Radiology Physics Equations

Front 1

Equation for quantiative transmission (ie how many photons penetrate through a certain substance)

Back 1

N = No x e^-ut

No= # of original photons
u- linear attenuation coefficient
t= thickness

Front 2

Grid Ratio

Back 2

grid ratio = H/W

H=height of lead
W= width of gap

Front 3

Bucky Factor

Back 3

BF = dose to patient with grid/dose to patient without grid

Front 4

Minification gain

Back 4

input area/output area

i.e.
(di/do)^2
di=input diameter
do=output diameter

Front 5

Brightness gain

Back 5

flux gain x minification gain

Front 6

CTDIvol

Back 6

CTDIvol=CTDIw/Pitch

Front 7

Dose length product (DLP)

Back 7

DLP = CTDIvol x scan length

Front 8

# of nuclei at time t (Nt)

Back 8

Nt = No e^-h-t

No= # of original nuclei
h=decay constant
t=time

Front 9

Decay constant (h)

Back 9

h = 0.69/T1/2

*long T1/2 = short h

Front 10

Activity

Back 10

Activity = h Nt

Front 11

Cummulative Activity

Back 11

A = 1.44 x f x initial activity x effective half life

A= cummulative activity
f = 1 for whole body (different weights for different organs)

Front 12

Effective half life

Back 12

1/Te = 1/Tp + 1/Tb

Te= effective half life
Tp= physical half life
Tb = biological half life

Front 13

Dose to a a particular organ

Back 13

D = S x A

S= S factor (from a book)
A =Activity

Front 14

Hounsfield Units

Back 14

HU = 1000 (ux - uwater)/uwater

ux = annenuation of material
uwater = attenuation of water

Front 15

Pitch

Back 15

Pitch = D/W

D= distance per revolution
W= beam width

Front 16

Wave equation

Back 16

velocity = frequency x wavelength

Front 17

Acoustic impedance

Back 17

Acoustic impedance (Z) = p x v

p = density
v= velocity

Front 18

Wavelength based on transducer thickenss

Back 18

wavelength = 2 x trasnducer thickness

Front 19

Pulse length

Back 19

pulse length = 2 * wavelength

Front 20

Near field in US

Back 20

near field = r^2 x wavelength

r = radius of transducer

Front 21

Axial resolution in US

Back 21

Axial resolution = SPL/2

Front 22

fractional SD

Back 22

SD = 1/sqrt N

Front 23

Power

Back 23

power = voltage x current

measured in watts (joule/s)

Front 24

Energy

Back 24

energy = power x time

measured in joules

Front 25

Best achievable digital resolution

Back 25

best achievable digital resolution = 0.5 x (1/pixel size)

Front 26

Sensitiivty

Back 26

Sensitivity = TP/(TP + FN)

Front 27

Specificity

Back 27

Specificity = TN/(TN + FP)

Front 28

Accuracy

Back 28

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

i.e. true positives and true negatives /over everything

Front 29

Prevalence

Back 29

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

i.e. true positives + things that are actually true but were construed as false/over everything

Front 30

Positive predictive value

Back 30

PPV = TP/(TP + FP)

Front 31

Negative predictive value

Back 31

NPV = TN/(TN + FN)

Front 32

Mass attenuation

Back 32

u/p

u = linear attenuation coefficient
p= density thus mass attenuation is independent of density!

Front 33

HVL

Back 33

HVL = 0.693/u

u = linear attenuation coefficient

Front 34

Photon energy

Back 34

E = h f = h (c/wavelength)

f= Planck's constant
c= speed of light
f= frequency

Front 35

Inverse square law

Back 35

(x1/x2)^2

x1 = distance 1
x2 = distance 2

Front 36

optical density

Back 36

OD = log (Io/It)

Io = light incident on film
It = light transmitted