Biomechanics of Bone Adaptation Federica Caselli University of Rome “Tor Vergata” A.A. 2012/2013

Definition of biomechanics “mechanics applied to biology” Y. C. Fung, Biomechanics: motion, flow, stress, and growth. Springer (1990) Biomechanics has been defined as “development, extension and application of mechanics for the purposes of understanding better physiology and pathophysiology as well as the diagnosis and treatment of disease and injury” J. D. Humphrey, Proc. R. Soc. Lond. A 459 (2003) but it is much more

Topics of biomechanics (examples)

Peculiar features of biological tissues Living matter: Extremely complex structure: multiscale, non-homogeneous, anisotropic

Peculiar features of biological tissues Living matter: Extremely complex behaviour: nonlinear, multiphysics, active, growth & adaptation Biological tissues have the unique property that cells can alter tissue matrix in response to the history of external environmental stimuli

Biomechanics & Mechanobiology Biomechanics aims to study the mechanical properties of the cells and the tissues by taking into account the complexity of the structures being studied Biomechanics & Mechanobiology structure mechanical properties Mechanobiology aims to discover how mechanical forces modulate morphological and structural fitness of the tissues mechanical stimuli structure

Bone tissue

Osteoblasts, bone formation Osteoclasts, bone resorption Remodeling osteoclasts and osteoblasts closely collaborate at same site from growth to death; the only physiological mechanisms for replacing old bone in adult at beast lead to maintenance of bone (with age net loss) Bone is a dynamic structure Modeling osteoclast and osteoblasts act independently at different sites growth and healing potential to create or resorbe large amount of bone

Bone tissue material properties Anisotropy, heterogeneity, visco-elasticity (cortical b.)

Overview of bone adaptation Adaptational capability cells within the tissues can sense some aspect of the mechanical stimulus, judge whether this stimulus is appropriate, and then alter the tissue matrix in an appropriate manner to respond to the mechanical stimulus Clinical implications Unbalanced adaptation capability (e.g. in osteoporosis)  response does not correspond to mechanical demand and lead to tissues that cannot withstand functional loads and fracture

Overview of bone adaptation Adaptational capability: cells within the tissues can sense some aspect of the mechanical stimulus, judge whether this stimulus is appropriate, and then alter the tissue matrix in an appropriate manner to respond to the mechanical stimulus Clinical implications Unfavorable mechanical environment (e.g. stress shielding)  adverse tissue adaptation, even if the adaptation mechanisms works properly

A physiological control system

Error-driven control (Roux 1858)  there exist some “remodeling equilibrium” point homeostasis

A physiological control system What is sensed signal ? it must be a physically measurable manifestation of the changed mechanical environment  ?  ?  ? damage?  /  t ?  ?

A physiological control system What is actuation mechanism? Many hypotheses e.g.: fluid flow in canaliculi  strain-generated potential  osteocytes membrane modification  inter- & intra- cellular signaling Bio-chemo-mechanics

A physiological control system How net remodeling helps to achieve an adapted structure? i.e.: how are stress and strain influenced by remodeling?

Milestones  Culmann & Von Meyer drawings (1867) Swiss anatomist Von Meyer, line drawing of cancellous bone structure in the proximal femur end Swiss engineer Culmann, line drawing of principal stress trajectories in a cranelike curved bar Striking visual similarity (but different meaning!) trajectorial theory of trabecular bone

Milestones  Wolff’s law ( ) "Every change in the form and function of a bone or of their function alone is followed by certain definitive changes in their internal architecture, and equally definite secondary alteration in their external conformation, in accordance with mathematical laws.“ (Wolff JD: Das geretz der transformation der knochen, Berlin, 1892, Hirschwald.) Moreover, bone adapts optimally (minimize mass to carry load)  Roux, German surgeon (1881) How? Cell based apposition and reposition, regulated by values of local stress  Koch, American anatomist (1917) Bone density is highest in area of highest shear stress (optimality)

Milestones  Frost, surgeon (1960) Bone could adapt by either modeling or remodeling Adaptational response are different in adolescent and adult: since adult skeleton could only remodel, its bone structure is less sensitive to mechanical stimulus. However, excessive stimuli would cause damage in any skeleton and lead to a pathologic response involving both modeling and remodeling

Modeling bone adaptation Equations equilibrium structure-function relationship (effective stiffness as a function of microstructural stiffness and structural arrangement of material) evolution equation (how bone structure changes based on the current mechanical environment) equilibriumevolution structure- function

Cornerstones Presently, active research area!  Cowin & Hegedus, Theory of adaptive elasticity (1976)  Fhyrie & Carter, Optimization goal (1984)  Huiskes et al, strain energy density as the mechanical stimulus, lazy zone (1987)  Fhyrie & Shaffer (1995), Turner et al (1997),... See, e.g., Cowin, S. C. (editor), Bone Mechanics Handbook, CRC Press, Boca Raton, FL, 2001 Cowin, S. C. and Doty, S. B., Tissue Mechanics, Springer, 2007

Example of simulation scheme (for C&H approach) 1. Update bone structure (e.g. with explicit Euler method) 2. Update effective bone stiffness based on updated bone structure 3. Solve equilibrium equation with new stiffness to determine new stress and strain fields 4. Return to 1 and update bone structure; repeat until convergence

A spot on vascular adaptation

Modeling issues in biomechanics Aims Needs Challenges Understanding physiopathology Prediction of disease development and evolution Treatment optimization Reliable and effective Patient-specific Model formulation Geometric modeling (image-guided) Model parameters and boundary conditions Simulation strategies Computational efforts