The Cancer and Ligand Show! A spectacle in five acts.

Transcription

1 The Cancer and Ligand Show! A spectacle in five acts.

2 Outline 1) 2) 3) 4) 5) Mystery fun times Model Overview Equations COMSOL Tutorial Parameter Sweeps Hint: This Mary Poppins chimney sweep is surprisingly relevant.

3 Outline 1) 2) 3) 4) 5) Mystery fun times Model Overview Equations COMSOL Tutorial Parameter Sweeps Hint: This Mary Poppins chimney sweep is surprisingly relevant.

4 Let us first tell you our system story

5 Let us first tell you our system story holistically

6 Let us first tell you our system story holistically through dance. Hit the lights!

7 Blood Lymph In every job that must be done there is an element of fun. Hit the lights!

8 Outline 1) 2) 3) 4) 5) Mystery fun times Model Overview Equations COMSOL Tutorial Parameter Sweeps Thank you for watching. And now we clarify.

9 Autologous Chemotaxis Cells release chemicals in velocity fields. They follow some of these chemicals. Like Meghan following goldfish.

10 System Definition Uniform Interstitial Velocity No initial ligand Initial blob of tumor cells Exuding ligand Resulting gradient

11 Outline 1) 2) 3) 4) 5) Mystery fun times Model Overview Equations COMSOL Tutorial Parameter Sweeps Because interpretive dance doesn t treat cancer [well]. Sadly.

12 Equations C = cancer cells G = ligand

13 COMSOLing our Chemotaxis Well, This is Awkward. How do we implement cross-dependence?

14 Outline 1) 2) 3) 4) 5) Mystery fun times Model Overview Equations COMSOL Tutorial Parameter Sweeps Because we don t do dance tutorials for free.

15 3 1.Add Physics 1 2.Coefficient Form PDE 2 3.Number of Species

16 Enter Your Parameters

17 Set Up Your Geometry

18 Declare your initial conditions

19 Declare your boundary conditions

20 The coefficient form master equation is really scary. Don t worry: most of it is set to 0. First-- Basic random motion (Diffusion) Equation for Affected by Cancer Ligand Cancer Ligand Dcc Dgg

21 Next-Advection Equation for Affected by Cancer Ligand Cancer Ligand hap*vif Vif

22 Now, Reaction Terms! Equation for Affected by Cancer Ligand -kp kd Cancer Ligand

23 ...aaaand Chemotaxis. We can actually use one of our variables! Equation for Affected by Cancer Ligand Cancer Ligand Dcc -Dcg*u Dgg

24 Go, COMSOL, Go!

25 Cells Ligand Cry with joy!

26 Outline 1) 2) 3) 4) 5) Mystery fun times Model Overview Equations COMSOL Tutorial Parameter Sweep Now with less emphasis on the dancing and more emphasis on the sweeping.

27 Ok, so now that s figured out what s all this stuff actually doing?

28 Equation

29 Equation With random migration dominating

30 Graph of cells: diffusion dominated

31 Equation With flow dominating

32 Graph of cells: flow dominated LINE

33 Fun times with Péclet High Convection Peclet number is the ratio between convection and diffusion High Diffusion

34 Equation Now let s add in a *little* bit of chemotaxis

35 Graphs with just a dash of chemotaxis Chemotaxis makes cells concentrate where the ligand is as opposed to moving as a block and diffusing some

36 But if there s more chemotaxis... Diffusion has little effect. The cells bunch up and get *really* close together as they slowly float toward the lymph. The ligand appears to be swept away and reproduced with each timestep.

37 And with literature values? Ooops, we did *not* have that figured out

38 We re blaming it on COMSOL Moral of the story: Very different timescales are challenging for solvers to actually compute. We can, as humans, make good predictions, but calculating them? G C

39 We re blaming it on COMSOL COMSOL: Moral of the story: Very different timescales are challenging for solvers to actually compute. We can, as humans, make good predictions, but calculating them? G Us: C

40 What happens if we pump up inflammation? We can predict that increasing the inflammation will increase the interstitial velocity We think metastasis would happen more quickly :) So perhaps we should decrease inflammation around tumors :)

41 Fun times with Péclet High Convection Peclet number is the ratio between convection and diffusion High Diffusion

42 Did we say less emphasis on dancing...?

43 Us: Hopefully Alisha:

44 Us: Probably Alisha:

45 So questions?