Topic 6: Bone Growth and Remodeling

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Topic 6 Bone Growth and Remodeling

• Bone continually remodels
• growth, reinforcement, resorption
• depends on stress and strain
• There is an optimal range of stress for maximum
  strength
• understressed or overstressed bone can weaken
• stresses on fractured bone affect healing
• stress-dependent remodeling affects surgical
  implant and prosthesis design, e.g. fracture
  fixation plates, surgical screws, artificial
  joints
• 1978 radiographic evidence of bone resorption
  seen in 70 of total hip replacement patients

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Stress-Dependent Remodeling

• Osteoclasts - cells responsible for resorption
• Osteoblasts - cells responsible for growth
  (hypertrophy)
• compressive stress stimulates formation of new
  bone and is important for fracture healing
• loss of normal stress ? loss of calcium and
  reduced bone density
• Time scales
• remodeling - months/years
• fastest remodeling is due to change in mineral
  content
• healing - weeks
• growth/maturation - years

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Types of Bone Remodeling

• Two types of remodeling in bone
• 1. surface (external) remodeling
• change in bone shape and dimensions
• deposition on to or resorption of bone material
  from inner or outer surfaces
• 2. internal remodeling
• change in
• bulk density
• trabecular size
• orientation
• osteon size, etc.

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Functional Adaptation

• Principal of Functional Adaptation, Roux (1895)
• "the ability of organs (and cells, tissues and
  organisms) to adapt their capacity to function in
  response to altered demands by practice
• Functional adaptation in bone is remodeling of
  structure, geometry and mechanical properties in
  response to altered loading
• Related to the engineering concept of optimal
  design

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Some Optimal Design Principles

• Theory of Uniform Strength attempts to produce
  the same maximum normal stress (brittle material)
  or shear stress (ductile material) throughout the
  body for a specific loading
• Theory of Trajectorial Architecture
  concentrates material in the paths of force
  transmission, such as principal stress lines,
  e.g. fiber reinforcing of composite
  (kevlar-mylar) sails
• Principle of Maximum-Minimum Design maximize
  strength for minimum weight or cost
• These theories have been verified in many cases

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Stress Adaptation of Trabecular Bone

• G.H. von Meyers trabecular bone architecture in
  human femur (1867)

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Remodeling of Trabecular Bone Wolff's Law

• Wolff (1872) when loads are changed by trauma or
  change in activity, functional remodeling
  reorients bone trabeculae so they align with the
  new principal stress axes
• Wolff never actually proved this
• Wolff's law of bone transformation (1884)
  there is a perfect mathematical correspondence
  between the structure of cancellous bone in
  proximal femur and Culmanns trajectories
• Culmanns trajectories and other of Wolffs
  assertions were suspect, but photoelastic studies
  (Pauwels,1954) confirmed Wolff's law

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Cowin's Mathematical Statement of Wolff's Law

• In remodeling equilibrium
• TH HT
• The stress tensor T and the fabric tensor H
  commute (they have the same principal axes)
• The principal axes of H are parallel to the
  trabecular trajectories

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Theories of Stress-Adaptive Bone Remodeling
Two main analytical models of bone adaptation to
stress 1. The theory of surface bone
remodeling 2. The theory of internal bone
remodeling
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Remodeling Theories Assumptions
1. Bone is a linearly elastic porous solid
(matrix, mineral, cells) perfused with fluid
(interstitial and blood) 2. Fluid phase can be
converted to solid and vice- versa by cells.
Mass transfer to or from the bone matrix is slow
compared with the time constants for dynamic
mechanical effects 3. Inertial and other dynamic
mechanical effects are neglected 4. Reaction
rates of solid-fluid conversion at a point depend
on strain, stress or strain energy 5. Internal
and external remodeling differ by the site of
reactions and how mass is added/removed
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Theory of Surface Remodeling

• Solid-fluid conversion occurs only on boundary
  surfaces
• Mass is only added/removed to/from bone solid by
  changes in external shape of bone
• Bone interior bulk density is unchanged
• The rate of surface deposition/resorption at a
  point is a function of surface strain, stress or
  strain energy at that point

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Theory of Internal Remodeling

• Solid-fluid conversion occurs everywhere
  throughout porous bone
• Mass is added/removed by altering bulk density
  through changes in bone porosity, mineral
  content, etc.
• Exterior bone dimensions are constant
• Rate of change of density at a point is a
  function of strain, stress or strain energy at
  that point

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Example Diaphysial Surface Remodeling
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Example Diaphysial Surface Remodeling
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Diaphysial SurfaceRemodeling Solution

• 8 steady-state solutions for a? and b? at
  remodeling equilibrium
• solutions depend on P, E and remodeling rate
  constants, Rp and Re, for given initial
  conditions, a0, b0 and T0zz

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Bone growth and remodeling Summary of key points

• Historical principles
• Wolffs Law
• Functional adaptation (stress-adaptive
  remodeling)
• Types of bone remodeling
• internal remodeling
• changes of bone density (and hence strength and
  stiffness)
• changes of trabecular architecture
• external remodeling
• changes of bone geometry
• Remodeling laws
• strain-energy dependent density remodeling
  (Carter)
• strain-dependent surface remodeling (Cowin)
• stress-dependent fabric tensor remodeling
  (Cowin)