Biomedical Engineering Reference
In-Depth Information
i.
Consider a six-stage differentiation process (N
6), in which the last population, X
6
,
produces a cytokine, G, at a per-cell rate of q
G
. This cytokine has a half-life of t
0.5
(
¼
¼
2 hrs)
fn([G]), where [G] is the
concentration of the growth factor G. Extend the base set of differential equations to
describe the dynamics of [G].
ii.
Incorporate into the equations
and influences the growth rate of the stem cells—that is, u
1
¼
u
1
ð½
G
Þ ¼
u
=ð
1
þ
K
½
G
Þ
where K is the binding constant for the growth factor. What does the function f([G])
describe physiologically?
iii.
Make the equations dimensionless using the growth rate as the scaling factor for time, and
K for the cell concentration.
iv.
Describe the meaning of the dimensionless groups and estimate their numerical values.
v.
Obtain the numerical values for a simulation starting from a single stem cell. Examine the
effect of varying the numerical values of the parameters.
vi.
Obtain the numerical values for a simulation starting from the steady-state solution and
perturb the value of X
3
by 20 percent. Discuss your results.
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