;; Note: 600 ticks is one "hour" ; Decalaring variables breed [Tcells Tcell] ; There are two "breeds" of cells, tumour and healthy, represented by Tcells and Hcells, respectively breed [Hcells Hcell] Tcells-own [hypoxic?] ; Each cell can also have a variable. See Extending The Model on the Info tab. globals[ Tsurvive ; number of tumour cells remaining Hsurvive ; number of healthy cells remaining numdoses ; number of fractions completed lifeT ; lifetime of tumour cells lifeH ; lifetime of healthy cells ] ;; The other variables are declared through creating the inputs in the interface tab: ;; "fractions", "hours", "dose", "alpha" and "beta". ;; This is what happens when the SETUP button is pushed to setup clear-all ;all old data is cleared set lifeT 720 ; in hours. set lifeH 2160 create-Tcells 5000 [ ;Make 5000 tumour cells setxy (random 45) random-ycor ; Distribute them randomly on the right side of the tissue sample set shape "dot" ; Gives their shape, colour, and size set color red set size 4 ] create-Hcells 5000 [ ; Same for the healthy cells, put put them only on the left setxy (random -45) random-ycor set shape "dot" set color green set size 4 ] reset-ticks ;reset the counter end ;; This is what happens when the GO button is pushed to go if (count Tcells <= 5 or count Hcells <= 20) [ ; Set cutoff point: If there are 5 or less Tcells or 20 or less Hcells, the program stops output-write round (100 * count Hcells / 5000) ; This prints the information that shows up in the box in the interface output-print "% of the healthy cells remain and " output-write numdoses output-print " treatments were given." output-print "Total dose delivered:" output-write numdoses * dose output-print " Gy" stop] plot-surviving ; calls the plotting procedures (see below) plot-logSurvival ;; put tick here instead if you don't want the radiation to start on tick 0 ask Hcells [ ;; on each tick, the healthy cells have a probability of dividing if (random-float lifeH * 600 <= 1) [hatch 1];; if (count turtles-here > 1)[ ; if there is more than one cell in a region ifelse xcor > 0 ; if the cells position is to the right of the center of the sample [set heading 270] ; Spins cell to be "facing" to the left - corresponds to when xcor>0 [set heading random-float 359] ; Has cell point in a random direction - corresponds to when turtles-here>1 fd 1] ; move forward in direct of heading by one unit ] ask Tcells [ if (random-float lifeT * 600 <= 1) [hatch 1] if (count turtles-here > 1)[ ifelse xcor < 0 [set heading 90] [set heading random-float 359] fd 1] ] ;; Procedure for when treatment is given if (ticks mod (hours * 600) = 0 and ticks < Fractions * hours * 600) [ ; specifies when radiation is applied ; The following equations determines if each cell survives the treatment ask Tcells [ ; call on each tumour cell if (random-float 1.0 < 1 - exp((-1 * ((Dose * alpha) + (beta * Dose ^ 2))))) [die]] ; this is where you could add an extra condition to check if the cell is hypoxic, and have only oxic cells die. ask Hcells [ if (random-float 1.0 < 1 - exp((-1 * ((Dose * 0.1) + (0.1 * Dose ^ 2))))) [die]] set numdoses numdoses + 1 ; counts the number of treatments given ] tick ; Raises tick counter by 1 end ;; the two plotting procedures: to plot-surviving ; plots the number of remaining cells after each tick set-current-plot "Survival" set-current-plot-pen "Tumour" plotxy ticks count Tcells ;; plots the number of Tcells versus the number of ticks so far set-current-plot-pen "Healthy" plotxy ticks count Hcells end to plot-logSurvival set-current-plot "logSurvival" set-current-plot-pen "TumourL" plotxy ticks log count Tcells 10 ; the 10 specifies log base 10 set-current-plot-pen "HealthyL" plotxy ticks log count Hcells 10 end @#$#@#$#@ GRAPHICS-WINDOW 230 11 628 410 -1 -1 4.29 1 10 1 1 1 0 0 0 1 -45 45 -45 45 0 0 1 ticks 30.0 BUTTON 14 508 69 541 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 103 509 158 542 NIL go T 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 640 371 960 676 Survival ticks Number of remaining cells 0.0 10.0 0.0 10.0 true true "" "" PENS "Tumour" 1.0 0 -2674135 true "" "" "Healthy" 1.0 0 -10899396 true "" "" INPUTBOX 88 339 144 399 beta 0.04 1 0 Number INPUTBOX 7 339 66 399 alpha 0.3 1 0 Number INPUTBOX 88 173 151 233 hours 8.0 1 0 Number INPUTBOX 91 81 153 141 Fractions 30.0 1 0 Number PLOT 638 10 964 322 logSurvival ticks log (number of remaining cells) 0.0 10.0 0.0 4.0 true true "" "" PENS "TumourL" 1.0 0 -2674135 true "" "" "HealthyL" 1.0 0 -14439633 true "" "" OUTPUT 229 447 631 555 15 TEXTBOX 11 54 214 92 Enter the number of fractions 15 0.0 1 TEXTBOX 8 138 231 203 Enter the time between fractions 15 0.0 1 TEXTBOX 9 297 221 335 Enter the alpha and beta values for the tumour cells 15 0.0 1 TEXTBOX 9 236 227 274 Enter the dose per fraction 15 0.0 1 TEXTBOX 6 407 223 502 Press \"setup\" before each trial and \"go\" to start. The program will stop automatically when only 0.1% of the tumour cells remain. 15 0.0 1 TEXTBOX 11 10 161 35 Set-up options 20 0.0 1 TEXTBOX 642 327 960 403 The above is a semi-log plot of the number of cells remaining versus elapsed time. 15 0.0 1 TEXTBOX 644 685 970 761 The above is a plot of the number of cells remaining versus elapsed time. 15 0.0 1 SLIDER 8 259 180 292 dose dose 0 6 1.2 0.2 1 NIL HORIZONTAL @#$#@#$#@ # A NetLogo Model For Fractionated Radiation Treatment ## WHAT IS IT? This is a basic model of the effect of radiation treatment on healthy tissue and tumour tissue as predicted by the Linear Quadratic (LQ) model of cell survival. The healthy tissue is modelled in green and the cancer cells in red. As predicted by the LQ model, the two types of cells respond differently to radiation. The LQ model assumes the surviving fraction to be given by: S = exp (-α*d -β*d2) where d is the dose and α and β are free parameters used to fit the model to experimental results from the irradiation of different tissue types. The "tissue sample" seen in the interface represents the interface between a tumour and the surrounding normal tissue. This model can be used to develop an understanding of fractionated radiation treatment planning. During fractionated radiation treatment, a patient receives small doses of radiation over many treatments. ## HOW IT WORKS Each cell has a probability of undergoing cell division; since cancerous cells divide more rapidly, their probability of dividing is higher. When the radiation is applied, each cell has a probability of dying, according to the LQ model. By adjusting the time between treatments and the dose per fraction, an ideal treatment can be developed such that a maximum about of healthy tissue remains after 99.9% of the cancer has been eliminated. The model starts with 5000 of each type of cell, and the first fraction is applied on the first tick. ## HOW TO USE IT The SETUP button creates the tissue sample. The GO button runs the treatment simulation. The set-up options determine the type of treatment. The `Fractions` input sets the maximum number of fractions that are applied. The time between fractions is given by the `hours` input. The dose applied per fraction, in Gray, is given by the `dose` input. The `alpha` and `beta` inputs can be used to adjust the parameters for the tumour. ## THINGS TO NOTICE #### Interface layout If you want to re-adjust the layout of the interface tab to better fit your computer screen, you can select each item and move it or adjust its size. #### Plots There are two plots included in the model. On the Survival plot, the number of each cell type is plotted for each tick, while on the logSurvival plot, the population is a semi-log plot, meaning the log of the population is plotted. Most of the plots of cell survival in the literature are on semi-log scales. Looking at the equation for cell survival in the LQ model, what is the benefit to a semi-log scale? Consider how the plots look when the populations are small. #### Regrowth Looking at the Survival plot, notice the increase in population between fractions. The tumour cells are more likely to divide and therefore have more regrowth between fractions. ## THINGS TO TRY * Apply only a single fraction of radiation. Compare the ratio of surviving tumour and healthy cells directly after treatment using the Survival plot. What is the dose at which more tumour cells survive the radiation than healthy cells? Allow the simulation to continue running. What happens? * Use the graphing software of your choice to plot the above equation for cell survival for alpha beta values of (0.1, 0.1) and (0.3, 0.04). Use a semi-log plot and a range of 0 to 8. Verify that the dose you found for the point at which equal amounts of tumour and healthy cells survive corresponds to the point where the two equations cross. * Develop a fractionated treatment schedule by adjusting the time between doses and the dose amount. Set the number of fractions to 20 so that the program ends before the treatment ends. Try some of the following: * A conventional treatment: 2 Gy every 24 hours * Hyperfractionation: 1 to 1.5 Gy multiple times in a day * Accelerated hyperfractionation: 1 to 1.5 Gy three times a day for one week * Adjust the parameters until you find a treatment with the maximum number of surviving healthy tissue. Consider the plot you made in the last activity. Where does there seem to be the largest potential for keeping healthy tissue alive? Look at the gap between the two equations. * Run a fractionated treatment a few times and determine the average number of treatments applied before the program stops. Run the model again with `Fractions` set to be one less than this number. What happens? How long after treatment does the tumour population overtake the number of healthy cells? * The lifetime of a cell varies greatly between different types of tissues. This model uses a lifetime of 1 month for the cancer cells and 3 months for the healthy tissue. Try adjusting these values by changing the values of `lifeT` and `lifeH` within the `setup` command procedure in the code. * Have the model also output the biologically effective dose (BED) in the Output box. BED is given by: (numdoses * Dose * ( 1 + Dose / (alpha / beta) )) The above is properly formatted syntax. Look at the code for printing the output at the beginning of the `go` command procedure and add this in. Note: `numdoses` is the actual number of treatments applied, NOT the maximum number you set with the `Fractions` variable. * Select the dose slider and adjust the range of allowed values and experiment with doses even higher than 6 Gray. You might get an error. Why? Try and fix this. * Adjust the `alpha` and `beta` values for the tumour cells to correspond to different types of cancer. Warning: you should first plot the survival curve for these new values and the values used for the healthy cells (0.1, 0.1) to check that they are reasonable. ## TROUBLE SHOOTING #### The program takes too long to run The program can take up to 10 minutes to run, especially when there is a long time between fractions. To help speed it up, deselect "view updates" at the top of the interface tab. #### Runtime Error: "Can't take logarithm of 0" This error occurs when high doses are used; the population decreases too rapidly for the program to end before reaching an error. Click "Dismiss" and run the simulation again. You may need to use a smaller dose, or adjust the cut-off point in the code. #### Slider Stops Working Select the dose slider by right clicking it, move it around the interface, and deselect it by clicking elsewhere on the screen. Repeat until it works. ## EXTENDING THE MODEL * Develop treatment schedules other than evenly spaced fractionated treatments. Often patients will only receive treatment 5 days a week. Adjust the code to have radiation applied in fractions which are not equally spaced. * Hypoxic cells are significantly less sensitive to radiation than well-oxygenated (oxic) cells (Steel, 2010). After irradiation, most of the oxic cells will be killed, leaving a tumour consisting of nearly entirely hypoxic cells. It has been found that after irradiation the tumour undergoes reoxygenation, which restores the ratio of hypoxic to oxic cells. It can take anywhere from minutes to days for a tumour to undergo reoxygenation. If the next fraction of radiation is applied while most of the tumour is still hypoxic, the radiation will be less effective. This sets a lower limit on the time between fractions and a treatment planner should be aware of balancing regrowth with reoxygenation. Expand the model to include reoxygenation by using the variable `hypoxic?`. * Hypoxic cells are also more likely to undergo metastasis. Allow hypoxic cells to spread into the healthy tissue on the left side of the tissue sample. ## CREDITS AND REFERENCES For a good overview of alpha-beta ratios and the LQ model, see: Eye Physics, 2014. _Biological Models._ [online] Available at: For a more in-depth explanation of the rationale behind the LQ model, and its validity compared to other models, see: Brenner, D., 2009. Point: The linear-quadratic model is an appropriate methodology for determining iso-effective doses at large doses per fraction. _National Institutes of Health_, 18(4), pp.234–239. For more information about the effects of hypoxia on radiosensitivy in fractionated treatment, see chapters 15 and 16 in: Steel, G. ed., 2002. _Basic Clinical Radiobiology_. 3rd ed. London: Arnold. This model was developed by Alexandra Kasper as part of ISCI 3A12 at McMaster University during the winter term of 2014. 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