Population Balances in Biomedical Engineering: Segregation Through the Distribution of Cell States

Nomenclature

Symbol

Variable

Units

?

Cell age

Time

C P

Product concentration

Concentration

C S

Substrate concentration

Concentration

C Sf

Substrate feed concentration

Concentration

D

Dilution rate

Time -1

f( z, t)

Normalized distribution of states with respect to cell state parameter z

Inverse units of z

h( z)

A priori distribution of division states

Inverse units of z

m

Cell mass

Mass

M n

nth moment of f( z, t)

N( t)

Cell number concentration

Inverse volume

p( z, )

Distribution of birth states

Inverse units of z

r

Single-cell growth rate

(Unit of the state parameter)/time

t

Time

Time

W( z, t)

Cell number concentration distribution of states

(Volume units of z) -1

Y

Yield

(Rate of formation of z)/(rate of substrate consumption)

z

Arbitrary cell state parameter

?( z)

Division intensity

Time -1

?( z)

Dirac delta function

?( z)

Death intensity

Time -1

?

Specific growth rate of a population of cells

Time -1

v

Specific growth rate of a single cell

Time -1

?( z)

Distribution of division states

Inverse units of z

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