Carter and Hayes tested how marrow, apparent density and loading rate shape the compressive strength and stiffness of trabecular bone.
In vitro compression tests of human tibial plateau and bovine femoral condyle trabecular cylinders, with and without marrow, from 0.001 to 10 per second.
Methods
Model
100 human tibial plateau trabecular cylinders
24 bovine femoral condyle trabecular cylinders
Constructs
Marrow left in situ vs marrow removed
10 human specimens per group at each strain rate
Loading
Confined compression (uniaxial strain) in a rigid steel annulus
Five strain rates from 0.001 to 10.0 per second
Porous upper platen that let marrow escape
Outcome measures
Compressive strength
Compressive modulus
Energy absorption
Regression on apparent density and strain rate
Key Findings
Compressive strength scaled with apparent density squared over a very wide density range (Sc = 68 ε^0.06 ρ², MN/m²).
Compressive modulus scaled with apparent density cubed (E = 3790 ε^0.06 ρ³, MN/m²).
Strength and modulus of both compact and trabecular bone rose only weakly with loading rate, roughly with strain rate to the 0.06 power.
Marrow raised stiffness, strength and energy absorption only at 10 per second (p < 0.01 for each), with no significant effect at the four slower rates.
That marrow effect came mainly from restricted viscous flow out through the test platen rather than through trabecular pores.
Applying their square law to cited densitometry showing ulnar density as low as one‑third of normal in osteoporosis, the authors suggest compressive strength falls to one‑ninth of normal.
Board pearl
In the Carter–Hayes relationships, apparent density rather than marrow governs trabecular bone mechanics at physiologic loading rates. Strength varies with density squared and modulus with density cubed.
Authors' conclusion
These power relationships, which were shown to hold for all bone in the skeleton, allow meaningful predictions of bone tissue strength and stiffness based on in vivo density measurements.
Carter and Hayes tested how marrow, apparent density and loading rate shape the compressive strength and stiffness of trabecular bone.
In vitro compression tests of human tibial plateau and bovine femoral condyle trabecular cylinders, with and without marrow, from 0.001 to 10 per second.
Methods
Model
100 human tibial plateau trabecular cylinders
24 bovine femoral condyle trabecular cylinders
Constructs
Marrow left in situ vs marrow removed
10 human specimens per group at each strain rate
Loading
Confined compression (uniaxial strain) in a rigid steel annulus
Five strain rates from 0.001 to 10.0 per second
Porous upper platen that let marrow escape
Outcome measures
Compressive strength
Compressive modulus
Energy absorption
Regression on apparent density and strain rate
Key Findings
Compressive strength scaled with apparent density squared over a very wide density range (Sc = 68 ε^0.06 ρ², MN/m²).
Compressive modulus scaled with apparent density cubed (E = 3790 ε^0.06 ρ³, MN/m²).
Strength and modulus of both compact and trabecular bone rose only weakly with loading rate, roughly with strain rate to the 0.06 power.
Marrow raised stiffness, strength and energy absorption only at 10 per second (p < 0.01 for each), with no significant effect at the four slower rates.
That marrow effect came mainly from restricted viscous flow out through the test platen rather than through trabecular pores.
Applying their square law to cited densitometry showing ulnar density as low as one‑third of normal in osteoporosis, the authors suggest compressive strength falls to one‑ninth of normal.
Board pearl
In the Carter–Hayes relationships, apparent density rather than marrow governs trabecular bone mechanics at physiologic loading rates. Strength varies with density squared and modulus with density cubed.
Authors' conclusion
These power relationships, which were shown to hold for all bone in the skeleton, allow meaningful predictions of bone tissue strength and stiffness based on in vivo density measurements.