Tumour progression

Tumour progression

Tumour progression

Tumour progression

Tumour progression

Tumour progression

cadherin switch angiogenic switch

Tumour progression

Avascular phase Tumour spheroid Max diameter ~ 2 mm Necrotic core

Angiogenesis and vascularization Capillary network formation Further rapid growth

Invasion and metastasis Reduced adhesion and collagenasis Intra-vasation and extra-vasation Adhesion in secondary sites

3 phases of growth

~ 10 6 cells Maximum diameter ~ 2 mm Necrotic core Quiescent region Periferic proliferation Nutrient diffusion limit

Spheroid from V-79 Chinese hamster lung cells Folkman & Hochberg, Exp Med. 138:745-753 (73)

Multicellular spheroids

v

Cell volume ratio changes

because they duplicate/die

because they move

V

Mass balance equations

Chemical factors and nutrients diffuse

Greenspan (50): j = j = const.

R(t)

X Single population with constant density

Spherical symmetry

Only tumour cells in 1D

- H. Byrne & M. Chaplain, J. Theor. Med. 1, 223-235 (1998) - H. Byrne, Math. Models Methods Appl. Sci. 9, 541-568 (1999)- A. Friedman & F. Reitich, Math. Models Methods Appl. Sci. 11, 601-626 (2001) (analytical)- ....

1. Single population with constant density2. Spherical symmetry 3. Chemical factors and nutrients diffuse

R(t)

Question: What is it?

Only tumour cells in 1D

If and are constant over the entire volume

time

dim

ensi

on

8 times in 1 week 66 times in 2 weeks 8000 times in 1 month

If days-1 e days-1 the radius increases

R(t)

Only tumour cells in 1D

If is restricted to an outer layer of depth and is constant over the entire volume

R

7 times in 1 week 12 times in 2 weeks 19 times in 1 month 26 times in 2 months 29 times in 3 month

If days-1 and days-1 the radius increases

Only tumour cells in 1D

linear

time

dim

ensi

on

t

N ~ t3

L ~ t

Freyer & Sutherland, J. Cell Physiol. 124:516-524 (1985)Drasdo & Hohme, Phys. Biol. 2:133147 (2005)

EMT6/Ro multicellular spheroid

If is restricted to an outer layer of depth and is constant over the entire volume

Only tumour cells in 1D

e.g., if = 10and = 40 m Limit radius = 1.2 mm

stationary

If is restricted to a outer layer of depth and is constant over the entire volume

linear

time

dim

ensi

on

Limit radius =

Only tumour cells in 1D

1-D Tumour (Cartesian)

Cylindrical Tumour

R

Tumour cord

Only tumour cells in 1D

If and are constant over the entire volume

21

If is restricted to a outer layer of depth and is constant over the entire volume

2121

21

22 C

Solutions

1. Constant density

2. Potential flow

n

Only tumour cells in 3D

X

1. Constant density X2. Potential flow

n

Only tumour cells in 3D

Macklin & Lowengrub JTB (2008)

Nutrient diffusion

Cel

l mot

ility

Fingering

Fragmenting

Radiotherapy

Compact

Original movies atbiomathematics.shis.uth.tmc.edu/Multimedia.php

Only tumour cells in 3D

file:///C:/Users/Luigi/Archivio/ppt/movies/Macklin/fingering_tumor_xvid_med.avifile:///C:/Users/Luigi/Archivio/ppt/movies/Macklin/fragmenting_tumor_xvid_med.avifile:///C:/Users/Luigi/Archivio/ppt/movies/Macklin/LongTimeRadiotherapy_xvid.avifile:///C:/Users/Luigi/Archivio/ppt/movies/Macklin/compact_tumor_xvid_med.avi

Macklin & Lowengrub JTB (2008)

Original movies atbiomathematics.shis.uth.tmc.edu/Multimedia.php

Only tumour cells in 3D

file:///C:/Users/Luigi/Archivio/ppt/movies/Macklin/NIHMS29593-supplement-01.avifile:///C:/Users/Luigi/Archivio/ppt/movies/Macklin/xvid768_5.avifile:///C:/Users/Luigi/Archivio/ppt/movies/Macklin/xvid768_7.avi

Metastasis

Primary tumor

Abnormal proliferation

Membrane degradation and local invasion

Angiogenesis

Invasion

Genetic mutations

Molecule

Cell

Tissue

Organ

6

710

9

8

12

14

Dysplasia

Cancer in situ

Com

plex

ity/

spac

e

Hypoxia and nutrient depletion

p53 detects hypoxia

p53 regulates angiogenesis

Excessive proliferation promotes hypoxia and nutrient

depletion

Cell-cell and cell-ECM contact regulate cell

potential for proliferation

Membrane and tissue degradation leads to tissue re-oxygenation

Hypoxia leads to cell quiescence

Secretion of angiogenic factors

Oxygen and nutrient delivery regulate the angiogenic process

The degree of vasculature regulates cell potential to metastasize

Genes and proteins responsible for cell cycle

regulation

p53, pRb, Cyclin:CDK

Genes and proteins responsible for cell-ECM contact (cadherins,

catenin)

Uncontrolled proliferation leads to new mutations

Angiogenesis is also regulated by cell-cell and

cell-ECM contact

Tumour progression

A. Bru

Fractal dimension of tumour surface

Fractal dimension of tumour surface

Morfologicalcharacteristics diagnosis

objectivequantification

perception

Diagnosis

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