ABR Equations

Field Size Correction Factor (FSCF)

FSCF = S_cS_p

Collimator Scatter and Phantom/Patient Scatter

Field matched gap size

gap = depth / 2 * (Field1/SSD + Field2/SSD)

SAD = SSD for this procedure

Hinge Angle, Φ

θ = 90 - Φ/2

θ is wedge angle

CTDI calcs.. (CTDI, CTDI_w, CTDI_vol)

CTDI = DL/T

CTDI_w = (1/3)CTDI_center + (2/3)CTDI_periph

CTDI_vol = CTDI_w / pitch

number of field junctions for whole body

Junction # = Dose / (Tolerance - dose)

spinal cord tolerance = 4500 cGy

Sensitivity of a diagnostic test

TP / (TP + FN)

Sensitivity = True Positive Fraction

Specificity of a Diagnostic test

TN / (TN + FP)

Specificity = True Negative Fraction

Positive Predictive Value

TP / (TP + FP)

Negative Predictive Value

TN / (TN + FN)

Accuracy of a Diagnostic test

(TP + TN) / (TP + FN + FP + FN)

False Positive Fraction

FP / (FP + TN)

CNR (Contrast to Noise Ratio)

CNR = (N_s - N_bg) / σ_bg

Doppler shift

Δf = 2f_tvcosθ / c

f_t = transmitted freq

c = speed of sound

Image magnification

M = SID / SOD

SID = Source to image receptor distance

SOD = Source to object distance

Collimator Grid ratio

Grid ratio = grid height / interspace distance

Impedance of Quarter Wave Matching Layer (between skin and PZT)

Z_QWM = sqrt(Z_PZT* Z_skin)

Geometric mean of PZT and skin impedances

Linear Quadratic Model

S(D) = exp(-αD-βD²)

S(D) is surviving fraction given a dose

αD is probability of cell death due to “single hits”

βD² is probability of cell death due to “double hits” (sparsely ionizing)

Biologically Effective Dose (BED)

BED = nd[1 + d / (α/β) ]

n is number of fractions

d is dose per fractions

Equivalent Dose (EQD)

EQD_x = nd{ [d + (α/β)] / [x + (α/β)] }

x is dose per fraction

EQD₂ is most often used for fractionation schemes (“2 Gray per day”)

Bremsstrahlung efficiency

Z*E(9×10^-9)

convert Air Kerma Strength (U) from mCi

U = X_mCi ∗ Γ ∗ f

mg-Ra equivalent

mg-Ra equivalent = X_mCi ∗ (Γ_x / Γ_Ra)

Effective Diameter from rectangular field

sqrt(AP ∗ LAT)