**3.5 Calculation of EQD2 taking into account the reduction of days of treatment**

Irradiation is carried out according to the scheme of 6 fractions per week for 5 weeks. Dose per fraction is 2 Gr. EQD2 needs to be calculated.

The available data are entered; factions are mandatorily transferred to Saturdays. And the answer of 64.5 Gy is obtained (**Figure 8**).

## **3.6 Accounting for incomplete reparation with multi-fraction irradiation per day**

Irradiation of the head and neck tumor was planned with the parameters of a dose per fraction of 2 Gy 35 fractions, 5 fractions per week. The spinal cord accounts for 50 Gy (1.43 Gy per fraction). In order to reduce late complications before the treatment, it was decided to switch to 2 fractions per day with a six-hour break. It is necessary to calculate the dose per fraction and the equivalent dose to the spinal cord.

The solution to this problem consists of two stages. In the first stage, we find what dose per fraction is necessary to irradiate the tumor with an increase in the number of fractions by 2 times. To do this, we enter the data from the condition of the problem are entered. The situation, in which the number of days of treatment is doubled, is simulated. The desired value of 1.08 Gy is obtained (**Figure 9**).

At the second stage, it is necessary to pre-calculate from the proportion, which in this case is equal to the dose per fraction for the spinal cord. It is 0.77 Gy per fraction. Next, we simulate a situation in which irradiation is carried out 2 times a day. The value of a dose per fraction is changed until the values in the cells of the calendar are equal to 0.77 Gy. And the answer that the equivalent dose to the spinal cord in this case is 42.7 Gy is obtained (**Figure 10**).



#### **Figure 8.**

*Calculation of EQD2 taking into account the reduction of days of RT course.*

## *Linear Quadratic Model in the Clinical Practice via the Web-Application DOI: http://dx.doi.org/10.5772/intechopen.109621*


#### **Figure 9.**

*Accounting for incomplete reparation with multi-fraction irradiation per day. The first stage.*

### **3.7 Correction of errors in dose dispensing**

Irradiation of a lung tumor. Dose per fraction of 2 Gy for 33 fractions is planned. After the twentieth fraction, it was found that due to an error (prescription or normalization), 1.8 Gy was supplied instead of 2 Gy. How to correct the treatment?

To find the value to which it is necessary to correct the radiation dose, it is necessary to carry out several stages of working with the application. In the first stage, the values of the already treated 20 fractions of 1.8 Gy per fraction are entered and the equivalent dose is defined (**Figure 11**).

Further, using an intermediate calculation, it is necessary to find the difference in equivalent doses between the value of the equivalent dose planned for the end of the course and the value for the first 20 fractions of 1.8 Gy: ∆EQD = 66–35.4 = 30.6 Gy. After that, the values for the remaining 13 fractions are entered into the program and the value of a dose per fraction is selected, which will correspond to the obtained value of the equivalent dose of 30.6 Gy.

### *Radiation Therapy*


#### **Figure 10.**

*Accounting for incomplete reparation with multi-fraction irradiation per day. The second stage.*

#### **Figure 11.**

*Correction of errors in dose dispensing. The first stage.*

The equivalent dose is to be tracked. The value of the dose per fraction is changed so that the equivalent value is 30.6 Gy (**Figure 12**). In our case, this is 2.3 Gy. This means that it is necessary to adjust the dose per fraction to a value of 2.3 Gy.
