Modeling origin and natural evolution of low-grade...

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Modeling origin and natural evolution of low-grade gliomas Mathilde Badoual Paris Diderot University, IMNC lab 2nd HTE workshop: Mathematical & Computer Modeling to study tumors heterogeneity in its ecosystem, November 14th, 2018

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Modeling origin and natural evolution of low-grade gliomas

Mathilde BadoualParis Diderot University, IMNC lab

2nd HTE workshop: Mathematical & Computer Modeling to study tumors heterogeneity in its ecosystem, November 14th, 2018

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Gliomas

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Grade I: the grade I tumors may be curable by surgeryGrade II diffuse astrocytomas or oligodendrogliomas: evolve 7-8 years in anaplastic tumorsGrade III anaplastic gliomas: fatal evolution in 2 to 4 years.Grade IV glioblastoma multiforme: Average survival of 6 months to 2 years (based on feasible treatment).

solid tumor only solid tumor+ isolated tumor cells isolated tumor cells only

Grade I Grade III and IV Grade II

Solid tumor tissue

Isolated tumor cells

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Gliomas

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Grade I: the grade I tumors may be curable by surgeryGrade II diffuse astrocytomas or oligodendrogliomas: evolve 7-8 years in anaplastic tumorsGrade III anaplastic gliomas: fatal evolution in 2 to 4 years.Grade IV glioblastoma multiforme: Average survival of 6 months to 2 years (based on feasible treatment).

solid tumor only solid tumor+ isolated tumor cells isolated tumor cells only

Grade I Grade III and IV Grade II

Solid tumor tissue

Isolated tumor cells

heterogeneity

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Gliomas are rare tumors, but grade II (and more) gliomas cannot be cured

systematic recurrence, even after treatments

Glioma cells migrate normal surrounding tissue, causing recurrence of the tumor.⇒ Invasion plays a key role in the poor outcome of patients

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Shibahara, I et al (2015) Malignant clinical features of anaplastic gliomas without IDH mutation , Neuro Oncol., 17, 136-144.

Diffuse low-grade gliomas: recurrence

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Mandonnet E et al (2003) Continuous growth of mean tumor diameter in a subset of grade II gliomas. Ann Neurol 53, 524–528

A linear growth of the tumor radius

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C(r,t) =N0

(4πDt)3 / 2eκte−r

2 / 4DtSolution in 3D:

large

κD

small

⇥C(⇤r, t)

⇥t= r(D(⇤r, t)rC(⇤r, t)) + �(⇤r, t)C(⇤r, t)

⇥C(r, t)

⇥t= Dr2C(r, t) + �C(r, t)

Cook J et al. (1995) Resection of gliomas and life expectancy, J Neurooncol. 24, 131

if D and κ are uniforms and constants

κD

Modeling tumor growth

r(t) =

s

4Dt(�t+ ln(N0

C⇤(4⇥Dt)3/2)) r(C⇤, t ! 1) =

p4D�t

Assumption: diameter of the tumor on a MRI scan= iso cell density curve (C*)

- <v> = 2 mm/yr - Linear evolution since r = 10 mm ⟹ for the model rmin = 15 mm

detection threshold

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The natural history of low grade gliomas

-Very invasive tumors but patients can live more than ten years after diagnosisPallud J et al, (2008) Les gliomes infiltrants de bas grade, REG, Neurologies 11, 94-101

no symptoms symptoms

Onset

Time

Mea

n tu

mor

dia

met

er

Epilepsy

No mass effect no contrast

enhancement

Anaplastic transformation

Mass effectEdema

Contrast enhancement

Necrosis

Clinical diagnosis Death

anaplastic transformation = trigger of angiogenesis?

Grade II ∼ 10 years Grade III and IV ∼ 1 year

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➣ OPCs are the most widely distributed population of cycling cells in adult brain. ➣ In contrast, a small population of NSCs is found in the SVZ lining the lateral ventricles.

Geha S et al., (2010), NG2+/Olig2+ cells are the major cycle-related cell population of the adult human normal brain, Brain Pathol., 20, 399-411

Oligodendrocyte precursor cells (OPCs)

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➣ Cycling cells in the adult brain are mainly OPCs (NG2+ cells)

Ilkanizadeh S et al, (2014), Glial Progenitors as Targets for Transformation in Glioma, Adv Cancer Res., 121, 1–65.

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OPCs at the origin of gliomas?

Zong H et al , (2012) The cellular origin for malignant glioma and prospects for clinical advancement, Expert Rev Mol Diagn., 12, 383-94

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➣ Mutated OPCs trigger gliomas in mouse.

⇒ OPCs (Oligodendrocyte Precursor cells) are strongly suspected to be the cell of

origin of some gliomas.

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OPCs organize in a grid-like manner, with individual cells occupying almost non-overlapping domain

Xu G et al, (2014), Spatial organization of NG2 glial cells and astrocytes in rat hippocampal CA1 region, Hippocampus, 24, 383-95

OPCs dynamics in vivo

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Hughes EG et al, (2013), Oligodendrocyte progenitors balance growth with self-repulsion to achieve homeostasis in the adult brain, Nat Neurosci., 16, 668-76.

OPCs maintain a constant density in vivo

death

differentiation

proliferation

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Modeling OPCs dynamics

100μm

Model: a cellular automaton without lattice (continuous space)

Rules

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A cell can:1. proliferate (⇒ proliferation rule)2. migrate (⇒ migration rule)3. and disappear (differentiate or die) (differentiation rule)

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The formation of a glioma: different scenarios

- Apparition of an immortal cell.

- Apparition of a cell that has lost its contact inhibition.

- Apparition of a highly proliferative cell.

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The daughter cells have the same proliferative properties than the mother cells.

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The formation of a glioma: different scenarios

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First scenario: Apparition of an immortal cell

Time (days)500 1000

1600

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X-Title

Y-Title

Time (days)

# c

ell/m

m3

TumorNormal

400 900

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2000

2400

2800

500 10000

20

40

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X-Title

Y-Title

400 9000

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# c

ell/m

m3 /d

ay

Cell density in a 1mm3 volume Proliferative cell density

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The formation of a glioma: different scenarios

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First scenario: Apparition of an immortal cell

Time (days)500 1000

1600

2000

2400

2800

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X-Title

Y-Title

Time (days)

# c

ell/m

m3

TumorNormal

400 900

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2800

500 10000

20

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Y-Title

400 9000

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# c

ell/m

m3 /d

ay

Cell density in a 1mm3 volume Proliferative cell density

The tumor cell proliferation goes to

zero !Not compatible with experimental data

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The formation of a glioma: different scenarios

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100 150 200

2000

6000

10000

# c

ell/m

m3

TumorNormal

0 50 100 100 150 2000

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200

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Time (days)

# c

ell/m

m3 /d

ay

0 50 100Time (days)

Second scenario: Apparition of a cell without contact inhibition

Cell density in a 1mm3 volume Proliferative cell density

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The formation of a glioma: different scenarios

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100 150 200

2000

6000

10000

# c

ell/m

m3

TumorNormal

0 50 100 100 150 2000

100

200

300

400

500

Time (days)

# c

ell/m

m3 /d

ay

0 50 100

Very high cell and proliferation cell density⇒ high-grade glioma

Cell density in a 1mm3 volume Proliferative cell density

Second scenario: Apparition of a cell without contact inhibition

Time (days)

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High-grade vs low-grade glioma

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MIB-1

Singh SK et al (2004), Identification of human brain tumour initiating cells, Nature, 432, 396-401.

Low grade

H & E(immunostaining of proliferative cells)

High grade

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Low-grade glioma

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0

5

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0

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600

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# c

ell/m

m2

1200

400

0

800

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5

0

10

# M

IB-1

pos

itive

cel

ls/m

m2

Normal Tumor Normal Tumor

H&E staining of a tumor tissue

MIB1 immunostaining

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The formation of a glioma: different scenarios

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150 350 550 7501800

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# c

ell/m

m3

Normal Tumor

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0

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# c

ell/m

m3 /d

ay

0 200 400 600

Cell density in a 1mm3 volume Proliferative cell density

Third scenario: Apparition of a highly proliferative cell

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The formation of a glioma: different scenarios

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150 350 550 7501800

2000

2200

Time (days)

# c

ell/m

m3

Normal Tumor

18000 200 400 600 150 350 550 750

0

20

40

60

Time (days)

# c

ell/m

m3 /d

ay

0 200 400 600

Cell density in a 1mm3 volume Proliferative cell density

Third scenario: Apparition of a highly proliferative cellHigher cell and proliferation cell density inside the tumor but not too high (a new equilibrium)

⇒ low-grade glioma

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A highly proliferative cell at the origin of low-grade glioma

A very proliferative cell in redNormal OPCs are in blue

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Modeling the formation of a glioma

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0

1000

2000

X-Title

Y-Title

200 400 600

Distance to the center (µm)

2000

1000

0

# c

ell/m

m3

Tumor cells are yellow to red (cell clock increasing)Normal OPCs are in blue to green (cell clock increasing) Red curves: tumor cells; blue curves: normal cells

Dufour A et al, (2018), Modeling the dynamics of oligodendrocyte precursor cells and the genesis of gliomas, PLoS Comput Biol., 14, e1005977.

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0 50 100 150 200 250 3000

100

200

300

400

500

600

700

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0 100 200 300

200

400

600

0

Time (days)

Mea

n ra

dius

(µm

)

800

Modeling the formation of a glioma

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With reasonable parameters, v ≃ 1 mm/yr

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0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800

0 100 200 300

200

400

600

0

Time (days)

Mea

n ra

dius

(µm

)

800

Modeling the formation of a glioma

With reasonable parameters, v ≃ 1 mm/yr ⇒ consistent with clinical dataMandonnet E et al (2003) Continuous growth of mean tumor diameter in a subset of grade II gliomas. Ann Neurol, 53, 524–528

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First step of formation of a glioma

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Dufour A et al, (2018), Modeling the dynamics of oligodendrocyte precursor cells and the genesis of gliomas, PLoS Comput Biol., 14, e1005977.

OPC: oligodendrocyte precursor cell.

The appearance of a highly proliferative OPC among normal OPCs leads to the formation of a glioma-like tumor:

- invasive- slow linear increase of the radius, compatible with clinical data

⇒ first step of heterogeneity: mixture and competition between normal and cancer cells

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Increasing heterogeneity

-Very invasive tumors but patients can live more than ten years after diagnosisPallud J et al, (2008) Les gliomes infiltrants de bas grade, REG, Neurologies, 11, 94-101

no symptoms symptoms

Onset

Time

Mea

n tu

mor

dia

met

er

Epilepsy

No mass effect no contrast

enhancement

Anaplastic transformation

Mass effectEdema

Contrast enhancement

Necrosis

Clinical diagnosis Death

anaplastic transformation = trigger of angiogenesis

Grade II ∼ 10 years Grade III and IV ∼ 1 year

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x 28

P1

P3

P4

16

0

-6

-16

outs

ide

the

tum

orin

side

the

tum

or

: area fraction of edema

Quantification of edema

-40 -20 0 20

100

200

Distance (mm)

Grey

leve

l

P4 P3 P2 P1

P1P2P3P4

-16 -6 5 160

(mm)

⇠ = 0.92(1.01� 10�2(Re �Ge))

Tumor tissue: normal cells + tumor cells + edema + ECM +….

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0 20 40 60 800

2

4

6

8

10

Edema fraction at x=0

Patie

nt n

umbe

r

−20 −10 0 10 20 300

20

40

60

80

100oedema

0

x (mm)

Edem

a fra

ctio

n

123

54

76

89

Edema fraction

Patie

nt n

umbe

r

29

inside the tumor outside the tumor

Edema/border of the tumor

Gerin C, et al (2013) Quantitative characterization of the imaging limits of diffuse low-grade oligodendrogliomas, Neuro-Oncology, 15, 1379.

d

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⇤⇥

⇤t= Dr2⇥+ �⇥(1� ⇥)

⌅⇥

⌅t= �⇤(1� ⇥)� µ⇥⌫

A model with edema

ρ: tumor cell densityξ: edema fraction

κ: proliferation D: diffusion λ: edema production μ: edema clearance

Equation for the cell density evolution:

Equation for the edema fraction evolution:

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At the center, when ρ=1, reaches its maximum value that verifies: 1 � ⇠e =�

µ⇠e

⌫⇠

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Low-grade gliomas and radiotherapy

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Delay between the end of the radiotherapy and the regrowth of the tumor: Why?

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Fit of clinical data

32Badoual M, et al (2014) An oedema-based model for diffuse low-grade gliomas: application to clinical cases under radiotherapy, Cell Prolif, 47, 369

clinical data

model

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Conclusion

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➣ When the tumor grows the heterogeneity increases.

➣ In low-grade gliomas, the heterogeneity is still low: easier for modeling. Two models, with increased heterogeneity, corresponding to different stages of evolution of a glioma.

➣ Next step: study of the apparition of heterogeneity between tumor cells (hypoxia)

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Acknowledgments

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Emilie Gontran, PhD studentAloys Dufour, undergraduate studentBasile Grammaticos Christophe Deroulers

Johan Pallud, neurosurgeonPascale Varlet, pathologist

Catherine Oppenheimer, radiologist

IMNC laboratory, Orsay, France Collaborators: Sainte-Anne hospital, Paris

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Thank you for your attention !

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