A multiphase model for three-dimensional tumor growth

Video recordings

welcome to a multi page model for three-dimensional tumour growth

there are three stages in to grow the a vascular stage the vascular stage and

the method static stage we are interested here in the a vascular stage where we

observe an increase in the proliferation rate of the tumour cells in a decrease in

their death rate yielding a comp of tumour cells growing faster than the house

there is however it limited the scroll because of the balance between nutrient consumption by

the tumour cells and the nutrient transport into the cost

low nutrient level triggers cell data and results in the formation of an aquatic region

in the vascular stage the to make developed its own vessels for enhanced blood supply

once the tumour has achieved that the tumour cells can escape the primary tumour and

ma task to side

this is them at a static stage

the physical model of the a vascular tumour is composed of the extracellular matrix as

the followed phase the tumour and host cell populations as a piece of liquid phase

it

and the interest initial fluid phase which transports the nutrient of interest

the model equations are obtained via the remote dynamically constraint averaging theory which starts from

microscopic description with reference to a representative elementary volume which must contain all data

it must be large enough to the averages of properties are independent of the sample

size and small enough that partial derivatives at the macroscopic level makes cents

the governing equations at macroscopic level are obtained by up scaling

these equations supplemented by appropriate constitutive relationships are discrete time and space by means of

the finite element method and in time by the finite difference method and solved numerically

the final model equations to be solved are the infection diffusion equation of the nutrient

in module one

the map balance equations of the tumour cells the host cells the sum of the

mass balance equation of the file and the interest social fluid and the mathematically you

know than a crowd excel in module to

then we have the linear momentum balance equation of the mixture and model three

the primary variables are the degree of saturation of the tumour and herself the pressure

of the interest social fluid the mass fraction of the nutrient and the solid displacement

we solve three cases

the first deals with the multi cellular too much sphere void in a cell culture

medium

initial conditions consider small tumour cell population of about twelve self at the center surrounded

by nutrient carry included

the boundary conditions respect the symmetry of the problem

here we see the growth curve obtained in silicone as a continuous line in black

and for comparison our data points taken from in vitro experiments like annual and coworkers

and you have been coworkers

the growth curve balls the compared see in growth pattern

on the upper left we see the evolution of the viable random and other than

a crack region

the plot below that shows oxygen concentration

on the right side is the distribution of the living tumour cells and of the

crowd expelled after three hundred sixty hours there is no sharp interface between this to

sell types

the second case deals with two cell populations of it in the people experiment at

the center of the model is a small number two were cells surrounded by helping

samples

the initial and boundary conditions are shown and the primary variables are listed

here we see the influence of television on the growth pattern

we need to teach you know the ourselves then tumour cells is equal the growing

tumour cells displaced the host self as shown in the top figure

there it in a separation between the two were cells in red and the host

cells in orange chronic cells shown in purple appear at the center

in the lower figure be teaching of the host cell higher than that of the

to herself

in this case we see the tumour invading the host self eight

the third case deals with the tumour growing near my crevasse culture

these vessels are to distance that either at your one hundred mike

it small two male population shown in red develops initially at the left vessel

nutrient sources blood in the vessels and mutually restraint supported by the inter social fluid

again the initial and boundary conditions are shown

the leading to herself the host cells and the oxygen mask fraction are shown for

the case of then at my current distance from the blood vessels at one hundred

sixty eight and three sixty hours respectively

for the same case we should the tumour growth for the first twenty days

it can be seen clearly that the tumour grows toward the second blood vessel which

is a new source of nutrient

at the same time the crowd excels look here away from the nutrients source

in conclusion this model is that an early stage of development

however it already contains the initial fluid be on the cell populations and the couple

interactions between the different features are fully taking into account

it is it really multi-phrase model rather building blocks can be added such as vast

literature additional nutrients temperature and more

at this stage we need more experimental data for further validation

thank you for your attention