Problem $1$

Write a python script to import a DICOM CT image and plot $3$ different $2-$dimensional cross sectional

image views: axial, sagittal, and coronal. On each $2$D dimensional image, include axes with correct coor$-$

dinates$/$units$.$ Enable functionality such that, after plotting the initial $3$ views, the user of the script can

somehow determine visually a new cross$-$sectional point of interest, enter those coordinates, and replot the $3$

images to cross the volumetric dataset at the desired new point coordinate. For the homework assignment,

include screenshots and text descriptions of the code output along with the code itself.

Problem $2$

Initialize a list$/$array to contain conversion factors for CT Hounsfield Unit to Stopping$-$Power$-$Ratio. Search

the literature, pubmed, etc, to find an appropriate conversion table.

Choose a single axial slice of the CT for this problem. Write a computer script to compute the $2$D $(xz)$

dose distribution from a single proton pencil beam of $100$MeV incident on an axial slice of the patient CT$.$

You can choose whatever slice you wish and you can choose the beam angle of the proton pencil beam.

You will please calculate dose in every CT voxel in this slice. Assume the proton beam is initially $1-mm$

wide, perfectly parallel, and incident in the beam direction you have chosen. As in the previous homework

assignment, use the equations from Schardt et al$.2010$ to model the depth dose Bragg peak, range straggling,

and off$-$axis Gaussian functions. Compute the composite $2$D dose distribution within this CT slice. Plot this

dose distribution as a $2$D colormap image, with a legend for dose value vs$.$ color scale. Label all coordinate

axes.

Bonus: Overlay a color image of the dose map over the colormap of the CT image. $($So that we can see

where the dose falls within the patient

Problem $3$

Same as problem $2,$ but make the proton beam wider. Recompute $2$D dose $(xz)$ for a $100-$mm wide proton

beam $($everything the same as above except the initial beam width is $100-mm).$ Can you demonstrate that

your dose algorithm "sees" the heterogeneities inside the patient affecting the range of the proton beam,

which likely varies off axis?