Physics of medical diagnosis and treatment. Four principal sub-fields: (i) radiotherapy physics — treatment planning, dosimetry, and quality assurance for tele- and brachytherapy (linear-accelerator beams, stereotactic radiosurgery,…
medical-physics
Beer-Lambert I(x) = I₀ exp(−μx): photoelectric + Compton + pair-production
Photon attenuation in matter under narrow-beam / good-geometry conditions follows the Beer-Lambert exponential law I(x) = I₀ · exp(−μ x),…
HVL = ln 2 / μ: thickness halving narrow-beam intensity
Half-value layer (HVL) is the thickness of absorber that halves the narrow-beam intensity under Beer-Lambert attenuation: I₀ · exp(−μ ·…
H = w_R · D: w_R(photon)=1, w_R(α)=20, w_R(neutron)=f(E)
Dosimetric quantities for radiation protection. Absorbed dose D (units gray, 1 Gy = 1 J/kg) is the physical energy deposited per unit mass…
μ·HVL = ln 2; TVL/HVL = log(10)/log(2) ≈ 3.32
Sympy-exact symbolic witness of the HVL / TVL relations. Step 1 — HVL from Beer-Lambert: I(HVL) = I₀ / 2 gives exp(−μ · HVL) = 1/2, thus μ…
exp(−μ·n·HVL) = 2^{−n}: 1/2, 1/4, 1/8 at n=1,2,3; 1/1024 at n=10
Sympy-exact symbolic witness of the multiplicative Beer-Lambert attenuation evaluated at integer multiples of the HVL. Setup: substitute μ…
w_R(α) = 20: 1 Gy α absorbed ⇒ 20 Sv equivalent
Sympy-exact symbolic witness of the ICRP 103 alpha-particle radiation-weighting factor w_R = 20 applied to a 1 Gy absorbed-dose scenario. …