Giuseppe Romanazzi

University of Campinas | UNICAMP · Departamento de Matemática Aplicada (DMA)

This work analyzes the transport and effect of the chemotherapy drug doxorubicin in tumors. Specifically, we model the diffusion-convection process of doxorubicin delivered by bolus injection across the tumor and interstitium by a system of partial differential equations. We present a stability analysis of the system solution and implement a finite...

This paper proposes a finite difference method for a differential-algebraic system that couples an elliptic equation with a convection-diffusion-reaction equation with mixed derivatives. Herein the parabolic equation depends on the gradient of the solution of the elliptic equation. If the numerical approximation for this gradient presents lower acc...

Colorectal cancer morphogenesis begins at the cellular level from cell mutations in the intestinal epithelium cavities called crypts. These mutations lead to a pressure difference in the epithelium crypt walls, which can cause deformation and generate visible abnormalities in the epithelium. The geometrical modeling of these crypts and the mathemat...

Morphological changes due to colorectal cancer propagation by an abnormal crypt fission is an interesting application arising in medicine and biology, that we try to analyse by a differential equations model coupled with a discrete crypt fission model. A colonic crypt can slowly change its shape in three steps: growth, bifurcation and fission. Fiss...

Drug release from viscoelastic polymeric matrices is a complex phenomenon where the main actors are the fluid, the polymeric structure and the drug. As the fluid enters into the polymer, the polymeric chains relax inducing a resistance to the fluid entrance. In contact with the fluid, a dissolution processes takes place and the dissolved drug diffu...

Colonic polyps, which are abnormal growths in the colon, are a major concern in colon cancer diagnosis and prevention. Medical studies evidence that there is a correlation between histopathology and the shapes of the orifices in colonic crypts. We propose a biomathematical model for simulating the appearance of anomalous shapes for the orifices of...

The so-called Serre or Green and Naghdi equations are a well-known set of fully nonlinear and weakly dispersive equations that describe the propagation of long surface waves in shallow water. In order to extend its range of application to intermediate water depths, some modifications have been proposed in the literature. In this work, we analyze a...

We consider a polymeric spherical platform containing a solid dispersed drug that is in contact with a solvent fluid. While swelling, a non-Fickian sorption of the solvent molecules occurs induced by the effect of the viscoelastic properties of the polymer. The solid drug in contact with the solvent fluid dissolves and a Fickian release of dissolve...

Several explanations can be found in the literature about the origin of colorectal cancer. There is, however, some agreement on the fact that the carcinogenic process is a result of several genetic mutations of normal cells. The colon epithelium is characterized by millions of invaginations, very small cavities, called crypts, where most of the cel...

In this paper, an incompressible single phase and single component flow in a porous media presenting a non-Fickian behaviour is studied. The model is composed by a parabolic equation for the pressure, with homogeneous Dirichlet or Neumann boundary conditions, coupled with a mass conservation equation for the concentration, a transport equation for...

In this paper, an incompressible single phase and single component flow in a porous media presenting a nonfickian behaviour is studied. The model is composed by a parabolic equation for the pressure, with homogeneous Dirichlet or Neumann boundary conditions, coupled with a mass conservation equation for the concentration, a transport equation for t...

Colorectal cancer is believed to be initiated in colonic crypts as consequence of several genetic mutations in normal cells. Clusters of abnormal crypts, called Aberrant Crypt Foci (ACF), are thought to be the first manifestation of a possible carcinogenic process. Assuming that the formation of an ACF is due to the accumulation of abnormal cells w...

Integro-differential equations of Volterra type arise, naturally, in many applications such as for instance heat conduction in materials with memory, diffusion in polymers and diffusion in porous media. The aim of this paper is to study a finite difference discretization of the mentioned integro-differential equations. Second convergence order with...

It is generally accepted that colorectal cancer (CRC) occurs as a consequence of sev-eral genetic mutations in the colonic mucosa. The detection and assessment of aberrant crypt foci (ACF), which are clusters of abnormal colonic crypts and believed to be the precursors of CRC, is therefore of crucial importance. This paper models and describes the...

We propose a model for describing and predicting the parallel performance of multigrid numerical software on distributed memory architectures for which differ- ent data partitioning and mapping strategies may be used. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large number of proc...

We propose a model for describing and predicting the parallel performance of a broad class of parallel numerical software on distributed memory architectures. The purpose of this model is to allow reliable predictions to be made for the performance of the software on large numbers of processors of a given parallel system, by only benchmarking the c...

It is generally accepted that colorectal cancer is initiated in the small pits, called crypts, that line the colon. Normal crypts exhibit a regular pit pattern, similar in two-dimensions to a U-shape, but aberrant crypts display different patterns, and in some cases show bifurcation. According to several medical articles, there is an interest in co...

Colorectal cancer is initiated in colonic crypts as a consequence of alterations leading to the disruption of the normal colonic cellular process. We propose a model, which couples a convection-diffusion type equation with a level set equation, for tracking the time evolution of an epithelial cell set, inside a colonic crypt, until it reaches the t...

We consider linear systems with coefficient matrices having the ABD or the Bordered ABD (BABD) structures. These systems arise in the discretization of BVPs for ordinary and partial differential equations with separated and non-separated boundary conditions, respectively. We describe the cyclic reduction algorithm for the solution of BABD linear sy...

We propose a model for describing and predicting the performance of parallel numerical software on distributed memory architectures within a multi-cluster environment. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large number of processors of a given parallel system, and on a combin...

We propose a model for describing and predicting the performance of practical parallel engineering numerical software on a multi-cluster environment with different distributed memory architectures. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large number of processors of a given pa...

We propose a model for describing and predicting the performance of practical parallel engineering numerical software on a multi-cluster environment with different distributed memory architectures. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large number of processors of a given pa...

We propose a model for describing the parallel performance of multigrid software on distributed memory architectures. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large number of processors, of a given parallel system, by only benchmarking the code on small numbers of processors. Th...

We consider linear systems with coefficient matrices of Bordered ABD structure. They arise in the discretization of BVPs for ordinary and partial differential equations with non-separated boundary conditions. We report on tests (and comparisons with the well-known code COLROW) of the Fortran 90 cyclic reduction algorithm BABDCR, inserted in a modif...

The development of Grid environments over recent years now allows scientists access to a range of shared resources which may be located across different site s. These include computational resources such as large parallel computers which may be used to produce accurate numerical simulations in a relatively short time. Since different computer archi...

BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with bordered almost block diagonal coefficient matrices. It is designed to handle matrices with blocks of the same size, that is, having a block upper bidiagonal structure with an additional block in the right upper corner. The algorithm implemented in the package per...

We generalize the cyclic reduction algorithm to the solution of Bordered ABD linear systems with blocks of different sizes and with different overlaps. This kind of sys- tem often arises from the numerical approximation of BVPs with nonseparated boundary conditions. In particular, in our experiments we refer to spline collocation techniques with mono...

BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with bordered almost block diagonal coefficient matrices. It is designed to handle matrices with blocks of the same size, that is, having a block upper bidiagonal structure with an additional block in the right upper corner. The algorithm implemented in the package per...

In this paper we analyze the solution of Borderd Almost Block Diagonal (BABD) linear systems arising from the discretization of BVPs with nonseparated boundary conditions using some well known numerical methods, for example spline collocation at Gaussian points. Several approaches based on cyclic reduction are proposed and compared.

We consider the solution of linear systems whose coefficient matrices having a Bor-dered ABD structure. This kind of system arises in the discretization of BVPs for ordinary and partial differential equations with non-separated boundary conditions. The aim of this paper is to test the Fortran 90 package BABDCR, based on a cyclic reduction algorithm...