0:01

Now, that is just to give you an idea of what the three

0:05

milestone, the milestone enable the CT technology to

0:08

get a major jump in the field. But

0:12

the fundamental basics, whether it's the prior to helical

0:16

CT or with the multiple detector CT, the CT

0:19

basic physics is the same.

0:22

Now one other thing is that here's the, just to get the diagram of a

0:26

basic data acquisition in CT, X-ray tube, the

0:30

beams are in a divergent fan beam that is the principle of a

0:33

third generation CT.

0:36

Here's a detector, and now the X-ray tube is continuously

0:39

rotates while the patient moves in and out of the table.

0:43

Therefore, you're able to do a long scan in a very short period of

0:47

time or cover a larger area.

0:50

What is the fundamental physics behind here is it still

0:54

goes back to the fundamental physics called the fundamental measurement of

0:58

attenuation.

1:00

So let's imagine here you have an object of certain

1:04

thickness,

1:05

and you want to characterize what the particular object is.

1:10

The way that mathematically we can do is if we measure

1:14

the intensity of the X-rays before hitting the

1:18

object and measure the intensity of the X-ray coming

1:22

out of the object and assign it as transmitted X-ray

1:25

intensity, we can mathematically write an equation

1:29

like this. This is a famous attenuation equation, one of

1:33

the few equation which I'm going to show in these lectures on the CT physics,

1:37

and this is called the Lambert Beer Law.

1:40

Basically, the idea telling this, the intensity of the

1:44

transmitted X-rays is equal to the intensity

1:48

of the original X-ray prior to the object

1:52

multiplied by an exponential factor.

1:56

This exponential factor is called the exponential

1:59

factor or the attenuation factor.

2:02

Means as the X-ray pass through the object, they either get

2:06

absorbed, scattered, or transmitted, working

2:10

under the principle of photoelectric absorption or Compton

2:14

scattering and so forth. We're not going to go into the details, but just

2:18

fundamentally.

2:19

So if we write an equation like this where mu is

2:23

actually called the attenuation factor.

2:26

It's called the linear attenuation coefficient, and that is

2:30

very unique to each material, and that's almost like

2:34

a characteristic of a material. So if you take a bone, it has a different

2:38

attenuation coefficient. If you take a water, it has different attenuation

2:41

coefficient and so forth. So if there is only one

2:45

object,

2:46

the I sub t can derive from this

2:50

equation. Therefore, if we know how to measure the intensity of

2:54

the transferred X-rays,

2:56

intensity of the original X-ray,

2:59

or input X-ray, you can actually calculate what the

3:03

mu is by transposing and do

3:06

the integral of this particular equation.

3:10

So now what I meant to say here is,

3:12

one, if we know one, two, and delta x, the thickness of the

3:16

material, you can actually characterize the material.

3:19

And that is the principle behind the X-ray attenuation.

3:23

In reality, when we are collecting a beam of X-rays

3:27

passed into the object, in each for the X-ray beam, we

3:31

can write an equation like this.

3:34

Then you can write an equation because this particular path,

3:38

X-ray is passing through the multiple objects, so you can actually

3:42

have a exponential of the attenuation caused from

3:45

each component. I'm not going to complicate this particular equation,

3:49

but this is the type of equation we can write.

3:53

By solving the equation, we can put back what the object is,

3:58

and that's the beauty of this as CT is without

4:02

having to slice the patient, we can see what's inside the patient.

4:07

And it's a very complicated issue.

4:09

Because it is not one object, there's multiple object,

4:13

the principle, the basic principle is you need to have the

4:17

data at least half of the rotation around the

4:21

object.

4:23

Generally, we collect data through a 360 degree for

4:26

overabundance to eliminate some of the errors and so forth,

4:30

but that is what the principle behind it.

4:32

So by solving this equation, we can arrive

4:36

what is called as an image,

4:39

and in the image, we have fundamental definition of a pixel.

4:43

Pixel is a measure of X-ray attenuation in a very

4:47

small element in a two-dimensional image.

4:50

And voxel is considered as a volume element which

4:54

accumulate the depth of the pixel element that is associated

4:58

with the slice thickness. So if you look in a CT

5:01

image, the CT image, imagine this as a matrix of

5:05

small pixels, and each pixel has its own

5:09

unique attenuation coefficient values derived from this equation.

5:13

And that's what the CT image is made up of.

5:17

So now,

5:18

there's another fundamental which has been

5:20

common to across all the CT

5:25

images is how the CT numbers are derived.

5:30

The way CT numbers are derived is the CT number in Hounsfield

5:34

units is expressed in Hounsfield unit, giving the

5:37

recognition to the person who developed the early CT, Hounsfield.

5:41

So that's why all the CT numbers have unit of HU,

5:45

Hounsfield unit. By definition, we define

5:49

CT number equal to a scaling factor

5:53

multiplied by the ratio of the attenuation coefficient,

5:58

the difference in attenuation coefficient of any material

6:02

with that of water divided by the water.So in

6:05

reality, from the fundamental is every CT

6:10

number which we see on the images is

6:13

based with tag to respect to the CT number of the water.

6:17

And the CT number of water by definition is assigned at

6:21

zero. Because here if the attenuation coefficient of

6:25

water here and the attenuation coefficient of the object is also water,

6:29

then this will become zero. Therefore, the CT number

6:33

for water is always zero.

6:36

Any tissues denser than water has positive CT

6:40

number, and anything less dense than water has negative

6:44

CT numbers.

6:46

So you can see these CT numbers now are

6:49

mapped onto a gray scale. For example, here in this

6:53

image, you have four metrics and four different object,

6:57

and you are seeing these CT numbers as follows, 1000,

7:01

-20, 400, and -100. If these numbers are

7:05

mapped into a gray scale, the image looks like this.

7:09

So that's the principle, the fundamental, it's true across the board.

7:13

So how does that implies for CT number displays for

7:17

different organs and different display?

7:20

Earlier days, radiologist had to window and center

7:24

the images to see different aspect.

7:26

Now, the CT display are automatically set

7:30

to display certain areas. But the principle is still the

7:34

same.

7:35

So the way the Hounsfield Scale works like this, the

7:39

Hounsfield Scale goes from -1000 to +1000.

7:43

That is pretty much standard across all the vendors.

7:47

In this, the CT number of water is pegged at zero.

7:51

Anything dense than water, such as bone and muscle and

7:55

other things are more than plus numbers.

7:59

And anything

8:00

less dense than water, such as fat, lungs, air, have

8:04

negative CT number.

8:06

So generally, the way the CT numbers are displayed is

8:10

you have a central point called the window centering, and then you

8:14

have a different windowing level.

8:16

So for example, if you have a narrow window width, means the

8:20

whole 256 grayscale account for all these

8:24

different CT number, then you can actually see the difference

8:28

between kidney, pancreas, blood, and liver.

8:32

On the other hand, if you have a wider window, the center is

8:36

different in a different location, have a different window, you can see different

8:39

aspect. That is showing here the effect of

8:43

windowing on CT display.

8:46

What's shown here is like, for example, if the window width is

8:50

only this much,

8:52

any object in the image will appear like this.

8:55

It is mentioned as CT centered around -50 with a

8:59

window width of 400 will display all the

9:03

CT's number around this -50 is displayed here.

9:07

So this CT image has a accommodation between

9:11

-50 Hounsfield to 150 Hounsfield.

9:15

Anything beyond it will become bright.

9:17

Anything below that will become dark, and this is how a typical chest

9:21

CT image is displayed.

9:23

On the other hand, if you have a wider window, let's say it's centered

9:27

around 1000, and you have a wide window of 2500,

9:31

in that case, the image looks like this, and you hardly see any of these

9:35

things because they all fall under the dark area, and this is called

9:39

the bone window. We can only see the bone.

9:42

This is called the mediastinal window, or this is called the lung

9:46

window, where you can display different aspect.

9:49

So the principle of the fundamental of the CT display goes

9:53

back to this CT number normalized to water.

9:58

And in fact, this is one of the things every day morning the CT scanner

10:02

does a quality control by the technologist where they want to make

10:06

sure the CT number of the water is still around zero.

10:10

Because if that is off chart, then every other organ

10:14

displayed will be incorrect, and that becomes a fundamental for quality

10:18

control.