A Composite Synergistic Systems Model for Exploring the Efficacies of Different Chemotherapeutic Strategies in Cancer
Table 1
(a) Initial parametric values for simulation. (b) Initial parametric values (assumed) of HSC for simulation. (c) () cross-section along with initial microvessel diameter in micrometer, TAF concentration in ng/L, and FNT concentration in ng/L. Positional coordinates are shown in parentheses. Presently used values are shown in bold while the other values are kept the same as those mentioned in previous works [22, 23]. (d) Change in doubling time of the tumor cells depending on the different vasculature ranges during the course of dynamics [25]. For initialization, we have considered that tumor cells have crossed a stage of dormancy but having ample microenvironment (in terms of MV/MVD) for their growth. The parametric values are the same as those depicted in the earlier work except the second column (values of MV diameters are assumed) of the table. The values in the parentheses of the third and fourth columns of the table indicate the multiplication rate corresponding to the doubling time.
(a)
Variable
Symbol used in model
Unit
Value
Comment
VG
FD
Tumor cell (sensitive type) count
Number of cells
Initial value at the time of diagnosis
Tumor cell (resistive type) count
Number of cells
Initial value at the time of diagnosis
Microvasculature (MV) cell count
—
Number of cells
(VG)
Initial value at the time of diagnosis
Microvasculature (MV) diameter
—
m
10 (FD)
Initial value at the time of diagnosis
Multiplication rate of sensitive cells
Cells/day
Table Id
—
Multiplication rate of resistive cells
Cells/day
Table Id
—
Conversion rate of sensitive to resistive cells
Cells/day
†0
In presence of exogenous HSC, it changes to 0.001
Conversion rate of resistive to sensitive cells
Cells/day
†0
—
Anoxia sensitivity of sensitive-type cells
% of cells
†1.0 (VG), 1.0 (FD)
Full sensitivity Value for FD is assumed
Anoxia sensitivity of resistive-type cells
% of cells
†0.5 (VG), 0.5 (FD)
Half of the total cells resist Value for FD is assumed
AAG drug sensitivity of TAF
% of TAF concentration
*0.25
th amount of existing TAF will be inactivated
Duration between two successive AAG drug applications
Day
*15
Once in two-week interval
Amount of AAG drug dose
Fraction of cell killing and/or TAF concentration decrease per day
†0.25
On the day of drug application, fraction of MV cells destroyed and/or fraction of TAF concentration reduced
Amount of AAG drug retention on the subsequent day of drug application
% of drug of the preceding day
†80% (VG), 80% (FD)
Effectiveness decay, reaches almost zero after 10 days Value for FD is assumed
Chemotherapeutic drug sensitivity of sensitive-type cells (MCT/MTD)
% of cells
*0.9 (MTD), *0.9 (MCT)
90% cells are sensitive to drug Value for VG is assumed
Chemotherapeutic drug sensitivity of resistive-type cells (MCT/MTD)
% of cells
*0.3 (MTD), *0.3 (MCT)
30% cells are sensitive to drug Value for VG is assumed
Chemotherapeutic drug sensitivity of MV cells (MCT/MTD)
—
% of cells
0.5 (MTD), 0.5 (MCT)
Effect of MTD on MV cells is calibrated with a multiplying factor 15 Value is assumed
Chemotherapeutic drug sensitivity of MV diameter (MCT/MTD)
—
% of cell diameter
*0.5 (MTD), *0.5 (MCT)
Effect of MTD on MV diameter is calibrated with a multiplying factor 107
Chemotherapeutic (MCT) drug sensitivity to TAF
—
% of TAF concentration
*0.25
th amount of existing TAF will be inactivated
Duration between two successive MCT/MTD chemotherapeutic drug applications
Days
*1 (MCT), *21 (MTD)
Daily application of drug in MCT and once in three weeks in MTD
Chemotherapeutic drug dose (MCT/MTD)
Fraction of cell killing and/or MVD reduce and/or fraction of TAF concentration decrease per day
0.0079 (MCT), 0.1667 (MTD)
Multiplying factor 1.25 (MCT) and 1.5 (MTD). Hence, effective dose 0.01 (MCT), =0.25 (MTD) Values are assumed
Amount of chemotherapeutic drug (MCT/MTD) retention on the subsequent day of drug application
% of drug of the preceding day
*90%
Retention of 90% drug of the previous day drug amount Value for VG is assumed
MTD drug sensitivity of sensitive-type cells in strategy 2
% of cells
*0.9
90% cells are sensitive to drug Value for VG is assumed
MTD drug sensitivity of resistive-type cells in strategy 2
% of cells
*0.3
30% cells are sensitive to drug. Value for VG is assumed
MTD drug sensitivity of MV cells in strategy 2
—
% of cells
0.5
Value is assumed Effect of MTD on MV cell is calibrated with a multiplying factor 15
MTD drug sensitivity of MV cell diameter in strategy 2
—
% of cell diameter
*0.5
Effect of MTD on MV diameter is calibrated with a multiplying factor 107
MTD drug dose in strategy 2
Fraction of cell killing and/or MVD reduction per day
0.1667
Value is assumed Multiplying factor 1.5. Hence, effective dose = 0.25
Amount of MTD drug retention on the subsequent day of drug application in strategy 2
% of drug of the preceding day
*90%
Retention of 90% drug of the previous day drug amount
Coefficient denoting both types of tumor cells supported by one MV cell (VG)
—
Ratio
†500 (VG)
Derived from initial values supplied for , , and
Parametric value is taken from [18, 22, 23]. †Parametric value is taken from [25].
(b)
Variable
Symbol used in model
Unit
Value
VG
FD
Count
Number of cells
1
Multiplication rate
% of cells
2%
Apoptosis rate
% cells
2.1%
Conversion rate to vasculature
% change to cell number (VG), % change to MVD (FD)