Modelling macrophage dynamics and their therapeutic ...jas/talks/edinburgh_july08_woundhealing.pdf · Introduction to Diabetic Wound Healing A Simple Mathematical Model An Expanded

Introduction to Diabetic Wound HealingA Simple Mathematical Model

An Expanded ModelUsing the Model to Understand the Treatments

Conclusions

Modelling macrophage dynamicsand their therapeutic implications

in diabetic wound healing

Jonathan A. Sherratt

Department of MathematicsHeriot-Watt University

ECMTB08, Edinburgh, 1 July 2008

This talk can be downloaded from my web sitewww.ma.hw.ac.uk/∼jas

Jonathan Sherratt www.ma.hw.ac.uk/∼jas Macrophage dynamics in diabetic wound healing



Conclusions

In collaboration withHelen Waugh




Conclusions

Diabetic Wound HealingWhy is Wound Healing Impaired in Diabetics?

Outline

1 Introduction to Diabetic Wound Healing

2 A Simple Mathematical Model

3 An Expanded Model

4 Using the Model to Understand the Treatments

5 Conclusions




Conclusions


Diabetic Wound Healing

Wound healing in diabetics is impaired

In some cases, wounds fail to heal over long periods(> 6 months ↔ diabetic ulcer)

Limb amputation is required in extreme cases

Annual cost in UK is £17M




Conclusions


Why is Wound Healing Impaired in Diabetics?

There is not a clear understanding of why wound healing isimpaired in diabetics




Conclusions




One component is that some aspects of repair fail toprogress beyond the inflammatory phase




Conclusions





In particular, macrophages persist for long times, withsignificant numbers present after a month (cf clearanceafter a few days in normal healing)




Conclusions





In particular, macrophages persist for long times, withsignificant numbers present after a month (cf clearanceafter a few days in normal healing)

We develop a mathematical model to investigate thispersistence of macrophage numbers (and associatedphenotype imbalance)




Conclusions

Model IngredientsModel EquationsTypical Model SolutionSteady States and Model Predictions

Outline



3 An Expanded Model


5 Conclusions




Conclusions


Model Ingredients

Monocytes migrate to the wound in response to TGFβ (T )

In the wound, monocytes differentiate into one of threemacrophage phenotypes, in response to micro-environmental signals:Inflammatory macrophages (φI) release various cytokines

that promote migration and proliferation offibroblasts and endothelial cells

Repair macrophages (φR) remodel the extracellular matrixCytocidal macrophages remove bacteria and other debris

(not included in the model)

The balance between inflammatory and repairmacrophages is different in normal and diabetic wounds




Conclusions


Model Equations

dφI/dt =

influx︷︸︸︷

αK (T ) +

proliferation︷︸︸︷

k1ΦI(k2 − ΦI − ΦR)−

removal︷︸︸︷

d1ΦI

dφR/dt = (1 − α)K (T ) + k1ΦR(k2 − ΦI − ΦR) − d1ΦR

dT/dt = k3ΦI︸︷︷︸

production

− d2T︸︷︷︸

decay

αdiabetic > αnormal




Conclusions


Typical Model Solution

Normal wound (α = 0.5):

0 20 400

125

250

Time, days

φ I, cel

ls/c

ubic

mm

0 20 400

125

250

Time, days

φ R, c

ells

/cub

ic m

m

0 20 400

3

6

Time, days

TG

F−

B, p

g/cu

bic

mm

Diabetic wound (α = 0.8):

0 20 400

500

1000

Time, days

φ I cel

ls/c

ubic

mm

0 20 400

150

300

Time, days

φ R, c

ells

/cub

ic m

m

0 20 400

4

8

Time, days

TG

F−

B, p

g/cu

bic

mm




Conclusions


Steady States and Model Predictions

Non-negative steady states are:

Predictions:The non-healing steady state appears abruptly, via abifurcation, as α is increasedThe healed steady state persists and remains stable up toα = 1, so that effective treatment is a possibility




Conclusions

Key Interactions in the Expanded ModelTypical Solution of the Expanded ModelApligraf and Dermagraft TreatmentsSimulation of Apilgraf TreatmentSimulation of Dermagraft Treatment

Outline



3 An Expanded Model


5 Conclusions




Conclusions


Key Interactions in the Expanded Model

To investigatepossibletherapies,we use anexpanded model.

� � � � � � � � � � � � � � � � � � � � � � � � �� α 1−α

� � � � ! � ! � � � � � � � � � � � � � � � � � � � � �" � � � � � � � � � � � � � � �Jonathan Sherratt www.ma.hw.ac.uk/∼jas Macrophage dynamics in diabetic wound healing



Conclusions


Typical Solution of the Expanded Model

Model variables: inflammatory macrophages, repairmacrophages, fibroblasts, collagen, TGFβ, PDGF,hyaluronan

0 50 100 150 2000

200

400

600

800

1000

time, days

infla

mm

ator

y M

φ

Normal wound

Diabetic wound

0 50 100 150 2000

50

100

150

200

250

time, days

repa

ir M

φ

Normal wound

Diabetic wound

0 50 100 150 2000

500

1000

1500

time, days

Col

lage

n, u

g m

m−

3 Normal wound

Diabetic wound




Conclusions


Apligraf Treatment

Apligraf (Organogenesis, US) is an artificial skin comprisingdermal and epidermal layers in a bioabsorbable scaffold.

Component 100 % Density(per cubic mm)Neonatal Fibroblasts 1550 cellsTGF-β 0.4 pgPDGF 1 pgCollagen 0.45 µgTotal Hyaluronan 18.0 µgDermal Hyaluronan 15.5 µgEpidermal Hyaluronan 2.5 µg

Protocol: one application per week for five weeks.




Conclusions


Apligraf Treatment

Apligraf (Organogenesis, US) is an artificial skin comprisingdermal and epidermal layers in a bioabsorbable scaffold.

Component 100 % Density(per cubic mm)Neonatal Fibroblasts 1550 cellsTGF-β 0.4 pgPDGF 1 pgCollagen 0.45 µgTotal Hyaluronan 18.0 µgDermal Hyaluronan 15.5 µgEpidermal Hyaluronan 2.5 µg

Protocol: one application per week for five weeks.

A separate modelling study suggests that the epidermal layerdoes not play a significant role in initiating wound repair.




Conclusions


The Apligraf Web Site




Conclusions


Dermagraft Treatment

Dermagraft (Advanced Biohealing Inc, US) is an artificial dermallayer.

Component 100 % Density(per cubic mm)Neonatal Fibroblasts 8000 cellsTGF-β 0.4 pgPDGF 1 pgCollagen 18.75 µgTotal Hyaluronan 80 µgDermal Hyaluronan 80 µgEpidermal Hyaluronan 0 µg

Protocol: one application per week for eight weeks.




Conclusions


The Dermagraft Web Site




Conclusions


Simulation of Apilgraf Treatment

0 50 100 150 2000

200

400

600

800

1000

time, days

Infla

mm

ator

y M

φ

Treated diabetic wound

Untreated diabetic wound

Normal wound

0 50 100 150 2000

200

400

600

time, days

Rep

air

Mφ

Normalwound

Treated diabeticwound

Untreated diabeticwound

0 50 100 150 2000

500

1000

1500

time, days

Col

lage

n



Normal wound




Conclusions


Simulation of Dermagraft Treatment

0 50 100 150 2000

200

400

600

800

1000

time, days

Infla

mm

ator

y M

φ

Treated diabetic wound


Normal wound

0 50 100 150 2000

100

200

300

400

500

time, days

Rep

air

Mφ

Normalwound



0 50 100 150 2000

500

1000

1500

time, days

Col

lage

n



Normal wound




Conclusions

Separating the Treatment ComponentsSeparating Fibroblast FunctionsDemonstration that Hyaluronan Production is Critical

Outline



3 An Expanded Model


5 Conclusions




Conclusions


Separating the Treatment Components

Included: TGFβ, PDGF and collagen

Excluded: hyaluronan, fibroblasts

0 50 100 150 2000

200

400

600

800

1000

time, days

Infla

mm

ator

y M

φ



Normalwound

0 50 100 150 2000

200

400

600

time, days

Rep

air

Mφ

Normal wound



0 50 100 150 2000

500

1000

1500

time, days

Col

lage

n



Normal wound




Conclusions



Included: fibroblasts

Excluded: TGFβ, PDGF, collagen and hyaluronan

0 50 100 150 2000

200

400

600

800

1000

time, days

Infla

mm

ator

y M

φ



Normalwound

0 50 100 150 2000

200

400

600

time, days

Rep

air

Mφ

Normal wound



0 50 100 150 2000

500

1000

1500

time, days

Col

lage

n



Normal wound




Conclusions


Separating Fibroblast Functions

Fibroblasts secrete a range of regulatory chemicals:

TGFβ

PDGF

collagen

collagenase

hyaluronan




Conclusions




TGFβ

PDGF

collagen

collagenase

hyaluronan

Question: which of these are critical to treatment success?




Conclusions




TGFβ

PDGF

collagen

collagenase

hyaluronan

Question: which of these are critical to treatment success?

Answer: our model predicts that only hyaluronan secretionis critical




Conclusions


Demonstration that Hyaluronan Production is Critical

Using the model, we simulate treatment with fibroblasts thathave been modified to not produce hyaluronan, but areotherwise normal.

0 50 100 150 2000

200

400

600

800

1000

time, days

infla

mm

ator

y M

φ

Normalwound


Modified fibroblast treated diabetic wound

0 50 100 150 2000

100

200

300

400

500

time, days

repa

ir M

φ



Normal wound

0 50 100 150 2000

500

1000

1500

time, days

colla

gen,

ug



Normal wound




Conclusions

ConclusionsPredictionsReferences

Outline



3 An Expanded Model


5 Conclusions




Conclusions


Conclusions

The key component ofApligraf and Dermagrafttreatments is theproduction of hyaluronanby the added fibroblasts

Hyaluronan initiateshealing by switchingmacrophages from theinflammatory to therepair phenotype

� � � � � � � � � � � � � � � � � � � � � � � � �� α 1−α

� � � � ! � ! � � � � � � � � � � � � � � � � � � � � �" � � � � � � � � � � � � � � �Jonathan Sherratt www.ma.hw.ac.uk/∼jas Macrophage dynamics in diabetic wound healing



Conclusions


Predictions

1 For both therapies, the current protocols could be improved2 Diabetic wound healing can be initiated simply by the

addition of hyaluronan

0 50 100 150 2000

200

400

600

800

1000

time, days

Infla

mm

ator

y M

φ



Normalwound

0 50 100 150 2000

200

400

600

time, days

Rep

air

Mφ

Normal wound



0 50 100 150 2000

500

1000

1500

time, days

Col

lage

n



Normal wound




Conclusions


The Hyalofill Web Site




Conclusions


References

H.V. Waugh, J.A. Sherratt.Macrophage dynamics in diabetic wound healing.Bulletin of Mathematical Biology 68, 197-207 (2006)

H.V. Waugh, J.A. Sherratt.Modelling the effects of treating diabetic wounds withengineered skin substitutes.Wound Repair and Regeneration 15, 556-565 (2007)

These papers are available from my web site:www.ma.hw.ac.uk/∼jas

Both the basic and extended models have been translated intoCellML by the University of Auckland; see www.cellml.org




Conclusions


List of Frames


Diabetic Wound Healing


2 A Simple Mathematical ModelModel Ingredients

Model EquationsTypical Model SolutionSteady States and Model Predictions

3 An Expanded ModelKey Interactions in the Expanded ModelTypical Solution of the Expanded ModelApligraf and Dermagraft Treatments

Simulation of Apilgraf Treatment

Simulation of Dermagraft Treatment




Demonstration that Hyaluronan Production is Critical

5 ConclusionsConclusionsPredictionsReferences


Modelling macrophage dynamics and their therapeutic ...jas/talks/edinburgh_july08_woundhealing.pdf · Introduction to Diabetic Wound Healing A Simple Mathematical Model An Expanded

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