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Nuclear structure
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A = mass number, #nucleons

Z = #protons

A-Z = #neutrons


Characteristic photon energy (higher j shell to lower i shell)
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Eij = Ej - Ei


Ejected Auger electon energy
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Eijk = (Ei - Ej) - Ek

(Ejected electron from higher k shell as a result of a transition from the higher j shell to the lower i shell)


Half life
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t1/2 = ln2/λ = 0.693/λ

A(t) = A0e-λt

A(t) = A0e-((0.693 x given time)/half-life)

 A0 = A(t)e((0.693 x given time)/half-life)


Effective half-life
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Effective half-life denotes the halving of radioactive material in a living organism by means of radioactive decay and biological excretion.

{\lambda_e} \, = {\lambda_p} \, + {\lambda_b} \,

 t_{1/2} = \frac{\ln (2)}{\lambda_e}

 t_{e} = \frac{t_{p}\times t_{b}} {t_{p} + t_{b}}.


Mean/average life
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tavg = 1.44t1/2

Total dose = (initial dose rate)(time)(1.44)


Specific activity
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SA=A/M=λ·NA/AW

NA= avogadro's number

AW= atomic weight

λ = disintegration rate


Time required to reach a certain activity
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t=1.44·t1/2ln[A(t)/A0]


Brachy exposure rate calc
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X=ΓA/d2

Γ= gamma constant (R·cm2/mg·hr)

A= radionuclide activity

d= distance from source


mgRaEq --> mCi
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mgRaEq = (Γradionuclide/ Γradium)(# mCi of radionuclide)

 # mCi of radionuclide = (Γradium/ Γradionuclide)(mgRaEq)


Brachy PDD
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PDD = Dose at distance d from surface of cylinder/dose a surface of cylinder.


Inverse square
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I2/I1 = (r1/r2)2


Inverse square factor
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ISF = [(SSDcal+dmax)/(SSDtreat+dmax)]2


Mayneord F-factor
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Standard table of PDD are usually generated at the calibration SSD.  It is sometimes necessary to increase the SSD in order to treat a large field.  Since PDD is dependent on SSD, thistable of PDD will not be correct for the new SSD.  The Mayneord F-factor five the PDD at the new SSD.

F={[(SSD2+dmax)/(SSD1+dmax)][(SSD1+d)/(SSD2+d)]}2

Mayneords F overestimates PDD at large SSD's.


PDD at different SSD's
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PDDSSD2=

PDDSSD1[(SSD1+d)(SSD2+dmax)/(SSD2+d)(SSD1+dmax)]2


Equivalent square
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=4A/P

or

=2ab/(a+b)


TMR (Tissue maximum ratio)
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TMR=TAR/BSF



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Electron cutout thickness to reduce dose to 5%
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For lead = electron energy/2mm

For cerrobend=1.2(lead thickness)


Gap Calc (S)
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S=S1+S2=(d/2)(L1/SSD1 + L2/SSD2)

Sn=(d/SSD)(Ln/2)

d= depth of junction

L= field length

If technique is SAD, this can be substituted for SSD.


CSI collimator angle
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Θcoll = arctan(L1/2·SSD)

L1= legnth of posterior spine field

SSD is for the posterior spine field


CSI couch kick angle
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Θcouch = arctan(L2/2·SAD)

L2= legnth of lateral cranial field

SAD is for the cranial field.


Hinge Angle

Wedge Angle


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HA=180-2WA

 WA = (180 - HA)/2


Half-value layer
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HVL=0.693/μ

 μ: linear attenuation coefficient


Tenth value layer
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TVL=3.32·HVL


Electron range, 90%, and 80% isodose
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Range=e-energy/2

80%=e-energy/3

90%=e-energy/4


TBI distance calc
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(desired field size/standard field size)SAD=treatment distance to obtain desired field size


Factors for TMR MU calc
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MU=dose/(CAL)(TMR)(TSF)(OAF)(WF)

CAL: Calibration factor

TMR: Tissue maximum ratio (dose at depth d/dose at d max)

TSF: Tissue scatter factor

OAF: Off axis factor

WF: wedge factor


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