Related papers: A mathematical model for the progression of dental…
We develop a theoretical model of the carious lesion progress caused by acids diffusing into the tooth enamel from the dental plaque. The acids react with static hydroxyapatite, which leads to demineralization of the enamel, and…
We address the problem of diffusion on a comb whose teeth display a varying length. Specifically, the length $\ell$ of each tooth is drawn from a probability distribution displaying the large-$\ell$ behavior $P(\ell) \sim…
Based on a data set obtained in a dental longitudinal study, conducted in Flanders (Belgium), the joint time to caries distribution of permanent first molars was modeled as a function of covariates. This involves an analysis of multivariate…
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic…
As a consequence of shearing, wing cracks can emerge from pre-existing fractures. The process involves the interaction of sliding of the existing fracture surfaces and the tensile material failure that creates wing cracks. This work devises…
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant…
Tooth arrangement is a crucial step in orthodontics treatment, in which aligning teeth could improve overall well-being, enhance facial aesthetics, and boost self-confidence. To improve the efficiency of tooth arrangement and minimize…
Background: Dental caries diagnosis requires the manual inspection of diagnostic bitewing images of the patient, followed by a visual inspection and probing of the identified dental pieces with potential lesions. Yet the use of artificial…
Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
We present ToothCraft, a diffusion-based model for the contextual generation of tooth crowns, trained on artificially created incomplete teeth. Building upon recent advancements in conditioned diffusion models for 3D shapes, we developed a…
Atherosclerosis is a chronic inflammatory disease occurs due to plaque accumulation in the inner artery wall. In atherosclerotic plaque formation monocytes and macrophages play a significant role in controlling the disease dynamics. In the…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
Stylolites are spectacular rough dissolution surfaces that are found in many rock types. Despite many studies, their genesis is still debated, particularly the time scales of their formation and the relationship between this time and their…
Inorganic scintillating crystals can be modelled as continua with microstructure. For rigid and isothermal crystals the evolution of charge carriers becomes in this way described by a reaction-diffusion-drift equation coupled with the…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…