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![Page 1: Steven R McDougall Institute of Petroleum Engineering Heriot-Watt University Edinburgh Scotland Mathematical Modelling of Dynamic Adaptive Tumour-Induced.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d5e5503460f94a3dbb1/html5/thumbnails/1.jpg)
Steven R McDougallInstitute of Petroleum Engineering
Heriot-Watt University
Edinburgh
Scotland
Mathematical Modelling of Dynamic Adaptive
Tumour-Induced Angiogenesis
Tumour Growth and Angiogenesis, 11-19 January 2006, Hsinchu, Taiwan
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Co-Investigators
• M A J Chaplain Dept. of MathematicsUniversity of Dundee
• A R A Anderson Dept of Mathematics, University of Dundee
• A Stéphanou Institute of Petroleum Engineering,
Heriot-Watt University
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Outline• Background
• Modelling Tumour-Induced Vasculature
– Continuum scale formulation of growth
– Discrete (capillary) scale growth
– Improved continuous-discrete coupling through MMP
• Incorporating Flow
– Flow in porous media
– Blood flow and drug delivery
• 3D Dynamic Adaptive Tumour-Induced Angiogenesis
– Vascular remodelling and evolving bed architecture
• Conclusions and future work
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Petroleum Engineering and Medicine??
• Multiphase flow at the micro-scale has been investigated over the past 15 years at Heriot-Watt University
• Software resulting from this research is widely used by the oil industry to interpret laboratory experiments and reservoir behaviour
• However, the underlying modelling framework can also be adapted to examine a wide range of problems in the clinical arena
• We will focus here upon a particular application in clinical oncology – tumour-induced angiogenesis
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Modelling Rationale
• Use mathematical modelling techniques to give some insight into the underlying physical and biological processes governing tumour-induced angiogenesis
• Reproduce experimental observations and suggest additional laboratory studies
• Use insights gained from modelling to suggest new treatment strategies and scheduling protocols
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Modelling Tumour-Induced Vasculature
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3 Phases of Solid Tumour Growth
• Early avascular phase– tumour spheroid 106 cells– max diameter ~ 2mm– necrotic core– thin proliferating rim
• Angiogenesis and vascularisation– capillary network formation– blood supply to tumour– additional growth
• Invasion and metastasis– attachment to BM– collagenase production– addressins at distant sites
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• Hypoxic tumour cells secrete tumour angiogenic factors (TAFs)
• Endothelial cells degrade their basement membrane
• These migrate towards the tumour
• Capillary branching increases towards the tumour
• Tumour penetrated and nutrient supply begins
Tumour-Induced Angiogenesis
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Vascular Growth SchematicParent Vessel
Tumour Surface
TAF
FN
TISSUE
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Vascular Growth - Continuum Approach
f(x,f(x, y,y, t)t)tt
==
n(x,n(x, y,y,t)t)
tt == DD n n 22 (n(nf )f )
n fn f
c(x,c(x, y,y,t)t)
tt ==
ncnc
(n(nc )c )
nn
c (x,y,t) ~ c (x,y,t) ~ TAF ConcentrationTAF Concentration
f (x,y,t) ~ f (x,y,t) ~ Matrix Macromolecule (fibronectin)Matrix Macromolecule (fibronectin)
n (x,y,t) ~ n (x,y,t) ~ Endothelial Cell DensityEndothelial Cell Density
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EC Density Profile
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• Use discretised form of continuum equations to migrate capillary sprouts and grow capillaries
• Capillary branching, anastomosis and cell mitosis all included in the model
• 2 tumour geometries considered
– linear TAF source
– circular TAF source
Discrete Model
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Discrete Model
l,l, mmqq++11
l,l, mmqq
00 ll++ 1,1, mmqq
11 ll-1,-1, mmqq
22 l,l, mm + + 11qq
33 l,l, mm -1-1qq
44
l,l, mmqq++11
l,l, mmqq
nn == nn PP nn PP nn PP nn PP nn PP
cc == cc
ff == ff l,l, mmqq++11
l,l, mmqq kk nn
l,l, mmqq
1 1 kk l,l, mmqqnn
1 1
withwith x=lhx=lh, , y=mhy=mh andand t=qkt=qk
00 PP
33 PP
22 PP
44 PP
11 PP
kk nnl,l, mmqq
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Movement Weighting
11 22 22
22 22 22
33 22 22
44 22 22
PP ==k Dk Dhh
kk
44hh
PP == k Dk Dhh
++kk
44hh
PP == k Dk Dhh
kk
44hh
PP == k Dk Dhh
++ kk
44hh
) ) (( ll++1,1,mmqq
ll-1,-1,mmqqcc cc
l,l,mm++11qqff ff l,l,mm-1-1
qq(( ))
) ) (( ll++1,1,mmqq
ll-1,-1,mmqqff ff++
) ) (( ll++1,1,mmqq
ll-1,-1,mmqqcc cc ) ) (( ll++1,1,mm
qqll-1,-1,mmqqff ff++
l,l,mm++11qqcc cc l,l,mm-1-1
qq(( )) ++
l,l,mm++11qqff ff l,l,mm-1-1
qq(( )) l,l,mm++11qqcc cc l,l,mm-1-1
qq(( )) ++
00PP == 1 1 44 k Dk Dhh
22
ll++1,1,mmqq
ll-1,-1,mmqq
l,l,mmqq
l,l,mm++11qq
l,l,mm-1-1qq kk
hh(( cc ++ cc -- 44cc ++ cc ++ cc )) 22
ll++1,1,mmqq
ll-1,-1,mmqq
l,l,mmqq
l,l,mm++11qq
l,l,mm-1-1qq kk
hh(( ff ++ ff -- 44ff ++ ff ++ ff ))22
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Numerical Simulation
• At each time step
– Solve fibronectin and TAF equations
– Generate 5 directional coefficients (7 in 3D) P0 to P4
– Compute probability ranges R0 to R4
– Generate random number in (0,1)
– Determine appropriate growth direction
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Branching and Anastamosis
Sprout SproutSprout
Loop formed by anastomosis
Branching at sprout tipto form two new sprouts
Parent Vessel
Sprout tip
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Sample Results
Linear Source Circular Source
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• Matrix metalloproteinases explicitly included
• MMP produced locally by individual ECs
• MMP also diffuses and decays
• n equation now only used to extract directional coefficients
,)(2 haptotaxischemotaxisrandom
fncncnDt
n
.
,
,
2 mmnt
m
mfnt
f
cnt
c
i
i
i
Improved Continuum-Discrete Coupling
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Simulation Results – Large Tumour
Tumour Surface Tumour Surface
Parent Vessel Parent Vessel
Capillary Network Enzyme Concentrations
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Tumour Surface Tumour Surface
Parent Vessel Parent Vessel
Capillary Network Enzyme Concentrations
Simulation Results – Small Tumour
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Comparison with Experiment
Experiment Simulation
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Experiment Simulation
Comparison with Experiment
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Incorporating Flow
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a
N S
ShaleAmalgamation surfaceOutcrop termination
100 m
Flow Through Porous Media
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Flow Through Porous Media
(q)i . t = (VbS)i
Qo
Qw
Qo
Qw
Vb, ,So, Sw
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Network Model
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Observing the PhysicsPressure depletion in a reservoir
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Simulation vs Experiment
Oil displacing water from a water-wet micromodel
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We Have the Fluid Distributions - What About
Flow?Pin Pout
qi=0
qi
Large set of pressure equations
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Viscous-Dominated Gasflood
Isolate each phase and flow
its networkGAS OILOIL
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Apply to Vasculatures
Vasculature 1 - Linear TAF source Vasculature 2 - Circular TAF source
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Chemotherapy Modelling
• Single-phase tracer algorithm developed
• “Chemotherapy drug” at concentration Cmax is injected into the upstream end of the parent vessel
• At each timestep
– total mass of drug flowing into each node calculated
– perfect mixing assumed at nodes
– drug uptake instantaneous within 40m of tumour surface
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Initial Assumptions
• Rigid, impermeable cylinders used for capillaries
• Blood treated as Newtonian fluid (constant viscosity)
– no correlation with haematocrit
• No reaction kinetics included in uptake function
• Vascular network is 2D
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Input Data• Four suites of simulations performed
– 2 vasculatures x continuous infusion
– 2 vasculatures x 30s bolus injection
• 5 sets of input data for each suite (0<t<2500s)
Base Run Run 1 Run 2 Run 3 Run 4
blood (Pa.s) 4 x 10-3 1 x 10-3 8 x 10-3 4 x 10-3 4 x 10-3
P (Pa) 800 800 800 800 800Rcap (m) (4, 4.01) (4, 4.01) (4, 4.01) (2, 2.01) (3, 3.01)Rart (m) 10 10 10 10 10
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Continuous Infusion into Vasculature 1
Vasculature 1
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Effect of Blood ViscosityMass in Vasculature
0
2
4
6
8
10
12
0 5 10 15 20 25 30
t*
M*
M* 1cP <r>=4
M* 4cP <r>=4
M* 8cP <r>=4
Uptake in Tumour
0
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25 30
t*
Upt
ake
in T
umou
r
MT* 1cP <r>=4
MT* 4cP <r>=4
MT* 8cP <r>=4
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Effect of Mean Capillary Radius
Mass in Vasculature
0
5
10
15
20
25
30
0 5 10 15 20 25 30
t*
M*
M* 4cP <r>=2
M* 4cP <r>=4
M* 4cP <r>=6
Uptake in Tumour
0
2
4
6
8
10
12
14
16
18
20
0 5 10 15 20 25 30
t*
Upt
ake
in T
umou
r
MT* 4cP <r>=2
MT* 4cP <r>=4
MT* 4cP <r>=6
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Continuous Infusion into Vasculature 2
Vasculature 2
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Drug Delivery Comparison
Tot Mass in Vasc Circ
0
2
4
6
8
10
12
0 5 10 15 20 25 30
t*
M* M* 4cP <r>=4
Mcirc* 4cP <r>=4
Mass in Tum Circ
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30
t*
MT
* MTcirc* 4cP <r>=4
MT* 4cP <r>=4
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Bolus Injection into Vasculature 2
Vasculature 2
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Drug Delivery Comparison
M* Linear vs Circular Bolus
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25 30
t*
M* M* 4cP <r>=4 bolus
M* 4cP <r>=4 circ bolus
Uptake in Tum. Lnear vs Circular Bolus
0
0.01
0.02
0.03
0.04
0.05
0.06
0 5 10 15 20 25 30
t*
MT
* MT* 4cP <r>=4 bolus
MT* 4cP <r>=4 circ bolus
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Early Findings
• Bolus injection into a capillary network generated from a circular TAF source
– drug bypasses the tumour completely
• Important implications for chemotherapy strategies
– structure of associated vasculature should be considered when planning chemotherapy treatments
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Targeting Strategies• 3 a posteriori pruning
algorithms considered
– random
– low-flow
– bottlenecks
• Motivation comes from possible targeting of different areas of vasculature with different cytotoxic compounds
Vessel maturation
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Targeting “High Shear” VesselsDrug targeting high-shear vessels
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However …
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Limitations of Early Model
• Two-dimensional
– is bypassing as significant in 3D?
• Blood treated as a Newtonian fluid
– blood is non-Newtonian and biphasic
– blood viscosity is not constant
• Capillaries treated as rigid and impermeable
– in reality, vasodilation/vasoconstriction occurs
– capillary architecture (i.e. bed topology) is not static
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Additional Limitations• Flow only incorporated after growth has
ended
– in fact, perfusion occurs during growth
• Growth and flow towards a tumour
– what about growth and flow within a tumour
– tumour cords around blood vessels
• Other limitations?
– coupled low-pressure venous system absent
– …….??
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Now begin to relax some of the earlier
assumptions…
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Relaxing Earlier Assumptions
3D Extension
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)1(
d
dPZ th
• Bypassing in 3D not necessarily less than that seen in 2D
• Delivery initially slower in 3D
• Anastomosis density, dimensionality, and duration of infusion all affect uptake
• 97-99% of drug injected bypasses the tumour
• Percolation theory can help here
• Really need Z(y) distribution to understand impact of vascular architecture
Relaxing Earlier Assumptions
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• Blood is non-Newtonian
• Capillaries are dynamic entities
• Dynamic feedback must be addressed
– Blood rheology
– Capillary radius = f1 (shear stress)
– Branching probability = f2 (shear stress)
Relaxing Earlier Assumptions
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(i) Blood is non-Newtonian
Red Blood Cells
Endothelial Cells
22
45.0 1.12
2
1.12
2)()1(1
R
R
R
RHf Drel Blood viscosity depends upon
haematocrit and capillary radius…
1211121115.0
)2(06.017.045.0
)2(101
1
)2(101
11)8.0(
1)45.01(
1)1()(
,44.22.360645.0
RReC
HHf
ee
R
C
CD
D
RR
…parameterised as follows
Relaxing Earlier Assumptions
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),( Dapp HRLHR
PRQ
Dapp ),(8
4
Relaxing Earlier Assumptions
(i) Blood is non-Newtonian
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sD
refmerefwttt
tt
kQH
QkPtRRR
RRR
log)(loglog1
1
Wall shear stress
Transmural pressure
Metabolic stimulus
Shrinking tendency
(ii) Shear stress affects vessel radii
Relaxing Earlier Assumptions
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Haematocrit distribution Radius distribution
R(m)% red cells
HD, R, app are interrelated(Haematocrit/Radius -> Viscosity -> Shear stress -> Radius -> Flow -> Haematocrit. . .)
Relaxing Earlier Assumptions
(ii) Shear stress affects vessel radii
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Sprout Branching
- TAF Concentration
- age of the vessel > thr
Vessel Branching
- magnitude of the WSS
- TAF concentration
- min < age of the vessel < max
(iii) Shear stress affects branching
Relaxing Earlier Assumptions
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Age of the vessels in days
(iii) Shear stress affects branching
Relaxing Earlier Assumptions
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WSS / WSS in Parent Vessel
connection connection
(iii) Shear stress affects branching
Relaxing Earlier Assumptions
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Coupling Growth and Flow
Angiogenesis
(cell migration)
Flow Modelling and
Blood Rheology
Dynamic Adaptive Tumour-Induced
Angiogenesis
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Dynamic Adaptive Tumour-Induced
Angiogenesis(DATIA)
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DATIA• A mathematical model which
simultaneously couples vessel growth with blood flow through the vessels – dynamic adaptive tumour-induced angiogenesis
• Radial adaptations and network remodelling occurs as immediate consequences of primary anastomoses
• Capillary network architectures from the dynamically adaptive model differ radically from those obtained using earlier models.
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Modelling Rationale
• Examine the effects of changing various physical and biological model parameters on the developing vascular architecture
• Simulate chemotherapeutic treatments under different parameter regimes
– identify a number of new therapeutic targets for tumour management.
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Simulation Procedure• Capillaries migrate via the discrete form of the
extended PDE formulation (MMP)
– only tip branching possible initially
– no remodelling without flow
• Vessel branching and remodelling considered only after first anastomoses form
• However
– timescale of EC migration ~ days
– timescale of network perfusion ~ minutes
– so we cannot simply remodel as the migration simulation proceeds
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• Idealised procedure
– model the growth of the capillary network using the endothelial cell migration model;
– pause the migration model whenever a new anastomosis (loop) forms;
– switch timescales (t = MIN(Vcap/Qcap))
– flow/remodel the entire capillary bed using flow model until a new steady-state has been reached (~100s of perfusion);
– resume network growth using the cell migration model on the longer timescale.
• Practical procedure
– flow the network to steady-state at regular intervals during the growth process (determine optimum interval).
Simulation Procedure
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A Posteriori Remodelling
t=0.8 t=2.4 t=3.0
t=4.5 t=72.0 t=300.0
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Full DATIA Simulation
4.0 8.0 8.0+1 12.0
12.0+2 12.0+2+3 30.0
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Increased Sensitivity to max
7.5 8.0 8.5
11.5 12.0
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Additional Sensitivities
P(vb)/2.5 P(vb)/5.0 =0.18 pl*=4.0 HD=0.675
HD=0.225 Pin Pout Pin Pout kp
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Transport Through Adapted Networks
• Use tracer algorithm to quantify the efficiency of different networks in carrying blood-borne material e.g. nutrients, chemotherapy drugs, to the tumour
• Almost all of the drug flows through the dilated backbone
• Poor treatment efficiency
• The architecture of the backbone determines delivery to tumour
t=1.0 t=5.0 t=10.0
t=20.0 t=50.0 t=300.0
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• All masses normalised to the total mass injected into the parent vessel over the course of the simulation.
• Only around 1.5% of the infused tracer-drug even enters the capillary network
• Total mass in the network reaches a plateau after approximately 50s
• It takes another 200-250s before uptake commences.
Transport Through Adapted Networks
0
0.005
0.01
0.015
0 100 200 300 400 500
Time (s)
Mas
s in
Bed
(n
orm
alis
ed)
0.00E+00
2.00E-07
4.00E-07
6.00E-07
0 100 200 300 400 500
Time (s)
Up
take
(n
orm
alis
ed)
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Comparison with Homogeneous Bed
• Uptake values are approximately three orders of magnitude higher that those obtained from the remodelled vasculature
• Highlights the need for incorporating vessel adaptations (dilation/constriction) into any angiogenesis model involving transport issues
0.00E+00
2.00E-04
4.00E-046.00E-04
8.00E-04
1.00E-03
0 100 200 300 400 500
Time (s)
Up
take
(n
orm
alis
ed)
0.00E+00
2.00E-07
4.00E-07
6.00E-07
0 100 200 300 400 500
Time (s)
Up
take
(n
orm
alis
ed)
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Effect of Reducing Haptotaxis• Total mass of tracer-drug
entering the supplying vasculature is almost identical to that observed in the base case simulation (=0.28)
• But drug uptake by the tumour is fifty times greater when lateral migration and vessel branching are reduced
• This suggests that tumours supplied by this type of vasculature would be well-supplied with nutrients and could be expected to grow rapidly
• Paradoxically, such tumours would also be highly susceptible to infused treatments
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 100 200 300 400 500
Time (s)
Mas
s in
Bed
(n
orm
alis
ed)
Rho=0.28
Rho=0.16
0.00E+00
5.00E-06
1.00E-05
1.50E-05
2.00E-05
2.50E-05
3.00E-05
0 100 200 300 400 500
Time (s)
Up
take
(n
orm
alis
ed)
Rho=0.28
Rho=0.16
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Effect of Reducing Haematocrit
• A depressed haematocrit was found to lead to the formation of highly dilated arcades close to the parent vessel
• Could be a possible mechanism for generating vasculatures that are detrimental to tumour growth
• The therapeutic implications of this
– more drug enters the capillary network than entered in the base-case simulation
– but drug delivery to the tumour is reduced by more than three orders of magnitude.
0
2E-11
4E-11
6E-11
8E-11
1E-10
0 100 200 300 400 500
Time (s)
Up
take
(n
orm
alis
ed)
0.00E+00
2.00E-07
4.00E-07
6.00E-07
0 100 200 300 400 500
Time (s)
Up
take
(n
orm
alis
ed)
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Other Pieces of the Puzzle
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Flow Within the Tumour• Tumour
vasculature poorly connected
• Tumour capillary radii larger on average
• Capillaries “leaky”
• Examine flow to and within tumour
• Treatment scheduling
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Flow Within the Tumour
Optimise scheduling to build-up high local drug concentrations
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Examine heterogeneous distributions of nutrient
supply and drug delivery
Transmural Diffusion
Feed oxygen tensions into model => evolving TAF sources
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Conclusions and Future Work
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Conclusions• An extensive theoretical investigation of the process of
tumour-induced angiogenesis has been presented incorporating:
– blood rheological properties
– metabolic constraints
– vessel branching = f(wall shear stress )
• Results from computational simulations have highlighted a number of possible new targets for therapeutic intervention
– manipulating sensitivity to wall shear stress
– haptotactic response of the endothelial cells
– haematocrit
– intravascular pressure
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Conclusions• Explicit coupling of growth and flow leads to
network architectures that differ radically from those found in all previous models.
• Dilated loops (anastomoses) form at an earlier stage close to the parent vessel
– positively reinforcing,
– proximally-dilated capillaries undergo further vessel branching.
– subsequent migration of these additional branches result in high capillary densities in regions distal to the parent vessel
– the number of high-conductivity pathways is consequently greatly reduced close to the tumour surface
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Conclusions• It is apparent from the transport simulations that
highly-dilated loops proximal to the parent vessel remove any possibility of effective treatment via intravenous or intra-arterial infusion.
• However, if a tumour-induced capillary network could be forced to develop in just such a way, by means of some clinical intervention perhaps, then nutrient supply to the tumour could be effectively curtailed.
• The DATIA model provides a useful biomechanical framework within which to examine the possibility of managing high conductance pathways as a means of effectively treating solid tumours
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Future Work• Couple flow model to continuum and CA
tumour models
• Use digitised images of real 2D and 3D vasculatures
• Migration of tumour fragments -> metastases
• Heterogeneous tissues
• Other applications (lymphangiogenesis, therapeutic angiogenesis, wound healing, retinopathy…)
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Discussion Topics
• Tumour-vessel coupling
– increased tumour pressure
– leaky vessels
• Venous system
– low pressure
• Lymphangiogenesis
– how does this differ from angiogenesis?
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Tumour/Vessel Coupling• Potts model for
tumour integrity?
• Appropriate for breast cancer modelling
– used to examine interface region between disrupted tumour surface and healthy perimeter tissue
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Wound Healing
• Similar techniques are being used to study healing rates in dermal wounds.
• Future work will focus upon the design of dressings that could accelerate the healing process and reduce scarring
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Therapeutic Applications
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Random Targeting
What if we end treatment here?
Broad-based indiscriminate drug
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Targeting Poorly Perfused Vessels
Anti-angiogenic drug targeting immature, poorly perfused vessels
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Outcomes• Random targeting
– Increased flow in distal regions
– Decrease in Z4 and increase in Z3 and Z2
– 130% increase in delivery
– Delivery optimised if we can decrease Z4 proximal to parent vessel but maintain good connectivity close to tumour
• Low-flow targeting
– Flow distribution essentially unchanged
– Treatment accelerated in modified network
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• High shear targeting
– Bottleneck (percolation radius) capillaries removed
– Network shut down effectively after 5% vessels removed
– No delivery of drug but also no delivery of nutrients
• Delivery highly sensitive to network architecture
• Main flowing backbone plays a dual role
– Helps carry treatment to tumour
– Increases bypassing
• Treatments should be aimed at managing this backbone
Outcomes
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S R McDougall1 and J A Sherratt2
1 Dept of Petroleum Engineering, Heriot-Watt University
2 Dept of Mathematics, Heriot-Watt University
Discrete Modelling of Collagen Deposition and Alignment During Dermal
Wound Repair
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Dermal Wound
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Collagen Alignment
• Post wounding, fibroblasts respond chemotactically and migrate into wound area
• Collagen deposited
• Fibrin degraded
• Scarring due to collagen alignment
• How can we reduce this?
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Matrix Orientation Model
(After Dallon et al, 1999)
)
)s )
(t
(t(t
dt
t dii
v
vf ) ( f
)
)
(t
(tt t ti
ii
f
fv
) ), ( ( ) 1( ) (f c
) sin() , (
fdt
t dx
)
)
(t
(tt x w ti
i N
ii
f
f
1
) , ( ) , (x f
C
FB
f(x,y)
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Results
Speed=5m/hr Speed=15m/hr
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Tissue Regeneration Model
)
)s( )
(t
(t(t
dt
t dii
v
vf) ,
) (b c
f
)
)
(t
(t
t t
t tti
i
i
i
f
fv
) ), ( (
) ), ( () 1( ) (
f u
f u
) sin() , (
fdt
t dx
) , ( ) , ( ) 1( ) , (t t tx x xb c u
C
b
FB
f(x,y)c
b
)
)
(t
(tt x w ti
i N
ii
f
f
1
) , ( ) , (x f
![Page 98: Steven R McDougall Institute of Petroleum Engineering Heriot-Watt University Edinburgh Scotland Mathematical Modelling of Dynamic Adaptive Tumour-Induced.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d5e5503460f94a3dbb1/html5/thumbnails/98.jpg)
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Tissue Regeneration Model
),()),((),(
1
twtdpdt
td N
iicc xxc
xc
),(),(),(
1
twtddt
td N
iib xxb
xb
C
b
FB
![Page 99: Steven R McDougall Institute of Petroleum Engineering Heriot-Watt University Edinburgh Scotland Mathematical Modelling of Dynamic Adaptive Tumour-Induced.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d5e5503460f94a3dbb1/html5/thumbnails/99.jpg)
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Results
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Leukocyte Signalling
212
2
kaka
aD
t
a
aka
aD
t
a12
2
HEALTHY PERIMETER
212
2
kaka
aD
t
a
aka
aD
t
a12
2
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Results
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Future Work
• Clinical applications (TGF isoform issue)
• Wound contraction
• Blood flow and angiogenesis