Introduction to Biomedical Engineering: Basic concepts and Bone Biomechanics Fall 2016, AKUT G. Rouhi
Biomechanics The field of biomechanics applies principles of mechanics to study the structure and function of biological systems Biomechanics aims to explain the mechanics of life and living. From molecules to organisms, everything must obey the laws of mechanics (Y.C. Fung, 1990) Biomechanics has the following salient features: Material constitution The constitutive equations Growth and remodeling of living tissues under stress The existence of residual stress Hierarchy of sizes
Salient Features of Biomechanics
Stress Normal Stress F A Shear Stress
True Stress & Strain True stress True Strain T F A i ln T i o T T 1 ln 1
Linear Elastic Properties Modulus of Elasticity, E: Hooke's Law: = E E F Linearelastic F simple tension test
Young s modulus: Young s Modulus 7MPa EPolymers 4GPa 48GPa EMetals 410GPa 70 GPa E Ceramics 500 GPa
Stress Homogeneity & Isotropy A homogeneous material: A material for which there is no local variations in its composition Isotropy: A material which has the same mechanical properties in all directions. Anisotropy in natural materials: bone A A B B Strain
Musculoskeletal system A musculoskeletal system gives animals (including humans) the ability to move using the muscular and skeletal systems. The musculoskeletal system provides form, support, stability, and movement to the body. It is made up of the body's bones (the skeleton), muscles, cartilage, tendons, ligaments, joints, and other connective tissue.
Bone Biomechanics
Cortical and cancellous bones At the macroscopic level: Cortical (Haversian or compact) & Cancellous (spongy or trabecular)
Compact bone It is a dense, solid mass with only microscopic channels; cover the outer walls of long bones The basic structural unit is Osteon or HS An Osteon: Haversian canal, osteocyte lacunae,osteocytic processes within canaliculi Max. density: 1.9 gr/cm 3 ; 80% of the skeletal mass; largely responsible for the supportive and protective function of the skeleton Haversian system or Osteon
Compact bone A typical osteon is a hollow cylinder with the outer and inner diameters of about 200 (or 250) and 50 μm, respectively. An osteon is made up of 20 to 30 concentric lamellae, and surrounding the outer border of each osteon there is a cement line, a 1-2 μm thick layer of mineralized matrix deficient in collagen fibers, which it is believed they act as crack stoppers when cracks are present.
Spongy bone Basic structural unit: a trabecula; networks of plates and rods
Spongy bone If the stress pattern in spongy bone is complex, then the structure of the network of trabeculae is also complex and highly asymmetric.
Spongy bone An inhomogeneous porous anisotropic structure The symmetry depends upon the direction of applied loads- If the stress pattern in SB complex, then the structure of the network is also complex and highly asymmetric In bones where the loading is largely uniaxial, such as the vertebrae, the trabeculae often develop a columnar structure with cylindrical symmetry The average thickness of a trabecula is 100-150 µm The trabeculae are surrounded by marrow that is vascular and provides nutrients and waste disposal from the bone cells Approximately 20% of the skeletal mass in the adult human skeleton
Bone surfaces Free surfaces: Endosteum, periosteum, trabeculae, and Haversian canals Cancellous bone surface contributes more than 61% of the total bone surface The mean trabecular surface to volume ratio is 8 times greater that in CB Bone surfaces: resorption (OCs), formation (OBs), or quiscent (BLc)
Bone cells Osteoclasts, osteoblasts, osteocytes, and bone lining cells
Osteoclasts Osteoclasts: Bone resorbing cells; form a ruffled border when resorbing bone; proton pumps
Osteoblasts Osteoblasts: bone forming cells
Osteocytes Mechanosenors, most abundant cell type in mature bone; lie within 150µm of a blood vessel; celluelr density of 20000 OCs within 1 mm 3, Most of the OCs lie within 150µm of a blood vessel
A revolution in bone biomechanics! Wolff s law: Every change in the form and function of a bone is followed by certain definite changes in their internal architecture,and equally definite secondary alterations in their external conformation, in accordance with mathematical laws. Ruimerman et al., J. Biomech., 38(931-941), 2005
Viscoelasticity
Mechanical behavior of bone Mechanical behavior of bone is affected by: its mechanical properties its geometric characteristics the loading mode applied direction of loading rate of loading frequency of loading
Suggested texts D.L. Bartel, D.T. Davy and T.M. Keaveney, Orthopaedic Biomechanics, Mechanics and Design in Musculoskeletal Systems, Prentice Hall, 2006. S.C. Cowin, Bone Mechanics Handbook, 2nd Edition, CRC Press, 2001.