Events
Mathematical Models in biology: cell growth, remodelling and response to hyperthermia treatments
Continuum Mechanics and Mixture Theory provide efficient tools to study biological relevant problems.
In particular, the mechanical description of living cellular aggregates, described as a biphasic mixture, is considered.
At first we focus on the mechanical response of a quiescent aggregate and we derive an elasto-visco-plastic model able to qualitatively reproduce the stress relaxation curve and the shape recovery phenomenon observed during biomechanical experiments of uniaxial homogeneous compression.
Then we include the growth of cells, in order to make a further step towards a more realistic representation of tumor growth and remodelling.
The interplay between the internal reorganization of the tissue and cell proliferation is exploited and the model is applied to the description of cancer-spheroid growth inside healthy tissue. The proposed model is able to map the continuum change of tissue geometry of tumor aggregates and the surrounding tissue, to consider the influence of stress and nutrient availability on tumor growth and to describe the influence of cell reorganization on the overall process.
Finally we studied the feasibility of hyperthermic treatments through the stimulation by exogenous alternate magnetic fields of a portion of tissue with nanoparticles embedded into it.
The Pennes' bioheat equation, coupled with an equation representing the evolution of blood perfusion in the tissue, is solved through finite element method to predict the temperature field increase in a biological tissue as a function of the blood perfusion and operating AMF conditions.
All parameters of the model were obtained through biological experiments performed at
the Methodist Hospital Research Institute - Department of Translational Imaging (Houston, Texas).
The predictions of the model can be used to rationally design hyperthermia treatments and identify the proper route of administration depending of the magnetic nanoparticles.
contact/reference: pasquale.ciarletta@polimi.it
Mathematical Seminars
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometry and Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica