K Space in MRI

MRI and K space with FFT

1. K SPACE Presented by : Miss Kajal Jha BSC MIT-2016 BPKIHS-Dharan Presented to: Dr Arun Gupta Phd,Soeul University ,South Korea BPKIHS Dharan

2. What is K in K Space? Thousand???? Element Potassium???

3. It actually means “ spatial frequency   ” Image resolution is often described in terms of "line pairs per mm," the closest spacing of black and white bars that can be resolved. Since a pair of lines are like crests and peaks of adjacent waves, line pairs per mm is a measure of spatial frequency.

4. Image can be decomposed into planar waves varying in amplitude, frequency, phase and direction. Spatial frequency is the number of wave cycle (or line pairs) per unit distance.

5. The concept is simple. A wave is characterized by its wavelength ( λ ), the distance between two corresponding points or successive peaks. The  wave number  ( k )  is simply the reciprocal of the wavelength, given by the expression  k = 1 / λ       The wave number ( k ) is therefore the number of waves or cycles per unit distance . Since the wavelength is measured in units of  distance , the units for wave number are (1/ distance ), such as 1/m, 1/cm or 1/mm.  

6. The  k -space representation of an MR image is merely an organized collection of these spatial frequencies reflecting that image's spatial harmonic content.

7. So what exactly is K SPACE?? K SPACE is the space in which MRI imaging data is acquired . Introduced in 1979.

8. In MRI physics K space is the 2D or 3D transform of the mystery of the image. Unit is rad/m Its coz spatial frequency is represented as a phase change over distance along a gradient. Spatial frequency measures the change of phase between the magnetic moments of a row of spins along the gradient.

9. The frequency data of FID from our body is stored in the K Space. It is related to the Fourier transformation technique which is basicially just a method to store data, be it 2D or 3D. It helps in the image acquisitation as a image of human body(part/organ).

10. What is there in K Space Its imaginary Still storage device Stores digitized data produced from spatial frequencies created from spatial encoding.

11. What does it look like? Its rectangular Has two axes perpendicular to each other. Frequency axis Horizontal Centered in the middle of several horizontl lines Data from frequency encoding are positioned in k space along this axis. Phase axis Vertical Centered in the middle of K space perpendicular to the frequency axis. Data from phase encoding are placed in k space along this axis.

12. So how is K S pace filled??? In simplest method of K space filling, data are stored in horizontal lines that are parallel to the frequency axis and perpendicular to the phase axis of K Space.

13. So does the single point of K space determine single section of image??

14. Interstingly Each   k -space point contains spatial frequency and phase information about  every  pixel in the final image. Conversely, each pixel in the image maps to  every  point in  k -space.  Its important to know that there is not a one to one relationship between image and k space. Each individual point on image space depends on all of the points contained in k space.

15. K Space is NOT IMAGE. Data stored in the top line do not end up being the top of the image.

16. Important facts about K Space K space is not an image. Data are symmetrical in the K Space Data acquired in the central lines contribute signal and contrast, while data acquired in the outer lines contribute reslution.

17. S.NO FREQUENCY ENCODING GRADIENT(FEG) PHASE ENCODING GRADIENT(PEG) 1 Determines how far to the left and right K Space is travelled. Determines how far up and down a line of K space is filled. 2 Determines the size of FOV. Determines the phase matrix of the image. 3 FEG positive: K space transvered from left to right. PEG positive: fills top hal;f of K Space. 4 FEG negative: K space transvered from right to left. PEG negative : Fills bottom half of K Space.

18. Types of acquisition There are three types of acquition of data Sequential- it acquiries all the data from slice1 and then go on to acquire all the data from slice 2(all the lines in K Space are fille for slice 1 and then all the lines of K Space are filled for slice 2,etc.).The slice are so displayed as acquired(not likely as CT) 2D Volumetric acquisition : fill one line of K Space for slice 1 , and then go on to fill the same line of K space for slice 2,etc. When this line has been filled for all the slices, the next line of K Space is filled for slice 1,2,3,etc. This is the most common type of data acquisition. 3D Volumetric

19. Fourier transform The Fourier transform is a mathematical technique that allows an MR signal to be decomposed into a sum of sine waves of different frequencies, phases, and amplitudes.

20. Fourier transformation  is the mathematical procedure connecting  s(t)  and  S ( ω ). If  s(t)  is specified,  S ( ω ) may be computed, and vice versa .

21. Lets know that Fast Fourier Transform(FFT) and Fourier Transform(FT) is same. GRADIENTS SPATIALLY LOCATE SIGNAL ACCORDING TO THEIR FREQUENCY,NOT THEIR DOMAIN so FFT converts time domain to frequency amplitudes in the frequency domain.

22. To summarize The central portion of K Space contains data that have high signal amplitude and low resolution. The outer portion of K Space contains data that have low signal amplitude and high resolution.

23. REFERENCES MRI in practise,4th Edition Questions and answere in MRI

24. THANK YOU