Mary PW Chin 钱碧慧博士
PhD (Wales), MSc (Surrey)
This is a virtual lab with a slant towards radiation physics. Scientific computing is a playground for understanding science. Many experiments which are either impractical or unethical in the real world spring to life in the computer. Scientific computing is becoming essential even for experimentalists, as data grow by terabytes. Without scientific computing, we won't be able go far beyond the classic 2D displacement-versus-time curve from an oscillating pendulum.

Python programming

for beginners
first bytes of Python
☞ slides

Matlab / Octave

for beginners
Matlab from scratch
☞ slides


for beginners
C from scratch
☞ slides


Command-line Linux
☞ slides


Build your own website
html css
☞ slides

Intro to image processing

Digital photos -> medical images
pixels and voxels from digital photos to medical images
☞ slides

Intro to radiotherapy

Geography -> dosimetry
various radiotherapy modalities in context
☞ slides

Photon interactions I

photon interactions with matter
☞ slides

Photon interactions II

photon interactions with matter II
☞ slides

Photon interactions III

photon interactions with matter III
☞ slides

Meeting of Nobel Laureates

☞ 55th Lindau Meeting

Laboratory #1

Derive CT numbers

Laboratory #2

Map photon interaction dominance

Multilingual programming

Matlab, Octave, Python, Perl, GNUplot

Questions for revision

Medical application of ionising radiation

Periodic table & nuclide chart

coming soon

External goodies

Worm Atlas

Personal statement

My journey in science

Laboratory #1: derive CT numbers
definition of the Hounsfield Unit
Equation 1. The Hounsfield Unit defined.
    Part A: Body tissues
  1. To derive HU, first we need find μwater and μ for each material we wish to derive HU for.
  2. We are going to lookup the XCOM database for μwater and μ.
  3. Before giving us the answer, XCOM will first ask us for
    • the elemental composition of the material we want the μ for.
    • the energy of the photons from the CT machine. Refer to the CT chapter by your favourite author, convince yourself that 80 to 120 keV is about the reasonable approximate.
  4. From the NIST tissue composition database: extract both data columns: the atomic number and the fractional weight. Translate the atomic number in the first column to element names, e.g. H, C, N, … In case you need help, refer to the periodic table.
    ICRP lung.
    fractional weight
    H 0.101278
    C 0.102310
    N 0.028650
    O 0.757072
    Na 0.001840
    Mg 0.000730
    P 0.000800
    S 0.002250
    Cl 0.002660
    K 0.001940
    Ca 0.000090
    Fe 0.000370
    Zn 0.000010
    ICRP cortical bone.
    fractional weight
    H 0.047234
    C 0.144330
    N 0.041990
    O 0.446096
    Mg 0.002200
    P 0.104970
    S 0.003150
    Ca 0.209930
    Zn 0.000100
  5. Go to NIST's XCOM online database; select 'Mixture' and click 'Submit Information'.
  6. Paste the data (in pure text format) you obtained from step 4 into the window asking for relative weights. This window does not like tabs, so please remove any tabs.
  7. Click 'Submit Information'. In return, expect to get a graph followed by a table.
  8. Locate the row in the table where the 2nd column (Photon Energy) says 8.000E-02 MeV (80 keV). Along the same row, take the value in the column under 'Total Attenuation with Coherent Scattering'. This is the mass attenuation coefficient (μ/ρ) at 80 keV for the material at hand.
  9. You should get 1.824E-01 cm2/g and 2.221E-01 cm2/g for lung and cortical bone, respectively.
  10. We still need to find μwater. For this, go back to NIST's XCOM online database; select 'Compound' and click 'Submit Information'.
  11. Enter 'H2O' in the window asking for 'Formula for compound'. Click 'Submit Information'. Repeat step 8. You should get 1.837E-01 cm2/g for water.
  12. The mass attenuation coefficient (μ/ρ) is independent of density and is therefore a more fundamental property than the linear attenuation coefficient (μ). Do not be misled by the presence of 'gram' in its unit (cm2/g), mistaking it as carrying density effects embedded within. The linear attenuation coefficient (μ) is the one which depends on density; to make it independent of density we divide μ by the density and this is how that 'gram' in μ/ρ came to be. We know that CT scanning, and therefore HU, is a measure of density (as well as the elemental composition). HU therefore cannot be independent of density. So, Equation 1 rightly asks for μ, not μ/ρ.
  13. We are now ready to convert μ/ρ to μ by multiplying with the density. Let us use 0.260 g/cm3 and 1.850 g/cm3 as density for lung and cortical bone, respectively.
    1.837E-01 cm2/g × 1.000 g/cm3 = 1.837E-01 cm-1 [water]
    1.824E-01 cm2/g × 0.260 g/cm3 = 0.474E-02 cm-1 [lung]
    2.221E-01 cm2/g × 1.850 g/cm3 = 4.109E-01 cm-1 [cortical bone]
  14. We are finally ready for Equation 1:
    HU = 1000 ( 1.915E-01 - 1.837E-01 ) / 1.837E-01 = -742 [lung]
    HU = 1000 ( 4.109E-01 - 1.837E-01 ) / 1.837E-01 = 1237 [cortical bone]
    Part B: Contrast agents
  15. Now let us derive the HU for barium and iodine.
  16. Go back to NIST's XCOM online database; select 'Element' and click 'Submit Information'.
  17. Enter 'Ba' in the window asking for 'Symbol'; click 'Submit Information'. Repeat step 8 to grab μ/ρ for barium at 8.000E-02 MeV.
  18. Go back to the previous page where the form asks for the 'Symbol' for an element. Enter 'I' in the in the window asking for 'Symbol'; click 'Submit Information'. Repeat step 8 to grab μ/ρ for iodine at 8.000E-02 MeV.
  19. We should get μ/ρ = 3.963 cm2/g and 3.510 cm2/g, respectively.
  20. Applying ρ = 3.500 g/cm3 and 4.930 g/cm3 for barium and iodine, respectively, we get:
    HU = 1000 ( 3.963 × 3.500 - 1.837E-01 ) / 1.837E-01 = 74506 [barium]
    HU = 1000 ( 3.510 × 4.930 - 1.837E-01 ) / 1.837E-01 = 93199 [iodine]

    This explains how barium and iodine act as CT contrast agents, causing the pixels to be very bright, differentiating enhanced regions from other tissues. Note that barium has a higher μ/ρ than iodine, but a lower ρ, effectively a lower μ. Iodine ends up a stronger contrast agent.
    Part C: Megavoltage imaging
  21. Repeat steps 1 to 14 for 2 MeV instead of 80 keV. We find that HU at 2 MeV for cortical bone is now 746 rather than 1237. The difference between cortical bone and water is therefore 1237 at 80 keV and 746 at 2 MeV. This reduction in contrast is a numeric demonstration of the undesirable feature of megavoltage CT, which operates at photon energies optimised for therapy rather than imaging.
    A summary of our exercise, with some bonus materials included.
    ρ (g/cm3) μ/ρ (cm2/g) HU
    80 keV2 MeV80 keV2 MeV
    water 1.00 1.837E-01 4.942E-02 0 0
    lung 0.26 1.824E-01 4.893E-02 -742-743
    cortical bone 1.85 2.221E-01 4.663E-02 1237 746
    barium 3.50 3.963E+00 4.078E-02 74506 1888
    iodine 4.93 3.510E+00 4.124E-02 93199 3114
    air 1.20479E-03 1.650E-01 4.452E-02 -1000 -1000
    adipose 0.92 1.806E-01 4.963E-02 -96 -76
    blood 1.06 1.824E-01 4.896E-02 52 50
    brain 1.03 1.838E-01 4.933E-02 31 28
    compact bone 1.85 2.087E-01 4.733E-02 1102 772

    The calculations above are estimations. CT numbers are never exactly so. Uncertainties include variations in density and most importantly, tissue composition. We have used the tissue composition provided by ICRP. Measuring elemental composition is a highly specialised field of its own, with many challenges. Samples have inevitably been in-vitro, if not cadavers'.

Laboratory #2: map photon interaction dominance
Z versus E graph. Cross-section dominance of photon interactions: photoelectric effect, Compton scattering, pair production Figure 1. Dominance by three competing photon interaction types.

Does this plot look familiar? It appears in every textbook on radiation physics. What is x axis? What is y axis? What are their units?

X-axis is in energy (MeV). Y-axis is the atomic number (Z). The plot shows the dominant interaction type for different elements at different energies. The three competing interaction types are photoelectric absorption, Compton scatter and pair production.

  1. Go to NIST's XCOM database for elements.
  2. In the window asking for 'Atomic Number' enter '1'. Click 'Submit Information'.
  3. We should get a new page showing a graph followed by a table.
  4. In the table, check the tick boxes on the header row for 'Coherent', 'Incoherent', 'Photoeletric Absorption', 'In Nuclear Field', 'In Electron Field' and 'With Coherent Scattering'.
  5. Click 'Download data'.
  6. Once a new page containing columns of data appears, use your browser to save the file (usually Ctrl-S works).
  7. Repeat steps 1 to 6 for atomic numbers up to, say, 70. It is your choice whether to download every step of Z (Z = 1, 2, 3, …, your graph will look nicer) or to download at intervals of Z (Z = 1, 10, 20, 30, …, your graph shall have data points spaced apart).
  8. We now have a collection of text files saved, each containing the photon μ/ρ for different elements. Each file begins with 3 header rows. Data start from the 4th row. The 1st column is the energy (MeV). The remaining columns contain the μ/ρ for different interaction types, including the three main types of interest to us: Compton scattering ('Incoherent'), photoelectric absorption and pair production ('In Nuclear Field' plus 'In Electron Field').
  9. Each file (corresponding to the respective Z) we downloaded will contribute two data points towards constructing our own version of Figure 1.
    • E1: the energy where photoelectric absorption passes over its dominance to Compton scattering;
    • E2: the energy where Compton scattering passes over its dominance to pair production.
    That is to say:
    • at E < E1, photoelectric cross section exceeds those of Compton scattering and pair production;
    • within the range E1 < E < E2, Compton scattering cross section exceeds those of photoelectric absorption and pair production;
    • at E > E2, pair production cross section exceeds those of photoelectric absorption a nd Compton scattering.
  10. Finding the two data points row by row for each file would not only be tedious but error prone. Manual handling is not the way. So, let's automate the process. In what follows, I provide a multi-lingual solution, whichever programming language you prefer: Except Matlab, all are freely downloadable. Octave is ala-Matlab, but free; most functions work equally well. Python, Perl and GNUplot usually come packaged with the Linux operating system already. Programming languages differ by syntax, but the algorithm to complete a given task is the same no matter which language is it implemented with.
  11. Putting on our computing hat, here is the input we need to process/crunch/compute in order to produce the output we desire (that is, Figure 2):
    • Input: a collection of files (downloaded from step 6), one for each element. The files are in pure text format (as opposed to the binary format and the rich text format). Each file contains:
      • two rows of text headers;
      • a blank row;
      • many rows of spaced-delimited numbers, where the energy increases row by row;
      • 7 columns to each row: the first column is the energy in MeV, the remaining columns are the μ/ρ for different components.
    • Process:
      • scan each file row by row;
      • compare μ/ρ for photoelectric effect (column 4), Compton (column 3) and pair production (column 5 plus column 6, which are components from the nuclear and electron fields, respectively);
      • find the dominant interaction for each row (i.e. for each energy);
      • find the energy where the dominance switches from photoelectric to Compton, and where the dominance switches from Compton to pair production.
    • Output:
      • (optional) save the data we obtained in three columns: the atomic number (Z), the energy where the dominance switches from photoelectric to Compton, and the energy where the dominance switches from Compton to pair production.
      • plot the data we obtained, in the spirit of Figure 1. That is, Z on the vertical axis and energy on the horizontal axis, which should be set to the logarithmic scale. This would produce Figure 2.
  12. Taking a level down, closer to the computer's psyche rather than ours, the tasks outlined in step 12 translate into the following algorithm, which is exactly what the three program listings (Matlab/Octave, Python, Perl+GNUplot) do.
    open a new file for output                              
    scan the directory for input files                      
    loop over each input file                               
      initialise user variable                              
      decipher Z from the filename                          
      write Z on the output file                            
      open the input file                                   
      loop over each row in this input file                 
        read the energy                                     
        read μ/ρ for Compton scatter                 
        read μ/ρ for photoelectric absorption        
        read and compute μ/ρ for pair production    
        if photoelectric dominates, set thisflag to 1      
        if Compton scatter dominates, set thisflag to 2    
        if pair production dominates, set thisflag to 3    
        if dominance switches from photoelectric to Compton,
          record the energy on the output file              
        if dominance switches from Compton to pair,         
          record the energy on the output file		    
        in case of other switches of dominance,             
          announce the unexpected on the screen             
        remember thisflag by storing as lastflag            
    finished writing, close the output file                 
    read the file we have just written                      
    set graph to superposition mode                         
    plot (E,Z) where E is the energy where dominance switches  
    set horizontal axis to log                              
    print the legend                                        
    label the axis                                          
    turn grid on                                            
    Listing 1. The algorithm.
  13. To track the switch of dominance, I use two variables: thisflag (for the current row) and lastflag (to remember the previous row). They take on the value 1 if photoelectric absorption is dominant, 2 if Compton scattering is dominant, 3 if pair production is dominant.
  14. Note that I saved the files from step 6 as 01.txt, 02.txt, 03.txt … for hydrogen, helium, lithium, … According to your file-naming convention, you probably need to modify line 2 of Listing 2 (for Matlab/Octave), line 6 of Listing 3 (for Python), line 2 of Listing 4 (for Perl).
  15. Whereas Matlab/Octave and Python (assuming Matplotlib is installed) readily plot graphs within the same environment, Perl doesn't. Perl is excellent for data handling though. Output can be easily written to file, which can be readily plotted using GNUplot. This is exactly the option I provide here.
  16. For consistency between the three programming options provided here, I opt to write the output to a file anyway — even when ready plotting is available within the same environment. I also opt to read from file the data to be plotted, for the sake of consistency. I could have stored the data in memory as an array instead.
  17. I have colour-coded all 4 program listings as a learning aid to readers new to programming. I encourage beginners to try colour-coding whatever program listings they encounter; this will provide a leg up on programming.
    • Built-in commands intrinsic of the programming language appear in blue. These we can't change as we like, or we knock the program out of order.
    • Variables defined by the user appear in red. These we can change according to our liking. Take Listing 1, for example, we can replace all occurrences of out to donkey, alice or smile, and the program will still sing and dance all the same. The worse we could do would be to confuse ourselves, wondering what is the donkey's role here or what is Alice doing here. So, best to name variables meaningfully — when you revisit the program next time, or if you pass the program to someone else, your program will be less painful to decrypt.
    • Instantaneous values appear in limegreen. In computing terms, values may be numbers or characters.
    out = fopen('dominance.mout','w');
    file = dir('*.txt');
    for f = 1:numel(file)
      lastflag = 0;
      field = strsplit(file(f).name,'.');
      Z = str2num(field{1});
      fprintf(out,'%d ',Z);
      a = importdata(file(f).name,' ',3);
      for row = 1:size(,1)
        E =,1);
        compt =,3);
        photo =,4);
        pairp =,5) +,6);
        if (photo>compt && photo>pairp)
          thisflag = 1;
        elseif (compt>photo && compt>pairp)
          thisflag = 2;
        elseif (pairp>photo && pairp>compt)
          thisflag = 3;
        if (lastflag==1 && thisflag==2)
          fprintf(out,'%.3e ', E);
        elseif (lastflag==2 && thisflag==3)
          fprintf(out,'%.3e\n', E);
        elseif (thisflag~=lastflag && lastflag>0)
          fprintf(out,'Exception! %.3e %d\n', E, Z);
        lastflag = thisflag;
    b = load('dominance.mout');
    hold on
    legend('Photoelectric to Compton','Compton to Pair','location','northwest')
    legend boxoff
    xlabel('Photon energy (MeV)')
    ylabel('Atomic number')
    grid on
    Listing 2. Matlab script for this exercise; works equally well in Octave. ☞ download
    import glob
    import numpy as np
    import matplotlib.pyplot as plt
    out = open("dominance.pyout","w")
    for file in glob.glob("[0-9]*.txt"):
      lastflag = 0
      field = file.split(".")
      Z = int(field[0])
      out.write("%d " % Z)
      with open(file) as xcom:
        for tisline in xcom.readlines()[3:]:
          field = tisline.split()
          E = float(field[0])
          compt = float(field[2])
          photo = float(field[3])
          pairp = float(field[4])+float(field[5])
          if (photo>compt and photo>pairp) :
            thisflag = 1
          elif (compt>photo and compt>pairp) :
            thisflag = 2
          elif (pairp>photo and pairp>compt) :
            thisflag = 3
          if (lastflag==1 and thisflag==2) :
            out.write("%.3e " % E)
          elif (lastflag==2 and thisflag==3) :
            out.write("%.3e\n" % E)
          elif (thisflag!=lastflag and lastflag>0) :
            out.write("Exception! %.3e %d\n" % (E,Z))
          lastflag = thisflag
    b = np.loadtxt("dominance.pyout")
    plt.xlabel('photon energy (MeV)')
    plt.ylabel('Atomic number')
    Listing 3. Python script for this exercise. ☞ download
    while(defined( $file=glob("[0-9]*.txt") )) {
      $lastflag = 0;
      @field = split /\./, $file;
      $Z = $field[0];
      printf out "%d ",$Z;
      <xcom>; <xcom>; <xcom>; 
      while($thisline = <xcom>) {
        @field = split /\s+/, $thisline; 
        $E = $field[0];
        $compt = $field[2];
        $photo = $field[3];
        $pairp = $field[4] + $field[5];
        if ($photo>$compt && $photo>$pairp) {
          $thisflag = 1;
        elsif ($compt>$photo && $compt>$pairp) {
          $thisflag = 2;
        elsif ($pairp>$photo && $pairp>$compt){
          $thisflag = 3;
        if ($lastflag==1 && $thisflag==2) {
          printf out "%.3e ",$E;
        elsif ($lastflag==2 && $thisflag==3) {
          printf out "%.3e\n",$E;
        elsif ($thisflag!=$lastflag && $lastflag>0) {
          printf "Exception! %.3e %d\n",$E,$Z;
        $lastflag = $thisflag;
    Listing 4. Perl script for this exercise. ☞ download
    set logscale x
    set xlabel "Photon energy (MeV)"
    set ylabel "Atomic number"
    set key left top
    set grid
    plot "dominance.plout" using 2:1 title 'Photoeletric to Compton', \
         "dominance.plout" using 3:1 title 'Compton to Pair'
    Listing 5. GNUplot script for this exercise. ☞ download
    Z versus E graph. Cross-section dominance of photon interactions: photoelectric effect, Compton scattering, pair production
    Figure 2. The outcome of this exercise.
    Dominance of photon cross sections for Z = 20.
    energy rangedominant interaction
    E < 0.1 MeV photelectric absorption
    0.1 MeV < E < 12 MeV Compton scattering
    E > 12 MeV pair production
  18. Voila, we should then be able to plot from our own produce (Figure 2) a graph similar to Figure 1.
  19. Pick a point on the graph, for instance Z = 20 and E = 0.1 MeV, where the curve separates photoelectric dominance (left of the curve) from Compton dominance (right of the curve). That means for Z = 20 (which is calcium), photons at energies up to 0.1 MeV will most likely undergo photoelectric absorption, dominating over Compton scatter and pair production. Compton scattering and pair production may still occur, but less likely compared to photoelectric absorption. If we send a 0.09 MeV photon into a sea of calcium, it may undergo photoelectric absorption, Compton scattering or pair production; I wouldn't bet on a single photon. But if we send in a thousand of these photons, I may then safely bet that the majority of the interactions would be photoelectric absorption.

    Along Z=20 on the same plot, there is a second curve intersecting at E = 12 MeV. In combination with the first intersection (E = 0.1 MeV), the energy domain is divided into three sections, as shwown in the table, each dominated by one of the three competing interaction types.

Matlab/Octave, Python, Perl, GNUplot side-by-side

Whether for drilling or learning, it would be fun to put the three programming solutions (Listing 2, Listing 3, Listing 4) from the preceding section side by side to see how the corresponding syntax and commands compare.

Matlab/Octave, Python & Perl: file and data handling.
import glob
import numpy as np
import matplotlib.pyplot as plt

out = open("dominance.pyout","w")

open(out,"> dominance.plout");

file = dir('*.txt');
for f = 1:numel(file)

for file in glob.glob("*.txt"): while(defined( $file=glob("*.txt") )) {

field = strsplit(file(f).name,'.');
Z = str2num(field{1});
field = file.split(".")
Z = int(field[0])
@field = split /\./, $file;
$Z = $field[0];
fprintf(out,'%d ',Z); out.write("%d " % Z) printf out "%d ",$Z;
a = importdata(file(f).name,' ',3);
for row = 1:size(,1)
with open(file) as xcom:
for tisline in xcom.readlines()[3:]:
<xcom>; <xcom>; <xcom>;
while($thisline = ) {
E =,1); E = float(field[0]) $E = $field[0];
if (photo>compt && photo>pairp)

elseif (compt>photo && compt>pairp)

if (photo>compt and photo>pairp) :

elif (compt>photo and compt>pairp) :
if ($photo>$compt && $photo>$pairp) {

} elsif ($compt>$photo && $compt>$pairp) {

Matlab/Octave, Python & GNUplot: plotting.
b = load('dominance.mout');
hold on
legend('Photoelectric to Compton',...
'Compton to Pair',...
legend boxoff
xlabel('Photon energy (MeV)')
ylabel('Atomic number')
grid on
plt.xlabel('Photon energy (MeV)')
plt.ylabel('Atomic number')
set logscale x
set xlabel "Photon energy (MeV)"
set ylabel "Atomic number"
set key left top
set grid
plot "dominance.plout" using 2:1 \
title 'Photoeletric to Compton',\
"dominance.plout" using 3:1 \
title 'Compton to Pair'
Questions for revision
  1. Medical accelerators conventionally deliver 6 MV and 10 MV photon beams. In the patient's body, energy is deposited by
    photons only
    electrons only
    photons and electrons
    neither photons nor electrons
  2. During commissioning and quality assurance for radiotherapy, a water phantom is so frequently used to represent the human body because
    over 50% of an average adult human body is water
    ion chambers are calibrated for measurements in water
    radiation properties of the human body approximate those of water
    density of the human body approximates that of water
  3. The ideal dose distribution on a treatment plan would be
    100% perfectly uniform throughout the outer target volume, zero outside
    97%% perfectly uniform throughout the outer target volume, zero outside
    95%% perfectly uniform throughout the outer target volume, zero outside
    varying according to local biological response in the target volume, zero outside
  4. Neutron contamination is present when a linac operates in the following modes
    6 MV and above
    10 MV and above
    18 MV and above
    all electron modes
  5. In BNCT the therapeutic dose is delivered by
    alphas and lithiums
    alphas only
  6. The Bragg peak drops abruptly at the far extent of the target volume. This is principle underlying
  7. In bunker design, walls and mazes play the following principal roles:
    walls reduce penetration, mazes reduce scatter
    walls reduce scatter, mazes reduce penetration
    walls reduce both penetration and scatter, mazes do not reduce the dose outside
    walls and mazes reduce penetration and scatter all the same
  8. In proton therapy, peak-to-entrance dose ratios between a pencil beam and a SOBP beam
    differ significantly
    differ negligibly
    equal exactly
    differ significantly or not, depending on body site
  9. The mass attenuation coefficient
    is density dependent
    is the inverse of linear attenuation coefficient
    provides a measure of tissue mass
    none of the above is correct
  10. For radiation protection around a megavoltage linac, the most desirable interaction would be
    Compton scattering
    positron annihilation
    pair production
    photoelectric effect
  11. Particles which are directly ionising include
    electrons and protons but not photons and neutrons
    electrons, protons and photons but not neutrons
    electrons, protons, photons and neutrons
    electrons only
  12. On a treatment plan typically we expect envelops of increasing areas
    GTV < CTV < PTV
    PTV < CTV < GTV
    CTV < PTV < GTV
    PTV < GTV < CTV
  13. A bolus is in contact with the skin; a compensator is attached to the treatment unit.
    Skin sparing is considerable amd comparable in both cases.
    Skin sparing is achieved with a bolus, given the direct contact.
    Skin sparing is achieved with a compensator, given the large air gap.
    Skin sparing is lost in both cases.
  14. Dose computations from convolution techniques and Monte Carlo simulations differ most
    in the head and neck area
    in the thorax
    in the abdomen
    in the limbs
  15. During PET examinations the patient is injected with a positron-emitting radioisotope e.g. 18F-FDG. Signal for image construction relies on coincident gamma pairs. A coincident gamma pair is a product of positron annihilation with an electron. Where does the electron come from?
    atoms within the patient's body
    the PET scanner
    the radioisotope supplies both positrons and electrons
    none of the above
  16. Which of the following windows or filters are always in operation during PET?
    all of the above
    linear attenuation coefficient versus energy
    Figure 3.
    mass attenuation coefficient versus energy
    Figure 4.
  17. How do Figure 3 and Figure 4 differ?
Personal statement

Science is never meant to be exclusive. It is not true that only those from the elite pack can do science. This is the most grievous misconception I grew up realising that it is so untrue. On its heels are two other misconceptions: one reduces mathematics to arithmetics, the other reduces physics to mechanics.

My own journey defies all prophecies. I never set out to prove prophets wrong, but it did turn out that everyone was actually quite wrong. All the years I was persistently told that I could never do science, and that it was time to drop out of school to take on the role of a house servant. As life unfolded, I got scholarships and later, I worked at CERN, the largest laboratory in the world. No, it is absolutely not about fighting or being strong. Life is not about fighting or being strong. I got where I am by going with the flow of nature. May the voice of nature swamp every noise.

Science is for everyone. It makes our lives whole. It complements arts.