luigi preziosi - Profile on Academia.edu (original) (raw)
Papers by luigi preziosi
Applied Mathematics Letters, 2021
We consider a continuum mechanical model for the migration of multiple cell populations through p... more We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the membranes, is then reduced to a limiting transmission problem whereby each thin membrane is replaced by an effective interface. In order to close the limiting problem, a set of biophysically-consistent transmission conditions is derived through a formal asymptotic method. Models based on such a limiting transmission problem may find fruitful application in a variety of research areas in the biological and medical sciences, including developmental biology, immunology and cancer growth and invasion.
Biomechanics and Modeling in Mechanobiology, 2021
The active response of cells to mechanical cues due to their interaction with the environment has... more The active response of cells to mechanical cues due to their interaction with the environment has been of increasing interest, since it is involved in many physiological phenomena, pathologies, and in tissue engineering. In particular, several experiments have shown that, if a substrate with overlying cells is cyclically stretched, they will reorient to reach a well-defined angle between their major axis and the main stretching direction. Recent experimental findings, also supported by a linear elastic model, indicated that the minimization of an elastic energy might drive this reorientation process. Motivated by the fact that a similar behaviour is observed even for high strains, in this paper we address the problem in the framework of finite elasticity, in order to study the presence of nonlinear effects. We find that, for a very large class of constitutive orthotropic models and with very general assumptions, there is a single linear relationship between a parameter describing th...
Axioms
Cell migration in highly constrained environments is fundamental in a wide variety of physiologic... more Cell migration in highly constrained environments is fundamental in a wide variety of physiological and pathological phenomena. In particular, it has been experimentally shown that the migratory capacity of most cell lines depends on their ability to transmigrate through narrow constrictions, which in turn relies on their deformation capacity. In this respect, the nucleus, which occupies a large fraction of the cell volume and is substantially stiffer than the surrounding cytoplasm, imposes a major obstacle. This aspect has also been investigated with the use of microfluidic devices formed by dozens of arrays of aligned polymeric pillars that limit the available space for cell movement. Such experimental systems, in particular, in the designs developed by the groups of Denais and of Davidson, were here reproduced with a tailored version of the Cellular Potts model, a grid-based stochastic approach where cell dynamics are established by a Metropolis algorithm for energy minimization....
Kinetic & Related Models
The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and... more The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and Preziosi (2019a). We split the population in two subgroups and perform a linear stability analysis. We show that pattern formation results from modulation of one nondimensional parameter that depends on the tumbling frequency, the sensing radius, the mean speed in a given direction, the uniform configuration density and the tactic response to the cell density. Numerical simulations show that our linear stability analysis predicts quite precisely the ranges of parameters determining instability and pattern formation. We also extend the stability analysis in the case of different mean speeds in different directions. In this case, for parameter values leading to instability travelling wave patterns develop.
Computing and Visualization in Science
In the present work we embrace a three scales asymptotic homogenization approach to investigate t... more In the present work we embrace a three scales asymptotic homogenization approach to investigate the effective behavior of hierarchical linear elastic composites reinforced by cylindrical, uniaxially aligned fibers and possessing a periodic structure at each hierarchical level of organization. We present our novel results assuming isotropy of the constituents and focusing on the effective out-of-plane shear modulus, which is computed exploiting the solution of the arising anti-plane problems. The latter are solved semi-analytically by means of complex variables and successfully benchmarked against the results obtained by finite elements. Our findings can pave the way for multiscale modeling of complex hierarchical materials (such as bone and tendons) at a negligible computational cost.
Models for Tumor Growth
Encyclopedia of Nanotechnology, 2016
On an invariance property of the solution to Stokes' first problem for viscoelastic fluids
Journal of Non Newtonian Fluid Mechanics, Oct 1, 1989
ABSTRACT
Mechano-transduction in tumour growth modelling
The European Physical Journal E, Mar 1, 2013
The evolution of biological systems is strongly influenced by physical factors, such as applied f... more The evolution of biological systems is strongly influenced by physical factors, such as applied forces, geometry or the stiffness of the micro-environment. Mechanical changes are particularly important in solid tumour development, as altered stromal-epithelial interactions can provoke a persistent increase in cytoskeletal tension, driving the gene expression of a malignant phenotype. In this work, we propose a novel multi-scale treatment of mechano-transduction in cancer growth. The avascular tumour is modelled as an expanding elastic spheroid, whilst growth may occur both as a volume increase and as a mass production within a cell rim. Considering the physical constraints of an outer healthy tissue, we derive the thermo-dynamical requirements for coupling growth rate, solid stress and diffusing biomolecules inside a heterogeneous tumour. The theoretical predictions successfully reproduce the stress-dependent growth curves observed by in vitro experiments on multicellular spheroids.
Modelling the early stages of vascular network assembly
Modelling of Biological Materials
We present a hybrid computational framework, the aim of which is to reproduce and analyze the ear... more We present a hybrid computational framework, the aim of which is to reproduce and analyze the early growth of a solid tumor. The model couples an extended version of the discrete Cellular Potts Model, used to represent the phenomenological behavior of malignant cells, with a continuous approach of reactiondiffusion equations, employed to describe the evolution of microscopic variables, as the growth factors and the matrix proteins present in the host tissue and the proteolytic enzymes secreted by the tumor. The behavior of each cancer cell is determined by a balance of interaction forces, such as homotypic (cell-cell) and heterotypic (cellmatrix) adhesions and haptotaxis, and is mediated by its molecular state, which regulates the motility and proliferation rate. The resulting model captures the different phases of the development of the tumor mass, i.e. its exponential growth and the subsequent stabilization in a steady-state due to limitations in vital molecules. The proposed approach also predicts the influence on the cancer morphology of changes in specific intercellular adhesive mechanisms.
Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model
Biomechanics and modeling in mechanobiology, Jan 8, 2016
Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor... more Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely grow...
Progress in Industrial Mathematics at ECMI 96, 1997
The pa.per deduces a new model to simulate industrial processes involving infiltration in deforma... more The pa.per deduces a new model to simulate industrial processes involving infiltration in deformable porous media. If the porous material is not rigid, then it can deform under the action of the forces associated with the flow, both in the infiltrated and in the uninfiltrated region. The coupled flow/deformation problem in the two interfaced regions is then formulated with the proper evolution equations for the boundaries delimiting the two domains and with the relative boundary and interface conditions. The unsteady problem is solved numerically, putting in evidence the influence of the deformations on the bulk flow and on the propagation of the advancing front and allowing as a by-product a prediction of the stress and deformation states. M. Brøns et al. (eds.
Tumour cells usually live in a environment formed by other host cells, extra-cellular matrix and ... more Tumour cells usually live in a environment formed by other host cells, extra-cellular matrix and extra-cellular liquid. Cells duplicate, reorganise and deform while binding each other thanks to adhesion molecules exerting forces of measurable strength. In this paper it is illustrated a macroscopic mechanical model of solid tumour which takes such adhesion mechanisms into account. The extracellular matrix is treated as an elastic compressible material, while, in order to define the relationship between stress and strain for the cellular constituents, the deformation gradient is decomposed in a multiplicative way distinguishing the contribution due to growth, to plastic rearrangement and to elastic deformation. On the basis of experimental results at a cellular level, it is proposed that at a macroscopic level there exists a yield condition separating the elastic and viscoplastic regimes. Previously proposed models are obtained as limit cases, e.g. fluid-like models are obtained in the limit of fast cell reorganisation and negligible yield stress. A numerical test case shows that the model is able to account for several complex interactions: how tumour growth can be influenced by stress, how and where it can generate plastic reorganisation of the cells, how it can lead to capsule formation and compression of the surrounding tissue.
In ltration process in composite materials manufacturing: modeling and qualitative results
Mathematical Framework to Model Migration of Cell Population in Extracellular Matrix
Chapman & Hall/CRC Mathematical & Computational Biology, 2010
Cell migration is an essential feature of both normal and pathological biological phenomena. Tiss... more Cell migration is an essential feature of both normal and pathological biological phenomena. Tissue formation in embryonic development requires cell movements and coordination among cells. Migration of cells plays a fundamental role in immune response ...
Journal of mathematical biology, Jan 26, 2014
In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the... more In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts. Dynamical numerical simulations are performed to show the behavior of the model and its qualitative and quantitative accuracy to describe the evolution of the cell aggregate.
Deformable Porous Media and Composites Manufacturing
Modeling and Simulation in Science, Engineering and Technology, 2000
ABSTRACT
Infiltration of a Polymerizing Resin in a Deformable Preform for Fiber Reinforced Composites
Applied and Industrial Mathematics, Venice—2, 1998, 2000
Applied Mathematics Letters, 2021
We consider a continuum mechanical model for the migration of multiple cell populations through p... more We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the membranes, is then reduced to a limiting transmission problem whereby each thin membrane is replaced by an effective interface. In order to close the limiting problem, a set of biophysically-consistent transmission conditions is derived through a formal asymptotic method. Models based on such a limiting transmission problem may find fruitful application in a variety of research areas in the biological and medical sciences, including developmental biology, immunology and cancer growth and invasion.
Biomechanics and Modeling in Mechanobiology, 2021
The active response of cells to mechanical cues due to their interaction with the environment has... more The active response of cells to mechanical cues due to their interaction with the environment has been of increasing interest, since it is involved in many physiological phenomena, pathologies, and in tissue engineering. In particular, several experiments have shown that, if a substrate with overlying cells is cyclically stretched, they will reorient to reach a well-defined angle between their major axis and the main stretching direction. Recent experimental findings, also supported by a linear elastic model, indicated that the minimization of an elastic energy might drive this reorientation process. Motivated by the fact that a similar behaviour is observed even for high strains, in this paper we address the problem in the framework of finite elasticity, in order to study the presence of nonlinear effects. We find that, for a very large class of constitutive orthotropic models and with very general assumptions, there is a single linear relationship between a parameter describing th...
Axioms
Cell migration in highly constrained environments is fundamental in a wide variety of physiologic... more Cell migration in highly constrained environments is fundamental in a wide variety of physiological and pathological phenomena. In particular, it has been experimentally shown that the migratory capacity of most cell lines depends on their ability to transmigrate through narrow constrictions, which in turn relies on their deformation capacity. In this respect, the nucleus, which occupies a large fraction of the cell volume and is substantially stiffer than the surrounding cytoplasm, imposes a major obstacle. This aspect has also been investigated with the use of microfluidic devices formed by dozens of arrays of aligned polymeric pillars that limit the available space for cell movement. Such experimental systems, in particular, in the designs developed by the groups of Denais and of Davidson, were here reproduced with a tailored version of the Cellular Potts model, a grid-based stochastic approach where cell dynamics are established by a Metropolis algorithm for energy minimization....
Kinetic & Related Models
The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and... more The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and Preziosi (2019a). We split the population in two subgroups and perform a linear stability analysis. We show that pattern formation results from modulation of one nondimensional parameter that depends on the tumbling frequency, the sensing radius, the mean speed in a given direction, the uniform configuration density and the tactic response to the cell density. Numerical simulations show that our linear stability analysis predicts quite precisely the ranges of parameters determining instability and pattern formation. We also extend the stability analysis in the case of different mean speeds in different directions. In this case, for parameter values leading to instability travelling wave patterns develop.
Computing and Visualization in Science
In the present work we embrace a three scales asymptotic homogenization approach to investigate t... more In the present work we embrace a three scales asymptotic homogenization approach to investigate the effective behavior of hierarchical linear elastic composites reinforced by cylindrical, uniaxially aligned fibers and possessing a periodic structure at each hierarchical level of organization. We present our novel results assuming isotropy of the constituents and focusing on the effective out-of-plane shear modulus, which is computed exploiting the solution of the arising anti-plane problems. The latter are solved semi-analytically by means of complex variables and successfully benchmarked against the results obtained by finite elements. Our findings can pave the way for multiscale modeling of complex hierarchical materials (such as bone and tendons) at a negligible computational cost.
Models for Tumor Growth
Encyclopedia of Nanotechnology, 2016
On an invariance property of the solution to Stokes' first problem for viscoelastic fluids
Journal of Non Newtonian Fluid Mechanics, Oct 1, 1989
ABSTRACT
Mechano-transduction in tumour growth modelling
The European Physical Journal E, Mar 1, 2013
The evolution of biological systems is strongly influenced by physical factors, such as applied f... more The evolution of biological systems is strongly influenced by physical factors, such as applied forces, geometry or the stiffness of the micro-environment. Mechanical changes are particularly important in solid tumour development, as altered stromal-epithelial interactions can provoke a persistent increase in cytoskeletal tension, driving the gene expression of a malignant phenotype. In this work, we propose a novel multi-scale treatment of mechano-transduction in cancer growth. The avascular tumour is modelled as an expanding elastic spheroid, whilst growth may occur both as a volume increase and as a mass production within a cell rim. Considering the physical constraints of an outer healthy tissue, we derive the thermo-dynamical requirements for coupling growth rate, solid stress and diffusing biomolecules inside a heterogeneous tumour. The theoretical predictions successfully reproduce the stress-dependent growth curves observed by in vitro experiments on multicellular spheroids.
Modelling the early stages of vascular network assembly
Modelling of Biological Materials
We present a hybrid computational framework, the aim of which is to reproduce and analyze the ear... more We present a hybrid computational framework, the aim of which is to reproduce and analyze the early growth of a solid tumor. The model couples an extended version of the discrete Cellular Potts Model, used to represent the phenomenological behavior of malignant cells, with a continuous approach of reactiondiffusion equations, employed to describe the evolution of microscopic variables, as the growth factors and the matrix proteins present in the host tissue and the proteolytic enzymes secreted by the tumor. The behavior of each cancer cell is determined by a balance of interaction forces, such as homotypic (cell-cell) and heterotypic (cellmatrix) adhesions and haptotaxis, and is mediated by its molecular state, which regulates the motility and proliferation rate. The resulting model captures the different phases of the development of the tumor mass, i.e. its exponential growth and the subsequent stabilization in a steady-state due to limitations in vital molecules. The proposed approach also predicts the influence on the cancer morphology of changes in specific intercellular adhesive mechanisms.
Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model
Biomechanics and modeling in mechanobiology, Jan 8, 2016
Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor... more Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely grow...
Progress in Industrial Mathematics at ECMI 96, 1997
The pa.per deduces a new model to simulate industrial processes involving infiltration in deforma... more The pa.per deduces a new model to simulate industrial processes involving infiltration in deformable porous media. If the porous material is not rigid, then it can deform under the action of the forces associated with the flow, both in the infiltrated and in the uninfiltrated region. The coupled flow/deformation problem in the two interfaced regions is then formulated with the proper evolution equations for the boundaries delimiting the two domains and with the relative boundary and interface conditions. The unsteady problem is solved numerically, putting in evidence the influence of the deformations on the bulk flow and on the propagation of the advancing front and allowing as a by-product a prediction of the stress and deformation states. M. Brøns et al. (eds.
Tumour cells usually live in a environment formed by other host cells, extra-cellular matrix and ... more Tumour cells usually live in a environment formed by other host cells, extra-cellular matrix and extra-cellular liquid. Cells duplicate, reorganise and deform while binding each other thanks to adhesion molecules exerting forces of measurable strength. In this paper it is illustrated a macroscopic mechanical model of solid tumour which takes such adhesion mechanisms into account. The extracellular matrix is treated as an elastic compressible material, while, in order to define the relationship between stress and strain for the cellular constituents, the deformation gradient is decomposed in a multiplicative way distinguishing the contribution due to growth, to plastic rearrangement and to elastic deformation. On the basis of experimental results at a cellular level, it is proposed that at a macroscopic level there exists a yield condition separating the elastic and viscoplastic regimes. Previously proposed models are obtained as limit cases, e.g. fluid-like models are obtained in the limit of fast cell reorganisation and negligible yield stress. A numerical test case shows that the model is able to account for several complex interactions: how tumour growth can be influenced by stress, how and where it can generate plastic reorganisation of the cells, how it can lead to capsule formation and compression of the surrounding tissue.
In ltration process in composite materials manufacturing: modeling and qualitative results
Mathematical Framework to Model Migration of Cell Population in Extracellular Matrix
Chapman & Hall/CRC Mathematical & Computational Biology, 2010
Cell migration is an essential feature of both normal and pathological biological phenomena. Tiss... more Cell migration is an essential feature of both normal and pathological biological phenomena. Tissue formation in embryonic development requires cell movements and coordination among cells. Migration of cells plays a fundamental role in immune response ...
Journal of mathematical biology, Jan 26, 2014
In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the... more In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts. Dynamical numerical simulations are performed to show the behavior of the model and its qualitative and quantitative accuracy to describe the evolution of the cell aggregate.
Deformable Porous Media and Composites Manufacturing
Modeling and Simulation in Science, Engineering and Technology, 2000
ABSTRACT
Infiltration of a Polymerizing Resin in a Deformable Preform for Fiber Reinforced Composites
Applied and Industrial Mathematics, Venice—2, 1998, 2000