Table 2 Model parameters
Paramaters | Value | Units | Description |
|---|---|---|---|
t 0 | 35 | years | minimum time considered by system, in days |
t τ | 40 | years | time in which transplantation occurs, in days |
k e | 1 | μ g/l/year | constant environment antigen entry into the body |
k xec | 1.5 | μ l/cell/year×10−3 | second order C dependent E elimination rate constant |
k xsc | 0.15 | μ l/cell/year×10−3 | second order C dependent S elimination rate constant |
k xlc | 0.7 | μ l/cell/year×10−3 | second order C dependent L elimination rate constant |
k xuc | 0.5 | μ l/cell/year×10−3 | second order C dependent U elimination rate constant |
k xyc | 0.5 | μ l/cell/year×10−3 | second order C dependent Y elimination rate constant |
k xzc | 1 | μ l/cell/year×10−3 | second order C dependent Z elimination rate constant |
k xe | 1 | year−1 | first order elimination rate from compartment E |
k xl | 0.7 | year−1 | first order elimination rate from compartment L |
k xu | 0.001 | year−1 | first order elimination rate from compartment U |
k xy | 0.001 | year−1 | first order elimination rate from compartment Y |
k xz | 1 | year−1 | first order elimination rate from compartment Z |
k ls | 1.5 | year−1 | first order transfer rate from compartment S to L |
k zy | 6 | year−1 | first order transfer rate from compartment Y to Z |
k xc | 1 | year−1 | first order elimination rate from compartment C |
k xce | 1 | l/μ g/year | second order E dependent C e elimination rate constant |
k xcs | 0.02 | l/μ g/year | second order S dependent C l elimination rate constant |
k xcl | 0.02 | l/μ g/year | second order L dependent C l elimination rate constant |
k xcu | 0.02 | l/μ g/year | second order U dependent C u elimination rate constant |
k xcy | 0.02 | l/μ g/year | second order Y dependent C z elimination rate constant |
k xcz | 0.02 | l/μ g/year | second order Z dependent C z elimination rate constant |
k c | 0.3 | cell/μ l/year×103 | basal lymphocyte production |
k s | 2 | 1/year | first order S dependent S production and elimination rate |
constant | |||
S ∗ | 7 | μ g/l | allograft maximum regeneration rate |
κf | 0 | ng/ml/year | drug delivery rate - scenario 1 (no drug treatment) |
κf | 36500 | ng/ml/year | drug delivery rate - scenario 2 (moderate drug treatment) |
κf | 127750 | ng/ml/year | drug delivery rate - scenario 3 (high drug treatment) |
k xf | 365 | 1/year | first order elimination rate from compartment F |
k cacF | 2.92 | l/μ g/year | T-cells production rate (T-cells clonal expansion), A and c |
dependent | |||
S τ | 1000 | μ g/l | antigen S concentration at time t τ |
U τ | 1000 | μ g/l | antigen U concentration at time t τ |
Y τ | 1000 | μ g/l | antigen Y concentration at time t τ |
λ | 0.01 | ml/ng | k cac decreasing coefficient, F dependent |
E 0 | 1.38 | μ g/l | E initial condition |
S 0 | 0 | μ g/l | S initial condition |
L 0 | 0 | μ g/l | L initial condition |
U 0 | 0 | μ g/l | U initial condition |
Y 0 | 0 | μ g/l | Y initial condition |
Z 0 | 0 | μ g/l | Z initial condition |
F 0 | 0 | ng/ml | F initial condition |
C e 0 | 1.1 | cell/μ l×103 | C E value at t=t0 |
C l 0 | 0.3 | cell/μ l×103 | C L value at t=t0 |
C u 0 | 0.3 | cell/μ l×103 | C U value at t=t0 |
C z 0 | 0.3 | cell/μ l×103 | C Z value at t=t0 |