Bioimaging

Practice Set 1A:

Limiting Spatial Resolution (measured in line pairs/mm): tells you how many pairs of lines the imaging system can distinguish in 1mm, (how well it can distinguish between closely spaced lines

more lines = better spatial resolution

Approximate Resolvable Size (mm): smallest object that system can distinguish

the smaller the better

Which imaging modality would you use for each thing
1. Brain Tumor: MRI - high resolution for soft tissue
2. Ovarian Cyst: Ultrasound - fluid filled and superficial so ultrasound
3. Colon Polyp: Endoscopy w/ visible colonoscopy - REALLY small so need good resolution
List 7 different applications of in vivo imaging based on radiopharaceutical labeling
1. Brain
2. Heart
3. Tumor
4. Blood
5. Kidneys
6. Thyroid
7. Lungs!

Ask againg or questions later:

MRI - bone marrow

CT - is for hard bone

CT - kidney stones

CT - blood clots

SPECT is good for bones, PET is good for cancer

Bloodflow - Ultrasound or SPECT

Practice Set 1B:

sketch objective function (just start from y = 0, and the image is how much went through the surfaces)
1. light rays completely reflected = no image, 0%
2. 50% attenuated by dark, and not attenuated by white areas (100%, 50%, 100%, 50%)
3. gamma passed without attenuation = 100%
express statement as one mathematical expression and define terms
1. Principle of Superposition: if you have two input objects into a system, the end result image is the sum of the images of them if taken separately
  1. F(ag + bh) = aF(g) + bF(h)
  2. where F is the imaging function, a and b are constants, g is position of object 1 and h is position of object 2'
  3. images from different points can be added together
2. Space Invariant: the PSF (blurry point) stays blurry even if you move it
  1. h(x2, y2) | (x,y) = h(x2 - x, y2 - y) for all positions x, y
  2. Function of H (point spread function) remains the same regardless of where you move it
  3. every point gets the same PSF
3. Point spread function of imaging system is image of a point source
  1. how blurry psf makes an object
  2. PSF image produced, S is the imaging system, delta is a point source and is located at x y, x and y are the positions
  3. a psf is the image of a point source and is blurry bc of the imaging system
4. In a linear space invariant imaging system, output is convolution of input (object function) w/ point spread function
  1. image by linear space invariant imaging system is object convoluted w/ PSF
  2. convolution is how combining two functions to figure out how one function changes or blurs the other
  3. the imaging function of an object’s position is equal to the object’s position where PSF, how blurry the imaging system makes it, affects all points regardless of where they are positionally
  4. the image of any position is equal to the sum of all points where PSF is how much the point is blurred by the image system and is the same everywhere regardless of where the point is spatially

Models depict 3 object functions and their correspodning images
1. each point source creates a copy of PSF (end result that can end up blurry)
2. As each point source gets closer, it gets blurrier; when they’re far apart it is clear
  1. has to look like image 1 basically
  2. Determine the resolution: Rayleigh’s criterion: how close two point sources can be while still being two separate points (distinguishable)
    1. we use image 2 instead of image 1 because it’s closer but you can still see the peaks so you ust subtract the peaks (3.5 - 2 = 1.5 resolution)

Each point gets blurred into PSF
1. to get the image just make it blurry and have a cross section where half the gaussian is equal to omega
2. Minimum distance ot be resolved is 2 omega = 2(0.25) = 0.5um
3. What improves the limit of resolution? (inc resolution)
  1. magnification does not affect resolution, just the size
  2. magnification does not affect resolution, just the size
  3. increasing omega increases the standard deviation which increases the min distance to be resolved if that’s true you need them to be FARTHER apart to distinguish them from each other (you want resolution to be small) so no
  4. dec omega dec distance apart which means inc resolution

sketch the image
1. straight line up = looks the same
2. triangles go down, start from middle and go down by a/2

a
1. plug it in r = 214.3 nm for resolution which means you need to be at least this distance away for you to detect distinct points
2. so 25nm is way less than r, so how did they get the resolution to be good. They used PALM which fluoresces only certain molecules at a time so they get one and it blurs and then the other so the blurs don’t meld into each other

need to practice 5 and 6

A PSF (point spread function) is what an imaging system does to a point, bc imaging systems are not perfect, it tends to result in a blurry point, PSF tells us how much the imaging system makes stuff blurry TO ONE POINT

Convolution: how a system blurs an object TO THE ENTIRE OBJECT (sum of all points)

image = object * PSF

Practice Set 3:

femur bone
1. I know it goes bone to joint back to bone so I’ll look for the rise again and use the two values before that which is 100 and 75 as my high and low respectively which goes to 25/100 or 0.25
  1. Contrast: C = image intensity (high) - low / high
2. SNR (signal to noise ratio): Signal measured (high - low) / noise
  1. I set noise to 10, you look at the average and see how much it goes up and down a bit around the femur itself = 100 - 75 / 5 = 5
3. SNR = high - low / noise
  1. 8 - 4/ 10 = 0.4
4. How many noisyframes to get to part B (0.4 vs. 5 —> 5 / 0.4 for a factor of 12.5) and you square it for the number of frames
Contrast:
1. 210 - 160 / 210 = 0.24= contrast
2. SNR = 50 / 10 = 5 I took the noise around the background
  1. shot noise limited = Poisson Distribution = sqrt(N) where N is the peak
  2. 210 - 160 = 50 / sqrt N (270) =
  3. w
  4. w
3. what if you changed it from 200ms to 800ms
4. How would SNR change if 4 frames added together and adveraged
5. 11upm of object, pixels are 6.um by 6.5um
  1. magnification = image / object