Computerized Tomography Scan - CT SCAN

  There are two main limitations of using conventional x-rays to examine internal structures of the body. Firstly superimpositions of the 3-dimensional information onto a single plane make diagnosis confusing and often difficult. Secondly the photographic film usually used for making radiographs has a limited dynamic range and therefore only object that have large variation in the x-ray absorption relative to their surroundings will cause sufficient contrast differences on the film to be distinguished by the eye. Thus the details of bony structures can be seen, it is difficult to discern the shape and composition of soft tissue organ accurately.

                 CT uses special x-ray equipment to obtain image data from different angles around a body and then shows a cross section of body tissues and organs. i.e., it can show several types of tissue-lung,bone,soft tissue and blood vessel with great clarity. CT of the body is a patient friendly exam that involves little radiation exposure.

BASIC PRINCIPLE

                 In CT scanning, the image is reconstructed from a large number of absorption profiles taken at regular angular intervals around a slice, each profile being made up from a parallel set of absorption values through the object. ie, CT also passes x-rays through the body of the patient but the detection method is usually electronic in nature, and the data is converted from analog signal to digital impulses in an AD converter. This digital representation of the x-ray intensity is fed in to a computer, which then reconstruct an image.

                 The method of doing of tomography uses an x-ray detector which translates which translates linearly on a track across the x-ray beam, and when the end of the scan is reached the x-ray tube and the detector are rotated to a new angle and the linear motion is repeated. The latest generation of CT machines use a ‘fan-beam’ geometry with an array of detectors which simultaneously detect x-rays on a number of different paths through the patient.

CT SCANNER

                      CT scanner is a large square machine with a hole in the centre, something like a doughnut. The patient lies still on a table that can move up/down and slide in to and out from the centre of hole. With in the machine an X-ray tube on a rotating gantry moves around the patient’s body to produce the images.

PROCEDURE

                      In CT the film is replaced by an array of detectors which measures X-ray profile. Inside the scanner, a rotating gantry that has an X-ray tube mounted on one side an arc –shaped detector mounted on opposite side. An X-ray beam is emitted in a fan beam as the rotating frame spins the X-ray tube and detector around the patient. Each time the X-ray tube and detector make a 360 degree rotation and X-ray passes through the patient’s body the image of a thin section is acquired. During each rotation the detector records about 1000 images (profiles) of the expanded X-ray beam. Each profile is then reconstructed by a dedicated computer into two time.

Difference between x-ray image and ct scanned image

PHYSICS OF TOMOGRAPHY

                      X-ray photons interact with material in there principal ways: pair production, photoelectric absorption and scattering .Pair production only occurs if the photon energy is ›1.022mev,which is much higher than the energies used in medical tomography. Photoelectric absorption occurs when the photon is completely absorbed and transfers its energy to an electron .The electron then passes through the material giving up its energy until it comes to rest.

                      Scattering has two components-coherent or Raleigh scattering in which the direction of the photon is changed ,but it does not change frequency. The other is that Compton or incoherent scattering, where the photon gives  up some of its energy to an electron and continues on in a different directions  at lower energy. The combined effects of scattering and absorption results in an exponential attenuation of a beam of photons as it  passes through a material. A mono energetic beam with an input intensity of I0 photons passing through a length of material has an output intensity of

                      I=I0℮(-µx)

CALIBRATION

                 The projection p(x) depends on measurements of both the transmitted X-ray intensity I(0) and the incident X-ray intensity I0(x). The intensity variations with time can be measured by putting a reference X-ray detector in a portion of beam which does not intersect the patient, usually at the edge of the beam and sampling this detector at the same time as the measurement of the beam transmitted through the patient is sampled. The spatial fluctuations can be measured during an initial calibration run using a known object, such as a water filled cylinder in the place of patient.

SYSTEM COMPONENTS

All computed tomography system consists of four major subsystems.

·         Scanning System – takes suitable reading for a picture to be reconstructed. This includes x-ray source and detectors.

·         Processing Unit – converts these readings into intelligible picture information.

·         Viewing System – presents this information in visual form and includes other manipulative aids to assist diagnosis.

·         Storage Unit – here picture is stored in digital form.

     SCANNING SYSTEM

                The purpose of the scanning is to acquire enough information to reconstruct a picture for an accurate diagnosis. In basic scanning process, a collimated x-ray beam passes through the body and its attenuation is detected by a sensor that moves on a gantry along with the x-ray tube. The tube and the detector moves in a straight line.

                Inorder to get a clear image, rotation machines have been designed in which only the x-ray source rotates within a full circle of stationary detectors arranged around a patient. The individual detectors are lined up practically without gaps so that the radiation which has penetrated the patient is optimally used. The system permits calibration during scanning, which eliminates the problem of detector drift.

X-RAY SOURCE

                 In CT scanners, the highest image quality free from disturbing blurring effects is obtained with the aid of pulsed x-ray radiation. During rotation, high voltage is applied at all times. A grid tube prevents the electron current from striking the anode except when desired allowing the x-rays to be emitted in bursts. As the gantry rotates an electric signal is generated at certain positions of rotating system.

DETECTORS

                 For a good image quality, it is important to have a stable system response and in that detectors play a significant role. There are three types of detectors commonly used in CT scanning. They are xenon gas ionization detector, scintillation crystal and photomultiplier and scintillarc. A good detector is a pre-requisite to obtain optimal image quality, the measuring electronics must have a large dynamic range to backup the detector.

PROCESSING UNIT

             The information  received  by  the  computer  from  the  scanning  gantry  needs  processing  for  reconstructing  the pictures.  The  data  from  the  gantry  contains  information  on  the  following  parameters.

·         Positional information-such  as  which  traverse  is  being  performed  and  how far  the  scanning  frame  is  along  its  traverse.

·         Absorption  information-the  values  of  attenuation  coefficient  from  the  detectors.

·         Reference  information-obtained  from  the  reference  detector  that  monitors  the  X-ray       tube.

·         Calibration  information-Obtained  at  the  end  of  each  traverse.

                 The  first  stage  of  computation  is  to  analyze  and  convert  all  the  collected  data  in  to  a  set  of  profiles. However  the  main  part  is  of  processing  the  profiles  to  convert  the  information  which  can  be  displayed  as a  picture  and  used  for  diagnosis. In  general  the  reconstruction  method  can  be  classified  in  to  three  major  techniques.

·      Back  projection-which  is  analogous  to  graphic  reconstruction.

·      Iterative  methods-which  implement  some  form  of  algebraic  solution.

·      Analytical  methods-where  an  exact  formula  is  used. Two  of  these  are  filtered  back  projection, which  incoperates  the  convolution  of  the  data  and  fourier  filtering  of  the  image, and  two  dimensional  fourier  reconstruction  technique.

     The  method  of  back  projection  without  any  further  processing  is  simple  and  direct. In  This  method  each  of  the  measured  profiles  is  projected  back  over  the  image  area  at  same  angle  from  which  it  was  taken. At  the  same  time  each  projection  not  only  contributes  to  the  point  that  originally  formed  the  profile  but  also  to  all  the  other  points  in  its  paths. The  technique  in  fact  produces  starred  images  and  blurring  and  this  makes  it  totally  unsuitable  for  providing  pictures  of  adequate  clarity  for  medical  diagnosis.

                 The  earlier  scanners  used  iterative  technique  which  took  a  succession  of  back  projection  correcting  at  each  stage  until  an  accurate  reconstruction  was  achieved. The  method  requires  several  steps  to  modify  the  original  profiles  in  to  a  set  of  profiles  which  can  be  projected  back  to  give  an  un blurred  image. This  technique  however  tends  require  long  computation  time.

                 Current  commercial  scanners  use  a  mathematical  technique  known  as  convolution  of  filtering. This  technique  employes   a spatial  filter  to  remove  the  artifacts.

VIEWING SYSTEM

                 In  most  of  the  CT  system  the  final  picture  is  available  on  a  television  type  picture  tube. The  picture  is  constructed  by  a  number  of  elements  in  a  square  matrix  wherein  each  element  has  a  value  representative  of  the  absorption  value  of  the  point  in  the  body  which  it  represents.  This  technique  enables  to  have  a  much  larger  dynamic  range  than  the  eye  can  possibly  have.

STORING  AND  DOCUMENTATION

                 For  subsequent  processing  or  evaluation  of   a  CT  picture,  various  methods  of  storage  are  used.  The  picture  is  stored  in  the  digital  form  so  that  the  evaluation  is  convenient  on  a  computer  assisted  program. For  this  purpose  the  data  carries  generally  employed  are  magnetic  disc ,magnetic  tape  and  floppy  disc.  The  magnetic  disc  normally  hold  a  small  number  of  pictures.  So  it  cannot  be  employed  as  a  long  term  storage  medium.  Most  manufactures  of  CT  units  use  magnetic  tape  and  floppy  disc  and  floppy  disc  provide  medium  storage  range.  For  long  term  storage  magnetic  tapes  are  performed.

IMAGE RECONSTRUCTION

                 Computed tomography scans are a very powerful tool in medicine. X-rays passing through an object can be absorbed or scattered and the resulting loss in intensity is given by

                      I=Iexp(-µx)

Where µ is the linear attenuation coefficient

X is the distance the X-ray has traveled.

                      The initial ground work for computed tomography was laid by Radon, and he demonstracted that  an object could be reconstructerd  from an infinite number of projections through that object .In a modern CT scanner an X-ray fan beam and dector sweep around the patient obtaining thousands of projections at different angles .The CT scanner measures the intensity of the X-ray beam which pass through the object .The average linear attenuation coefficient along the projected line through the object is given by

                                  µ=ln(I/I0)/-Nt(delta t)

where  µ is the average attenuation coefficient

I/I0  is the normalized intensity

Delta t  is the  product of step size

Nt  is the number of steps

RECONSTRUCTION                                                                                                                   There have been many different algorithms developed to accomplish this task and while they have all been shown to be fundamentally identical the actual techniques appear quite different.  One of the most popular algorithm is the filtered back projection technique .As its name implies this technique involves two parts. Back projecting along the projection lines used ,and filtering the image.

BACK PROJECTION

                 Back projection is a relatively elementary process .One simply assigns the mean attenuation coefficient given by the equation

ln(I/I0)/Nt(delta t) to each point along that line.

                 This back projection is repeated for all angles .The attenuation coefficient for a particular point will be built up from all projection passing through that point  .In imaging jargon, each of these points pixel ,that is an element of the final image or picture.

                      In reality ,this process is not quite trival .The image under reconstruction is not continuous ,but is composed of discrete pixels. The projection lines will not pass perfectly through the centre of each pixels in their path and it is necessary to establish a method for describing the projection lines in terms of individual pixel with in a matrix.

                 By establishing an N/N matrix reconstruction matrix –g(x,y)-where N is the number of translation pixels in the t axis. For a given angle in measurement space a value at can be calculated for each pixel in the N/N matrix as follows.

t=xcosq+ysinq

This pixels in the N/N matrix can be assigned attenuation coefficient values from measurement

               G(x,y)=µ(t,q)

                 This process is repeated for each angle.

Ie           g(x,y)=(1/N)εg(x,y)

                 And the matrices are summed and divided by the number of angles to obtain the final back projected image.

FILTERING

                 Back projection alone results in a blurred reconstruction image .Filtering must be applied to correct for this and obtain an accurate image of the object.

                 There are a number of choices in the type of filter to use .The simplest and most rigorous one is the ramp filter.

                 H(w)=p(w)

                 The most commonly used filter is the Shepp-Logan filter, which combines a sine function with ramp filter.

Hsl(w)=p|w|sine(w/wmax)

This filter results in a small amount of blurring, but is much less sensitive to noise.

                                  Filtering and back projections are both linear operations. Filtering is performed by multiplying the fourier transform of a wave form by the filter function ,the result is then inverse fourier transformed to produce the filtered waveform. In fourier transforms, multiplication in Fourier space is equivalent to a convolution in normal space.

G(w)=F(w)*H(w)

g(t)=f(t)*h(t)

                 where G(w) and H(w) are fourier transforms of g(t),f(t) and h(t) respectively and * represents a convolution integral. The convolution integral is defined by

zf(u)h(t-u)du.

CT Numbers

                      Once both filtering and back projections have been performed ,the result is a two dimensional array of attenuation coefficient.

                 For historical reasons ,the attenuation  coefficients are converted into CT numbers in units of Houvsfield.

                      CT Number=1000(µ-µw)/µw

Where μw  is the attenuation coefficient for water.      

                 The main problem with CT has been the potential danger it represents because of radiation exposure .The developments in CT imaging  have made marked improvements in its technological capabilities ,the radiation effects problem has not received the same degree.

                      The new processing data method reduces the amount of radiation exposure needed while maintaining ,CT’s high resolution. The method is based on an algorithm that reconstructs the wavelet coefficients of an image from the radon transform data. The properties of wavelets are used to localize the radon transform and reconstruct a local region of the cross section of a body, using almost completely local data. This significantly reduces the radiation exposure and less computation time. The variance of the elements of the null space is negligible in the locally reconstructed image. An upper bound for the reconstruction error in terms of data used is also determined by the algorithm, which  for example requires 2% of full exposure data to reconstruct a local region 16 pixels in radius in a 256*256 pixel image.

                      After scanning the patient the operator can go straight to the wavelet transform without having to first reconstruct the image. To obtain wavelet transform the algorithm can be applied to full data or local data. Local image reconstruction is achieved with superior definitions in shortest time and with less radiation exposure to the patient.

                 That is in summary

·         Reconstructs with high accuracy and with few computations the wavelet transform of an image directly from the tomographic measurements.

·         Computes to high accuracy a small region of the image from measurements on line passing only through the region reducing computation time and radiation exposure.

·         Reconstructs the density at a point using only line integral data on lines that pass through a small region containing that point ,achieving reduced radiation exposure.

  

BENEFITS AND RISKS

BENEFITS

·         Unlike other imaging methods CT scanning offers detailed view of many types of tissues , including lungs, bones, soft tissues and blood vessels.

·         CT scanning is painless , noninvasive and accurate.

·         CT examinations are fast and simple.

·         Diagnosis made with the assistance of CT scan eliminate the need for invasive exploratory surgery and surgical biopsy.

·         CT scanning can identify both normal and abnormal structures, making it a useful tool to  guide radiotherapy , needle biopsies and other minimally producers.

·         CT has been shown to be a cost-effective imaging tool for a wide range of clinical problems.

RISKS

·         CT does involve exposure to radiation in the form of X-rays , but benefits of an accurate diagnosis far outweighs the risks .The effective radiation does from this procedure is about 10mv , which is about the same as the average person receives from background radiation in 3 years.

·         Special care is taken during X-ray examination to ensure maximum safety for the patient by shielding the abdomen and pelvis being imaged.

·         The risk of serious allergic reaction to iodine containing contrast material is rare and radiology departments are well equipped to deal them.

Limitations of CT scanning of the body

                 Very fine soft tissues details in areas such as a shoulder or knee can be more readily and clearly seen with MRI. In some situations soft tissues are may be unclear by near by bone structures. The exam is not generally indicated for pregnant women.

FUTURE DEVELOPMENTS

                 The current trends in the industry appear to be improve picture quality primarily resedation improvement and artifact reduction, and to lower the cost with existing quality. In the future, there is much interest in developing a real time heart tomography machine, allowing radiologists to observe sequences of heat functioning throughout its cycle of operation.

                 Industrial tomography is another future direction in which tomography is heading. Tomography allows detailed inspection of complex and critical parts. Two important potential applications are inspection of jet engines and machine parts such as blades and disks & inspection of rods in nuclear reactives.

 

Conclusion

                 When CT scanners first appeared it used to take four minutes to scan a section, thus making it impossible to image moving organs like the heart. But the machines of today can complete the scan in few seconds. Special machines are being developed for heart scanning which completes scans in milliseconds. Also the developments in CT imaging have made marked improvements in its technological capabilities the radiation effects problem has not received the same degree. The properties of wavelets are used here. This significantly reduces the radiation exposure and less computation time.