Numerical Dose Calculations, Case Studies, and Treatment Planning in Radiation Therapy
1. Numerical Dose Calculations in Radiotherapy
Accurate dose calculations ensure optimal radiation treatment by delivering the required dose to the tumor while sparing healthy tissues.
1.1 Basic Dose Calculation Formula
The absorbed dose (D) in Gray (Gy) is calculated as:
D= E/m
where:
- D = Absorbed dose (Gy)
- E = Energy deposited (Joules)
- m = Mass of tissue (kg)
1.2 Example 1: Dose Delivered to a Tumor
Given:
- A 6 MV linear accelerator delivers 2.5 Gy per fraction.
- Total prescribed dose = 50 Gy.
- Patient receives radiation 5 days a week.
Find:
- The total number of fractions.
- The total treatment duration.
Solution:
Number of fractions=Total DoseDose/ per Fraction=50 Gy/2.5 Gy=20 fractions
Total duration = Number of fractions/Fractions per week = 20/5 = 4 weeks
Interpretation:
The patient will complete radiation treatment in 4 weeks with 20 fractions of 2.5 Gy each.
1.3 Example 2: Inverse Square Law in Radiation Therapy
The inverse square law states that radiation intensity (I) is inversely proportional to the square of the distance (d):
I2 = I1*(d1/d2)2
Problem:
A LINAC delivers 100 cGy/min at 100 cm from the source. Find the intensity at 150 cm.
Solution:
I2=100×(100/150)2 =100×(2/3)2
I2=100×9/4 = 44.4 cGy/min
Interpretation:
At 150 cm, the dose rate decreases to 44.4 cGy/min, emphasizing the importance of distance in dose control.
2. Case Studies in Radiotherapy
Case Study 1: Breast Cancer Treatment with External Beam Radiotherapy
Patient Profile:
- 52-year-old female with left-sided breast cancer.
- Stage IIA (T2N0M0).
- Treatment: Whole breast irradiation + boost to tumor bed.
Treatment Plan:
- External Beam Radiation Therapy (EBRT)
- Total dose: 50 Gy in 25 fractions (2 Gy/fraction).
- Technique: 3D Conformal Radiotherapy (3DCRT).
- Beam Arrangement: Opposed tangential fields.
- Boost Radiation
- Tumor bed dose: Additional 10 Gy in 5 fractions.
- Electron beam therapy to minimize deep tissue exposure.
Outcome:
- Acute effects: Skin erythema (resolves in weeks).
- Long-term effects: Reduced recurrence risk with minimal lung/heart exposure.
Case Study 2: Prostate Cancer Treatment with IMRT
Patient Profile:
- 65-year-old male with localized prostate cancer (Gleason 7, PSA = 10 ng/mL).
- Treatment: Intensity-Modulated Radiotherapy (IMRT).
Treatment Plan:
- Dose Prescription:
- Prostate target dose: 78 Gy in 39 fractions (2 Gy/fraction).
- Pelvic lymph nodes: 50.4 Gy in 28 fractions.
- Technique:
- IMRT with 7-9 beam angles to shape dose distribution.
- Daily image guidance (IGRT) for precise positioning.
Outcome:
- High tumor control probability (>90% 5-year survival).
- Minimal rectal and bladder toxicity due to IMRT dose shaping.
3. Treatment Planning Examples
Example 1: Brain Tumor (Glioblastoma) Treatment Planning
Objective:
Deliver an optimal dose to the tumor while sparing healthy brain tissue.
Plan Parameters:
- Total dose: 60 Gy in 30 fractions (2 Gy/fraction).
- Radiation type: 6 MV X-rays from a LINAC.
- Beam arrangement:
- 3DCRT with 5 fields
- IMRT for better dose conformity
Dose Constraints:
- Brainstem max dose: <54 Gy.
- Optic nerve max dose: <55 Gy.
Plan Evaluation:
- 95% of the target volume receives 60 Gy.
- Dose to critical organs is minimized.
Example 2: Lung Cancer Stereotactic Body Radiotherapy (SBRT)
Patient Profile:
- 70-year-old male, Stage I Non-Small Cell Lung Cancer (NSCLC).
- Tumor size 2.5 cm, inoperable.
Treatment Approach:
- SBRT technique with high precision.
- Total dose: 54 Gy in 3 fractions (18 Gy/fraction).
- Dose constraints:
- Spinal cord max dose: <18 Gy.
- Esophagus max dose: <27 Gy.
Outcome:
- High local tumor control (~90%).
- Minimal side effects compared to conventional radiotherapy.
4. Conclusion
- Dose calculations help ensure accurate and effective treatment.
- Case studies show how different cancers are managed with personalized radiation plans.
- Treatment planning balances tumor control with normal tissue sparing.
