Medical implant-related infections remain notoriously difficult to treat due to the formation of bacterial biofilms. Systemic antibiotic delivery is often ineffective and antibiotic-eluting technologies remain immature in this field, at least in part due to limitations in adequately controlling the antibiotic release rate. A confounding factor is the lack of understanding of the most efficacious antibiotic release profile. In this paper, we introduce a novel theoretical framework that leverages functionally graded materials to achieve tunable, spatially controlled antibiotic delivery – addressing both of these key challenges. Specifically, we develop a new coupled nonlinear partial differential equation model that simultaneously captures antibiotic release from a functionally graded material coating and its transport dynamics within an evolving biofilm. Our results reveal that functionally graded material coatings can outperform homogeneous coatings in sustaining local antibiotic concentrations and suppressing biofilm growth. This study thus establishes functionally graded materials as a promising, previously underexplored design paradigm for infection-resistant medical implants and provides a quantitative basis for optimizing antibiotic release profiles in biofilm-prone environments.

In this paper we propose a mathematical model of the capillary and permeability properties of lime-based mortars from the historic built heritage of Catania (Sicily, Italy) produced by using two different types of volcanic aggregate, i.e. ghiara and azolo. In order to find a formulation for the capillary pressure and the permeability as functions of the saturation level inside the porous medium we calibrate the numerical algorithm against imbibition data. The validation of the mathematical model was done by comparing the experimental retention curve with the one obtained by the simulation algorithm. Indeed, with the proposed approach it was possible to reproduce the main features of the experimentally observed phenomenon for both materials.

The present work focuses on a non-local integro-differential model reproducing Cancer-on-chip experiments where tumor cells, treated with chemotherapy drugs, secrete chemical signals stimulating the immune response. The reliability of the model in reproducing the phenomenon of interest is investigated through a global sensitivity analysis, rather than a local one, to have global information about the role of parameters, and by examining potential non-linear effects in greater detail. Focusing on a region in the parameter space, the effect of 13 model parameters on the in silico outcome is investigated by considering 11 different target outputs, properly selected to monitor the spatial distribution and the dynamics of immune cells along the period of observation. In order to cope with the large number of model parameters to be investigated and the computational cost of each numerical simulation, a two-step global sensitivity analysis is performed. First, the screening Morris method is applied to rank the effect of the 13 model parameters on each target output and it emerges that all the output targets are mainly affected by the same 6 parameters. The extended Fourier Amplitude Sensitivity Test (eFAST) method is then used to quantify the role of these 6 parameters. As a result, the proposed analysis highlights the feasibility of the considered space of parameters, and indicates that the most relevant parameters are those related to the chemical field and cell-substrate adhesion. In turn, it suggests how to possibly improve the model description as well as the calibration procedure, in order to better capture the observed phenomena and, at the same time, reduce the complexity of the simulation algorithm. On one hand, the model could be simplified by neglecting cell–cell alignment effects unless clear empirical evidences of their importance emerge. On the other hand, the best way to increase the accuracy and reliability of our model predictions would be to have experimental data/information to reduce the uncertainty of the more relevant parameters.

Since the Laplace transform plays a central role in the solution of differential equations, it seems natural to extend it in the field of fractional calculus, since many applications of this topic have been proposed, and are becoming more and more important. In this paper we extend the classical Laplace Transform by replacing the usual kernel with a suitable one, both in the classical and Laguerre-type case, obtained by constructing the reciprocal of some exponential-type functions with respect to an appropriate differential operator. Some examples are shown, derived using the computer algebra system Mathematica.

Using a mathematical model of concrete carbonation that describes the variation in porosity as a consequence of the involved chemical reactions, we both validated and calibrated the related numerical algorithm of degradation. Once calibrated, a simulation algorithm was used as a forecasting tool for predicting the effects on the porosity of concrete exposed to increasing levels of CO2 emissions, as well as to rising temperatures. Taking into account future projections of environmental modifications deriving from climate changes, some scenarios were produced numerically by the mathematical algorithm that showed the effects of different pollution levels and global warming on the porosity of Portland cement in a time window of years. Finally, a theoretical study on the effects of pollution levels on the carbonation constant determining the advancement in the carbonation front was carried out for the analyzed scenarios.

The present work extends a previous paper where an agent-based and two-dimensional partial differential diffusion model was introduced for describing immune cell dynamics (leukocytes) in cancer-on-chip experiments. In the present work, new features are introduced for the dynamics of leukocytes and for their interactions with tumor cells, improving the adherence of the model to what is observed in laboratory experiments. Each system's solution realization is a family of biased random walk trajectories, affected by the chemotactic gradients and in turn affecting them. A sensitivity analysis with respect to the model parameters is performed in order to assess the effect of their variation on both tumor cells and on leukocyte dynamics.

In recent years an increasing interest is registered in the direction of developing techniques to combine experimental data and mathematical models, in order to produce systems, i.e., in silico models, whose solutions could reproduce and predict experimental outcomes. Indeed, the success of informed models is mainly due to the consistent improvements in computational abilities of the machines and in imaging techniques that allow a wider access to high spatial and temporal resolution data. Here we present an interdisciplinary work in the framework of Organs-on-chip (OoC) technology, and, more precisely, in Canceron-Chip (CoC) technology.

Round Table of MACH2021

In this paper we present a survey about a series of works developed in the last 20 years, with our group, on chemical aggression of stone artifacts. Here we describe the modelling of different phenomena responsible for exterior and internal degradation of porous materials, such as the evolution of gypsum crust in marble stones, the sodium sulphate crystallization inside porous stone (masonry brick), or the effect of injection of consolidants in stones. For sulfation and other surface reactions we adapted our previous models to take into account more possible features, as for instance rugosity of stones and the possible interaction between chemical and mechanical damage, to evaluate the propagation of cracks in stones under stress. For the problem of salt crystallization, a new mathematical model describing the effect of protective products on sodium sulphate crystallization inside bricks has been proposed and tested against experiments. Finally, a mathematical model for evaluating the penetration and the ultimate depth of filtration of a consolidant product (ethyl silicate) on tuff was proposed and calibrated using experimental data. The proposed models were calibrated by tuning model parameters with numerical fitting procedures based on the comparison between simulation results and available experimental data. Since the obtained results were in qualitative and quantitative accordance with data, this confirmed the soundness of implemented procedures and the effectiveness of the proposed methods.

Real scientific contact between mathematical community and experts in cultural heritageResults of concrete collaboration projects are presentedMathematical models can provide an effective and non-invasive analysis tools in this field

The volume contains high quality articles in the framework of multiscale modelling including lab-on-chip framework It includes models of classification and tumour growth in patient-specific framework The present collection covers a large array of topical biomedical applications

Functionally graded materials (FGMs), possessing properties that vary smoothly from one region to another,have been receiving increasing attention in recent years, particularly in the aerospace, automotive andbiomedical sectors. However, they have yet to reach their full potential. In this paper, we explore the potentialof FGMs in the context of drug delivery, where the unique material characteristics offer the potential of finetuningdrug-release for the desired application. Specifically, we develop a mathematical model of drug releasefrom a thin film FGM, based upon a spatially-varying drug diffusivity. We demonstrate that, depending on thefunctional form of the diffusivity (related to the material properties) a wide range of drug release profilesmay be obtained. Interestingly, the shape of these release profiles are not, in general, achievable from ahomogeneous medium with a constant diffusivity.

The present work is devoted to modeling and simulation of the carbonation process in concrete. To this aim we introduce some free boundary problems which describe the evolution of calcium carbonate stones under the attack of $ {CO}_2 $ dispersed in the atmosphere, taking into account both the shrinkage of concrete and the influence of humidity on the carbonation process. Indeed, two different regimes are described according to the relative humidity in the environment. Finally, some numerical simulations here presented are in substantial accordance with experimental results taken from literature.

The present paper was inspired by recent developments in laboratory experiments within the framework of cancer-on-chip technology, an immune-oncology microfluidic chip aiming at studying the fundamental mechanisms of immunocompetent behavior. We focus on the laboratory setting where cancer is treated with chemotherapy drugs, and in this case, the effects of the treatment administration hypothesized by biologists are: the absence of migration and proliferation of tumor cells, which are dying; the stimulation of the production of chemical substances (annexin); the migration of leukocytes in the direction of higher concentrations of chemicals. Here, following the physiological hypotheses made by biologists on the phenomena occurring in these experiments, we introduce an agent-based model reproducing the dynamics of two cell populations (agents), i.e., tumor cells and leukocytes living in the microfluidic chip environment. Our model aims at proof of concept, demonstrating that the observations of the biological phenomena can be obtained by the model on the basis of the explicit assumptions made. In this framework, close adherence of the computational model to the biological results, as shown in the section devoted to the first calibration of the model with respect to available observations, is successfully accomplished.

In this paper we introduce a mathematical model of concrete carbonation Portland cement specimens. The main novelty of this work is to describe the intermediate chemical reactions, occurring in the carbonation process of concrete, involving the interplay of carbon dioxide with the water present into the pores. Indeed, the model here proposed, besides describing transport and diffusion processes inside the porous medium, takes into account both fast and slow phenomena as intermediate reactions of the carbonation process. As a model validation, by using the mathematical based simulation algorithm we are able to describe the effects of the interaction between concrete and CO on the porosity of material as shown by the numerical results in substantial accordance with experimental results of accelerated carbonation taken from literature. We also considered a further reaction: the dissolution of calcium carbonate under an acid environment. As a result, a trend inversion in the evolution of porosity can be observed for long exposure times. Such an increase in porosity results in the accessibility of solutions and pollutants within the concrete leading to an higher permeability and diffusivity thus significantly affecting its durability.

The present work is inspired by laboratory experiments, investigating the cross-talk between immune and cancer cells in a confined environment given by a microfluidic chip, the so called Organ-on-Chip (OOC). Based on a mathematical model in form of coupled reaction-diffusion-transport equations with chemotactic functions, our effort is devoted to the development of a parameter estimation methodology that is able to use real data obtained from the laboratory experiments to estimate the model parameters and infer the most plausible chemotactic function present in the experiment. In particular, we need to estimate the model parameters representing the convective and diffusive regimes included in the PDE model, in order to evaluate the diffusivity of the chemoattractant produced by tumor cells and its biasing effect on immune cells. The main issues faced in this work are the efficient calibration of the model against noisy synthetic data, available as macroscopic density of immune cells. A calibration algorithm is derived based on minimization methods which applies several techniques such as regularization terms and multigrids application to improve the results, which show the robustness and accuracy of the proposed algorithm.

Usually, clinicians assess the correct hemodynamic behavior and fetal wellbeing during the gestational age thanks to their professional expertise, with the support of some indices defined for Doppler fetal waveforms. Although this approach has demonstrated to be satisfactory in the most of the cases, it can be largely improved with the aid of more advanced techniques, i.e. numerical analysis and simulation. Another key aspect limiting the analysis is that clinicians rely on a limited number of Doppler waveforms observed during the clinical examination. Moreover, the use of simple velocimetric indicators for deriving possible malfunctions of the fetal cardiovascular system can be misleading, being the fetal assessment based on a mere statistical analysis (comparison with physiological ranges), without any deep physiopathological interpretations of the observed hemodynamic changes. The use of a lumped mathematical model, properly describing the entire fetal cardiovascular system, would be absolutely helpful in this context: by targeting physiological model parameters on the clinical reliefs, we could gain deep insights of the full system. The calibration of model parameters may also help in formulating patient-specific early diagnosis of fetal pathologies. In the present work, we develop a robust parameter estimation algorithm based on two different optimization methods using synthetic data. In particular, we deal with the inverse problem of recognizing the most significant parameters of a lumped fetal circulation model by using time tracings of fetal blood flows and pressures obtained by the model. This represents a first methodological work for the assessment of the accuracy in the identification of model parameters of an algorithm based on closed-loop mathematical model of fetal circulation and opens the way to the application of the algorithm to clinical data.

The present work is inspired by the recent developments in laboratory experiments madeon chips, where the culturing of multiple cell species was possible. The model is based on coupledreaction-diffusion-transport equations with chemotaxis and takes into account the interactions amongcell populations and the possibility of drug administration for drug testing effects. Our effort isdevoted to the development of a simulation tool that is able to reproduce the chemotactic movementand the interactions between different cell species (immune and cancer cells) living in a microfluidicchip environment. The main issues faced in this work are the introduction of mass-preserving andpositivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passingthrough interfaces between 2D and 1D domains of the chip and the development of mass-preservingand positivity preserving numerical conditions at the external boundaries and at the interfacesbetween 2D and 1D domains.

A (2+2)-dimensional kinetic equation, directly inspired by the run-and-tumble modelingof chemotaxis dynamics is studied so as to derive a both ''2D well-balanced'' and''asymptotic-preserving'' numerical approximation. To this end, exact stationary regimesare expressed by means of Laplace transforms of Fourier-Bessel solutions of associatedelliptic equations. This yields a scattering S-matrix which permits to formulate a timemarchingscheme in the form of a convex combination in kinetic scaling. Then, in thediffusive scaling, an IMEX-type discretization follows, for which the ''2D well-balancedproperty'' still holds, while the consistency with the asymptotic drift-diffusion equation ischecked. Numerical benchmarks, involving ''nonlocal gradients'' (or finite samplingradius), carried out in both scalings, assess theoretical findings. Nonlocal gradients appearto inhibit blowup phenomena.