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Evolutionary Solid Bodies - Growth and Remodelling of Biological Tissues

Structure of the Summer School

The Summer School will start on Sunday evening, September 8, 2013, with a reception and will finish on Saturday afternoon, September 14.

 

1. Seminar

The lectures will concentrate on the fundamentals, on the linkages of both pillars as well as on selected advanced problems. Special emphasis will be given to discussions between speakers and participants.

 

2. Workshop

The research field splits up in several branches and representative applications which can hardly be unified. The goal of the Workshop is to let PhD students and post-docs present specific problems related to the core topics. Participants intending to present a talk are asked to register and submit a title and one-page abstract before May 15, 2013.

 

3. Tutorial

The comprehension of the theoretical contents presented in the seminar lectures will be increased by computing and programming tutorials devoted to the computational details.




Updated schedule

(04-09-2013)

 

Seminar and Tutorial

Workshop and Tutorial

Arrival Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

08:30 - 09:15

Registration

Mechanical behaviour of bone tissue

E. de Brosses

Remodelling of fluid saturated
biological tissue


Ricken

Introduction to biological evolution. Part II: surface growth.

Ganghoffer

Computational modeling of multiplicative growth and remodelling
Menzel

Continuation of tutorials

09:15 - 10:00

Efficient computation of the elastography inverse problem in biological soft tissue
Mosler

10:00 - 10:30

Welcome and opening of the summer school

Coffee break

10:30 - 11:15

Basics on Continuum Mechanics & Nonlinear Finite Element Method

Barthold

Micromechnics of bones

Ganghoffer, Ibrahim Goda

Introduction to tissue engineering of ligament

Wang

Introduction to the topological derivative in shape optimization

Laurain

Evolutionary solid bodies:
The structural optimisation viewpoint

Barthold

Continuation of tutorials

11:15 - 12:00

Questions and answers
Final discussion

12:00 - 14:00

Questions and Answers / Lunch

13:30h: Talks of participants

13:30h: Talks of participants

13:30h: Talks of participants

14:00 - 14:45

Basics on Continuum Mechanics & Nonlinear Finite Element Method
Barthold

Mechanical analysis of bone distraction osteogenesis

Bonnet

Computer-aided tissue engineering: overview and case study

Laurent

Computational modeling
of density growth


Menzel

Tutorials on presented model problems

Continuation of tutorials

14:45 - 15:30

Basics on Inverse Problems
and Structural Optimisation

Materna

15:30 - 16:00

Coffee break

Closure & Departure

16:00 - 16:45

Basics on Inverse Problems
and Structural Optimisation


Materna

Introduction to biological evolution. Part I: volumetric growth.

Ganghoffer

Growth of fluid saturated
biological tissue


Ricken

Tutorial: Computational modeling
of density growth


Menzel

Tutorials on presented model problems

16:45 - 17:30

17:30 - 19:30

Questions and Answers / Dinner

19:30 - 21:00

Presentation of speakers

Social event

Social event

Discussions / Tutorials

 

 

 

Abstracts

Basics on Continuum Mechanics and Nonlinear Finite Element Method.
Franz-Joseph Barthold


The fundamental concepts of continuum mechanics which are relevant to understand and to model the different growth phenomena are summarised. A uniform notation is introduced which should ease the comprehension of the follwing presentations. Furthermore, those model problems used throughout the summer school are described. A framework of the nonlinear finite element method is outlined. Consequently, the forthcoming presentations could concentrate on the central ideas of modelling and computing growth phenomena relating their add-ons to the outlined framework.

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Basics on Inverse Problems and Structural Optimisation.
Daniel Materna


The fundamental concepts needed to understand the theory and the computation of inverse problems are summarised. Those elements needed throughout the summer school in various presentations are presented in a uniform notation. Additionally, model problems are formulated and discussed. The computational details of topology and shape optimisation are outlined. The participants gain a detailed insight into the implementation and computation of those problems. This session offers a framework for all forthcoming tutorials which refer to the outlined schemes.

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Mechanical behaviour of bone tissue.
Emilie de Brosses


Given the ageing population, bone fractures are considered as a major public health issue. Identifying the mechanisms of those fractures may help to generate strategies for prevention and treatment. The mechanical properties of the bone tissues are one of the determinants of the strength of the whole bone. Therefore, the quantification and the prediction of these material properties are important in understanding the mechanisms of bone diseases. This course is an introduction to bone tissue mechanics. On the one hand, the laws representing the behaviour of the cortical bone and the cancellous bone considered as continuous media will be reviewed. This part deals with the elastic properties of bone and their determinants (species, anatomical sites, orientation, strain rate …), the strength of the bone tissues under different modes of loading. Secondly, the experimental methods commonly used for the evaluation of thephenomenological behaviour of both cortical and cancellous bone will be presented. The difficulties specific to the biological tissues will be highlighted.

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Micromechnics of bones.
Jean-François Ganghoffer, Ibrahim Goda


Anisotropic micropolar continuum models of vertebral trabecular bone are developed, accounting for the influence of microstructure-related scale effects on the macroscopic effective properties. Vertebral trabecular bone is modeled as a cellular material with an idealized periodic structure made of open 3D cells. The micromechanical approach relies on the discrete homogenization technique, considering lattice microrotations as additional rotational degrees of freedom at the microscale. In the first part of the lecture, a reminder of homogenization techniques is given in a general sense, while the second part is devoted to the construction of homogenized responses for bone based on a geometrical and mechanical model of the underlying bone microstructure at trabecular level. The effective elastic properties of 3D lattices made of articulated beams taking account axial, transverse shearing, flexural and torsional deformations of the cell struts representing the trabeculae are derived versus the geometrical and mechanical microparameters. The scaling laws of the effective moduli versus effective density are determined in situations of low and high effective densities to assess the impact of the transverse shear deformation. The classical and micropolar effective moduli and the internal flexural and torsional lengths are identified versus the microparameters. A finite element model of the local architecture of the trabeculae performed over a representative unit cell gives values of the effective moduli that are in satisfactory agreement with the homogenized moduli and measurements reported from the literature. The development of second order gradient models for bone is mentioned.

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Mechanical analysis of bone distraction osteogenesis.
Anne-Sophie Bonnet


Distraction osteogenesis (DO) is a surgical technique used to lengthen limb bones or to correct severe bone defects. In the maxillofacial specialty, DO accounts for one of the best procedures to treat severe traumas as ballistic wounds. During the surgical act, a gap is created between two bone segments. This gap is rapidly fulfilled by mesenchymal tissue. The distraction protocol consists in daily applying a displacement on the gap tissue through an internal or external mechanical device. The mechanical loading imposed on the regenerated tissue directly influences the cells differentiation (Ilizarov [1]). Consequently, the parameters of the distraction protocol have to be carefully chosen in order to produce bone tissue of good quality (Richards et al. [2], Bocaccioet al. [3]). The evolution of forces acting on the bone callus during DO is known to be strongly influencing the clinical issue of the treatment. The first aim of this courseis, after a presentation of this surgical procedure and of the biological processes associated, to describe an experimental method for the determination of the time-dependent forces imposed on the bone regenerate by the distraction device(Bonnet et al. [4]). In a second time, an identification methodof the mechanical properties of bone calluswill be presented(Bonnet et al.[5]).

References:
[1] Ilizarov, G.A., 1989b, "The Tension-Stress Effect on the Genesis and Growth of Tissues. Part II. The Influence of the Rate and Frequency of Distraction", Clin.Orthop.Relat. Res., 239, pp. 263-285.
[2] Richards, M., Wineman, A.S., Alsberg, E., Goulet, J.A., and Goldstein S.A., 1999, "Viscoelastic characterization of mesenchymal gap tissue and consequences for tension accumulation during distraction", ASME J. Biomech. Eng., 121, pp. 116-123.
[3] Boccaccio A., Pappalettere C., Kelly D.J., 2007, "The Influence of Expansion Rates on Mandibular Distraction Osteogenesis: A Computational Analysis", Ann Biomed Eng, 35, pp. 1940-1960.
[4] Bonnet, A.S., Dubois, G., Lipinski P. &Schouman T. In vivo study of human mandibular distraction osteogenesis. Part I: Bone transport force determination, Acta of Bioengineering &Biomechanics, 14, 4, 2012.
[5] Bonnet, A.S., Dubois, G., Lipinski P. &Schouman T. In vivo study of human mandibular distraction osteogenesis, Part II: Determination of callus mechanical properties, Acta of Bioengineering &Biomechanics, 15, 1, 2013.

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Introduction to biological evolution.
Part I: volumetric growth.
Part II: surface growth.
Jean-François Ganghoffer


One outstanding problem in developmental biology is indeed the understanding of the factors that may promote the generation of biological form, involving the processes of growth (change of mass), remodeling (change of properties), and morphogenesis (shape changes), a classification suggested by Taber (1995). These three aspects of the development of a biological structure have tied connections to each other, and are due to a combination of both genetic and epigenetic factors, such as chemical agents and mechanical stress and strains. It is generally acknowledged that hard tissues undergo surface growth (e.g. bones), whereas soft tissues are more prone to volumetric growth. The lecture presents in its first part the possible routes to extend the classical framework of continuum mechanics to describe the evolutionary aspects of biological tissues, including open systems mechanics and thermodynamics, large strains constitutive models for soft biological (fibrous) tissues, especially arteries, the consideration of evolving anisotropy and residual stresses in relation with kinematic incompatibilities. In the second part, the surface growth of hard biological tissues is analyzed in the framework of the thermodynamics of surfaces, relying on Gibbs approach, but extended to a tensorial formulation. From a kinematic point of view, growth is assumed to occur in a moving referential configuration, considered as an open domain exchanging mass, work, and nutrients with its environment. The growing surface is endowed with a superficial excess concentration of moles in line with Gibbs approach of interfaces, which is ruled by an appropriate kinetic equation. A thermodynamic formulation of surface growth is presented that entails the surface driving forces for growth: they involve a surface Eshelby stress, the curvature tensor of the growing surface, the gradient of the chemical potential of nutrients, and a surface force field. Simulations of bone external remodeling illustrate the potentialities of the developed formalism.

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Remodelling of fluid saturated biological tissue.
Tim Ricken


Biological soft tissues like muscles, cartilage or organs have of a highly complex inner texture. They are mostly composed of a porous tissuematrix filled with fluid and show an overall anisotropic, viscoelastic andporo-incompressible material behavior. The anisotropy is caused by inner, heterogeneously distributed reinforcing textures like collagen fibers. Since soft tissue contains 70% and more water, the incompressibility is mostly generated by the incompressible fluid. Finally, the viscoelasticity results from the frictionary fluid filter velocity. Tissue achieves the capability to react on outer loading changes by a remodeling of the inner structure like change of fibre orientation, pore structure or stiffness. In this paper, an enhanced biphasic model is presented which predicts the behavior of different biological tissues. The applicability will be demonstrated by numerical calculations on tissue behavior including remodeling.

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Introduction to tissue engineering of ligament.
Xiong Wang


Ligaments and tendons play a crucial role in joint movement and stability. Some of them have bad or no healing capacity (e.g. the anterior cruciate ligament). Today tissue engineering is emerging as a new technique which aims at the regeneration or reconstruction of tissues. By using autologous cells and biodegradable materials, it would allow to overcome the limitations of human grafts. The objective of this presentation is to give an overview of tissue engineering of ligaments and we will cover basically the following topics: 1) the potential of the use of the mesenchymal stem cell (MSC), in particular, effects of mechanical cyclic stretching; 2) a biocompatible and biodegradable braided scaffold seeded with MSCs; 3) a new bioreactor specially designed for anterior cruciate ligament which allows to impose synchronized stretching and torsion on a scaffold in sterile culture conditions, and 4) in vivo implantation of the scaffold in the Rabbit.

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Computer-aided tissue engineering: overview and case study.
Cédric Laurent


Despite of the promising advances that tissue engineering may enable in the field of reconstructive surgery, few applications have actually reached the clinics so far. This is particularly due to the large numbers of interacting fields associated with the proposition and the biological characterization of adapted scaffolds for a particular clinical application. Recently, numerous computer-aided strategies have appeared: they aim at modelling the mulitphysic and multiscale phenomenon involved in the optimization of the shape, composition, seeding and culture of scaffolds. In this seminar, we propose to provide with a brief review of the computer-aided methods currently used in such strategies, including finite-element modelling of scaffolds behaviour, mechanobiological models for cellular growth, computed fluid dynamics of physiological fluids within the scaffolds, and technical points such as medical imaging and rapid prototyping.

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Growth of fluid saturated biological tissue.
Tim Ricken


Within the framework of the theory of porous media a ternary model is discussed describing growth processes in soft tissues. Thereby, the porous tissue consists of a deformable tissue matrix saturated by an interstitialfluidcontaining mobile nutrient solutes. With respect to this model a set of field equations (saturation condition and the balance equations of mass, momentum, moment of momentum and energy for each individual phase) is obtained. In order to specify constitutive equations, a consistent evaluation of the mixture entropy inequality in conjunction with dissipation mechanism will be treated. The method of finite elements will be used for the numerical simulation. Examples of use are a trauma healing process oreccentric and concentric heart growth.

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Introduction to the topological derivative in shape optimization.
Antoine Laurain


The topological derivative measures the first-order variation of a real-valued functional taking as argument the geometry of a domain, when a small change in the topology of this domain is created. Here, a change in the topology means a singular domain perturbation such as the creation of a small hole, an inclusion, defects, or cracks, among others. The variety of shape changes allowed by using the topological derivative has led to tremendous improvements in the resolution of shape optimization problems over the last decade, in comparison to previous shape optimization techniques. Nowadays, the topological derivative is used in various fields of applied mathematics such as structural mechanics, free boundary problems, optimal design of microstructures, fracture mechanics, damage evolution modeling, image processing and inverse problems.

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Computational modeling of density growth.
Andreas Menzel


Biological tissues, such as bones, are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of density accompanied by pronounced anisotropic mechanical properties. In this lecture a well-established framework of energy-driven isotropic functional adaptation is generalised to anisotropic microstructural growth and density evolution. A so-called micro-sphere concept is adopted, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. Related numerical examples can be referred to the simulation of bones but also soft biological tissues as well as applications in structural design.

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Tutorial: Computational modeling of density growth.
Andreas Menzel


Changes in mass are introduced by a mass source assumed to coincide with the rate of referential density. Based on this, the referential density is treated as an internal variable and, from a computational viewpoint, implemented as a history variable. An implicit Euler integration scheme is applied to the resulting evolution equation and iteratively solved by means of a Newton scheme. The model will be implemented into Matlab and, based on this, several numerical examples can be simulated which, however, will be restricted to homogeneous deformations. As a result, the saturation-type evolution of the referential density at constant loading levels can be computed and a similar behaviour is observed for representative stress components.

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Computational modeling of multiplicative growth and remodelling.
Andreas Menzel


Biological materials exhibit the ability to adapt according to their particular loading conditions. This lecture places emphasis on the phenomenological modelling of such phenomena, including changes in mass, volume, and material anisotropy also denoted as remodelling. By analogy with finite deformation plasticity, a multiplicative decomposition is adopted, which enables to model time-dependent adaptation processes. The formulation will be restricted to displacement degrees of freedom but also accounts for fiber reorientation, respectively turn-over, by means of evolution equations of related internal variables. Related numerical examples can be referred to typical soft biological tissues, such as arteries.

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Efficient computation of the elastography inverse problem in biological soft tissue.
Jörn Mosler


Elasticity imaging, also known as elastography, is a powerful method for visualizing the stiffness distribution in soft tissue in vivo. Conceptually, the deformation is measured first by comparing ultrasound or MRI signals of a tissue sample before and after prescribing a certain loading and subsequently, by applying correlation-based algorithms or by minimization of a suitable objective function. The computed deformation field serves as input data for an inverse analysis allowing to determine the underlying stiffness distribution. Since pathologies affect in many cases the stiffness, elastography is very promising for detecting such critical regions. More precisely, diseased tissue tends to be stiffer than the surrounding material. This is particularly common in breast cancer and prostate tumors where hard lumps are usually observed. This lecture is concerned with efficient algorithms suitable for the elastography inverse problem.

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Evolutionary solid bodies: Summary of the structural optimisation viewpoint.
Franz-Joseph Barthold


Models of growth and adaptation are similar to models of structural optimization in that both involve design variables in addition to the usual mechanical and thermomechanical state variables. In growth problems such design variables are treated by evolution laws, while in structural optimization they are controlled by optimality criteria. A novel presentation of growth based on local coordinates will be outlined. The essential theoretical and computational aspects of the advocated approach will be discussed and compared with traditional growth formulations in the presentation. Furthermore, technical details on the implementation are discussed.

References:
Barthold, F.-J., A structural optimisation viewpoint on growth phenomena. Bulletin of the Polish Academy of Sciences. Technical Series., 2012,
Vol. 60, No. 2, pp. 247-252,
DOI: 10.2478/v10175-012-0033-6

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