Relative Biological Effectiveness (RBE)

1. Introduction to RBE

The Relative Biological Effectiveness (RBE) is a measure used to compare the biological effectiveness of different types of radiation. It is defined as the ratio of the dose of reference radiation (typically low LET, such as γ rays) to the dose of the test radiation (typically high LET) that produces the same biological effect.

Mathematically, it can be expressed as:

RBE = dL / dH

Where:

dL is the dose of the reference (low LET) radiation.
dH is the dose of the high LET radiation.

Important Note:

The RBE varies depending on the type of tissue, the dose of radiation, and the radiation quality (e.g., LET). Higher LET radiations are generally more biologically effective due to increased energy deposition in a smaller volume of tissue.

2. Calculating RBE

Let's calculate the RBE using an example. Assume the following data:

Low LET dose, dL = 2 Gy
High LET dose, dH = 0.4 Gy

The RBE is calculated using the formula:

RBE = dL / dH

Let's compute it using Math.js:

Using Math.js for RBE Calculation:

Formula: RBE = dL / dH

Given: dL = 2 Gy, dH = 0.4 Gy

3. Example of RBE Calculation

Now, let's see the result using the following JavaScript code that evaluates the RBE using Math.js:

Computed RBE: