Hydrodynamics in Porous Media with Applications to Tissue Engineering - Porous Media: Applications in Biological Systems and Biotechnology - page 76

3.5.3.1 Modeling of Transport Processes in Bone

Tissue-Engineered Implants ............................... 100

3.5.3.2 Microfluidic Bioreactor: A Numerical Driven

Experiment for Cartilage Culture ......................... 105

3.6 Conclusion .................................................................. 109

3.7 References ................................................................... 111

3.1 Nomenclature

Parameter Notation Unit

Substrate overall length scale L m

Porosity of the medium φ

Length scale of the pore a m

2 φ
a

m − 1

Specific pore wall area S V ≈

Effective pore length of the
sample

L P m

T = L p L 2

Tortuosity

K = φ (2 a ) 2
96

1
T

m 2 Porous medium permeability ×

φ 3
S V ×

= 1

6 ×

T

m − 3 Concentration of the

nutrient (oxygen, ...)
molecules

C mol ×

m − 3

Michaelis-Menten constant K M mol ×

cel − 1

sec − 1

Cellular nutrient maximal
consumption rate

V Max mol × ×

m − 2 sec − 1 Rate of nutrient

(oxygen, ...) consumption
by unit area

R S mol × ×

m − 2

Surface density of the cells σ cel cel ×

m − 2 sec − 1 Maximum ratio of cell oxygen

consumption

R max = σ cel × V max mol × ×

m − 3 sec − 1

Rate of nutrient (oxygen, ...)
consumption by unit
volume

R V = R S × S V mol × ×