Angélica María Ramírez Martínez

A biochemical hypothesis on the formation of fingerprints using a turing patterns approach

BackgroundFingerprints represent a particular characteristic for each individual. Characteristic patterns are also formed on the palms of the hands and soles of the feet. Their origin and development is still unknown but it is believed to have a strong genetic component, although it is not the only thing determining its formation. Each fingerprint is a papillary drawing composed by papillae and rete ridges (crests). This paper proposes a phenomenological model describing fingerprint pattern formation using reaction diffusion equations with Turing space parameters.ResultsSeveral numerical examples were solved regarding simplified finger geometries to study pattern formation. The finite element method was used for numerical solution, in conjunction with the Newton-Raphson method to approximate nonlinear partial differential equations.ConclusionsThe numerical examples showed that the model could represent the formation of different types of fingerprint characteristics in each individual.

A model of cerebral cortex formation during fetal development using reaction-diffusion-convection equations with Turing space parameters

The cerebral cortex is a gray lamina formed by bodies of neurons covering the cerebral hemispheres, varying in thickness from 1.25 mm in the occipital lobe to 4mm in the anterior lobe. The brains surface is about 30 times greater that of the skull because of its many folds; such folds form the gyri, sulci and fissures and mark out areas having specific functions, divided into five lobes. Convolution formation may vary between individuals and is an important feature of brain formation; such patterns can be mathematically represented as Turing patterns. This article describes how a phenomenological model was developed by describing the formation pattern for the gyri occurring in the cerebral cortex by reaction diffusion equations with Turing space parameters. Numerical examples for simplified geometries of a brain were solved to study pattern formation. The finite element method was used for the numerical solution, in conjunction with the Newton-Raphson method. The numerical examples showed that the model can represent cerebral cortex fold formation and reproduce pathologies related to gyri formation, such as polymicrogyria and lissencephaly.

A mathematical model of the process of ligament repair: effect of cold therapy and mechanical stress.

This article proposes a mathematical model that predicts the wound healing process of the ligament after a sprain, grade II. The model describes the swelling, expression of the platelet-derived growth factor (PDGF), formation and migration of fibroblasts into the injury area and the expression of collagen fibers. Additionally, the model can predict the effect of ice treatment in reducing inflammation and the action of mechanical stress in the process of remodeling of collagen fibers. The results obtained from computer simulation show a high concordance with the clinical data previously reported by other authors.

Appearance and formation of seed and pericarp may be explained by a reaction–diffusion mechanism? A mathematical modeling

Abstract This paper proposes a phenomenological model describing plant seed cortex (testa) and pericarp pattern formation by reaction–diffusion equations with Turing space parameters. Numerical examples for the seed’s simplified geometries in order to study pattern formation were done. The finite element method in conjunction with the Newton–Raphson method was used for the numerical solution to approximate nonlinear partial differential equations. Numerical examples showed that the model can represent the formation of different types of seed cortex and pericarp.