A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles

The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored

Methods and Algorithms for Cardiovascular Hemodynamics with Applications to Noninvasive Monitoring of Proximal Blood Pressure and Cardiac Output Using Pulse Transit Time

Advanced health monitoring and diagnostics technology are essential to reduce the unrivaled number of human fatalities due to cardiovascular diseases (CVDs). Traditionally, gold standard CVD diagnosis involves direct measurements of the aortic blood pressure (central BP) and flow by cardiac catheterization, which can lead to certain complications. Understanding the inner-workings of the cardiovascular system through patient-specific cardiovascular modeling can provide new means to CVD diagnosis and relating treatment. BP and flow waves propagate back and forth from heart to the peripheral sites, while carrying information about the properties of the arterial network. Their speed of propagation, magnitude and shape are directly related to the properties of blood and arterial vasculature. Obtaining functional and anatomical information about the arteries through clinical measurements and medical imaging, the digital twin of the arterial network of interest can be generated. The latter enables prediction of BP and flow waveforms along this network. Point of care devices (POCDs) can now conduct in-home measurements of cardiovascular signals, such as electrocardiogram (ECG), photoplethysmogram (PPG), ballistocardiogram (BCG) and even direct measurements of the pulse transit time (PTT). This vital information provides new opportunities for designing accurate patient-specific computational models eliminating, in many cases, the need for invasive measurements. One of the main efforts in this area is the development of noninvasive cuffless BP measurement using patient’s PTT. Commonly, BP prediction is carried out with regression models assuming direct or indirect relationships between BP and PTT. However, accounting for the nonlinear FSI mechanics of the arteries and the cardiac output is indispensable. In this work, a monotonicity-preserving quasi-1D FSI modeling platform is developed, capable of capturing the hyper-viscoelastic vessel wall deformation and nonlinear blood flow dynamics in arbitrary arterial networks. Special attention has been dedicated to the correct modeling of discontinuities, such as mechanical properties mismatch associated with the stent insertion, and the intertwining dynamics of multiscale 3D and 1D models when simulating the arterial network with an aneurysm. The developed platform, titled Cardiovascular Flow ANalysis (CardioFAN), is validated against well-known numerical, in vitro and in vivo arterial network measurements showing average prediction errors of 5.2%, 2.8% and 1.6% for blood flow, lumen cross-sectional area, and BP, respectively. CardioFAN evaluates the local PTT, which enables patient-specific calibration and its application to input signal reconstruction. The calibration is performed based on BP, stroke volume and PTT measured by POCDs. The calibrated model is then used in conjunction with noninvasively measured peripheral BP and PTT to inversely restore the cardiac output, proximal BP and aortic deformation in human subjects. The reconstructed results show average RMSEs of 1.4% for systolic and 4.6% for diastolic BPs, as well as 8.4% for cardiac output. This work is the first successful attempt in implementation of deterministic cardiovascular models as add-ons to wearable and smart POCD results, enabling continuous noninvasive monitoring of cardiovascular health to facilitate CVD diagnosis

Characterization of mechanical properties of biological tissue – Application to the FEM analysis of the urinary bladder

An approach is presented for studying the mechanical behavior of soft biological tissue using the finite‐element method and a general constitutive model. The overall computational approach is used for the analysis of the mechanical behavior of the urinary bladder. Bladder tissue is modeled as a composite material formed by a soft matrix reinforced with preferentially oriented fibers. A procedure for identifying the mechanical properties of the main constituents of the bladder tissue by an inverse method is detailed. The mechanical parameters are used for the numerical simulation of the mechanical behavior of the bladder during filling within the finite‐element method

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R2 >.95) with experimental blood pressure data.Fil: Ventre, Jeanne. Centre National de la Recherche Scientifique; FranciaFil: Politi, Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fernández, Juan M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Ghigo, Arthur R.. Université de Toulouse; FranciaFil: Gaudric, Julien. Centre National de la Recherche Scientifique; Francia. Université de Toulouse; FranciaFil: Wray, Sandra. Universidad Favaloro; ArgentinaFil: Lagaert, Jean Baptiste. Université Paris Sud; FranciaFil: Armentano, Ricardo Luis. Universidad de la República; UruguayFil: Capurro, Claudia Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fullana, José Maria. Centre National de la Recherche Scientifique; FranciaFil: Lagrée, Pierre Yves. Centre National de la Recherche Scientifique; Franci

Variational methods for modeling and simulation of tool-tissue interaction

Ph.DDOCTOR OF PHILOSOPH

Numerical simulation and experimentation of pulsatile flows in axisymmetric arterial models

ABSTRACT NUMERICAL SIMULATION AND EXPERIMENTATION OF PULSATILE FLOWS IN AXISYMMETRIC ARTERIAL MODELS by TADESSE GEBREEGZIABHER December 2011 Co-advisors: 1. Dr. Emmanuel Ayorinde 2. Dr. Trilochan Singh Major: Mechanical Engineering Degree: Doctor of Philosophy The primary motivation for this dissertation is the fluid flow and structural response to unsteady blood flow in the human body. The research work is a synergistic merging of numerical simulation and experimentation. For the experiments, an all-encompassing, highly flexible experimental apparatus was designed and fabricated to facilitate a wide range of operating conditions, the range of which was chosen to accommodate mammalian cardiovascular system for both human and animal species. The parameters that were varied during the course of the experimentation include the frequency of the flow pulsation, tubular materials having various structural properties, and blockages of the tube cross sections to simulate the presence of plaque in arteries. The main outcome of the experimentation was a connection between the amplitude and frequency of the pulsations and the volumetric flow rate of the flowing fluid. Of equal importance is the extent of the response of the wall to the nature of the pulsating flow which was detected, located and characterized using a non-invasive acoustic emission equipment. The simulations that were performed represent a major advance over prior attempts to simulate pulsating flows in flexible- and rigid-walled tubes. That advance was embodied in the model that was used to characterize the flow. In most of prior studies, a particular flow regime was selected and used throughout the entire solution domain. This selection ignored the fact that flowing fluids passing through variable cross sections undergo changes of flow regime. In particular, a flow initiated in a relatively large upstream cross section may be laminar based on inlet conditions. However, as the fluid travels downstream and enters a constricted cross section, the laminar regime may undergo a transition and subsequently experience turbulence. The capability to accommodate all these flow regimes by a single model was first accomplished in this research. Of special relevance is that the capability to simulate the proper flow regime enabled a more realistic response of the bounding wall of the tube to the imposed pulsations. Comparisons were made between the experimental results and the predictions of the simulations for two purposes. One was to establish the ranges of applicability of the simulation model. The other established a body of archival-quality information based on confirming experimental and simulated results. Another unique contribution of this research is the determination of the presence of flow-induced acoustic emissions. The motivation for this part of this work is the development of a diagnostic tool to detect, locate, and characterize blockages in arterial models

A numerical study of isotropic and anisotropic constitutive models with relevance to healthy and unhealthy cerebral arterial tissues

This paper presents an analysis of hyperelastic constitutive models for continuous bodies both from a modeling and numerical point of view. Contributions are made within the context of finite element numerical simulations. Numerical results with relevance to flows in the cardiovascular system are outlined in the case of a sophisticated fluid–structure interaction problem, in specific complex geometries of anatomically accurate cerebral arteries in diseased state. In this regard, the work carefully outlines the numerical validation of constitutive models for healthy and unhealthy cerebral arterial tissues by means of simulations of static inflation tests on an idealized specimen of anterior cerebral artery (ACA). The healthy tissue is described by means of isotropic and anisotropic models that, are fitted with respect to experimental data describing the mechanical behavior of the ACA; the numerical results are presented highlighting the most important numerical aspects influencing the correct and efficient simulation of the mechanics of continuous bodies such as, for instance, the arterial wall. We further consider numerical simulations of unhealthy conditions of the tissue by taking into account different levels of weakening of its mechanical properties. Taking the cerebral cardiovascular system as a challenging test problem, we focus on the study of the effects of the imposed mechanical levels of degradation on kinematic quantities of interest by simulating static inflation tests for the different models. This work does not aim to propose a new mathematical model for the mechanical damage occurring at the onset of cardiovascular diseases such as cerebral aneurysms. The modeling and numerical techniques presented may be applied to a wide range of problems, equally challenging to that of the cardiovascular system with complex structural models and fluid–structure coupling

Bridging spatiotemporal scales in biomechanical models for living tissues : from the contracting Esophagus to cardiac growth

Appropriate functioning of our body is determined by the mechanical behavior of our organs. An improved understanding of the biomechanical functioning of the soft tissues making up these organs is therefore crucial for the choice for, and development of, efficient clinical treatment strategies focused on patient-specific pathophysiology. This doctoral dissertation describes the passive and active biomechanical behavior of gastrointestinal and cardiovascular tissue, both in the short and long term, through computer models that bridge the cell, tissue and organ scale. Using histological characterization, mechanical testing and medical imaging techniques, virtual esophagus and heart models are developed that simulate the patient-specific biomechanical organ behavior as accurately as possible. In addition to the diagnostic value of these models, the developed modeling technology also allows us to predict the acute and chronic effect of various treatment techniques, through e.g. drugs, surgery and/or medical equipment. Consequently, this dissertation offers insights that will have an unmistakable impact on the personalized medicine of the future.Het correct functioneren van ons lichaam wordt bepaald door het mechanisch gedrag van onze organen. Een verbeterd inzicht in het biomechanisch functioneren van deze zachte weefsels is daarom van cruciale waarde voor de keuze voor, en ontwikkeling van, efficiënte klinische behandelingsstrategieën gefocust op de patiënt-specifieke pathofysiologie. Deze doctoraatsthesis brengt het passieve en actieve biomechanisch gedrag van gastro-intestinaal en cardiovasculair weefsel, zowel op korte als lange termijn, in kaart via computermodellen die een brug vormen tussen cel-, weefsel- en orgaanniveau. Aan de hand van histologische karakterisering, mechanische testen en medische beeldvormingstechnieken worden virtuele slokdarm- en hartmodellen ontwikkeld die het patiënt-specifieke orgaangedrag zo accuraat mogelijk simuleren. Naast de diagnostische waarde van deze modellen, laat de ontwikkelde modelleringstechnologie ook toe om het effect van verschillende behandelingstechnieken, via medicatie, chirurgie en/of medische apparatuur bijvoorbeeld, acuut en chronisch te voorspellen. Bijgevolg biedt deze doctoraatsthesis inzichten die een onmiskenbare impact zullen hebben op de gepersonaliseerde geneeskunde van de toekomst

Modelling of viscoelasticity in pressure-volume curve of an intact gallbladder

Like other organs such as artery, bladder and left ventricle, human intact gallbladders (GBs) possess viscoelasticity/hysteresis in pressure-volume curves during in vitro or in vivo dynamic experiments made by using saline infusion and withdrawal cycle to simulate GB physiological emptying-filling cycle in normal and diseased conditions. However, such a viscoelastic property of GBs has not been modelled and analysed so far. A non-linear discrete viscous model and a passive elastic model were proposed to identify the elastic, active and viscous pressure responses in the experimental pressure-volume data of an intact GB under passive and active conditions found in the literature in the paper. It turns out that the elastic, viscous and active pressure responses can be separated in less than 2% error from the pressure-volume curves. The peak active state in the GB occurs at 30% dimensionless volume. The GB stimulated with cholecystokinin (CCK) or treated with indomethacin is subject to almost constant stiffness at low dimensionless volume (≤ 70%) but quick increasing stiffness at high dimensionless volume (>70%) and a larger work-to-energy ratio (0.57–0.61) compared with the normal GB in the passive state. The models are sensitive to the change in the biomechanical property of the GBs stimulated or treated with hormonal or pharmacological agents, showing a potential in clinical application. These results may contribute fresh content to the biomechanics of GBs and be helpful to GB disease diagnosis