RTH-00 · laboratory
LQ, BED, TMR, equivalent square, Clarkson scatter and MU calculation.
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32 governing sheets
S = e^{−αD−βD²}. Cell-survival LQ model.
RadiobiologyBED = n d (1 + d/(α/β)). n fractions of d Gy.
RadiobiologyEQD2 = D (d + α/β)/(2 + α/β). The 2 Gy-fraction isoeffect.
RadiobiologyTMR(d) = D(d)/D(dmax) at fixed SAD. The SAD cousin of PDD.
Beam dataPDD = 100 e^{−μ(d−dm)} ((SSD+dm)/(SSD+d))². Inverse-square plus attenuation.
Beam dataMU = D / (Ḋ_cal (SCD/r)²). Calibration output scaled by inverse square.
Monitor unitss = 2ab/(a+b) = 4A/P. Sterling's equivalent square.
Beam dataS = (1/n) Σ SAR(r_i). Irregular-field scatter by circular sectors.
ScatterF = [((SSD2+dm)/(SSD1+dm)) ((SSD1+d)/(SSD2+d))]². Converts PDD between SSDs.
Beam dataTPR(d,dref) = D(d)/D(dref) at fixed SAD. TPR20,10 indexes beam quality.
Beam dataS_{c,p}(s) = 1 + m log(s/10). Relative output versus 10 cm square.
OutputWF = D_wedge / D_open on the central axis.
OutputD(x) = D0 exp(−½ (x/σ)²). A Gaussian look at an off-axis point.
ProfilesOAR(x,d) = D(x,d)/D(0,d). The relative profile at depth d.
ProfilesD_SAD / D_SSD = ((SSD+d)/SAD)². Inverse-square between the two setups.
GeometryP = s (SSD − SDD)/SDD. Source size s seen through the diaphragm.
ProfilesD(z) = Dmax (1 − e^{−z/z0}). Charged-particle equilibrium growing in.
Beam dataRp (cm water) ≈ E(MeV)/2. The bedside rule of thumb.
ElectronsRp = 0.521 E − 0.376 (cm water, E in MeV). ICRU-style fit.
ElectronsR50 = E0 / 2.33. Depth of 50 % dose indexes the mean energy.
ElectronsDw = M kQ ND,w PTP. Chamber reading to water dose.
Calibrationθ = arctan((z_toe − z_heel)/x). Tilt of an isodose between toe and heel.
Wedgesg = ½ L1 d/SSD1 + ½ L2 d/SSD2. Adjacent fields match at depth d.
MatchingD_j / D0 ≈ 1 + k Δg / P. Gap error times penumbra slope.
MatchingHI = (D2% − D98%)/D50%. Zero is a perfectly flat PTV.
Plan qualityCI = (TV_PIV)² / (TV × PIV). Unity is a perfectly conformal cloud.
Plan qualityGI = V50% / V100%. How fast the dose falls outside the target.
Plan qualityNTCP = Φ((D − TD50)/(m TD50)). Probit of a uniform organ dose.
RadiobiologyTCP = exp(−N0 S), S = e^{−αD−βD²}. Zero clonogens left.
Radiobiologyα/β = (n2 d2² − n1 d1²)/(n1 d1 − n2 d2). Two equal-BED schedules.
RadiobiologyG = 2(μT − 1 + e^{−μT})/(μT)². Lea–Catcheside for a pulse of length T.
RadiobiologyS_h = exp(−α D/OER − β D²/OER²). Oxygen-rescaled LQ.
Radiobiology