterization problem is tackled through the minimization of a cost functional that measures the mechanical disequilibrium of the known material configuration and the discrepancy between the predicted and observed displacement of the outer vessel boundary. To illustrate the feasibility of the proposed methodology a manufactured-solution example is presented.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

Estimation of stresses in arterial tissue: from residual stresses to material parameters

In the past decades a considerable amount of literature has been published addressing the study of the mechanical behavior of arterial walls. In these works, researchers have developed constitutive models and characterized the typical ranges for the values of material parameters of vascular tissues. Moreover, the existence of residual stresses in configurations free of loads was revealed, and its impact in the general stress state of the tissue was quantified. Currently, ex-vivo experiments such as inflation-extension tests and biaxial stress tests are extensively used for the estimation of the constitutive parameters in arterial wall probes. Also, destructive experiments involving radial cutting of specimens and the separation of arterial layers are used to identify layer-specific residual deformations (and stresses). For the latter scenario, material parameters are assumed to be known. In this context, a technique for the simultaneous characterization of residual deformations and material parameters in the arterial wall is proposed. This approach is based on data tipically obtained from inflation-extension tests, assuming that the material configuration and the radial displacement of the vessel is known for different load conditions given by fixed axial stretch and internal pressure values. The characterization problem is tackled through the minimization of a cost functional that measures the mechanical disequilibrium of the known material configuration and the discrepancy between the predicted and observed displacement of the outer vessel boundary. To illustrate the feasibility of the proposed methodology a manufactured-solution example is presented.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

Estimation of stresses in arterial tissue: from residual stresses to material parameters

In the past decades a considerable amount of literature has been published addressing the study of the mechanical behavior of arterial walls. In these works, researchers have developed constitutive models and characterized the typical ranges for the values of material parameters of vascular tissues. Moreover, the existence of residual stresses in configurations free of loads was revealed, and its impact in the general stress state of the tissue was quantified. Currently, ex-vivo experiments such as inflation-extension tests and biaxial stress tests are extensively used for the estimation of the constitutive parameters in arterial wall probes. Also, destructive experiments involving radial cutting of specimens and the separation of arterial layers are used to identify layer-specific residual deformations (and stresses). For the latter scenario, material parameters are assumed to be known. In this context, a technique for the simultaneous characterization of residual deformations and material parameters in the arterial wall is proposed. This approach is based on data tipically obtained from inflation-extension tests, assuming that the material configuration and the radial displacement of the vessel is known for different load conditions given by fixed axial stretch and internal pressure values. The characterization problem is tackled through the minimization of a cost functional that measures the mechanical disequilibrium of the known material configuration and the discrepancy between the predicted and observed displacement of the outer vessel boundary. To illustrate the feasibility of the proposed methodology a manufactured-solution example is presented.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

A Cellular Automata-Based Mathematical Model for Thymocyte Development

Intrathymic T cell development is an important process necessary for the normal formation of cell-mediated immune responses. Importantly, such a process depends on interactions of developing thymocytes with cellular and extracellular elements of the thymic microenvironment. Additionally, it includes a series of oriented and tunely regulated migration events, ultimately allowing mature cells to cross endothelial barriers and leave the organ. Herein we built a cellular automata-based mathematical model for thymocyte migration and development. The rules comprised in this model take into account the main stages of thymocyte development, two-dimensional sections of the normal thymic microenvironmental network, as well as the chemokines involved in intrathymic cell migration. Parameters of our computer simulations with further adjusted to results derived from previous experimental data using sub-lethally irradiated mice, in which thymus recovery can be evaluated. The model fitted with the increasing numbers of each CD4/CD8-defined thymocyte subset. It was further validated since it fitted with the times of permanence experimentally ascertained in each CD4/CD8-defined differentiation stage. Importantly, correlations using the whole mean volume of young normal adult mice revealed that the numbers of cells generated in silico with the mathematical model fall within the range of total thymocyte numbers seen in these animals. Furthermore, simulations made with a human thymic epithelial network using the same mathematical model generated similar profiles for temporal evolution of thymocyte developmental stages. Lastly, we provided in silico evidence that the thymus architecture is important in the thymocyte development, since changes in the epithelial network result in different theoretical profiles for T cell development/migration. This model likely can be used to predict thymocyte evolution following therapeutic strategies designed for recovery of the thymus in diseases coursing with thymus involution, such as some primary immunodeficiencies, acute infections, and malnutrition

An anatomically detailed arterial-venous network model. Cerebral and coronary circulation

In recent years, several works have addressed the problem of modeling blood flow phenomena in veins, as a response to increasing interest in modeling pathological conditions occurring in the venous network and their connection with the rest of the circulatory system. In this context, one-dimensional models have proven to be extremely efficient in delivering predictions in agreement with in-vivo observations. Pursuing the increase of anatomical accuracy and its connection to physiological principles in haemodynamics simulations, the main aim of this work is to describe a novel closed-loop Anatomically-Detailed Arterial-Venous Network (ADAVN) model. An extremely refined description of the arterial network consisting of 2,185 arterial vessels is coupled to a novel venous network featuring high level of anatomical detail in cerebral and coronary vascular territories. The entire venous network comprises 189 venous vessels, 79 of which drain the brain and 14 are coronary veins. Fundamental physiological mechanisms accounting for the interaction of brain blood flow with the cerebro-spinal fluid and of the coronary circulation with the cardiac mechanics are considered. Several issues related to the coupling of arterial and venous vessels at the microcirculation level are discussed in detail. Numerical simulations are compared to patient records published in the literature to show the descriptive capabilities of the model. Furthermore, a local sensitivity analysis is performed, evidencing the high impact of the venous circulation on main cardiovascular variables

Mechanical Characterization of the Vessel Wall by Data Assimilation of Intravascular Ultrasound Studies

Atherosclerotic plaque rupture and erosion are the most important mechanisms underlying the sudden plaque growth, responsible for acute coronary syndromes and even fatal cardiac events. Advances in the understanding of the culprit plaque structure and composition are already reported in the literature, however, there is still much work to be done toward in-vivo plaque visualization and mechanical characterization to assess plaque stability, patient risk, diagnosis and treatment prognosis. In this work, a methodology for the mechanical characterization of the vessel wall plaque and tissues is proposed based on the combination of intravascular ultrasound (IVUS) imaging processing, data assimilation and continuum mechanics models within a high performance computing (HPC) environment. Initially, the IVUS study is gated to obtain volumes of image sequences corresponding to the vessel of interest at different cardiac phases. These sequences are registered against the sequence of the end-diastolic phase to remove transversal and longitudinal rigid motions prescribed by the moving environment due to the heartbeat. Then, optical flow between the image sequences is computed to obtain the displacement fields of the vessel (each associated to a certain pressure level). The obtained displacement fields are regarded as observations within a data assimilation paradigm, which aims to estimate the material parameters of the tissues within the vessel wall. Specifically, a reduced order unscented Kalman filter is employed, endowed with a forward operator which amounts to address the solution of a hyperelastic solid mechanics model in the finite strain regime taking into account the axially stretched state of the vessel, as well as the effect of internal and external forces acting on the arterial wall. Due to the computational burden, a HPC approach is mandatory. Hence, the data assimilation and computational solid mechanics computations are parallelized at three levels: (i) a Kalman filter level; (ii) a cardiac phase level; and (iii) a mesh partitioning level. To illustrate the capabilities of this novel methodology toward the in-vivo analysis of patient-specific vessel constituents, mechanical material parameters are estimated using in-silico and in-vivo data retrieved from IVUS studies. Limitations and potentials of this approach are exposed and discussed.Fil: Maso Talou, Gonzalo Daniel. Laboratorio Nacional de Computacao Cientifica; BrasilFil: Blanco, Pablo Javier. Laboratorio Nacional de Computacao Cientifica; BrasilFil: Ares, Gonzalo Damián. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Departamento de Mecanica. Grupo de Ingeniería Asistida Por Computador; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Guedes Bezerra, Cristiano. Heart Institute (Incor); BrasilFil: Lemos, Pedro A.. Heart Institute (Incor); BrasilFil: Feijóo, Raúl Antonino. Laboratorio Nacional de Computacao Cientifica; Brasi

Modelado multiescala de materiales: análisis de condiciones de borde en micro-estructuras con poros y/o inclusiones que alcanzan la frontera del RVE

En este trabajo se aborda el modelado constitutivo de materiales heterogéneos mediante el uso de técnicas multiescalas basadas en el concepto de RVE (Elemento de Volumen Representativo) y empleando el Método de la Potencia Virtual Multiescala (MPVM, ver Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models, P.J. Blanco et. al, Arch. of Comp. Met. in Eng., 23(2), pp. 191-253, (2016)). La construcción y definición del dominio micro-estructural, considerando distribuciones geométricamente representativas de heterogeneidades, resulta ser un paso de fundamental importancia en este tipo de aproximaciones. Las restricciones que garantizan admisibilidad cinemática entre las escalas macro-micro, en términos de condiciones de contorno sobre la frontera del RVE, juegan en este sentido un rol crucial. Este hecho se pone de manifiesto de forma más notoria aún si el modelado incluye comportamientos constitutivos no lineales que inducen modos de deformaciones localizados, como por ejemplo plasticidad y daño. El objeto del estudio presente es analizar el efecto de las condiciones de borde convencionales (típicamente el modelo periódico y el denominado de mínima restricción) en la respuesta constitutiva homogeneizada del material. Se hace especial énfasis en diseños de micro-celdas con poros y/o inclusiones que alcanzan la frontera del RVE, situación extremadamente común en materiales compuestos con distribución aleatoria de heterogeneidades (como por ejemplo aleaciones metálicas u hormigones). También se analizan y fundamentan condiciones de borde intermediarias a las mencionadas anteriormente, las cuales se proponen como aporte original de este trabajo.Publicado en: Mecánica Computacional vol. XXXV, no. 24Facultad de Ingenierí

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations