January 27 – 28, 2010
Role of Smooth Muscle Cells in Residual Stress Formation in Vascular Tissues
Elena DiMartino (University of Calgary)
Abstract
When observed on a sufficiently long time scale, i.e., long enough for cells to sense and respond to chemical and mechanical cues, biological soft tissues are “open systems” that exchange mass and energy with the external environment. This characteristic makes their mathematical analyses inherently more complex than simple mechanical systems that behave as closed systems. Residual stresses, as revealed by the tendency of aortic rings to open when they are cut radially, are a hallmark of cardiac and vascular tissues and they are intimately related to remodeling. As such, understanding the relative effect on residual stresses of the various cellular and extracellular components of cardio-vascular tissues may lead to improved remodeling theories. In this talk I will discuss our experimental, theoretical and numerical experiments aimed at studying the effect of smooth muscle cells contraction on residual stresses. The “opening angle” was measured on aortic rings from healthy small animals in a controlled bath with activating and relaxing solutions. An analytical method was developed to calculate residual strains/stresses from opening angle measurements. The equations were also implemented in a finite element model to further investigate how smooth muscle cell contraction and related residual stresses influence stresses under physiological loads. Preliminary results show that activation increases residual stresses in the intact but unloaded configuration. Confocal images of the tissue in relaxed and activated configuration confirmed a difference in the collagen structure.
In Silico Estimates of the Free Energy Changes in Growing Tumor Spheroids
Krishna Garikipati (University of Michigan)
Abstract
The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary in time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical byproducts. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy changes of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.
Modeling Biological Tissue Growth by Cell Division and Multigenerational Interstitial Growth of Extracellular Matrix
Gerard Ateshian (Columbia University)
Abstract
This presentation will focus on modeling biological tissue growth that explicitly addresses cell division, using a homogenized representation of cells and their extracellular matrix (ECM). The model relies on the description of the cell as containing a solution of water and osmolytes, and having a porous solid matrix. The division of a cell into two nearly identical daughter cells is modeled as the doubling of the cell solid matrix and osmolyte content, producing an increase in water uptake via osmotic effects. This presentation will also address multigenerational interstitial growth of the extracellular matrix whereby each generation has a distinct reference configuration determined at the time of its deposition. In this approach, the solid matrix of a growing tissue consists of a multiplicity of intermingled porous permeable bodies, each of which represents a generation, all of which are constrained to move together in the current configuration. Each generation’s reference configuration has a one-to-one mapping with the master reference configuration, which is typically that of the first generation. This mapping is postulated based on a constitutive assumption with regard to that generations’ state of stress at the time of its deposition. For example, the newly deposited generation may be assumed to be in a stress-free state, even though the underlying tissue is in a loaded configuration. The mass content of each generation may vary over time as a result of growth or degradation, thereby altering the material properties of the tissue.
Non-Linear, Inhomogeneous Viscoelasticity of Native Ligament and Tendon and of Tissue Engineered Ligaments
Ellen Arruda
Abstract
The incidence of ligament and tendon rupture in the US has increased drastically in recent years; particularly acute among the pediatric population is the increased incidence of knee ligament rupture. A common autograph approach to anterior cruciate ligament (ACL) reconstruction uses a portion of the patient’s patellar tendon as a graft. Previous investigations have shown differences in the viscoelastic responses of ligaments and tendons suggesting limitations in the ultimate efficacy of a tendon as a ligament graft. These limitations have led to an increased urgency for engineered replacement tissues for ligament and tendon reconstructions. The goal of our tissue engineering efforts is to form viable constructs that can replicate the biomechanical function of native tissue, with biomechanically compatible and biochemically relevant interfaces between the engineered musculoskeletal tissue and native tissue. The design of optimal structures for skeletal tissue replacement requires understanding of the function of native tissue and tissue interfaces, including growth and remodeling mechanics, at various developmental stages.
The first part of this talk will describe the non-linear, inhomogeneous viscoelastic responses of ligaments and tendons and the fundamental differences between these two tissue types. A micromechanical model assuming non-linear viscoelastic collagen and non-linear elastic elastin as the main structural proteins in ligament and tendon is used to describe the non-linear viscoelastic responses. This model is incorporated within a finite element framework to examine the heterogeneity in the mechanical response of native ligament and tendon and also to examine the altered biomechanics of the knee in response to tendon grafts. Next, our current tissue engineering approach to develop a multi-phasic, self-organized, scaffold-free construct for knee ligament replacement or reconstruction with mechanically viable, biochemically relevant tissue interfaces from patient-harvested cells will be discussed. The use of our bone/ligament/bone BLB construct, engineered from bone marrow stromal cells, as either a medial collateral ligament replacement tissue (MCL) in a rat model or an ACL replacement tissue in a sheep model will be described. The response of the ligament portion of the BLB constructs to a cyclic loading protocol is examined both for in vitro constructs and for explants after several months in vivo. The non-linear viscoelastic response of these engineered constructs is compared to that of native tissue. Our constructs exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for implantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established.
Arterial Growth and Remodeling – 3D Approach
Igor Karsaj (Zagreb University)
Abstract
Growth and remodeling (G&R) of arteries can be described via the turnover of different constituents possessing different natural configurations and mechanical properties and exhibiting different rates of turnover that can change with mechanical stimuli [1]. Thus, in addition to complex instantaneous nonlinear mechanical behaviors, time varying changes in composition resulting from mass turnover are important determinants of arterial biomechanics. We developed model restricted to elastostatics but capable of describing 3D behaviours of arteries. Only structurally significant constituents are modeled, elastin, collagen (4-fibre family) and smooth muscle cells. Each constituent has its own natural configuration, generally different from others, which is taken as a possibly evolving stress free reference configuration. Deformations and G&R of a constrained mixture of all constituents are tracked within the current mixture configuration. The model is capable of describing evolving residual stresses, revealed in a reference mixture configuration through the classical opening angle. Using a cylindrical geometry (carotid artery), key features of the developed model are examined prior to implementation in finite element models.
[1] Humphrey, J. D. and Rajagopal, K. R. A constrained mixture model for growth and remodeling of soft tissues. Math Models Methods Appl Sci, 12: 407-30, 2002.
And J.D. Humphrey
On Integrating Mathematical Models and Laboratory Experiments in Biomechanics
Larry Taber (Washington University)
Abstract
Most modelers agree that laboratory experiments are an indispensable part of the process of modeling biological systems. Experiments are required to determine model parameters, as well as to test model predictions. In this way, modeling drives experiments. On the other hand, experiments also drive modeling. For example, models can be used to help interpret experimental results. In addition, when new data contradict the predictions of a model, the model needs to be modified. Here, we illustrate the dynamic coupling between models and experiments for problems in morphogenesis.
Biomechanics & Remodeling of Engineered Arteries: Motivating the Design of Coronary By-pass Grafts
Rudy Gleason (Georgia Institute of Technology)
Abstract
Despite advances over the past 25 years, a pressing clinical need remains to develop small diameter tissue engineered blood vessels (TEBV) with low thrombogenicity and immune responses, suitable mechanical properties, and a capacity to remodel to their environment. One promising technology for developing a TEBV is the self-assembly approach. This approach consists of culturing vascular cells to form sheets of cells and extracellular matrix, then rolling these sheets around a mandrel and culturing them to form a tubular structure. Sheets made from different cell types (e.g. SMCs versus fibroblasts) can be combined to produce heterogeneous vessels containing media-like and adventitia-like layers; vessels may also be seeded with endothelial cells to form a functional endothelium. This presentation reviews recent studies conducted in our lab that characterize the biomechanical properties of both native arteries and engineered tissues and the implications of these findings on defining appropriate design criteria for a coronary by-pass graft. Biomechanical testing and parameter estimation to characterize the mechanical behavior of the media-like and adventitia-like self assembly-derived TEBV are be presented and compared to TEBV constructed from competing tissue engineering strategies (e.g., collagen gels), as well as representative data from human coronary arteries taken from the literature. The predictive capability of the constitutive model is be demonstrated by comparing modeling predictions to experimental data from two-layer self assembly-derived TEBV. Finally, modeling results are presented to test novel fabrication strategies to control the mechanical behavior of self assembly-derived TEBV.
Growth and Structural Adaptation of Microcirculation in Normal and Tumor Tissues
Tim Secomb (University of Arizona)
Abstract
Microvascular networks are dynamic structures, and adapt to changing conditions and demands. Tumors show abnormal network structures, affecting their responses to radiation and chemotherapy. We have used theoretical models to investigate how vascular responses to mechanical stresses, metabolites and growth factors lead to well organized and efficient microvessel network structures in normal tissues, and how these processes are perturbed in tumors. The results indicate that the abnormal structure of tumor microcirculation is caused by impaired mechanisms for information transfer along vessel walls.
Patient-Specific Blood Flow Simulation: A Gateway to Modeling Biomechanical Stimuli for Arterial Wall Growth & Remodeling
Alberto Figueroa (Stanford University)
Abstract
In recent years, significant progress has been made in understanding the biology of vascular growth and remodeling in response to altered hemodynamics. We have recently demonstrated the application of a computational framework for fluid-solid-growth that brings together advances in computational biosolid and biofluid mechanics to enable simulations of vascular adaptations [1]. Specifically, we described the growth and remodeling of an idealized cylindrical basilar aneurysm mediated by biomechanical stimuli such as tensile stress and wall shear stress. In our current study, we expand our previous work in two ways:
1. We generalize the framework to perform fluid-solid-growth simulations in patient-specific vascular models. We briefly describe the computational tasks required to do this.
2. We include other biomechanically-relevant stimuli for vascular growth and remodeling such as cyclic stretch. This task is facilitated by recent advances made in fluid-structure interaction techniques that enable the computation of realistic deformations. We utilize feedback control techniques [2] to guide the vessel wall dynamics using wall motion measured from medical image data.
[1] C.A. Figueroa, S. Baek, C.A. Taylor, J.D. Humphrey. A Computational Framework for Coupled Fluid-Solid Growth in Cardiovascular Simulations (2009). Computer Methods in Applied Mechanics and Engineering Vol. 198, pp. 3583-3602
[2] P. Moireau, D. Chapelle, and P. Le Tallec. Filtering for distributed mechanical systems using position measurements: Perspectives in medical imaging (2009). Inverse Problems, 25(3):035010 (25pp). doi:10.1088/0266-5611/25/3/035010.
Fluid-Solid-Growth Simulation of Stress-Mediated Vascular Adaptation: Towards Patient-Specific Modeling
Seugik Baek (Michigan State University)
Abstract
Theoretical advances in modeling growth and remodeling of soft tissues, computational biomechanics, and medical imaging allow an increasing role of computational mechanics in the study of cardiovascular diseases. Previously, we have demonstrated the utility of fluid-solid-growth (FSG) modeling framework in simulating the progression of vascular diseases using an idealized geometry [1]. In our current work, we expand the computational framework to account for patient-specific anatomical information from medical images. We also develop an inverse method for estimating the spatial distribution of the wall thickness and fiber alignment to identify initial conditions for the FSG simulation. The computational framework is applied to modeling early stages of abdominal aortic aneurysm expansion from a healthy aorta and the effects of alterations of hemodynamic loads and spatial and temporal distributions of wall damage on aneurysm expansion are studied.
[1] C.A. Figueroa, S. Baek, C.A. Taylor, J.D. Humphrey. A Computational Framework for Coupled Fluid-Solid Growth in Cardiovascular Simulations (2009). Computer Methods in Applied Mechanics and Engineering Vol. 198, pp. 3583-3602.
Shahrokh Zeinali-Davarani; C. Alberto Figueroa; Charles A. Taylor; and Jay D. Humphrey
On the Structure-function Relationship in Electro-active Cardiac Tissue
Ellen Kuhl (Stanford University)
Abstract
Skeletal muscle and cardiac muscle are typical examples of electro-active biological tissue: They are activated by traveling electric depolarization waves and contract upon excitation. Their characterization naturally involves the coupled field equations of electric activity and mechanical equilibrium. In this presentation, we will discuss the governing equations for excitation-contraction coupling and potential approaches towards their computational solution. While electro-mechanical phenomena have typically been solved with explicit staggered finite dierence schemes in the past, we propose a robust, stable, and extremely efficient solution strategy based on a fully coupled finite element framework. We demonstrate the validation of the electric module by means of patient-specific electrocardiograms and the calibration of the mechanical module by means of rat heart slice experiments. Examples of healthy and fibrillating hearts will illustrate the potential of this novel approach.
And Serdar Goktepe
Deformation and Failure of Protein Materials in Extreme Conditions
Markus Buehler (Massachusetts Institute of Technology)
Abstract
Biological protein materials feature hierarchical structures, ranging through the atomistic, molecular to macroscopic scales, forming functional biological tissues as diverse as spider silk, tendon, bone, skin, hair or cells. Here I will present computational studies, focused on how protein materials deform and fail due to extreme mechanical conditions, disease and injuries. Based on a multi-scale atomistic simulation approach that explicitly considers the architecture of proteins including at the chemistry level, we have developed predictive models of protein materials, validated through quantitative comparison with experimental results. This bottom-up approach enables us to extract fundamental physical concepts that control the properties of protein materials. I will present studies of several major classes of protein materials, including cellular alpha-helix rich protein networks, beta-sheet structures as found in spider silk and amyloids, as well as collagenous tissues that form tendon and bone. Materials failure in the contact of genetic diseases will be discussed.