Logistic Heterogenous Growth of Cancer

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WHAT IS IT?

This system dynamics model shows a growth behavior of a cancer which will be composed from more than one cell in a body.

The Heterogenous cancer model assumes that the cancer is composed from 3 main types of cells: the cells that divide (proliferating cells or P-cells), the cells that don't divide (quiescent cells or Q-cells), and The cells that will die (dead cells or D-cells).

Note that this model is more advanced and complex than the Homogenous model, which assumes that the cancer is composed from one cell that divides forever and grow exponentially.

This model is a modefied version of model found in [1].

HOW IT WORKS

The body first produces the P-cells. some of these cells will produce other P-cells while the others will stop dividing (converting to Q-cells or becomes dead due to treatment or other factors). The production of P-cells is controlled by the Capacity (that is why it is called logistic growth).

Q-cells that are produced from P-cells will convert to P-cells again because there are mutuations in genes that regulate the growth and apoptosis of these cells. Some of Q-cells will also die due to various reasons (e.g. Tissue hypoxia or treatment).

The treatment is added to the model. when presseing the administration of a cytotoxic drug button, the cytotoxic drug will kill P-cells and Q-cells (at some extended) and the number of dead cells will be increased.

The D-cells then are removed from the body.

HOW TO USE IT

Press the SETUP button to initialize the model. To run the model continuously, press GO. The administration of a cytotoxic drug button can be used once or pressed many times or you can run it continuously. Adjust the initial populations of the cells and the parameters.

THINGS TO NOTICE

Let the model run and see what will happen to these cells. what will happen to the Total, P, Q , and D if you press the administration of a cytotoxic drug button multiple times?

THINGS TO TRY

Try to play with initial populations and change the parameters then observe what will happen.

EXTENDING THE MODEL

try to add other variables such as oxygen delivery to the tumor side, presence of immune cells , metastasis.... and so on. If you are good in netlogo coding, try to make agent-based simulation of this model featuring P, Q, and D cells with treatment, angiogenesis then metastasis and so on.

NETLOGO FEATURES

system dynamics modeler

RELATED MODELS

Cancer growth, Logistic growth, Exponential growth

CREDITS AND REFERENCES

[1] Luigi Preziosi. Cancer modelling and simulation. CRC Press, 2003.

[2] Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Comments and Questions

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Click to Run Model

; by pressing setup, the initial values will be plotted and other procedures will run.

to setup
  clear-all                         ; clear the graph and reset it to its initial values that the observer began with
  system-dynamics-setup             ; defined in system dynamics modeler code
  system-dynamics-do-plot           ; defined in system dynamics modeler code
  do-plot                           ; this one is specific for total Variable that is not defined in system-dynamics-do-plot procedure
end 

; The go button will give you the graph of the functions P, Q , D , and Total as time passes

to go
  system-dynamics-go                ; defined in system dynamics modeler code
  system-dynamics-do-plot           ; defined in system dynamics modeler code
  do-plot
end 

; adding Total variable to the plot

to do-plot
  if plot-pen-exists? "Total" [
    set-current-plot-pen "Total"
    plotxy ticks Total
  ]
end 

; we need to add a therapy so that it killes the cancer cells.
; if you press forever = this means that you are giving a continuous injection
; if you are not = this means that you are giving a periodic infusion. (This one is preffered for observation )

to Add-Drug-Injection
  set P P - 100                     ; using the fact that the cytotoxic drugs work primerly on P-cells, their number will be reduced dramatically upon injection.
  set Q Q - 45                      ; cytotoxic drugs can also cause damage to the non dividing cells Q-cells but the damage is lower compared with damage of P-cells
 set D D + 100 + 45                 ; the number of dead cells is equal to the number of already existing D-cells plus the number of cells that are killed by a cytotoxic drug.
end

There is only one version of this model, created over 3 years ago by Emmanuel Albazi.

Attached files

File	Type	Description	Last updated
Logistic Heterogenous Growth of Cancer.png	preview	Preview for 'Logistic Heterogenous Growth of Cancer'	over 3 years ago, by Emmanuel Albazi	Download

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