Patient specific finite element analysis of femur and tibia

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Patient specific finite element analysis of femur
and tibia

• Sune H. Pettersen

Norwegian orthopaedic implant research unit, St.
Olavs Hospital. Department of structural
engineering, NTNU.
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Why use FE analysis?

• Bone adapts to loading
• FE models helps us understand changes in the bone
  tissue
• Improve prosthetic design
• Diagnostic use
• Risk of femoral neck fracture?
• Assess fracture healing
• Stability of leg lengthenings
• We have
• General descriptive FE models.
• We want
• Predictive patient specific FE models.

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Bone tissue

• Cancellous bone
• Porosity 75-95
• E 500 MPa

• Cortical bone
• Porosity 5-10
• E 20 GPa

• Callus tissue (immature bone)
• Porosity ?
• E ?

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Building the FE models

• Mechanical properties related to porosity (BV/TV,
  ?app) and/or mineralization (?min ). E f(?)
• Computed tomography (CT)
• Segmenting the scans to retrieve geometry.
• Pixel attenuation values (HU) to assess local
  mechanical properties HU g(?, wfi,CT
  parameters) ? ? h(HU)

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Case I Tibial lengthening
Callus distraction latency period (1 week),
distraction phase (1-2 months), consolidation
phase (6-8 months) When can we remove the
frame??? Can we use CT and FE analysis to
determine the stability?
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Step I Properties of callus tissue

• Aro et al. (1989), Rat
• Flat indentation (Modified Brinell hardness)
• Porosity , Ca2 µg/mm3.
• Markel et al. (1990), Dog
• Spherical indentation
• Porosity , Ca2 mg/g dry weight.
• Normalize their results
• Composition ?wet, wfmineral, wfcollagen, wfwater
• Mechanical properties Youngs modulus.

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Composition of callus tissue

• wfwater ?-3, R20.95
• wfmin. 0.7(?-1), R20.95
• wfcoll. 1- wfmin. - wfwater,
• R20.52

?app. ?(wfwater -1) ?min.. ?wfmin.
The results also correspond very well with weight
fractions of highly mineralized tissues (Hellmich
and Ulm 2002).
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Aro et al. Flat indentation

• We need a1E/ I1
• Given a, h and I1 (modified Brinell hardness,
  MBH).
• FEA Axisymmtric mesh, varying Youngs modulus
  (50MPa-25GPa) and ? (0.1-0.5).
• Analytic solutiona1 p (1 ?2)/(2 ?),
  where ? f(a/h, ?)

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Aro et al. Flat indentation (cont.)

• Dependent of aspect ratio (a/h 0.17) and ?.
• Independent of E and ?o Assuming ? 0.3 ? a1
  E/I1 1.28

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Markel et al Spherical indentation

• We need a2E/ I2
• Given a, h, and I2 at ?o0.375mm
• FEA Axisymmtric mesh, varying Youngs modulus
  (50MPa-25GPa) and ? (0.1-0.5).

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Markel et al Spherical indentation (cont.)

• Dependent on ?o and ?.
• Independent of E Assuming ? 0.3 ? a2 E/I2
  1.28

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Material properties of callus tissue
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Step II FE analysis of callus distraction

• Patient CT scanned 4 ½ months after end of
  distraction and 2 months later directly after
  removal of fixation.
• FE model, brick elements.
• Dwyer et al. (1996) Safe level, SB 15Nm/o

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FE models and load cases
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Material properties
Q Which material model is most representative of
callus distraction in late consolidation phase?

• Callus tissue
• E 201? -201
• Open cell porous bone
• E 70 802?2app
• Closed cell porous bone
• E 3790?3app e0.06,
• e0.06 0.53 (Harp Aronson 1994)

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Results of FE analyses
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Discusssion

• Dwyer et al. (1996) safe level of bending 15
  Nm/o
• Callus tissue not representative of distracted
  callus in late consolidation phase.
• Closed cell porous bone bending stiffness
  slightly above safe level at final state.
• Open cell porous bone bending stiffness beneath
  safe level at final state.
• Human porous bone is dominated by open cell
  structure? Material properties of open cell
  porous probably most representative of
  distracted callus in late consolidation phase

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Case II Stress shielding around femoral
prosthetic stem
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dePuy strain study

• 11 pairs of human cadaver femurs
• Intact femur, implanted femur
• 3 types of prostheses

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FE model of femur
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FE model of femur

• 2. order tetrahedral elements
• Use CT attenuation to assign local material
  properties to elements
• Orthotropic material for compact bone
• Load cases represent max. forces during gait
  cycle ? ignore yielding
• Static loading ? ignore viscoelasticity