Some variables used in this module
S1: The linearquadratic cell survival (S) for one fraction with dose dmin; the LQ S1(dmin), where K1 = 1S1.
K1: Probability of the cell kill for each healthy cell of a tissue volume (Vol) irradiated with dmin.
dmin: Dose per fraction that receives a tumor in its region with Dmin.
Dmin: Minimum dose of the dosevolume histogram (DVH) tumor.
Alfa: Parameter α of the LQ S(d) model for one fraction.
AlfaBeta: Parameter α/β of the LQ S(d).
NTC: Number total of cell in a volume Vol with cellular density Cden.
nvs: Number of virtual simulations.
nkc: Number of killed cells.
nslc1: Number of sublethally damaged cells in the first fraction.
nrc: Number of repaired cells.
CR: Probability of the cell repair for the sublethally damaged cells.
nslcj: Number of sublethally damaged cells in the j th fraction.
nudc: Number of undamaged cells.
gnum, gnum1 and gnum2: Randomly generated numbers
KSL: Maximum number between the gnum1 and (1gnum1).
NKC: Number total of killed cells.
NSLC: Number total of sublethally damaged cells.
TC: Counter of the condition of tumor control.
TCOK: Number of times that nkc ≥ NTC; i.e. Total cell kill (K) is equal to 100%
The proposed TPS will let to the radiation oncologists to decide the selection of the determined treatment parameters: dmin and n as part of the optimization/evaluation processes.
The selected DVH tumor must satisfy the condition: Dim/n = dmin. Our TCP methodology only involves Dmin.
When a living tissue tumor is irradiated in a fractionated treatment, the final result of this irradiation may be:1) All tumor cells are wholly killed; or 2) There is an amount of survived tumor cells. Due to these two possibilities, the effectiveness (Point 1) of the radiation oncology treatments is evaluated with TCP, which evaluates how likely a tumor control is to occur.
As is shown in the diagram of the Fig. 1, for simulating a fractioned treatment, one should consider:

The first fraction generates a mean nkc killed cells, nslc sublethally damaged cells, and nudc undamaged cells.

For the second and successive fractions, the three kinds of cells are analyzed in their possible final outcomes in each fraction.

The Matlab function rand is used for generating a random number gnum < = 1. The probability of meeting a killed cell (PMKC) is calculated as nkc/NTC, then if gnum < PMKC, the analyzed cell is died, but this is survived.

For a killed cell, the simulator will analyze a new cell; but for a survived cell, there are two possibilities: the cell is undamaged or sublethally damaged. The probability of meeting a sublethally damaged cell is defined with a new gnum > nslc/(nslc + nudc).

For an undamaged cell, if a new gnum < probability for K, this cell will die, but if gnum < = K + probability for SL, this is become in a sublethally damaged.

For a sublethally damaged cell (SLDC) there is a range of damage degree. Two new random numbers gnum1 and gnum2 are generated, and let us defining KSL = max(gnum1;1gnum1). If gnum2 < = KSL, the cell will die, but is kept as a sublethally damaged. The previous condition is associated to a major probability of killing the SLDC.

While the number of fractions increases, nkc increases, and nudc decreases. The nslc increases after the first fractions, and can increase or decrease and finally decreases after the second or successive fractions.

The cell repair is a temporalcellular process; and the number of repaired cells is determined after each fraction as: nrc = nslcjnslcj*CR.

If nkc ≥ NTC after n fractions, there is tumor control. The TCP is calculated as: TCP = TCOK/nvs.
As responsible of the radiation treatments, the radiation oncologists with collaboration of the medical radiation physicists will choose or estimate the values of the radiobiological and tissue parameters.
The steps for executing the simulator are:
a) Introduce for a tumor nonhomogeneously irradiated:
 dmin in Gy.
 α in Gy− 1
 α/β in Gy
 SL in %
 CR of the SLDCs during interfractions in %:
 Vol in mm3 (It is suggested using always values greater or equal than 1mm3)
 Cden in cells/cm3
b) Introduce for the virtual simulations:
 nvs (It is suggested using always values ≥ 30)
 n
c) Press the “For calculating” button for obtaining the simulated TCP
Given the tumor region with dmin has the maximum S; i.e. minimum cell kill (K), the simulations should be done only in this region, where radiation has the lowest probability of killing tumor cells. The Fig. 2 provides explanations about that.
The current radiosensitivity studies are described with S, which probabilistically is related with K, cell sublethal damage (SL) and cell undamaged (U) as K + SL + U = 1 (100%), where S = SL + U. Due to little available information of the SL, in many cases the SL values should be assumed taking into account that SL ≤ S. The TCPsim reports the LQ S(dmin) for being compared with the assumed value of the SL, which should be ≤ S.
The Table 2 and Table 3 show TCP reported in some references, and obtained with the TCPsim.
Table 2
Simulated mean TCP results and TCP values reported in their respective references. Abbreviations: ρ Cden; and Ref. Reference.
No.

dmin
[Gy]

α
[Gy− 1]

α/β
[Gy]

ρ*107
[cell/cm3]

SL
[%]

CR
[%]

n

Ref.

TCP reported
[%]

TCP simulated
[%]

Obs.

1

2

0.262

7

1

10

40

35

(5)

70

72

TCP reported for α/β = 10 Gy

2

3.1

0.307

10

1

25

40

20

(6)

80

85


3

18

0.06

5

0.01

1

10

3

(7)

85

80


Table 3
Simulated TCP in % for tumor characterized with α and α/β (0.307 Gy− 1 and 10 Gy respectively of (6); Cden = 107 cell/cm3; SL = 25%30%; and CR = 40%.
dmin [Gy]
n

10

15

20

25

30

1

0

0

0

3

10

1.8

0

2

50

67

92

2

0

7

57

82

97

2.5

0

13

61

85

99

3.1

0

15

85

97

100

3.5

0

56

88

99

100
