Statistical calculation of beta radiotherapy dose using I-131: analysis and simulation method.

Radioiodine-131 (I-131) treats hyperthyroidism and differentiated thyroid carcinoma. In I-131, beta radiation (β−) is utilized for treatment and gamma radiation (γ) is used for diagnostic. This research sought to determine if a patient would be treated by establishing an equation for beta-thyroid cell interaction. The prospective study included 35 thyroid cancer patients receiving I-131 treatment. Beta and gamma readings were taken at different distances and sent to the statistical shop to find the coefficients of change on which the beta reaction depends and the equation that depends on it to find the beta range involved in healing. The strongest equation was R square (98.1%). To measure beta at 1 m, use the equation with a 99% association between variables and independent variables, and improve with ANOVA with a p-value of 0.00 0.05. The equation is: β_1m= -123.893+(0.947*δ) +(0.123*ε) -(0.002*π) -(2.11*Log Gamma). The discrepancy between true beta readings (mean = 1040) and the equation (mean = 1087, p-value = 0.411) is more than 0.05. That indicates the values are same. The equation that measures beta during iodine therapy has been achieved, which is the first step to improved thyroid cancer treatment.


1.Introduction
Global thyroid cancer rates are rising due to enhanced diagnostic imaging and monitoring.In 2015, 62,000 new instances of thyroid cancer were reported in both men and women, making it the fifth most prevalent cancer in women in the US [1][2][3][4][5].Tellurium dioxide is neutron-irradiated in a nuclear reactor to yield 131 I.The decay of 131 I results in stable 131 Xe with an 8.04-day half-life, emitting 606 keV β-particles and 364.5 keV gamma rays with 81.7% abundance.The abundance of β-particles peaks in 131 I is 89.9% per transition [6][7][8][9][10].
131 I decays into beta and gamma particles while treating thyroid cancer.Previous study only spoke about gamma particles that patients emitted after receiving radioactive sources 131 I but never addressed beta particles that treated thyroid carcinoma cells [11][12][13][14][15].
Radioiodine 131 I ablation is a standard treatment procedure for differentiated thyroid cancer (DTC) patients.This is followed by a whole-body scan (WBS) to discover leftover thyroid tissue or metastatic illness and ablation and treatment of any confirmation [16][17][18][19][20]. Differentiated thyroid

2.Methodology
The study population included two groups: group (A) got radioiodine 131 I for therapeutic dosages for remaining tissues following thyroidectomy surgery to ablate the thyroid, and Group (B) received 131 I for follow-up.
The nuclear medicine department at Al-Ahli Hospital in Palestine randomly chose 40 thyroid cancer patients (35 females, 5 males) with an average age of 44 years for males and 39 years for females.The radioactivity administered to individuals matched their weight.The quantity of radioactivity injected into group (A) ranged from 70mCi to 150mCi for therapeutic WBI, whereas group (B) received 5 mCi for follow-up diagnostic WBI.
The survey meter ATOMEX AT6130 measured dose rates of radiopharmaceutical 131 I samples at various distances, with the Geiger-Muller placed at 0, 50, 100, and 200 cm from the patient's side region.Gamma (γ) in (Sv/h) and beta (β) in (1/min×cm2) dose rates were measured for each patient.The radiation dose rate was assessed 48 hours after the 131 I injection in both groups.The data was analyzed using SPSS (25).
Ethical approval was obtained from the Al-Ahli Hospital/Hebron, NGO medium size Hospital, with the written consent of all patients before treatment.In addition, the identities and names of the patients were hidden to preserve their privacy before any access by the authors.

3.Results
Of the 40 participants, 87.5% were female and 12.5% were male, with an age ratio of 44.60 ± 17.30.193for men and 39.97 ± 9.56 for females.
Table 1 shows the correlation coefficient R between the dependent variable (gamma at 1 m) and the independent variable (beta at 1 m), which is (0.970), the square of the correlation coefficient (R square), which is (0.941), which shows the percentage of variation between the two coefficients (strongly dependently), and the ANOVA table, which shows ANOVA values of 0.00.The regression cubic equation for this relationship is shown in Equation ( 1): Where  is the gamma coefficient, and  the gamma measurement after 1m from the patient.
Radioactive activity fluctuates with time equation (2), thus the standard decay law may be used to calculate it: Where A1 is Activity after time; A0 the initial activity which given to patient; Teff is the effective half-life for 131 I; Tr is the time when the reading (measurement) done.The effective half-life can calculate using following equation (3): Where T (1⁄2 b) is the biological half-life for 131 I in the human body which equals to 6.3 day as the previous study shows [26][27][28][29][30][31][32][33]., and T1/2p is the physical half-life for 131 I which is 8.04 day.Table 2 displays the correlation coefficient R between the dependent variable (Activity) and the independent variable (beta at 1m), which is equal to (0.723), as well as the square of the correlation coefficient (R square), which is (0.523), which shows the percentage of variation between the two coefficients (moderate dependently), and the ANOVA table, which displays the value of (0.00), indicating a strong relationship between the variable's Activity and beta.The regression cubic equation using following equation ( 4 where ε is the activity amount coefficient, and A is the activity amount given to patient.Table 3 shows the correlation coefficient R between the dependent variable (weight) and the independent variable (beta at 1m), which is 0. 145, the square of the correlation coefficient (R square), which is 0. 021, which shows the percentage of variation between the two coefficients (mild dependently), and the ANOVA table, which shows a weak relationship between weight and beta.
Table 3. Weight coefficient confidence level and beta emission measurement.

Sum of Squares
Table 4 displays the correlation coefficient R between the dependent variable (height) and the independent variable (beta at 1m), which is equal to (0.303), as well as the square of the correlation coefficient (R square), which is (0.092), which shows the percentage of variation between the two coefficients (mild dependently), and the ANOVA table, which displays the value of (0.168), indicating a weak relationship between the variable's height and beta.The regression quadratic equation using looks to find the height coefficient ϑ following equation ( 6): Table 5 shows the correlation coefficient R between the dependent variable (Age) and the independent variable (beta at 1m), which is 0. 506, the square of the correlation coefficient (R square), which is 0. 256, which shows the percentage of variation between the two coefficients (mild to dependently), and the ANOVA table, which shows the value of 0. 013, indicating a strong relationship between Age and beta.This is the regression cubic equation to find the age coefficient π using equation ( 7  The strongest equation was R square (98.1%).Thus, the equation where the connection between the factors and the independent variable is 99% (very strong relationship) and the ANOVAa test with p-value 0.00 may be used to measure beta at 1 m with confidence.Equation ( 8 Using the equation.The discrepancy between actual beta readings with a mean of 1040 and the equation with a mean of 1087 and a p-value of 0.411 is more than 0.05 using Paired Samples Test (see Table 6).That indicates the values are same.The equation to determine beta may use the error rate, which is less than 2% see Figure 1.

4.Conclusion
The study showed that activity quantity, Gamma, and age coefficients dominate outcomes.This equation provides the beta range for thyroid therapy with According to this study, the researcher suggests: Using this equation to establish the patient's dosage based on beta's interaction with thyroid cancer cells; the researcher suggests extending West Bank research and investigation.Finally, thorough research should examine the association between age and therapy.

Figure 1 .
Figure 1.A relationship between real measurement and equation measurement for beta particle.

Table 1 .
Gamma coefficient confident level affecting on beta emission measurement.

Table 2 .
Activity amount coefficient confidence level and beta emission measurement.

Table 4 .
Height coefficient confidence level and beta emission measurement.

Table 5 .
Age coefficient confidence level and beta emission measurement.

Table 6 .
Differences between the real measurement of beta using device and the measure using equation.