On the mathematical transport theory in microporous media: The billiard approach

Bianca, Carlo

doi:10.1016/j.nahs.2010.04.007

Cited by 20 publications

(7 citation statements)

References 128 publications

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“…), unless the therapeutics are injected locally, they will be passively transported by the circulation system through which they can pass through the capillary bed of the targeted area. It is worth stressing that in the application of nanomedicine the onset of anomalous transport strongly depends on the dimension of pores [36,37]. Therefore in order to reach the targeted cells, they have to first extravasate from the local vasculature and then penetrate the interstitium.…”

Section: Nano-therapeutic Strategiesmentioning

confidence: 99%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis is a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades.

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Section: Nano-therapeutic Strategiesmentioning

confidence: 99%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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“…Indeed the study of the transport phenomena occurring in living systems appears fundamental. The properties of the transport are strictly related to the dimension of the media, and in particular the onset of anomalous transport has gained much attention, see papers [39,40] and the references cited therein. The standard transport of a scalar quantity (temperature or density) is modeled by the Fourier-Fick's law which establishes a local relationship between the flux and the gradient of the quantity.…”

Section: Transport Of Anti-fibrotic Therapiesmentioning

confidence: 99%

Multiscale modeling of fibrosis – What's next? Reply to Comments on “Towards a unified approach in the modeling of fibrosis: A review with research perspective” by Martine Ben Amar and Carlo Bianca

Amar

Bianca

2016

Physics of Life Reviews

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“…As is known, therapeutical actions generally depend on the mechanics of drug delivery and therefore it results in fundamental understanding of the nature of the transport. 12 The modeling of space phenomena can be described, and possibly derived, by asymptotic analysis of the underlying microscopic models delivered by the kinetic theory approach. 6,23 Speci¯c models may describe di®usion, or propagation phenomena with¯nite velocity.…”

Section: Critical Analysis and Perspectivesmentioning

confidence: 99%

Mathematical Modeling for Keloid Formation Triggered by Virus: Malignant Effects and Immune System Competition

Bianca

2011

Math. Models Methods Appl. Sci.

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This paper deals with the modeling of a wound healing disease, the keloid, which may provoke onset of malignant cells with higher progression feature, thus generating cells with heterogeneous phenotype. According to medical hypothesis, it is assumed that viruses and the genetic susceptibility of patients are the main causes that trigger the formation. The mathematical model is developed by means of the tools of the kinetic theory for active particles. The competition of the immune system cells with viruses, keloid¯broblast cells, and malignant cells is taken into account. Numerical simulations, obtained by considering the sensitivity analysis of the parameters in the model, show the emerging phenomena that are typical of this disease. Math. Models Methods Appl. Sci. 2011.21:389-419. Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 12/15/14. For personal use only.result of age-related loss of regulatory control. The process and the risk factors that can a®ect the normal organ repair and wound healing are brie°y reviewed in this paper in view of the mathematical modeling approach. Indeed, the main aim of this paper is to develop a mathematical model which can be tuned according to the patient data provided by medics.The construction of mathematical models for biological systems of the life sciences is a hot theme of this new century that involves experts coming from di®erent sci-enti¯c¯elds: mathematics, physics and bioinformatics. Mathematical models attempt to describe, by equations, the dynamics in time and space of real systems that, in the case under consideration, belong to the living matter. All mathematical models (predictive or explorative) need the identi¯cation of the parameters that appear in the equations. Once this assessment has been properly performed, the model can be used to provide an approximate description of physical reality. In some special cases, the model can even depict emerging behaviors only partially shown by empirical data. Finally, it contributes to the re¯nement of experiments.The modeling of biological systems needs to tackle the additional di±culty generated by the peculiarities of the living matter. Among various issues, the lack of invariance principles that are typical of systems of the inert matter. A critical analysis of these issues is developed in the papers by Herrero, 20 May 25 and Reed. 30 Hartwell et al. 19 propose a deep insight into the above issues. The main conceptual idea is that invariance principles are modi¯ed by the ability of living systems to express speci¯c strategies that depend on survival purposes and adaptation to environmental conditions. Therefore, living systems have the ability of extracting energy for their own bene¯t. Moreover, their adaptation ability generates mutations, which occur at the molecular scale of genes and induce phenotype mutations. This evolution may even be very rapid in some speci¯c pathologies.Recently, various complex systems in the life and applied sciences such as cancer disease, tra±c, social systems, behavioral...

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On the mathematical transport theory in microporous media: The billiard approach

Cited by 20 publications

References 128 publications

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Multiscale modeling of fibrosis – What's next? Reply to Comments on “Towards a unified approach in the modeling of fibrosis: A review with research perspective” by Martine Ben Amar and Carlo Bianca

Mathematical Modeling for Keloid Formation Triggered by Virus: Malignant Effects and Immune System Competition

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