In CT scan variable intensity X Ray is passed through the object and an 3D image is recorded (Computed Tomography). Brain is covered by skull, made of high Z of Calcium. Inside skull brain is made up of low Z of C, H, O. How X ray is passing through skull and carries necessary information for image of brain and coming out from the opposite side, where again skull is present? Confused.
Dear Debasish,
you know the exponential Lambert Beer law of x-ray attenuation:
I = Io *exp(-µ*d), with Io as the incomming radiation, I the transmitted radiation captured at the detector, µ the linear x-ray attenuation coefficient and d the length of the pass way the x-ray travells in the sample. However for a head (skull + brain) the attenuation coefficoent µ is not a constant,
but µ
a) depends on the coordinates of space (for example x and y) of local x-ray attenuation in the imaged slice and
b) on the material composition (i.e C%, O%, H%, Ca%, etc.) at these places (x, y).
so µ = µ(x, y; C%, O%, H%, Ca%, etc.).
The term µ*d of the Lambert beer equation in this case changes into the line integral:
µ*d ---> integral [µ(x, y; C%, O%, H%, Ca%, etc.)*ds] with ds as the infinitesimal small length element of the pathway of x-rays across the sample (here the head) *).
Thus the signals picked up by the detector elements are of the kind:
I = Io*exp(- integral [µ(x, y; C%, O%, H%, Ca%, etc.)*ds]).
Thus the line-integral in the exponent of that projection bears the all informations on the elemental composition of each point xi, yi of that special projection trajectory.
When doing CT a lot of projections having a lot of line-integrals are measured.
The data evaluation of CT (called the tomographic reconstruction) in principle inverts this set of equations ending up with an presentation of µ(x, y) values.
According to these values µ(x, y) we can see a 2 dimensional distribution (i.e. an image) map of the local x-ray attenuation. Here low values are attributed to small atomic numbers such as H, C and O (brain) whereas high µ values (high x-ray attenuation) arises from Ca (here the skull) for example.
So in short: both, the brain and the skull, together contribute to the individual detector signals and from these the tomographic reconstruction delivers the x-ray attenuation map of that imaging slice.
*) if you are a not so familiar with an interal representation your may in a very simple view divide the individual x-ray pathways into three discrete sections:
i) dskull1 when the x-rays enter the head, µskull being active here,
ii) dbrain when the x-rays pass the brain; µbrain being active here,
and
iii) dskull2 when the x-rays leave the head; µskull being active here
The above mentioned line-integral reduces in this case to:
µskull*dskull1 +µbrain*dbrain+µskull2*dskull2 and the Lambert Beer law to :
I = Io*exp[-(µskull*dskull1 +µbrain*dbrain+µskull*dskull2 )]
= Io *exp (-(µskull*dskull1) * exp(-µbrain*dbrain) * exp(-µskull*dskull2)
From here in this simple 'picture' you can see that both the skull, the brain and again the skull contribute to the x-ray signal at the detector.
https://en.wikipedia.org/wiki/Tomographic_reconstruction
Yes, the skull provides significantly more attenuation per distance but it is rather thin:
https://www.researchgate.net/profile/Byungdu_Jo2/publication/258309932/figure/fig1/AS:297548603510788@1447952523994/The-mass-attenuation-coefficient-as-a-function-of-photon-energy-for-bone-and-tissue.png
Gerhard Martens detailed really well how the attenuation works along a line, resulting in a single projection (you may consider this a classical X-ray image), a bit more on how the image is formed from this:
The basic idea behind the CT is that the set of projections (X-ray images from various angles around the head) combined together yields the Radon-transform of the µ(x,y) image (the map of Z-density).
This 'set of projections' (called a sinogram -not the examination of the sinuses, in this case the name comes from the fact that the projections of a single 2D point yield a shape of a sine (or cosine) function) essentially means, that a series of line integrals of µ(x,y) are recorded by rotating the X-ray source and the detector around the object (head), at least for each rotation angle from the [0;pi] range (the density of sampling may be varied, i.e. steps of 1°, or higher may be used obviously with penalities on image quality).
From the resulting sinogram, the CT-image (µ(x,y)) is obtained by inversion. There are several approaches yielding the inverse Radon-transformation, the simplest is the filtered back-projection (FBP), modern CT-scanners generally use some iterative approach (e.g. a maximum likelihood -ML-EM- approach), some approaches use Legendre-polinomials for the inversion, etc...
The resulting CT-image is then scaled to reflect the Z-density in a conventional way, showing Hounsfield-units (HU) (defined by HUair=-1000, HUwater=0).
All in all, remember, that with high enough energy, the X-ray is not completely absorbed in the skull, only attenuated and by measuing the attenuation from all directions around the head, the Z-density can be reconstructed with the appropriate mathematical framework.
Computed tomography, more commonly known as a CT or CAT scan, is a diagnostic medical test that, like traditional x-rays, produces multiple images or pictures of the inside of the body. The cross-sectional images generated during a CT scan can be reformatted in multiple planes, and can even generate three-dimensional images. These images can be viewed on a computer monitor, printed on film or by a 3D printer, or transferred to a CD or DVD.
CT images of internal organs, bones, soft tissue and blood vessels provide greater detail than traditional x-rays, particularly of soft tissues and blood vessels. CT scanning provides more detailed information on head injuries, stroke, brain tumors and other brain diseases than regular radiographs (x-rays). Regarding to physical procces of x-rays in brain, please extensively read about Lambert Beer law of x-ray attenuation .
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