Mechanobiology

Mchanical stimulation influences the growth, adaptation, regeneration and engineering of cells and tissues. For example, in mechanobiology of skeletal tissues around orthopedic implants, regeneration of bone tissue is a function of shear stress transfer at the bone-implant interface. Osteoblasts are sensitive to mechanical stimulation and so it is important to study their reaction in a situation which is similar to the mechanical boundary conditions at the bone-implant interface.

In mechanobiology , this interaction between mechanical stimulations and biological process in living tissues is studied. In vivo and in vitro experiments plus computational modeling tools are used to explain the link between mechanics and biology.

lattice modelling approach

Comparing to the continuum-based models, lattice model is well adapted to map the ordered or random anisotropic microstructure of composite materials. The other advantage of lattice model is the simplicity of the physical interpretation of a phenomenon like fracture in each step of the analysis.

The main idea of lattice model is simulation of the material structure and mechanical properties by construction of a network of interconnected discreet line elements. The defined network can be two-dimensional or three-dimensional and has random or regular structure.

This approach was first developed to study the theory of elasticity (Hrennikoff 1941). Later lattice model was used in modeling the fracture process by removing the elements reaching a strength criterion at different loading steps. VanMier were one among of the first who used the lattice fracture model in concrete, aiming to simulate the quasi-brittle material behavior (Schlangen and VanMier 1992). In this model, beam elements were chosen in such a way that they represented the different phases of concrete (aggregates, matrix and interfaces). After that, the lattice fracture model was applied for several years in analyzing the concrete and sandstone fracture. All these studies confirmed that lattice fracture model is successful in predicting the influence of material microstructure on the pre-peak and softening behavior of force-displacement curve and crack propagation paths.

Now, lattice model is a well known approach in analysing the mechanical behavior and mechanism of fracture in cellular and fibrous structure such as wood, bone and soft tissues.

Different microstructure of softwood and hardwood

Trees are classified into two main groups, softwoods (narrow leaf trees) and hardwoods (broad leaf trees). The major difference between the anatomy of hardwoods and softwoods is the lack of vessels in softwood. Vessels are created to conduct the fluid in the tree trunk. In softwood, the longitudinal tracheids perform the role of conducting the fluid (Wangaard 1979). These microstructural differences are the origin of different mechanical properties in softwood and hardwood.

Cross sectional views of two hardwood and softwood specimens, photo by Marjan 2006

Bone

The primary tissue of bone is osseous tissues which is a hard and lightweight composite of ‘calsium phosphate’ in the chemical arrangement termed calcium hydrocylapatite. Bone has a relatively high compressive strength and poor tensile strength. It is essentially brittle with anisotropic mechanical properties. All bones consist of living cells embedded in the mineralised organic matrix that makes up the osseous tissue.


Cortical bone:

It is one of two main types of osseous tissues. It has a dense structure and forms the surface of bones, contributing 80% of the weight of a human skeleton.

Cortical bone has anisotropic mechanical properties which are due to different mechanical properties of the constituents (ostenic and interstitial lamellae) and the hierarchical structural organization of material.

microscopic image of ostenic and interstitial lamellae

Trabecular (cancellous ) bone:

It has a spongy structure and makes up the bulk of the interior of most bones, including the vertebra, tibia and femur.

Young's moduli and the strength of cancellous bone are proportional to the square of apparent density of the tissue and are therefore proportional to one another (Rice et al 1988).

	Strength Mpa	Modulus MPa
Cancellous bone in tension and compression	5-10	50-100
Cortical bone in compression	130-220	17000-20000
Cortical bone in tension	80-150	17000-20000

Bone Eng. By Davies

Poromechanics

Poromechanics is a branch of physics and specifically continuum mechanics and acoustics that studies the behavior of fluid-saturated porous media. A porous media consists of a solid matrix containing interconnected fluid-saturated pores and is called poroelastic when the matrix is elastic and the fluid is viscous. A poroelastic medium is characterized by its porosity, permeability as well as the properties of its constituents (solid matrix and fluid).

In physical terms the theory postulates that when a porous material is subjected to stress, the resulting matrix deformation leads to volumetric changes in the pores. Since the pores are fluid-filled, the presence of the fluid not only acts as a stiffener of the material, but also results in the flow of the pore fluid (diffusion) between regions of higher and lower pore pressure.

The concept of a porous medium originally emerged in soil mechanics while now has a wide application in biological cellular tissues and man made materials such as foam and ceramics.