SME
Tissue Engineering
Scaffolds
Use this for “A PCL scaffold weighs 0.229 g/cm³; solid PCL is 1.145 g/cm³ with E = 400 MPa. How porous is it, and how stiff?”
Diagram
ρ∗
÷
ρₛ
=
0.229
1.145
=
0.2:
the
struts
are
0.287
of
a
cell
wide,
so
3
(0.287)
2
−
2
(0.287)
3
=
0.2
of
each
cell
is
solid
and
80%
is
pore.
Open
cells
bend
at
their
struts:
E∗
=
Eₛ
(ρ∗ ÷ ρₛ)
2
=
400
×
0.2
2
=
16
MPa.
This is an example. Type your own values to start a new problem.
ρᵣₑₗ
=
ρ∗ (g/cm³)
÷
ρₛ (g/cm³)
P
%
=
(1
−
ρᵣₑₗ
)
×
100%
E∗ (MPa)
=
Eₛ (MPa)
×
ρᵣₑₗ
2
Formulas
ρᵣₑₗ = ρ∗ ÷ ρₛ
0.2
=
0.229
1.145
P
=
100
×
(1
−
ρᵣₑₗ)
80 = 100 × (1 − 0.2)
E∗
=
Eₛ
×
ρᵣₑₗ
2
16
=
400
×
0.2
2
Assumptions
•
The scaffold is an open-cell foam whose struts bend under load (Gibson–Ashby).
•
The pores connect, and the struts are one solid material of density ρₛ.
•
The pores hold no mass, so the scaffold weighs only its solid share: ρ∗ < ρₛ.
Step-by-step
WE KNOW
ρₛ = 1.145 g/cm³, ρ∗ = 0.229 g/cm³, Eₛ = 400 MPa
FIND
relative density (ρᵣₑₗ), porosity (P), modulus of the scaffold (E∗)
Step 1 · Find relative density (ρᵣₑₗ)
Use ρᵣₑₗ = ρ∗ ÷ ρₛ
The scaffold weighs this share of the same volume of solid: its solid share.
ρᵣₑₗ
=
0.229
1.145
ρᵣₑₗ = 0.2
Step 2 · Find porosity (P)
Use P = 100 × (1 − ρᵣₑₗ)
What is not solid is pore; times 100 makes it a percent.
P
=
100
×
(1
−
0.2)
P
=
100
×
0.8
P
=
80%
Step 3 · Find modulus of the scaffold (E∗)
Use E∗ = Eₛ × ρᵣₑₗ²
Struts that bend make the stiffness fall as the relative density squared.
E∗
=
400
×
0.2
2
E∗ = 400 × 0.04
E∗ = 16 MPa
Check
Put the numbers back in. Both sides should match.
0.2
=
0.229
1.145
✓
80 = 100 × (1 − 0.2) ✓
16
=
400
×
0.2
2
✓
Topic check
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