RadPhysics E12a: MU Calculations (SSD & SAD Formulas)

Welcome back to the RadOnc Smart Review Physics Series! We've gathered all the ingredients: Calibrated Output (CAL), Output Factors (Sc,p), Beam Modifiers (WF, TF), and Patient Attenuation Factors (PDD, TMR). Now, in Episode P12a: MU Calculations (SSD & SAD Formulas), we finally put them together! We'll construct and explain the complete formulas used to calculate Monitor Units (MUs) for both common treatment techniques: fixed Source-to-Surface Distance (SSD) and isocentric Source-to-Axis Distance (SAD).

Episode Transcript

(00:00):
Welcome back to Radonk Smart Review Physics Edition.
We've we've spent quite a bit oftime laying the groundwork in
previous sessions, talking aboutmachine calibration, dose
distributions, all sorts of, youknow, correction factors like
output factors and modifiers. Today was going to pull it all
together for something absolutely fundamental.

(00:22):
Calculating the monitor units needed for external beam
radiation therapy. The MUS.
That's right, this is really where the rubber meets the road,
isn't it? You've designed a treatment
plan, you figured out the dose you want to deliver, and now you
need to tell the linear accelerator, the linac, exactly
how many pulses of radiation, how many Mus it needs to produce

(00:42):
to well to achieve that prescribed dose right at the
target location. Yeah, and it's not just like
simple arithmetic. It's the critical link between
the physics of the machine and the actual dose the patient
receives. Getting this right is just,
well, it's non negotiable for accurate and safe treatment
delivery. So we're going to walk through
this step by step today, focusing on the 2 main
techniques you'll encounter pretty much daily SSD that's

(01:06):
source to surface distance setups and SAD or source to
access distance setups. And our goal here is for you to
not only you know know the formulas, but to really
understand the logic behind eachterm.
By the end of this session, these calculations should
hopefully feel less like rope memorization and more like a
logical process, like you're accounting for how your specific

(01:29):
treatment setup differs from themachine sort of ideal
calibration conditions. OK, let's dive in then.
Let's impact the core idea. First, think about how the
machine is actually calibrated. It's set up to deliver a
specific dose per monitor unit, right?
Let's say 1 cgy per MU usually, but only under a very very
precise set of reference conditions.
Maybe a 10 by 10 centimeter field size at a standard depth

(01:53):
like D Max and a standard distance maybe 100 centimeters
SSD. That's your baseline output.
Exactly that calibrated output, which we call CALCAL, that's the
starting point. That's the dose you get per MU
if everything is perfect and matches those calibration specs.
Right. But I mean, let's face it, when

(02:13):
you're treating a patient, you're almost never operating
under those exact reference conditions.
Your field size is different, the depth you care about is
different. The distance might be different.
Maybe you've got wedges or traysin the beam path.
It's always something. Right.
So the actual dose delivered perMU during a real patient
treatment is going to be different from that Cal value.
It gets modified by a whole bunch of factors that account

(02:35):
for all these differences. Yeah, changes in field size, the
effect of tissue, the distance from the source, all that stuff.
Essentially, the dose delivered per MU in your specific
treatment setup is the Cal multiplied by a whole string of
these correction factors. Precisely, and if the dose
delivered per MU is the baselineCal multiplied by all these

(02:56):
factors, then well to figure outthe number of MUS you actually
need to deliver a target prescription dose, right?
Call it D sub RX. D Sub RX here.
And to flip that relationship around, you take your
prescription dose and you divideit by the dose per MU you expect
to get in that specific treatment setup.
So the core concept, it always boils down to this MUS needed
equals the prescription dose divided by the dose per MU at

(03:19):
the calculation point, right? And that dose per MU is the Cal
adjusted by all the relevant factors for that setup.
That's the foundation. Now if we wanted to write down
the most like general form of the MU equation, including
basically every factor you mightever encounter clinically, it
would look pretty intimidating. Oh yeah, it's something like MUS
equals D sub RX divided by open bracket, Cal multiplied by an

(03:43):
output factor multiplied by a depth, those correction factor
multiplied by an inverse square factor multiplied by off axis
ratio. That's OAR multiplied by tray
factor TF multiplied by wage factor, WF close bracket.
I cover the main ones anyway. OK, yeah, take a deep breath
after that one. That's a lot to track.
But the good news is right that for most core understanding and

(04:06):
really importantly for tackling board exam questions, we often
simplify this down. We do.
We can kind of peel back the layers and focus on the
absolutely fundamental components that are always
involved in the basic calculation, Things like the
OARTF and WF, They're definitelyimportant clinically, no doubt.
Oh, for sure. But you usually think of them as

(04:26):
modifiers you apply on top of the core calculation, don't you?
Exactly for the bedrock understanding, we simplify, we
focus on the factors that account for the machines
inherent output, the influence of the field size, how the beam
interacts with the patient and of course the effect of
distance. So the simplified general
formula, the one that really forms the basis of, I don't
know, 99% of what we do day-to-day.

(04:48):
So this MUS equals D sub RX divided by the roduct of open
bracket Cal multiplied by subc comma.
That's C multiplied by the patient attenuation factor AF,
AF multiply by the inverse square factor ISFIS close
bracket. OK, that feels much more
manageable. Let's break down each piece of

(05:10):
that simplified core formula then, because really
understanding what each term represents and why it's sitting
there in the denominator is absolutely key.
First up, D sub RX. That's easy enough, right?
That's just the dose you're aiming to deliver, usually in
CGY. Correct your target dose.
Simple. Next is Cal, the calibrated
output. As we said, this is your
machine's baseline dose rate perMU.

(05:31):
It's measured and specified under those really strict
standardized reference conditions I mentioned.
The ideal setup. Yeah, think of it as the dose
per MU when everything is just perfect, Typically one cgy per
MU in a 10 by 10 field at the reference depth and distance.
Any treatment plan in the MU calculation that starts with
this baseline output number? Got it.
Ideal output under standard conditions.

(05:52):
Then we have sub C comma CP. This one's fundamental to field
size changes, isn't it? It really is sub C comma.
P stands for a total scatter output factor.
It's a crucial factor because the dose rate per MU.
It changes significantly with the size of the radiation field
as it leaves the treatment head.See, as you open up the

(06:12):
columnator jaws to create a larger field, you actually
increase the amount of scatter radiation generated within the
machine head itself. You get scatter from the jaws,
from the flattening filter, the air, you name it, and this head
scatter contributes to the dose the patient receives.
So S sub C comma P basically accounts for that extra dose
contribution from head scatter as the field size changes from

(06:33):
the 10 by 10 reference field to whatever your actual treatment
field size is. Precisely.
It corrects the Cal for that change in head scatter
contribution. And here's a really critical
point. We'll definitely repeat this.
S sub C comma P is determined bythe size of the open field
defined by the columnator jaws. Right.
The jaws themselves. Yes, it's a property of the
machine heads interaction with the beam for that specific

(06:54):
columnator opening. Open field size for S sub C
comma P OK locking that one in. Next up, the patient attenuation
factor, PAF. This one clearly has to do with
the patient, as the name suggests.
Exactly. The PAF accounts for what
happens to the beam inside the patient's body.
As the beam travels through tissue, it gets attenuated.

(07:16):
Some photons are absorbed, some are scattered out of the main
beam, but also scatter radiationis generated within the
patient's tissue itself. The PAF is, well, it's a single
term in the simplified formula that basically encompasses both
these effects, the attenuation and the patient's scatter, and
how they influence the dose delivered to your point of
interest inside the patient relative to some reference

(07:37):
point. OK.
And what we actually use for thePAF depends on the treatment
technique, right? You mentioned SSD and SAD use
different things here. Correct.
For SSD treatments, source the surface distance, the PAF is
represented by the percent depthdose PDDPDD at your depth of
interest. For SAD treatments, source to
axis distance, it's represented by the tissue maximum ratio

(07:58):
TMRTMR or sometimes tissue phantom ratio TPRTPR.
And here's the other side of that critical point.
We'll revisit these factors, PDDand TMR.
They depend on the blocked or effective field size at the
depth of calculation, because that's the volume of tissue the
beam is actually interacting with that point.

(08:19):
So let me get this straight. S sub C comma P relates to the
open field, the collimator setting, the machine head well
PAF. So PDD or TMR relates to the
field size within the patient, potentially after blocks or
MLC's at the depth we care about.
That seems like a really vital distinction.
It truly is. Get that wrong and your
calculation is off. And finally, the last piece of

(08:41):
the puzzle in our simplified formula, the inverse square
factor ISF. This is all about the dose rate
changing with distance from the source.
Yes, the classic inverse square lot like how you know the
brightness of a light bulb seemsto decrease as you move further
away. The intensity drops off is the
square of the distance. Perfect analogy.
Yeah, that's exactly it. The ISF corrects the dose rate

(09:01):
if the distance from the radiation source to the point
where you're calculating the dose is different from the
distance used for your baseline C AL definition, right?
The linear accelerator source isfor practical purposes a point
source, or very close to it, so the radiation intensity follows
that inverse square relationshippretty closely.
If your Cal is valid at distanceD1 and you want to know the dose
rate at distance D2, you multiply by the ratio D 1 / d

(09:25):
two squared. So the ISF just adjusts the
baseline Cal to account for the distance relevant to your
specific calculation point in the patient.
Got it. Makes sense.
So just to summarize that core Formula One more time MUS equal
D sub RX divided by the product of C AL baseline ideal output
times, S sub C comma P correcting for head scatter

(09:46):
based on the open field size times, PAF correcting for
patient attenuation and scatter based on the field size of depth
and times ISF correcting for thedistance difference.
Those are kind of the four pillars of the basic
calculation. All right, that framework makes
a lot of sense. D sub RX divided by the Bose per
MU at the point you care about, where that dose per MU is built
up from the calibrated output times, factors for head scatter,

(10:08):
patient interaction and distance.
OK, now let's get specific and alley this to the workhorse D
technique first. Right the D setup source to
surface distance. In this setup, the atient's skin
surface is placed at a fixed distance from the source.
Very often this is 100 centimeters, but you know,
technically it could be anything.

(10:29):
OK. And the dose is typically
prescribed to a specific depth below that surface, maybe along
the central axis, or perhaps to D Max right as a surface.
And we said the PAF, the patientattenuation factor for SSD is
the PDD percent depth dose. How does that specifically
factor into the formula? For SSD, the Bayesian
attenuation factor term is literally the PDD value.

(10:50):
You look at the PDD for the depth D, where you want to
calculate the dose for the relevant field size at that
depth, measured at the specific treatment SSD you're using.
The PDD values are typically given as a percentage relative
to the dose at D Max on the central axis.
So in the MU formula you need touse the fractional PDD value,
meaning you just divide the percentage by 100.
OK, so we use PDD divided by 100as our PAF term.

(11:13):
Got it. But you also mentioned earlier
that PDD already incorporates the inverse square law relative
to D Max. Doesn't that mean PDD already
includes some kind of distance correction?
Why do we need a separate ISF? That's a really great point, and
it's definitely a common source of confusion.
You're right. PDD is defined as the dose at a
depth D divided by the dose of DMax, both measured at the same

(11:36):
SSD. Because both measurements are at
the same, SSDPDD does inherentlyinclude the inverse square fall
off from the surface down to depth D relative to the point of
maximum dose D Max at that specific SSD.
It tells you the percentage of the D Max dose.
You get a depth D for that fixedsurface distance.
So if PDD accounts for the distance fall off from the

(11:57):
surface down to depth D relativeto D Max at the treatment SSD,
where does the ISF sub SSD in the formula come from then?
What's it correcting? OK so the ISF sub SSD in the
SSDMU somula is not correcting for the distance from the
surface down to depth. Like you said, PDD handles the
depth dependence relative to D Max at the treatment SSD right?

(12:19):
The ISF sub SSD is specifically correcting the Cal value itself.
Remember the Cal is defined at areference depth.
Use AD Max but at a specific calibration SSD.
If your treatment SSD is different from that calibration
SSD, then the dose rated D Max on the surface changes simply
due to the inverse square law effect of moving the patient's

(12:39):
surface closer or further from the source.
The ISF sub SSD corrects the baseline Cal output from the
calibration SSD distance to the treatment SSD distance,
specifically to the D Max point at that treatment distance.
Oh OK I think I'm seeing it now.The Cal is measured at a certain
distance from the source to the D Max point at the calibration
SSD. The ISF sub SSD effectively

(13:01):
moves that reference dose from that distance to the distance to
the D Max point at the treatmentSSD.
Exactly. And then the PDD factor takes
over and tells you what fractionof that adjusted D Max dose
makes it down to your desired depth D.
We got it. You're we're adjusting the
reference dose rate, the Cal forthe difference in distance from
the source to the patient's surface, specifically to the D

(13:22):
Max depth relative to that surface, and then using PDD to
figure out the percentage that reaches your target depth D The
ISF sub SSD formula reflects this perfectly.
ISF sub SSD equals open bracket.The square of the quantity open
parenthesis SSD calibration plusD Max reference, close
parenthesis, close bracket divided by open bracket.

(13:43):
The square of the quantity Open parenthesis, SSD treatment plus
D Max reference, close parenthesis, close bracket.
OK, so that formula is calculating the ratio of the
distances squared, the distance from the source to the
calibration D Max point squared divided by the distance from the
source to the treatment D Max point squared.
That scales the Cal appropriately based on distance.

(14:04):
And naturally if your treatment SSD happens to be the same as
your calibration SSD, then the distances in the formula are
identical, the ratio is just oneand the ISF sub SSD becomes 1.0.
No correction needed. Exactly, which happens a lot for
standard SSD treatments like 100centimeter SSD, and that
simplifies the formula nicely. So putting it all together now,

(14:26):
the complete SSDMU formula lookslike this.
MUS for SSD equals D sub RX divided by the product of open
bracket CA L * S sub C comma P Remember for the open field size
multiplied by open parenthesis PDD for depth blocked field size
of depth treatment. SSD divided by 100 ).

(14:47):
Blocked field for PD. Multiplied by ISF sub SSD to
correct C AL for treatment SSD. And then of course you'd include
any other modifiers in there like wedge factor or tray factor
if they're in the beam close bracket.
That comprehensive formula really covers all the bases for
SSD. Let's let's try an example to
make this more concrete. A little mini case study maybe?

(15:09):
Sounds good. Let's imagine our Linux is
calibrated to deliver 1 cgy per MU at D Max.
Let's say D Max for a six MV beam MV is 1.5cm and this
calibration is for a standard 10by 10 centimeter field at 100
centimeters SSD. Now a patient needs 300 cgy

(15:29):
delivered to a depth of 6 centimeters using a six MV beam
directed PA. It's posterior to anterior.
PA got it. The treatment SSD is set to 100
centimeters and the field size defined by the collimator jaws
is 6 by 8 centimeters. Let's say no wedges or trays are
involved. OK, perfect.
Let's break this down logically,step by step, like we would in
clinic. Identify the prescription dose

(15:49):
and the setup. Type D sub RX IS300 CGY and it's
clearly an SSD setup in 100 centimeters.
Easy enough. Step 2.
Define the reference conditions and check the ISF.
The Cal is 1.00 CGY per MU defined at D Max, which is 1.5cm
for a 10 by 10 field at 100 centimeter SSD.

(16:10):
Our treatment SSD is also 100 centimeters right?
So since SSD calibration equals SSD treatment, our ISF sub SSD
is just the square of 100 + 1.5 divided by the square of 100 +
1.5 which is obviously 1.0. Simple.
No correction needed for distance here.
Excellent step three. Determine the field sizes we
need for our lookups. We have an open field size set

(16:33):
by the jaws of 6 by 8 centimeters.
We'll need the equivalent squarefield size for this open field
to look up S sub C, comma P We also need the equivalent square
of the field size at the calculation depth for PDD.
Now in this specific case, sincethere are no blocks or ML CS
mentioned, the field size at 6 centimeters depth is still
effectively defined by that 6 by8 opening, just projected

(16:54):
further. So we calculate the equivalent
square for a 6 by 8 centimeter feel.
Right, the equivalent square formula FS sub equiv equals ( 2
times length times width close parenthesis divided by open
parenthesis length plus width close parenthesis.
So for 6 by 8, that's 2 * 6 * 8.That's 96 / 6 + 8, which is 14,

(17:20):
so 96 / 14. Let me grab a calculator.
It comes out to about 6.86 centimeter. 6.86 OK And for
looking up values and typical tables, we usually round to the
nearest standard equivalent square size, right?
So we probably use 7 centimetersfor our lookups here.
Yeah, that's standard practice. Use 7 centimeters equivalent
square for the lookups. Right, step four.

(17:40):
Look up our factors using that 7centimeter equivalent square.
First we need S sub C comma P for the open field using a
lookup table indexed by the equivalent square of the open
field. For a 7 by 7 field representing
our 6 by 8 open field, let's just say the cable gives us an S
sub C comma P of 0.944, OK 0.944.

(18:02):
Next we need PDD. This is for 6 centimeters depth
at 100 centimeters SSD, and for the field size equivalent to our
6 by 8 at that depth. Again using the 7 centimeter
equivalent square for the lookup.
Let's say our PDD table for six MV beam gives us 79.7% for these
conditions, 79.7%, so as a fraction for the formula that's
0.797. Perfect, so let's list what we

(18:24):
have. D sub RX equals 300C GYCA L =
1.00 CG GUI per MUS sub C comma P for the 7 centimeter open
square open field 0.944 PDD for 6 centimeter depth, 7 centimeter
quively square blocked field 100centimeter SSD equals 0.797 ISF

(18:49):
sub SSD since treatment SSD equals calibration SSD equals
1.0. Great, now Step 5.
Plug all those numbers into our SSD formula.
MU equals 300 divided by open bracket. 1.00 * 0.944 * 0.944 is
obviously 0.944. 0.944 * 0.797 Let's see that it's just about

(19:13):
0.752468 and multiplying by 1.0 doesn't change it.
So the denominator is roughly 0.7525 if we round a bit.
OK, so 300 / 0.7525 calculator again.
And that calculation gives us approximately 398.67 MUS.
398.67. So if we were asked to round to

(19:34):
the nearest whole number, that would be 399 MUS, just like the
source example indicated. Fantastic 399 Mus for that SSD
treatment. And it makes sense, right?
Every number in the denominator except the Cal and ISF here was
less than 1 S of C Comma P was less than one, meaning our small

(19:54):
6 by 8 field had left head scatter than the 10 by 10
reference field. Makes sense?
And PDD was less than one obviously because dose falls off
with depth. So those factors reduce the
effect of dose per MU from the ideal Cal, meaning you needed
more MUS to reach the target dose of 300 CAG.
That's the logic exactly. Each factor adjusts the dose MU

(20:17):
based on how the treatment setupdiffers from calibration.
Great. OK, now that we've navigated
SASAD pretty thoroughly, let's shift gears to the equally
important SAD technique, the isocentric setup.
Right, SAD source to axis distance.
In the SAD technique, the sourceto axis distance is fixed to
typically at 100 centimeters. The machine, the Gumtree,

(20:39):
rotates around this point in space, which we call the ISO
center, and that ISO center is usually placed somewhere inside
the patient, ideally right within the target volume you're
trying to treat. And for SAD, we switch our
patient attenuation factor, we use TMR tissue maximum ratio or
maybe TPR. Yeah, you mentioned earlier that
TMR is distance independent. This seems like a really key

(21:00):
concept for SAD, right? Why is that so important?
Here it absolutely is key. TMR is defined as the ratio of
the dose at a given depth D in aphantom to the dose at the depth
of maximum dose D Max in the same phantom.
Here's the important part when both doses are measured at the
same distance from the source. OK, same distance for both
measurements. Exactly.

(21:20):
Usually this distance is the machines SAD like 100
centimeters. Because both the numerator dose
at depth D and the denominator dose at D Max are measured at
the same SAD. The effect of the inverse square
law fall off from the source to the SAD cancels out completely
in that ratio. That cancellation is what makes
it distance independent. So TMR tells you the dose at

(21:44):
depth D relative to the dose at D Max, specifically at the ISO
center distance, and it doesn't matter how far the patient's
surface is from the source at that moment.
Precisely. Which is absolutely perfect for
SAD treatments because as the gantry rotates around the
patient, the surface to source distance is constantly changing,
isn't it? Constantly changing TMR neatly
sidesteps that problem. It accounts for the attenuation

(22:07):
and scatter in the tissue below D Max, but it's not tied to a
specific surface position like PDD is.
OK, that makes sense. So if TMR handles the patient
and scatter in a distance independent way, where does the
ISF sub SAD come in for SAD calculations?
Why do we still need an ISF sometimes?
Good question. It's for the same reason as in
SSD. Fundamentally, the ISF sub SAD

(22:30):
corrects the Cal value if your clinic Cal was defined at a
different distance than your SADtreatment distance.
Which is pretty common right, ifyou calibrate using an SSD
setup. Very common if you calibrate at
say SSD calibration plus D Max reference distance from the
source. But your SAD treatment is
happening at a different distance, namely the SAD itself,

(22:50):
usually 100 centimeters. Well, you need to adjust that
baseline Cal for the distance difference using an inverse
square correction. So the ISF sub SAD scales the
Cal from its definition distanceto the SAD treatment distance.
The formula for ISF sub SAD, assuming you have an SAD based
Cal is open bracket, the square of the quantity open parenthesis

(23:12):
SSD calibration plus D Max reference close parenthesis
close bracket divided by open bracket, the square of the SAD
treatment distance close bracket.
OK. So it's the square of the
distance where Cal was defined divided by the square of the
distance where the treatment dose is being delivered, The
SAD. This factor essentially moves
the Cal value from its definition point right to the
ISA center distance using inverse squared law.

(23:34):
That's it. And logically, if you're Cal was
already defined directly at the SAD for the reference field,
some clinics might do this. Then this ISF sub SAD would just
be 1.0 right? Correct, if Cal distance equals
SADIS F = 1. So with that the complete SADMU
formula again assuming an SSD based Cal which is common is MUS

(23:57):
for SAD equals D sub RX divided by the product of open bracket
Cal multiplied by S sub C comma P for the open field size
multiplied by TMR for depth D which is surface to ISO center
and the blocked field size at ISO center.
Blocked field for TMR. Multiplied by ISF sub SAD to
adjust the Cal to the SAD and then again any other modifiers
like wedges or trays would go inthere too.

(24:18):
Close brackets. Perfect time for another example
I think. Let's do that classic urgent
whole brain case you mentioned. Seems like a good sad scenario.
Definitely a staple. OK, let's use the same clinic
calibration as before. 1 CGY perMU at D Max 1.5cm for six MV for
a 10 by 10 field at 100 centimeters SSD.

(24:40):
So an SSAD based calibration. OK.
We need to deliver 300 cgy totaldose to the ISO center.
The SAD is 100 centimeters. We use two oppose lateral 6 MV
beams. Let's say the patient's head
separation, measured laterally, is 16 centimeters.
You have 2cm separation. This means the depth from the
surface to the ISO center on each side is half of that, so 8

(25:02):
centimeters. Depth is 8 centimeters for each
beam, and let's say the open field size by the column meters
is 13 by 15 centimeters. All right, classic opposed
lateral whole brain setup. Let's walk through it.
Dose per beam. We're delivering 300 cgy total
to the ISO center with two opposed beams.
Assuming equal weighting, each beam needs to contribute half

(25:23):
the dose to that point. So D sub RX per beam is 300 / 2
which is 150 cgy. Good.
Calculate MUS per beam. Step 2.
Reference conditions for Cal andthe ISF.
Our Cal is 1 cgy per MU defined at 100 centimeters SSD plus 1.5

(25:43):
centimeter D Max. So that calibration point is
101.5 centimeters from the source, right?
Our treatment is at 100 centimeters SAD.
These distances are different sowe definitely need the ISF sub
SAD to adjust the Cal. OK, let's calculate it.
ISF sub SAD equals the square ofthe Cal distance divided by the
square of the SAD distance. So square of 101.5 divided by

(26:05):
the square of 100. 101.5 ^2 is 10,302.25 and 100 ^2 is
obviously 10,000 so 10,302.25 / 10,000 that equals 1.030225.
That's our ISF sub Sad. 1.030225.
And it's slightly greater than one, which makes sense, right?

(26:25):
Because the Cal was defined slightly further away on her 1.5
centimeter than the treatment SED 100 centimeters, moving the
calculation point closer to the source means a slightly higher
dose rate per MU just due to inverse square law.
Good check. OK, step three.
Equivalent square. The open field is 13 by 15

(26:47):
centimeters. We need the equivalent square
for this to look up S sub C comma P We also need the
equivalent square of the blockedfield at the ISIS Center for
TMR. In this Case, No blocks are
mentioned, so it's still effectively a 13 by 15 field at
the ISIS center. OK, same calculation.
FS sub equiv equals 2 * 13 * 15.That's 390 / 13 + 15, which is

(27:09):
28, so 390 / 28. That gives us approximately
13.93 centimeters. 13.93 So again, for lookup in standard
tables, we'd probably round thatto 14 centimeters.
Yep, use 14 centimeters equivalent square for lookups.
OK, step four. Look U our factors using that 14
centimeter equivalent square first sub C comma P for the open

(27:31):
field using a table indexed by equivalent square of the open
field for a 14 by 14 field representing our 13 by 15 open
field. Let's just say the table gives S
sub C comma P as 1.050. 1.050. And that's greater than one,
which also makes sense for a 13 by 15 field.
Being larger than the 10 by 10 reference field, you expect more

(27:54):
head scatter contribution. Good.
Next we need TMR. This is for 8 centimeters depth
surface to ISIS Center for a field size equivalent to our 13
by 15 at the ISIS center. Using the 14 centimeter
equivalent square lookup with our six MV beam, let's say our
TMR table gives us value as 0.844.

(28:14):
OK, 0.844 excellent. So for calculating the MU's for
one being we have D sub RX150C GYCA L = 1.00 GY per MUS sub C
comma P for the 14 centimeter Q square open field G 1.050 TMF 8
centimeter depth 14 centimeter Qsquare block field 0.844 ISF sub

(28:40):
SAD. Adjusting Cal from 101.5
centimeters to 100 centimeters equals 1.030225.
Perfect Step 5. Plug all those numbers into the
SAD formula for one beam. Mus per beam equals 150 divided
by open bracket 1.00 * 1.050 * 0.844 * 1.0302250.
Yeah, let's breakdown that denominator multiplication

(29:00):
carefully. 1.00 * 1.050 is just 1.050 now. 1.050 * 0.844 =
0.8862. Finally, 0.8862 multiplied by
our ISF 1.030225 that comes out to approximately 0.91302.

(29:23):
That is maybe around that slightly for ease and use 0.913
for the denominator. OK, 0.913 in the denominator.
So Mus per beam equals 150 / 0.9131. 150 / 0.913 is
approximately 164.29 Mus. 164.29.

(29:43):
Our example source rounded that to 164 Mus per beam.
We'll stick of that. 164 Mus perbeam, and since it's two opposed
beams delivering the total dose right, the total Mus for the
entire fraction is just 2 * 164,which is 328 Mus exactly.
There you have it, the SAD calculation process step by
step. Notice again how the TMR value

(30:04):
.844 and the ISF one are both inthe denominator, modifying that
baseline Cal and. That really covers the core
calculations for both SSD and SAD.
We've used the simplified formulas here, but the
principles are exactly the same.When you start adding things
like wedge factors, tray factors, or off access ratios,
you just multiply by another correction factor down there in

(30:26):
the denominator. Each factor accounts for one
specific aspect of the setup, deviating from calibration.
Now, we've mentioned it a coupleof times already, but let's
really, really drill this home because this is definitely a
point where people get tripped up, especially on exams.
It's that critical distinction regarding which field size to
use for which factor. Yes, this is absolutely

(30:47):
essential. Cannot stress this enough.
Remember how we said S sub C comma P uses the open field size
and PDD or TMR use the block field size?
Let's just be crystal clear about that again and maybe
reiterate the Y, OK? Rule #1 Factors related to the
machine head scatter and the overall output change before the
beam even hits the patient. Like S sub C comma P, These are

(31:09):
based on the open field size setby the collimator jaws.
Right. Think about where the scatter
for S sub C actually comes from.It's scatter generated by the
columnators and maybe the flattening filter other
components in the head. That depends directly on how
wide those jaws are open. OK, makes sense.
Machine head columnator opening.Where does the scatter that
influences PDD or TMR primarily come from?

(31:31):
It's scatter generated within the phantom or patient.
OK. Now S of C comma P technically
combines head scatter, SC and phantom scatter relative to the
reference. But the key thing for
calculation table look up is that S sub C comma P is indexed
by the columnator opening the open field size.
It describes the output for thatsetting.

(31:52):
Got it. It's a machine characteristic
for that defined opening OK rule#2 then factors that account for
the beams interaction within thepatient.
Things like attenuation and patient scatter, which are
captured by PDD and TMR. These depend on the blocked or
effective field size at the calculation depth.
Exactly because PDD and TMR are describing how the dose changes

(32:13):
with depth within tissue that interaction, the amount of
scatter generated within the patient depends on the actual
cross section of the beam as it passes through the patient at
the depth you're interested in, right?
So if you have blocks or maybe MLCS that are shaping the beam
after it leaves the head, the relevant field size for these
factors PDDTMR is the size of the beam after that shaping

(32:34):
projected down to the depth of interest.
OK. So to really simplify, the Y is
about the machine head and the initial beam shape coming out.
PDD and TMR are about the patient's body and how it
interacts with the beam that actually reaches that depth.
That's a great way to put it andthat.
Mnemonic we mentioned. Let's say it again.
It's worth repeating until it's absolutely burned into your
brain. SKOMP is about the collimator

(32:56):
opening. PDTMR are about the patient
interaction volume at depth. STOMP Collimator PDDT.
Mr. Occles patient OK, that really helps separate them
conceptually. Get this distinction right?
Committed to memory and you avoid a major, major pitfall in
these calculations. You really do and avoiding.
Pitfalls in these calculations is so critical because, you

(33:16):
know, as we said right at the start, this isn't just some
academic exercise we're doing for fun.
Absolutely. Why is getting MU calculations
right so fundamentally vital in the real world, beyond just, you
know, passing your physics boards?
Well, the most direct and obvious.
Answer is dose accuracy radiation therapy.
Our entire field relies on delivering incredibly precise

(33:39):
doses to the tumor volume while minimizing as much as possible
the dose to surrounding healthy tissues.
Errors in MU calculations translate directly 1 to 1 into
delivering the wrong dose to thepatient.
A small percentage error might sound minor like 5%, but it can
have really significant consequences for tumor control
or for normal tissue toxicity for sure, especially given the

(34:01):
steep dose response occur as we often work work with in
radiation oncology. Absolutely that 5.
Percent or even less sometimes could genuinely mean the
difference between hitting the tumor effectively and maybe
under dosing it, or between manageable side effects and
potentially severe complicationsfor the patient.
These calculations are the absolute bedrock of every single

(34:21):
treatment fraction delivered. They form the basis of the
treatment plan generated by the physicist or the dosimetrist and
you know, as residents. You play such a crucial role in
the whole safety system when youreview treatment plans, when you
erform chart checks before treatment, your understanding of
MU calculations allows you to perform vital independent

(34:43):
checks. You're not just, you know,
signing off on a piece of paper.You're applying your knowledge
to try and catch potential errors before they ever reach
the patient. Can you look at a plan and spot
if a calculated MU value seems wildly out of line for the dose,
the field size, the depth? That kind of clinical intuition
comes directly from understanding these underlying
principles. It's such a vital safety net.
Isn't it? Relying solely on the output

(35:05):
from the treatment planning system without having a grasp of
the underlying physics is just inherently risky.
Knowing how those MU numbers were derived empowers you to
question things, to verify, and ultimately to ensure patient
safety. It's absolutely a layer.
Of quality assurance that requires the clinician to you to
have a solid grasp of the physics.

(35:28):
It's foundational knowledge for a very good reason.
OK, well said. Let's try and.
Condense all of this down now into our must remember points,
the kind of clinical pearls and high yield board exam facts that
you absolutely need to walk awaywith from this discussion.
Alright, sounds good. Parole number one may be the
overarching concept. MUS are calculated by taking the
prescription dose D sub RX and dividing it by the product of

(35:50):
factors that describe the dose per MU at the calculation point
in the patient. And that product is essentially
your Cao times your output factors like SCP times your
patient attenuation factor PDD or TMR times your inverse square
factor ISF, plus any specific modifiers like wedges or trays.
Understand the role of each factor in modifying that

(36:12):
baseline CL. Got it, ro #2.
Focusing on D setups, the patient attenuation factor is
PDD. Remember to use the value for
the calculation depth, the relevant blocked field size and
the treatment SSD and divide thepercentage by 100 right and the
ISS sub SSD corrects the Cal. If the treatment SSD is

(36:32):
different from the calibration SSD, remember it's specific
formula. Open bracket SSD calibration
plus D Max reference squared close bracket divided by open
bracket SSD Treatment plus D Maxreference squared close bracket.
Perfect Pearl #3. For SAD setups, the patient
attenuation factor is usually TMR or TPR.

(36:53):
Use the value for the depth fromthe surface of the ISO center
and the relevant blocked field size of the ISO center.
Remember TMR is key advantage. Its distance independence makes
it ideal for isocentric treatments.
Whereas SD changes and the ISF sub SAD corrects the Cal if it
was defined at a distance different from the treatment S
Ed which is common. If you have an SSD based Cal,

(37:15):
its formula is open bracket, SSDcalibration plus D Max reference
squared close bracket divided byopen bracket, SAD treatment,
distance squared close bracket OK and Pearl #4 May be.
The most critical distinction for lookups, the one we keep
hammering S sub C comma P, uses the open field size set by the
columnators because it's primarily a machine head factor

(37:36):
open field for SATP. DD and TMR.
Use the blocked or effective field size at the calculation
depth because they describe how the beam interacts with the
patient volume at that depth. Remember the mnemonic SCOMP
columnator PD TMR patient? You absolutely must commit this
one to memory. Cannot emphasize that enough.
And Pearl. #5 May be a practicalpoint.
Always know how your machine wascalibrated.

(37:57):
Is your Cal defined at SAD plus D Max, or was it defined
directly at the SAD? This dictates whether you need
to apply an ISF factor at all, and if so, which ISF formula is
the correct one to use. Don't just assume.
Know your calibration conditions.
Yeah, that's a really good practical.
Point you know, trying to keep all these factors and formulas
straight, especially when you'refirst learning them, it can

(38:19):
definitely feel like you need a separate hard drive installed in
your brain just for physics yeahit.
Feels that way sometimes you feel like we keep saying
everything is. Vital.
Which I guess it kind of is, butsorting it all out and making it
second nature just takes practice, doesn't it?
It absolutely does repetition. And working through problems.
And Speaking of practice, maybe let's solidify all this with a

(38:40):
quick board review blitz, apply what we've just discussed to
some typical questions. Love it.
All right, let's hit it, question one.
A Leanoc is calibrated to deliver 1.00 C GY per MU at D
Max. Let's say D Max is 1.5cm for a
10 by 10 centimeter field at 100centimeter SSD, you need to

(39:02):
deliver 180 GY to a depth of 10 centimeters using a 12 by 12
centimeter open field at 100 centimeter SSD.
Given S subsequamma POV for the 12 by 12 field is 1.015 and PDD
for 10 centimeter depth 12 by 12field at 100 SSD is 68.0%.
No wedges or trays. Calculate the required MUS.

(39:23):
Your options are A-258-B261C-266-D278.
OK, let's think through this one.
It's clearly an. SSD calculation Yep,
prescription dose D sub RX is A180C, GICAL is 1.0 CGMU.
The treatment SSC is A1 field size which is the same as the
calibration. SSF is ISF sub SSD is one point.
0 Easy now we need S sub C commaP for the open field size which

(39:45):
is 12 by 12. They give us that value 1.015
and we need PDVD at 10. Centimeter depth for the 12 by
12 field size. Since it's an open field, the
block size is the same here. Think of that as 68.0% which is
a fraction. Is 0.680.
OK, looks like we have all the pieces.
Plug them into the SSD formula MUSD sub RXCALSCPPD D100 ISF.

(40:07):
So MUS is 1.0150.6801.0. OK, let's calculate that
denominator 1. .015 * 0.6801 OK 0.6902 SO.
The calculation is 180 / 0.6902180 / 0.69. 02 is
approximately 260.79 MUS 260.79.Rounding to the nearest whole

(40:29):
number, that's 261 MUS 261. Let's check the options, yes?
That's option B Nailed it. OK, next question.
Question 2 same leanoc, same calibration as in question 11C
GMEU at D Max 1.5 centimeters 10by 10 field, 100 centimeters SSD
you need to deliver 200 CGY isocentrically.
So SAD equals 100 centimeters toa depth of 7 centimeters from

(40:52):
the surface. The treatment uses an 8 by 8
centimeter blocked field size. Given S sub C comma P for the
open field corresponding to the setup is 1.005 TMR for 7
centimeter depth 8 by 8 field is0.860.
No modifiers. Calculate the required MUS 220 B
220. 5C230 D 235 OK, this one isan SAD calculation.

(41:15):
And notice the Cal is still the SSD based one from question one,
right? Prescription dose D sub RX is
200, CDF CL is 1.7. The calibration distance was 100
centimeter SAD plus 1.5 centimeter D Max.
So I don't have .5 centimeters from the source.
The treatment is at 100 centimeter SAD.
These distances are different. So we do need the ISF sub SAD.

(41:36):
OK, let's calculate that ISF. Sub SAD again, it's the square
of the Cal distance divided by the square of the SAD distance.
Square of 100 + 1.5 divided by the square of 100 which we found
earlier was only 1.5 A. 200-200-7302 Point 2 five
201.030225 Got it 1.0302. 25 OK what other factors do we need?
We need S sub C comma. P The question gives us the

(41:58):
value for the open field 1.005. It mentions the blocked field is
8 by 8, but specifies the SCP for the corresponding open
field. Good catch.
Use the value given for SCP. 1.005 and we need TMR this is.
For seven centimeter depth and for the blocked field size,
which is 8 by 8 centimeters, they give us the TNR value
0.860. OK, seems we have everything.

(42:18):
Let's look. Into the SAD formula MUS equals
D sub RXCALSCPTMRISF sub SAD so MUS equals 201.005 times brain
8601.8643. OK, now multiply that by the
ISF. 1 .8643 * 1.8023 OK, now multiply that by the ISF. .8643
* 1.8904 All right, so the calculation is 200.

(42:40):
Divided by 0.8904200 / 0.890. 4 gives about 224.6 MUS 224.6.
Rounding to the nearest whole number gives 225, MUS 225.
Checking the options. Yes, that's option B.
Again, beautiful question 3. This one's testing that key

(43:01):
distinction we hammered on when performing an MU check for an
SAD treatment using TMR. The total scatter factor S sub C
comma P should be chosen based on which field size A the
blocked field size at the patient's surface, B the blocked
field size at the ISO center depth, C the equivalent square
of the blocked field size, or D the open field size defined by

(43:22):
the columnator jaws. OK, this goes right back to our
rule. In mnemonic S sub C comma P
scampa, it's a collimator. It relates to the machine head
scatter determined by the collimator opening.
So it has to be. It has to be the open.
Field size defined by the. Collimator draws option D
exactly, that's why we kept repeating it.
OK. Final question for this blitz
question 4. The primary reason TMR is

(43:42):
preferred over PDD for isocentric or SAD calculations
is because TMR. What?
A accounts for electron contamination more accurately, B
is easier to measure in a water phantom, C is independent of the
SSAD, or D directly provides thedose at D Max.
Why do we use TMR for? SAD we talked about this PDD

(44:04):
changes with SSD because it includes the inverse square
effect from the surface TMR's definition, right?
The definition cancels out. The inverse square effect
between D Max and depth D because both are measured at the
same distance. Usually the SAD, which means TMR
itself doesn't depend. On the SSD, as the gantry
rotates and the SSD changes, theTMR value for a given depth and

(44:24):
field size stays the same. Perfect for isocentric
treatment. So the.
Answer is. The answer is CTMR is.
Independent of the SSD. Excellent, you've successfully.
Navigated the core MU calculations for both SSD and
SAD setups and hopefully everyone listening feels a bit
more confident with these concepts now yeah just to
quickly recap them we. Started with that fundamental
idea. MUS equals prescription dose

(44:45):
divided by the dose delivered per MU in the specific treatment
setup, right? And that dose per MU.
Is just the baseline Cal adjusted by all the factors.
SCP for head scatter output based on open field PAF.
Which is. PDD or TMR for patient
attenuation and scatter BS on blocked field ASF.
For distance correction. And any other modifiers like

(45:06):
wedges or trays, we applied thatlogic.
Specifically to SSD where PDD divided by 100 is the PAF and
the ISF sub SSD corrects the Calfor differences between
calibration SSD and treatment SSD.
Specifically to D Max at those SSDs and we applied it to SAD.
Using TMR or TPR as the PAF, highlighting its crucial

(45:28):
distance independence and calculating the ISF sub SAD to
adjust an SSD based C AL to the SAD distance and maybe the most
critical take away the one. Worth saying one last time, S
sub C comma P is always based onthe open field size, the call
meter setting, while PD and TMR are based on the blocked or
effective field size at the calculation depth, how the beam

(45:49):
interacts with the patient volume.
Get that distinction absolutely clear understanding these
factors and. How they all combine is just
absolutely essential for both your board exams and much more
importantly, for safely treatingpatients every day and
confidently performing those critical plan checks.
It definitely takes practice. But hopefully breaking it down
into these individual component pieces, head scatter, patient

(46:11):
interaction distance makes the whole process feel much more
logical and manageable. Exactly thinking.
Through where each factor originates really helps solidify
which field size to use and which inverse square factor is
relevant, if any. OK, well next time in our
continued. Radonic smart review, we're
going to transition a bit. We'll move from calculating dose

(46:32):
at a single point to defining the actual volumes we care about
treating. We'll dive into the ICRU
framework. That's ICRU discussing gross
tumor volume, CTV target volume.CTV.
Planning target volume PTVPTV and also.
Organs. At risk OA Rs.
This is really the crucial language we use to define what

(46:52):
we're aiming at and what we're trying to avoid, which obviously
precedes planning the dose delivery itself.
Absolutely looking forward. To that and remember, you can
complete practice oral boards atradonsmartlearn.com.
That's radonsmartlearn.com. And subscribe to Radonsmart
Review for our next episode. Thanks for tuning in.