0:00:06welcome to a multi page model for three-dimensional tumour growth
0:00:14there are three stages in to grow the a vascular stage the vascular stage and
0:00:19the method static stage we are interested here in the a vascular stage where we
0:00:23observe an increase in the proliferation rate of the tumour cells in a decrease in
0:00:28their death rate yielding a comp of tumour cells growing faster than the house
0:00:34there is however it limited the scroll because of the balance between nutrient consumption by
0:00:39the tumour cells and the nutrient transport into the cost
0:00:43low nutrient level triggers cell data and results in the formation of an aquatic region
0:00:48in the vascular stage the to make developed its own vessels for enhanced blood supply
0:00:54once the tumour has achieved that the tumour cells can escape the primary tumour and
0:00:59ma task to side
0:01:00this is them at a static stage
0:01:05the physical model of the a vascular tumour is composed of the extracellular matrix as
0:01:10the followed phase the tumour and host cell populations as a piece of liquid phase
0:01:15it
0:01:16and the interest initial fluid phase which transports the nutrient of interest
0:01:23the model equations are obtained via the remote dynamically constraint averaging theory which starts from
0:01:30microscopic description with reference to a representative elementary volume which must contain all data
0:01:37it must be large enough to the averages of properties are independent of the sample
0:01:41size and small enough that partial derivatives at the macroscopic level makes cents
0:01:47the governing equations at macroscopic level are obtained by up scaling
0:01:52these equations supplemented by appropriate constitutive relationships are discrete time and space by means of
0:01:58the finite element method and in time by the finite difference method and solved numerically
0:02:07the final model equations to be solved are the infection diffusion equation of the nutrient
0:02:12in module one
0:02:13the map balance equations of the tumour cells the host cells the sum of the
0:02:18mass balance equation of the file and the interest social fluid and the mathematically you
0:02:23know than a crowd excel in module to
0:02:25then we have the linear momentum balance equation of the mixture and model three
0:02:30the primary variables are the degree of saturation of the tumour and herself the pressure
0:02:36of the interest social fluid the mass fraction of the nutrient and the solid displacement
0:02:42we solve three cases
0:02:44the first deals with the multi cellular too much sphere void in a cell culture
0:02:48medium
0:02:49initial conditions consider small tumour cell population of about twelve self at the center surrounded
0:02:55by nutrient carry included
0:02:57the boundary conditions respect the symmetry of the problem
0:03:02here we see the growth curve obtained in silicone as a continuous line in black
0:03:07and for comparison our data points taken from in vitro experiments like annual and coworkers
0:03:13and you have been coworkers
0:03:15the growth curve balls the compared see in growth pattern
0:03:21on the upper left we see the evolution of the viable random and other than
0:03:25a crack region
0:03:26the plot below that shows oxygen concentration
0:03:30on the right side is the distribution of the living tumour cells and of the
0:03:35crowd expelled after three hundred sixty hours there is no sharp interface between this to
0:03:40sell types
0:03:43the second case deals with two cell populations of it in the people experiment at
0:03:48the center of the model is a small number two were cells surrounded by helping
0:03:53samples
0:03:54the initial and boundary conditions are shown and the primary variables are listed
0:04:00here we see the influence of television on the growth pattern
0:04:04we need to teach you know the ourselves then tumour cells is equal the growing
0:04:08tumour cells displaced the host self as shown in the top figure
0:04:12there it in a separation between the two were cells in red and the host
0:04:16cells in orange chronic cells shown in purple appear at the center
0:04:21in the lower figure be teaching of the host cell higher than that of the
0:04:26to herself
0:04:27in this case we see the tumour invading the host self eight
0:04:33the third case deals with the tumour growing near my crevasse culture
0:04:37these vessels are to distance that either at your one hundred mike
0:04:42it small two male population shown in red develops initially at the left vessel
0:04:47nutrient sources blood in the vessels and mutually restraint supported by the inter social fluid
0:04:52again the initial and boundary conditions are shown
0:04:58the leading to herself the host cells and the oxygen mask fraction are shown for
0:05:03the case of then at my current distance from the blood vessels at one hundred
0:05:07sixty eight and three sixty hours respectively
0:05:14for the same case we should the tumour growth for the first twenty days
0:05:18it can be seen clearly that the tumour grows toward the second blood vessel which
0:05:23is a new source of nutrient
0:05:25at the same time the crowd excels look here away from the nutrients source
0:05:31in conclusion this model is that an early stage of development
0:05:35however it already contains the initial fluid be on the cell populations and the couple
0:05:40interactions between the different features are fully taking into account
0:05:45it is it really multi-phrase model rather building blocks can be added such as vast
0:05:50literature additional nutrients temperature and more
0:05:54at this stage we need more experimental data for further validation
0:05:58thank you for your attention