Module 3

Question 1

Beam theory

Answer 1

Distribution load q(x) = P/L
Deflection v(x) = LONG EQUATIONS
- first derivative = slope
- second derivative = moment
- third derivative = shear
Elastic foundation pushing back p(x) = k*v(x)

Question 2

Centroidal Axis

Answer 2

will not necessarily coincide with coordinate system of a moment applied to an unsymmetric beam and thus cannot assume the beam will bend in the coordinate plane.

Question 3

Fracture Fixation Devices

Answer 3

• immobilisation and surgery on fracture may facilitate healing
• similar to implants in that:
  1. need to be sufficiently stiff and strong
  2. be compatible with biological system (established for bulk materials but not always on a particle level)
• unique in that:
  1. device needs to be tuned to the changing biological state of the healing fracture
  2. rigidity should decrease as fracture heals (removal? reabsorb-able plates?) (unlike implants which are permanent)
• main material property is ductility for customisation to personal bone contours

Question 4

Replacing Articulating surfaces

Answer 4

• bearing surfaces must transmit normal joint loads and motion
• low friction is important as this decreases shear, thereby decreasing the chance of loosening and debris build up that can lead to infection
• metal/pe is therefore the best/most commonly used material combination as it is low friction
• at the surface, the pe component is forced to conform to the shape of the metal surfaces, exposing it to tensile, compressive and shear forces (whilst the metal component is considered a rigid body as its deformation is negligible).
• increased damage is a function of joint motion, time since implantation (ie. number of loading cycles) and increasing patient weight/magnitude.
  1. normal compressive stresses (contact stresses)
  2. tangential tensile and compressive stresses
  3. shear stresses

Question 5

Principal stresses

Answer 5

1. MIN principal stresses = the largest magnitude compressive stress
2. MAX principal stresses = the largest magnitude tangential stress

Question 6

Total Hip Replacement

Answer 6

• goal is to maintain normal kinematic and structural relationships
• if geometry is changed, ie. by head and cup placement, loads will change.
• load carried by the bone varies with stiffness of prosthesis (want to keep natural to avoid stress shielding and subsequent loosening - permanent implant)
• in a structure with parallel load paths, the stiffest path carries the greater load (calcar region).
• decrease in load carried by bone with increase in rp/rb and increase in Ep/Eb
• dont want to decrease in bending moment carried by bone (<40%)
• cemented or cementless? cemented if its the last implant (can cause damage if removed)

Question 7

Total Knee Replacement

Answer 7

• both femoral and tibial components are always replaced. may be tricompartmental, bicondylare or unicondylar.
• mimics the natural motion of knee better then hinged design.
• can control relative motion by controlling loads across the joint, geometry of articulating surfaces and the subsequent soft tissue requirements (work with existing/replace removed) ie. total condylar designs.
• required soft tissue (stability) partially unloads the implant, protecting critical interfaces and structures from failure.
• usually non-conforming. pitting is frequently observed as damage mode, contact changes as the knee flexes and extends. -> one point will always be subject to varying stresses.
• can decrease possibility of A-P liftoff by increasing flexural rigidity of beam, decreasing foundation stiffness (cannot change directly but will remodel positively or negatively dependent on the loads its experiencing) or decreasing beam length.
• however, curved M-L surfaces mean contact area will not shift to edge (ie. by medial directed component of ground contact force that causes varus moment), decreasing lift off and maximising conformity when radii are the same. but this decreases laxity necessary for soft tissue loading. If soft tissues can’t carry the load, the bone-implant interface may fail

Question 8

External Fixators (FFD)

Answer 8

• Pins dictate stiffness as they are the weakest component (as pins length increase stiffness decreases) -> stiffness equation is predominantly pin dependent. They incur most of the deformation.
• side bars and bone relatively much more stiff then pins
• allow the control of callus strain by changing the material of the side bars (to change the stiffness)
• can actuate the side bars to introduce controlled loads that encourage the bone to remodel towards healing

Question 9

Intramedullary Rods (FFD)

Answer 9

• Assume bone and rod to be concentric cylinders with the rod filling the intramedullary cavity
• at fracture site, rod alone may carry the load -> beam theory
• away from fracture site, rod and bone act as a unit -> composite beam theory

Question 10

Bone Plates (FFD)

Answer 10

• Must provide stability and not fail (analyse strength and stiffness)
• can be achieved through material propeties or could increase thickness to increase strength or use multiple plates at multiple locations
• plate geometry, stiffness and location must be carefully considered as to not decrease load borne by bone via an overshift in neutral axis. Bone remodelling is very sensitive to even small changes in cyclic stresses.
• Mechanical consequences of bone screw holes are typically ignored as stress concentrations of similar magnitude typically exist in heterogeneous bone.

Question 11

Finite Element Analysis

Answer 11

Can control element wise properties

• such as varying properties of bone ie. stiffness, thickness
• varying designs
• varying loading scenarios